What is the equation of the line with a y-intercept of -3 and slope of 2? Write the equation in slope intercept form.

Answer:

Solution point is (-1,-9)

Step-by-step explanation:

Put the value of y in the first equation into the second equation.

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Solve for y

Answer:

There are 10 wizards in the magic club.

Step-by-step explanation:

if 6/5 (or 20% more) is how many goblins in comparison to wizards, there are 120/6 or 20=1/5. 5/5 is how many wizards there are so: 5*20=100 wizards

[tex]\left\{\begin{array}{ccc}-x+5y=20\\12y=2x+60&\text{subtract 2x from both sides}\end{array}\right\\\left\{\begin{array}{ccc}-x+5y=20\\-2x+12y=60&\text{divide both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-x+5y=20\\x-6y=-30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=-10\to\boxed{y=10}\\\\\text{Put the value of y to the second equation:}\\\\x-6(10)=-30\\x-60=-30\qquad\text{add 60 to both sides}\\\boxed{x=30}\\\\Answer:\ \boxed{x=30\ and\ y=10\to(30,\ 10)}[/tex]

Answer: Student A did not correctly solve the equation because they subtracted 3c to 5c instead of added.

If order matters, then there are 12 ways to do this

If order does not matter, then there are 6 ways to do this

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

We have 4 choices for the first slot and 3 choices for the next (we can't reuse a letter) so that's where 4*3 = 12 comes from

If order doesn't matter, then something like AB is the same as BA. So we are doubly counting each possible combo. To fix this, we divide by 2: 12/2 = 6

To be more formal, you can use nPr and nCr to get 12 and 6 respectively (use n = 4 and r = 2)

In combinatorics, you can choose 2 letters from 4 (A, B, C, D) without replacement in 6 ways, according to the 'combination' principle in probability.

The subject of this question is combinatorics, a topic in Mathematics, particularly probability. You are asked to choose 2 letters without replacement from a set of 4 different letters {A, B, C, D}. To do this, we can use the formula for combinations, which is denoted as nCr, where n is the total number and r is the number being chosen. In this case, we can see it as 4C2.

To execute this, the formula is ‘n! / [r!(n-r)!]’ where '!' denotes factorial, meaning you multiply all natural number up to that number. Hence, 4C2 = 4! / [2!(4-2)!]. Factorial 4 (4!) = 4 * 3 * 2 *1 = 24. Factorial 2 (2!) is simply 2 * 1 = 2. Thus the calculation becomes 24 / [2*(2!)], simplifying to 24 / 4 which equals 6. So, there are 6 ways to choose 2 letters from 4 without replacement.

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Answer: 90 people

Step-by-step explanation:

3 ladles per person = 150 people x 3

= 450 ladles full

450 ladles full = 5 ladles per one person = 450/5 = 90 people

[tex]6d-7>11[/tex]             add 7 to both sides

[tex]6d>18[/tex]       divide both sides by 6

[tex]d>3[/tex]

Answer:

a = 2  

b = 4

Step-by-step explanation:

4x² - y² = 16  

General equation for a horizontal hyperbola:  

(x-h)²/a² - (y-k)²/b² = 1  

with center (h,k)  & vertices (h±a,k)  

Divide by the constant  

4x²/16 - y²/16 = 1  

x²/4 - y²/16 = 1  

x²/2² - y²/4² = 1  

center (h,k) = (0,0)  

a = 2  

b = 4

Answer:

a = 2  

b = 4

Hope this helps you

Answer:

Patrick earned $262.50 by mowing lawns

Step-by-step explanation:

500*0.75=375

375*.7=262.5

Answer:

$262.50

Step-by-step explanation:

It is a poorly worded question.

25 Percent of the 500 was from his birthday money.

500 * .25 = 125

That leaves 500-125 = 375

He saved 30 % of the 375 from his allowance

375 * .3 =112.50

375-112.50 =262.50

The rest is from mowing lawns.

Answer:

[tex]-13a+22[/tex]

Step-by-step explanation:

we have

[tex]2(a+5)-3(5a-4)[/tex]

step 1

Apply the distributive property  both terms

[tex]2a+2(5)-3(5a)+3(4)[/tex]

[tex]2a+10-15a+12[/tex]

step 2

Combine like terms

[tex](2a-15a)+(10+12)[/tex]

[tex](-13a)+(22)[/tex]

[tex]-13a+22[/tex]

Answer: Choice D) ordered pair is not a solution to the second equation

We can see this by replacing x and y with 1 and -4 respectively

2x + y = 4

2*1 + y = 4 .... replace x with 1

2*1 + (-4) = 4 ... replace y with -4

2 - 4 = 4

-2 = 4 .... this equation is false because -2 and 4 are different values

The last equation being false means that the original equation 2x+y = 4 is also false when (x,y) = (1,-4). Therefore, this ordered pair is not a solution to the second equation 2x+y = 4

A solution to the system must make BOTH equations true simultaneously, not just one.

Answer:

D

Step-by-step explanation:

2x + y = 4

If you substitute x = 1, and y = -4, then

2(1) - 4 = 2 - 4 = -2  not 4

Answer: We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States

Step-by-step explanation:

The mathematical expression for the given phrase "the difference of 3ab and 7bc" is 3ab - 7bc

To translate the phrase "the difference of 3ab and 7bc" into a mathematical expression, we can use the subtraction operation, which is denoted by the "-" symbol.

The difference between two terms is the result of subtracting one term from the other. In this case, we have two terms: 3ab and 7bc. To find the difference between them, we need to subtract one from the other.

The phrase "the difference of 3ab and 7bc" can be written mathematically as: 3ab - 7bc

Read more about inequality at

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Answer: 11.88

Step-by-step explanation: First You Add 8.09 then you add 3.79 Therefore your answer is 11.88

Hope This Helps You Ace Your Test

Answer:

$70.77

Step-by-step explanation:

Let  represents the total cost. We know for our problem that each yard of satin fabric costs $8.09, so  yards will cost . similarly,  each yard of cotton fabric costs $3.79, so  yards will cost . We can also infer that the total cost, , will be the sum of the yards of satin fabric and the yards of cotton fabric, so:

Now, to determine the amount that Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, we just need to replace  and  in our expression:

We can conclude that if Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, she would spend $70.77

Answer: 5 feet 5 inches

Step-by-step explanation:

2 2/3 + 2 3/4 is equal to 5 5/12 so the drapes will be 5 5/12 feet long (or 5 feet 5 inches)

Answer:

The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]            

Step-by-step explanation:

Given : Lee needed to make Drapes the length from the floor to the top of the window the wall beneath the window had the height of [tex]2\frac{2}{3}[/tex] feet and the height of just the window measured [tex]2\frac{3}{4}[/tex] feet.

To find : How long do the Drapes have to be?

Solution :

The height of the wall beneath the window is [tex]2\frac{2}{3}=\frac{8}{3}\ ft[/tex]

The height of the window is [tex]2\frac{3}{4}=\frac{11}{4}\ ft[/tex]

The total height from the floor to the top of the window is

[tex]H=\frac{8}{3}+\frac{11}{4}[/tex]

[tex]H=\frac{32+33}{12}[/tex]

[tex]H=\frac{65}{12}[/tex]

[tex]H=5\frac{5}{12}\ ft[/tex]

Therefore, The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]

Answer:

A. The cost of a bracelet without any charm is $25

Step-by-step explanation:

The initial value, or the value when x=0 is the cost of the bracelet when the number of charms is 0.

Answer:

The answer is A

Step-by-step explanation:

for one I took the test

two because as the addition of a charm grows so does the price (by 15$) But the *initial* value of a bracelet with no charms is 25$.

Answer:

Step-by-step explanation:

The awnser is -279936

Answer:

6^7 = 279936

Step-by-step explanation:

(-6) ^ 2  * (6) ^5

We can take the negative outside

(-1) ^2 (6)^2  (6)^5

When the base is the same, we can add the exponents

(-1)^2 * 6^ (2+5)

(-1)^2 6^7

Negative 1 squared is (-1)*(-1) = 1

6^7

279936

Answer:

Transformation that produces an image that is the same shape but different size is known as Dilation.

Step-by-step explanation:

There are many types of translations.

1. Rotation

2. Reflection

3. Translation

4. Dilation

We know that rotation, reflection and translation are rigid transformation. It means these transformation can not effect the size of the preimage.

Dilation represents the enlargement and compression of the figure according to the scale factor k.

If |k|>1, then it represent enlargement and if |k|<1, then it represent compression.

Therefore the transformation that produces an image that is the same shape but different size is known as Dilation.

Hello from MrBillDoesMath!

Answer:

"He plans to sell the carrots for $5 per bunch..."  is not needed

Discussion:

The question asked is "About how many bunches will the farmer make?   The text "He plans to sell the carrots for $5 per bunch..." is not needed as it does not relate to the question asked.

Regards,  

MrB

Answer:

He plans to sell the carrots for $5 per bunch is not needed and around 313 bunches can be made

Step-by-step explanation:

To find out how many days 1/3 of a packet of milk powder will last, divide 1/3 by 2 to get 1/6 of a day.

To find out how many days 1/3 of a packet of milk powder will last, we can use the information given. Kate uses 2 packets of milk powder per day. This means in one day, she uses 2 packets. So, in order to calculate how many days 1/3 of a packet will last, we need to divide 1/3 by 2. This gives us 1/6.

Therefore, 1/3 of a packet will last 1/6 of a day.

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1/3 of a packet of milk powder will last 1/6 of a day, or 4 hours, for Kate who uses 2 packets of milk powder per day.

If Kate uses 2 packets of milk powder per day, to determine how many days 1/3 of a packet of milk powder will last, you can perform a simple division. Since she uses 2 packets per day, you would divide the amount she has, 1/3 of a packet, by her daily usage, which is 2 packets. Therefore:

1/3  packets / (2 packets/day) = (1/3) / 2 days = 1/6 days

Thus, 1/3 of a packet of milk powder would last for 1/6 of a day. To determine the number of hours this represents, you can multiply 1/6 of a day by the number of hours in a day:

(1/6 day) times (24 hours/day) = 4 hours

Therefore, 1/3 of a packet of milk powder will last for 4 hours based on her current usage.

Answer:

n = - 6

Step-by-step explanation:

divide both sides by 2

n + 5 = - 1 ( subtract 5 from both sides )

n = - 6

OR

distribute the parenthesis by the 2 outside

2n + 10 = - 2 ( subtract 10 from both sides )

2n = - 12 ( divide both sides by 2 )

n = - 6

Answer: The scale factor of the dilation is C. 5/2

Step-by-step explanation:

Answer:

Paul's average speed for his bicycle trip is 12 miles/hour.

Step-by-step explanation:

Since Paul rode a total of 42 miles, we need to add up the total time it took him to complete all 42 miles.  Since her rode 1.5 hours in the morning and another 2 hours in the afternoon, he rode a total of 3.5 hours.  Speed is calculated by dividing distance by time.  Since his total distance is 42 and his total time is 3.5, we divide 42 by 3.5 to get 12.  Since our calculations included miles and hours, then our final answer would be 12 miles per hour.  

Answer:

option-B

Step-by-step explanation:

we are given system of inequality as

[tex]y\leq x^2-4[/tex]

[tex]y>2x-1[/tex]

now, we can check solution

At (0,0):

we can plug x=0 and y=0

and check inequality

[tex]0\leq 0^2-4[/tex]

[tex]0\leq -4[/tex]

so, this is FALSE

now, we can check second inequality

[tex]0>2\times 0-1[/tex]

[tex]0>-1[/tex]

So, this is TRUE

so, option-B

Answer: Hello mate!

we want to know if the pair (0,0) is a solution for the system, where the usual notation for a pair is (x,y), and the system is:

y ≤ x^2 - 4

y > 2x - 1

The first step is replacing the numbers in the system by the numbers in the pair, and look if the pair is a solution or not.

the first inequality gets:

y ≤ x^2 - 4

0 ≤ 0^2 - 4

0 ≤ - 4

This is false, so (0,0) is not a solution for this inequality.

Now let's see the second one:

y > 2x - 1

0 > 2*0 - 1

0 > -1

This is true, then the pair (0,0) is a solution for this inequality.

then the answer is the option B, the pair (0,0) is not a solution for the system, satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4.

Answer:

y =5x

Step-by-step explanation:

k = y/x  is the ratio for proportional relationships

k = 10/2

k = 5

Rewriting this equation

y= kx

y =5x

Answer: y=5x

Step-by-step explanation:

2x5=10

4x5=20

Answer: 10 dessert bowls.

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. Rewrite 1 1/4 ounces as a fraction:

[tex](4+1)/4=\frac{5}{4}[/tex]

2. You must add 5/4 ounces of strawberry preserve and 7/8 ounce of strawberry preserve, as following:

[tex]\frac{5}{4}ounces+\frac{7}{8}ounces=\frac{17}{8}ounces[/tex]

3. Now you must divide the result obtained by 1/5:

[tex]\frac{17}{8}[/tex]÷[tex]\frac{1}{5}=10.62[/tex]

4. Therefore, you can conclude that 10 dessert bowls can be completely fill.

Answer:

Very confident

Step-by-step explanation:

The closer the correlation coefficient is to 1, the stronger the correlation.  Anything above .4 is relatively strong.    So I would be very confident.

Answer:

slope = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = [tex]\frac{2}{3}[/tex] x is in this form

with slope m = [tex]\frac{2}{3}[/tex] and c = 0