A right triangle is shown in the figure what is the value of x

A Right Triangle Is Shown In The Figure What Is The Value Of X

Answers

Answer 1

So,

We could use the pythagorean theorem as follows:

[tex](3x)^2+x^2=(\sqrt[]{40})^2[/tex]

And then solve for x:

[tex]\begin{gathered} 10x^2=40 \\ x^2=\frac{40}{10} \\ x^2=4 \\ x=2 \end{gathered}[/tex]

Therefore, x=2.


Related Questions

tell whether you can prove that each quadrilateral is a parallelogram. Explain.

Answers

WE know that in any quadrilateral the interior sum of its angles is 360. The missing angle in this case is:

[tex]360-121-59-59=121[/tex]

Now, we also know that if the oposite angles in a quadrilateral are equal then the quadrilateral is a parallelogram.

Therefore the figure shown is a parallelogram.

Hello! I need help with this:Calculation of the confidence interval Statistics.The confidence interval should be calculated for the percentage of people who chose the answer spruce:Sample: 313Answers:Spruce - 272Pine - 41Confidence level - 0.9

Answers

We have to calculate a 90% confidence interval for the proportion that chose the answer "Spruce".

The sample proportion is p = 0.869:

[tex]p=\frac{X}{n}=\frac{272}{313}\approx0.869[/tex]

The standard error of the proportion is:

[tex]\begin{gathered} \sigma_p=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma_p=\sqrt{\frac{0.869\cdot0.131}{313}} \\ \\ \sigma_p\approx\sqrt{0.0003637} \\ \sigma_p\approx0.019 \end{gathered}[/tex]

The critical z-value for a 90% confidence interval is z = 1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot\sigma_p=1.645\cdot0.019\approx0.031[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]\begin{gathered} LL=p-z\sigma_p=0.869-0.031=0.838 \\ UL=p+z\sigma_p=0.869+0.031=0.900 \end{gathered}[/tex]

Answer: The 90% confidence interval for the population proportion is (0.838, 0.900).

Is ⅓ greater that 3/9?

Answers

1/3 and 3/9

Simplify 3/9 by 3

(3/3) / (9/3 ) = 1 /3

So, both fractions are equal

1/3 is not greater than 3/9

how do you solve 4 1/4 + 7/8

Answers

The given expression is,

[tex]4\frac{1}{4}+\frac{7}{8}[/tex]

So, this can be solved as,

[tex]\begin{gathered} \frac{4\times4+1}{4}+\frac{7}{8}=\frac{17}{4}+\frac{7}{8} \\ \rightarrow\frac{8\times17+4\times7}{8\times4}=\frac{164}{32}=\frac{41}{8} \end{gathered}[/tex]

Explanations:

To solve the mixed fraction,

[tex]4\frac{1}{4}\rightarrow\frac{(4\times4)+1}{4}=\frac{17}{4}[/tex]

So, now we are adding the terms, as given in the expression,

[tex]\frac{17}{4}+\frac{7}{8}=\frac{(8\times17)+(7\times4)}{4\times8}[/tex]

Here we are employing the rule,

[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd}[/tex]

Hi, The area of a circle is 100 quare millimeters. The radius is 5.64 millimeters. what is the circumference?

Answers

The area A of a circle is given by

[tex]A=\pi r^2[/tex]

where Pi is 3.1416 and r is the radius. In our case, we get

[tex]100\operatorname{mm}=\pi r^2[/tex]

and we need to find r. In this regard, if we move Pi to the left hand side we get

[tex]\frac{100}{\pi}=r^2[/tex]

then, r is given by

[tex]r=\sqrt[]{\frac{100}{\pi}}[/tex]

Now, the circunference C is given by

[tex]C=2\pi\text{ r}[/tex]

then, by substituting our last result into this formula, we have

[tex]C=2\pi\sqrt[]{\frac{100}{\pi}}[/tex]

since square root of 100 is 10, we get

[tex]C=2\pi\frac{10}{\sqrt[]{\pi}}[/tex]

we can rewrite this result as

[tex]\begin{gathered} C=\frac{2\pi\times10}{\sqrt[]{\pi}} \\ C=\frac{2\sqrt[]{\pi\text{ }}\sqrt[]{\pi}\times10}{\sqrt[]{\pi}} \end{gathered}[/tex]

and we can cancel out a square root of Pi. Then, we have

[tex]C=2\sqrt[]{\pi}\times10[/tex]

and the circunference is

[tex]C=20\text{ }\sqrt[]{\pi}\text{ milimeters}[/tex]

I only need part bb) A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.

Answers

Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.

So, let's list which areas we need:

- We need the lateral areas of the external parts, which are 4 rectangles.

- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.

- We need the interior aread, which is the same as the lateral area of a cylinder.

For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.

The area of each of them is:

[tex]A_{\text{rectangle}}=300mm\cdot1.8m=0.3m\cdot1.8m=0.54m^2[/tex]

Since we have 4, the total exterior lateral area is:

[tex]A_{\text{lateral}}=4\cdot0.54m^2=2.16m^2[/tex]

For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.

First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:

[tex]r=\frac{0.15m}{2}=0.075m[/tex]

The area of a circle given its radius is:

[tex]A=\pi r^2[/tex]

So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:

[tex]\begin{gathered} A_{\text{top/ottom}}=2((0.3m)^2-\pi(0.075m)^2) \\ A_{\text{top/ottom}}=2(0.09m^2-0.005625\pi m^2) \\ A_{\text{top/ottom}}=2(0.09-0.005625\pi)m^2 \end{gathered}[/tex]

We deal with π later on.

For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.

the circumference of a circle is:

[tex]C=2\pi r[/tex]

The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:

[tex]\begin{gathered} A_{\text{cylinder}}=1.8m\cdot2\pi(0.075m) \\ A_{\text{cylinder}}=(1.8\cdot0.15\pi)m^2 \\ A_{\text{cylinder}}=(0.27\pi)m^2 \end{gathered}[/tex]

So, the total surface area is the sum of all of these:

[tex]A=2.16m^2+2(0.09-0.005625\pi)m^2+(0.27\pi)m^2[/tex]

Now, we just need to evaluate:

[tex]\begin{gathered} A=2.16m^2+2\cdot0.072328\ldots m^2+0.848230\ldots m^2 \\ A=2.16m^2+0.144657\ldots m^2+0.848230\ldots m^2 \\ A=3.152887\ldots m^2 \\ A\approx3.15m^2 \end{gathered}[/tex]

So, the lateral area is approximately 3.15 m².

a construction company orders tile flooring for the kitchen in three bathrooms of a new home the kitchen floor measures 48 square feet 2 bathrooms have floor that each Measure 30 and 1/2 square feet the third bathroom floor measures 42 1/2 square feet if the tile cost 2.39 per square foot what is that the least amount of money to the nearest cent the company spends on tile for all three bathrooms

Answers

We are not concerned with the tiles needed for the kitchen.

From the given information, there are two bathroom floors with the same measurement in terms of area. The area of each floor is 30.5 square feet

Area of both bathroom floors = 30.5*2 = 61 square feet

Area of the third bathroom = 42.5 square feet

Area of the three bathroom floors = 61 + 42.5 = 103.5 square feet

Given that the tile costs 2.39 per sqare foot, the least amount of money that the company would spend for all three tiles is

103.5 * 2.39 = 247.365

Rounding up to the nearest cent means rounding up to the nearest hundredth or 2 decimal places

Rounding up to the nearest cent, it becomes 247.37

A particular lawn requires 6 bags of fertilizer. A lawn next door requires 4 bags of fertilizer. How big is the lawn next door?A. 10 feet square feetB. 24 feet square feetC. 50 feet square feetD. Not enough information is given

Answers

Answer:

D. Not enough information is given

Explanation:

To know the size of the lawn next door, we would need a relation between the square feet and the number of bags of fertilizer.

Since all we know is the bags of fertilizer for the particular lawn and the lawn next door, we can say that we didn't have enough information to answer the question.

Therefore, the answer is:

D. Not enough information is given

name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. identify the transversal that connects each angle pair.

Answers

[tex]\begin{gathered} \text{Alternate interior angles} \\ 10,5\text{ transversal l} \\ 4,15\text{ transversal m} \\ 13,2\text{ transversal }l\text{ } \\ 7,12\text{ transversal }m \\ \text{Alternate exterior angles} \\ 1,14\text{ transversal l} \\ 9,6\text{ transversal l} \\ 11,8\text{ transversal }m \\ 3,6\text{ transversal }m \\ \end{gathered}[/tex]

which number is divisible by "644532"

Answers

Answer:

2

Step-by-step explanation: 2 can be divided by 644532

A ball is thrown from an initial height of 6 feet with an initial upward velocity of 21 ft/s. The ball's heighth (in feet) after t seconds is given by the following,6+21 167Find all values of t for which the ball's height is 12 feet.Round your answer(s) to the hearest hundredth(If there is more than one answer, use the "or" button.)

Answers

The given expression in the question is

[tex]h=6+21t-16t^2[/tex]

with the value of h given as

[tex]h=12ft[/tex]

By equating both equations, we will have

[tex]\begin{gathered} 12=6+21t-16t^2 \\ 12-6-21t+16t^2=0 \\ 6-21t+16t^2=0 \\ 16t^2-21t+6=0 \end{gathered}[/tex]

To find the value of t we will use the quadratic formula of

[tex]ax^2+bx+c=0[/tex]

which is

[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where} \\ a=16 \\ b=-21 \\ c=6 \end{gathered}[/tex]

By substitution, we will have

[tex]\begin{gathered} t=\frac{-(-21)\pm\sqrt[]{(-21)^2-4\times16\times6}}{2\times16} \\ t=\frac{21\pm\sqrt[]{441-384}}{32} \\ t=\frac{21\pm\sqrt[]{57}}{32} \\ t=\frac{21\pm7.5498}{32} \\ t=\frac{21+7.5498}{32}\text{ or t=}\frac{21-7.5498}{32} \\ t=\frac{28.5498}{32\text{ }}\text{ or }t=\frac{13.4502}{32\text{ }} \\ t=0.89\text{ or t=0.42} \end{gathered}[/tex]

Alternatively, Solving the equation graphically we will have

Therefore,

The values of t( to the nearest hundredth) t= 0.89sec or 0.42sec

the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?

Answers

Answer:

-144 feet

Step-by-step explanation:

-211 plus the added 67 feet it is above equals an altitude of -144ft

Use the table to write an equation that relates the cost of lunch Y and the number of students X

Answers

In order to determine what is the equation which describes the values of the table, consider that the general form of the equation is:

y = mx

where m is the constant of proportionality between both variables x and y.

To calculate m you calculate the quotient between any pair of data from the table.

If you for example use the following values:

Students = 8.00

Lunch cost = 2

the constant of proportionality is:

m = 8.00/2 = 4.00

Next, you replace the value of m in the equation y=mx:

y = $4.00x

Assume the hold time of callers to a cable company is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.4 minute. Determine the percent of callers who are on hold between 3.4 minutes and 4.5 minutes. % (Round to two decimal places as needed.)

Answers

According to the problem, we have

[tex]\begin{gathered} \mu=4.0\min \\ \sigma=0.4\min \end{gathered}[/tex]

We have to find the percent of callers who are on hold between 3.4 minutes and 4.5 minutes.

First, we find the z-score

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For x = 3.4

[tex]z=\frac{3.4-4.0}{0.4}=\frac{-0.6}{0.4}=-1.5[/tex]

For x = 4.5

[tex]z=\frac{4.5-4.0}{0.4}=\frac{0.5}{0.4}=1.25[/tex]

The probability we have to find is

[tex]P=(3.4Using a z-table, we have[tex]\begin{gathered} P(3.4Then, we multiply by 100 to express it in percetange.[tex]0.2351\cdot100=23.51[/tex]Hence, the probability is 23.51%.

1/10+1/2=____ options 3/5

Answers

we are given the sum of the following fractions:

[tex]\frac{1}{10}+\frac{1}{2}[/tex]

To sum these fractions we may multiply the numerator and denominator of the second fraction by 5, like this:

[tex]\frac{1}{10}+\frac{5}{10}[/tex]

Since now they have the same denominator we can add the numerators and leave the same denominator, like this:

[tex]\frac{1}{10}+\frac{5}{10}=\frac{1+5}{10}=\frac{6}{10}[/tex]

Now we can simplify the resulting fraction by dividing the numerator and denominator by 2:

[tex]\frac{6}{10}=\frac{3}{5}[/tex]

Therefore, the sum of the two fractions is 3/5

Sofia got a raise from her annual salary of $43,000 to $44,505. whay percent was her raise?

Answers

[tex]\begin{gathered} \text{ The raise is given by} \\ R=1-\frac{\text{ Final salary}}{\text{ Initial salary}} \\ \\ R=1-\frac{44505}{43000} \\ \\ R=1-1.035 \\ R=0.035 \\ \text{ thus the increment is }3.5\text{ \%} \end{gathered}[/tex]

all i need is for question 14 to be answered please help

Answers

Given

The path of particle 1 is,

[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]

And, the path of second particle is,

[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]

To model the path of the two particles in cartesian form and to find whether, the two particles collide.

Explanation:

It is given that,

The path of the first particle is,

[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]

That implies,

[tex]x=2t-6,\text{ }y=t^2-2t[/tex]

Consider,

[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]

Also, the path of second particle is,

[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]

That implies,

[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]

Consider,

[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]

Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.

The graph of the path of the two particles are,

From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).

Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Frozen orange juice:$1.57 for 14 ounces$0.57 for 4 ounces----------------------------Find the unit price of a frozen orange juice which costs $1.57 for 14 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Find the unit price of a frozen orange juice which costs $0.57 for 4 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Which is the better buy?A. $1.57 for 14 ouncesB. $0.57 for 4 ounces

Answers

The different sizes of the given brands are

Frozen orange juice:

$1.57 for 14 ounces

$0.57 for 4 ounces

The unit price of a frozen orange juice which costs ​$1.57 for 14 ounces is

1.57/14 = 0.112

The unit price of a frozen orange juice which costs ​$0.57 for 4 ounces is

0.57/4 = 0.1425

The better buy is the size that has the lowest cost per ounce. Looking at our calculations, the lowest cost per ounce is $0.112

Therefore, the frozen orange juice which costs ​$1.57 for 14 ounces is the better buy.

Use substitution to solve the system of equations. y = x + 2 4x - 5y = 14 A. (-22,-24) C. (-4,-2)B. (-24, -22) D. (-14, -12)

Answers

Solve by substitution;

[tex]\begin{gathered} y=x+2---(1) \\ 4x-5y=14---(2) \\ \text{Substitute for the value of y into equation (2)} \\ 4x-5(x+2)=14 \\ 4x-5x-10=14 \\ \text{Collect like terms} \\ 4x-5x=14+10 \\ -x=24 \\ \text{Divide both sides by -1} \\ x=-24 \\ \text{Substitute for the value of x into equation (1)} \\ y=x+2 \\ y=-24+2 \\ y=-22 \end{gathered}[/tex]

Who am I? I am a quadrilateral with opposite sidescongruent and parallel, all of my angles are 90° andmy diagonals are congruent.d

Answers

Let's list all information we have:

- quadrilateral (4 sides)

- opposite sides congruent and parallel.

- all angles are 90°

- diagonal are congruent.

So, if we have a quadrilateral, we have something like this:

However, it is given that all anlges are 90°, which limits our possible drawing. So, something like this:

Let's see, this is a rectangle, it has opposite side congruent (equal length), the opposite sides are parallel, all the angles are 90° and the Diagonals have equal lengths, because they form congruent triangles.

It could also be a square:

Beucase it has all of the characteristics given.

(x - 5) (4x - 5) = 0 there are two answers

Answers

The solutions are the values of x that makes the expression equal to zero:

x-5 =0

Add 5 to both sides

x=5

4x-5=0

Add five to both sides

4x=5

Divide both sides by 4

x= 5/4

x=1.25

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.

Answers

Average rate of changeInitial explanation

The average rate of change is given by the rate of change of both variables.

"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:

Δy/Δx

("Δ" means "change").

We want to analyze the change over the interval 3 ≤ x ≤ 9.​

Step 1: change of x (Δx)

The change from x = 3 and x = 9 is

Δx = 9 - 3 = 6

Step 2: change of y (Δy)

We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.

The change from y = 28 to y = 4 is

Δy = 4 - 28 = -24

Step 3: rate of change

Then, the average rate of change is:

Δy/Δx = -24/6 = -4

Answer: -4

The dimensions of a rectangular prism are measured in centimeters. What unit will the volume of the prism be measured in?centimeterssquare centimeterscubic centimetersmeters

Answers

Given:

The dimensions of a rectangular prism are measured in centimetres.

Required:

What unit will the volume of the prism be measured in?

Explanation:

The volume of the prism will be measured in square centimetres

Final Answer:

Square centimeters

5. SOLVE THe linear equation : 13x – 5 + 171 = x

Answers

Answer:

x = -83/6 = -13.833

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

13*x-5+171-(x)=0

1.1     Pull out like factors :

  12x + 166  =   2 • (6x + 83)

2.2      Solve  :    6x+83 = 0

Subtract  83  from both sides of the equation :

                     6x = -83

Divide both sides of the equation by 6:

                    x = -83/6 = -13.833

X-1 what is the answer ​

Answers

Answer:

x - 1 = x - 1

Step-by-step explanation:

If you were expecting a singular solution, you won’t get it. You’ll likely instead get a lot of smart alecks snidely answer your question. Looks like you already have actually.

But they speak true. x – 1 on its own like that wont really get you anything. Now if you asked something along the lines of “What is x – 1 equal to if x is equal to 5?” then you’d get one solid definitive solution: 4.

Answer:

YES!!!!!

Step-by-step explanation:

LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLLOLOLOLOLOLOLOLOL

Kindly assist in answering these questions

Answers

The point of origin on the graph is (0,0) and the constant of proportionality is equal to 3.

Equation of Line

The equation of a straight line is y=mx + c.  y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.

In the given question, we are asked to find several values relating to the graph attached.

5) The point of origin on the graph is at (0,0) because the graph passes through the center along the straight line.

6) The constant of proportionality (k) is the value before the variable x.

The equation of the line is y = 3x.

The constant of proportionality of the equation is equal to 3.

7) The value of the ratio k is given as y/x

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how many apples are in 4 dozen

Answers

Answer:

There are 48 apples in 4 dozen

Explanations:

1 dozen = 12

This means that:

1 dozen of apples = 12 apples

4 dozen = 12 x 4

4 dozen = 48 apples

A model rocket is launched with an initial upward velocity of 156 ft/s. The rocket's height h (In feet) after t seconds is given by the following.
h=156t-16t²
Find all values of t for which the rocket's height is 60 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Explanation
Check
ground
t = 0 seconds
☐or D
X
5
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I need help

Answers

The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.

What is a quadratic equation?

A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.

The initial velocity of the rocket = 156 ft./s upwards

The given equation of the rocket is: h = 156·t - 16·t²

The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:  

h = 60 = 156·t - 16·t²

156·t - 16·t² - 60 = 0

4·(39·t - 4·t² - 15) = 0

Therefore: [tex]39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0[/tex]

39·t - 4·t² - 15 = 0

-4·t² + 39·t - 15 = 0

From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;

[tex]x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}[/tex]

The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:

[tex]t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}[/tex]

Therefore, when the height of the rocket is 60 feet, the times are: [tex]t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35[/tex] and [tex]t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40[/tex]

The times when the height of the rocket is 60 feet, the times are:

t ≈ 9.35 s, and t ≈ 0.40 s

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Ready for me for a quadratic function with vertex (3,9)

Answers

We have to write an equation of a quadratic function that has a vertex at (3,9) and pass through the origin.

We can use the vertex form of the quadratic equation:

[tex]y=a(x-h)^2+k[/tex]

where the vertex has coordinates (h,k).

In this case, (h,k) = (3,9).

From the formula we can see that the parameter a that can take any value and still have the same vertex. We will use the parameter "a" to make it pass through the origin.

The vertex form of the equation is then:

[tex]y=a(x-3)^2+9[/tex]

As it pass through the origin, then the equation should be satisfied when x = 0 and y = 0:

[tex]\begin{gathered} 0=a(0-3)^2+9 \\ 0=a(-3)^2+9 \\ 0=a\cdot9+9 \\ -9=9a \\ -\frac{9}{9}=a \\ a=-1 \end{gathered}[/tex]

Then, as a = -1, we can write the equation as:

[tex]y=-(x-3)^2+9[/tex]

Answer: An example of quadratic function with vertex (3,9) that pass through the origin is y = -(x-3)² + 9.

How to fill out an income summary

Answers

Answer: Pick a Reporting Period. ...

Generate a Trial Balance Report. ...

Calculate Your Revenue. ...

Determine the Cost of Goods Sold. ...

Calculate the Gross Margin. ...

Include Operating Expenses. ...

Calculate Your Income. ...

Include Income Taxes.

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Which operation comes first in the problem below? 4(3.7 +1.23) -12 A. Addition B. Subtraction C. Multiplication D. Division Needing assistance with question in the photo (more than one answer) Which of the following is not a correct way to name the plane. Jose applies a force of 20 N North, Johnny applies a force of 10 N West and Janie applies a force of 25 N south on a heavy dresser. Find the resultant force on the dresser. when magazines publish special versions of an issue that contain editorial content and advertising geared to a specific demographic or regional grouping, this is known as what is y= 12x6 on a graph Can u tell me what the right answer I need help with some problems on my assignment please help A box contains six red pens, four blue pens, eight green pens, and some black pens. Leslie picks a pen and returns it to the box each time. The outcomes are recorded in the table.a. what is the experimental probability of drawing a green pen?b. if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box Find the reminder when 2 to the 100th power is divided by 5 explain your work 6. What is the most likely reason the author included paragraph 1?To emphasize the rapid growth in popularity ofbackyard bird feedingTo introduce an issue faced by the large number ofpeople who feed birdsTo explain the results of recent studies on bird-feeding habitsTo recommend the best types of seeds to place in birdfeeders A lab assistant needs to create a 1000 ML mixture that is 5% hydroelectric acid. The assistant has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equation that describes the situation the situation.Enter the equations below separated by a comma How many milliliters of the 3.5% solution should be used?How many milliliters of 6% solution should be used? 3. Given the perimeter of the figure is 76 ft, Findthe dimensions of the shape.(4x-5) ft(25-x) ft(13 + x) ftT(3x + 1) ft A student learns that a certain comet in the solar system is considered a short-period comet. Based on this knowledge, what is the student most justified in concluding?. the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. what is the cutoff interest rate for the highest 15% of banks in this area? For the compound inequalities below (5-7), determine whether the inequality results in an overlapping region or a combined region. Then determine whether the circles are open are closed. Finally, graph the compound inequality. Simplify if needed. x-1>_5 and 2x A box of cereal states that there are 84 calories in a 3/4-cup serving. What is the unit rate for calories per cup? How many calories are there in 3 cups of the cereal? lewis says that we can see the tao in the traditional teachings of all major religions and philosophies. true or false? lewis thinks that all of those teachings are consistent with one another. Use the binomial expression (p+q)^n to calculate abinomial distribution with n = 5 and p = 0.3. What is the slope-intercept of (-4,-5) and slope is 1/2