Linear or Non - Linear

C(x) = 4x³+7x²-14x-6

Step-by-step explanation:

Given that the amount of water used in normal days is given by the equation;

W(x) = 5x³ +9x²-14x +9 -----(i)

The amount of decrease in water used is modeled by the equation;

D(x)= x³+2x² +15--------(ii)

To get the function C(x) that models the water used by the car wash on shorter day you subtract equation (ii) from equation(i)

 5x³ +9x²-14x +9

-  x³+2x² +15

-------------------------

4x³+7x²-14x-6

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Answer:

C(x) = 4x³ + 7x² − 14x - 6

Step-by-step explanation:

In a shorter day the water used by the car wash is computed as the difference between the original usage and the decrease, that is:

C(x) = W(x) - D(x)

Replacing with data:

C(x) = 5x³ + 9x² − 14x + 9 - (x³ + 2x² + 15)

C(x) = 5x³ + 9x² − 14x + 9 - x³ - 2x² - 15

C(x) = (5-1)x³ + (9-2)x² − 14x + (9-15)

C(x) = 4x³ + 7x² − 14x - 6

Answer:

800

Step-by-step explanation:

Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number

Answer:

832 --> ???

832 - we must round the underlined digit

832 --> ???

832 --> 800

The rounding rule is:

4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].

So with that rule, 832 becomes 800.

800 is your answer.

I hope this helps!

Answer:

The equation representing the statement is [tex](x-1)+x=6[/tex].

Step-by-step explanation:

Given:

Distance from Sue house to Gill house = 6 miles.

Let the distance from Gill to Taco Town restaurant be 'x'.

Also Given:

Sue lives 1 mile closer to Taco Town restaurant than Gill does.

Hence Distance from Sue to Taco Town restaurant will be = [tex]x-1[/tex]

We need to write the equation for the below statement.

the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.

Framing in equation form we get;

[tex](x-1)+x=6[/tex]

Hence the equation is [tex](x-1)+x=6[/tex].

Step-by-step explanation:

I don't know if this helps, but none of the above.

first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)

P.S. but 83 degrees and 7 degrees would be complementary...

hope you at least know why i say none of the above

Answer:

12 square units.

Step-by-step explanation:

I just took the test.

Answer:

The answer is 50.

Step-by-step explanation:

The answer is 50 because, the line that the Exterior angle is on is equal to 180. So you take the two interior angels and add them. Then subract that from 180 and you get 50.

Hope this helps :))

Answer:

The correct answer is 110°.

Step-by-step explanation:

The Exterior Angle Theorem states, "the exterior angle of a triangle is equal to the sum of its non-adjacent angles".

This means we would add 50 + 60 to get 110°.

Or we could look at the exterior angle and the adjacent angle to it. The two angles form a supplementary angle - this equals 180°. To find our answer this way, we subtract the known angle form 180:

180 - 70 = 110°

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer:

The relationship between time and distance is Velocity = Distance / Time

Step-by-step explanation:

Answer:

Option 1 is correct.

Step-by-step explanation:

Let there is a line A which is perpendicular to line L at point O.

Now, rotating line A about point O by 360° will give the plane R.

So, plane R is perpendicular plane to line L.

Again, let there is a line B which is perpendicular to line L at point P.

Now, rotating line B about point P by 360° will give another plane S.

So, plane S is perpendicular plane to line L.

Since line A and line B are parallel (As they are perpendicular to the same line L) so, plane R containing line A and plane S containing line B will also be parallel to each other.  

Hence, option 1 is correct. (Answer)

Answer:

TU ⊥ MN and MN ║ PQ

Step-by-step explanation:

TU ⊥ MN

As the angle that is created where TU and MN intersect is a 90° angle, these two lines must be perpendicular to each other.

MN ║ PQ

As both MN and PQ intersect the line TU, we can use this to prove that they are parallel.

Both MN and PQ create a 90° angle where they intersect with TU. This means that MN is ⊥to TU and PQ is ⊥ to TU.

As both MN and PQ are perpendicular to TU, they must be parallel.

Answer:

Step-by-step explanation:

1. [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex]

2. [tex]y=-5x+30[/tex]

Preliminary Material:

A line that is perpendicular to another has the opposite reciprocal slope of the other line.

A line parallel to another has the same slope.

With this in mind, we can begin to answer this question.

1.

Setup for question 1:

A line perpendicular with [tex]-5x+5[/tex] that goes through the point (7, 5).

Before going over the point this perpendicular line must go through, let's make an equation with the slope of the perpendicular line.

A linear function can be represented with this formula: [tex]y=mx+b[/tex].

We know the slope of this function must be an opposite reciprocal to -5, and using the information I first gave in the beginning of this problem, we can have the slope of the function.

If we take this slope and insert it into the linear equation, we will have the function...

So we now know the slope of this function, but what about the y intercept, [tex]b[/tex]? This is where the point given to us in the beginning of this problem comes into play. If we plug the point (7, -5) into our x and y coordinates in the above equation, we can solve for [tex]b[/tex].

Algebra:

[tex]-5=\frac{1}{5}(7)+b[/tex]

[tex]-5=\frac{7}{5}+b[/tex]

[tex]-\frac{25}{5}=\frac{7}{5}+b[/tex]

[tex]-\frac{32}{5}=b[/tex]

Answer:

Our final answer is: [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex].

2.

There will be no setup for 2. I'll show the algebra without explanation as well. If there's any confusion you can ask me :).

Algebra:

[tex]y=mx+b[/tex]

[tex]y=-5x+b[/tex]

[tex]-5=-5(7)+b[/tex]

[tex]-5=-35+b[/tex]

[tex]b=30[/tex]

Answer:

Answer:

Brainly User: eletricblu3s@*********.com

Should college be free? It’s a classic question with a complicated and arguably unclear answer. The affordability of college education, as well as the current student debt crisis, is always one of the center-stage issues for presidential political seasons. In fact, many candidates build their platforms around college costs as a key issue.

As with any major decision, especially relating to higher education, there are pros and cons to consider. Let me help break down the positives and negatives of tuition-free college.

The PROS of Tuition-Free College

More Lower-Income Students Might Reach Graduation if There’s No Tuition

Some students drop out because they do not have the ability to pay for tuition all four years. Getting rid of tuition would eliminate this reason for not graduating. This would also serve to improve college graduation rates, as fewer students would feel the need to drop to part-time status or take a break from education for financial reasons.

Student Debt Will No Longer Crush the Younger Generations

If an American college student is able to graduate with less than $10,000 in student loan debt, they are considered lucky (the average is $37,000). However, students from other countries that don’t have tuition already have that luxury; most of their loans come from living expenses and books. Without the weight of student loan debt, more college graduates might buy houses rather than renting apartments. They might buy cars, spend more on healthy food, travel more: In essence, they could contribute more to the economy.

Students Might Have More Freedom to Choose a Major They Enjoy

Whether it is the influence of parents or knowing you need to pay loans back as quickly as possible, current students are often guided toward “practical” majors that have a more lucrative post-graduation income. If shelling out thousands upon thousands of dollars is no longer a factor, parents and students might feel more relaxed about studying for majors that don’t necessarily have a large paycheck associated with them. Interest and enjoyment from a field of study goes a long way in helping students stick with it and avoid burning out.

More People Would Go to College

By negating the large bill of a college education, we could see an increase in the number of students able to attend college. This then creates a more well-educated workforce and a population that has better critical thinking skills. This could lead to more innovation in all areas of society. This would also help people with financial need to earn an education

Answer: 11,056.1

Step-by-step explanation: Because you have to add the first 7

Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.

To find the total amount that Jerome has paid in interest over the 7 months, we need to sum up the interest paid each month. The interest for each month is calculated as follows:

[tex]\[ \text{Interest for the month} = \text{Previous balance} \times \text{APR} / 12 \][/tex]

Let's calculate the interest for each month:

1. For the second month:

 [tex]\[ \text{Interest} = \$2200.00 \times 0.18 / 12 = \$33.00 \][/tex]

2. For the third month:

[tex]\[ \text{Interest} = \$2189.00 \times 0.18 / 12 = \$32.84 \][/tex]

3. For the fourth month:

[tex]\[ \text{Interest} = \$2178.06 \times 0.18 / 12 = \$32.67 \][/tex]

4. For the fifth month:

[tex]\[ \text{Interest} = \$2167.16 \times 0.18 / 12 = \$32.51 \][/tex]

5. For the sixth month:

[tex]\[ \text{Interest} = \$2156.33 \times 0.18 / 12 = \$32.34 \][/tex]

6. For the seventh month:

 [tex]\[ \text{Interest} = \$2145.55 \times 0.18 / 12 = \$32.18 \][/tex]

Now, sum up these monthly interest amounts:

[tex]\[ \$33.00 + \$32.84 + \$32.67 + \$32.51 + \$32.34 + \$32.18 = \$195.54 \][/tex]

So, Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.

Answer:

The equation to represent the distance traveled by Olive in here solar powered scooter can be given as:

D: [tex]m=30h[/tex]

Step-by-step explanation:

Given:

Speed of Olive's solar powered scooter = 30 miles/hour

[tex]m\rightarrow[/tex] miles traveled

[tex]h\rightarrow[/tex] hours of travel

To find the distance traveled by Olive.

Solution:

Distance traveled = [tex]Speed\ \times \ Time[/tex]

Thus, the equation to represent the distance traveled by Olive in here solar powered scooter can be given as:

[tex]m=30\times h[/tex]

∴ [tex]m=30h[/tex]

The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Solution:

Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall

A small tree in her back yard is about 7 times as the shurd

To find: height of tree

From given information,

Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]

Given that small tree in her back yard is about 7 times as the shurb

So we get,

height of tree = 7 times the height of shrub

[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]

Therefore on solving we get,

[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]

Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Option A and Option F

The expressions that represent the perimeter of rectangle are 4s + 1 and [tex]2(2s + \frac{1}{2})[/tex]

Solution:

From figure,

Length = s

Width = [tex]s + \frac{1}{2}[/tex]

The perimeter of rectangle is given as:

perimeter = 2(length + width)

Substituting the values we get,

[tex]perimeter = 2(s + s + \frac{1}{2})\\\\perimeter = 2(2s + \frac{1}{2})[/tex]

Thus option F is correct

On further simplification,

[tex]perimeter = 2(2s + \frac{1}{2})\\\\perimeter = 4s + 2(\frac{1}{2})\\\\perimeter = 4s + 1[/tex]

Thus Option A is correct

Answer:

11/5

Step-by-step explanation:

5x-7=4

5x=4+7

5x=11

x=11/5

The required solution of the function at x = 4 is f(4) = 13.

Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,

f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13

Thus, the required solution of the function at x = 4 is f(4) = 13.

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Answer:

f(x): {y| y > 0 }

g(x): {y| y > 6 }

Step-by-step explanation:

Hope this helps!

Because both of these are exponential functions with positive bases, we conclude that the range for both is:

{y| y > 0}.

Here we have two exponential functions:

f(x) = (4/5)^x

g(x) = (4/5)^(x + 6).

You can see that both of these are exponential functions with positive bases, then neither of these can have negative outcomes, while, as x increases, the outcome will also increase.

Then we can see both functions are exponential growths, so the range for both of these are the set of all real positive values, written in both cases as:

{y| y > 0}

If you want to learn more about exponential functions, you can read:

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Answer:

  Yes

Step-by-step explanation:

2 × 2/3 = 4/3 yards of fabric needed for 2 scarves. This amount is less than 1 1/2 yards. The amount of fabric that Jessica has is more than 1 1/2 yards, so is more than enough.

Jessica can make 2 scarves.

Answer   5

Step-by-step explanation:

Question:

You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence.  What fraction of the fence did you paint?

Answer:

The fraction of the fence painted is [tex]\frac{1}{12}[/tex]

Solution:

Given that:

You have a 32-foot fence around a square garden. There are 4 equal sections

Find the length of each section:

4 sections = 32 foot

[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]

Find the length that is painted:

[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]

Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted

Find the fraction that that is painted:

Total length of fence = 32

[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]

Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted

Answer:

v = 1/2(1 + i√23) ,  1/2(1 - i√23).

Step-by-step explanation:

-2v^2 - v + 12 =  -3v^2 + 6

-2v^2 + 3v^2 - v + 12 - 6 = 0

v^2 - v + 6 = 0

This will not factor so we could use the quadratic formula to solve it:

For the equation ax^2 + bx + c = 0 the roots are:

x = [ - b +/-  sqrt(b^2 - 4ac) ] / 2a.

So here we have:

v = [-(-1) +/- sqrt((-1)^1 - 4*1*6)] /  2

v = [ 1 +/- sqrt (-23)] / 2

= 1/2 +  i√23/2 ,    1/2 -  i√23/2

= 1/2(1 +  i√23) ,  1/2(1 -  i√23).

Answer:

Part a) [tex]AC=135.95\ m[/tex]

Part b) [tex]BC=124.14\ m[/tex]

The diagram in the attached figure

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]

substitute the given values

[tex]53^o+61^o+m\angle C=180^o[/tex]

[tex]114^o+m\angle C=180^o[/tex]

[tex]m\angle C=180^o-114^o[/tex]

[tex]m\angle C=66^o[/tex]

step 2

Find the distance AC

Applying the law of sines

[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}[/tex]

see the attached figure to better understand the problem

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}[/tex]

[tex]AC=\frac{142}{sin(66^o)}(sin(61^o))[/tex]

[tex]AC=135.95\ m[/tex] ---> rounded to the nearest hundredth

step 3

Find the distance BC

Applying the law of sines

[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}[/tex]

[tex]BC=\frac{142}{sin(66^o)}(sin(53^o))[/tex]

[tex]BC=124.14\ m[/tex] ---> rounded to the nearest hundredth

Answer:

I sell 12 bracelets and 24 necklaces.

Step-by-step explanation:

The selling price of each bracelet is $2 and that of each necklace is $3.

I collect $96, selling a total of 36 jewelry items.

Let us assume that I sell x bracelets and y necklaces.

So, x + y = 36 ........ (1) and  

2x + 3y = 96 .......... (2)

Now, solving equations (1) and (2) we get, 3y - 2y = 96 - 72

⇒ y = 24

Hence, from equation (1) we get x = 36 - y = 36 - 24 = 12

Therefore, I sell 12 bracelets and 24 necklaces. (Answer)

Answer:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C)

Step-by-step explanation:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).  

Lets take an example, if we have 81°F and want to convert in (°C). So, here is the procedure:

                            C = (5/9) (81 - 32)

                                = (5/9) (49)

                                 = 27.22 °C

So, it is clear that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).

Keywords: linear equation, converter, C = (5/9)(F-32)

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The profit Haddie makes from selling scarves at a craft fair can be represented by the algebraic expression P = 12s - 25. Here, P represents profit, s represents the number of scarves sold, 12 represents the price of each scarf, and 25 represents the cost of booth rental.

The subject of the question deals with the concept of profit in a business transaction, which falls under Mathematics, specifically algebra and economics. It's a High School level problem since it involves creating a basic algebraic expression.

Haddie's profit can be determined by subtracting her costs (the booth fee) from her earnings (the sale of the scarves). She earns $12 for each scarf sold, represented as 12s (where s is the number of scarves sold), and she has a fixed cost of $25 for the booth rental.

Therefore, the expression for Haddie's profit, P, for selling s scarves is: P = 12s - 25. This expression represents the total amount Haddie will earn from selling s scarves after deducting her cost for the booth rental.

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Length and width of book is 5.91 inches and 2.36 inches respectively

Solution:

Given that a book is 15 centimeters long and 6 centimeters wide

To find: length and width of book in inches

From given question,

Length of book = 15 cm

Width of book = 6 cm

The conversion factor used is:

1 cm = 0.393701 inches

Therefore, length of book in inches is:

[tex]15 \text{ cm} = 15 \times 0.393701 \text{ inches }= 5.905515 \text{ inches }[/tex]

Rounding off rules:

First look at the digit to immediate right of rounding off digit

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

On rounding to nearest hundredth, ( two decimal places )

[tex]5.905515 \text{ inches } = 5.91 \text{ inches }[/tex]

Width of book in inches:

[tex]6 \text{ cm} = 6 \times 0.393701 \text{ inches } = 2.362206 \text{ inches }[/tex]

On rounding to nearest hundredth, we get 2.36 inches

Final answer:

The book measures approximately 5.91 inches in length and 2.36 inches in width.

Explanation:

To convert the dimensions of the book from centimeters to inches, we use the conversion factor that 1 inch is equal to 2.54 centimeters.

The length of the book in inches is calculated as follows:

Similarly, the width of the book in inches is:

Therefore, the book measures approximately 5.91 inches in length and 2.36 inches in width.

Answer:

ℝ

Step-by-step explanation:

[tex]\displaystyle 10 - 2x = [5 - x] - [x - 5][/tex]

All linear functions have a range and domain of all real numbers.

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]

Answer:

D

Step-by-step explanation:

Using the rule of logarithms

log x - log y = log([tex]\frac{x}{y}[/tex])

Given

[tex]log_{7}[/tex]([tex]\frac{n}{2}[/tex])

= [tex]log_{7}[/tex] n - [tex]log_{7}[/tex] 2 → D

Answer:

yoink im eating them points nomnomnom

Step-by-step explanation:

Answer:

The midpoints of the given graph are ( - 1, 3 ).

Step-by-step explanation:

By the graph we have to given that the endpoints are  R ( -5, 4) and S (3, 2)-

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex]) and  ( [tex]x_{2}, y_{2}[/tex]  ) then the mid points C are-  

C = (  [tex]\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{2}[/tex] )

Here,

R ( - 5, 4 ) and S ( 3, 2 )

then the  midpoints C are-

C = ( [tex]\frac{ - 5 + 3}{2}[/tex] , [tex]\frac{4 + 2}{2}[/tex]

C= ( - 2/2 , 6/2 )

C = ( -1, 3 )

Hence the midpoints are ( - 1, 3 ).