PLEASE HELP 30 POINTS
The graph below shows the trajectory of a ball that is thrown upward from the ground. What is the approximate value of the ball's maximum height, in feet?

Answer:

x³ + 2x² -3x +6

Step-by-step explanation:

We need to find the polynomial whose roots are ,

Say of we have zeroes as , α , β and γ , then the polynomial is ,

=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]

=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]

=> p(x) = k[ (x+2)(x² - 3)]

=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]

=> p(x) = k[ x³ - 3x + 2x² - 6 ]

=> p(x) = k[ x³ + 2x² - 3x - 6 ]

Answer:

u² + 2u + 1

Step-by-step explanation:

In the question it's asking to find the the number in the blank to make the expression a perfect square.

Let the number in the blank be 'x'.

To guess 'x' , use the algebraic identity :- [tex](a + b)^2 = a^2 + (2 \times a \times b) + b^2[/tex]

While matching the expression with identity , the expression will look like this :- u² + 2ux + x²

In the expression given in the question , it's "2u" but after matching the expression with identity , it is found to be "2ux".

⇒ x = 1 (∵ If x will be 1 , then 2ux = 2×u×1 = 2u)

⇒ x² = 1

∴ The number in the blank is 1.

Answer:

It's just negative, just enter this sign -

Step-by-step explanation:

The coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]

"The coordinates of any point on the circle [tex]x^{2}+ y^{2}= r^{2}[/tex] are [tex](r~cos\theta,r~sin\theta)[/tex]"

sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

For given question,

We need to find the coordinates of the point on the unit circle at an angle -135°

We know, for unit circle radius = 1

So, the coordinates of any point on the unit circle would be [tex](cos\theta, sin\theta)[/tex]

Here, [tex]\theta=-135^{\circ}[/tex]

Now, we find the the value of [tex]sin(-135^{\circ}),~cos(-135^{\circ})[/tex]

[tex]sin(-135^{\circ})\\\\=-sin(135^{\circ})\\\\=-sin(180^{\circ}-45^{\circ})\\\\=-[sin(180^{\circ})cos(45^{\circ})-cos(180^{\circ})sin(45^{\circ})]\\\\=-[0\times \frac{1}{\sqrt{2} }-(-1)\times \frac{1}{\sqrt{2} } ]\\\\=-(0+\frac{1}{\sqrt{2} } )\\\\=-\frac{1}{\sqrt{2} }\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }\\\\=-\frac{\sqrt{2} }{2}[/tex]

and cos(-135°) would be,

[tex]cos(-135^{\circ})\\\\=cos(135^{\circ})\\\\=cos(180^{\circ}-45^{\circ})\\\\=cos(180^{\circ})sin(45^{\circ})+sin(180^{\circ})sin(45^{\circ})\\\\=((-1)\times \frac{1}{\sqrt{2}} )+(0\times \frac{1}{\sqrt{2} }) \\\\=-\frac{1}{\sqrt{2} }+0\\\\ =-\frac{1}{\sqrt{2}}\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2}\times \sqrt{2}}\\\\=-\frac{\sqrt{2} }{2}[/tex]

Therefore, the coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]

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Answer:

3, 8

Step-by-step explanation:

19x__=9x__-5

24x_=9x_

8x_=3x_

8x3=3x8

24=24

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Answer:

  71°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  ∠H = 180° -109° = 71°

_____

Additional comment

The above rule comes from the more general rule that the measure of an inscribed angle is half the measure of the arc it intercepts. Here, inscribed angle J intercepts arc GHI, so that arc has measure 2×109°. Then the measure of short arc GI is 360° -2×109°, and inscribed angle H is half that:

  ∠H = (1/2)(360° -2×109°)

  ∠H = 180° -109° = 71°

========================================

Explanation:

First factor out the GCF 7

7x^2 + 7x - 42

7*x^2 + 7*x + 7*(-6)

7(x^2 + x - 6)

Now focus on factoring x^2+x-6

We need to find two numbers that multiply to -6 and add to 1. Those values are 3 and -2. That means x^2+x-6 factors to (x+3)(x-2).

The 7(x^2 + x - 6) then turns into 7(x+3)(x-2)

The factor out front, the "7", is the integer factor. The other factors (x+3) and (x-2) are binomial factors.

7, (x + 3), and (x - 2) are the three factors of the given expression.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

We can factor out the common factor of 7 from the given expression to get:

[tex]7(x^2 + x - 6)[/tex]

Now, we need to factor the quadratic expression x^2 + x - 6. We can do this by finding two numbers that multiply to -6 and add to 1 (the coefficient of x).

The two numbers are 3 and -2, since 3 x -2 = -6 and 3 + (-2) = 1.

So we can write [tex]x^2 + x - 6[/tex] as (x + 3)(x - 2).

Substituting this back into the expression we have:

[tex]7(x + 3)(x - 2)[/tex]

Therefore, the three factors are 7, (x + 3), and (x - 2).

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Answer:

Solution given:

height[p]=20m

angle of depression [a]=25°

base[b]=?

we have

Tan a=p/b

tan 25=20/b

b=20/tan25

b=42.89 or 43

the tower is 43m far from the vehicle .

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Answer:

  an = 2(-4)^(n-1)

Step-by-step explanation:

The general form of the explicit formula for a geometric series with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Your sequence has a1=2 and r=-8/2 = -4. So, the explicit formula is ...

  an = 2(-4)^(n-1)

Answer:

1) Yes

2) No

Step-by-step explanation:

1) x+6=14. To solve this you first have to isolate x by subtracting 6 from both sides. x=8. This means that it is correct.

2) s/4=5. To solve this you have to isolate s. You can do this by multiplying 4 in both sides. this will make the equation s=5x4. Simplify to get s=20. 20 is not equal to 24 so it is no.

If this has helped please mark as brainliest

Answer: 23

Step-by-step explanation:

Answer:

2,050 dollars is how much she will have to pay

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

Belle is my fav.

Step-by-step explanation:

She loves to read books like me and I hate people who always go out there and try to impress me with something.

Answer:

5 hours

Step-by-step explanation:

Answer:

7,300

Step-by-step explanation:

6900x2 years=13,800 total tuition.

13800-2500-4000 (2000x2)=7,300

Answer:

200π

Step-by-step explanation:

Surface area is abbreviated to SA

TOTAL SA of cone = Base area + πrl

Base area = πr² = π x 8² = 64π

Curved SA = πrl = π x 8 x l

to work out l, use pythagoras theorem: √(15)² + (8)² = 17

so, curved SA = π x 8 x 17 = 136π

Total SA of cone = 64π + 136π = 200π

Answer:

14,700 butterflies

Step-by-step explanation:

Given the following data;

Time, x = 7 years

f(x) = 2,000(1.05)x

To find the population;

A population can be defined as the total number of living organisms living together in a particular place and sharing certain characteristics in common.

Substituting into the equation, we have;

f(7) = 2,000(1.05) * 7

f(7) = 2,100 * 7

f(7) = 14,700 butterflies

Answer:

x=65

Step-by-step explanation:

that is all. It is isoceles triangle so if p is 65, l is also 65

Answer:

65 degrees

Step-by-step explanation:

The two sides of the angle is equal which means it is an isosceles triangle, the value will be 65 degrees

Answer:

The second answer choice

Step-by-step explanation:

The pyramid shown is a triangular pyramid. A triangular pyramid consist of 4 faces; 1 triangular base and 3 triangular lateral faces.

Hence, the correct answer would be the second choice.

Answer:

$60

Step-by-step explanation:

To find how much Zoe paid before the sales tax and tip, we first need to consider the amount she paid in sales tax and tips.

Sales tax  + Tips = $18.60

Let x = original price

Sales tax = 11% * original price

Sales tax = 0.11 * x

x= 0.11x

Tips = 20% * original price

Tips = 0.20 * x

x = 0.2x

Now that we have a value for both the sales tax and tips, we can then proceed to find the original price by:

0.11x + 0.2x = 18.60

0.31x = 18.60

Now we need to divide both sides by 0.31 to find x.

x = 60

Zoe's dinner before the sales tax and tips was $60.

Answer:

$60?

Step-by-step explanation:

Answer:

The probability that they will meet is 0.4375

Step-by-step explanation:

Let A and B be two friends who choose to meet  the same one-hour period.Since there are 60 minutes in an hour therefore n= 60

A can wait for 15 minutes

So the probability of A to meet is given by P(A)=  (15/60)= 1/4

Similarly

B can wait for 15 minutes

So the probability of B to meet is given by P(B)=  (15/60)= 1/4

The  probability  that A cannot meet is given by 1- P(A)=  1-1/4= 3/4

Similarly

The  probability  that B cannot meet is given by 1- P(B)=  1-1/4= 3/4

And

The  probability  that both  A  and B cannot meet is given by = 3/4*3/4= 9/16

So the probability that both will meet = 1- 9/16= 7/16= 0.4375

Answer:

(-5, -7)

Step-by-step explanation:

-x, y-> -x, -y

Answer:

Step-by-step explanation:

Is that what you mean? If it is the picture shows

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Answer:

  x = 20

Step-by-step explanation:

Corresponding sides are proportional:

  x/15 = 24/18

  x = 15(24/18) = 15(4/3)

  x = 20

Answer:

According to the property of corresponding sides

x1/x2 = y1/y2

x/15 = 24/18

x/15 = 4/3

x = 4 × 15/3

x = 4 × 5

x = 20

[tex] \\ [/tex]

Answer:

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.

This means that [tex]n = 42, \pi = \frac{26}{42} = 0.619[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 - 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.472[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 + 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.766[/tex]

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

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Answer:

  B, D

Step-by-step explanation:

The quadratic expands to ...

  (2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1

The coefficients can be factored out of the sum, so ...

  ∑(4n²) = 4∑n² for example

The sum of 60 ones is 60:

  [tex]\displaystyle\sum_{n=1}^{60}{1}=1+1+1+\dots+1=60[/tex]

So, the sum can be written as ...

  [tex]\displaystyle\sum_{n=1}^{60}{(2n-1)^2}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+\sum_{n=1}^{60}{1}}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+60}[/tex]

_____

It appears that the key to choosing the correct answers is paying attention to signs.

Answer: Step number 2 is 287,980

Step-by-step explanation:

Just did the assignment.

Answer:

D

The light reflected during the first quarter and third quarter moon phases appears equal because the sun, moon, and Earth are at right angles.