Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.

The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

To learn more about the quadratic equation visit:

brainly.com/question/28038123

#SPJ1

The best way to assign values for a simulation using random digits table will be option A.

The best way to assign values for a simulation using a random digits table would be to use a table with at least 10 digits (0-9) in each row.

For Country X, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. If a digit outside of these ranges is generated, it would be ignored.

For Country Y, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. Again, if a digit outside of these ranges is generated, it would be ignored.

Learn more about simulation on;

https://brainly.com/question/158924

#SPJ1

Answer:

8 feet.

Step-by-step explanation:

Let's denote the width of the sandbox as "w".

We know that the perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

So, we can plug in the given values:

46 = 2(15 + w)

Now, we can solve for "w":

46 = 30 + 2w

Subtracting 30 from both sides:

16 = 2w

Dividing by 2:

w = 8

Therefore, the width of the sandbox is 8 feet.

a. The shape οf the distributiοn οf the sample mean time is nοrmal.

b. The standard error is 0.5345.

Standard deviatiοn is: It is a measure οf hοw spread οut numbers are. It is the square rοοt οf the Variance, and the Variance is the average οf the squared differences frοm the Mean.

Given that:

μ =35

σ = 2

n = 14

a. The shape of the distribution of the sample mean time is normal.

b. To calculate the standard error of the mean time, we would apply this formula,

Standard error :

[tex]$ \rm SE = \frac{ \sigma}{\sqrt{(n)} }[/tex]

[tex]$ \rm SE = \frac{ 2}{\sqrt{(14)} }[/tex]

SE = 0.5345

Thus, the standard error is 0.5345.

To learn more about standard deviation, Visit

https://brainly.com/question/475676

#SPJ1

Complete question:

Majesty Videο Prοductiοn Inc. wants the mean length οf its advertisements tο be 30 secοnds. Assume the distributiοn οf ad length fοllοws the nοrmal distributiοn with a pοpulatiοn standard deviatiοn οf 2 secοnds. Suppοse we select a sample οf 16 ads prοduced by Majesty.

a. What can we say abοut the shape οf the distributiοn οf the sample mean time?

b. What is the standard error of the mean time?

Answer:

(2x)(4x)= 8x^22x + 4x = 6x(x+1)+ 2x = 3x + 1(x+1)(2x) = 2x^2 + 2x3x + (2x) = 5x(3x)(2x) = 6x^2

Step-by-step explanation:

hope this helped

The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:

Second table.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:

1000/10 = 100 square feet per minute.

For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:

1100/7 = 157 square feet per minute.

It is more quickly than Killian's as the rate of change is greater.

More can be learned about the average rate of change of a function at brainly.com/question/11627203

#SPJ1

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

To learn more about Pythagorean please click on below link        

https://brainly.com/question/29069676

#SPJ1

Answer:

The integers are 5 and 7.

Step-by-step explanation:

im 99% sure that is right! hope i helped!

Answer:0

Step-by-step explanation: just like you did on my question and stole the points :) xx

The x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL, as x-coordinate of AJ'K'L' = -y-coordinate of AJKL and y-coordinate of AJ'K'L' = x-coordinate of AJKL.

We create the x-axis and y-axis in the coordinate plane. the origin, where the x- and y-axes cross, and the coordinates ( 0,0 ). The horizontal axis represents the x-axis. The vertical axis represents the y-axis. The first and second coordinates are for the horizontal and vertical axes, respectively. On the coordinate plane, coordinates are expressed by ( x ,y ). The x-coordinate stands for the first coordinate.

When a point is rotated 90° clockwise about the origin, its x-coordinate becomes the negative of its original y-coordinate, and its y-coordinate becomes the positive of its original x-coordinate.

So, for point A(x,y), its new coordinates after a 90° clockwise rotation about the origin would be A'(-y,x). Similarly, for point J, K, and L, their new coordinates would be J'(-yj,xj), K'(-yk,xk), and L'(-yl,xl) respectively.

Therefore, the x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL as follows:

x-coordinate of AJ'K'L' = -y-coordinate of AJKL

y-coordinate of AJ'K'L' = x-coordinate of AJKL

To know more about coordinate plane visit:

https://brainly.com/question/30227780

#SPJ1

The missing coordinate of line is r = 8.

A straight line is a geometrical object that extends infinitely in both directions and has no curvature or bending. It is a one-dimensional object that is defined by two points on the line, called its endpoints, or by its slope and a point on the line.

the slope formula to find the slope of the line given two points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Plugging in the coordinates we have:

-4 = (-16 - r) / (1 - (-5))

Simplifying:

-4 = (-16 - r) / 6

Multiplying both sides by 6:

-24 = -16 - r

Adding 16 to both sides:

-8 = -r

Dividing both sides by -1:

r = 8

Therefore, the missing coordinate is r = 8.

To know more about curvature, visit:

https://brainly.com/question/30106465

#SPJ9

Answer:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

For the given triangular prism, the volume value is obtained as Option B: 31.5 in³.

What is a triangular prism?

The pentahedron Triangular Prism contains nine different nets. The bases' vertices and edges are connected by means of their three rectangular sides. The rectangular sides of the triangular prism are joined to one another side by side. Every cross-section that is perpendicular to the base faces is a triangle.

The height of the triangular prism is given as 2 inches.

The base of the triangular prism is given as 7 inches.

The length of the triangular prism is given as 4.5 inches.

The volume of a triangular prism is given by the formula -

V = (1/2) × b × h × l

where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism.

Substituting these values into the equation, we get -

V = (1/2) × 7 inches × 2 inches × 4.5 inches

V = 7 inches × 1 inch × 4.5 inches

V = 31.5 cubic inches

Therefore, the volume of the triangular prism is 31.5 cubic inches.

To learn more about triangular prism from the given link

https://brainly.com/question/23178481

#SPJ1

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

Answer: The answer should be 20 hours

Step-by-step explanation:

That is when the 2 lines meet up so that is when they are the same difference from Kansas City.

Answer:

Step-by-step explanation:

To calculate the equal monthly payments under this loan, we can use the formula for the present value of an annuity due, since the payments are due at the end of each period. The present value of the equal monthly payments can then be set equal to the loan amount of R250,000, and we can solve for the payment amount.

First, we need to calculate the present value factor for an annuity due with 12 payments per year over a four-year period, using a nominal annual rate of 6%.

PVIFA(due) = (1 - (1 + r/n)^(-nt))/((r/n)(1 + r/n))

Where:

r = nominal annual rate = 6%

n = number of compounding periods per year = 12

t = number of years = 4

PVIFA(due) = (1 - (1 + 0.06/12)^(-12*4))/((0.06/12)(1 + 0.06/12)) = 43.232

Next, we can use the formula for the present value of an annuity due to calculate the equal monthly payments:

PMT = PV / PVIFA(due)

Where:

PV = present value of the loan = R250,000

PMT = 250000 / 43.232 = R5,785.97

Therefore, your equal monthly payments will be R5,785.97. At the end of the four-year period, you will also need to make a final balloon payment of R50,000 to fully pay off the loan.

Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

The scaling factor for given transformation is 3.

What exactly is scaling factor?

The scaling factor, also known as the scale factor, is a value that indicates how much a geometric figure is enlarged or reduced. It is the ratio of the length of a side or dimension of the original figure to the length of the corresponding side or dimension of the new figure. The scaling factor can be greater than 1, which indicates an enlargement, or less than 1, which indicates a reduction. When the scaling factor is 1, the two figures are congruent, which means they have the same shape and size.

Now,

We can find the scale factor by comparing the corresponding side lengths of the two polygons. Let's start by finding the side lengths of the original polygon:

HI: √[(4-0)² + (-5+3)²] = √20

IJ: √[(6-4)² + (0-0)²] = 2

JK: √[(4-6)² + (5-0)²] = √41

KL: √[(0-4)² + (3-5)²] = √20

LH: √[(0-0)² + (-3+5)²] = 2

Now let's find the corresponding side lengths of the dilated polygon:

H'I': √[(12-0)² + (-15+9)²] = √600

I'J': √[(18-12)² + (0-0)²] = 6

J'K': √[(12-18)² + (15-0)²] = √600

K'L': √[(0-12)² + (9-0)²] = √600

L'H': √[(0-0)² + (-9+3)²] = 6

We can see that the side lengths of the dilated polygon are all 3 times as long as the corresponding side lengths of the original polygon. Therefore, the scale factor is 3.

To know more about scaling factor visit the link

brainly.com/question/30215119

#SPJ1

Answer:

Dan eat 2 2/3 of a pizza

Step-by-step explanation:

the answer is above

Let

x-----> amount of pizza Jay ate

y-----> amount of pizza Dan ate

we know that

----> equation A

-----> equation B

substitute equation A in the equation B and solve for y

Convert to mixed number

The value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

Mathematical statements called expressions must have a minimum of two words with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are words with an addition operator between them. Mathematical expressions may be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

The given expression is tan(arcsin (2/7)).

The value of arcsin(2/7) = 16.60

Now substitute the value:

tan(16.60) = 0.29

Hence, the value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

Learn more about expressions here:

https://brainly.com/question/953809

#SPJ1

The trigonometric expression tan(arcsin (2/7)) has a value of 0.29.

What are trigonometric expressions?

Mathematical statements called expressions must have a minimum of two words with either numbers, variables, or both, joined by an operator.

The addition, subtraction, multiplication, and division operations are the four distinct categories of arithmetic operators.

For instance, the expression x + y is an expression where x and y are words with an addition operator between them.

Mathematical expressions may be divided into two categories: algebraic expressions, which include both numbers and variables and numerical expressions, which solely contain numbers.

The given expression is tan(arcsin (2/7)).

The value of arcsin(2/7) = 16.60

Now substitute the value:

tan(16.60) = 0.29

Hence, the value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

Learn more about expressions here:

brainly.com/question/953809

#SPJ1

Answer:

Step-by-step explanation:

Cash

(1)

(7)

(9)

(4)

(8)

(3)

(2)

25,000 (3)

11,900 (5)

9,700 (6)

(8)

James Ralston, Capital

(1)

Accounts Receivable

9,900 (9)

James Ralston, Drawing

7,000

Supplies

12,500

Fees Earned

(4)

Answer:

Step-by-step explanation:

5/9 + (-4/9) - (-2)

5/9 - 4/9 + 2

[tex]5-4+18/9[/tex]

19/9 or 2.1, 2 1/9

Answer:

The answer would be C (1,4)

Step-by-step explanation:

The maximum refers to the highest point on the graph.

In this graph, the highest point lands 1 point to the right of zero and then four points up from there.

Making the maximum (1,4)

Answer:

Step-by-step explanation:

The maximum occurs at (1,4). The maximum is the highest point a function will reach. You can see on the graph that the highest point occurs when x = 1 and y = 4.

So the maximum is at (1,4)

A trick you can use to easily find it next time, imagine a horizontal line is coming down the graph from the top. When the line touches the function, that will be the maximum

The answer to the puzzle is (3)O (7)N which makes word ON, (4)T (10)H (1)E which makes word THE, (6)B (8)E (2)A (9)C (5)H which makes the word BEACH

What is a quadrilateral?

A quadrilateral is a 4 sided polygon. On the basis of its properties quadrilaterals are classified as Trapezium,Kite, Parallelogram, Rectangle, Rhombus and square.

Complete the sentence:

1.Parallelogram-(E)

2.Quadrilateral-(A)

3.Supplementary-(O)

4.Bisect-(T)

5.Congruent-(H)

Using the diagram:

6.Given that KG=17 units, KJ=14 units.

As we know from the figure, GH is congruent to KJ and HJ is congruent to side KG.

Therefore, GH=KJ=14units- (B)

7.∠GKJ=86° and ∠GHJ=(x+6)°

We know that ∠GKJ is congruent to ∠GHJ

Therefore, x+6 = 86

                      x=86-6

                      x=80-(N)

8.Given KH=20 & KF= KH÷2  {diagonal pf parallelogram bisect}

                                  =20 ÷ 2

                                  =10 units-(E)

9.Given ∠HJK=82° & We know ∠HJK+∠GKJ=180°  {consecutive angles}

                                                               ∠GKJ=180-∠HJK

                                                                         =180-82

                                                                         =98°-(C)

10.Give that, ∠HJK=82° & we know  ∠HGK=∠HJK {opposite angles of parallelogram}

                                                            ∠HGK=82°-(H)

To know more about quadrilaterals, visit:

https://brainly.com/question/29635320

#SPJ1

Answer:

y = 3x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 and c = - [tex]\frac{1}{2}[/tex] , then

y = 3x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer:

     6.75 inches.

Step-by-step explanation:

[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]

[tex]= 56.52 + 18.84h[/tex]

[tex]183.69 - 56.52 = 18.84h[/tex]

[tex]127.17 = 18.84h[/tex]

[tex]=\frac{127.17}{18.84}[/tex]

[tex]=6.75[/tex]

Answer:51,000

Step-by-step explanation:

ther is 1000 grams every kilogram so 17x3 is 51 and 51x1000 is 51,000