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2 years ago

15

The triangular base of the given prism has an interior angle with a measure of 80° and an interior angle with a measure of 55°.

What is the measure of the unknown angle?
A. 45°
B. 65°
C. 75°
D. 85°

1 answer:

Tju [1.3M]2 years ago

6 0

Answer:

A. 45°

Step-by-step explanation:

When we are given two measurements of interior angles we add both of those angles together.

Also know that a triangle equals 180 degrees

So when we write out this expression $80+55+x=180$

$135+x=180\\-135=-135\\x=45$

Hope this helps

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

What is the distance between (-3,5) (7,5)

Firlakuza [10]

Answer:

10 units

Step-by-step explanation:

use distance formula: d = square root of the difference of the y-values minus the difference of the x-values

d = $\sqrt{(5-5)^2+(7--3)^2}$

d = $\sqrt{(0)^2+(10)^2}$

d = $\sqrt{100}$

d = 10 units

4 0

3 years ago

Read 2 more answers

Help please , 20 points

alex41 [277]

The top-left one because 3ba is the same as 3ab

8 0

3 years ago

Read 2 more answers

Can somebody please help me? :(

Natasha2012 [34]

Answer:

143 square meters

Step-by-step explanation:

The surface has a width of 11 meters and a length of 13 meters.

13 x 11 = 143.

Is this correct?

5 0

2 years ago

10 in.<br> 13 in.<br> 16 in. <br> What is the Surface area of the triangular prism

Marianna [84]

Answer:

about 704 in 2

Step-by-step explanation:

surface area-2Ab+Pb*h

=2(13*8)+49.6(10)

=704

3 0

3 years ago