how many solutions does 3x+-20=4(0.5x-5) have

Answer:

Explanation:

The plastic pencil case has form of a triangular prism.

This triangular prism has five faces:

Surface area:

        area = (1/2) base × height

         area of one triangle = 10 cm × 12 cm × (1/2) = 60 cm²

          area of the two triangles = 2 × 60 cm² = 120 cm²

        area of a rectangle = length × width

         area of the trhee triangles = 24 cm × 10 cm + 2 × 24 cm × 13 cm = 240 cm² + 624 cm² = 864 cm².

Answer: first choice, 984 cm²

The two plants are 5 feet apart.

Step-by-step explanation:

Given,

Point of tomato plant = (1, 3)

Point of pepper plant = (5, 6)

Here,

[tex]x_1=1,\ \ \ \ \ y_1=3\\x_2=5,\ \ \ \ \ y_2=6[/tex]

Distance between two plants = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

[tex]Distance=\sqrt{(5-1)^2+(6-3)^2}\\Distance=\sqrt{(4)^2+(3)^2}\\Distance=\sqrt{16+9}\\Distance=\sqrt{25}\\Distance=5[/tex]

As the unit is feet, therefore,

The two plants are 5 feet apart.

Keywords: addition, points

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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:

Option B) triple the height

Step-by-step explanation:

The rest of the question is the container has a shape of the cylinder and the options to select the answer.

The options are:

A) triple the radius

B) triple the height

C) triple the diameter

D) triple the circumference

=========================================

the container has a shape of the cylinder

The volume of the cylinder is = π r² h

It is required to choose which option is suitable so change the dimensions so that the volume is tripled.

So, the volume will be V' =  ( 3 π r² h )

Check the options:

A) triple the radius

The new radius = 3r

∴ V = π (3r)² h = 9 π r² h

B) triple the height

The new height = 3h

∴ V = π r² (3h) = 3 π r² h

So, it is no need to check the other options.

The answer is option B

Note: both of option C and D will lead to the same result of option A

Answer: X=2.7

Step-by-step explanation:

25*2-8x=12x-4

50-8x = 12x-4

subtract 50 from both sides

-8x = 12x-54

subtract 12x from both sides

-20x= -54

divide both sides by -20

X=2.7

Answer:x=2/5

Step-by-step explanation:

25x2-8x=12x-4

25x2-8x-12x+4=0

25x2-20x+4=0

25x2-10x-10x+4=0

5x(5x-2)-2(5x-2)=0

(5x-2)(5x-2)=0

5x-2=0 and 5x-2=/

5x=2 and 5x=2

X=2/5

Answer:

18 miles

Step-by-step explanation:

If Daniel ran 24 miles take away the 6 more miles he ran to get 19 miles.

Distance covered by Jasmine is 18 miles when Daniel had ran 6 miles

What is an expression?

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

It is given that Daniel ran 6 miles more than Jasmine last week which means that if Daniel ran 24 miles than jasmine had ran 6 miles less then Danial that is 24 miles subtract 6 miles which comes out be 18 miles :

Distance covered by Jasmine = 24 miles - 6 miles = 18 miles in total

Therefore, Distance covered by Jasmine is 18 miles when Daniel had ran 6 miles.

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Answer:

In photomath

Step-by-step explanation:

1.) 6p-12 or 6(p-2)

2.) -4n-3

3.)-58-55b

4.) 22-41p

5.)8(3n-5) or 24n-40

6.)-2(2x+3) or -4x-6

Answer:

1) 5p - 4     2) -4n - 3   3) -55b -58   4) -41p + 22   5) 24n - 40   6) -4x - 6

Step-by-step explanation:

1) 3(2p - 4) - (p + 8)= 6p - 12 - p + 8  = 5p - 4

2) -3(n + 3) - (n - 6)= -3n - 9 - n + 6 = -4n - 3

3) -4(7 + 5b) - 5(7b + 6)= -28 - 20b - 35b - 30 = -55b -58

4) 8(2 - 5p) - (p - 6)= 16 - 40p - p + 6 = -41p + 22

5) 8(n + 2) + 8(2n - 7)= 8n + 16 + 16n - 56 = 24n - 40

6) -(6x + 4) - 2(-x + 1)= -6x - 4 + 2x - 2 = -4x - 6

Answer:

10.5

Step-by-step explanation:

84×0.75=63

63÷6=10.5

Answer:

  3 3/8

Step-by-step explanation:

We assume your intended question is ...

  "Find the actual sum of 1 3/4 + 1 5/8 to determine how much David grew in two years. Explain ..." (Proper word choice and punctuation help communication.)

The sum of the two given mixed numbers can be found several ways. One way is to write the fractions using a common denominator:

  1 3/4 + 1 5/8 = 1 6/8 + 1 5/8 = (1 +1) +(6/8 +5/8) = 2 + 11/8 = 3 3/8

David grew 3 3/8 in two years.

__

Both numbers are near and slightly more than 1.5, so their sum will be near and slightly more than 3.

Answer:

d. thirty residents who live within a 2-miles radius of Natasha’s school

Step-by-step explanation:

got it right

The valid sample for the survey would be students in Natasha’s social studies class and parents who live within a 2-mile radius of Natasha’s school.

The valid sample for the survey would be students in Natasha’s social studies class and parents who live within a 2-mile radius of Natasha’s school.

The students in Natasha's social studies class are directly affected by the speed limit in front of her school, and the parents who live nearby are likely to have an opinion on the matter as well.

While the other options may provide some insight, they are not as directly relevant to Natasha's goal of determining the neighborhood's support for lowering the speed limit.

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Let's label the number you're trying to find x. You have to set up a system of equations.

1. Five times a number can be labeled as 5x.

2. Subtracted from 20 gives us 5x-20.

3. The problem says this is the same as simply tripling the original number. So set the first equation equal to 3x.

4. 5x-20=3x

5. Move like terms onto the same side. We can do this by subtracting 3x from both sides and adding 20 to both sides.

6. 5x-3x=20

7. 2x=20

8. Divide both sides by 2 to get x by itself.

Answer: x=10

The number is 2.5.

Let the number is = x.

According to the question:

20 - 5x = 3x

Add 5x.

20 = 5x + 3x

20 = 8x

Divide by 8.

x = 20/8 = 2.5

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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:

5

(

2

x

+

7

)

Step-by-step explanation:

Answer: 5 (2x-7)

Step-by-step:

Answer:

58,608

Step-by-step explanation:

Answer:

58,608

Step-by-step explanation:

[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:

[tex]x=\frac{1}{5}[/tex]

Step-by-step explanation:

Step 1 :-

given [tex]y= \frac{-7}{5 x} -3[/tex]

substitute given y=-10

[tex]-10+3 = \frac{7}{5 x}[/tex]

[tex]-7 = \frac{-7}{5 x}[/tex]

cancelled (-7) on both sides, we get

[tex]1= \frac{1}{5 x}[/tex]

cross multiplication, we get

[tex]5 x =1[/tex]

[tex]x=\frac{1}{5}[/tex]

Final answer:- [tex]x=\frac{1}{5}[/tex]

verification:-

given [tex]y= \frac{-7}{5 x} -3[/tex]

substitute [tex]x=\frac{1}{5}[/tex]

we get y= -10

Final answer:

Using the properties of similar triangles and the given side lengths, we solve for x and find that ED equals 8 units.

Explanation:

We're dealing with a geometry problem involving parallel lines and the properties of triangles. Since sides AB and CD are parallel, and triangles ABE and DCE share a common vertex at E, we can find the length ED using similar triangles and the given side lengths. The corresponding sides of similar triangles are proportional, so:

AB / AE = CD / ED
9 / (2x + 4) = 6 / (x + 4)

To solve for x, cross multiply and obtain the equation:

9(x + 4) = 6(2x + 4)
Then solve for x:
9x + 36 = 12x + 24
3x = 12
x = 4
Having x, we can find ED:
ED = x + 4 = 4 + 4 = 8 units

Answer:

One cup of lemonade will cost $2.

Step-by-step explanation:

From simple observation and visual inspection we can conclude that one cup of lemonade costs $2.

If 9 cups of lemonade cost $18 then one cup of lemonade will cost $18÷9 = $2

If 2 cups of lemonade cost $4 then one cup of lemonade will cost $4÷2 = $2.

Therefore we can conclude that one cup of lemonade will cost $2.

Answer:

4 ft

Step-by-step explanation:

missing height = 12 - 8 = 4 ft

Answer:

The missing height = 12 - 8 = 4ft

Step-by-step explanation:

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: 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:

small boxes = 5 and large boxes = 10

Step-by-step explanation:

Given:

The volume of each small box is 7 cubic feet.

volume of each large box is 13 cubic fee.

There were twice as many large boxes shipped as small boxes shipped.

Total volume of all boxes was 165 cubic feet.

Question asked:

The number of small boxes shipped and the number of large boxes shipped?

Solution:

Let  number of small boxes shipped = x

Then, the number of large boxes shipped = 2x (given)

Total volume of all boxes = 165 cubic feet.

no. of small boxes [tex]\times[/tex] vol. of each small box +  no. of large boxes [tex]\times[/tex] vol. of each large box =  165 cubic feet. (Total volume of all boxes)

[tex]x \times7 + 2x \times 13 = 165\\7x + 26x = 165\\33x = 165[/tex]

Dividing both side by 33

[tex]x = \frac{165}{33}\\ x = 5[/tex]

The number of small boxes shipped = [tex]x[/tex] = 5

The number of large boxes shipped = 2 [tex]x[/tex] = 2[tex]\times[/tex] 5 = 10

Answer:

18

Step-by-step explanation:

Answer: 18

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

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:

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.

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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:

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]

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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Answer:

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

Answer:

20/50

Hope this helps :)

Step-by-step explanation: