To solve this problem, you will need to use the Pythagorean theorem. According to this theorem, a^2 + b^2 = c^2, where a and b are the two sides of a right-angled triangle and c is the hypotenuse or the longest side. In this case, the two sides are the distance traveled by Pepper and Lemon respectively, and the hypotenuse is the distance between them.
Distance between Lemon and Pepper. Let's say that after 15 minutes, Lemon has traveled a distance of d1, and Pepper has traveled a distance of d2. Since they are moving in perpendicular directions, we can say that the distance between them is the hypotenuse of the right-angled triangle formed by their paths.
Using the Pythagorean theorem, we can write this as:d^2 = d1^2 + d2^2Distance traveled by LemonIn 15 minutes, Lemon travels a distance of 40 x 15/60 = 10 miles.Distance traveled by PepperIn 15 minutes, Pepper travels a distance of 25 x 15/60 = 6.25 miles.Distance between Lemon and Pepper. Using the Pythagorean theorem, we can find the distance between Lemon and Pepper:d^2 = 10^2 + 6.25^2d^2 = 100 + 39.0625d^2 = 139.0625d = sqrt(139.0625)d = 11.7858 miles.
Differentiating this expression with respect to time (t), we get:d/dt (d^2) = d/dt (d1^2 + d2^2)2d * (dd/dt) = 2d1 * (dd1/dt) + 2d2 * (dd2/dt)(dd/dt) = (d1 * dd1/dt + d2 * dd2/dt)/dd/dt = (10 * 40/60) + (6.25 * 25/60)dd/dt = 6.25 + 2.6042dd/dt = 8.8542 miles per hourThe distance between Lemon and Pepper is increasing at a rate of 8.8542 miles per hour. Therefore, the answer is that the distance between them is increasing.
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Calculate the length of AC
The calculated length of AC from the right triangles is 320 units
Calculating the length of ACfrom the question, we have the following parameters that can be used in our computation:
The right triangle
The length of the segment AC is calculated as
sin(30) = 160/AC
Make AC the subject
So, we have
AC = 160/sin(30)
When evaluated, we get
AC = 320
Hence the length of AC is 320 units
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A laundry basket has 24 t-shirts in it. Four are
navy, 12 are red, and the remaining are white. What is the probability of not selecting a white shirt?
A. 1/3
B. 2/3
C. 3/3
D.0
After answering the presented question, we can conclude that probability Therefore, the probability of not selecting a white shirt is 16/24 = 2/3. So, the answer is (B) 2/3.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.
There are 24 t-shirts in the basket, and 4 are navy, 12 are red, so the remaining (24 - 4 - 12) = 8 t-shirts must be white.
The probability of not selecting a white shirt can be found by dividing the number of non-white shirts by the total number of shirts in the basket.
The number of non-white shirts is 4 (navy) + 12 (red) = 16.
Therefore, the probability of not selecting a white shirt is 16/24 = 2/3.
So, the answer is (B) 2/3.
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Question
The state of Wyoming has a population of 581,000. This same state has just 81 health clubs throughout the entire state
What is the number of health clubs per capita in the state of Wyoming? Round to 6 decimal places.
The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.
what is unitary method ?In mathematics, the unitary approach is a way for handling proportional problems. The unitary technique involves determining the value of one unit and using that value to estimate the worth of other units or the total. It is frequently applied in scenarios found in daily life, such as figuring out the cost of a single item when the cost of several are known, or figuring out how long it will take to finish a task when only a portion of the time is known. The unitary approach is a quick and effective method for resolving a variety of mathematical issues.
given
We must divide the overall number of health clubs by the entire population in order to calculate the number of health clubs per capita:
Health club density is calculated as the sum of all clubs divided by the total population.
Per-person health club availability is 81 out of 581,000.
Per-person health club density = 0.000139
The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.
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rovide an example of when you might want to take a systematic random sample instead of a simple random sample, and explain what the advantages of a systematic random sample might be
A stratified random sample is preferred when the population is heterogeneous, ensuring a proportional representation of each subgroup, and allowing for more accurate comparisons and reliable inferences about the population.
When the community under study is heterogeneous, which means it can be broken down into different divisions or sectors, a stratified random sample is usually favored over a basic random sample.
In this situation, a stratified random sample makes it possible for each stratum to be proportionally reflected in the sample, guaranteeing that each subset is properly represented. When analyzing the differences or parallels between various subgroups, this method can be especially helpful.
For instance, a business might want to poll to find out how satisfied customers are with its offerings. They might choose to select a stratified random sample based on customer demographic categories or regions as opposed to a straightforward random sample.
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The question is -
Provide an example of when you might want to take a stratified random sample instead of a simple random sample and explain what the advantages of a stratified random sample might be.
20/23 as a decimal rounded
Answer:
≈ 0,9
Step-by-step explanation:
To the nearest tenth:
[tex] \frac{20}{23} ≈0.9[/tex]
A triangular pyramid with a volume of 90 cubic inches has a height of 15 inches. A triangular prism with a volume of 270 cubic inches has a height of 15 inches What must be true of their bases?
The area of the bases of the second triangular pyramid will be 3 times the first one.
What is a triangular pyramid?
A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.
We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.
So, area of the bases is
⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H
⇒ 90 = [tex]\frac{1}{3}[/tex] * A * 15
⇒ 90 = A * 5
⇒ A = 18 square inches.
Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.
So, area of the bases is
⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H
⇒ 270 = [tex]\frac{1}{3}[/tex] * A * 15
⇒ 270 = A * 5
⇒ A = 54 square inches.
Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.
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Thabang used 1/5 of his money to buy a CD. Calculate how much the CD cost
Answer: divide 1/5 by the price of the CD
Formula: A = P(1+r/n)(nt)
Step-by-step explanation: , if you have a $1,000 CD with a term of three years and an APY of 5%, you can multiply $1,000 by 5% to find the interest
Answer:
20% of his money
Step-by-step explanation:
it's 1/5 of 100% of his money
Pleaseeee help me find this answerrrrrrrr
The function is linear because as the x-value increases, the y-values increases.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the y-intercept or initial number.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 3)/(0 - 1)
Slope (m) = -2/-1
Slope (m) = 2
Based on the information provided above at point (0, 9), an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 5x + 9
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Please help me, its homeowkr
Determine the proper prism's base. The base takes the form of the prism's base. Calculate the base's area. The appropriate prism's height should be measured. Multiply the base's area by the prism's height.
What is prism in geometry?A prism is a three-dimensional geometric object with two parallel, congruent bases and rectangular sides connecting the bases. The prism's name is derived from the design of its base. For instance, the bases of a triangular prism, rectangular prism, and so on, are all triangular. The distance between the two parallel bases of a prism determines its height. The formula V = Bh, where B is the area of the base and h is the height of the prism, can be used to determine the volume of a prism.
The formula V = Bh can be explained as follows:
Determine the proper prism's base. The base takes the form of the prism's base. The base, for instance, might be a triangle, square, rectangle, or any other polygon.
Calculate the base's area. The formula's B stands in for this.
The appropriate prism's height should be measured.
To get the volume, multiply the base's area by the prism's height.
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A ship leaves port at noon and travels at a bearing of 214" The ship's average rate of speed is 15 miles per hour
Describe the location of the ship at 2:30 pm by writing a vector in component form. Then explain what these components mean terms of the scenario in
Drag a value into each box to correctly complete the statements
The first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.
What is vector?A mathematical entity with both magnitude (size) and direction is called a vector. It can be depicted graphically as an arrow, with the direction and length of the arrow representing the magnitude and direction, respectively.
To describe the location of the ship at 2:30 pm, we need to find its position vector relative to the port. Since the ship travels at a bearing of 214°, we can represent its motion by a vector with magnitude 15 (the average speed in miles per hour) and direction 214° (measured counterclockwise from due south).
First, let's convert the direction to radians:
214° = (214/180)π = 1.1868π
Then, we can write the vector in component form as follows:
v = (15 cos(1.1868π), 15 sin(1.1868π)) ≈ (-6.20, -13.56)
So the ship's position at 2:30 pm can be represented by the vector v ≈ (-6.20, -13.56), which means that it is approximately 6.20 miles west and 13.56 miles south of the port.
In the scenario, the ship's average speed of 15 miles per hour means that it travels 15 miles in one hour. Therefore, in two and a half hours (from noon to 2:30 pm), the ship travels 37.5 miles in the direction of 214°. The components of the position vector indicate the distance the ship has traveled in the westward and southward directions, respectively, relative to the port. Therefore, the first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.
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Pleaseeeeee Helppppp Meeeeeeeeeeeeeee-
(Subject: Highschool, Algebra)
Answer:
I have graphed it in the explanation part.
Step-by-step explanation:
First, we have to rewrite the two equations in the form y = mx + b.
2x - y = 4
-y = -2x + 4
y = 2x - 4
x - y = -2
-y = -x - 2
y = x + 2
As we see from the graph, the intersect point is at (6, 8)
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 10 feet. Container B has a diameter of 8 feet and a height of 17 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Answer:
the height of the water in Container B is 22.48 feet.
Step-by-step explanation:
HELPPPPPPPPP PLEASE HURRY !!!!!!!!!!!!!!!!! GIVING 40 POINTS!!!!!!!!!!!!!!!!!!
HELPPPPPPPPPPPPP
This is used to calculate the height of the object at any time t during its flight.
The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.
The acceleration due to gravity is taken to be -9.8 m/[tex]s^2[/tex] (negative since it acts downward), and the formula for the height is derived from the equation of motion:
h(t) = -1/2 [tex]gt^2[/tex] + vt + hi
Where:
g = 9.8 m/[tex]s^2[/tex] (acceleration due to gravity)
t = time (in seconds)
v = initial velocity (in meters per second)
hi = initial height (in meters)
The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).
This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/[tex]s^2[/tex] until it reaches the maximum height and then starts to fall back down.
So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.
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A circle with a radius of 7 ft is cut into 6 equal pieces. How many sq ft are 2 of the pieces? Use 22/7 for pi
1. 7 1/3 sq ft
2. 14 2/3 sq ft
3. 51 1/3 sq ft
4. 205 1/3 sq ft
2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.
what is circle ?A circle is a two-dimensional object in geometry made up of all points in a plane that seem to be equidistant from a certain point known as the centre. The radius of a circle is the distance from the centre to any point on the circle. The diameter is the length of a line joining two points on a circle and running through its centre. The area of a circle is the space inside of it, and the circumference is the distances around the edge. Tangent lines perpendicular to radii, inscribed and encircled angles in relation to the diameter, and a constant diameter to diameter ratio (pi) are only a few of the crucial characteristics of circles.
given
The circle has a radius of 7 feet, and its area is:
A=r2 = (22/7)x7/2 = 154 square feet
The circle is divided into six equal sections, each of which will have the following area:
6 / 154 = 25.67 square feet (rounded to two decimal places)
An region of two of the pieces will include:
2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.
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A family of 10 purchased tickets to the county fair. Tickets for adults cost $6 and tickets for children cost $3. If the total cost of the tickets was $42, how many family members were adults and children?
Answer:
Let the no. of adults be x and no. of children be y
Cost of ticket if there are x adults = 6x
Cost of ticket if there are y children=3y
Step-by-step explanation:
Hope this helps!!
mark me brianliest!
Answer:
6 children and 4 adults
Step-by-step explanation:
Mary is 3 times as old as her son. In 12 years Mary will ve twice as old as her son. How old are each of them now
Answer:
Mary is 36 years old
Her son is 12 years old
Step-by-step explanation:
Let's assume, that Mary's son is x years old and Mary is 3x years old
Let's write 2 equations according to the given information:
x = 3x (Mary is 3 times older than her son)
3x + 12 = 2(x + 12) (after 12 years, she will be 2 times older than her son)
3x + 12 = 2x + 24
3x - 2x = 24 - 12
x = 12
That means, Mary's son is 12 years old
Mary is 3 × 12 = 36 years old
(x + 4) (2x - a) = 0 In the given equation, a is a constant. If the equation has the solutions X = 4 and x = -4, what is the value of a?
Since we know that the equation has the solutions [tex]x = 4[/tex] and [tex]x = -4[/tex] the value of a could be either [tex]8[/tex] or [tex]-8[/tex] .
What is the product of two factors?We know that the product of two factors is equal to zero only when at least one of the factors is zero.
[tex](x + 4) \ (2x - a) = 0[/tex]
This equation has two factors: [tex](x + 4)[/tex] and [tex](2x - a)[/tex] . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.
Setting [tex](x + 4)[/tex] equal to zero, we get:
[tex]x + 4 = 0[/tex]
[tex]x = -4[/tex]
This means that [tex]-4[/tex] is one of the solutions of the equation.
Setting [tex](2x - a)[/tex] equal to zero, we get:
[tex]2x - a = 0[/tex]
[tex]2x = a[/tex]
[tex]x = a/2[/tex]
This means that [tex]a/2[/tex] is another solution of the equation.
Since we know that the equation has the solutions [tex]x = 4[/tex] and [tex]x = -4[/tex] , we can substitute these values into the expression we found for x in terms of a to get:
[tex]a/2 = 4[/tex] or [tex]a/2 = -4[/tex]
Solving for a in each case, we get:
[tex]a = 8[/tex] or [tex]a = -8[/tex]
Therefore, the value of a could be either [tex]8[/tex] or [tex]-8[/tex] .
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x^3 = -216/343
Round to the nearest tenth. Put the negative sign in the numerator.
Putting the negative sign to the numerator, we have the value of x = -6/7.
What is Algebraic expression?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
The given equation is:
x³ = -216/343
To solve for x, we can take the cube root of both sides of the equation:
∛(x³) = -∛(216/343)
x = -∛(216/343)
Solving for numerator:
216 = 6 × 6 × 6
∛216 = 6
Solving for denominator:
343 = 7 × 7 × 7
∛343 = 7
Therefore,
x = -∛(216/343)
x = -(6/7)
x = -6/7
Putting the negative sign to the numerator, we have the value of x = -6/7.
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What is the y-coordinate of the point that divides the
directed line segment from J to K into a ratio of 5:1?
v = (m²+ n )(V₂ - V₁) + V₁
-8
O-5
00
06
o
The point with the y-coordinate of 0 splits the directed line segment from J to K into a 5:1 ratio.
What is x and y-coordinate?An X coordinate value denotes a location that is relative to a point of reference to the east or west. A Y coordinate value denotes a location that is relative to a point of reference to the north or south.
Considering J (1, -10) and K (7, 2)
In this case, let's suppose that point L divides the directed line segment from J to K into a 5:1 ratio.
We know that from coordinate geometry's inherent characteristics.
The point's coordinates are (x1, y1), (x2, y2) where they meet in the ratio of m:n.
[tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]
Now putting the respective values,
= ([tex](\frac{(5 .1)(1 .1) }{5 +1} , \frac{(5 . 2)(1 . (-10))}{5+1}[/tex]
= (6, 0)
Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
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Graph the following:
y ≥-x+2
y - intercept =
slope =
line =
Answer:
- Y-intercept: (0, 2) or just 2
- Slope: -1
- Line: y + x = 2 or y = -x + 2
Step-by-step explanation:
What is the probability of the spinner below landing on blue and rolling an even number on a 6-sided die?
Show work! If it’s correct I will give brainliest
Answer:
1/6
Step-by-step explanation:
There is a 1/3 chance that you will get either a blue, red or green.
It is also a 1/2 chance that you will get an even number on a die.
1/3x1/2=1/6.
Therefore our answer is 1/6
The rectangle shown is to be dilated by a scale factor of 3.5.
(a) Calculate the length of each side of the dilated image. Show your calculations for each side length.
(b) Draw the new image and label it
A B D C . (It does not have to be to scale) .
The rectangle shows two sides being 18 cm and the other two being 8 cm
Answer:
The answer to your problem is:
AB= 30cm
BD= 16cm
Step-by-step explanation:
Since the one shown is to be dilated by a factor of 2, our new dimensions are 2x / 2y. We multiply each side length by two to get our new dilated image.
Which the side lengths being:
AB= 30cm
BD= 16cm
Thus the answer to the problem is:
AB= 30cm
BD= 16cm
Susan will rent a car for the weekend she can choose one of two plans. the first plan has an initial fee of $75 cost an additional $0.40 per mile driven. the second plan has no initial fee but cost 0.90 per mile driven. how many miles would Susan need to drive for the two plans to cost the same?
HELP!
For the polynomial function f(x) = x3 - 7x2 + 10x , what is the average rate of change over the interval [2 , 4]
Answer:
The average rate of change of the given function over the interval [2, 4] is -4.
Step-by-step explanation:
To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
Given function:
[tex]f(x) = x^3 - 7x^2 + 10x[/tex]
To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).
[tex]\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}[/tex]
[tex]\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}[/tex]
Substitute the values into the formula for the average rate of change over the interval [2, 4]:
[tex]\textsf{Average rate of change} = \dfrac{f(4) - f(2)}{4 - 2} = \dfrac{-8-0}{4-2}=\dfrac{-8}{2}=-4[/tex]
Therefore, the average rate of change of the given function over the interval [2, 4] is -4.
If AABC is a triangle with mzC = 90°, which of the
following must be true about angles A and B?
OA.
1
sin A
O C.
=
O B. cos A = 1
tan A +
O D. sin A
sin B
=
1
tan B
cos B
cos B
=
1
Answer:
C. cos A = 1 and sin B = 1.
Step-by-step explanation:
The angles in a triangle must add up to 180°. Since angle C is 90°, angles A and B must add up to 90°. Therefore, the sine of angle A and the sine of angle B must both equal 1. Since the sine of an angle is equal to the cosine of its complement, cos A = 1 and sin B = 1.
(3(2)^5 + 8(2)^3) +(7(2)^2 - 6(2)^3)
Answer:
140.
Step-by-step explanation:
Answer:140
Step-by-step explanation:
ralph's map of virginia beach uses a scale of 1 inch for every 7 miles. ralph runs a distance of 13.2 miles from his house in virginia beach every weekend. which is closest to the number of inches needed to represent this distance on ralph's map?
The distance on Ralph's map is 1.89 inches.
To find the number of inches needed to represent 13.2 miles on Ralph's map of Virginia Beach using a scale of 1 inch for every 7 miles, follow these steps
1. Divide the actual distance (13.2 miles) by the scale ratio (7 miles per inch): 13.2 miles ÷ 7 miles/inch = 1.8857 inches
2. Round the result to the nearest inch: 1.8857 inches ≈ 2 inches
So, the closest number of inches needed to represent the 13.2-mile distance on Ralph's map is 2 inches.
Ralph's map of Virginia Beach uses a scale of 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
The closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
The scale of Ralph's map of Virginia Beach is 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
To determine the number of inches needed to represent this distance on Ralph's map, we can use a proportion as follows:
1 inch / 7 miles = x inches / 13.2 miles
Cross-multiplying gives:
7x = 13.2x = 13.2 / 7x ≈ 1.89
So, the closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
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Answer the question Good Luck
Answer:
96
Step-by-step explanation:
Because it is
Find the missing side lengths. Leave your answers as radicals in simplest form.
The lengths of the missing sides are:
x = 6
y = 3√2
How to find the missing side lengths of the triangle?Here we can see a right triangle, we want to find the two missing lengths in it.
We know the measure of one angle, and the length of the adjacent cathetus of it, then we can use trigonometric relations:
cos(a) = (adjacent cathetus)/hypotenuse
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the values that we know, we will get:
cos(45°) = 3√2/x
Solving for x:
x = ( 3√2)/cos(45°) = 3√2*(2/√2) = 6
And to get the value of y we use the other:
tan(45°) = y/ ( 3√2)
1 = y/ ( 3√2)
( 3√2) = y
These are the lengths.
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4
Triangle ABC is shown. Use the graph to answer the question.
Determine the coordinates of the image if triangle ABC is translated 5 units down
OA(-4,-2), B(4,-2). C'(0, 2)
OA(1, -7), 8(9,-7). C'(5,-3)
OA(1, 3), B(9, 3), C'(5, 7)