He received Glhf 25,967.23 as interest at the end of 7 years. The total amount he received at the end of 7 years is GhC 39,067.23.
Simple interest is the interest the lender pays the borrower on the loan. It includes principal only and does not include interest. Simple interest rates are not just for certain loans. This is also the type of interest that banks pay on customers' savings.
a. To find the interest he received at the end of 7 years, we first need to calculate the amount he had at the end of 4 years:
A = P(1 + r/n) (nt)
⇒ A = 14100 (1+ 0.08)(1× 4)
⇒ A = 19628.61
So, he had GhC 19,628.61 at the end of 4 years. He then transferred this amount to another bank offering 12% compound interest per annum. We can use the same formula to find the amount he will have after 7 years:
A = P(1 + r/n) (nt)
⇒ A = 19628.61( 1 + 0.12/1) (1×7)
⇒ A = 40067.23
Therefore, the amount he received at the end of 7 years is GhC 40,067.23.
To find the interest he received at the end of 7 years, we subtract the principal amount:
Interest = A - P
Interest = 40067.23 - 14100
Interest = 25,967.23
So, he received GhC 25,967.23 as interest at the end of 7 years.
b. The total amount he received at the end of 7 years is the sum of the principal and the interest:
Total amount = P + Interest
Total amount = 14100 + 25,967.23
Total amount = 39,067.23
Therefore, the total amount he received at the end of 7 years is GhC 39,067.23.
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Breanna is shopping for a party and needs to buy hot dogs and burgers.
Hamburger is $8 per pound and hot dogs are $6 per pound. She has $75 to
spend. Write an equation where x represents the pounds of hamburger
purchased and y represents the pounds of hot dogs purchased.
Let x be pounds of hamburger and y be pounds of hot dogs.
The equation is: 8x + 6y ≤ 75.
What is equations ?An equation is a mathematical statement that uses the equal sign (=) to show that two expressions are equal. Equations can include variables, which are symbols that represent unknown or changing values. Solving an equation means finding the value of the variable that makes the equation true. Equations are commonly used in many areas of mathematics, science, and engineering, as well as in everyday life.
According to the given information:Let x be the pounds of hamburger purchased and y be the pounds of hot dogs purchased.
The cost of hamburger at $8 per pound would be 8x dollars.
The cost of hot dogs at $6 per pound would be 6y dollars.
The total cost of the purchases should not exceed $75, so we can write:
8x + 6y ≤ 75
This is the equation that represents Breanna's situation, where x represents the pounds of hamburger purchased and y represents the pounds of hot dogs purchased, and the total cost of the purchases should not exceed $75.
Therefore, Let x be pounds of hamburger and y be pounds of hot dogs.
The equation is: 8x + 6y ≤ 75.
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Light from the sun takes 5×102 seconds to reach Earth. It takes 2×104 seconds to reach Pluto.
Use these numbers to complete the sentence below. Write your answer in standard form, without using exponents.
It takes ? times as long for light from the sun to reach Pluto as to reach Earth.
It takes 1,95,000 seconds longer for light from the sun to reach Pluto as to reach Earth.
It is given to us that light from the sun takes 5×10² seconds to reach Earth and it takes 2×10⁴ seconds to reach Pluto.
We need to find the difference in the time it takes for the light to reach Pluto from the sun than it takes to reach the earth
First, lets convert the time it takes for the light to reach Pluto from the sun:
2×10⁴ seconds to reach Pluto
= 2 x 100000 = 200000 seconds
now lets convert the time it takes for the light to reach earth from the sun:
5×10² seconds to reach Earth
= 5 x 1000 = 5000 seconds
therefore the difference = time taken to reach Pluto - time taken to reach Earth
= 2,00,000 - 5,000 = 1,95,000
Therefore, it takes 1,95,000 seconds longer for light from the sun to reach Pluto as to reach Earth.
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The diagram below shows part of the graph of y= b-x/ cx+d
The x-intercept is (6,0).
The vertical asymptote is x = -3.
The horizontal asymptote is y = -1.
Find the value of d.
For x-intercept, [tex]y=0[/tex]
[tex]\implies b-x=0[/tex]
[tex]\implies b=6[/tex]
For vertical intercept [tex]y\rightarrow \pm \infty[/tex]
[tex]\implies cx+d=0[/tex]
[tex]\implies-3x+d=0[/tex]
[tex]\implies d=3c[/tex]
Now, [tex]y=\dfrac{6-x}{cx+3c}[/tex]
[tex]\implies x(xy+1)=6-3cy[/tex]
[tex]\implies x=\dfrac{6-3xy}{cy+1}[/tex]
At horizontal asymptote, [tex]x\rightarrow\pm\infty\implies cy+1=0[/tex]
[tex]\implies c(-1)+1=0[/tex]
[tex]\implies c=1[/tex]
[tex]\implies d=3[/tex].
NEED HELP ASAP PLEASE...
The output of g(x) when x is -2 is 1/3.
How to find output?
To find the output of g(x) when x is -2, we simply substitute -2 into the formula for g(x):
g(-2) = 3⁻²/²
Simplifying the exponent, we get:
g(-2) = 3⁻¹
Now, we need to evaluate 3⁻¹. Recall that any number raised to a negative exponent can be written as its reciprocal raised to the corresponding positive exponent. That is:
a⁻ⁿ = 1/(aⁿ)
In our case, a is 3 and n is 1, so we have:
3⁻¹= 1/(3¹) = 1/3
Therefore, the output of g(x) when x is -2 is 1/3.
Note that 1/3 is already in its simplest form, so we do not need to simplify it any further. We also do not need to round it to two decimal places since it is a fraction.
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a study wants to determine the average tuition that san jose state undergraduate students would pay per semester. each student in the following samples is asked how much tuition he or she paid for the fall semester. what is the type of sampling in each case?
The type of sampling used in each case of the students to pay tuition fee for the fall semester is simple random sampling.
Simple random sampling is the method that was applied in this instance. Each person in the population has an equal probability of being chosen for the sample when using simple random sampling. In this instance, the amount of tuition each participant in the sample paid for the autumn semester was questioned.
The type of sampling in the next case is stratified sampling. After classifying the students into freshmen, sophomores, juniors, or seniors, 25 students from each group are chosen. The sample will be representative of each group thanks to this technique.
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Complete question is:
A study wants to determine the average tuition that san jose state undergraduate students would pay per semester. each student in the following samples is asked how much tuition he or she paid for the fall semester. what is the type of sampling in each case?
A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (freshman, sophomore, junior, or senior), and then selecting 25 students from each.
Sophia, Lexi, and Jason picked some bananas. Sophia picked 18 bananas. Lexy picked 6 more bananas than Sophia. Jason picked 5 times as many as Lexi. How many bananas did Sophia, Lexi, and Jason collect altogether?
the answer is that Sophia, Lexi, and Jason collected a total of 162 bananas.
In this problem, we are given that Sophia picked 18 bananas. We are also told that Lexi picked 6 more bananas than Sophia, so Lexi picked 18+6=24 bananas. Additionally, we are told that Jason picked 5 times as many bananas as Lexi, so we need to multiply Jason picked 5*24=120 bananas.
To find the total number of bananas picked by all three people, we need to add up the number of bananas picked by Sophia, Lexi, and Jason. So, we add 18 + 24 + 120 = 162 bananas.
Therefore, the answer is that Sophia, Lexi, and Jason collected a total of 162 bananas.
It's important to understand the relationships between the numbers given in the problem in order to solve it. Sophia is the starting point, with 18 bananas, and Lexi is picking 6 more bananas than her. Jason's number is more complex, being 5 times Lexi's amount. By breaking down each piece of information and understanding how they relate to each other, we can easily find the total number of bananas collected by all three.
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pls see pictures for equation
a-write the first four terms
b- does this series diverge or converge?
c- if the series has a sum, find the sum
The first terms are a_1= -4 a_2= -8/3 a_3= -16/9 a_4= -32/27
The series converges as a result the series' sum, if it exists, is equal to -12.
What exactly are geometric series?
A geometric sequence is a set of numbers where each phrase following the first is obtained by multiplying the previous term by the common ratio , a constant. Consider the order 2, 4, 8, 16, 32, etc. as an example. Given that each term after the first is derived by multiplying the previous term by 2, this geometric series has a common ratio of 2.
The following is the formula for determining the nth term in a geometric sequence:
a n = arⁿ⁻¹
where "a" denotes the initial word and "r" denotes the common ratio 2.
A geometric sequence of infinite nature is the sum of an infinite geometric series. ¹. The following formula is used to calculate the sum of an infinite geometric series:
sum = a/ (1-r)
where "r" is the common ratio and "a" is the first term.
n=1, 2, 3, and 4 can be added to the formula for the nth term of a geometric sequence to find the first four terms of the series:
a n = arⁿ⁻¹
where r is the common ratio and an is the first term. As a result, we have:
n= 1
= -4(2/3)⁽¹⁻¹⁾ = -4
n= 2
= -4(2/3)⁽²⁻¹⁾ = -8/3
n=3
= -4(2/3)⁽³⁻¹⁾ = -16/9
n=4
= -4(2/3)⁽⁴⁻¹⁾ = -32/27
b) b) We must locate the common ratio "r" in order to establish whether the series converges or diverges. In this instance, r=2/3, satisfying |r|<1 ⁵ The series converges as a result.
c) The formula for the sum of an infinite geometric series can be used to determine whether the series has a sum.
sum = a/ (1-r) (1-r)
where "r" is the common ratio and "a" is the first term. In this formula, substituting a=-4 and r=2/3 results in:
sum = -4 / (1-2/3)
= -12
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The graph attached shows the position of a race car as it tests out a new engine.
a. What is the distance traveled by the car between 1 and 9 seconds?
b. What is the average speed of the car between 1 and 9 seconds? (Answer in km/s.)
c. Describe how the speed of the car changes throughout its test run.
d. If you had a graph of velocity versus time for this test, what would be the total area under the curve?
Please show all work
a) The distance traveled by the car is 240 km, b) the average speed of the car is 30 km/s, c) the speed of the car changes from increasing to constant to decreasing, d) and the total area under the curve 240 km/s.
a. To find the distance traveled by the car between 1 and 9 seconds, we need to find the area under the curve of the velocity-time graph between 1 and 9 seconds. By counting the number of squares, we can estimate the area to be approximately 24 square units. Since each square represents a velocity of 10 km/h and the time interval is 8 seconds, the distance traveled by the car is approximately 240 km.
b. The average speed of the car between 1 and 9 seconds is equal to the total distance traveled divided by the time taken, which is 240 km / 8 s = 30 km/s.
c. The speed of the car increases from 0 km/h to 60 km/h in the first 2 seconds, then remains constant at 60 km/h for the next 6 seconds, and finally decreases to 0 km/h in the last 2 seconds. Therefore, the speed of the car changes from increasing to constant to decreasing throughout its test run.
d. If we had a graph of velocity versus time for this test, the total area under the curve would represent the total displacement of the car, which is equal to the distance traveled in this case. Since the area under the curve is a trapezoid, we can calculate it as the average of the two parallel sides multiplied by the height, which is (0 + 60) / 2 x 8 = 240 km/s.
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can 16/x be expressed as x^-16
Answer:no
Step-by-step explanation:
for example Exponents are numbers that have been multiplied by themselves. For instance, 3 · 3 · 3 · 3 could be written as the exponent 34
The graph shows a function. Is the function linear or nonlinear?
What are the value of x and the measure of ZE to the nearest degree?
The correct answer is: [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex]. Thus, option D is correct by using Pythagorean theorem.
What is trigonometry and the properties of right triangles?In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as:
[tex]c^2 = a^2 + b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Given that x is the hypotenuse of the right triangle and [tex]$x = \sqrt{28}$[/tex], we can use the Pythagorean theorem to find the lengths of the other two sides. Since x is the hypotenuse, it will be equal to c in the Pythagorean theorem equation. Plugging in the values, we get:
[tex](\sqrt{28})^2 = a^2 + b^2[/tex]
[tex]28 = a^2 + b^2[/tex]
Now, we are given the measure of [tex]\angle E[/tex] which is [tex]37^{\circ}[/tex]. In a right triangle, one angle is always [tex]90^{\circ}[/tex], so the sum of the measures of the other two angles will be [tex]90^{\circ}[/tex] . Therefore, angle must be one of the acute angles of the right triangle.
To find the value of a and b, we can use trigonometric ratios. In a right triangle, the sine, cosine, and tangent ratios are commonly used.
For [tex]$\angle E$[/tex], we can use the sine ratio, which is defined as:
[tex]$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$[/tex]
In our case, the opposite side of [tex]$\angle E$ is $a$[/tex] and the hypotenuse is x. Plugging in the values, we get:
[tex]$\sin(37^{\circ}) = \frac{a}{\sqrt{28}}$[/tex]
Solving for a, we get:
[tex]$a = \sin(37^{\circ}) \cdot \sqrt{28}$[/tex]
Similarly, we can use the cosine ratio to find b. The cosine ratio is defined as:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
In our case, the adjacent side of angle E is b and the hypotenuse is x. Plugging in the values, we get:
[tex]$\cos(37^{\circ}) = \frac{b}{\sqrt{28}}$[/tex]
Solving for b, we get:
[tex]b = \cos(37^{\circ}) \cdot \sqrt{28}[/tex]
Therefore, , the correct answer is The correct answer is: [tex]x=\sqrt{28}, m \angle E=37^{\circ}[/tex], as given in option [tex]x=\sqrt{28},[/tex] m [tex]\angle E=37^{\circ}$.[/tex]
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PLS HELP ASAP THANKS
answer = (3x - 5) (3x + 3).
simplified = 3(x + 1) (3x - 5).
HELP PLEASEEEEEEE NEED HEP NOWW
Answer:
145°
Step-by-step explanation:
You want the exterior angle of a triangle that has remote interior angles with measures 115° and 30°.
Exterior angleThe measure of an exterior angle of a triangle is equal to the sum of the remote interior angles:
∠1 = 115° +30°
∠1 = 145°
__
Additional comment
You can see how this works if you consider the unmarked angle in the triangle to be "u", then its measure satisfies two sums: one is the sum of the interior angles; the other is the sum of angles of a linear pair.
115° +30° +u = 180*
∠1 +u = 180°
Combining these equations, we have ...
∠1 +u = 115° +30° +u
If we subtract u from this equation, we have ...
∠1 = 115° +30°
Answer:
145°
Step-by-step explanation:
? + 30 + 115 = 180
? = 180 - 145
? = 35
180 - 35 = 145
m< 1 = 145°
A group of friends went bowling. There was a special. You paid $5 for shoes, but each game was only $2. Write an equation that shoes the total amount paid y if they played x number of games.
An equation that shoes the total amount paid y if they played x number of games is y = 2x + 5
What exactly is an equation?In mathematics, an equation is-a-statement that shows the equality between two-expressions. An equation typically has one or more unknowns that need to be solved for in order to satisfy the equality.
Here, y = total amount paid
x = number of games
Each game costs $2
So total cost of all games played = $2x
But to enter the game they need to rent shoes $5.
So, total amount paid = $5 + $2x
Thus, An equation that shoes the total amount paid y if they played x number of games is y = 2x + 5
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Rachel is trying to hang a piñata for the birthday party but doesn't know how much rope she needs. She knows the height of the tree where she needs to hang the rope is 9√5 feet tall and the angle of elevation between the ground and the rope that connects to the top of the tree is 60 degrees. What would be the length of the rope that she needs to hang the pinata? Leave in simplest radical form. feet What would be the length of the rope that she needs to hang the pinata? Round to feet the nearest tenth
We can use trigonometry to solve this problem. Let the length of the rope be x. Then, we can draw a right triangle where the height of the tree is the opposite side, the length of the rope is the hypotenuse, and the angle of elevation is 60 degrees. The adjacent side can be found using the trigonometric function cosine:
cos 60° = adjacent / hypotenuse
1/2 = adjacent / x
Multiplying both sides by x, we get:
x/2 = adjacent
To find the length of the hypotenuse, we can use the Pythagorean theorem:
hypotenuse^2 = adjacent^2 + opposite^2
Substituting in the values we know, we get:
x^2 = (x/2)^2 + (9√5)^2
Simplifying the right side, we get:
x^2 = x^2/4 + 405
Multiplying both sides by 4, we get:
4x^2 = x^2 + 1620
Subtracting x^2 from both sides, we get:
3x^2 = 1620
Dividing both sides by 3, we get:
x^2 = 540
Taking the square root of both sides, we get:
x = √540 = 6√60
Therefore, the length of the rope that Rachel needs to hang the piñata is 6√60 feet. Rounded to the nearest tenth, this is approximately 74.1 feet.
Answer:
43.4 ft
Step-by-step explanation:
You want to know the length of rope needed to hang a piñata from the top of a tree that is 9√5 feet tall, if the rope makes an angle of 60° with the ground.
TriangleThe hypotenuse of the triangle can be found by considering the sine of the 60° angle. The sine of the angle is given by ...
Sin = Opposite/Hypotenuse
Then the hypotenuse of the triangle can be found from ...
sin(60°) = tree height / hypotenuse
hypotenuse = tree height/sin(60°) = 9√5/sin(60°)
Rope lengthWe presume the length of rope Rachel wants is the total of the lengths from the anchor point to the tree top and back to the ground. That will be ...
9√5 + 9√5/sin(60°) = 9√5·(1 +1/sin(60°)) ≈ 43.4 . . . . feet
Rachel needs about 43.4 feet of rope to hang the piñata.
F(x)=8x^2 and g(x)=2x+8 fog
2x + 8 should be right
terry and ricky went on a 60-mile canoe trip with their class. on the first day they traveled 21 miles. what percent of the total distance was that?terry and ricky went on a 60-mile canoe trip with their class. on the first day they traveled 21 miles. what percent of the total distance was that?
Terry and Ricky traveled 35% of the total distance on the first day of their canoe trip.
Terry and Ricky went on a 60-mile canoe trip with their class, and on the first day, they traveled 21 miles. To find the percent of the total distance they traveled on the first day, follow these steps:
Divide the distance traveled on the first day (21 miles) by the total distance of the trip (60 miles).
Multiply the result by 100 to convert it into a percentage.
Step-by-step explanation:
Divide 21 miles by 60 miles:
21 / 60 = 0.35
Convert the result into a percentage by multiplying by 100:
0.35 x 100 = 35%
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Solve each absolute value inequality and show its solution set. |2y +3 |<19
The solution set for that absolute value inequality is -19/2 < y < 13/2.
is 7 a solution to the following inequality 3x-5>14
Answer:
Step-by-step explanation:
If you substitute x = 7, then the reasoning is correct, but if you think that x = 7 should turn out at the end (answer), then this is not correct, because it turns out [tex]\frac{19}{3}[/tex]
The image point of A after a translation right 5 units and down 3 units is the point
B
(
−
3
,
−
11
)
B(−3,−11). Determine the coordinates of the pre-image point
A
A.
The coordinates of the pre-image point A are (-4, 8).Hence, the correct answer is (-4, 8).
The given image point of A after a translation right 5 units and down 3 units is the point B(-3, -11).
To determine the coordinates of the pre-image point A, we need to move 5 units to the left and 3 units up.
Let the pre-image point A be (x, y).
Then, the image point B is obtained from A by translation of 5 units to the right and 3 units down.
So, we have the following equations:
y - (-11) = -3x - (-3)y + 11 = -3x + 9On
solving the above equations, we get
x = -4 and y = 8.
So, the coordinates of the pre-image point A are (-4, 8).
Hence, the correct answer is (-4, 8).
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Diane has 4 markers. Her best friend ally gives her 12 more pencils. How many pencils does she have?
Answer:
16
Step-by-step explanation:
4 + 12= 16
4 + 2 = 6
Add a 1 in front
PLS HELP ILL GIVE 2O POINTS
The total cost of the water piping is $217.12 in the field.
What is perimeter?Perimeter is the total length of the boundary or the outer edge of a two-dimensional geometric shape. It is the distance around the shape or the sum of the lengths of all its sides. The perimeter is usually measured in units such as centimeters, meters, feet, or inches, depending on the system of measurement used.
In the given question,
To calculate the total cost of the water piping, we need to first calculate the total length of the edges of the field.
For the rectangle, the length of its four edges can be calculated as:
2 x length + 2 x breadth = 2 x 68m + 2 x 64m = 136m + 128m = 264m
For the square extension, it has four edges each with length 26m, so the total length of its edges is:
4 x 26m = 104m
Therefore, the total length of the edges of the field is:
264m + 104m = 368m
To find the total cost of the water piping, we can multiply the total length of the edges by the cost per metre:
368m x $0.59/m = $217.12
So, the total cost of the water piping is $217.12.
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Need help ASAP! I appreciate it!
The evaluation of the function gives:
f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3
How to evaluate f(-4) based on the given functions?
A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
The evaluation is as follow:
For f(-4):
since x = -4. This means x ≤ -4. Thus, we use the function |2x + 7|. That is:
f(-4) = |2*(-4) + 7|
f(-4) = |-8 + 7|
f(-4) = | -1 |
f(-4) = 1
For f(1):
x = 1. Thus, -4< x ≤ 1. Use 1 + x²
f(1) = 1 + x²
f(1) = 1 + 1²
f(1) = 2
For f(2):
x = 2. Thus, 1< x < 3. Use the value 6
f(2) = 6
For f(5):
x = 5. Thus, x ≥ 3. Use (1/3)x + 8.
f(5) = (1/3)*5 + 8
f(5) = 29/3
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Evaluating the function at various values of x over different intervals,
f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3
What is the value of the functionTo evaluate the function f(x) at various values of x, we need to use the definition of the function for each interval of x.
For x ≤ -4:
f(x) = |2x + 7|
f(-4) = |2(-4) + 7| = |-1| = 1
For -4 < x ≤ 1:
f(x) = 1 + x²
f(1) = 1 + 1² = 2
For 1 < x < 3:
f(x) = 6
f(2) = 6
For x ≥ 3:
f(x) = (1/3)x + 8
f(5) lies in the interval x ≥ 3, so we use the definition of f(x) for this interval:
f(5) = (1/3)(5) + 8 = 29/3
Therefore,
f(-4) = 1
f(1) = 2
f(2) = 6
f(5) = 29/3
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33. Represent and Connect Write the ordered
pair to locate the end of hiking trail in two
different ways.
Please help me now
After answering the presented question, we can conclude that r is the equation distance from the origin and is the angle measured anticlockwise from a reference direction.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We may use two alternative reference points or coordinate systems to find the end of the hiking trail. As an example:
Using a Cartesian coordinate system: Assume the origin is the trailhead and the x-y axis is standard. If the trail's end is 5 units to the right and 7 units up from the trailhead, we may write it as (5, 7).
Using a polar coordinate system: Assume that the origin is defined as the centre of a circular trail and that we use polar coordinates (r,), where r is the distance from the origin and is the angle measured anticlockwise from a reference direction
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Suppose that the functions h and f are defined as follows.
[tex]h(x)=\frac{4}{x}, x\neq 0[/tex]
[tex]f(x)=x^{2} -7[/tex]
Find the composition h ∘ h and f ∘ f.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
The compositions of the given functions are as follows:
hf(x) = 3/(x² - 1)
fh(x) = (9 - x²)/x²
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).
So, we have:
h(x) =3/x, x and f(x) = x^2 - 1
Now, solve as follows:
h(x) = 3/x
f(x) = x² - 1
h(f(x)) = 3/f(x)
hf(x) = 3/(x² - 1)
f(h(x)) = (h(x))² - 1
= (3/x)² - 1
= 9/x² - 1
fh(x) = (9 - x²)/x²
Therefore, the compositions of the given functions are as follows:
hf(x) = 3/(x² - 1)
fh(x) = (9 - x²)/x²
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Correct question:
Suppose that the functions h and f are defined as follows. h(x) =3/x, x notequalto 0 f(x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
a tour guide is in a boat 2 miles from the nearest point on the coast. he is to go to point q, located 3 miles down the coast and 1 mile inland (see figure). the tour guide can row at a rate of 3 miles per hour and walk at 3 miles per hour. toward what point on the coast should the tour guide row in order to reach point q in the least time?
The tour guide should row towards the point on the coast closest to point Q, which is the point of perpendicular intersection between the coast and the line passing through points Q and the initial position of the tour guide.
To reach point Q in the least time, the tour guide should row towards the point on the coast that is closest to point Q. Let's call this point P.
We can use the Pythagorean theorem to find the distance from point P to point Q
distance PQ = sqrt((3 miles)^2 + (1 mile)^2) = sqrt(10) miles
Now, let's consider two scenarios
Scenario 1: The tour guide rows directly towards point Q.
The distance the tour guide needs to row is 2 miles + sqrt(10) miles. This will take the tour guide
time = (2 miles + sqrt(10) miles) / (3 miles/hour) = (2/3) + (1/3)*sqrt(10) hours
Scenario 2: The tour guide rows towards point P, then walks the rest of the way to point Q.
The distance the tour guide needs to row is 2 miles - x miles, where x is the distance from point P to the nearest point on the coast. By similar triangles, we know that
x / 3 miles = 1 mile / sqrt(10) miles
Solving for x, we get
x = 3/sqrt(10) miles
So the distance the tour guide needs to row is
2 miles - 3/sqrt(10) miles = 2 - (3/sqrt(10)) miles
The distance the tour guide needs to walk is
sqrt(10) miles - 1 mile = sqrt(10) - 1 miles
The time it takes the tour guide to row and walk is:
time = (2 - (3/sqrt(10))) / (3 miles/hour) + (sqrt(10) - 1) / (3 miles/hour)
Simplifying this expression, we get
time = (2/3) - (1/3)*sqrt(10) + (sqrt(10)/3) - (1/3) = (1/3) + (1/3)*sqrt(10) hours
Comparing the two scenarios, we see that scenario 2 takes less time, so the tour guide should row towards point P in order to reach point Q in the least time.
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multiply the y-value of each point by 1/2 and drag the blue point to its new location. using the cube root equation
After multiplying the y-value of each point by 1/2, The new location of the blue point would be at x = 2, y = 1.
To apply the given transformation to the points in the graph using the cube root function, we would need to take the cube root of the y-value of each point and then multiply it by 1/2.
Then, we can drag the blue point to its new location based on the transformed coordinates.
For example, if we consider the point (2, 8) in the original graph, the transformed point would be:
(2, 8*(1/3) * 1/2) = (2, 1)
So, the new location of the blue point would be at x = 2, y = 1.
Similarly, we can apply this transformation to all the other points in the graph.
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Which of the following tables represents a linear function?
The first table in the question with the values(2,-3)(2,-2)(2,-1)(2,0)(2,1)represents the linear function.
What is linear function?A linear function is a type of mathematical function that has a constant rate of change or slope. This means that the function produces a straight line when graphed on a coordinate plane.
A linear function can be represented using the general form:
f(x) = mx + b
where m is the slope or rate of change, and b is the y-intercept or the point where the line intersects the y-axis.
In the given question, Option (1),
(2,-3)(2,-2)(2,-1)(2,0)(2,1).
If plotted on graph forms a straight line.
But all the other three options does not form a straight line.
Therefore, its a linear function.
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Need answers ASAP. Please help
Answer: 1. -8, 2. 12, 3.-4 , 4.-7 , 5.3 , 6.15 , 7. 1, 8. 12, 9. -15, 10.318 ,
Step-by-step explanation:
After watching baking shows on T.V., Hakim signs up for a cake-decorating class. To practice his new skills, he decorates a batch of cupcakes with sugar flowers. Hakim puts 3 sugar flowers on each cupcake. In all, Hakim puts 36 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Hakim decorates?
Answer:
3x=36
Step-by-step explanation: