The cost to rent a van is $19.50 per day plus $0.25 per mile. If you have $157 to
rent a van, what is the number of miles that you can drive if you want to rent the van
for 2 days and you want to stay below your budget? Let m represent the number of
miles.

Answer:

Step-by-step explanation:

Let x be the smallest number (first)

Let (x + 2) be the second number (second)

Let (x + 4) be the greatest number (third)

Set equation according to the given information

-4 [x + (x + 4)] = 192

Simplify parentheses

-4 [x + x + 4] = 192

-4 [2x + 4] = 192

Expand bracket and apply the distributive property

(-4) · 2x + (-4) · 4 = 192

-8x - 16 = 192

Add 16 on both sides

-8x - 16 + 16 = 192 + 16

-8x = 208

Divide -8 on both sides

-8x / -8 = 208 / (-8)

[tex]\boxed{x=-26}[/tex]

Find the value of the second term

x + 2 = (-26) + 2 = [tex]\boxed{-24}[/tex]

Find the value of the third term

x + 4 = (-26) + 4 = [tex]\boxed{-22}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Sqrt(-108)=6i*sqrt(3)

Step-by-step explanation:

-108=3*6*6*(-1). Sqrt(-108)=6i*sqrt(3) where i is iota

Answer:

In a representation of 100, the percent change is just a number change, meaning 65 - 52, or 13 is that change. This means that the percent change from 65 to 52 is 13%  

Step-by-step explanation:

Answer:

22:25   26:Yes 4900  27: 6 and 18  28: 44,100 and 48,024,900

Step-by-step explanation:

for 22-25 see answer #2. They gave a better answer in total.

Answer:

22.  30

prime factorization of 30

2 × 3 × 5

so there is no simplification needed here

23. 126

2 × 3 × 3 × 7

simplification

2 ×  × 7

24.  4900

2 ×2 × 5 × 5 × 7 ×7

simplification

25.  39204

2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

simplification

26 .  

Yes 4900 is a square number it's square root is 70

you can even cross-check

70 × 70

= 4900

and even 39204 is a square number it's square root is 198

you can even cross-check

198 × 198

= 39204

Hence 2 numbers 4900 and 39204 are square numbers

27 .

i. highest common factor of 30 and 126

factors of 30 are 2 × 3 × 5  

factors of 126 are 2 × 3 × 3 × 7

now find common between them

common factors are 2 and 3

so multiply 2 and 3

2 × 3

= 6

6 is the highest common factor

ii. 126 and 39204

factors of 126 are 2 × 3 × 3 × 7

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

now find common between them

common factors are 2 × 3 × 3

= 18

18 is the highest common factor

28 .

1 .  126 and 4900

factors of 126 are 2 × 3 × 3 × 7

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers

2 ×2 × 5 × 5 × 3 × 3 × 7 ×7

= 44100   least common multiple

ii. 4900 and 39204

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers  

2 ×2 × 3 x 3 x 3 x 3 x 5 x 5 x 7 x 7 x 11 x 11

= 48024900 least common multiple

Answer:

Its C.

Step-by-step explanation:

I had this and its C. trust me

Answer:

Here is your answer . Hope this helps you.

Answer:

[tex]\boxed {\boxed {\sf \sqrt{218} \ or \ 14.76}}[/tex]

Step-by-step explanation:

The formula for calculating the distance between 2 points is:

[tex]d= \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. The 2 points we are given are (-4, 6) and (3, -7). If we match the value with the corresponding variable we see that:

Substitute the values into the formula.

[tex]d= \sqrt{(3 - -4)^2 + (-7-6)^2[/tex]

Solve inside the parentheses.

[tex]d=\sqrt {(7)^2 + (-13)^2[/tex]

Solve the exponents.

[tex]d= \sqrt{ (49)+(169)[/tex]

Add.

[tex]d= \sqrt{218}[/tex]

[tex]d=14.76482306[/tex]

If we round to the nearest hundredth place, the 4 in the thousandth place tells us to leave the 6.

[tex]d \approx 14.76[/tex]

The distance between the points (-4, 6) and (3, -7) is √218 or approximately 14.76.

Answer:

n=12

Step-by-step explanation:

3.3(n-8)-n=1.2

Distribute

3.3n -26.4 -n = 1.2

Combine like terms

2.3n -26.4 = 1.2

Add 26.4 to each side

2.3n -26.4+26.4 = 1.2 +26.4

2.3n = 27.6

Divide each side by 2.3

2.3n/2.3 = 27.6/2.3

n=12

the solution to the equation is n = 12. Let's simplify the given equation step by step: [tex]\(3.3(n - 8) - n = 1.2\)[/tex]

Step 1: Distribute the 3.3 to the terms inside the parentheses:

[tex]\(3.3n - 3.3 \times 8 - n = 1.2\)[/tex]

Step 2: Perform the multiplication:

[tex]\(3.3n - 26.4 - n = 1.2\)[/tex]

Step 3: Combine like terms:

[tex]\(3.3n - n = 1.2 + 26.4\)\\\(2.3n = 27.6\)[/tex]

Step 4: Isolate n by dividing both sides by 2.3:

[tex]\(n = \frac{27.6}{2.3}\)\\\(n = 12\)[/tex]

So, the solution to the equation is n = 12.

To know more about equation:

https://brainly.com/question/8651602

#SPJ3

Answer:

S=(2,-2) ...............

Answer:

The answer would be A

Step-by-step explanation:

Answer:

37 degees

Step-by-step explanation:

..........m.........

Answer:

x=37

Step-by-step explanation:

here,

143+x=180

x=180-143

x=37

The cube root of 27 is 3!!

Answer:

Point-slope form:

[tex]y-4=\displaystyle\frac{1}{3}(x+4)[/tex]

[tex]y-8=m(x-8)[/tex]

Slope-intercept form:

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

Standard form:

[tex]-x+3y=16[/tex]

Step-by-step explanation:

Hi there!

1) Point-slope form

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and m is the slope

First, determine the slope:

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the points (-4,4) and (8,8):

[tex]m=\displaystyle\frac{8-4}{8-(-4)}\\\\m=\displaystyle\frac{8-4}{8+4}\\\\m=\displaystyle\frac{4}{12}\\\\m=\displaystyle\frac{1}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{1}{3}[/tex]. Plug this into  [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=\displaystyle\frac{1}{3}(x-x_1)[/tex]

Now, for [tex](x_1,y_1)[/tex], we can either plug in (-4,4) or (8,8):

[tex]y-4=\displaystyle\frac{1}{3}(x-(-4))\\\\y-4=\displaystyle\frac{1}{3}(x+4)[/tex]

or

[tex]y-8=m(x-8)[/tex]

2) Slope-intercept form

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

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

Plug in the slope

[tex]y=\displaystyle\frac{1}{3}x+b[/tex]

Now, to determine the y-intercept, plug in one of the points (-4,4) or (8,8) and solve for b:

[tex]8=\displaystyle\frac{1}{3}(8)+b\\\\8=\displaystyle\frac{8}{3}+b\\\\8-\displaystyle\frac{8}{3}=b\\\\b=\frac{16}{3}[/tex]

Therefore, the y-intercept is [tex]\displaystyle\frac{16}{3}[/tex]. Plug this back into [tex]y=\displaystyle\frac{1}{3}x+b[/tex]:

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

3) Standard form

Standard form:

[tex]Ax+By=C[/tex] where A, B, and C are numbers which are typically integers

[tex]y=\displaystyle\frac{1}{3}x+\displaystyle\frac{16}{3}[/tex]

Organize this into standard form:

[tex]-\displaystyle\frac{1}{3}x+y=\displaystyle\frac{16}{3}[/tex]

Multiply both sides by 3 so A, B, and C are integers:

[tex]-x+3y=16[/tex]

I hope this helps!

Answer:

Step-by-step explanation:

y=(-1/3)x + 3

Answer:

3

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

     = ( 3 - -3)/( 7-5)

     = (3+3)/(7-5)

     = 6/2

      = 3

Answer:

[tex]m = 3[/tex]

Step-by-step explanation:

[tex]slope \: = m = \frac{y1 - y2}{x1 - x2} \\ = \frac{ - 3 - 3}{5 - 7} \\ = \frac{ - 6}{ - 2} \\ = 3[/tex]

The answer is 60 inches.

Answer:

Mandy is 1.613 m tall

Step-by-step explanation:

Let us consider

Mary is A, Misa is B and Mandy is C

According to question,

A + B + C = 4.84 m...... (i)

From qsn

9 cm/0.009 m

= 9 cm/ 0.9 cm

= 10 cm

= 0.1 m

Then, A is 0.1 m shorter than B

i.e. A= B - 0.1 m

Also, B is 0.05 m taller than C

i.e B = C + 0.05m

We have to find height of C ( Mandy)

From eqn (i)

C = 4.84 - B - A

or, C = 4.84 - (C + 0.05) - ( B - 0.1)

or, C = 4.84 - C - 0.05 - B + 0.1

or, 2C = 4.89 - B

or, 2C = 4.89 - ( C + 0.05)

or, 2C = 4.89 - C - 0.05

or, 3C = 4.84

or, C = 4.84/3

or, C = 1.613 m

Answer:

It's a statistical question.

and there between 250-300 feet.

Answer:

.55555555 infinitely or .556

Step-by-step explanation:

Answer:

4 cassettes and 5 CDs

Step-by-step explanation:

Create a system of equations

c is cassettes and d is CDs

6c+10d=74

c+d=9

I will use substitution

c=9-d

6(9-d)+10d=74

54-6d+10d=74

4d=20

d=5

Plug 5 back into the equation

c+5=9

c=4

2.

Simply do 166 divided by 83 and you'll have your answer

Answer:

170.25

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 15 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 15, so we can write it down as 100%=15.

4. We know, that x% equals 1135 of the output value, so we can write it down as x%=1135.

5. Now we have two simple equations:

1) 100%=15

2) x%=1135

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=15/1135

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 1135 is what percent of 15

100%/x%=15/1135

(100/x)*x=(15/1135)*x       - we multiply both sides of the equation by x

100=0.013215859030837*x       - we divide both sides of the equation by (0.013215859030837) to get x

100/0.013215859030837=x

7566.6666666667=x

x=7566.6666666667

now we have:  170.25

We have to find,

→ 15% of 1135

The value of the percentage is,

→ 15 ÷ 100

→ 0.15

Let's find the solution,

→ 1135 × 0.15

→ 170.25

Hence, the answer is 170.25.

Answer:

isn't it just -2 it's the greatest common factor (GCF) of -2800 and -2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the greater part = x

Smaller part = 105 - x

2*(greater part) = (3*smaller part) - 15

2*x = 3*(105 -x) - 15

Use distributive property

2x = 3*105 - 3*x - 15    

2x = 315 - 3x - 15

2x =  300 - 3x

Add 3x to both sides

2x +3x = 300

5x = 300

Divide both sides by 5

x = 300/5

x =60

Smaller part = 105 - 60  = 45

Greater part = Rs. 60

Smaller part = Rs. 45

Answer: First Choice. 5ft

Step-by-step explanation:

Here we need to know the idea of the Pythagorean theorem.

Since a building is straight, the base angle is a right angle, thus it would be a right triangle.

Pythagorean Theorem: a² + b² = c²

**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)

Solve:

Given information

a = 12 ft

c = 13 ft

b = unknow base length

Given formula for Pythagorean Theorem

a² + b² = c²

Substitute values into the formula

12² + b² = 13²

Simplify exponents

144 + b² = 169

Subtract 144 on both sides

144 + b² - 144= 169 - 144

b² = 25

Square root both sides

√b² = √25

[tex]\boxed{b=5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

what's the question? we solving or simplify?

Answer and Step-by-step explanation:

When multiplying exponents:

- Product of Powers: When the base of the exponents are the same, and the bases are being multiplied to each other, the exponents are added together.

- Different bases Same Exponents: When the bases of the exponents are different, but the exponents are the same, the bases multiply together (within a parenthesis) with the exponent on the parenthesis.

- Quotient of Powers: When the base of the exponents are the same, and they are being divided by each other, the exponents will subtract from each other.

- Power of a Power: When a base has an exponent, and that entire term has and exponent, the exponents multiply together.

- Power of a Product: The opposite of Different bases Same Exponents. Distribute the exponent onto the different bases.

- Power of a Quotient: The opposite of Quotient of Powers. Distribute the exponent to the dividing bases.

- Zero Power: Any number raised to the 0 power equals 1.

- Negative Exponent: Any number raised by a negative number goes to the denominator of a fraction (if not already in the denominator), and vise versa (goes to the numerator if not already in the numerator).  

- Power of One: Any number raised to the power of 1 is the same number.

7.

[tex](-5y^3)^3 = -125y^6[/tex]

8.

[tex](-a^9b)^4 = -a^{13}b^4[/tex]

9.

[tex](\frac{1}{2}x^4 )^7 = \frac{1}{2^7 (=128)} x^{11}[/tex]

10.

[tex]2(3a^2)^3 = 2(27a^5) = 54a^5[/tex]

11.

[tex]\frac{1}{2} (4k^5)^2=\frac{1}{2} (16k^7) = 8k^7[/tex]

12.

[tex]-6(\frac{2}{3}p^8 )^3=-6(\frac{6}{27} p^{11}) = -6(\frac{2}{9}p^{11})=\frac{-12}{9} p^{11}=-\frac{4}{3}p^{11}[/tex]

13.

[tex](m^5n^3)^7 * m^2n = m^{12}n^{10}*m^2n=m^{14}n^{11}[/tex]

14.

[tex](2xy)^2(-3x^2)(4y^2) = (4x^2y^2)(-3x^2)(4y^2) = (-12x^4y^2)(4y^2)=-48x^6y^4[/tex]

15.

[tex](2x^3y^2z^2)^3(x^2z)^4=(8x^6y^5z^5)(x^6z^4)=8x^{12}y^5z^9[/tex]

16.

[tex](-xy)^2(2x^9y^5)^4 = (x^2y^2)(16x^{13}y^9)=16x^{15}y^{11}[/tex]

17.

[tex](-4mn)^3(-2m^2)^3 = (-64m^3n^3)(-8m^5)=512m^8n^3[/tex]

18.

[tex]-3(2x^4)(4x^5y)^2 = (-6x^4)(16x^7y^2)=-96x^{11}y^2[/tex]

19.

[tex](-18m^2n)^2(-\frac{1}{6} mn^2)=(324m^4n^2)(-\frac{1}{6} mn^2)=-54m^5n^4[/tex]

20.

[tex](3r^3s^5)^2-r^6s^{10} = 9r^5s^7-r^6s^{10} = r^5s^7(9-rs^3)[/tex]

21.

[tex](-2x^5y^7)^3+7x^{15}y^{21} = -8x^8y^{10}+7x^{15}y^{21} = x^8y^{10}(7x^7y^{11}-8)[/tex]

#teamtrees #PAW (Plant And Water)

I hope this helps!

Step-by-step explanation:

a) gradient= y2-y1/x2-x1

gradient of AB:

gradient=-4-1/2-3

=-5/-1

=5

gradient of BC:

=-5+4/7-2

=-1/5

b) as the priduct of both gradient is -1 ,both lines are perpendicular.

c) as we have seen lines are perpendicular so it is a right angled triangle.

Answer:

965.31sq.km

Step-by-step explanation:

Area of the triangle = 1/2 xy sina

a=52° , x=49 , y=50

area of triangle= 1/2 * 49 *50 *sin52°

area= 965.31 sq.km