Toni ran 4/5 mile in 1/5 hour. Write an equation for the distance in miles y that she ran in x hours if she ran at a constant rate.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 0.875}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3[ x + 3(4x - 5)]  = 15x - 24}[/tex]

Distribute 3 through the parentheses

⇒[tex] \sf{3[ x + 12x - 15 ]  = 15x - 24}[/tex]

Collect like terms : 12x and x

⇒[tex] \sf{3[ 13x - 15 ]  = 15x - 24}[/tex]

Distribute 3 through the parentheses

⇒[tex] \sf{39x - 45 = 15x - 24}[/tex]

Move 15x to left hand side and change it's sign

Similarly, move 45 to right hand side and change it's sign

⇒[tex] \sf{39x - 15x = - 24 + 45}[/tex]

Collect like terms

⇒[tex] \sf{24x = - 24 + 45}[/tex]

Calculate

⇒[tex] \sf{24x = 21}[/tex]

Divide both sides of the equation by 24

⇒[tex] \sf{ \frac{24x}{24} = \frac{21}{24}} [/tex]

Calculate

⇒[tex] \sf{x = 0.875}[/tex]

Hope I helped!

Best regards! :D

Answer:

2f

3f

−f+4g

3g

2g

−2f−4g

Step-by-step explanation:

Hope this helps!

Answer: OPTION B

Step-by-step explanation:

First of all, you need to know the concept of imaginary number or i.

i (imaginary number)= √-1 ⇔ In real number world, √-1 will be undefined,  

                                               and thus this is called imaginary number

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

√-2=√2 × √-1

√-2=√2× √-1

√-2=√2 × i

√-2= √2 i

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

√-18=√9 × √2 × √-1

√-18= √9 × √2 × √-1

√-18= 3 × √2 × i

√-18= 3√2 i

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

Addition in radical numbers is as usual as normal number. HOWEVER, only numbers that has the same radical (i.e 2√3 and 7√3) can combine.

 √-2 + √-18

=√2 i + 3√2 i

=4√2 i

Hope this helps!! :)

Please let me know if you have any question

Answer:

1325

Step-by-step explanation:

53 x 25 is 1325

Not sure how it can be simplified more.

Answer:

a) 2x² - 32 = 2(x-4)(x+4)

e) 3x² - 75 y² = 3(x-5y)(x+5y)

i) (x+5)² - 16 = (x+1)(x+9)

j) (x-4)² - 9 = (x-7)(x-1)

m) (3x+5)² - x² = (2x+5)(4x+5)

Step-by-step explanation:

Basically first you expand the expression into terms and then you refactor again.

Answer:

(4) 0

Step-by-step explanation:

Given:

Looking at the angles measures, they form series of:

This is AP with the first term of 27 and common difference of 7

We can see one of the terms of this AP is 90

Since cos 90° = 0 ⇒ cos²90° = 0 and therefore given series equals to zero as one of the terms of multiplication is zero.

So correct answer choice is  Option 4) 0

Answer:

>3 means any number on the number line larger than 3, so the answer is yes

Answer:

The number of cheese pizza sold is 200 cheese pizzas

The number of sausage pizza sold is 80 sausage pizzas

The number of pepperoni pizza sold is 120 pepperoni pizzas

Step-by-step explanation:

The price at which the pepperoni  pizza was sold is $14

The price at which the sausage pizza was sold is $11

price at which the cheese pizza was sold is $10

The total number of pizzas sold = 400

The total amount made = $4560

The number of cheese pizza sold = 80 + the number of pepperoni pizzas

Let the number of cheese pizza sold = C

The number of sausage pizza sold = S

The number of pepperoni pizza sold = P

We have;

C + S + P = 400..........................(1)

C = 80 + P...................................(2)

10·C + 11·S + 14·P = $4560.......(3)

Substituting the value for C from equation (2) in equation (1), we get;

C + S + P = 400 = 80 + P + S + P = 400

2·P + S = 400 - 80 = 320

∴ S = 320 - 2·P..........................(4)

Substituting the value for C from equation (2) and the value for S from equation (4) into equation (3), we get;

10·C + 11·S + 14·P = $4560

10·(80 + P) + 11·(320 - 2·P) + 14·P = 4560

800 + 10·P + 3,520 - 22·P + 14·P = 4560

4,320 + 2·P =  4560

2·P =  4560 - 4,320 = 240

P = 240/2 = 120

P = 120

C = 80 + P = 80 + 120 = 200

C = 200

S = 320 - 2·P = 320 - 2×120 = 320 - 240 = 80

S = 80

Therefore;

The number of cheese pizza sold = C = 200

The number of sausage pizza sold = S = 80

The number of pepperoni pizza sold = P = 120.

[tex]2 \frac{2}{7}[/tex] ÷ [tex]\frac{4}{7}[/tex]

First, let's turn the first fraction into an improper fraction.

[tex]\frac{16}{7}[/tex] ÷ [tex]\frac{4}{7}[/tex]

Since both of these fractions share the same denominator, we can drop the denominator and simply divide the numerators.

16 ÷ 4 = 4

The quotient = 4

Answer:

the answer is -2

Step-by-step explanation:

3-(-1)

= -3--1

= -3+1

= -2

Greetings from Brasil....

Let us call X the equal distances GH = HI = IJ

GH = X

HI = X

IJ = X

Note that HJ = HI + IJ, so

HJ = X + X

10 = 2X

X = 5

Looking at the figure we can conclude that:

GJ + JK = GK

GJ = GH + HI + IJ

GJ = 15

GJ + JK = GK

15 + JK = 24

JK = 9

Each length of the line segments GH = HI = IK and JK will be 5 and 9.

A line segment in mathematics has two different points on it that define its boundaries.

A line segment is sometimes referred to as a section of a path that joins two places.

GK = 24, HJ = 10, and GH = HI = IJ.

Then the length HI will be

HJ = HI + IJ

10 = HI + HI

2HI = 10

HI = 5

Then the length of the line segments GH, HI, and IJ will be

GH = HI = IJ = 5

The length of the JK will be

GK = GJ + JK

24 = 3GH + JK

24 = 3 * 5 + JK

JK = 24 - 15

JK = 9

Then each length of the line segments GH = HI = IK and JK will be 5 and 9.

More about the line segment link is given below.

https://brainly.com/question/25727583

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Answer:

1/4x + -1/2

Step-by-step explanation:

Step 1 :

-4x - 3 = -16j -5

Step 2:

-16j − 5=−4x+3

Step 3:

−16j−5+5=−4x+3+5

−16j=−4x+8

Step 3:

-16j/-16 = -4x + 8/-16

Answer:

j = 1/4x + -1/2

Answer:

9 pennies, 6 dimes, 12 quarters.

Step-by-step explanation:

Pennies = $0.01

Dimes = $0.10

Quarters = $0.25

Let x be the number of dimes. Then (x + 3) is the number of pennies and 2x is the number of quarters.

We have x($0.10) + (x + 3)($0.01) + 2x($0.25) = $3.69

x($0.10) + (x + 3)($0.01) + 2x($0.25) = $3.69

$0.1x + $0.01x + $0.03 + $0.5x = $3.69

$0.61x = $3.66

x = 6.

Therefore Bob has 9 pennies, 6 dimes and 12 quarters.

Answer:

It will be 25 cm.

Answer:

-2x(x^2+2x+3)

Step-by-step explanation:

-2x^3-4x^2-6x

You can only factor out the 2x the other part is not factorable.

The height of the flagpole is: 12 ft.

A theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Let the height of the flagpole be: x ft.

Now, we can model this problem with the help of a right angled triangle such that the hypotenuse of the triangle is: 20 feet

and one of the leg of the right triangle is: 16 feet

Now, in order to find the other leg i.e. x we need to use the Pythagorean Theorem.

[tex]20^2=x^2+16^2\\\\\\400=x^2+256\\\\\\x^2=400-256\\\\\\x^2=144\\\\\\x=\pm12[/tex]

i.e.

But the height can't be negative.

Hence, we get: x=12

To know more about Pythagorus theorem follow

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Answer:

18

Step-by-step explanation:

Answer: 56

Explanation: Add 6 to your sum every time until you get to the 10th term. It should look like this:

2

8

14

20

26

32

38

44

50

56

This is a total of 10 numbers.

Hope it helps!

Answer:

45+n = 9 (8n+5)-3n

or, 45+n = 72n+45-3n

or, 45-45=72n-4n

or, 68n=0

or, n=0

Answer:

1. rate = 171.6 feet/second

2. 1716 feet

Step-by-step explanation:

1. To convert from miles per hour to feet per second,

1 mile = 5280 feet

  117 miles = 617760 feet

  1 hour = 3600 seconds

Thus the rate in feet per second will be;

    = [tex]\frac{617760}{3600}[/tex]

    =  171.6 feet/second

2. In 10 second of free fall,

       speed = [tex]\frac{distance}{time}[/tex]

distance = speed x time

              = 171.6 feet/second x 10 second

              = 1716 feet

The parachutist would fall 1716 feet in 10 seconds of free fall.

Answer:

Assuming that m does not = 0, then the function has a non horizontal slope, so the value will increase as the position moves away from zero in either the negative or positive direction depending on whether the slope (m) is negative or positive. The furthest that the position can be from 0 is at one of the endpoints of the interval [3, 7), therefore, the maximum value of the function on the same interval must be at one of the endpoints.

Answer:

X=-3/2

Step-by-step explanation:

1/4+1/2+X=-3/4

X=-3/4-1/4-1/2

X=-3/2

Answer:

140

Step-by-step explanation:7 ft per minute; there are 60 minutes in an hour therefore 7 x 60 = 420ft in hour

there are 3 feet in yard, 420 feet divided by 3 = 240

Answer:

A because 63/4 is 15.75

Answer:

500

Step-by-step explanation:

if one side is 125 cm on a square all the sides are equal so you should multiply 125x4 which gives you 500

Answer:

[tex]\boxed{\bold{\huge{\boxed{\sf Perimeter = 500\ cm}}}}[/tex]

Step-by-step explanation:

Given that Length = 125 cm

So,

Perimeter = 4 ( 125 )

Perimeter = 500 cm

Answer:

the number which produces a given number when cubed

[tex]\frac{20.8}{9}[/tex]

Set [tex]x[/tex] to 2.31 with 1 repeating.

[tex]x=2.31...[/tex]

Now multiply the value by 10 so we can have canceling values.

[tex]10x=23.1...[/tex]

Then we can use elimination.

[tex]10x=23.1...[/tex]

[tex]x=2.31...[/tex]

[tex]9x=20.8[/tex]

[tex]x=\frac{20.8}{9}[/tex]

Hope this helps.

頑張って!

Answer:

Set  to 2.31 with 1 repeating.  

Now multiply the value by 10 so we can have canceling values.

Then we can use elimination.

Hope this helps.

Step-by-step explanation:

Answer:

Step-by-step explanation:

solution

We going to do this process in a stepwise manner

given the expression

18=6(2x – 8)

1. open bracket on the left-hand side (distributive property)

18=12x-48

2. collect like terms

18+48=12x

66=12x

3. divide both sides by 12 we have

x= 66/12

x= 33/6

x=11/2

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

So we have the equation:

[tex]4(-x+4)=12[/tex]

First, divide both sides by 4. The left side will cancel. The right will reduce to 3:

[tex](4(-x+4))/4=(12)/4\\-x+4=3[/tex]

Subtract 4 from both sides. The left cancels:

[tex]-x=-1[/tex]

Divide both sides by -1:

[tex]x=1[/tex]

So, the value of x is 1.

And we're done!

Answer:

x = 1

Step-by-step explanation:

4(-x + 4)= 12

Step 1 : Distribute

-4x + 16 = 12

Subtract 16 from both sides

-4x = -4

Divide

[tex]\frac{-4x}{-4}[/tex] = [tex]\frac{-4}{-4}[/tex]

x = 1