Use the distributive property to write an equivalent expression: 4(x -3)

Answer: 42 nickles 19 quarters

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Camille has 42nickels and 19 quarters.

The price depends on how much amount of product one has/consumes.

Let, Camille has 'y' no. of nickels.

Therefore, she has (61-y) no. of quarters.

We know that,

1 nickel = 5cents

1 quarter =25 cents

$6.85 = 685cents (as 1 dollar = 100cents)

now,

5*y+25*(61-y)=685

or,5y-25y=685-1525

or, 20y = 840

or, y= 42

Therefore, Camille has 42 nickels and (62-41)=19 quarters.

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Answer:

The numbers are 12 and 32.

Step-by-step explanation:

x = One number

x - 20 = Another number

3x - (x - 20) = 84 (If the lesser number is subtracted from three times the greater number, the difference is 84)

Let's solve for x, this way:

3x - (x - 20) = 84

3x - x + 20 = 84

2x = 84 - 20 (Subtracting 20 at both sides)

2x = 64

x = 64/2

x = 32 ⇒ x - 20 = 12

For the given problem, by denoting the lesser number as 'x', we can form and solve an algebraic equation to find 'x=12' and 'x+20=32', which are the lesser and the greater numbers respectively.

This problem involves the concepts of algebraic equations. Let's denote the lesser number as 'x'. Therefore, the greater number becomes 'x+20' because it is 20 more than the lesser number. The problem states that three times the greater number subtracted by the lesser number is 84. So, we can translate that into the equation: 3*(x+20) - x = 84.

Solving this equation we get: 3x + 60 - x = 84, which simplifies further to 2x + 60 = 84. Deducting 60 from both sides gives 2x = 24. Finally, dividing by 2 gives x = 12 which is the lesser number. So the greater number becomes x + 20 = 12 + 20 = 32.

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Step-by-step explanation:

8/100(8 over 100)×16000=1280

1280+16000=17280

Answer:

$21,767.82

Step-by-step explanation:

48 months = 48/12 = 4 years

16000 × (1 + 8%)⁴

16000 × 1.08⁴

= 21,767.82336

Answer:

Sam

Step-by-step explanation:

Sam: Longest ski trail >3x    x = shortest ski trail

Eli: Longest ski train< 3x

Sam is correct because the longest ski trail has to be greater than the shortest and it can't be less than.

Answer:

D

Step-by-step explanation:

Given

C = 2πr ( isolate r by dividing both sides by 2π )

[tex]\frac{C}{2\pi }[/tex] = r → D

The circumference of a circle is defined as the distance around the circle.

The formula that represents r in terms of C is r =  C/ 2π. The correct option is Option D

From the question, we are given the formula for the circumference of the circle C as :

C = 2πr

To represent in terms of C,

2πr = C

Divide both sides by 2π

2πr/2π = C/ 2π

r =  C/ 2π

Therefore,  the formula that represents r in terms of C is r =  C/ 2π. The correct option is Option D

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Answer:

12

Step-by-step explanation:

3X4=12

Answer:

8 tablespoons

Step-by-step explanation:

its is 8 because 4 teaspoons per dozen and there are 6 dozens so 4 times 6 is 24, then 24 divided by 3 because thats how many teaspoons are in 1 tablespoon so its 8 tablespoons

Answer:

Perimeter: 16 centimeters

Area: 15 square centimeters

I hope this helps! :)

Answer:

Step-by-step explanation:

so, the perimeter is 5+5+3+3 which is 16

and  the area is 5 x 3 so it is 15

Answer:

True

Step-by-step explanation:

Answer: True

Step-by-step explanation:

In electromagnetic waves, the more the work, the greater the energy expended.

Answer:

C) 3, 4, 5

Step-by-step explanation:

5² = 3² + 4²

25 = 9 + 16

25 = 25

Answer:

20

Step-by-step explanation:

To get the answer, you have to find what number 15 is 75 percent of.

Answer:

[tex]946.4\ m[/tex]

Step-by-step explanation:

Let

h(t) ---> the height of an object in meters

t ----> the time in seconds

we have

[tex]h(t)=-2.6t^2+40t+800[/tex]

For t=6 sec

substitute in the quadratic equation  the value of t and solve for h

[tex]h(6)=-2.6(6)^2+40(6)+800[/tex]

[tex]h(6)=946.4\ m[/tex]

Answer:

[tex] {(x + 3)}^{2} = 16[/tex]

Step-by-step explanation:

The given equation is

[tex] {x}^{2} + 6x - 7 = 0[/tex]

To find the equation that has the same solution, we complete the square.

Add the square of half the coefficient of x to both sides

[tex] {x}^{2} + 6x + {3}^{2} = {3}^{2} + 7 [/tex]

This becomes:

[tex] {x}^{2} + 6x + 9 = 9 + 7 [/tex]

Factor the first three terms to get a perfect square;

[tex]{(x + 3)}^{2} = 16[/tex]

The correct answer is C

The equation c. (x+3)^2=16 has the same solutions as the given equation x^2+6x−7=0.

The equation that has the same solutions as the given equation x^2+6x−7=0 is c. (x+3)^2=16.

Therefore, the equation (x+3)^2=16 has the same solutions as the given equation x^2+6x−7=0.

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Answer:

The tenth term is

[tex] \frac{1}{20} [/tex]

Step-by-step explanation:

The 3rd term of an AP is 1/16.

This implies that:

[tex]a + 2d = \frac{5}{16} - - - (1)[/tex]

The 6th term of an AP is 1/5.

This means that:

[tex]a + 5d = \frac{1}{5} - - - (2)[/tex]

Subtract equation 1 from equation 2.

[tex]5d - 2d = \frac{1}{5} - \frac{5}{16} [/tex]

[tex]3d = - \frac{9}{80} \\ \implies \: d = - \frac{3}{80} [/tex]

From equation (1)

[tex]a + 2( - \frac{3}{80} )= \frac{5}{16} \\ a - \frac{3}{40} = \frac{5}{16} \\ a = \frac{5}{16} + \frac{3}{40} \\ a = \frac{31}{80} [/tex]

The tenth term is:

[tex]a + 9d = \frac{31}{80} + 9( - \frac{3}{80} ) \\ = \frac{31}{80} - \frac{27}{80} = \frac{4}{80} = \frac{1}{20} [/tex]

Answer:

1/26

Step-by-step explanation:

the probably is 1/26 becasue there is 26 letter in the alphabet

Step-by-step explanation:

[tex]area \: of \: rectangle \: = 60 \: {yards}^{2} \\ \therefore \: (w + 4) \times \: w = 60\\ \\ \therefore \: {w}^{2} + 4w -60 = 0 \\ \\ \therefore \: {w}^{2} + 10w - 6w -60 = 0 \\ \\ \therefore \: w({w} + 10) - 6(w + 10)= 0 \\ \\ \therefore \: ({w} + 10) (w- 6)= 0 \\ \therefore \: {w} + 10 = 0 \: or \: w- 6 = 0 \\ \therefore \: {w} = - 10 \: or \: w = 6 \\ \because \: sides \: of \: rectangle \: cant \: be \: negative \\ \therefore \: w \neq \: - 10 \\ \\ \therefore \: w = 6 \\ \\ \therefore \: w + 4 = 6 + 4 = 10 \\ \\ length \: of \: rectangle \: = 10 \: yards.[/tex]

The length of a rectangle is 10 yards, and its width is 6 yards. The rectangle's area is 60 square yards. The length is 4 yards more than the width.

Let's call the width of the rectangle "W" in yards. According to the information given, the length of the rectangle is 4 more than the width, so the length can be represented as "W + 4" yards.

The formula for the area (A) of a rectangle is:

A = Length × Width

In this case, we know that the area is 60 square yards, so we can set up the equation:

60 = (W + 4) × W

Now, we can solve for the width (W). First, expand the equation:

60 = W^2 + 4W

Next, rearrange the equation to set it equal to zero:

W^2 + 4W - 60 = 0

Now, we can solve this quadratic equation for W. You can do this by factoring, completing the square, or using the quadratic formula. In this case, I'll use the quadratic formula:

W = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = 4, and c = -60. Plug these values into the formula:

W = (-4 ± √(4^2 - 4 * 1 * (-60))) / (2 * 1)

W = (-4 ± √(16 + 240)) / 2

W = (-4 ± √256) / 2

W = (-4 ± 16) / 2

Now, you have two potential solutions for W:

1. W = (-4 + 16) / 2 = 12/2 = 6

2. W = (-4 - 16) / 2 = -20/2 = -10

Since the width of the rectangle cannot be negative, we take the positive value, which is W = 6 yards.

Now that we know the width, we can find the length, which is W + 4:

Length = 6 + 4 = 10 yards

So, the length of the rectangle is 10 yards.

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Answer:

40°  

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

2q+y+5

Step-by-step explanation:

Simplify the expression

Answer:

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Step-by-step explanation:

The following are the formulas used to find the area and the perimeter of a rectangle:

Area = L · W

Perimeter = L + L + W + W

If you group common variables, you can simplify the formula used to find the perimeter down to:

Perimeter = L + L + W + W

Perimeter = 2L + 2W (Since you're adding 2 of each)

Using these formulas, we can insert our values into them. We know that the rectangle has an area of 56 square inches meaning:

L · W = 56

We know that the rectangle has a perimeter of 36 inches meaning:

2L + 2W = 36

Answer:

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Step-by-step explanation:

Answer:

37.70 feet

Step-by-step explanation:

-The radius of each tire is given as 6 feet.

-Distance around each tire is equivalent to the circumference of each tire.

#Circumference is calculated as:

[tex]C=\pi D=2\pi r\\\\=2\pi \times 6 \\\\=12\pi\\\\=37.70\ feet[/tex]

Hence, the distance around each tire is 37.70 feet

Answer:

18 square feet

Step-by-step explanation:

the table was most likely 6 by 6 before getting cut. that is an area of 36 you could half that making 18 or make one of the 6s a 3 so it is 3 by 6 after the table is cut.

Answer:

x=4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helps!!! Brainliest is appreciated.

x−3=−x+5

Add x to both sides.

x−3+x=−x+5+x

2x−3=5

Add 3 to both sides.

2x−3+3=5+3

2x=8

Divide both sides by 2.

2x /2 = 8 /2

x= 4

Answer:

y = 6,x = 2

Step-by-step explanation:

Answer:y = 6,x = 2

Step-by-step explanation:Geometric figure: Straight Line

 Slope = -6.000/2.000 = -3.000

 x-intercept = 6/3 = 2

 y-intercept = 6/1 = 6.00000

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    12*x+4*y-(24)=0

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  12x + 4y - 24  =   4 • (3x + y - 6)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   3x+y-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x+y-6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 6/1 so this line "cuts" the y axis at y= 6.00000

 y-intercept = 6/1  =  6.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000

 x-intercept = 6/3  =  2

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 6.000 and for x=2.000, the value of y is -0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.000 - 6.000 = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -6.000/2.000 = -3.000

Geometric figure: Straight Line

 Slope = -6.000/2.000 = -3.000

 x-intercept = 6/3 = 2

 y-intercept = 6/1 = 6.00000

Answer:

y = 7/3 x + 2

Step-by-step explanation:

y = mx+b is the slope intercept form of a line

where m is the slope and b is the y intercept

Substituting in what we know

y = 7/3 x + 2

Answer: 100

Step-by-step explanation:

4b squared where b= 5

Slot in 5 for b; 5 squared = 5x5= 25

4 (25)

=100

Answer:

100

Step-by-step explanation:

First we remove the b and put 5 in its place because that what the instructions say b stands for

4*5^2

We do PEMDAS to figure out what to do first, we do the exponent

5^2 or 5*5= 25

Now we do 4 * 25

4*25 =100

arc ABC = 4π[tex]\frac{134}{180}[/tex]

Step-by-step explanation:

Given,

∠BOA = 51° and ∠AOC=83°

We take O as the center

So, ∠BOC = 51°+83° = 134°

To find the arc ABC

Formula,

The relation between arc and radius is, s = rθ where s be the arc and θ be the angle measured in radian]

θ degree = θΠ×[tex]\frac{1}{180}[/tex] in radian

Hence,

arc ABC = 4π[tex]\frac{134}{180}[/tex]

Answer: 48 vegetables

Step-by-step explanation:

30 vegetables

Increase is by 60% = 0.6 x 30= 18

30+18= 48 vegetables

Answer:

48

Step-by-step explanation:

30 x 60% (.60) = 18.

30 + 18 = 48

Answer:

Option D, 7xy^5 + 2y^2 - 10

Step-by-step explanation:

Step 1:  Pull out 3xy from all of the top

[tex]\frac{3xy(7xy^5+2y^2-10)}{3xy}[/tex]

The 3xy on top and the 3xy cancel to make:  7xy^5 + 2y^2 - 10

Answer:  Option D, 7xy^5 + 2y^2 - 10