How do you solve it

By setting up a system of equations and solving it, we find that Janet has 8 five dollar bills and 12 one dollar bills in her wallet.

The student's question requires solving a system of linear equations to find out how many of each type of bill Janet has.

To solve this problem, let's use two variables: x for the number of five dollar bills and y for the number of one dollar bills.

Janet has 20 bills in total which gives us the first equation x + y = 20.

She also has a total of $52, so the value of her five dollar bills plus the value of her one dollar bills equals 52, providing us our second equation 5x + y = 52.

To solve the system of equations, we can use substitution or elimination.

Let's use substitution by expressing y from the first equation: y = 20 - x.

Now we can substitute y in the second equation with 20 - x, which after simplification gives 5x + 20 - x = 52, and then 4x = 32.

Dividing by 4 gives us x = 8.

This means Janet has 8 five dollar bills.

Now we can substitute x back into y = 20 - x to find out y, which gives us y = 20 - 8 = 12.

So, Janet has 12 one dollar bills.

Final answer:

Janet has 8 five dollar bills and 12 one dollar bills in her wallet. This was determined by setting up a system of equations and solving for the number of $5 and $1 bills based on the given total number of bills and the total cash amount.

Explanation:

To solve the problem concerning the number of $5 and $1 bills Janet has, you can set up a system of equations. Let's indicate the number of $5 bills as f and the number of $1 bills as o. We're given two pieces of information: the total number of bills is 20, and the total amount of money is $52. This can be translated into two equations:

f + o = 20 (total number of bills)

5f + o = 52 (total amount of money in dollars)

To find out how many of each bill Janet has, subtract the first equation from the second one:

5f + o - (f + o) = 52 - 20

5f - f = 52 - 20

4f = 32

f = 32 / 4

f = 8

Janet has 8 five dollar bills. To find the number of one dollar bills, subtract 8 from the total number of bills:

o = 20 - 8

o = 12

Janet has 12 one dollar bills.

To find the unit rate divide the total miles by the total hours:

225 / 4 = 56.25 miles per hour

The product of 4xy and (y^2 + 2x) is calculated by distributing 4xy to the terms in the parenthesis, resulting in the answer 4xy^3 + 8x^2y.

The question is asking to calculate the product of 4xy and (y^2 + 2x). To solve it, you can distribute 4xy to the terms inside the parenthesis. This gives you:

Therefore, the product of 4xy and (y^2 + 2x) is 4xy^3 + 8x^2y.

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Answer:

See explanation

Step-by-step explanation:

1. Draw the dotted line y=-x. This line must be dotted, because the inequality y<-x is with sign < (without notion "or equal to"). Then shade the region that contains all values of y that are less than -x (bottom part that is shaded in red on the attached diagram).

2. Draw the solid line y=x-2. This line must be solid, because the inequality y≤x-2 is with sign ≤ (with notion "or equal to"). Then shade the region that contains all values of y that are less or equal to x-2  (bottom part that is shaded in blue on the attached diagram).

3. Their common part (region that is shaded in both red and blue colors) represents both inequalities.

It's this one, just did the test.

Similar is when a figure has the same shape, but different size.

Answer: 3, 1, 2

Answer: to find f(-4)

Answer:

? = 10

Step-by-step explanation:

26 - 4 = 12 + ?

22 = 12 + ?

10 = ?

Answer:

10

Step-by-step explanation:

Let the missing number be x.

Then,

26 - 4 = 12 + x

12 + x = 22

x + 12 - 12 = 22 - 12 ( subtract 12 from both sides to single x in LHS)

x        = 10

∴ the missing number is 10.

Hope this helped you :)

Answer:

A: x > 3/4

Step-by-step explanation:

First you simplify the equation.

Simplify 1/3x

Then Simplify the left side.

1/2-x/3<x/3

Move x/3 to the left side of the equation by subtracting it from both sides.

1/2-x/3-x/3<0

Now simplify the left side.

1/2-2x/3<0

Find the LCD of the terms of the equation. In this case it's 6.

Multiply each term by 6 and simply.

3-2x<2x

Move all terms that contain a x to the left side of the inequality.

3-4x<0

Subtract 3 from both sides.

-4x<-3

Now divide each term by -4 and simplify.

This gives us our answer of x > 3/4.

Hope this helps. :)

Answer: 13/1, 195/15, 130/10

Step-by-step explanation: The easiest way to solve this problem is to work your way though each of the options. 13/1 is the original reduced by 5, 195/5 is both multiplied by 3 and 130/15 is both multiplied by 2. The other two options do not have a way to multiply or divide them to get the original number.

Answer:

Step-by-step explanation:

65/5 is reduceable to 13/1.  So is 195/15.  So is 130/10.  All of these ratios are proportional to 13/1.

Answer:

The equation in point slope form is y= 2/3x+13/3

Step-by-step explanation:

In order to find the equation you need to find the slope, to find the slope you need to graph the two points and use the rise over run method, after using this you can conclude that the slope (m) is 2/3.

To find the y intercept you should plug in one of the points into the point slope formula which is y=mx+b.

Using the first point I get the equation 5=2/3(1)+b, next you isolate the b to get the equation, -b=2/3-5

Then write all the numerators above the common denominator getting 2-15/3

With this you get -b=-13/3 and then you can divide both sides by -1 to get a positive b.

Plug all of these into y=mx+b getting y=2/3x+13/3

Answer:

0.1 repeating

Step-by-step explanation:

To write 5/45 as a decimal you have to divide numerator by the denominator of the fraction.  

We divide now 5 by 45 what we write down as 5/45 and we get 0.11111111111111  

divide 5 by 45 to find the decimal:

5 / 45 = 0.111 ( the one keeps repeating.

When a number in a decimal is repeating you put a line over it.

The answer would be 0.1 with a line over the one, which is the 3rd answer.

Answer: y = −2

Step-by-step explanation:

* Hopefully this helps:) Mark me the brainliest:)

Answer:

D

Step-by-step explanation:

(0.5, 0) and (0, -2)

Step-by-step explanation:

The prime factorization of 12 is

 12 = 2²×3

To find denominators suitable for your purpose, you need to group the factors

 {1, 2, 2, 3}

into two groups with different products that share at least one of the numbers that is not 1.

For example, your grouping could be (2, [2), 3], where a 2 is shared. That is, your denominators could be 2*2=4 and 2*3=6.

Another possible grouping is (1, [2), 2, 3], giving rise to denominators of 2 and 12.

Yet another is (1, [3), 2, 2], for denominators of 3 and 12.

Using the first grouping, a pair of mixed numbers matching your requirement might be

 1 3/4, 5 1/6

Answer:

104.65 km/hour

Step-by-step explanation:

We need to convert miles to kilometers.  The miles cancel so

65 miles         1.61 kilometers      104.65km

--------------- * -------------------   = -----------------

hour                1 mile                      hour

The speed limit is 104.65 km/hour

Answer:

79

Step-by-step explanation:

A square that has side length [tex]l=2 ft[/tex] has area [tex]2^2=4ft^2[/tex].

A circle that has a diameter 20 feet has area [tex]A=\frac{\pi d^2}{4}[/tex]

We substitute the diameter into the formula to obtain;

[tex]A=\frac{\pi \times 20^2}{4}=100\pi ft^2[/tex]

The number of squares that has area 4 feet square that can fit into a circle with area [tex]100\pi ft^2[/tex] is

[tex]=\frac{100\pi}{4}=25\pi=78.5398[/tex]

When we round to the nearest whole number; we have 79 squares.

Approximately 79 squares of size 2 ft by 2 ft can fit into a circle with a diameter of 20 feet.

To accurately determine how many 2ft by 2ft squares can fit into a circle with a diameter of 20 feet, let's perform a step-by-step calculation:

1. Calculate the area of the circle:

 [tex]\[ \text{Area of the circle} = \pi r^2 \][/tex]

  Given the diameter is 20 feet, the radius r is 10 feet:

[tex]\[ \text{Area of the circle} = \pi \times 10^2 = 100\pi \approx 314.16 \text{ square feet} \][/tex]

2. Calculate the area of one 2ft by 2ft square:

[tex]\[ \text{Area of one square} = 2 \times 2 = 4 \text{ square feet} \][/tex]

3. Calculate the theoretical maximum number of squares that can fit into the circle by dividing the area of the circle by the area of one square:

[tex]\[ \text{Theoretical number of squares} = \frac{\text{Area of the circle}}{\text{Area of one square}} = \frac{314.16}{4} \approx 78.54 \][/tex]

4. Round to the nearest whole number:

[tex]\[ \text{Rounded number of squares} = 79 \][/tex]

[tex] \cos(A) + \cos( B ) + \cos(C) \\ = 2 \cos( \frac{A + B}{2} ) \cos( \frac{ A- B}{2} ) + 1 - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2\cos( \frac{\pi - C}{2} ) \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}] \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A + B}{2} )] \\ = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2} +\frac{A - B}{2} }{2} ) \sin( \frac{ \frac{A + B}{2} - \frac{A - B}{2} }{2} ) \\ = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}[/tex]

Answer:

Step-by-step explanation:

A. 250 x .32 = 80

B. 250 x .44 = 110 So, the answer is berries.

Final answer:

Out of 250 surveyed individuals, 80 people prefer peaches. Berries are the preferred choice of more than 100 people.

Explanation:

A total of 250 people were surveyed about their favorite fruit. To find out how many people prefer peaches, we calculate 32% of 250 people. This calculation is done by multiplying the total number of people by the percentage of those who prefer peaches:

250 people x 32% = 250 x 0.32 = 80 people

Therefore, 80 people prefer peaches.

To determine which type of fruit more than 100 people prefer, we apply the same calculation method. Here are the calculations:

Berries: 250 x 44% = 110 people

Peaches: 250 x 32% = 80 people

Cherries: 250 x 24% = 60 people

More than 100 people prefer berries.

Answer:

The volume of the rectangular prism is [tex]V=442.341\ cm^{3}[/tex]

The surface area of the rectangular prism is [tex]SA=384.62\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

substitute the values

[tex]V=(12.7)(8.1)(4.3)=442.341\ cm^{3}[/tex]

The surface area of the rectangular prism is equal to the area of its six faces

so

[tex]SA=2(8.1)(4.3)+2(12.7)(8.1)+2(12.7)(4.3)=384.62\ cm^{2}[/tex]

20; 3g*h. Hd. So, adding in the. Variables. Then 20

Answer:B) 10$

Usatestprep

Answer:

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (0, 4) and (-2, -2). Substitute:

[tex]m=\dfrac{-2-4}{-2-0}=\dfrac{-6}{-2}=3[/tex]

Answer:

-3

Step-by-step explanation:

Answer:

y=2x+(-7)

Step-by-step explanation:

y=2x+c

solve for c

-1=2(3)+c

-1=6+c

-6-1=c

c=-7

y=2x+(-7)

Answer:

[tex]\large\boxed{y+1=2(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the slope m = 2 and the point (3, -1). Substitute:

[tex]y-(-1)=2(x-3)\\\\y+1=2(x-3)[/tex]

Answer:

B

Step-by-step explanation:

The volume (V) of a rectangular prism is

V = lbh

where l is the length, b the width and h the height

We are looking for 3 values that multiply together to give 10

Considering each of the options

A

100 × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 25 ≠ 10

B

10 × [tex]\frac{1}{2}[/tex] × 2 = 10

C

5 × 2[tex]\frac{1}{2}[/tex] × 2[tex]\frac{1}{2}[/tex] = 31.25 ≠ 10

D

10 × 10 × [tex]\frac{1}{2}[/tex] = 50 ≠ 10

B is the only possible dimensions for the prism

Answer:

81

Step-by-step explanation:

To evaluate substitute x = - 2 into the expression

4( - 2)² - 20(- 2) + 25

= (4 × 4) + 40 + 25 = 16 + 40 + 25 = 81

Answer:

1,2, and 5

Step-by-step explanation:

This can be determined by looking at the graph

Answer:

The correct answer would be "Animals with shells and fish appeared on earth before land plants." and "Humans were the last to appear at this site."

Step-by-step explanation:

On the graph, it shows that the land plants were a little further ahead in time from the shelled animals and the fish, And the humans were shown last, even after the plants.

I think it is the first.I would choose that.

Answer:

9/6 and 3/2

Step-by-step explanation:

Let's remember the definition of "constant of proportionality":

The constant of proportionality is the constant value of the ratio k of two proportional quantities x and y; usually written y = kx.

In our case, x is the cups of milk and y is the cups of pancake mix. We need to find out k.

9 = k*6

9/6 = k

If we simplified the fraction, we have 3/2 (is equivalent to 9/6).

The correct answers are 3/2 and 9/6.

Answer:

small and gaseous.

It would be A small and rocky and the planets names are Mercury, Venus, Earth, and Mars

Answer:

4/6, 6/9, 8/12, 10/15

A fraction that is equivalent to [tex]\frac{2}{3}[/tex] is [tex]\frac{20}{30}[/tex]

Although these fractions have different numerators and denominators, they still have the same value because they equal each other.

Answer:

 2.1125 feet

Step-by-step explanation:

the vertex will be the maximum value of this parabola.  

the general form for a quadratic equation is:  ax² + bx + c, for this equation,

a = -0.2, b = 1.3, and c = 0

find the vertex by first using the formula x = -b/(2a)

x = -1.3/(2*-0.2)

  x = -1.3/-0.4

    x = 3.25

Now plug in that x value to find the actual maximum height

y = -0.2(3.25)² + 1.3(3.25)

    y = -0.2(10.5625) + 4.225

          y = -2.1125 + 4.225

                  y = 2.1125 feet

The maximum height the mouse can jump is approximately 2.1125 feet.

To find the maximum height the mouse can jump, you need to determine the vertex of the parabolic path because the vertex represents the highest point on the path. The equation of the path is given as:

y = -0.2x^2 + 1.3x

To find the vertex, you can use the formula:

x_vertex = -b / (2a)

Where "a" is the coefficient of the x^2 term, and "b" is the coefficient of the x term in the equation.

In your equation, a = -0.2 and b = 1.3. Plug these values into the formula:

x_vertex = -1.3 / (2 * (-0.2))

x_vertex = -1.3 / (-0.4)

x_vertex = 3.25

Now that you have the x-coordinate of the vertex, you can find the corresponding y-coordinate by plugging it back into the equation:

y = -0.2x^2 + 1.3x

y_vertex = -0.2(3.25)^2 + 1.3(3.25)

Calculate:

y_vertex = -0.2(10.5625) + 4.225

y_vertex = -2.1125 + 4.225

y_vertex = 2.1125

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