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2 years ago

Find the measure of the missing angles.

Mathematics

1 answer:

Alenkinab [10]2 years ago

8 0

Answer:

d = 69°, e = 32°, f = 79°

Step-by-step explanation:

the 69° angle and d are vertical angles, so d is 69°.

same with e and the 32° angle, so e is 32°.

the 69° angle and f are on a straight angle, which means they, and e, add up to 180° when combined.

69 + 32 = 101

180 - 101 = 79

so f is 79°.

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Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -

GaryK [48]

Consider all parabolas:

$y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.$

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

$y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.$

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

$y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.$

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

$y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.$

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

$y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.$

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

$y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.$

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

3 0

3 years ago

Given the Arithmetic Sequence 9,12,15,18,21,...find the formula

Georgia [21]

Answer:

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6 0

3 years ago

What is the slope of the line through (-9,6) (-6,-9)

mina [271]

Answer:

The slope of the line through (−9,6) and (−6,−9) is −5

Step-by-step explanation:

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8 0

3 years ago

I can't find area of the triangle

Andreas93 [3]

Answer:

First do the Base multiplied by the Height.

After divide by 2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In May Mr. Lee's earings were 60 percent of the Lee family's total income. In June Mr. Lee earned 20 percent more than in May. I

murzikaleks [220]

Answer: 64.29%

Step-by-step explanation:

Let the total earnings of the Lee family in May be x

Amount earned by Mr Lee in May = 60% of x = 0.6x

Amount earned by other family members in May = x - 0.6x (total earnings - Mr Lee's earnings) = 0.4x

Amount earned by Mr Lee in June = 20% more than what Mr Lee earned in May.

That is, amount earned by Mr Lee in June = 1.2 × 0.6x = 0.72x

Amount earned by other members of the family in June remains unchanged, that is = 0.4x

Total amount earned by the Lee family in June = 0.72x + 0.4x = 1.12x

Percentage of total earnings in June earned by Mr. Lee = (0.72x/1.12x) × 100% = 64.29%.

QED!

6 0

3 years ago