A rectangular field is enclosed by 600 feet of fencing. What is the length, in feet, of the field if its length is 10 feet more than its width?

Answer:

x =  15

Step-by-step explanation:

Given in the question an equation

31 = 3x - 14

Solution

rearrange the constant to the right of equation

3x = 14 + 31

3x = 45

divide 3 on both sides of the equation

3x/3 = 45/3

      x = 15

Answer:

x=15

Step-by-step explanation:

The given equation is;

31=3x-14

Group similar terms:

31+14=3x

Combine the left hand side to obtain;

45=3x

Divide both sides by 3 to get;

[tex]x=\frac{45}{3}[/tex]

x=15

209 seats were used by men and boys. i took 45% of 380 which = 171. I subtracted that by 380 which = 209.

Answer with Step-by-step explanation:

0.45 of the total seats were used by women and girls.

i.e. Remaining 0.55(1-0.45) of the total seats were used by men and boys.

Seats used by men and boys=55% of 380

                                               [tex]= \dfrac{55}{100}\times 380\\\\ =209[/tex]

Hence, Seats used by men and boys is:

209

and the fraction of total number of seats used by men and boys(0.55) is greater than that of total seats used by women and girls(0.45).

Answer:

all rectangles are square

Step-by-step explanation:

Answer:

21 articles of clothing are clean.

Step-by-step explanation:

If 2/5 clothes, or 40% of them, are dirty, then 3/5, or 60% of them are clean.

Multiply 35 by 0.60, and you get your answer.

35 x 0.60 = 21.

We can check this answer by multiplying 0.40 by 35 to get the amount of dirty clothes and adding that amount to 21, which should equal 35.

35 x 0.40 = 14

14 + 21 = 35

To find out how many articles of clothing were clean, we set up a ratio equation using the given ratio of 2 to 5. By representing the number of clean clothes with a variable and using the total count of 35 clothes, we determined that Meredith found 10 clean articles of clothing.

When Meredith cleaned her room, she found that the ratio of clean clothes to dirty clothes was 2 to 5. If there were 35 articles of clothing in total, the problem can be approached by assigning a variable to represent the number of clean clothes. Let's denote the number of clean clothes by c and the number of dirty clothes by d.

Based on the given ratio, we can write the equation as 2/5 = c/d. Since we know that c + d = 35, we can use these two equations to solve for c.

We express d in terms of c as d = 35 - c.

Substituting this into the ratio equation, we get 2/5 = c/(35 - c). Cross multiplying gives us 5c = 2(35 - c), which simplifies to 5c = 70 - 2c.

Solving for c, we add 2c to both sides to get 7c = 70. Dividing both sides by 7 gives us c = 10. Therefore, Meredith found 10 clean articles of clothing.

Answer:

-72

Step-by-step explanation:

Divide by 3 on both sides (x and -216) and you get x= -72. It's negative because the three is positive and the product is negative, so x must be negative.

Answer:

-72

Step-by-step explanation:

-72 times 3=-216

Answer:

Variance σ² having standard deviation 2.5 is 6.25.

Step-by-step explanation:

The standard deviation is basically the square root of the variance.

So, if want to find the variance of the data we simply take square of standard deviation to get the variance of data.

standard deviation = σ = 2.5

taking square on both sides

(σ)² = (2.5)²

σ² = 6.25

So, variance σ² having standard deviation 2.5 is 6.25.

Answer:

D

Step-by-step explanation:

D, because 2.5 squared is 6.25; which rounds up to 6.3

Answer:

x= -7 , y= 9

Steps:

4x+3y=-1

5x+4y=1

First, multiply the top equations by -5, and the bottom by 4 to get :

-20x-15y=5

20x+16y=4

Then, you’re going to add the two equations with them being on top of each other so you can easily see what cancels out :

-20x-15y=5

+ 20x+16y=4

———————

0+1y=9

From this, you get :

y=9

Now that you have one variable, find x by substituting 9 for y in one of the equations, I choose :

4x+3y=-1

So :

4x+3(9)=-1

Then simplify by multiplying 3 and 9 :

4x+27=-1

Then subtract 27 on each side :

4x=-28

Then, divide by 4 to get that :

x= -7

Hope this helps!!

Answer:

[tex]\large\boxed{144^\frac{3}{2}=1728}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\144^\frac{3}{2}=144^{1\frac{1}{2}}=144^{1+\frac{1}{2}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=144^1\cdot144^{\frac{1}{2}}=144\sqrt{144}=144\cdot12=1728[/tex]

Simplify using [tex]a\frac{n}{m} =\sqrt[m]{a^{n} } =\sqrt{144^{3} }[/tex]

Now, we will factor it and rewrite the radicand in exponential form:

                                  [tex]\sqrt{144^{2}*144 }[/tex]

Rewrite the expression using:

[tex]\sqrt[n]{ab} =\sqrt[n]a}*\sqrt[n]{b} =\sqrt{144^{2} } *\sqrt{144}[/tex]

Now, we will simplify the radical expression:

                        [tex]144*\sqrt{144}[/tex]

Now, factor it and rewrite the radicand in exponential form:

                       [tex]144*\sqrt{12^{2} }[/tex]

simplify the radical expression: [tex]144*12[/tex]

                                               [tex]=1728[/tex]

The expression which is equivalent to [tex]144^{\frac{3}{2} }[/tex] is 1728.

The exponential form is an easier way of writing repeated multiplication involving base and exponents. For example, we can write 5 × 5 × 5 × 5 as 54 in the exponential form, where 5 is the base and 4 is the power. In this form, the power represents the number of times we are multiplying the base by itself. 1.

2*2*3 will be its exponential form.

Hence, we have represented 243 as a product of prime given as 243=3×3×3×3×3, and in the exponential form as 243=35.

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Answer:

x = 20

Step-by-step explanation:

Adjacent angles on straight line add up to 180º

7x + (x + 20) = 180

7x + x + 20 = 180

8x + 20 = 180

8x = 160

x = 20

Two angles whose sum is 180° are called supplementary angles. The value of x is 20°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The sum of the measure of the angle will be supplementary to each other because the two angles together will be a line. Therefore, the sum will be,

7x + (x+20°) = 180°

7x + x + 20° = 180°

8x = 160°

x = 20°

Hence, the value of x is 20°.

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Answer:

9090

Step-by-step explanation:

Answer:

I = $ 90.90

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4.5%/100 = 0.045 per year,

then, solving our equation

I = 505 × 0.045 × 4 = 90.9

I = $ 90.90

The simple interest accumulated

on a principal of $ 505.00

at a rate of 4.5% per year

for 4 years is $ 90.90.

[tex]\text{Hey there!}[/tex]

[tex]\bf{\frac{2}{3}=0.6\overline{6}7}\\\\ \bf{\frac{3}{5}=0.60}[/tex]

[tex]\text{Reason: if you use a fraction pie chart and compare}\frac{2}{3} \text{to}\frac{3}{5}, \text{you'd see that}\frac{2}{3}[/tex] [tex]\text{has more shaded areas than as for}\frac{3}{5}\text{has the least amount}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

See picture

Step-by-step explanation:

The equation f(x)=x+4 becomes f(3x) = 3x +4. The graphs are attached below. The original is in red and the blue is the new function.

Answer:

7.85 m

Step-by-step explanation:

Circumference is 2πr.

The radius (r) is half of the diameter, but multiplying r by 2 is the same as just using the diameter in this formula, so:

2.5π

When you multiply you get 7.85 to the nearest hundredth.

Answer:

7.8539 m

Step-by-step explanation:

Multiply 2.5 by 3.14159

Answer:

Option B: [tex]y=log_2(x-3)[/tex]

Step-by-step explanation:

To obtain the inverse of the function [tex]y= 2^x + 3[/tex], you need to solve the equation for the variable "x":

[tex]y= 2^x + 3\\\\y-3=2^x\\\\log_2(y-3)=log_2(2^x)\\\\x=log_2(y-3)[/tex]

Now you need to exchange the variable "x" with the variable "y". Then:

[tex]y=log_2(x-3)[/tex]

Finally, you get that the inverse of the function [tex]y= 2^x + 3[/tex] is:

[tex]y=log_2(x-3)[/tex]

This matches with the option B.

120 be cause it is not a straight line

Answer:

Your picture is not clear enough.

Step-by-step explanation:

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex]It is the area of the base of the prism

h: It is the height of the prism

Substituting the values:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

Then, the volume is:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

ANswer:

60

Answer:

True ~apex

Step-by-step explanation:

a point has zero dimension

True

A point has zero dimension.

Because every open cover in the space has a refinement made up of just one open set, a point is zero-dimensional in relation to the covering dimension.

So, A point is just a position in space and has no dimensions.

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Answer:

hope it helps you!!!!!!!!!

Answer:

Volume of cylinders in terms of pie is [tex\V= 896inc^3\pi[/tex]

Step-by-step explanation:

Volume of cylinder = V = π r^2 h

where r is radius and h is height

In the given question:

r= 8 and h = 14

Putting values in the formula:

[tex]V= \pi *(8^2)*(14)\\V = \pi * 64 * 14\\V = \pi *896\\or\\ V= 896\pi[/tex]

So, Volume of cylinders in terms of pie is [tex\V= 896inc^3\pi[/tex]

Answer:

Sample Response: Gerard determined that the squares of the two smaller sides did not equal the square of the longest side. The side lengths did not create a true statement of the Pythagorean theorem.

Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

Therefore, Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

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Answer:

B

Step-by-step explanation:

Given

pitchers of grape juice=g=4

picthers of orange juice=o=6

Each pitcher contains 64 oz of juice

So in order to calculate, we will calculate the total number of pitchers and then multiply it by 64 to get total oz.

=(6+4)*64

=10*64

=640 oz

We can see that we added count of pitchers and then multiplied the sum by 64.

So option B is the correct answer ..  

I think either A or D makes more sense

Answer:

8 7/20

Step-by-step explanation:

2+5=7

3/4+3/5=15/20+12/20=1 7/20

7+1 7/20=8 7/20

Answer:

11 + 28   For sure 100 %

4     5

Step-by-step explanation:

Plz MARK BRAINLIST!!!!!!!!!!!plzzz

p

pl

ple

plea

pleas

please

the answer is { } "an empty set or phi"

Answer:

the empty set { }

Step-by-step explanation:

A ∩ C represents the intersection of sets A and C, that is the members of set A which are also members of set C.

In this case there are no common members, thus

A ∩ C = { }

Answer:

1. B

A. Not true because the peak of the data is 2

B. True because 0-2 contains the most dots on the graph and they're bunched together

C. Not true because from 2-5 there is a big gap

D. Not true because there is an outlier

Thus, B. is the answer

2. F.

1 yard = 3 feet

So, divide 6,615 by 3 to get 2,205

I hope this helps! :)

Answer:

s = ∛756

Step-by-step explanation:

The volume of a cube is found by V = s³. To solve for the side of a cube with a specific volume, we use inverse operations to find it. s = ∛V. If the volume is 756 then the s = ∛756.

Answer:

5. 24°

6. 30°

7. 49°

Step-by-step explanation:

5. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,

[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{11}{27}\\ \\\theta=\sin^{-1}\left(\dfrac{11}{27}\right)\approx 24^{\circ}[/tex]

6. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,

[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{12}{24}=\dfrac{1}{2}\\ \\\theta=\sin^{-1}\left(\dfrac{1}{2}\right)\approx 30^{\circ}[/tex]

7. You are given right triangle with known adjacent leg and hypotenuse. By the cosine definition,

[tex]\cos \theta=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{13}{20}\\ \\\theta=\cos^{-1}\left(\dfrac{13}{20}\right)\approx 49^{\circ}[/tex]

Answer:

Step-by-step explanation:

first solve for x

x-16=8

add 16 to both sides to isolate x, you now have:

x=8+16

x=24

soooo...now you have to plug in x into the other equation.

3(x+7) turns into 3(24+7)

so now we solve.

3(24+7)

3 x 31

93=x

Hope this was helpful!

The value of x in the equation x-16=8 is found to be 24. Substituting x into the expression 3(x+7) yields a final result of 93.

The equation given in this question is: x-16=8. To find the value of x, add 16 to both sides of the equation. So, x = 8 + 16, which simplifies to x = 24.

Next, to find the value of 3(x+7), you first replace the x with the value we have just found. That gives you 3(24 + 7) which equals 3(31). Multiplying this out gives the final answer, 3(31) = 93.

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Answer:

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x -----> the possible lengths of the third side

Applying the Inequality Theorem

1) 12+8 > x

20 > x

Rewrite

x < 20 in

2) 8+x > 12

x> 12-8

x > 4 in

therefore

4 in < x < 20 in

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Answer:

Step-by-step explanation:

For this, both sides added together will need to equal 180°.

So you need to set up an equation: p+28+3p=180

Now, solve for p

p+28+3p=180

    -28 .       -28

p+3p=152

combine p            (the single p counts as 1, so add it to 3p to get 4p)

4p=152

/4 .   /4

p= 38

You get p is equal to 38.

[tex]

x+1=x-1-1\Longrightarrow x+1=x-2 \\

x=x-3\Longrightarrow x\notin\mathbb{C}\Longrightarrow x=no solution

[/tex]