An equilateral triangle has a perimeter of 54 ft. What is the length of one side? Answer:____ft.​

Answer:

Step-by-step explanation:

0 solution example

3x+2y=2

3x+2y=4

This is a zero solution example, because you can see that both equations are the same on the left, yet different on the right.

Infinite solution example

3x+2y=2

4y=4-6x

This is an infinite solution example because if you look at both equations, you can see that they are exactly the same.

One solution example

2x+3y=15

x-3y=3

This is an one solution example because if you add the equations you get 3x=18 x=6

plug it in, and you get that x=6, y=1

If a system a infinite solutions, that means that the lines overlap

If a system has no solutions, that means that the lines never touch, or that they are parallel

If a system has one solution, it means that the lines intersect at one point.

A system of two linear equations in two variables can have 0, 1, or infinitely many solutions. The number of solutions can be determined without graphing by comparing the slopes and y-intercepts of the equations. If the slopes are equal and y-intercepts are different, the system has no solution. If the slopes are equal and y-intercepts are equal, the system has infinitely many solutions. If the slopes are not equal, the system has exactly one solution.

One example of a system of two linear equations in two variables with 0, 1, or infinitely many solutions is:

Equation 1: 2x + 3y = 8

Equation 2: 4x + 6y = 16

To determine the number of solutions in this system without graphing, we can use the concept of slopes. If the slopes of the two lines are equal and the y-intercepts are also equal, then the system has infinitely many solutions. If the slopes are equal but the y-intercepts are different, then the system has no solution. If the slopes are not equal, then the system has exactly one solution.

In this example, both equations have the same slope of ½; however, the y-intercepts are different. Therefore, this system has no solution.

This reveals that the two lines in the graph of this system are parallel and will never intersect.

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Answer:

5/6

Step-by-step explanation:

Multiply both sides of equation by 10/3.

d = 1/4 × 10/3

d = 10/12 = 5/6

Step-by-step explanation:

If you divide by a fraction you can write it as multiplying with the opposite of that fraction

d=1/4 / 3/10

d=1/4 × 10/3=10/12=5/6

Answer:

[tex]y=\frac{3}{20}x[/tex]

Step-by-step explanation:

We want to write an equation of the form '

[tex]y=mx+b[/tex]

Now [tex]m[/tex] is the slope of the line or 'rise/run', and it is

[tex]m=\frac{ \Delta y }{ \Delta x } =\frac{3miles}{20minutes} =\frac{3}{20}[/tex]

Now for [tex]b.[/tex]

Since at x=0 y= 0 (Aja and Emile haven't traveled any distance)

[tex]0=0+b\\b=0[/tex]

Thus we have the equation

[tex]y=\frac{3}{20}x[/tex]

Answer:

17z + 9 = 4z + 5

13z + 9 = 5 (you have to take the 4x to the opposite of the equal sign to subtract it)

13z = 5 - 9

13z = -4

z = -4/13

Exactly one solution

Answer:

Step-by-step explanation:

Total number of households were 116 million.

Hence, 100% = 116 million.

33% of the total US households owned at least one cat.

Hence, the number of household having at least one cat is [tex]\frac{33\times116}{100} = \frac{3828}{100} = 38.28[/tex] million.

It is also given that 56% of that 38.28 million households owned at least 2 cats.

Hence, the number of households having 2 cats is [tex]\frac{56\times38.28}{100} = \frac{2143.68}{100} = 21.4368[/tex] million.

To find the number of households that owned at least two cats in 2009, we need to calculate 56% of the total number of households that owned cats. We can use the information provided by The Humane Society and the US Census Bureau to calculate this number.

To find the number of households that owned at least two cats in 2009, we need to calculate 56% of the total number of households that owned cats. First, we find the number of households that owned at least one cat by calculating 33% of the total number of households. Then, we multiply this number by 56% to find the percentage of households that owned at least two cats. Finally, we multiply this percentage by the total number of households to get the final answer.

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Answer:

10.5

Step-by-step explanation:

84×0.75=63

63÷6=10.5

Answer: 3 perfect squares

Step-by-step explanation: Between the numbers, 61 and 102, there are 3 perfect squares and they are 8 x 8, 9 x 9, and 10 x 10

I have also attached a list of perfect squares and put a yellow rectangle around the perfect squares between 61 and 102.

Answer:

Therefore, Equation of line and the slope is

[tex]y=-2x[/tex]

[tex]Slope = -2[/tex]

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 ,-6)

point B( x₂ , y₂ )≡ (-1 , 2)

To Find:  

Equation of Line AB =? ( Assumption)

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,  

[tex](y-y_{1})=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})[/tex]  

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 6) and B( x₂ , y₂ )≡ (-1 , 2) we get  

[tex](y-(-6))=\dfrac{2--6}{-1-3}\times (x-3)\\\\y+6=\dfrac{8}{-4}(x-3)\\\\y+6=-2(x-3)\\y+6=-2x+6\\y=-2x[/tex] .....Required Equation of line

Which is also in the form of

[tex]y=mx[/tex] ....Also called as Equation of line Passing through Origin.

where , m =slope

Therefore, Equation of line and the slope is

[tex]y=-2x[/tex]

[tex]Slope = -2[/tex]

To find the equation of a line passing through two given points, calculate the slope using the slope formula, and then substitute the slope and one of the points into the point-slope form of a line equation. The line passing through the points (3,-6) and (-1,2) is given by the equation y = -2x + 6.

To find the equation of the line that passes through the points (3, -6) and (-1, 2), we use the formula for the slope, denoted as 'm': m = (y2 - y1) / (x2 - x1).

Then, we substitute the given pair of points into this formula to find the slope: m = (2 - -6) / (-1 - 3) = 8 / -4 = -2.

After obtaining the slope, we use the point-slope form of an equation of a line, which is y - y1 = m(x - x1). Substitute one of the given points (3, -6) and the slope -2 in: y - -6 = -2(x - 3).

Simplify this to get the final equation: y = -2x + 6.

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Answer:

6/7 of a carton

Step-by-step explanation:

3 x 2= 6

6/7

Answer:

Part 1) [tex]m\angle RNP=135^o[/tex]

Part 2) [tex]m\angle NRS=45^o[/tex]

Step-by-step explanation:

The complete question in the attached figure

step 1

Find the value of x

we know that

[tex]m\angle RNP+m\angle NRS=180^o[/tex] ----> by supplementary angles (consecutive interior angles)

substitute the given values

[tex](8x+63)^o+5x^o=180^o[/tex]

Solve for x

[tex]8x+5x=180-63\\13x=117\\x=9[/tex]

step 2

Find the measure of angle RNP

substitute the value of x

[tex]m\angle RNP=(8(9)+63)=135^o[/tex]

step 5

Find the measure of angle NRS

substitute the value of x

[tex]m\angle NRS=5(9)=45^o[/tex]

Answer:

that statement is not true

Step-by-step explanation:

64=[(96÷8)5}-42

64={(12)5} - 42

64= (60)-42

64=18

but that with subtraction. if you multiply 60 by negative 42 you get -2520 which is still not true

Answer:

-0.7

Step-by-step explanation:

-2n+1.8=3.2

-2n=3.2-1.8

-2n=1.4

n=1.4/-2

n=-0.7

Answer:

-1/3

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

Answer:

Step-by-step explanation:

Using the initial value a = 16 and the common ratio r = 1/4, we can use the equation for the sum of an infinite geometric series as |r| < 1:

S = a / (1-r)

  = 16 / (1-(1/4))

  = 16 / (3/4)

  = 64/3

The sum of the series is 64/3.

A geometric sequence is one where each phrase is discovered by multiplying the term before it by the same number.

The given series is 16 + 4 + 1 +...

Note that each term of the series is 1/4 of the preceding term, therefore, the series is a geometric series with a common ratio of r = 1/4.

The sum of an infinite geometric series is:

s= a/(1-r)

s= 16/(1-1/4)

s = 64/3

Hence, the sum of the series is 64/3.

Learn more about the geometric sequence:

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The standard form of the line is [tex]6y-x=30[/tex]

Step-by-step explanation:

The equation of the line in this problem, written in the point-slope form, is

[tex]y=\frac{1}{6}x+5[/tex] (1)

We want to rewrite it in the standard form with integers, that means in the form

[tex]ax+by=c[/tex]

where a, b and c are integer numbers.

We start by manipulating eq.(1), by multiplying both terms of the equation by 6:

[tex]6y = \frac{1}{6}x\cdot 6+5\cdot 6\\6y=x+30[/tex]

Now we subtract [tex]-x[/tex] on both sides:

[tex]6y-x = x-x+30[/tex]

So we find

[tex]6y-x=30[/tex]

Which is the standard form of the line.

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The value of f(5) is [tex]f(5)=-5[/tex]

Step-by-step explanation:

The function is [tex]f(x)=-2x+5[/tex]

To find [tex]f(5)[/tex] substitute [tex]x=5[/tex] in [tex]f(x)=-2x+5[/tex]

[tex]f(5)=-2(5)+5[/tex]

Multiplying the terms, we get,

[tex]f(5)=-10+5[/tex]

Adding the terms, we get,

[tex]f(5)=-5[/tex]

Thus, the value of [tex]f(5)[/tex] is [tex]f(5)=-5[/tex]

Answer:

Step-by-step explanation:

Let c and m represent the number of commercials and movies playing Alexa's songs, respectively.

  20c +110m = 340 . . . . . total royalties earned

  c + m = 8 . . . . . . . . . . . . total number of plays

___

Alexa's songs were played in 6 commercials and 2 movies.

Answer:

she died

Step-by-step explanation:

Answer:

48 cubes

Step-by-step explanation:

The complete question is

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2 unit. How many 1/2 unit cubes does it take to fill the prism?

step 1

Find the volume of the cube

The volume of the cube is equal to

[tex]V=b^{3}[/tex]

where

b is the length side of the cube

we have

[tex]b=\frac{1}{2}\ units[/tex]

substitute

[tex]V=(\frac{1}{2})^{3}[/tex]

[tex]V=\frac{1}{8}\ units^{3}[/tex]

step 2

To find out how many half-unit cubes are needed to fill the prism, divide the volume of the prism by the volume of the cube

[tex]6:\frac{1}{8}=48\ cubes[/tex]

Answer:

-3/4

Step-by-step explanation:

3x + 4y = 8....find the slope

in y = mx + b form, the slope can be found in the m position...so lets put this equation in y = mx + b form

3x + 4y = 8.....subtract 3x from both sides

4y = 8 - 3x.....now divide both sides by 4

y = 2 - 3/4x....rearrange

y = -3/4x + 2

y = mx + b

y = -3/4x + 2

as u can see, the number in the m position (the slope) = -3/4

The slope of the line represented by the equation 3x + 4y = 8 is -3/4.

The slope of a line can be determined from its equation in slope-intercept form, which is of the form y = mx + b. The coefficient of x, m, represents the slope of the line. In the given equation 3x + 4y = 8, we can rearrange it to the slope-intercept form by isolating y: 4y = -3x + 8, y = (-3/4)x + 2. Therefore, the slope of the line represented by this equation is -3/4.

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Answer:

The sporting goods website had 485 visitors on the first day

Step-by-step explanation:

Let's answer the question correctly, this way:

Number of visitors to a sporting goods website today = 1,940 and 400% of the visitors on the first online day

How many visitors did the website have on the first day?

Let's use the Rule of Three Simple, this way:

x = Number of visitors to a sporting goods website on the first online day

Number of visitors     Percentage

1,940                               400%

  x                                    100%

400 * x = 1,940 * 100

x = 194,000/400

x = 1,940/4 = 485

The sporting goods website had 485 visitors on the first day

[tex]g=\frac{20}{3}[/tex]

Solution:

Given expression is [tex]-3\frac{1}{3}=\frac{-1}{2}g[/tex].

To solve the given expression:

Let us first convert the mixed fraction into improper fraction.

⇒ [tex]-3\frac{1}{3}=\frac{-1}{2}g[/tex]

⇒ [tex]-\frac{(3\times 3 )+1}{3}=\frac{-1}{2}g[/tex]

⇒ [tex]-\frac{10}{3}=\frac{-1}{2}g[/tex]

Do cross multiply on both sides of the equation.

⇒ [tex]-10\times2=(-1\times3)g[/tex]

⇒ [tex]-20 = -3g[/tex]

⇒ [tex]\frac{-20}{-3}=g[/tex]

Both minus in the numerator and denominator are cancelled.

⇒ [tex]\frac{20}{3}=g[/tex]

Hence, [tex]g=\frac{20}{3}[/tex].

Answer:

Slope: [tex]-\frac{1}{2}[/tex]

Y-Intercept: [tex]-\frac{5}{2}[/tex]

Step-by-step explanation:

~Hope this helps .^.~

Answer:

18

Step-by-step explanation:

Answer: 18

Step-by-step explanation: 6 x 3 = 18

Answers:

a) [tex]\frac{A}{r}=2.5 \pi=7.85[/tex]

b) [tex]\frac{A}{r^{2}}=\pi=3.14[/tex]

Step-by-step explanation:

Assuming each grid has dimensions of 1x1, the radius of this circle is:

[tex]r=2.5[/tex]

On the other hand, the area of a circle is:

[tex]A=\pi r^{2}[/tex]

With this information we will solve this exercise:

a) [tex]\frac{A}{r}[/tex]

[tex]\frac{\pi r^{2}}{r}=\pi r[/tex]

[tex]\pi r=(3.14)(2.5)=7.85[/tex]

b) [tex]\frac{A}{r^{2}}[/tex]

[tex]\frac{\pi r^{2}}{r^{2}}=\pi=3.14[/tex]

-9x - 5 = -95

-9x = -95 + 5

-9x = -90

x = -90/-9

x = 10

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Answer:

Step-by-step explanation:

2x + y = 5.....multiply by -3

3x - 2y = 4...multiply by 2

--------------------------

-6x - 3y = -15 (result of multiplying by -3)

6x - 4y = 8 (result of multiplying by 2)

-------------------------add

-7y = - 7 <===== here is one mistake.....its -7, not 7

y = -7/-7

y = 1

now sub 1 in for y in either of ur original equations to find x

not sure why u r multiplying again on ur paper when all u have to do is sub

2x + y = 5

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

solution is : (2,1)

the bad part about elimination is if there is a mistake made in the first part, it carries through to the end. So it is always best to check ur answers.

Answer:

  1 7/33

Step-by-step explanation:

To find the fraction when the repeating digits start at the decimal point, put the repeating digits over the same number of 9s. Here, your mixed number is ...

  [tex]1.\overline{21}=1\frac{21}{99}=1\frac{7}{33}[/tex]

Answer:

I think 20/50 is the answer you're looking.

Answer:

20/50

Hope this helps :)

Step-by-step explanation:

Answer:

8/12 < 3/4

8/12 is less than 3/4.

The relation symbol that makes the comparison 8/12 _____ 3/4 true is '<', meaning 8/12 is less than 3/4.

The student is dealing with a mathematical comparison of fractions. They are asked to find a relation symbol to correctly fill the blank between 8/12 and 3/4. To determine the correct symbol, we need to first compare these fractions correctly.

Applying simplification, we can reduce 8/12 to 2/3. Now, we have a comparison between 2/3 and 3/4. In order to compare them, we can convert these fractions to similar denominators or we could convert them to decimals. Using that method we have 2/3 which equals to approximately 0.667, and 3/4 which equals to 0.75.

Since 0.75 > 0.667, the relation symbol that makes 8/12 relates to 3/4 is '<' (less than).

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