Solve for x and verify:3(x+3)-2(x-1)=5(x-5)

Answer:

gradient = change in y/ change in X

= 7-2/3-2=5

the gradient = 5

use either one of the points to find the gradient

y-3/x-7 =5

y=5x-4

Answer:

1+5+7+10=23

hope that's what u meant?

Answer:

✔ 2/10 + 7/10

✔ 9/10

Step-by-step explanation:

Answer:

Length = [tex]5\ \text{ft}[/tex]

Breadth = [tex]5\ \text{ft}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the length of the garden

and [tex]y[/tex] be the width of the garden

From the details of the cost in the question we get

[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]

Now area of the garden is

[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]

Differentiating with respect to x we get

[tex]\dfrac{dA}{dx}=10-2x[/tex]

Equating with 0

[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]

Double derivative of the area is

[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]

So, area is maximum at [tex]x=5[/tex]

[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]

So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].

Answer:the answer is D

Step-by-step explanation:

it is

Answer:

7x-21

Solution:

7 times x and 7 times negative 3

Answer:

[tex]\huge\boxed{\sf{7x-21}}[/tex]

Step-by-step explanation:

Hello.

The Distributive property states that

a(b+c)=ab+ac

Where

a, b, and c = variables/constants

Now, simplify the expression:

7(x-3)

Multiply x and 3 times 7 and subtract the products:

7x-21

I hope it helps & have an outstanding day.

[tex]\boxed{imperturbability}[/tex]

Answer:

6.25 kilometers

Step-by-step explanation:

2.45km + 3.8km

= 6.25km

Answer: 6.25 Kilometers

Step-by-step explanation:

First, take 2.45 Kilometers from day one

Then take 3.8 Kilometers from day two

Now add them together for the result of

6.25 Kilometers

Answer: $9.25 an hour

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

cost of producing the 501st item = $9.92

Step-by-step explanation:

The function representing the cost is given by;

C(x) = 10000 + 90x - 0.08x²

To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.

Thus;

C(500) = 10000 + 90(500) - 0.08(500)²

C(500) = 10000 + 45000 - 20000

C(500) = $35000

Similarly;

C(501) = 10000 + 90(501) - 0.08(501)²

C(501) = 10000 + 45090 - 20080.08

C(501) = $35009.92

cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92

You can first condense the series to make it simpler to study. If n is odd, then n = 2k - 1, and if n is even, then n = 2k for some k ≥ 1. So for each k, you can pair up the k-th terms of the odd- and even-indexed series.

odd:

[tex]\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}[/tex]

even:

[tex]\dfrac1{3^{\frac n2}}=\dfrac1{3^k}[/tex]

So the series can be re-indexed as

[tex]\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}[/tex]

By the root test, the series converges, since

[tex]\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13<1[/tex]

Answer:

2 gallons an hour

Step-by-step explanation:

This is a fraction equal to

2 gal ÷ 1 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 1

2 gal

÷ 1

1 hours

÷ 1

=

2 gal

1 hour

=

2 gal

hour

= 2 gal per hour

Answer:

3/8

Step-by-step explanation:

1/4 ÷ 2/3 = 3/8

Answer:

Percentage increase= 37.5%

Step-by-step explanation:

Giving the following information:

Sales on weekdays (Q0)= 240 units

Sales on weekends (Q1)= 330 units

To calculate the percentage increase, we need to use the following formula:

Percentage increase= [(Q1/Q0) - 1]*100

Percentage increase= [(330/240) - 1]*100

Percentage increase= 37.5%

Answer:

Step-by-step explanation:

Find the diagram attached. From the diagram, we can see that;

<USW = <TSR (vertically opposite angles)

Given

<USW = 7x-34

<TSR = 4x+29

Equate

7x-34 = 4x+29

7x-4x = 29+34

3x = 63

x = 63/3

x = 21°

Find <USW

<USW =7x-34

<USW =7(21)-34

<USW = 147-34

<USW = 113°

Hence the measure of <USW is 113°

Answer:

B) Yes

C) C = 3x + 25

Step-by-step explanation:

Given that:

Yearly charge = $25

Charge per visit = $3

The yearly cost will depend on the number of visits for the year :

B.) Cost can be represented by a linear function, as the graph it yields is a straight line graph having intercept and slope.

C.) C = mx + b

Where ;

b = intercept = yearly cost

m = slope or gradient = cost per visit

C = total cost

x = number of visits

Hence,

C = 3x + 25

Answer:

$24.25

Step-by-step explanation:

$(17.75 + 6.5)

= $24.25

Hope this helped!

Answer:

The linear function that models the charge for hiring the technician for x hours is y=45*x + 55

Step-by-step explanation:

The linear function is defined by the equation

f(x) = mx + b or y = mx + b

where m is the slope of the line and b is the y-intercept.

In this case you want to represent a linear function that models the charge for hiring the technician for x hours, that is, y represents the charge for hiring the technician and x the number of hours.

Given the coordinates of two points (x1, y1) and (x2, y2), you can determine the equation of the line first knowing the slope m by:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

In this case, the points are:

So:

[tex]m=\frac{370-190}{7-3}[/tex]

Solving:

m=45

To obtain the value of b, once you have replaced the value of m in the equation, you must substitute the values ​​of x and y for the values ​​of the coordinates of one of the points, and solve for b to obtain its value. In this case you replace the value of point 1:

[tex]y=45*x+b[/tex]

[tex]190=45*3+b[/tex]

And you get:

190= 135 + b

190 - 135= b

55= b

So, the linear function that models the charge for hiring the technician for x hours is y=45*x + 55

We want to find a linear equation that models the charge for hiring the technician for x hours.

The correct option is D, the equation is:

y = ($45/h)*x + $55

We know that a general linear equation is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have two points, one given by:

(3 hours, $190)

The other given by:

(7 hours, $370)

Then the slope is given by:

[tex]a = \frac{\$ 370 - \$ 190}{7h - 3h} = \$ 45/h[/tex]

This means that he charges $45 per hour.

Replacing that in the general equation we get:

y = ($45/h)*x + b

To find the value of b, we use the fact that he charges $190 for 3 hours, then we can solve:

$190 = ($45/h)*3h + b

$190 = $135 + b

$190 - $135 = b = $55

Then the equation is:

y = ($45/h)*x + $55

So the correct option is D.

If you want to learn more, you can read:

https://brainly.com/question/2263981

Answer:

17.5

Step-by-step explanation:

The first step is to convert one bookshelf into feet, so 42 divided by 12=\

3.5

Now, we have 5 of these shelves, so we have to do 3.5 x 5=17.5.

Answer:

x^2+5x-14=0

Step-by-step explanation:

(x+7)(x-2)=0

x (x-2)+7 (x-2)=0

x^2-2x+7x-14=0

x^2+5x-14=0

Answer:

$45,000 at 13% =  B-rated bond

$5,000 at 3% = CD

Step-by-step explanation:

Let us assume the x amount at 13% be 0.13x

And, y amount at 3% be 0.03x

Total interest = $6,000

The equation is

0.13x + 0.03x = $6,000 ................(1)

Now the total amount is $50,000

So

x + y = $50,000

y = $50,000 - x ................(2)

Now put the y value in the equation 1

So,

0.13x + 0.03 ($50,000 - x)  = $6,000

0.13x + $1,500 - 0.03x = $6,000

0.10x = $6,000 - $1,500

0.10x = $4,500

x = $4,500 ÷ 0.10

= $45,000 at 13%

now y value would be

= $50,000 - $45,000

= $5,000 at 3%

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

Answer:

probably A

Step-by-step explanation:

Brainliest pls

Answer:

d

Step-by-step explanation:

ut is parrell in d because the bottom line is ac n the line parrell to that,is de

Answer:

The answer would be 100/3

Step-by-step explanation:

Answer: 33 1/3% as a fraction is 1/3. It cannot be simplified. Hope this helps!

Answer:

it would be 8 to 15

Step-by-step explanation:

you would write it as a fraction 8/15. then, you would try and simplify it. because you cant simplify 8/15 anymore, your answer would be 8/15! hope this helps :)

Answer:

c.155 the answer is C. 156

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as what is required of the question is not stated.

However, since the question is only limited to distance, a likely question could be to calculate the distance from Bayville to Colleyville.

Represent the distance from Atlanta to Colleyville with AC

Represent the distance from Atlanta to Bayville with AB

Represent the distance from Bayville to Colleyville with BC

So, we have that:

[tex]AC = 25.5\ miles[/tex]

[tex]AB = 10\frac{2}{3}\ miles[/tex]

The relationship between AB, AC and BC is:

[tex]AC = AB + BC[/tex]

Make BC the subject of formula:

[tex]BC = AC - AB[/tex]

[tex]BC = 25.5 - 10\frac{2}{3}[/tex]

Convert fraction to decimal

[tex]BC = 25.5 - 10.7[/tex]

[tex]BC = 14.8[/tex]

Hence, the distance from Bayville to Colleyville is 14.8 miles