The length of a rectangle is 9 inches more than half the width. Find the length if the perimeter is 60 inches.

Answers

Answer 1

Answer:

Length = 10.435 inches

Step-by-step explanation:

Let the length be l

Let the width be w

Since the length is 9 inches more than half the width.

Then;

L = 0.5w + 9

Perimeter of a rectangle is;

P = 2Lw

Thus;

P = 2w(0.5w + 9)

Since perimeter = 60

Then;

2w(0.5w + 9) = 60

w² + 18w = 60

w² + 18w - 60 = 0

From quadratic formula;

w ≈ 2.87 in

L = 0.5(2.87) + 9

L = 10.435 in


Related Questions

ILL GIVE POINTS!! PLS HELP !!!

Which set of polar coordinates describes the same location as the
rectangular coordinates (1. - 1)?
A. (sqrt2,315°)
B. (-1,135°) C. (sqrt2,225°)
D. (1,45°)

Answers

Answer:

The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.

[tex]r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2}\\[/tex]

You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.

If you would like to find it mathematically, this is the way to do it

[tex]\theta = atan(y/x) = -45[/tex]

Notice that -45 degrees is just 360 - 45 = 315

Your answer would be

[tex](\sqrt{2}, 315)[/tex]

helppppppppppppppp me

Answers

Answer:

42

Step-by-step explanation:

5²+3(2)+5+6

25+6+5+6

31+11

42

Hope it helps

Graph the inequality on the axes below.
-5x + 4y > -24

Answers

Step-by-step explanation:

-5x + 4y > -24

Plot and draw a graph that's it

Hello again! This is another Calculus question to be explained.

The prompt reads that "If f(x) is a twice-differentiable function such that f(2) = 2 and [tex]\frac{dy}{dx}[/tex] = [tex]6\sqrt{x^2 + 3y^2}[/tex], then what is the value of [tex]\frac{d^2y}{dx^2}[/tex] at x = 2?"

My initial calculation lead to 12, but then I guessed 219 as the answer and it was correct. Would any kind soul please explain why the answer would be 219? Thank you so much!

Answers

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Functions

Function NotationExponential Property [Rewrite]:                                                                   [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Property [Root Rewrite]:                                                           [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

We are given the following and are trying to find the second derivative at x = 2:

[tex]\displaystyle f(2) = 2[/tex]

[tex]\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}[/tex]

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

[tex]\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}[/tex]

When we differentiate this, we must follow the Chain Rule:                             [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big][/tex]

Use the Basic Power Rule:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')[/tex]

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big][/tex]

Simplifying it, we have:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big][/tex]

We can rewrite the 2nd derivative using exponential rules:

[tex]\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}[/tex]

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}[/tex]

When we evaluate this using order of operations, we should obtain our answer:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Please hurry I will mark you brainliest

Answers

Answer:

the answer is 120

Step-by-step explanation:

a trapezoid should measure 360 when all sides are added together

180-125=55

65+55=120

360-120=240

240÷2=120

Write the integer represented by H. List its opposite and absolute value.

Answers

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

Answer:The integer represented by H is -2

Step-by-step explanation:

18
The length of a rectangle is twice as long as the width of the rectangle.
The area of the rectangle is 32 cm.
Draw the rectangle on the centimetre grid.
.
4
54
B2
%

I did it wrong can someone help me

Answers

Answer:

Width = 4 cm

Length = 8 cm

Step-by-step explanation:

Hi there!

Let [tex]l[/tex] be equal to the length of the rectangle.

Let [tex]w[/tex] be equal to the width of the rectangle.

1) Determine equations to find the length and width

We're given that the length is two times the length of the width:

[tex]l=2w[/tex]

We're also given that the area of the rectangle is 32 cm². Recall that the area of a rectangle is [tex]A=lw[/tex]:

[tex]A=lw\\32=lw[/tex]

Now, we have our two equations:

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

2) Solve for the width using substitution

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

Replace [tex]l[/tex] in the second equation with [tex]2w[/tex] from the first equation:

[tex]32=(2w)w\\32=2w^2[/tex]

Divide both sides by 2 to isolate w²:

[tex]16=w^2[/tex]

Take the square root of both sides to isolate w:

[tex]\pm4=w[/tex]

Because width cannot be negative, w=4. Therefore, the width of the rectangle is 4 cm.

3) Solve for the length

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

Now, that we have the width (4 cm), we can solve for the length by plugging it back into one of the equations. Either of the equations work, but we can use the first:

[tex]l=2w\\l=2(4)\\l=8[/tex]

Therefore, the length of the rectangle is 8 cm.

3) Draw the rectangle

We can use what you had before as a foundation. You drew a rectangle with width 4 cm and length 7 cm. To draw the correct rectangle, add another row on top to make it 4 cm by 8 cm.

I hope this helps!

x+y=4 and 2x+3y=2 then find x and y​

Answers

Answer:

x=10, y=-6

Step-by-step explanation:

1) express x from the first equation x+y=4 x=4-y

2) It is the system of equations, so both equations are simultaneous.

you can replace x to 4-y in the second one

2 *(4-y) +3y=2

8-2y+3y= 2

y=-6

x= 4-y=4-(-6)=10

The answer is x=10, y=-6

Which of the following is equal to ….

Answers

Answer:

B option is your answer

Step-by-step explanation:

please mark as brainliest

Answer:

B. 4th root of 7

Step-by-step explanation:

denominator is the root. numerator is the exponent

4. 19 feet to inches

Answers

19feet in inches is 228
4.19 ft. = 50.28 in.

Type the equation for the graph
below.

Answers

Answer:

Step-by-step explanation:

This is a "regular" sin graph that's "taller" than the original. The amplitude is 3; other than that, its period is the same and it has not shifted to the right or left, so the equation, judging from the graph, is

[tex]y=3sin(x)[/tex]

i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)

Answers

Answer:

Step-by-step explanation:

Total amount in cents (unsimplified): 5N +17(10-N)

Simplified: 170-5N

Answer this question, if anyone just posts an answer that is not relevant to this question will be reported.

Answers

Answer:

A is the correct answer

Step-by-step explanation:

I have looked at your bar graph.

What about B?

B is wrong because the first bar doesn't reach 5.8 billion

And C & D are wrong for the same reason. I hope this helps you:)

Note:

My answer WAS relevant to your question.

Answer:

tysm have a great day! Go rose!

Step-by-step explanation:

express y=2x²+9x+4 in the form a(x+b)²+c . where a ,b,c are constant

Answers

Answer:

2(x+9)^2 + 4

Step-by-step explanation:

.............

How many solutions exist for the mixed-degree system graphed below?

Answers

The answer is one solution. Hope this helps

Answer:

The answer is one.

You will be marked brainliest if you tell me how step by step.

A. 92x + 280 < 1,108

B. 280x + 92 > 1,108

C. 280x + 92 < 1,108

D. 92x + 280 > 1,108​

Answers

Answer:

whats the question

Step-by-step explanation:

for me to help

which of the following represents 10 on a number line ​

Answers

Answer:

don't understand....................

Brwntwntenntejetntejeynegnegnwg

f(x)=square root 2x and g(x)=square root 50x find (f/g)(x)

Answers

Answer:

1/5

Step-by-step explanation:

(f/g)(x) = f(x)/g(x) = sqrt(2x)/sqrt(50x) = 1/5

For what value of k does the equation (2k+1)x^2+2x=10x-6 have two real and equal roots?

Answers

Answer:

[tex]\displaystyle k = \frac{5}{6}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle (2k+1)x^2 + 2x = 10x - 6[/tex]

And we want to find the value of k such that the equation has two real and equivalent roots.

Since the equation is a quadartic, we can find its discriminant (symbolized by Δ). Recall that:

If Δ < 0, we have no real roots (two complex roots). If Δ > 0, we have two real roots. And if Δ = 0, we have one real root, or two equivalent ones.

First, rewrite our equation:

[tex](2k+1)x^2 -8x + 6 =0[/tex]

The discriminant is given by:

[tex]\displaystyle \Delta = b^2 -4ac[/tex]

In this case, b = -8, a = (2k + 1), and c = 6.

Therefore, the discriminant is given by:

[tex]\displaystyle \Delta = (-8)^2 - 4(2k+1)(6)[/tex]

For it to have two equal roots, the discriminant must be zero. Hence:

[tex]\displaystyle 0 = (-8)^2 - 4(2k+1)(6)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} \displaystyle 0 &= (-8)^2 - 4(2k+1)(6) \\ 0 &= 64 - 48k - 24 \\ 0 &= 40 - 48k \\ -40 &= -48k \\ \\ k &= \frac{5}{6} \end{aligned}[/tex]

Hence, the value of k is 5/6.

What is the probability of a red on this spinner?
Be sure to reduce.

Answers

Answer:

2/8 or 1/4 simplified

Step-by-step explanation:

If you count how many equal sections there are, you will see there are 8, and 2 or those 8 sections are red so that would easily give you your answer, 2/8.

And to simplify it divide both the top and the bottom by 2 and that gives you 1/4.

Hope the helps! :)

The probability of a red on this spinner would be 1/4.

Used the concept of probability that states,

The term probability refers to the likelihood of an event occurring. Probability means possibility.

Given that,

A spinner is shown in the image.

Since there are a total of 8 parts with different colors.

And, the number of red colors on this spinner is 2.

Hence, the probability of a red on this spinner would be,

P = 2 / 8

P = 1 / 4

Therefore, the probability is 1/4.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ4

Jeremy is buying a new car. The total cost, including tax, is $18275. If the tax rate is 7.5% , what is the sticker price of the car?

Answers

Answer:

$17000

Step-by-step explanation:

Given

[tex]Total = 18275[/tex]

[tex]Tax = 7.5\%[/tex]

Required

The original price

This is calculated using:

[tex]Price(1 + Tax) = Total[/tex]

Make Price the subject

[tex]Price = \frac{Total}{(1 + Tax)}[/tex]

So, we have:

[tex]Price = \frac{18275}{(1 + 7.5\%)}[/tex]

[tex]Price = \frac{18275}{1.075}[/tex]

[tex]Price = 17000[/tex]

The following ordered pairs represent a function: {(-3, 1), (1, -2), (3, 0), (4, 5)}.

True or False

Answers

Answer:

false

Step-by-step explanation:

this is because there is no function of an unknown in this set

Graph the line that has a slope of -7/4 and includes the point (0,10).

Answers

Answer:

y=-7/4x +10

Step-by-step explanation:

that the graph, you can plug the equation in desmos,

hope it helps! :)

Isobel is pulling water up from an old-fashioned well. She lifts the bucket of water at a rate of 4 ft/s, and after 1 s, the bucket is 1 ft below the top of the well. Select the equation in point-slope form for the line that represents the height of the bucket relative to the top of the well.
A. y + 1 = 4x – 1
B. y – 1 = 4x + 1
C. y – 1 = 4(x + 1)
D. y + 1 = 4(x – 1)

Answers

it’s B. y - 1 = 4x + 1

A pendulum's height is modeled by the function h(t) = 4 cos(pi/4*t) + 8 where h is the
measure of the pendulum's height in feet and t is the number of seconds since the
maximum height. How many seconds does it take the pendulum to complete one
full swing?

Answers

Answer:  8 seconds

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

Explanation:

The general cosine template is

y = A*cos(B(t - C)) + D

where in this case

A = 4B = pi/4C = 0D = 8

We only really need to worry about the B value. To get the period T, we do the following

T = 2pi/B

T = (2pi)/(pi/4)

T = 2pi * (4/pi)

T = 8

Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).

The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).

The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the nearest whole number.​

Answers

Given:

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]              ...(i)

Surface area of a sphere:

[tex]A=4\pi r^2[/tex]                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

[tex]V=\dfrac{28}{3}\times A[/tex]

[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]

Multiply both sides by 3.

[tex]4\pi r^3=112\pi r^2[/tex]

[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]

[tex]r=28[/tex]

Using (i), the volume of the sphere is:

[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]

[tex]V\approx 91989[/tex]

Using (ii), the surface area of the sphere is:

[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]

[tex]A=9856[/tex]

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

Please help me please and thank you

Answers

Answer:

3x² + 2x - 9 = 0

Step-by-step explanation:

Standard form of a quadratic: ax² + bx + c

Move all terms to one side of the equation:

[tex]3x^2-9=-2x\\3x^2-9+2x=-2x+2x\\3x^2+2x-9=0[/tex]

Find the measure of the indicated angle to the nearest degree

Answers

Answer: 39

Explanation:

In this case, we must first find the hypotenuse of this triangle by the Pythagorean Theorem.

sqrt(a^2 + b^2) = c

1) sqrt( 23^2 + 28^2) = c
2) sqrt(529 + 784) = c
3) sqrt(1313) = c
4) c = 36.2353

Now that we have obtained our hypotenuse, we can easily find our missing angle by the sine rule.

sin(Angle)/opposing side = sin(Angle)/opposing side

1) sin90/36.2353 = sinx/23
2) 1/36.2353 = sinx/23
3) 23/36.2353 = sinx
4) x = sin^-1(23/36.2353) (SHIFT + Sin on your calculator to do this)
5) x ≈ 39

Hope this helps, brainliest would be appreciated :)

given that a random variable X has a geometric distribution that X- Geometry 0.67. Find the mean​

Answers

Answer:

Hello,

0,4925...

Step-by-step explanation:

A geometric random variable X with parameter p has probability function:

[tex]f(x)=p*(1-p)^x\ where\ x=0,1,2,3....\\\\mean=\dfrac{1-p}{p} =\dfrac{1-0.67}{0.67} =0.4925...[/tex]

Answer

hey my friend ur answer is 0,4925.

hope it is helpful

What is the slope of the line shown below?
(6,6)
m
O A. -2
B. 2
-5
6
O c. 7 /
IN
(1,-4)
5
1
O D.
D. -
2

Answers

Answer:

B

Step-by-step explanation:

answer is slope =2

use formula y2-y1 over x2-x1

two points of graph is (6,6) and (1,-4)

since 6 and -4 are both y, we take 6-(-4) over 6-1

we get 2

ask for further explanation if you need!!❤

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