A 56-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

Answer:

The answer is "in one day, Fran runs 5 miles"

Step-by-step explanation:

In order to determine the answer, I have attached an image that shows the graph of the equation. We know that "x" represents days and "y" represents miles that Fran runs.

In any function, the pairs of coordinates are represented by (x,y) that belong to the function.

So in this case, the pair (1,5) represents:

x=1

y=5

It means, in one day Fran runs 5 miles.

The number will be 7.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is given as;

'ten times the square of a non-zero number is equal to seventy times the number'

Now, Let a number = x

Then, By the given condition;

10x² = 70x

Solve the expression as;

10x² - 70x = 0

10x (x - 7) = 0

This given two condition,

10x = 0

x = 0

But the number is non zero, so x = 0 is not true.

Then, x - 7 = 0

x = 7

Thus, The number will be 7.

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Answer:

the correct answer is in the image

Step-by-step explanation:

The slope of the graph for the equation y + 9x = -6 is -9, and the y-intercept is -6, which corresponds to the point (0, -6) on the y-axis.

The equation y + 9x = -6 can be re-written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope and y-intercept from the given equation, we need to isolate y on one side. Here's how we do it step-by-step:

The slope (m) is the coefficient of x, which is -9, and the y-intercept (b) is the constant term, which is -6. Thus, the slope is -9, and the y-intercept is the point (0, -6) on the y-axis.

Answer:

Assuming that the longest blue whale on record  was about 18 scuba divers in length and a scuba diver is 6 feet length, we want to estimate the length of the whale.

Length of the whale = 18*6

You can multiply mentally by  using compensation. Substitute a number for 18 that is easy  to multiply.

20*6 = 120

Now adjust. Subtract 2 groups of 6, or 12.

120 - 12 = 108

and that is the length of the whale in feet

The ratio of quarters to pennies in Shaun's jar is 3:4, with 24 quarters and 32 pennies.

To find the ratio of quarters to pennies in the jar, we need to divide the number of quarters by the number of pennies.

Given:

Number of quarters = 24

Number of pennies = 32

The ratio of quarters to pennies can be expressed as:

[tex]\[ \text{Ratio} = \frac{\text{Number of quarters}}{\text{Number of pennies}} \][/tex]

Substitute the given values:

[tex]\[ \text{Ratio} = \frac{24}{32} \][/tex]

Now, simplify the fraction:

[tex]\[ \text{Ratio} = \frac{3}{4} \][/tex]

So, the ratio of quarters to pennies in the jar is  3:4 .

Answer:

[tex]x=\pm2[/tex]

Step-by-step explanation:

The given equation is

[tex]x^2-14=-10[/tex]

Add 14 to both sides of the equation.

[tex]x^2=-10+14\\\\x^2=4[/tex]

Now, take square root both sides. Whenever, we take square root both sides, we include plus minus sign

[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]

On simplifying, we get

[tex]x=\pm2[/tex]

Answer:

Yes, it will be interruped by the fence.

Step-by-step explanation:
I am assuming you are dealing with a 10-foot long rope. The pony is making a circle with a raidus of 10 around the center, (8,8). If we were to draw a straight line from the center to the left that was 10 feet long, it would be horizontal to the stake, and it would go to (-2,8) (8-10,-8). Since the fence lies on the y axis, which is (0,y), but the coordinate (-2,8) has an x value that is less than 0, then the pony would crash into the fence.

this also works if you go down 10 feet to (8,-2) and the fence on the x axis has the coordinate (x,0)

Without additional details such as the length of the pony's tether and the location of the fence, it's not possible to definitively answer if the pony's path will be interrupted by the fence. This question involves understanding of coordinate systems and the concept of radius in geometry.

The solution to this question depends on several factors not provided, including the length of the pony's tether and the location, shape, and size of the fence. The point (8,8) represents the pony's location in a two-dimensional coordinate system. If we know the length of the tether and the coordinates of the fence, we could then determine whether the pony's path would be interrupted by the fence.

For instance, if the pony's tether is 4 units long, then the pony can move in a circle (known as a radius) around the stake at (8, 8). If the fence is within that 4-unit radius, then the pony's path would be interrupted by the fence.

Without these additional details, we cannot provide a conclusive answer to this question. It's integral to have as much information as possible when working with coordinate systems and interpreting geometric movements and positions.

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Answer:

False

Step-by-step explanation:

I had this same assignment

she has 100

 subtract 40 for renting the room

100-40 =60

now divide 60 by 12 to find number of people

60/12 = 5

 she can invite 5 people

Answer:

1. 3/7

2. 6/11

Step-by-step explanation:

One and one half divided by one and one sixth equals 1 2/7, and three fourths divided by one and three eights equals 6/11. To solve, convert mixed numbers to improper fractions, then multiply by the reciprocal of the divisor fraction.

To find out what one and one half divided by one and one sixth is, we first need to express these mixed numbers as improper fractions. One and one half is the same as 3/2 (since 1 + 1/2 = 2/2 + 1/2 = 3/2), and one and one sixth is the same as 7/6 (since 1 + 1/6 = 6/6 + 1/6 = 7/6). When we divide fractions, we multiply by the reciprocal of the divisor. So, (3/2) / (7/6) = (3/2) * (6/7) = 9/7, or 1 2/7 when expressed as a mixed number.

Next, to divide three fourths by one and three eights, we express these numbers as improper fractions as well. Three fourths is already an improper fraction, 3/4, and one and three eights is 11/8 (since 1 + 3/8 = 8/8 + 3/8 = 11/8). Dividing these gives us (3/4) \/ (11/8) = (3/4) * (8/11) = 24/44, which simplifies to 6/11.

The total resistance for the given resistors connected in series is 2000 ohms.

To calculate the total resistance for resistors connected in series, you simply add up the individual resistances. In this case, the resistances are 650 ohm, 350 ohm, and 1000 ohm. So the total resistance would be:

Total Resistance = 650 ohm + 350 ohm + 1000 ohm = 2000 ohm

The expression for the perimeter of a rectangular field where the length is 30 more than twice its width, in terms of the width w, is 6w + 60.

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. According to the problem, the length (l) of the rectangular field is 30 more than twice its width (w). So we can express the length as l = 2w + 30.

Substituting this expression into the perimeter formula, we get:

P = 2(2w + 30) + 2w

Simplifying this expression, we get:

P = 4w + 60 + 2w = 6w + 60

So, the expression for the perimeter of the field in terms of its width w is 6w + 60, which is already in its simplest form.

Answer: 8.25 cm

Step-by-step explanation:

We know that the area of rectangle is given by :-

[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]

Given : The length of rectangle: l= 5.25 cm

The area of rectangle:[tex] A=44.625\ cm^2[/tex]

Substitute the values of A and l in the formula given above, we get

[tex]44.625=5.25\times\text{Width}[/tex]

Divide 5.25 both sides , we get

[tex]\text{Width}=\dfrac{44.625}{5.25}=8.5[/tex]

Hence , the other length of the rectangle have to be 8.25 cm.

Step-by-step explanation:

First you need to know that A=πr^2

And the equation to find the diameter is d=2r

So, the equation is d=2√A/3.14

A is 314, so 314 divided by 3.14 is 10

So all that's left is d=2*10

And the diameter is 20 feet.

The diameter of the circular pool is 20 feet.

A circle is a bounded figure which points from its center to its circumference is equidistant. The diameter is two times the value of the radius.

The first step is to determine the radius of the pool; Radius = √Area of a circle /π

Where :

√314/3.14 = 10feet

Diameter 10 x 2 = 20 feet

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