A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards
greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155
square yards. The situation is modeled by the equation h2 + 5h 155. Use the Quadratic Formula to find the
height that will give the desired area. Round to the nearest hundredth of a yard.
320 yards
c. 20.4 yards
b. 10.2 yards
d. 12.7 yards
a.

Answers

Answer 1

9514 1404 393

Answer:

  b.  10.2 yards

Step-by-step explanation:

The quadratic formula tells you the solutions to ...

  ax² +bx +c = 0

are given by ...

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

Here, the quadratic equation we have is ...

  h² +5h -155 = 0

So the solutions given by the quadratic formula are ...

  [tex]h=\dfrac{-5\pm\sqrt{5^2-4(1)(-155)}}{2(1)}=\dfrac{-5\pm\sqrt{645}}{2}=\{-15.2,10.2\}[/tex]

The negative solution is not applicable in this situation, so the height that gives the desired area is 10.2 yards.


Related Questions

The mean temperature for the first 7 days in January was 6 °C.
The temperature on the 8th day was 3 °C.
What is the mean temperature for the first 8 days in January?

Answers

Answer:

GIME SOME POINTS

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 4.5

What is the simplest form of each espression

Answers

Answer:

Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. The process entails collecting like terms, which implies adding or subtracting terms in an expression.

Suppose a person offers to play a game with you. In this game, when you draw a card from a standard 52-card deck, if the card is a face card you win "$2, and if the card is anything else you lose $1". If you agree to play the game, what is your expected gain or loss (in dollars) per game? (Recall that there are 12 face cards in a standard 52-card deck. Round your answer to two decimal places.) $

Answers

Answer:

Your expected loss per game is of $0.31.

Step-by-step explanation:

In a standard 52-card deck, we have that:

There are 12 face cards.

What is your expected gain or loss (in dollars) per game?

12/52 probability of winning $2.

1 - 12/52 = 52/52 - 12/52 = 40/52 probability of losing $1. So

[tex]E = \frac{12}{52}*2 - \frac{40}{52}*1 = \frac{24 - 40}{52} = -\frac{16}{52} = -0.31[/tex]

Negative, so a loss is expected.

Your expected loss per game is of $0.31.

Complete the square
to find the vertex
of this parabola.
2
x - 4y-12 x +68=0

Answers

Answer: (6,8)

Step-by-step explanation:

Answer:

(6, 8)

Step-by-step explanation:

convert (-2,2) into equivalent polar coordinates

Answers

(2rad2, 135) is the polar equivalent

Determine ſ(2) where f(x) =x+1/4x-2

Answers

f(X)= x+1/4x-2
f(2) = (2 + 1)/[(4)(2) - 2]
f(2) = 3/6 = 1/2

jannie has 2 liters of orange squash she also has some empty cups One full Beach club holds 30 mL of orange squash jennine files as many cups as possible How much orange squash does janine have after filing as many cups as possible

Answers

Answer:

The question is a bit incorrect as there isnt mentioned how many cups are there.But if you meant how many 30ml cups can Jannie fill it would be 66.66 cups or 67/66 cups .

Step-by-step explanation:

If you would correct your answer I would try my best to give you the brainliest answer.

Relationships in Figures

Line segment AB is one unit long. If point C cuts AB so that AC = 0.618, what is the ratio of AC to CB?

a. 1
b. 1.618
c. 1.32
d. 1.543

Please select the best answer from the choices provided

Answers

Answer:

B. 1.618

Step-by-step explanation:

I calculated it logically

Solve for x.
18x - 12
16x +8
x = [?]

Answers

Answer: x = 10;

Both the angles are congruent, therefore;

8x - 12 = 6x + 8

=> Now subtract 6x from each side of "="

2x - 12 = 8

=> Add 12 to each side;

2x = 20

=> Lastly divide each side by 2;

x = 10

Hope this helps!

Answer:

10

Step-by-step explanation:

From the image provided, it shows that both 8x - 12 would equal 6x + 8 because their angles are the same due to their placement. With that it turns into 8x - 12 = 6x + 8. Then you can simplify to 2x = 20 by adding 12 to both sides, and subtracting 6x. Then 20 divided by 2 to get x by itself equaling 10.

y=25 is a solution to the inequality y−24<16

Answers

Answer:

The answer should be true.y<401<16

Step-by-step explanation:

To solve this inequality, isolate the term of y from one side of the equation.

y-24<16

First, add 24 from both sides.

[tex]\sf{y-24+24<16+24}[/tex]

Solve.

Add.

[tex]\sf{24+16=40}[/tex]

[tex]\large\boxed{y<40}[/tex]

Therefore, the solution is y<40.

y=25 should be subtract by 24 is less than 16.

25-24<16

Solve.

Subtract.

25-24=1

Rewrite the problem down.

1<16

These statements are true.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{We know that }<\large\text{ is less than and }> \large\text{ is greater than.}[/tex]

[tex]\large\text{If y = 25, then substitute it into the given equation or inequality.}[/tex]

[tex]\mathsf{\underline{25}-24<16}[/tex]

[tex]\mathsf{25-24=\bf 1}[/tex]

[tex]\large\text{16 is \underline{greater than} 1 but 1 is \underline{less than} 16}[/tex]

[tex]\mathsf{1<16}[/tex]

[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \boxed{\mathsf{\bold{1<16}\ \& \ it \ is \bold{\ TRUE}}}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

juan creates a new recipe for brownies. For each pan of brownies, he adds 7 dashes of cinnamon. How many dashes of cinnamon will he use for 8 pans of brownies?

Answers

Answer:

56 dashes of cinnamon

Step-by-step explanation:

7 dashes of cinnamon = 1 pan of brownies

And we need to make 8 pans of brownies so...

7 dashes of cinnamon x 8 pans of brownies = 56 total dashes of cinnamon :)

The equation y-7/2=1/2(x-4) is written in point-slope form. What is the y-intercept of the equation

Answers

the third bullet would be correct

If the length of a rectangle is 1 cm more than three times the width and if the perimeter of the rectangle is 34 cm what is the dimension of the rectangle

Answers

Answer:

width: 4cm

length: 13cm

Step-by-step explanation:

Let the width of the rectangle be w. From the problem, we can infer that the length would be equal to 3w + 1. The formula for the perimeter of a rectangle is:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

We can substitute our values into the equation:

34 = 2(3w + 1 + w)

17 = 3w + 1 + w

17 = 4w + 1

16 = 4w

w = 4

We can substitute this into the length:

3w + 1

3(4) + 1

12 + 1

13

HELP PLEASE write an equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11)

Answers

The equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11) is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]

How to determine the ellipse equation?

We have:

Vertices = (0, ± 11),

Foci = (0, ± 10)

The vertices and the foci are represented as:

Foci = (0, ± a)

Vertices = (0, ± c)

So, we have:

a = 10

c = 11

The equation of b is calculated using:

b² = c²- a²

So, we have:

b² = 11²- 10²

Evaluate

b² = 21

The equation of the ellipse is then represented as:

[tex]\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]

This gives

[tex]\frac{x^2}{21} + \frac{y^2}{10^2} = 1[/tex]

[tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]

Hence, the equation of the ellipse is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]

Read more about ellipse equations at:

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Answer:

x^2/221+Y^2/121=1

Step-by-step explanation:

HURRY what is 1+1 please hurry ​

Answers

1 + 1 = 2 that is basic math you could’ve typed that in the calculator no offense have a nice day!


HELP Help HELP HELP

What is the equation of the trend line in the scatter plot ?

Answers

Answer:

increasing

Step-by-step explanation:

Guys Whats is 4+1037+76 I'll give branliest no calculator no search only brain all of u I eill give brainliest please help me​

Answers

[tex]\huge \pink\star\huge{ \pink{\bold {\underline {\underline {\red{Answer }}}}}} [/tex]

➭Doing it all using mental math

Step 1:

[tex] 1037 + 4 \\ =1041[/tex]

Step 2:

[tex]1041 + 76 \\ = 1117[/tex]

What is the value of the hypotenus?

Answers

Pythagorean theorem
a^2 + b^2 = hypothenuse^2
2^2 + 5^2 = hypothenuse^2
4 + 25 = hypothenuse^2
29 = hypothenuse^2
Hypothenuse = squareroot 29
Hypothenuse = 5.38516480713

Solution: hypothenuse = 5.4

Answer:

Step-by-step explanation:

in 5 games a basketball team scored 82, 42, 75, 97, and 86 points
what is the *median* of the scores? Type your answer below RIGHT NOW

Answers

Answer:

86

Step-by-step explanation:

Once you put the numbers in correct order, 86 would be in the middle making it the median.

Henry is fishing from a small boat. His fishing hook is in the water 8 meters directly below his boat. A fish is swimming at the same depth as the hook, however it is 15 meters away from the hook. What is the shortest distance between Henry and the fish?

Answers

Answer: 17

Step-by-step explanation:

What is the exponential regression equation for the data set?

yˆ=1.08⋅32.11x

yˆ=(1.08⋅32.11)x

yˆ=32.11⋅0.08x

yˆ=32.11⋅1.08x

Answers

Answer:

yˆ=32.11⋅1.08x

Step-by-step explanation:

just took the test

Option: A is the correct answer.

The quadratic regression equation for the data set is:

   A. y = 0.056x²+1.278x-0.886

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

We are given a set of data value as:

        x                y

        3             3.45

        5              6.9

        6             8.79  

        8             12.91

        10            17.48

        12            22.49

        15            30.85

On plotting these points on a scatter plot we see that the line that best fits these data points is a parabola i.e. the equation is a equation of a quadratic function.

The equation of the line of best fit is:

y = 0.056x²+1.278x-0.886

                 

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Use the formula R = log I, where R is the measurement of the Ritchter scale and i is the intensity, to find the Ritchter scale measurement of an earthquake with intensity 24,000,000. NO LINKS!!!

Answers

9514 1404 393

Answer:

  7.4

Step-by-step explanation:

Put the given value into the formula and do the arithmetic.

  R = log(2.4×10^7)

  R ≈ 7.3802 ≈ 7.4

The earthquake is about 7.4 on the Richter scale.

I need the answer don’t mind the shaded one≅

Answers

Answer:

i think it's solar

Step-by-step explanation:

okayyyyyyyyyyyyyyyyy

Answer:

solar

Step-by-step explanation:

oil ,coal and natural gas are fossil fuels

Round 89.288 to the nearest tenth

Answers

Answer:

89.3

Step-by-step explanation:

89.288

Eight is greater than five so we add 1 to the underlined number

Triangle ABC is shown
What is the measure of xº?
Help!

Answers

Answer:

answer is C

hope it is helpful..

9514 1404 393

Answer:

  C.  36°

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  x° +2x° +72° = 180°

  3x° = 108° . . . . subtract 72°

  x° = 36° . . . . divide by 3

ILL GIVE BRAINLIEST


Carl wants to prove that if a line is parallel to one side of a triangle, then it divides the other two sides

proportionally.


Select the appropriate rephrased statement for Carl’s proof.


Choose 1 answer:


A.) In UVW, if XY || then UX/XV= UY/ YW.


B.) In UVW, if UX/XV=UY/YW, then XY || VW.


C.) In UVW, if XY || VW, then UX/XV= XY/WV.


D.) In UVW, if UX/XV = XY/WV, then XY || VW.

Answers

Answer:

A. is the appropriate answer to carl's proof

In UVW, if XY || VW then UX/XV= UY/ YW. Then the correct option is A.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

Carl wants to prove that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

We know that if two triangles are similar, then the ratio of the corresponding sides will remain constant.

Let the triangle UVW and XY is parallel to the side VW.

Then the triangle UVW and UXY will be similar triangle.

Then the ratio of their corresponding sides will be

UX / XV = UY / YW

In UVW, if XY || VW then UX/XV= UY/ YW.

Then the correct option is A.

More about the triangle link is given below.

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Which of the following, to the nearest tenth, is a solution of f(x) = g (x) if f (x) = in (x + 5 ) - 1 and g(x) =x^3 - 2x+1
A) 0.5
B) -1.6
C) -2.3
D) 1.9

Answers

Answer:

c

Step-by-step explanation:

Which statement compares the limit as x approaches –4 for the two graphs? In both graph I and graph II, the limit is 5. In both graph I and graph II, the limit does not exist. In graph I, the limit does not exist, but in graph II, the limit is 5. In graph I, the limit is 8, but in graph II, the limit does not exist.

ANSWER: A

Answers

Answer:

(Thanks) it's A because the limit is in the same place on both graphs. The filled-in dot doesn't affect the limit at all, it just means the "real" value of x=-4 is 8, but the "limit" is still at 5 either way.

4×103 times what number is equal to 16×105?

Answers

Answer:4.077669903

Step-by-step explanation:

4×103 is 4.04 times the 16*105.

What is Algebra?

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

Let us consider the number be 'x'.

So, 4*103 of x = 16*105

      x= 16*105/4*103

       x= 4*1.01

       x= 4.04

Hence, the number is 4.04.

Learn more about concept here:

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Martha kicks a soccer ball

Answers

Answer:

I kick it back Martha :).......

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