given a system of equations, list three ways that we can write new equations that can be used to create equivalent systems

Answer:

y = 2

Step-by-step explanation:

When line is horizontal, all points on this line have the same value of y.

In this case , all points have to have y = 2.

y = 2, is an equation of horizontal line.

The equation of  line y = 2 represents the horizontal line passing through (-1,2).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have given a point (-1, 2) on a coordinate plane.

The distance from origin (0, 0) and (0, 2) is 2

And line y = 2 represents the horizontal line that passes through (-1, 2)

Thus, the equation of  line y = 2 represents the horizontal line passing through (-1,2).

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Answer:

She needs  15 Strawberries and 6 Oranges to make 12  servings of fruit salad

Step-by-step explanation:

Strawberries : (12 x 10)/ 8 = 15

Oranges: (12 x 4)/8 = 6

12 servings = 8 and half of 8 (8+4=12)

15 strawberries =10 and half of 10 (10+5=15)

6 oranges= 4 and half of 4(4+2=6)

Answer:

15 strawberries

6 oranges

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Answer:

2/3 is the answer

Step-by-step explanation:

Answer:

Our final answer is option B that is [tex]10x^2-42x+8[/tex]

Step-by-step explanation:

As we have to multiply the binomial.

Here is the work.

Using distributive law of multiplication.

Where [tex]a(b+c)=ab+ac[/tex]

⇒[tex](5x-1)(2x-8)[/tex]

  [tex]5x(2x-8)-1(2x-8)[/tex]

  [tex]10x^2-40x-2x+8[/tex]...     [tex](-1\times -8 =8)[/tex]

  As [tex]-40x[/tex] and [tex]-2x[/tex] are in negative so we will add these      

  numbers keeping the negative sign as it is.      

  [tex]10x^2-42x+8[/tex]

So the correct choice is option B that is [tex]10x^2-42x+8[/tex]

Answer:

Step-by-step explanation:

no but you are very close

you forgot to put the x next to the -4

because if you left it like that than it would be a horizontal line going through the y-axis at -4

the x is very important since it is the input value while y is the output

so y depends on the x

Answer:

[tex]\displaystyle YES[/tex]

Step-by-step explanation:

The equation you modeled here is [tex]\displaystyle y = -4x,[/tex]where the y-intercept and x-intercept are both located at the origin. This is what is called direct variation.

I am joyous to assist you anytime.

*Just attach the x to the equation because leaving it out would form a horizontal line [zero rate of change (slope)].

Answer:

24.5% are green

Step-by-step explanation:

Answer:

f(x)=1/2x-4.5

Step-by-step explanation:

so I used Desmos, so your starting point is -4.5 down from the 0 on the y line, then just do rise over run with 1/2 and it should pass through (1,-4)

For this case we must solve the following system of equations:

[tex]3x-3y = -3\\2x-y = -5[/tex]

To solve we follow the steps below:

We multiply the second equation by -3:

[tex]-6x + 3y = 15[/tex]

Thus, we have the equivalent system:

[tex]3x-3y = -3\\-6x + 3y = 15[/tex]

We add the equations:

[tex]3x-6x-3y + 3y = -3 + 15\\-3x = -3 + 15\\-3x = 12\\x = \frac {12} {- 3}\\x = -4[/tex]

We look for the value of the variable "y":

[tex]2 (-4) -y = -5\\-8-y = -5\\-y = -5 + 8\\-y = 3\\y = -3[/tex]

Thus, the solution of the system is given by:

[tex](x, y): (- 4, -3)[/tex]

Answer:

[tex](x, y): (- 4, -3)[/tex]

Answer:

-5/2

Step-by-step explanation:

Slope = change in y over change in x or  (y2-y1)/(x2-x1)

slope = (-13-(-3))/(6-2) = -10/4 = -5/2

Answer:

m=-5/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-13-(-3))/(6-2)

m=(-13+3)/4

m=-10/4

simplify,

m=-5/2

Answer:

Jack is five. so, it's A

Step-by-step explanation:

subtract 4 from both sides of the equation. You can cancel out the four on the left, and get 40 on the right (since you took four away from 44.)

Then, divide by 8 on both sides. The eight is canceled out on the left. eight goes into 40 five times, meaning a=5.

The correct option is (A) 5. To find Jack's age, subtract 4 from both sides of the equation 8a + 4 = 44 and then divide by 8. This results in a = 5, meaning Jack is 5 years old.

To solve the given equation, 8a + 4 = 44, for Jack's age, we first need to isolate the variable a, which represents Jack's age. This can be done by first subtracting 4 from both sides of the equation to undo the addition.

8a + 4 - 4 = 44 - 4

8a = 40

Next, we divide both sides of the equation by 8 to undo the multiplication and solve for a:

8a / 8 = 40 / 8

a = 5

Therefore, Jack's age is 5 years old, which corresponds to option A.

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

Explanation:

1/5 of the tiles are indian red

3/10 of the tiles are Tuscan blue

1/6 of the tiles are eucalyptus

x of the tiles are sand, where x is some fraction

The four fractions listed above add to 1. The "1" refers to a whole back splash, in which you can think of "1" as "100%"

-----------

We have the fractions 1/5, 3/10 and 1/6

To combine these fractions, we need a common denominator. In this case, the lowest common denominator (LCD) is 30 as this is the LCM of the denominators 5, 10, and 6.

Let's get each fraction to have a denominator of 30

1/5 = (6/6)*(1/5) = 6/30

3/10 = (3/3)*(3/10) = 9/30

1/6 = (5/5)*(1/6) = 5/30

-----------

So effectively we have these fractions: 6/30, 9/30, and 5/30

They add to the unknown fraction x to get 1

Let's solve for x.

-----------

(1/5) + (3/10) + (1/6) + x = 1

(6/30) + (9/30) + (5/30) + x = 1

(6/30 + 9/30 + 5/30) + x = 1

(6 + 9 + 5)/30 + x = 1

20/30 + x = 1

2/3 + x = 1

x + 2/3 = 1

x+2/3-2/3=1-2/3 ... subtract 2/3 from both sides

x = 1 - 2/3

x = 3/3 - 2/3

x = (3 - 2)/3

x = 1/3

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

1/3 of the tiles are the color of sand

Final answer:

One third of the tiles will be the color of sand. This is found by adding the fractions of the other colors, simplifying, and subtracting from one whole set of tiles.

Explanation:

To find the fraction of the tiles that will be the color of sand, we first need to calculate the total fraction of tiles that have already been assigned colors: Indian red, Tuscan blue, and eucalyptus. Then we subtract this total from 1, which represents the whole set of tiles, to find the remaining fraction for the sand-colored tiles.

Adding these fractions:

Now, we convert 10/15 to a simplified fraction:

To find the fraction for sand-colored tiles, subtract the total colored fraction from 1:

Therefore, one third of the tiles will be the color of sand.

a) The quantities vary directly

b) The constant of variation is 2.5

Step-by-step explanation:

Lets us revise the direct and inverse variation

∵ 16 factory workers made 40 pieces in a certain amount of time

- If the number of worker increased, then the number of pieces

   increased in the same certain time, if the number of worker

   decreased, then the number of pieces also decrease in the

   same certain time

∴ The the number of workers and the number of pieces produce

   vary directly

∴ Number of pieces produced = k × number of worker

a) The quantities vary directly

∵ The number of worker = 16

∵ The number of pieces produced = 40

- Substitute these values in the equation of variation above

∴ 40 = k × 16

- Divide both sides by 16

∴ k = 2.5

b) The constant of variation is 2.5

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Answer:

sales tax is $5.95, total price of jeans is $90.95 I believe

Answer:

1.36 or 34/25

Step-by-step explanation:

5/4=1.25

11/12=0.916

Answer:

15/13

Step-by-step explanation:

5/4 ÷  1 1/12

= 5/4 ÷  13/12

= 5/4 x 12/13

= (5 x 12) / (4x13)

= 60/52

=15/13

The 1/3 of the adult dosage of the medicine will be 60 milligrams(mg).

A fraction is a number that is less than 1.

For example, a number 0.5 than is called a fraction number because it is less than 1.

Given that the adult dosage of the medicine is 180 milligrams(mg).

The 1/3 of the 180 milligrams(mg) will be

⇒ 180×1/3

⇒ 60 hence, 60 milligrams(mg) is one-third of adult dosage.

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To find 1/3 of the adult dosage of 180 mg, you simply divide by 3, which results in a dose of 60 mg. This method ensures safe and accurate medication dosing.

If the adult dosage of the medicine is 180 milligrams (mg), then 1/3 of the adult dose can be calculated by dividing the adult dose by 3. So, you would perform the following calculation:

1/3 of 180 mg = 180 mg / 3 = 60 mg.

Therefore, 1/3 of the adult dosage of the medicine is 60 mg.

Answer:

log 5 5

= 1.

Step-by-step explanation:

Use the logarithm law  loga b - loga c = loga b/c:

log5 125 – log5 25

= log5 125 / 25

= log5 5.

= 1.

The expression log5 125 - log5 25 simplifies to 1.

To combine the logarithms log5 125 and log5 25 as one logarithm and simplify, we can use the properties of logarithms. Specifically, we'll use the property that states logb(x) - logb(y) = logb(x/y). Applying this property, we have:

log5 125 - log5 25 = log5 (125/25)

We simplify the fraction 125/25 to get 5. So, we have:

log5 (125/25) = log5 5

The logarithm of a number to the base of itself is always 1, so:

log5 5 = 1

Therefore, the expression log5 125 - log5 25 simplifies to 1.

Answer: Answer C

Step-by-step explanation:

12%___780 votes

100%___X= 6500 votes

(100*780)/12 = 6500

Answer:

To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.

To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.

Step-by-step explanation:

Mohammad will have collected T cards after m months, given that he buys 5 cards each month and he started with no cards.

The relationship describing this situation is

[tex]T=5m[/tex]

When [tex]m=6,[/tex] then [tex]T=5\cdot 6=30[/tex] cards.

When [tex]m=12,[/tex] then [tex]T=5\cdot 12=60[/tex] cards.

To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.

To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.

Answer:

50

Step-by-step explanation:

.3x=15

x=50

Answer:

The trip is 50miles far

Step-by-step explanation:

If they have travel 15miles which is equal to 30% of the trip.

To find how far the trip is.

Let x represent the trip in miles

Therefore:

30% of x is 15miles

30/100 * x = 15miles

x = 15 miles ÷ 30/100

x = 15 miles * 100/30

x = 1500miles/30

x = 50miles

Nina is correct,

Hope this helped

XD XD XD XD XD

To find the probability of at least one defective microscope in a batch of 50, we first calculate the probability of all 50 being non-defective and then subtract this from 1. The resulting probability of having at least one defective microscope in the batch is approximately 7.96%.

The question is about finding the probability that one of the first 50 microscopes manufactured by LabTech is defective. Given the probability of a microscope being defective is 0.17%, we can calculate this by multiplying the probability of a single microscope being defective by the total number of microscopes.

Firstly, convert the 0.17% to a decimal by dividing by 100, which gives us 0.0017. This is the probability of a single microscope being defective. Then, to find out the probability of at least one out of 50 being defective, we would consider the opposite - the probability of all 50 microscopes being non-defective. If one microscope has a 0.0017 chance of being defective, it has a 1-0.0017 = 0.9983 chance of being non-defective.

The chance of all 50 microscopes being non-defective is [tex](0.9983)^{50} = 0.9204.[/tex] Therefore, the probability of at least one out of 50 being defective is 1 - 0.9204 = 0.0796 or 7.96%.

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Final answer:

The probability that at least one of the first 50 microscopes manufactured is defective is calculated using the complement rule, by subtracting the probability of none being defective from 1, the answer is 0.082

Explanation:

To find the probability that at least one of the first 50 microscopes LabTech manufactures is defective, we use the complement rule. The probability that a microscope is not defective is 1 - 0.0017 (since 0.17% as a decimal is 0.0017). To find the probability that none of the microscopes out of the 50 produced are defective, we raise this to the power of 50:

P(no defective microscopes) = [tex](1 - 0.0017)^{50[/tex]

Then, to find the probability that at least one microscope is defective, we subtract this from 1:

P(at least one defective microscope) = [tex]1 - (1 - 0.0017)^{50[/tex]

P(at least one defective microscope)= 1-0.918= 0.082

Answer:

y-3=-1/5(x+6)

Step-by-step explanation:

Answer:

The surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters is[tex]1250.9 m^2[/tex]

Explanation:

Height of the conical grain storage tanks =41 m

Diameter of the conical grain storage tank=16 m

Hence radius = diameter/2=8 m

Suppose h is height and r is radius

Formula used:  

Surface area of a cone= A

A= [tex]\pi rl +\pi r^2[/tex]

= πr(l+r)

Where[tex]l =(r^2+h^2)^1^/^2[/tex]

=[tex]\pi r(r+(h^2+r^2)^1^/^2)[/tex]

Putting the values

=[tex]3.14 \times 8\left(8+\left(41^{2}+8^{2}\right)^{1 / 2}\right)[/tex]

=1250.9368

=[tex]1250.9 m^2[/tex]

[tex]1250.9 m^2[/tex] is the surface area of a conical grain storage tank

Answer:

The question is incomplete, complete question is:

What is the first term of the quotient of the following division problem?

(x^3 – 1) ÷ (x + 2)

A. –0.5

B. 1

C. x^2

D. x^4

option C

Step-by-step explanation:

(x^3-1) divide by x+2

Use long division

                x^2 -2x

             -----------------------

x+2          x^3 + 0x^2 +0x -1

               x^3 + 2x^2

             -----------------------------------(subtract it)

                     - 2x^2 +0x - 1

                     -2x^2 - 4x

            --------------------------------(subtract)

                                  5x -1

Thus the first term of the quotient is x^2.

11% of college costs was spent on books.

Step-by-step explanation:

Total cost for last semester = $2000

Amount spent on books = $220

Percent of amount spent on books = [tex]\frac{Amount\ spent\ on\ books}{Total\cost\ for\ semester}*100[/tex]

Percent of amount spent on books = [tex]\frac{220}{2000}*100\\[/tex]

Percent of amount spent on books = [tex]\frac{22000}{2000}[/tex]

Percent of amount spent on books = 11%

11% of college costs was spent on books.

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Answer:

-7

Step-by-step explanation:

j(x)=3x+(-1)

j(x)=3x-1

j(-2)=3(-2)-1

j(-2)=-6-1

j(-2)=-7

Answer:

-7

Step-by-step explanation:

plug in -2 for x

(3)(-2) = -6

and then add the -1

= -7