The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.

We also see that b = 123 as well since a = b (they are vertical angles).

Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.

c+123 = 180

c = 180-123

c = 57

-------------------------

To summarize, we have these three angles

a = 123

b = 123

c = 57

6 0

2 years ago

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What is the surface area of the regular pyramid given below?

VARVARA [1.3K]

Each trianglar side has an area: (1/2)*8*9=36
the base is a square with an area of 8*8=64
so the total surface area is 36+36+36+36+64=208

5 0

3 years ago

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SOLUTION: a diver jumps from a diving board that is 24 feet above the water. the height of the diver is given by h= -16(t-1.5)(t

lara [203]

Answer:

The diver will hit the water at 1.5 seconds

Step-by-step explanation:

Given

$h= -16(t-1.5)(t+1)$

Required (Missing from the question)

When will the diver hit the water?

To do this, we simply solve for t

When the diver hits the water, the height is 0 (at that point)

So, substitute 0 for h in $h= -16(t-1.5)(t+1)$

$0= -16(t-1.5)(t+1)$

Divide both sides by -16

$\frac{0}{-16} =\frac{-16(t-1.5)(t+1)}{-16}$

$\frac{0}{-16} =(t-1.5)(t+1)$

$0 =(t-1.5)(t+1)$

$(t-1.5)(t+1)=0$

Split

$t - 1.5 = 0$ or $t + 1 = 0$

Solve for t

$t = 1.5$ or $t = -1$

But time (t) can not be negative.

So:

$t = 1.5$

Hence, the diver will hit the water at 1.5 seconds

8 0

3 years ago

The equation c= 0.25n can be used to find the cost (c) of buying n number of apples.

aksik [14]

Answer:

(a) The constant of proportionality is 0.25

(b) 1 apple = $0.25

Step-by-step explanation:

Given

$c= 0.25n$

Solving (a): The constant of proportionality;

For an equation:

$c=kn$

Where

k = constant of proportionality

By comparing: $c=kn$ to $c= 0.25n$

$k = 0.25$

Hence, the constant of proportionality is 0.25

Solving (b): What information does $k = 0.25$ gives.

It represents the unit rate.

<em>So, it means that 1 apple costs $0.25</em>

Solving (c): Number of apples for $3.

This means that $c = 3$

Substitute 3 for c in $c= 0.25n$

$3 = 0.25n$

Make n the subject

$n = \frac{3}{0.25}$

$n = 12$

7 0

2 years ago

Graph the equation using the slope and y-intercept for 2y=4x+4​

Graph the equation using the slope and y-intercept for 2y=4x+4