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3 years ago

Find the value of x, question and choices attached above

Mathematics

1 answer:

Levart [38]3 years ago

8 0

Answer:

Step-by-step explanation:

Look at the picture.

The lines l and m are parallel, therefore alternate interior angles are congruent.

Therefore $\beta=50^o$

Supplementary angles add up to 180°.

Therefore

$(5x-16)+\theta=180$ add 16 to both sides

$5x+\theta=196$ subtract 5x from both sides

$\theta=196-5x$

We know: the sum of the triangle angle measures is 180°.

Therefore we have the equation:

$50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22$

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Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try

ryzh [129]

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

where

L is the length of rectangle

W is the width of rectangle

we have

$F(-2,5),R(-2,1),O(6,1),G(6,5)$

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

$FG=RO=L\\RF=OG=W$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance FG

$F(-2,5),G(6,5)$

substitute the values

$d=\sqrt{(5-5)^{2}+(6+2)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$FG=8\ units$

step 2

Find the distance RF

$R(-2,1),F(-2,5)$

substitute the values

$d=\sqrt{(5-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(4)^{2}+(0)^{2}}$

$RF=4\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$P=2(8+4)=24\ units$

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

$A=LW$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$A=(8)(4)=32\ units^2$

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A runner passes the 12-mi point after 2 hours and reaches the 15-mi point 30 minutes later. Assuming a constant rate, find th

Arturiano [62]

Answer:

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Step-by-step explanation:

Difference in distance

= 15 - 12

= 3 mi

time taken

= 30 mins

= 1/2 hour

Speed

= 3 ÷ 1/2

= 6 mph

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rjkz [21]

Answer:

X=1

Step-by-step explanation:

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3 years ago

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ValentinkaMS [17]

Answer:

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Step-by-step explanation:

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3 years ago

Find the HCF and LCM of the following pairs of numbers:

Marina86 [1]

Answer:

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LCM between 774&252=10836

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LCM between 770&385 is =770

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Step-by-step explanation:

a)because LCM=2×2×3×3×7×43

b)because LCM=2×2×2×2×2×3×17

c)because LCM=2×5×7×11

d)because LCM=2×2×2×3×23×149

4 0

3 years ago