How do the 3s in 7.315 and 893.5 compare?

The value of the 3 in 7.315 is 100 times the value of the 3 in 893.5.

The value of the 3 in 7.315 is 10 times the value of the 3 in 893.5.

The value of the 3 in 7.315 is 110 the value of the 3 in 893.5.

The value of the 3 in 7.315 is 1100 the value of the 3 in 893.5.

Answer:

B and F

Step-by-step explanation:

Option A is false, there is no information whether opposite sides are parallel.

Option B is true because of following parallelogram theorem.

Parallelogram theorem: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.

Option C is false, there is no information about any angles.

Option D is false, there is no information about any angles.

Option E is false, there is no information about any angles.

Option F is true because of following parallelogram theorem.

Parallelogram theorem:  If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.

Final answer:

The expression x(y-5) - y(5-y) can be rearranged and factored into (y - 5)(x + y), which is the expression written as a product of two polynomials.

Explanation:

To write the expression x(y-5) - y(5-y) as a product of two polynomials, we first distribute the variables across each term:

x(y-5) = xy - 5x

-y(5-y) = -5y + y²

Now, combining like terms:

xy - 5x - 5y + y²

This expression can't be factored as is, since it cannot be represented by the product of two simpler polynomials with real coefficients. However, we can rearrange the terms:

(xy - 5y) + (y² - 5x) = y(x - 5) + y(y - 5)

Here we can see a common factor of (y-5):

(y - 5)(x + y)

This is the expression written as a product of two polynomials.

Answer: 29 m

Step-by-step explanation: First find the width

Since Area = Length x Width

Width = Area/Length = 232/8 = 29

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The water will last for 3 days

Solution:

Given that, village having a population of 4000, requires 150 litres of water per head per day

Let us first find the volume of tank

The tank measuring 20m x 15m x 6m

Length = 20 m

Breadth = 15 m

Height = 6 m

[tex]volume\ of\ tank = length \times breadth \times height[/tex]

[tex]Volume\ of\ tank = 20 \times 15 \times 6 = 1800[/tex]

Thus volume of tank is 1800 cubic meter

From given,

Water required per person per day = 150 liters

Therefore, water required for 4000 people per day is:

[tex]\rightarrow 4000 \times 150 = 600000 \text{ liters }[/tex]

Convert to meters

[tex]600000 \text{ liters } = 600000 \times \frac{1}{1000}\ m^3\\\\600000 \text{ liters } = 600\ m^3[/tex]

How many days will the water of this tank last?

[tex]\text{Number of days water will last } = \frac{\text{volume of tank}}{\text{total water required per day}}[/tex]

[tex]\text{Number of days water will last } = \frac{1800}{600} = 3[/tex]

Thus the water will last for 3 days

Answer:

15/11

Step-by-step explanation:

Because the GCF is 20

Hope this helps:)

Answer:

15/11

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - y1 = m(x - x1)

(1,9)...x1 = 1 and y1 = 9

slope(m) = 2

now we sub

y - 9 = 2(x - 1) <===

The point-slope equation of the line with slope 2 that passes through the point (1, 9) is y - 9 = 2(x - 1).

To find the point-slope form equation of a line with a given slope and a point, use the formula y - y1 = m(x - x1),

where (x1, y1) is the point on the line and m is the slope.

In this case, the slope is given as 2 and the point is (1,9).

Substituting these values into the point-slope form formula yields the equation y - 9 = 2(x - 1), which represents the linear relationship between x and y corresponding to the described line.

Answer:

y = 150 - 11x

Step-by-step explanation:

Janelle is starting out with 150 surveys and if she is conducting 11 surveys an hour, then that means you need to subtract 11x from 150 because that will give you how many surveys she has left.

Step-by-step explanation:

To find, an algebraic expression for the given phrase = ?

6 times the length x = 6x

and

7 inches shorter than 6 times the length x

= 6x - 7

∴ 7 inches shorter than 6 times the length x of a table in inches = 6x - 7

Hence, the required "option d) 6x – 7" is correct.

Answer:

The solution of the system is the point (-1,-2)

Step-by-step explanation:

The question is

Enter the coordinates of the solution to the system of equations

we have

[tex]y=x-1[/tex] ----> red line

[tex]y=-2x-4[/tex] ----> blue line

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs. The solution is a point that satisfy both equations

using a graphing tool

The intersection point is (-1,-2)

The intersection point satisfy both equations

therefore

The solution of the system is the point (-1,-2)

see the attached figure to better understand the problem

Answer:

4 x 11 + 3 = 47

Step-by-step explanation:

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Four times a number, n, added to 3 is 47. Then the equation is given as,

4n + 3 = 47

Simplify the equation, then we have

4n + 3 = 47

4n = 47 - 3

4n = 44

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

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The graph that represents the sale of the company is the first graph as shown attached.

In the first pie chart, each salesperson's contribution is clearly depicted as a segment of the whole pie. Joe's 25%, Cindy's 40%, and Jamie's 35% are visually represented.

Pie charts are good for showing how much of something each person sells. They help us see who sells more without needing to do hard math.

With pie charts, it's easy to understand who sells the most just by looking at the colors and sizes of the slices. They make it simple to compare how much each person sells without having to do any fancy calculations.

Answer:

The area of a the parallelogram is 88meers squared

Answer:

Therefore the final elevation of the butterfly is 4 m.

Step-by-step explanation:

i) initial elevation = 20 m

ii) change in elevation = -16m

iii) therefore final elevation = initial elevation + change in elevation

               =   20 m + (-16 m)  

              =   (20 - 16) m

               =    4 m

Therefore the final elevation of the butterfly is 4 m.

Answer:

4

Step-by-step explanation:

Answer:

The equation of the line in point slope form is equal to

[tex]y+2=(x+2)[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,-2) and (2,2)

substitute the values

[tex]m=\frac{2+2}{2+2}=1[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(x1,y1)=(-2,-2)[/tex]

substitute the values in the formula

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

Answer:

1/8

Step-by-step explanation:

Check: 12.5 * 8 = 100

Answer:

1/8 is the simplest form

Step-by-step explanation:

12.5% = 12.5/100 = 125/1000

125/125 = 1

1000/125 = 8

= 1/8

Answer:

30,240 yards

Step-by-step explanation:

6*30 in an hour

6*30*24 in a day

6*30*24*7 in a week, solve for 30240

Context?                                                                                                                      

??????????????                              

Answer:

[tex]\frac{8}{3}[/tex]

Step-by-step explanation:=

= [tex]\frac{56}{21}[/tex]  ( Divide both sides by 7)

= [tex]\frac{8}{3}[/tex]

21 is 3/8 fraction of 56.

A fraction describes a part of a whole. For example, one slice of a pizza is a fraction of the whole pizza.

Given that, what fraction of 56 is 21,

Finding the fraction, we get,

21 / 56 = 7(3) / 7(8)

= 3 / 8

Hence, 21 is 3/8 fraction of 56.

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Step-by-step explanation:

To find a improper fraction, you must multiply the denominator by the whole number, then add the numerator to the product.

6 x 8 = 48 + 1 = 49.

Our numerator for the improper fraction is 49, we keep the denominator as the same as the whole number fraction, which is 8.

Therefore, your improper fraction is 49/8.

The improper fraction equivalent of 6 1/8 is 49/8.

Given that a mixed fraction 6 1/8, we need to convert it into improper fraction,

To change a mixed number like 6 1/8 into an improper fraction, you need to convert the whole number and the fraction into a single fraction.

Step 1: Multiply the whole number by the denominator of the fraction.

6 x 8 = 48

Step 2: Add the product from Step 1 to the numerator of the fraction.

48 + 1 = 49

Step 3: Write the result from Step 2 over the original denominator.

The original denominator is 8.

Therefore, the improper fraction equivalent of 6 1/8 is 49/8.

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Answer:

13

Step-by-step explanation:

First find the number of children attending elementary school

= 1349*2

= 2698 children

Now each school can accommodate 220 children so divide the number of children by 220

=  

= 12.26 which is the closest to 13 in the options so the answer is 13

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:

Answer:

7-3n

Step-by-step explanation:

3 less than 7.................. 7-3

times a number ............ n

Together ......................... 7-3n

Answer:

2

Step-by-step explanation:

(20÷4)-3

20÷4=5

5 x -3= 2

Answer:

2

Step-by-step explanation:

20 /4=5

5-3=2

Answer:

angle measurements of 35, 35, and 110°

angle measurements of 40°, 60°, and 80°

Step-by-step explanation:

we know that

The length sides of a triangle must satisfy the Triangle Inequality Theorem and the sum of their interior angles must be equal to 180 degrees

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means, I can have more than one triangle with the same internal angles

so

Verify each description

case 1) side lengths of 6 ft, 8 ft, and 10 ft

Remember that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Applying the triangle inequality theorem

1) 6+8 > 10 ---> is true

2) 6+10 > 8 ---> is true

3) 8+10 > 6 ---> is true

therefore

The description describe only one triangle

case 2) angle measurements of 35, 35, and 110°

The sum of the interior angles is equal to 180 degrees

therefore

The description can describe more than one triangle, by similar triangles

case 3) angle measurements of 30°, 40, and 50°

The sum of the interior angles is not 180 degrees

therefore

The description is not a triangle

case 4) angle measurements of 40°, 60°, and 80°

The sum of the interior angles is equal to 180 degrees

therefore

The description can describe more than one triangle, by similar triangles

case 5) side lengths of 4 cm, 6 cm, and 9 cm

Remember that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Applying the triangle inequality theorem

1) 4+6 > 9 ---> is true

2) 4+9 > 6 ---> is true

3) 6+9 > 4 ---> is true

therefore

The description describe only one triangle

Answer:

Angle measurements of 35, 35, and 110°

Angle measurements of 40°, 60°, and 80°

Step-by-step explanation:

took a test got the answer correct

The hypotenuse length is D. 2√29

Step-by-step explanation:

Here apply the Pythagorean relationship were the sum of squares of the sides equals the square of the hypotenuse.

Mathematically,

a²+b²=c²

a=10 ,b=4 ,c=hypotenuse

10²+4²=c²

100+16=c²

116=c²

√116=c

√4*29=c

√4 *√29=c

2√29 =c

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The range of function is { -1, 1 }

Solution:

Given that, the function is:

[tex]f(x) = \frac{x^2-2}{2}[/tex]

Domain is {0, 2 }

We have to find the range of function

The domain refers to the set of possible input values

The range is the set of possible output values

Here domain is x = 0 and x = 2

Substitute x = 0 in given function

[tex]f(0) = \frac{0-2}{2}\\\\f(0) = \frac{-2}{2}\\\\f(0) = -1[/tex]

Substitute x = 2 in given function

[tex]f(2) = \frac{2^2-2}{2}\\\\f(2) = \frac{4-2}{2}\\\\f(2) = \frac{2}{2} = 1[/tex]

Thus the range of function is { -1, 1 }

Answer: Its 2

Step-by-step explanation: PEMDAS Keep.Change.Flip.

5/6×3/2=15/12=1 3/12

1 3/12+3/4(3/3)

1 3/12+9/12=1 12/12=2. BOOM!

Answer:

19 L

Step-by-step explanation:

Given that the volume (V) varies inversely with the pressure (P) then the equation relating them is

V = [tex]\frac{k}{P}[/tex] ← k is the constant of variation

To find k use the condition V = 5 when P = 304

k = VP = 5 × 304 = 1520

V = [tex]\frac{1520}{P}[/tex] ← equation of variation

When P = 80, then

V = [tex]\frac{1520}{80}[/tex] = 19 L

Answer: Step 1. Divide all terms by a (the coefficient of x2).

Step 2. Move the number term (c/a) to the right side of the equation.

Step 3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

Step-by-step explanation: