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2 years ago

Find the x-intercepts for the parabola defined

Mathematics

1 answer:

Ulleksa [173]2 years ago

5 0

Answer:

(- 2, 0 ), (1, 0 )

Step-by-step explanation:

Given

y = 2x² + 2x - 4

To find the x- intercepts let y = 0, that is

2x² + 2x - 4 = 0 ← divide through by 2

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Thus x- intercepts are (- 2, 0) and (1, 0)

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3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie

allsm [11]

Answer:

<em>The building is 61.5 m tall</em>

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

$\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 53^\circ=\frac{150-x}{h}$

$\displaystyle \tan 48^\circ=\frac{x}{h}$

From the last equation:

$x=h.\tan 48^\circ$

Substituting into the first equation:

$\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}$

Operating on the right side:

$\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ$

Rearranging:

$\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}$

Solving for h:

$\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}$

Calculating:

h = 61.5 m

The building is 61.5 m tall

5 0

2 years ago

The jogging track is of a mile long. If Ashley jogged around it 4 times, how far did she run?

matrenka [14]

Answer: 4 miles

Step-by-step explanation:

If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.

<em>Hope it helps <3</em>

5 0

2 years ago

There are 24 girls in a class. The ratio of girls to boys is 3:8.

dangina [55]

Answer:

64 boys.

Step-by-step explanation:

There are 3 girls for every 8 boys.

24/3 = 8

8 * 8 = 64

7 0

2 years ago

What is the perimeter of the square?

kolezko [41]

Answer:

D.68ft

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

One hiking club charges $16 to become a member and $3 to participate on each hike. Another club charges no membership fee, but c

yawa3891 [41]

Answer:

x < 8

Step-by-step explanation:

x= # of hikes

3x +16 =5x

-3x. -3x

16=2x

16/2= 8

2x/2= x

8=x

x=8

check:

3(8) +16 =5(8)

24 +16 =40

40=40 ✓

there for at 8 hikes with either deal it would be the same but if you went up a number of hikes for the first option it would only be $43.00 spent in total. but with the second option it would be $45.00.

7 0

2 years ago