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3 years ago

Step 1: 12x – 15 – 12x = 7x + 20

Mathematics

1 answer:

stealth61 [152]3 years ago

5 0

Step-by-step explanation:

step 1. 12x - 15 - 12x = 7x + 20

step 2. 12x - 12x - 15 = 7x + 20 (grouping of terms)

step 3. -15 = 7x + 20 (adding like terms)

step 4. -35 = 7x (subtract 20 from both sides)

step 5. this step is incorrect.

step 6. -5 = x ( divide both sides by 7)

step 7. x = -5 (put the variable first).

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Nicholas drew a triangle with 45, 35, and 100 degree angles. Is there another triangle with the same three angles but different

Anna11 [10]

Answer:

Yes, there are infinite triangles with the same three angles but different side lengths

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

therefore

There are infinite triangles with the same three angles but different side lengths

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2 years ago

I’m so bad at slope

Travka [436]

Answer:

So slope 1 would be positive

Slope 2 would be negative

Slope 3 would be zero

Step-by-step explanation:

If the slope is moving up from left to right, then it is positive

If the slope is moving down from left to right, then it is negative

If the slope is a vertical line and is not moving left/right, then it is undefined

If the slope is a horizontal line and is not moving up/down, then it is zero

So slope 1 would be positive because it is moving up from left to right.

Slope 2 would be negative because it is moving down from left to right.

Slope 3 would be zero because it is a horizontal line that is not moving up or down.

Hope this helped!

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3 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

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