6
a The diagonals of a rectangle intersect at 76°
Find the angle that a diagonal makes with a longer side of the rectangle.
b The diagonals of a rectangle intersect at xº.
Find the angle that a diagonal makes with a longer side of the rectangle.
Answers
Explanation: A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem: where a and b are the sides of the rectangle and c is the length of the diagonal.
The angle that a diagonal makes with a longer side of the rectangle is 38°.
The angle that a diagonal makes with a longer side of the rectangle is (x/2)°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
a)
The diagonals of a rectangle intersect at 76°.
This means,
From the figure Triangle AOB.
AOB + OAB + OBA = 180
(180 - 76) + x + x = 180
2x = 180 - 180 + 76
2x = 76
x = 38
This means,
The angle with the longer side of the rectangle is 38.
b)
Similarly,
The diagonals of a rectangle intersect at xº.
This means,
AOB + OAB + OBA = 180
(180 - x) + y + y = 180
2y = 180 - 180 + x
2y = x
y = x/2
This means,
The angle with the longer side of the rectangle is x/2.
Thus,
The angle with the longer side of the rectangle is 38°.
The angle with the longer side of the rectangle is (x/2)°.
Learn more about triangles here:
https://brainly.com/question/25950519
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Answers
Answer:
11:30
learn how to count you bozo
The price of n tickets to a concert is is 9n + 6 dollars. What is the cost, in dollars, for 8 tickets to the play?
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Answer:
78
Step-by-step explanation:
do 9 x 8= 72
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Given that the following statement is true
"If a shape is a polygon, then it is a closed figure."
Which of the following statements must also be true?
A. If a shape is a closed figure, then it is a polygon.
B. If a shape is not a polygon, then it is not a closed figure
C. If a shape is not a closed figure, then it is not a polygon
D. If the shape is not a polygon, then it is a closed figure.
Answers
Answer:
C IS THE ANS COS ALL POLYGONS ARE CLOSED AND IF IT NOT CLOSED IT NOT A POLYGON
the bellah's pool is leaking. The pool leaked 3/4 gallon in 20 minutes, or 1/3 hour. how many gallon is the pool leaking each hour?
Answers
Answer:
9/4 gallons
Step-by-step explanation:
If the rate is 3/4 gallon per 1/3 of an hour, we need to figure out how to make the 1/3 into 1 hour.
Since it's 1/3, you have to multiply it by 3 to get 1. So, multiply 1/3 and 3/4 by 3:
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Answers
For what values of x is the trigonometric equation tan(x − 180°) − sin(x − 180°) = 0, where 0 ≤ x < 360°, true?
{0°, 90°}
{0°, 180°}
{90°, 180°}
{90°, 270°}
Answers
Answer:
It's the second option {0°, 180°}
Explanation:
Given a trigonometric equation in degrees where tan(x − 180°) − sin(x − 180°) = 0 .
Since this is multiple choice, you can use the process of elimination to get rid of the incorrect answers.
You can think of sin as the y or vertical component of a rotation, cos as the x or horizontal component of a rotation, and tangent as we know to be sin/cos. Remember, this rotation is oriented in the counterclockwise direction so it is going leftward starting at (1,0). We also know that 360° is a full rotation so the rotation rule for each interval of 90 degrees counter clockwise is 0° or 360° (x,y) → 90° (-y,x) → 180° (-x,-y) → 270° (y,-x).
So if sin(90°) is 1, cos must be 0 as (1,0) → (0,1) , which means tan is N/A (undefined) since 1/0 = N/A. And undefined + 1 ≠ 0 so anything with 90° is incorrect. That leaves us with the second option {0°, 180°} because it is the only one that excludes 90°.
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Answers
Answer:
the amount of each deposit is $45,555
Step-by-step explanation:
The computation of the each deposit is shown below:
Given that
Future value be $20,000
Time period = 15 × 2 = 30
And, the rate = 5% ÷ 2 = 2.5%
Now the formula is as follows
= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1
= ($20,000 × 2.5) ÷ (1 + 0.025)^30 - 1
= $50,000 ÷ 1.0975675791
= $45,555
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Step-by-step explanation:
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Answers
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