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3 years ago

Find the value of each variable.

Mathematics

1 answer:

kap26 [50]3 years ago

5 0

Answer:

EF = 18 in. & m∠F = 134 °

Step-by-step explanation:

Hi there,

In order to find the length of side EF, you should realize that this is an <u>isosceles triangle</u>. We know that two sides and two angles of this type of triangle are equal to each other. We also know that the lengths of the sides opposite of the congruent angles are equal to each other. Thus, we proved that length of side EF is equal to the length of side FG.

Therefore, EF is 18 inches because FG is 18 inches.

In order to find m∠F, you need to know that the sum of the angles in a triangle add up to 180°. You add all of the known angle values and subtract it by 180°.

m∠E + m∠G + m∠F = 180°

23° + 23° + m∠F = 180°

46° + m∠F = 180°

m∠F = 134°

Hope this explanation helps you understand this problem. Cheers.

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Marina86 [1]

Answer:

Step-by-step explanation:

Apply Only the Outside and Inside Method of the Foil Method.

$7 \times - \frac{1}{2} = - 3.5x$

$\frac{1}{2} \times 7x = 3.5x$

Add them together

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So our b value is 0.

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3 years ago

What is the standard form of the equation y=-5/2x-3 ?

butalik [34]

The standard form of an equation is the form where that equation has no fractions and is written in the form ax + by = c.

To get rid of the fractions in y = -5/2 x - 3, we need to multiply both sides by 2. That makes the equation become:

2y = -5x - 6

Now we need to get it into the form ax + by = c. We can do this by adding 5x to each side.

5x + 2y = -6 is our answer

6 0

3 years ago

Find the area of the triangle formed by the origin and the points of intersection of parabolas y=− 1/3 (x−1)^2+8 and y=x^2−2x−3.

Kobotan [32]

Answer:

The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.

Step-by-step explanation:

The two parabolas are $y = - \frac{1}{3}(x - 1)^{2} + 8$ and y = x² - 2x - 3.

Now, solving those two equations we will get the points of intersection.

So, $- \frac{1}{3}(x - 1)^{2} + 8 = x^{2} - 2x - 3$

⇒ - (x - 1)² + 24 = 3x² - 6x - 9

⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9

⇒ 4x² - 8x - 32 = 0

⇒ x² - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ (x - 4)(x + 2) = 0

So, x = 4 or - 2.

Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).

Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).

Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.

So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)

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3 years ago

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Gelneren [198K]

Step-by-step explanation:

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kari74 [83]

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2 years ago