If c=3k+4 and d=7+9k^2, what is d in terms of c?

Answers

Answer 1

Answer:

d = (c -4)² +7 = c² -8c +23

Step-by-step explanation:

Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.

Eliminating k

We recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.

c = 3k +4

c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k

Substituting into the equation for 'd', we have ...

d =7 +9k²

d = 7 +(3k)² . . . . . writing 9k² in terms of 3k

d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.

This can be simplified to ...

d = c² -8c +23 . . . . another form of d in terms of c.

Answer 2

Final answer:

To express 'd' in terms of 'c', solve the first equation for 'k' and substitute this value into the second equation. This yields: d=7+((c-4)^2)/3.

Explanation:

To express d in terms of c, we first need to make k the subject of c=3k+4. We do this by subtracting 4 from both sides, getting c-4=3k, and then dividing both sides by 3, which gives us k=(c-4)/3. Next, we substitute this value of k into the second equation: d=7+9k^2. Substituting, we get d=7+9*((c-4)/3)^2, which, when simplified, gives the result d=7+((c-4)^2)/3. This is the expression for d in terms of c.

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Related Questions

These parallelograms are similar. Compare the first to the second and give the ratio of their perimeters. Write the ratio in simplest terms.
P1= 8
P2= 6
A. 64:36
B. 16:9
C. 4:3
D. 8:6

Answers

its c. hope it helps. :)

what is the approximate volume of a cylinder with a radius of 4 cm and a height of 5 cm drag and drop the answer into the box

Answers

The formula for volume of a cylinder is V= πr2h. The two means to square it, not multiply by two. So you would have 3.14 x 16 x 5. The sixteen in the equation comes from squaring 4. The answer is 251.2.

BRAINLIEST TO PERSON WHO DOES ALL STEPS, KEEP IT SIMPLE AND EASY TO UNDERSTAND

The length of a rectangular floor is 4 ft. longer than its width w. The area of the floor is 525 ft^2.
a) Draw a picture of the situation.

b) Write a quadratic equation for the area in terms of w that represents the situation.

c) What are the dimensions of the floor? Explain how you found them.

Answers

Answer: The dimensions of the floor are 21 by 25.

For your drawing, you will have a rectangle with an x for the width and an x + 5 for the length.

If we multiply those together, we get the following equation for the area.
x(x + 5) = A
x^2 + 5x = A

Now, input 525 and solve for x.
x^2 + 5x = 525
x^2 + 5x - 525 = 0
x = 21 or x = -25

Only 21 makes sense for the width. Adding on 4 gives us 25 for the length.

Assume that the width of the floor is w.
The length is 4 ft longer than the width.
This means that:
Length = 4 + w

Part (a):
The drawing of the situation is shown in the attached image

Part (b):
Area of the rectangle is calculated as follows:
area = length * width
area = (w + 4) * w
area = w² + 4w
We are given that the area is 525 ft²
This means that:
525 = w² + 4w

Part (c):
To get the dimensions of the floor, we will need to solve the quadratic equation from part b.
area = w² + 4w
525 = w² + 4w
w² + 4w - 525 = 0
(w-21)(w+25) = 0
either w-21 = 0 ............> w = 21 ft .........> accepted solution
or w+25 = 0 ............> w = -25 ...........> rejected solution as the length cannot be negative
Now, we know that:
length = w + 4
length = 21 + 4
length = 25 ft
This means that:
length of floor = 25 ft
width of floor = 21 ft

Hope this helps :)

Can someone help me with this 2 step eqaution

Answers

The answer is: " 40 books " .
____________________________________________
Explanation:
____________________________________________
Let "x" equal the number of books that Jill started with. Solve for "x" :
____________________________________________
x – (1/2)x + 16 = 36 ;

1x – (1/2)) = (1/2)x ;

(1/2)x + 16 = 36 ;

Subtract "16" from EACH SIDE of the equation:

(1/2)x + 16 – 16 = 36 – 16 ;

(1/2)x = 20 ;

Multiply each side of the equation by "2" ;

2*(1/2)x = 20 * 2 ;

to get: x = 40 .
____________________________________________
The answer is: " 40 books " .
____________________________________________

Help with mathematics hw show all the work for each problem given Geniuses

Answers

7. A great way to do this is to use a recursive routine on a calculator.
Begin with {5000,0} to represent the starting amount of money and years passed. Hit enter. Then, put in: {Ans(1)x1.06,Ans(2)+1}.
The first part adds the compounded interest and the second adds a year.
Hit enter until the second value equals 8. You get {7969.24037265,8}.
Round that to the nearest cent to get $7,969.24 as the investment's value after 8 years.

9. Let's use the recursive routine again.
Begin with {1,1} to represent the starting 1 mile on week 1. Hit enter.
For the second part, use {Ans(1)x1.2, Ans(2)+1}. The first part increases the number of miles and the second goes to the next week. Hit enter until the second value is 10. The result is {6.1917364224,10}. The question says to round to the nearest mile, which is 6 miles.

4. This recursive routine will be different, since it is decreasing. Instead of multiplying it by something more than one, multiply it by 0.5. Start with {100,0} for the money and weeks. Hit enter. For the second part, use
{Ans(1)x0.5, Ans(2)+1}. Hit enter until the second value is 5. The result is
{3.125, 5}. Round to the nearest cent to get $3.13 left after 5 weeks.

Hope this helps!

MATH HELP PLEASE! WILL GIVE BRAINLIEST!
In circle A, mBEC is 290º.

What is the measure of ∠BAC ?

70º

130º

170º

360º

Answers

The answer is (A 70 ) (you must subtract the given degree and get 70) hope it helps and have a great day!

Suppose you borrow $1,200 at an add-on interest rate of 5% for 4 years. What will be the amount of your monthly payment ?

Answers

1200* (5% * 4) = 240
240 + 1200 = 1440
1440/12 = $120

The answer is $120 per month.

The amount can be calculated using the formula

[tex] A=P( 1+\frac{r}{100})^t [/tex]

Here P is the Principal ,r is the rate of interest and t is the formula .

In the given question P=$1200 ,r=5% ,t= 4 years.

Substituting these values in the formula

[tex] A=1200( 1+\frac{5}{100} )^4 [/tex]

[tex] A=1200(1.05)^{4} [/tex]

A=1458.60

Amount of monthly payment=[tex] \frac{1458.60}{12} =121.55 [/tex]

The amount of your monthly payment is $121.55.

Sum or difference of 1 5/12+ 2 1/12

Answers

The sum of the equation 1 5/12 + 2 1/12 would be 3 6/12 or 3 1/2. We can figure this out by first adding the wholes to get 3 and then adding the numerators of the fractions to get 6/12 or 1/2.
I hope this helped! :-)

1 5/12 + 2 1/12= 3 6/12. The answer is 3 1/2

Order these numbers from least to greatest

Answers

Least is closest to 0. If you convert the fractions to decimals, it may be easier to determine least to greatest.

Least= 3.311
3.32
27/8= 3.375
Greatest= 3 4/9= 3.444444

Hope this helps! :)

What is -5 1/2 - 4 1/4 + 6 3/4

Answers

I believe the answer is -3

Anyone know this? Don’t really understand it

Answers

The answer would be 8

The answer is 8 because 1/2 of 64 is 8.... 8 times 8 is 64

Which answer choice is equivalent to
−65
−12
?

Answers

What are the answer choices?

Which equation shows the relationship between x & y?

Question 21 options:

Y = x + 6

y = 3x

y = 2x + 3

y = 4x – 3

Answers

y=3x is correct. Hope this helped :)

Y=3x is the correct answer for sure

Olivia ate 1/4 of a pizza if there were 12 slices of pizza how many slices did Olivia eat

Answers

Hello!

There are many ways you can solve this question. I'll show you a few. Way 1:

Convert 1/4 to a decimal by dividing its numerator by its denominator.

1 ÷ 4 = 0.25

1/4 is 0.25 as a decimal.
Then, multiply the amount of slices of pizza by the decimal form.

12 × 0.25 = 3

Way 2:

Since the numerator is 1, simply divide ths number of slices by the denominator of the fraction. You will get the same answer.

12 ÷ 4 = 3

ANSWER:

Olivia ate 3 slices of pizza.

Which figure has the same area as the parallelogram show below

Answers

A trapezoid with a base of 6 but I do not see the other part of that answer.

Answer:

A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm.

Step-by-step explanation:

(I promise you this is right! :))

The equation 5x-10y=30is written in standard form. What is the first step when solving for x? Add 5x to both sides of the equation. Subtract 5x from both sides of the equation. Add 10y to both sides of the equation. Subtract 10y from both sides of the equation.

Answers

you would have to add 10y to both sides, and then divide by 5

The first step is Add 10y to both sides of the equation.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.

An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables.

Given:

5x- 10y =30

Now, to solve for x we must contain 'x' till the last step

so, we have to remove variable y

Then, Add 10y to both sides of the equation is the first step.

5x - 10y + 10y = 30 + 10y

5x = 30 +10y

Hence, Add 10y to both sides of the equation.

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Help me asap please! :D

Ki’von has a sink that is shaped like a half-sphere. The sink has a diameter of 20 inches. One day, his sink clogged. He has to use one of two different cups to scoop the water out of the sink. The sink is completely full when Ki’von begins scooping.

(a) What is the exact volume of the sink? Show your work. (3 points)

(b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points)

c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points)

Answers

Step 1
Find the volume of a sink
Volume sink=(4/6)*pi*r³ (half-sphere)
Diameter=20 in--------------> r=D/2-----------> r=10 in
Volume sink=(4/6)*pi*10³---------> (2000/3)*pi in³ --------> 2093.33 in³

(a) What is the exact volume of the sink?
the answer part a) is (2000/3)*pi in³ (2093.33 in³)

(b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it?

volume of a conical cup=pi*r²*h/3
diameter=8 in--------------> r=4 in
h=6 in
volume of a conical cup=pi*4²*6/3-----------> 32*pi in³
if one cup---------------------> 32*pi in³
X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(32*pi)------------> 20.83----------> 21 cups

the answer part b) is 21 cups

(c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it?

volume of a cylindrical cup=pi*r²*h
diameter=4 in--------------> r=2 in
h=6 in
volume of a cylindrical cup=pi*2²*6-----------> 24*pi in³
if one cup---------------------> 24*pi in³
X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(24*pi)------------> 27.77----------> 28 cups

the answer part c) is 28 cups

Answer: See each part below:

a) The volume of a sphere is (4/3)pi(r^3). If you input a 10 for the radius of sink, you will get 4000/3(pi). However, we have to divide it by 2 since it is a half-sphere. So the volume is 2000/3(pi).

For each cone, the volume formula is: pi(r^2)h/3.

b) With a radius of 4 and a height of 6, the volume is 100.53. Dividing the volume of the sink by this takes 21 scoops.

c) With a radius of 2 and a height of 6, the volume is 100.53. Dividing the volume of the sink by this takes 84 scoops.

Help please! Thanks:)))

Answers

it would be between the 3 m and the 4 m

hope this helps :)

According to the Bohr model, the radius of a hydrogen atom is approximately 5.29 × 10/-11 meters. What is this measurement written in standard form?
A. 0.00000000529 meters
B. 0.00000000000529 meters
C. 0.0000000000529 meters
D. 0.000000000529 meters

Answers

the answer is C, 0.0000000000529 because you move the decimal over as many places as the power says. For example, it says 10 to the -11th power so you move the decimal over 11 places to the left.

The measurement 5.29 × 10⁻¹¹ meters written in the standard form is option C, 0.0000000000529 meters.

Given that:

According to the Bohr model, the radius of a hydrogen atom is approximately 5.29 × 10⁻¹¹ meters.

It is required to write this number in scientific notation in the standard form.

Here the power of the 10 is negative.

So, the decimal point has to be shifted to the left.

Now, since the number to the power is 11, the decimal points have to be shifted 11 points to the left.

After shifting 1 point, the number is 0.529 × 10⁻¹⁰.

After shifting two points, the number is 0.0529 × 10⁻⁹.

In this way,

The number will have 10 zeroes before 5.

Hence the number is 0.0000000000529 meters, which is option C.

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Tomas works as an underwater photographer. He starts at a position that is 19 feet below sea level. He rises 9 feet, then descends 16 feet to take a photo of a coral reef. Enter an expression to find his position relative to sea level when he took the photo and then evaluate the expression.

Answers

19=9-16 would probably be something to go off of and begin your thought process with.

Answer:

Expression:

X = Xo + 9 feet - 16 feet
X = - 19 feet + 9 feet - 16 feet
X = - 26 feet (26 feet below the sea level)

Explanation:

1) Call Xo the initial position, and X the variable to indicate the actual position

2) Use position 0 for sea level

3) use negative sign for positions under the sea level

4) use positive sign for positions above the sea level

5) Expression:

Final position = initial position + movements upward - movements downward

X = Xo + 9 feet - 16 feet

X = - 19 + 9 feet - 16 feet = - 26 feet

Explain a scenario where you would use a frequency table to display data in the real world.

Answers

Many people have no occsasion to collect data in the real world. One basically has to dream up scenarios in which data collection might be desired, then sort through those to see if a frequency table would be of any value.

Some manufacturing processes produce parts that have a wide range of characteristics. Sometimes the range is much larger than is desired for a particular purpose, so the parts are "binned". That is, if they have characteristics in a specific narrow range, they are put into a bin with other similar parts.

Some customers want only parts with a particular specific characteristic (color or brightness, for example). If a request for quote comes that asks for a large number of these parts, it would be helpful to have on hand previously collected data about the percentage of production that falls into the specific bins desired. That is, a frequency table showing the number in each bin produced by a given operator, machine setting, environmental condition, material supplier, or other variable would be very helpful information when responding to the customer.
_____
Perhaps less complicated: a frequency table showing the zip codes of folks who show up for your art class might give you helpful information about where to target your advertising.

Billy made 1/2 gallons of juice for a picnic. He said that he made 3/4 quart of juice. EXPLAIN BILLY’S MISTAKE.

Answers

4 quarts are in 1 gallon, half of that is 2 quarts in 1/2 gallon.

My sister is buying new carpet for her bedroom floor. The length of the bedroom is 13 feet. The area of the bedroom is 175.5 square feet. How wide is my sister's bedroom?

A. 13.5 ft

B. 13.5 ft 2

C. 162.5 ft 2

D. 198.5 ft 2

Answers

Since the formula for the area of a rectangle is length × width = height, we can divide the area by the length to get the width.

175.5 ÷ 13 = 13.5

And since the width is one dimensional, the answer is A.

Hope this helps!

Area = length x width
Given: length = 13 , area = 175.5

175.5 = 13 x width
width = 175.5 ÷ 13
width = 13.5 feet

The width is 13.5 ft (Answer A)

plz answer the picture above

Answers

When a coordinate is reflected across the y axis, the x changes to the opposite and y stays the same.

X(0, -6) X' (0,-6)

Y(-10, 4) Y'(10, 4)

Z(3, -1) Z' (-3,-1)

Hopes this helped!!!!

Create a scale drawing of the original drawing using a horizontal scale factor of 80% any vertical scale factor of 175%.Write a numerically equation to find what the horizontal and vertical distances.

Answers

To answer this question I am going to create an example of a rectangle you could use. If the original width (horizontal distance) is 10, and the length (vertical distance) is 12, you would do the following to find the scaled version:

Length - 12 x 1.75= 21
Width - 10 x 0.8 = 8

Your scaled version would be 21 x 8.

Which set of statistics best describes a typical home value in Maya's neighborhood and how the values vary?

Answers

The answer is the median and the interquartile range. When you have data that is skewed ( more data points on one side or another, than the median is a good measure as well as the range of the middle half of the data (interquartile range -IQR).

Answer:

The typical home value is best described by the median.

The value variation is best described by IQR.

Step-by-step explanation:

For samples of data that have outliers, the set of statics that best describes central tendencies are the robust measures.

The median is a robust measure because the outliers will have very little impact on the result of the measure.

The IQR is a robust measure because it takes the difference between the 75th percentile and the 25th percentile of a sample, so the outliers are ignored.

Analysts determined that a basketball team had a 50% chance of winning its next game. Which simulation could you use to answer questions about winning the game?

Answers

As the team has 50% chance of winning, we should use a simulation that also has same chances.

so, flipping a coin can be used in this case, as it has 2 outcomes each with probability 1/2

Answer: On Imagine Math it is the flipping.

Step-by-step explanation:

heeeeeeeelppppppppppppppppppppppppp

Answers

The slope will be 7 because the equation is in slope intercept form.

slope intercept for is y = mx +b
m is the slope and b is the y intercept

Answer:
slope of line = 7

Explanation:
The slope-intercept form has the general formula:
y = mx + c
where:
m is the slope
c is the y-intercept

The given is:
y = 7x + 1/8

Comparing the given with the general formula, we will find that:
m is the slope = 7
c is the y-intercept = 1/8

Hope this helps :)

1.8y-9.3y-6.3y hope you can help

Answers

8y - 9.3y - 6.3y = -7.6

The answer is -13.8y

First subtract 1.8y from 9.3y which is 7.5y, but since you are actually subtracting a larger number from a smaller number, you add a negative sign because your answer is less than 1. Then you add -6.3y to to -7.5y because you have two negatives. While it may seem like you should add them, you will subtract because you are adding essentially more negative to the negative number. I hope that makes sense! Once you add -6.3y to -7.5y your answer is -13.8y.

A store marks up a jacket by 121%. the store's cost for the jacket is %87.62. Find the selling point of the jacket.

Answers

Selling point???

You mean selling price.

Let x = selling price

100 + 121 = 221

Here is your equation:

221/100 = x/87.62

100x = (221)(87.62)

Can you finish?

Solve for x.

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