The quadrilateral WXYZ has vertices W(3,-5) X(1,-3) Y(-1,-5) and Z(1,-7)
Perform r(90 degrees, 0) (WXYZ) and state the coordinates of the vertices
After performing a 90 degree rotation about the origin on the points, the new coordinates for W, X, Y, and Z respectively are (5,3), (3,1), (5,-1), and (7,1).
Explanation:In this problem, the task is to rotate a quadrilateral 90 degrees about the origin (0,0). The rule for rotation of points in the plane about the origin by 90 degrees is (x, y) -> (-y, x).
The new coordinates are,
For W(3,-5), it will become W'(-(-5),3) which equals W'(5,3) after rotating 90 degrees. For X(1,-3), it will become X'(-(-3),1) which equals X'(3,1) after rotating 90 degrees. For Y(-1,-5), it will become Y'(-(-5),-1) which equals Y'(5,-1) after rotating 90 degrees. For Z(1,-7), it will become Z'(-(-7),1) which equals Z'(7,1) after rotating 90 degrees. Learn more about Rotation of Coordinates here:
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two vertical cliffs are on opposite sides of a 90 foot wide river. From point A at the top of the shorter cliff, the angle of elevation of the top of the other cliff(b) is 28 degress and the angle of depression to the bottom is 38 degress.find the height of each cliff ,to the nearest foot
Final Answer:
The height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.
Explanation:
To find the height of each cliff, we will use trigonometry. Specifically, we will use the tangent function, which is the ratio of the opposite side to the adjacent side of a right-angled triangle.
First, let's consider the shorter cliff (point A). We know the angle of depression from A to the bottom of the river is 38 degrees. If we imagine a horizontal line at the height of point A, we can create a right-angled triangle with one angle at the bottom of the river, the vertical side as the height of the cliff, the horizontal side as the width of the river, and the angle of depression at point A.
Using the tangent of the angle of depression, we can set up the following equation to find the height of the shorter cliff (which we will call hA):
tan(38 degrees) = height_shorter_cliff / width_river
Solving for the height of the shorter cliff, we get:
height_shorter_cliff = width_river * tan(38 degrees)
Using a calculator or trigonometry tables, we find that the height of the shorter cliff is approximately 70 feet.
Next, let's consider the taller cliff (point B). The angle of elevation from A to B is given as 28 degrees. Now we can imagine another right-angled triangle, this time with one angle at point A, the vertical side as the difference in height between cliffs A and B, the horizontal side as the width of the river, and the angle of elevation at point A.
Using the tangent of the angle of elevation, we can set up an equation to find the height difference between cliffs A and B (which we will call hB - hA):
tan(28 degrees) = (height_taller_cliff - height_shorter_cliff) / width_river
We can rearrange this to solve for the height of the taller cliff:
height_taller_cliff = width_river * tan(28 degrees) + height_shorter_cliff
Now, using our previous result for the height of the shorter cliff (70 feet), we plug it into our equation:
height_taller_cliff = 90 * tan(28 degrees) + 70
Using a calculator or trigonometry tables to evaluate tan(28 degrees), we find that the height of the taller cliff is approximately 118 feet.
Therefore, to the nearest foot, the height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.
A right triangle has legs that are 16 inches and 20 inches long. What is the length of the hypotenuse? Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
What is the missing constant term in the perfect square that starts with x^2−4x
can someone check these questions?
Please show work! Thank you
Use a calculator to evaluate cot 3.14/5
1. Simplify the product.
7x (x+4)
A) 7x^2 + 4
B) 7x^2 + 28x
C) 8x + 4
D) 8x + 11,
The simplified product is 7x² + 28x.
Option B is the correct answer.
We have,
To simplify the product 7 x (x + 4), we need to distribute the 7x to both terms inside the parentheses.
The distributive property states that for any numbers a, b, and c,
a x (b + c) = a x b + a x c.
Applying this property to the given expression, we have:
(7x) x (x) + (7x) x 4
Multiplying 7x by x gives us 7x², and multiplying 7x by 4 gives us 28x.
So the simplified expression becomes:
7x² + 28x
Therefore,
The simplified product is 7x² + 28x.
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Victoria wants to purchase a skateboard. She has $125 to spend. She finds one that regularly sells for $139.99 and is on sale for 15% off. Sales tax is 7%. Victoria says that she has enough money to buy the skateboard. Is she correct? Explain.
Explain what defines direct variation. Then, check which of the following tables include directly proportional quantities x and y x 1 2 3 4 y 7 14 21 28
Find an equivalent fraction for the decimal number. Be sure that your answer is in lowest terms. Enter the numerator into the first box and the denominator of the fraction into the box below. a0 0.6 = ________ a1
Answer:
The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Given : The decimal number is 0.6
To find : An equivalent fraction for the decimal number in the lowest terms.
Solution : The decimal number 0.6 is written in fraction by removing decimal.
Step 1 - Write the decimal number
[tex]0.6[/tex]
Step 2- Remove the decimal
[tex]0.6 = \frac{6}{10}[/tex]
Step 3 - Reduced the fraction by dividing Nr. and Dr. by 2
[tex]0.6 = \frac{6}{10}=\frac{3}{5}[/tex]
Therefore, The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]
Numerator is [tex]a_0=3[/tex] and Denominator is [tex]a_1=5[/tex]
what is the simplified form of the following expression? sqrt 1/144
How would you use a model to determine the approximate formula for the circumference of a circle with a diameter of 8 cm, and connect the model to the actual formula?
Answer with explanation:
Take a thread of length x cm.Convert it into circle of radius r cm.
If you divide the Length of circle by value equal to 2 π, you will obtain radius of the circle.The value 2π is a constant Quantity is an Irrational number.
[tex]\rightarrow \frac{\text{Length of thread}}{2 \pi}=r\\\\ \rightarrow \frac{x}{2 \pi}=r\\\\ \rightarrow x=2 \pi r[/tex]
Diameter of Circle =8 cm
Circumference of a circle with a diameter of 8 cm has radius equal to 4 cm because radius is half of diameter
=2 × 3.14 × 4 cm
= 25.12 cm
⇒So, Actual Length of thread =25.12 cm
Irrational Quantity=2 π=2×3.14=6.28 cm
So Radius
[tex]=\frac{25.12}{6.28}\\\\=4 cm[/tex]
Diameter =Radius × 2
=4 cm × 2
= 8 cm
2/3 7/8 What is closer to 3/4
NEED HELP ASAP!
SHOW WORK FOR 1. b, c, d and e!!!
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Solve the inequality. Write the solution in interval notation. Choose the correct solution. 6x > – 24
A. [ –24, ∞ ) B. [ – 4, ∞ ) C. ( –∞, 24 ] D. ( – 4, ∞ ]
Divide the given inequality 6x > -24 by 6 to isolate x, resulting in x > -4, which in interval notation is (-4, ∞). The correct choice is D. ( -4, ∞) ].
To solve the inequality 6x > -24, we will divide both sides of the inequality by 6 to isolate x, keeping in mind that since 6 is positive, the direction of the inequality will remain the same.
Step-by-step solution:
Start with the inequality 6x > -24.
Divide both sides by 6, which gives us x > -4.
In interval notation, this translates to (-4, ∞).
The correct choice is D. ( -4, ∞) ]
Please help !! I fan and medal!!
1.)rewrite the following expression using the distributive property.
5(2x-8)
A.)-30x
B.)10x-40
C.)10x+40
D.)10x-8
2.)simplify the following expression:
-16-18/2+25/5+1. ( the -16 and -18 are both on top of the 2 it's a fraction)
A.)-18
B.)6
C.)10
D.)-6
What is the perimeter of rectangle EFGH?
+ units
+ units
22 units
39 units
Answer:
B. 2√10 + 2√29 units
**** IS MY ANSWER CORRECT? ***Suppose you push your physics book against a wall hard enough to keep it from moving. Does the friction force on the book point (a) into the wall, (b) out of the wall, (c) up, (d) down, or (e) is there no friction force? Explain.
The football coach bought enough sports mix to make 60 L of a sports drink.
How many cups of the sports drink can the coach make?
(1 L ≈ 2.11 pt)
Question 3 options:
56.9 cups
63.3 cups
253.2 cups
267.1 cups,
what is this difference of the polynomials? (x^4+x^3+x^2+x)-(x^4-x^3+x^2-x)
Answer:2x^3+2x
Step-by-step explanation:
NEED HELP WITH MY MATH
Can anyone help me on this problem, I have been stuck on it for a while now.
What is the length of the longest side of the triangle if the left side is 2x+12 and the bottom number is 6x-2 and the right side is 5x-9
To find the length of the longest side of the triangle, use the Pythagorean theorem to solve for x and determine the side lengths of the triangle.
Explanation:To find the length of the longest side of the triangle, we need to determine which side is the hypotenuse. In a right triangle, the hypotenuse is the side opposite the right angle. Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the length of the hypotenuse.
Let's denote the three sides of the triangle as A, B, and C. The left side is 2x + 12, the bottom side is 6x - 2, and the right side is 5x - 9. Since we can't determine which side is which based on the given information, we can use the variables.
By applying the Pythagorean theorem, we can set up the equation (2x + 12)^2 + (6x - 2)^2 = (5x - 9)^2. Expanding and simplifying this equation will allow us to solve for x and find the lengths of the sides of the triangle. Once we have the side lengths, we can determine which side is the longest.
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At a recent holiday party, 4/5 of the attendees were company employees and the rest were their guests. if 2/3 of the employees who attended were engineers, what was the number of non-engineer employees who attended? there were 225 total attendees at the party. there were 45 attendees who were guests of the employees.
how do you factorise 15x+10
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 2−x+1 intersect are the solutions of the equation 4−x = 2−x+1. (4 points) Part B: Make tables to find the solution to 4−x = 2−x+1. Take the integer values of x between −2 and 2. (4 points) Part C: How can you solve the equation 4−x = 2−x+1 graphically? (2 points)
how are three or more angles related
Can you check my work please?
Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.
Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.)
My Answer: Part one:
(360degrees/60minutes = 6 degrees per minute.)
1:25 to 1:50 is 25 minutes. 25 x 6 = 150.
150pi/180 = 5pi/6,