Question

Please help will give 100 points to BRAINLIEST!!!!!

5. What is the value of x? (the 1st picture)

6. What is the value of x? (the 2nd picture)
A.53
B.61
C.119
D.114

7.A cylinder has a radius of 5 cm and a height of 12 cm. What is the volume of the cylinder?
A.60π cm^3
B.300π cm^3
C.720π cm^3
D.1200 cm^3

8. A cone has a diameter of 12 in. and a height of 16 in. What is the volume of the cone? Use 3.14 as an approximation for π and express your final answer in hundredths.
______ in3

9. Rectangle ABCD is similar to rectangle FGHI. What is the value of x? (the 3rd picture)
______cm

10. Given quadrilateral ABCD ~ quadrilateral JKLM and AD = 14, JM = 6, and KL = 9, what is BC?
______

11. What transformation was performed on triangle ABC to create triangle A'B'C' ? (4th picture)
A.translation 8 units right
B.180° rotation about the origin
C.reflection across the x-axis
D.reflection across the y-axis

14. What is the value of x? Round to the nearest tenth. (5th picture)
_____cm

15. Which set of side lengths defines a right triangle?
A. 6, 8, 11
B. 5, 12, 13
C. 7, 9, 13
D. 6, 9, 11

Answer 1

Answer:

Part 5) ∠x=122°

Part 6) Option D. ∠x=114°

Part 7) Option B.300π cm^3

Part 8) The volume of the cone is $V=602.88\ in^{3}$

Part 9) The value of x is 12 cm

Part 10) BC=21 units

Part 11) Option D.reflection across the y-axis

Part 14)  $x=15.6\ cm$

Part 15) B. 5, 12, 13

Step-by-step explanation:

Part 5)  What is the value of x?

we know that

∠x+58°=180°------> by supplementary angles

solve for x

∠x=180°-58°=122°

Part 6)  What is the value of x?

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

The measure of the third interior angle of the triangle is equal to

180°-61°-53°=66°

so

66°+∠x=180° -----> by supplementary angles

solve for x

∠x=180°-66°=114°

Part 7) A cylinder has a radius of 5 cm and a height of 12 cm. What is the volume of the cylinder?

we know that

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=5\ cm$

$h=12\ cm$

substitute

$V=\pi (5)^{2} (12)$

$V=300\pi\ cm^{3}$

Part 8) A cone has a diameter of 12 in. and a height of 16 in. What is the volume of the cone?

we know that

The volume of the cone is equal to

$V=(1/3)\pi r^{2} h$

we have

$r=12/2=6\ in$ ------> the radius is half the diameter

$h=16\ in$

substitute

$V=(1/3)(3.14)(6)^{2} (16)$

$V=602.88\ in^{3}$

Part 9) Rectangle ABCD is similar to rectangle FGHI. What is the value of x?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

AB/FG=BC/GH

substitute the values

8/6=x/9

x=9*8/6

x=12 cm

Part 10) Given quadrilateral ABCD ~ quadrilateral JKLM and AD = 14, JM = 6, and KL = 9, what is BC?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

AD/JM/BC/KL

substitute the values

14/6/BC/9

BC=14*9/6

BC=21 units

Part 11) What transformation was performed on triangle ABC to create triangle A'B'C' ?

we know that

The rule for a reflection over the y -axis is (x,y)→(−x,y)

so

When reflecting across the y- axis the x-values will be multiplied by negative one, but the y-values will not change

This problem is a reflection across the y-axis

Part 14) What is the value of x? Round to the nearest tenth    

we know that

Applying the Pythagoras Theorem

$x^{2}=10^{2}+12^{2}\\ \\x^{2}=244\\ \\x=15.6\ cm$

Part 15) Which set of side lengths defines a right triangle?

we know that

If the set of side lengths defines a right triangle, then must satisfy the Pythagoras Theorem

Verify each case

case A. 6, 8, 11

$11^{2}=6^{2}+8^{2}\\ \\121=100$

Is not true

therefore

Is not a right triangle

case B. 5, 12, 13

$13^{2}=5^{2}+12^{2}\\ \\169=169$

Is true

therefore

Is a right triangle

case C. 7, 9, 13

$13^{2}=7^{2}+9^{2}\\ \\169=130$

Is not true

therefore

Is not a right triangle

case D. 6, 9, 11

$11^{2}=6^{2}+9^{2}\\ \\121=117$

Is not true

therefore

Is not a right triangle