Answer:
Missing leg = [tex]2\sqrt{14}[/tex]
Step-by-step explanation:
Pythagorean theorem
[tex]a^{2} +b^{2}=c^{2}[/tex]
[tex]12+b^{2} = 8^{2}[/tex]
[tex]12+b^{2} =64[/tex]
[tex]b^{2}=56\\[/tex]
[tex]b=\sqrt{56}[/tex]
[tex]b=2\sqrt{14}[/tex]
11. Hannah recorded the number of miles she jogged. She started jogging 3 41 miles. Every week she jogged an additional
1 21 miles. Select all true statements. The y-intercept is the rate of change. The y-intercept is the starting value. The slope is 121. The slope is 3 41. The y-intercept is 1 21. The y-intercept is 3 41
Using coordinate geometry,
The y-intercept is the starting value (true).The slope is 1/2 or 0.5, not 121 or 3/41 (false).The y-intercept is 3/41 is also false as it contradicts the first true statement, therefore, the y-intercept is the starting value and the y-intercept of 3/41 is also true.The problem provides two pieces of information about Hannah's jogging routine: she started with 3 41 miles and added 1/21 miles every week. We can use this information to create a linear equation that represents the number of miles Hannah jogged as a function of the number of weeks she has been jogging.
To create this equation, we first identify the starting value, which is 3 41 miles. This is also the y-intercept of the line. Next, we determine the slope of the line, which is the rate at which the number of miles increases each week. The slope is equal to the change in y (miles) divided by the change in x (weeks), which in this case is (1/21 - 3/41)/1 = -2/1 = -2. Therefore, the slope of the line is -2.
Putting these two pieces of information together, we get the equation y = -2x + 3 41, where y is the number of miles jogging and x is the number of weeks of jogging. This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 3 41.
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A cylinder has radius 1.6 meters. Its volume is 95 cubic meters. Find its height to the nearest tenth of a meter. Use 3.14 as approximation for
The height of the given cylinder with radius 1.6 meters is 11.81 meters.
Explain about the volume of cylinder?A cylinder is a solid made up of two congruent circles in parallel planes, respective interiors, and all the parallel line segments with ends on the circular regions that are perpendicular to the took the shape the centers of both circles.
A three-dimensional solid's volume is the amount of room it occupies up. When calculating the volume, make sure that each of the quantities belong to the same unit.
Radius r = 1.6 meters.
Volume of cylinder V = 95 cubic meters
Formulae for volume of cylinder = πr²h
Height = ?
V = πr²h
95 = 3.14 * 1.6² * h
h = 95 /(3.14 * 1.6²)
h = 11.81
Thus, the height of the given cylinder with radius 1.6 meters is 11.81 meters.
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do these 2 equations show growth or decay pls i need help. Y = 2x^2 + 9, and
y = 3/2 + .45x
I used desmos to graph the equations and this is what I got. Let me know if I've done a typo.
Angle r° = 2w°. What is the measure of angle r°?
A) 145°
B) 290°
C) 125°
D) 90°
Answer:
290
Step-by-step explanation:
19. INVESTMENTS Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account
that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year.
a. Write an expression that represents the amount of money invested in the traditional account.
b. Write a polynomial model in simplest form for the total amount of money T Kent has invested after one year.
(Hint: Each account has A + IA dollars, where A is the original amount in the account and I is its interest rate:)
c. If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?
Part a: Expression for conventional account: $(5000-x) at 5%pa.
Part b: polynomial model: T = 5250 - 0.01x
Part c: Sum of investments in retirement account: T= $5245.
Explain about the bond account?When they need to raise money, governments and businesses issue bonds.
a. Create an expression to show how much money is invested in the conventional account.
Back $(5000-x) at 5%pa
b. Construct a polynomial model in its simplest form to represent the entire sum of investments made by T. Kent after a year (possibility: thus every account has A + iA dollars, in Which a is the account's initial balance and I is the interest rate).
The bond will increase to after a year to : x + 0.04x
= x(1+0.04)
= 1.04x ...eq 1
So, after the time of one year this traditional account growth will be-
(5000-x) + 0.05(5000-x)
= 5000 - x + 0.05*5000 - 0.05x
= 5000 - x + 250 - 0.05x
= 5250 - 1.05x ..eq 2
From eq 1 and eq 2
T = 1.04x + 5250 - 1.05x
T = 5250 - 0.01x
c. If Kent invested $500 in bonds, how much will he have in the retirement account in a year?
x=500
T= 5250 - 0.01*500
T= 5250 - 5
T= $5245
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What is the constant (k) in this inverse variation?
y = 400/x
* x
* Not enough information given
* y
* 400
The constant (k) in this inverse variation y = 400/x is 400.
The correct answer choice is option D.
What is the constant (k) in this inverse variation?Inverse variation refers to the relationship that exists between two variables, such that the increase in the value of one variable decreases the value of the other variable.
It is written as;
y = k/x
Where,
k = constant of proportionality
x and y = the given variables
So,
y = 400/x
Therefore, it can be concluded that the constant of the inverse variation is 400
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Please help like ASAP now thxxx
Answer:
26
Step-by-step explanation:
Answer these for points
6. f(x)g(x)+h(x) = 20x3-4x. This answer is arrived at by using the rules of algebra and the values of the given functions.
7. f(x)g(x) = -15x2 - 18x - 15
What are polynomials?Polynomials are algebraic expressions consisting of variables and coefficients that are combined through addition, subtraction, multiplication and division operations. For example, the polynomial 4x² + 3x - 5 can be written as the sum of 4x², 3x and -5.
6. In order to calculate f(x) g(x)+h(x), it is necessary to first multiply f(x) and g(x). Since f(x)=4x and g(x) = 5x2-4, it follows that f(x)g(x)=20x3-4x. Next, it is necessary to add h(x) to this product. Since h(x) = 9x, it follows that f(x)g(x)+h(x) = 20x3-4x+9x = 20x3-4x. Since each coefficient is correctly represented in the answer, it follows that the correct answer is 20x3-4x.
Multiplying f(x) and g(x) gives the product of 20x3-4x, and adding h(x) to this product gives the sum of 20x3-4x. As each coefficient is correctly represented in the answer, the correct answer is 20x3-4x.
7. The product of two polynomials is found by multiplying each term of one polynomial by each term of the other polynomial. This is known as the FOIL method (First, Outer, Inner, Last).
The first term is the product of the first terms of each polynomial, which is 3x x 4x = 12x2.
The second term is the product of the outer terms, which is 3x x -5x = -15x2.
The third term is the product of the inner terms, which is 5 x -5x = -25x.
Finally, the fourth term is the product of the last terms of each polynomial, which is 5 x -3 = -15.
We can now combine the terms to get the product of the two polynomials, which is:
f(x)g(x) = -15x2 - 18x - 15.
Therefore, the correct coefficient for each term is -15x2 for the first term, -18x for the second term, and -15 for the third term.
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Which expression best represents the difference between triple a number and double a number
Answer: 3x-2x or (3x)-(2x)
Write an expression that best represents the difference between triple and double a number?
Step-by-step explanation: HOPE THIS HELPS!
Answer:
3x-2x
Step-by-step explanation:
I hope you this is it
A train travelling at 120 km/h goes through a tunnel 155m long. Calculate in seconds, the time a passenger on a train spends in the tunnel
passenger on the train spends approximately 4.65 seconds in the tunnel.
First, we need to convert the speed of the train from km/h to m/s (meters per second) since the length of the tunnel is given in meters. We can do this by dividing the speed in km/h by 3.6, which is the conversion factor from km/h to m/s:
Speed of the train = 120 km/h = (120/3.6) m/s = 33.33 m/s
Next, we can use the formula for time:
time = distance ÷ speed
where distance is the length of the tunnel, and speed is the speed of the train.
Plugging in the given values, we get:
time = 155 m ÷ 33.33 m/s ≈ 4.65 s
Therefore, a passenger on the train spends approximately 4.65 seconds in the tunnel.
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Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.
a. x^2+5/6x+___=(x+___)^2
b. x^2-11x+___=(x-__)^2
ANSWERS:
A ) x^2 + 5/6x + 25/144 = (x + 5/12)^2
B ) x^2 - 11x + 121/4 = (x - 11/2)^2
EXPLANATION:
a. To complete the square for the equation x^2 + 5/6x + ___,
first divide the coefficient of the linear term (5/6) by 2,
which gives you 5/12.
Then, square the result:
(5/12)^2 = 25/144.
So, the equation becomes:
x^2 + 5/6x + 25/144 = (x + 5/12)^2
b. To complete the square for the equation x^2 - 11x + ___,
first divide the coefficient of the linear term (-11) by 2,
which gives you -11/2.
Then, square the result:
(-11/2)^2 = 121/4.
So, the equation becomes:
x^2 - 11x + 121/4 = (x - 11/2)^2
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THIS IS URGENT AM I CORRECT PLEASE HALP!!!!!!
The total time that it took the fireman to be ready and aboard the firetruck can be obtained by summing all of the time spent. When summed, the total figure will be 32 seconds.
How much time did it take?The total time taken to board the firetruck can be calculated by summing all the time given in seconds. We start by getting the time it took the firefighter to reach the fire pole which is 9.5 seconds.
Next is the time it took him to slide down the pole which is 3.2 seconds. Next is 13.6 seconds for sliding down the pole and 5.7 seconds for climbing aboard. The sum of all these is 32 seconds.
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t is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $310 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?
The probability that a randomly chosen college student will spend between $300 and $400 on clothing in a year is approximately 0.6645 or 66.45%.
To solve this problem, we need to standardize the given range of values using the z-score formula:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation. For x = 300:
z = (300 - 310) / 50 = -0.2
For x = 400:
z = (400 - 310) / 50 = 1.8
Using a standard normal distribution table or calculator, we can find the probability of the z-score being between -0.2 and 1.8:
P(-0.2 ≤ z ≤ 1.8) = 0.6645
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Write the equation of the line that is parallel to y=- 3/2and passes through
point (2,3).
Answer:
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
Step-by-step explanation:
In order to find an equation that is parallel, it must have the same slope. This means the y intercept could literally be anything.
By equation of the line, we can write it in point slope form
[tex]y-y1=m(x-x1)[/tex]
where y1 and x1 are points on the coordinate plane and m is the slope.
We are already given the slope, so we just plug in the numbers.
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met. The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. What is the test statistic for this procedure? a. 5.50 b. 2.35 c. 1.59 d. 1.90
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. The test statistic for this procedure is 1.90. The correct option is D.
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met.
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90.
A t-test statistic for a paired sample is to be calculated to find out whether or not there is a statistically significant difference between the two treatments. The formula for a t-test statistic is given below:
t= x¯d/sd / √n
where x¯d is the mean difference,
sd is the standard deviation of the differences, and
n is the number of subjects.
Using the given values, we can substitute in the formula and solve for t as follows:
t=1.33/2.90 / √12t=1.90
Hence, the test statistic for this procedure is 1.90.
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PLEASE PLEASE HELP DUE TMRW !!!
A room has dimensions as shown.
3x (height)
4x +3 (length)
a) Find a simplified expression for the perimeter.
b) Find a simplified expression for thearea.
c) Repeat parts a) and b) if both the
length and width are doubled.
d) Has this doubled the perimeter?
Justify your answer.
e) Has this doubled the area? Justify your answer.
Answer:
a) The perimeter of the room is the sum of the lengths of all four sides. The length of two opposite sides is 4x + 3, and the length of the other two opposite sides is 3x. Therefore, the perimeter is:
P = 2(4x + 3) + 2(3x) = 14x + 6
b) The area of the room is the product of the length, width, and height. The length is 4x + 3, the width is 3x, and the height is 3x. Therefore, the area is:
A = (4x + 3)(3x)(3x) = 27x^2 + 12x
c) If both the length and width are doubled, the new dimensions are 2(4x + 3) = 8x + 6 for the length and 2(3x) = 6x for the width.
a) The new perimeter is the sum of the lengths of all four sides:
P' = 2(8x + 6) + 2(6x) = 28x + 12
b) The new area is the product of the length, width, and height:
A' = (8x + 6)(6x)(3x) = 144x^2 + 72x
d) The new perimeter is not twice the original perimeter because:
P' = 28x + 12
2P = 28x + 12 + 28x + 12 = 56x + 24
Therefore, 2P is not equal to P', so doubling the length and width does not double the perimeter.
e) The new area is not twice the original area because:
A' = 144x^2 + 72x
2A = 2(27x^2 + 12x) = 54x^2 + 24x
Therefore, 2A is not equal to A', so doubling the length and width does not double the area.
Find the length of the third side
Answer:
2 radical 11
Step-by-step explanation:
hyp= short (2)
x= √11 (2)
x= 2√11
A random sample of dogs at different animal shelters in a city shows that 10 of the 70 dogs are puppies. The city's animal shelters collectively house 1,960 dogs each year. About how many dogs in all of the city's animal shelters are puppies?
280 dogs in all of the city's animal shelters are puppies. The solution has been obtained by using ratios.
What is ratio?
The ratio between two amounts of the same unit can be used to determine how much of one quantity is included in the other.
We are given that different animal shelters in a city shows that 10 of the 70 dogs are puppies and the city's animal shelters collectively house 1,960 dogs each year.
So, from this we get the ratio as
⇒ [tex]\frac{10}{70}[/tex] = [tex]\frac{x}{1960}[/tex]
Now, by cross multiplying, we get
⇒ 19,600 = 70x
⇒ x = 280
Hence, 280 dogs in all of the city's animal shelters are puppies.
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If g(x) = -3x - 4, find g(4) + 8
Answer:
Step-by-step explanation:
To find g(4), we substitute x = 4 into the expression for g(x):
g(4) = -3(4) - 4 = -12 - 4 = -16
To find g(4) + 8, we add 8 to the value we just found for g(4):
g(4) + 8 = -16 + 8 = -8
Therefore, g(4) + 8 = -8.
The Computer has labeled the lines you graphed a and b. What are the equations of the lines? Enter them into the table below
The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.
Consider two points on the blue line.
The points are (5, -8) and ( -3,1 ).
Equation of the blue line is:
y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]
8 (y - 1) = -9 ( x + 3)
8y - 8 = -9x -27
9x + 8y + 19 = 0
Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.
Consider two points on the red line.
The points are (-3, 1) and ( 1,6 ).
Equation of the red line is:
y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]
4 (y - 1) = 5 (x + 3)
4y - 4 = 5x + 15
5x - 4y+ 19 = 0
Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.
Hence, the equations for the given blue and red lines are completed.
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hirty five discrete math students are to be divided into seven discussion groups, each consisting of five students. in how many ways can this be done?
Answer:76904685 ways
please give brainliest
find the closed formula for each of the following sequences by relating them to a well known sequence. assume the first term given is a1. (a) 2; 5; 10; 17; 26; : : : (b) 0; 2; 5; 9; 14; 20; : : : (c) 8; 12; 17; 23; 30; : : : (d) 1; 5; 23; 119; 719; :
a) an = 3n-1 · 2
b) an = 2·n
c) an = 5·n + 8
d) an = 4n-1 · 1
Let's dive deeper into the details below.
(a) The sequence 2, 5, 10, 17, 26 is a geometric sequence with common ratio 3 and a1 = 2. Therefore, the closed formula is an = 3n-1 · 2.
(b) The sequence 0, 2, 5, 9, 14 is an arithmetic sequence with common difference 2 and a1 = 0. Therefore, the closed formula is an = 2·n.
(c) The sequence 8, 12, 17, 23 is an arithmetic sequence with common difference 5 and a1 = 8. Therefore, the closed formula is an = 5·n + 8.
(d) The sequence 1, 5, 23, 119 is a geometric sequence with common ratio 4 and a1 = 1. Therefore, the closed formula is an = 4n-1 · 1.
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two angles are supplementary. if one angle is two times the sum of other angle and 3, find the two angle
The answer of the given question based on the supplementary angle is the two angles are 58° degrees and 122° degrees.
What is Angle?An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called sides or arms of angle. Angles are typically measured in the degrees or the radians.
The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.
Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:
x + y = 180
We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:
x = 2(y + 3)
Now we can substitute the second equation into the first equation to eliminate "x":
(2(y + 3)) + y = 180
Simplifying the equation, we get:
3y + 6 = 180
Subtracting 6 from both sides, we get:
3y = 174
Dividing both sides by 3, we get:
y = 58
Now that we know "y", we can substitute it back into the equation for "x" to find its value:
x = 2(y + 3) = 2(58 + 3) = 122
Therefore, the two angles are 58° degrees and 122° degrees.
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What are carbon compounds
Answer:
Carbon compounds are defined as chemical substances containing carbon i'd say.
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
use your z-score table. what percentage of scores (i.e., of a gaussian distribution) is between -1.96 and 1.96 z-scores? you don't have to put the % sign.
Approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is because the area under the standard normal distribution curve between these two values is approximately 0.95.
To calculate this, first calculate the area under the standard normal distribution curve between -1.96 and 1.96. This can be done by using a Z-score table, which provides the area under the curve to the left of a given value. To calculate the area between -1.96 and 1.96, subtract the area to the left of -1.96 from the area to the left of 1.96. This is approximately 0.95.
Since the total area under the curve is 1, this implies that approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is commonly known as the "95% Rule," and it is a useful way to quickly estimate the amount of scores that are within a certain range.
It is important to note that this calculation is only an approximation, as the exact value depends on the actual values that are used. Therefore, it is important to use a Z-score table with more accurate values if more precision is needed.
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evaluate the double integral. 8y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d
The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.
To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:
0 ≤ x ≤ 1
1 + x ≤ y ≤ 4 - x
The integral then becomes:
∫0^1 ∫1+x^4-x 8y^2 dy dx
Evaluating the integral with respect to y first, we get:
∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx
= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx
= 128/27 - 32/9 + 8ln2/3
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find the value of x?
Answer: x is equal to 1
Step-by-step explanation:
Find the are 22ft 37ft 38. 09ft 109degrees 138degrees
Answer:
B.
Step-by-step explanation:
I just took the test
The measure of the angle turns through 3/5 of 360°, true or false
Answer:
false, 216° turns 3/5 in a 360° rotation