At the buffet luncheon guests could choose one meat, one side and one salad. If there were 3 different meats, 7 sides and 4 salads, how many possible combinations would there be?​

Answer:

30 is the answer because you need to multiple 4 and 6

Answer: (-1,-6)

Step-by-step explanation:

x^2+6x+3

g(x) = f(x-2)

replace all value of x in the f(x) function to (x-2)

(x-2)^2 + 6(x-2) + 34

(x-2)(x-2) + 6(x-2) + 34

expand through FOIL and distribution

x^2-4x+4+6x-12+3

combine like terms

x^2+2x-5

-b/2a = x value of vertex

-2/2(1) = x value

x value = -1

plug in -1 for all values of x in the g(x) equation to solve for y value

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

1-2-5 = -6

y = -6

x = -1

(x,y) = (-1,-6)

The vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

So, we're given that:

Thus, we get:

[tex]g(x) = f(x-2) \\g(x) = (x-2)^2 + 6(x-2) + 3 \\g(x) = x^2 -4x + 4 + 6x - 12+3\\ g(x) = x^2 + 2x -5[/tex]

Converting g(x) to vertex form:

[tex]g(x) = x^2 + 2x - 5\\g(x) = x^2 + 2x + 1 - 1 -5\\g(x) = (x+1)^2 -9\\g(x) = (x - (-1) )^2 -6\\g(x) = (x-(-1))^2 + (-6)[/tex]

Comparing this with [tex]a(x-h)^2 + k[/tex], we get (h,k) = (-1,-6) as the coordinate of the vertex of the graph of g(x), as shown below.

Thus, the vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)

Learn more about vertex form of a quadratic equation here:

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Answer:

please the question is not clear

HCF for both I believe!

Answer:

The volume is 288 ft^3

Answer:

288

Step-by-step explanation:

The formula for finding the volume is to find the side and then multiplying it by the width. (half of the base times length times width) So, you first find the area of the triangle.

9x4=36, 36/2=18.

Then, 16x18=288.

Answer:

f(x) = 8 + 0.25x

Step-by-step explanation:

The minimum cost is $8, for up to 4 pounds.

The added cost is ($0.25/oz)(x), where x is trhe ounces over 4 pounds

The total cost is the sum of these two:

f(x) = 8 + 0.25x

Answer:

204 inches

Step-by-step explanation:

First, change the 5yd2ft to be just feet.

1 yard = 3 feet

5 yd × 3ft/yd = 15 ft

15 ft + 2ft = 17ft

Next, change to inches.

1 ft = 12 inches

17ft × 12in/ft = 204 in

5 yds 2 ft = 204 in

Answer:

204 inch-

Step-by-step explanation:

 1:    change the 5yard 2ft to be just feet.

1 yrd  = 3 feet

5 yrds  × 3ft/yd = 15 ft

15 ft + 2ft = 17ft

2:     change to inches.

1 ft = 12 inch

17ft × 12in/ft = 204 in

5 yards  2 ft = 204 in

~Jax~

Answer:

Floating point(Decimal) is 0.1

Fraction is [tex]\frac{1}{10}[/tex]

10^-1 is going to be 0.1 in this case. This is because 10^-1 is the same as [tex]\frac{1}{10^1}[/tex], which is the same as [tex]\frac{1}{10}[/tex], because anything times 1 remains the same.

[tex]\frac{1}{10}[/tex] is the same as 0.1

We get a 2-in-1 answer, which is perfect for this scenario!

Hence, the correct answers are [tex]\frac{1}{10}[/tex] and 0.1

Answer:

Slope intercept form does not dictate whether or not a function is linear. What determines if a function is linear is if there is one independent variable, one dependent variable, and it makes a STRAIGHT line. This function is linear because there are only 2 variables and a horizontal line.

Levi could have determined that the graph was linear by checking the conditions stated above or graphing it out. Then, he would see that y = 2 is a straight horizontal line with an independent and dependent variable.

Hope this helps!

Answer:

$39.80

Step-by-step explanation:

just 9.95 x 4

Answer:

y= -9

Step-by-step explanation:

y+6=-3

subtract 6 from both sides

y=-9

y=-9

Hope it helps.

Do comment if you have any query.

Answer:

A. 0.58

Step-by-step explanation:

Without going too much into the proofs angle ACD is congruent to angle DBA.

If ACD is ~= DBA then

ACD = 54 degrees

Explanation:

The figure is a reflection. While orientation isnt preserved in reflections side lengths and angle measures are.

This means that both triangles have the same side length measures and have the same angle measures.

You are given the angle measures of one of the triangles. We also know both triangles are congruent since they both fit perfectly inscribed in the circle.

With this in mind you can prove that all the angles of each triangle are congruent.

Thus

ACD = 54 degrees

Answer: 1 and 2

Step-by-step explanation: 1 and 2 because if you are graphing this the formula to find the slope / the line is y = x + some number. In the formula x is how much the line goes from the x axis and the number is how much it is from the y axis. On #2 the problem is 3y = 2x + 4 so to follow the formula you need to divide both sides by 3 to get y = 2/3x + 4. For #3 you do the same thing to get y = -3/2x -5. Finally for #1 the equation is 2x + 3y = 7 so to get the slope / line you need to put x on the other side so now it is 3y = 7-2x then you divide both sides by 3 and get y = -2/3x + 7 and on 1 and 2 there x is 2/3 (the negative doesn't matter and the random number) so they are parallel.

The cell phone plan is an illustration of a linear inequality

Adrian gigabyte usage must be less than 2.1 to spend under $70.

The given parameters are:

Base cost = $59.50

Rate = $5 per gigabyte

Let the number of gigabyte be x.

So, the total amount is:

Total = 59.50 + 5x

Adrian wants to spend under $70.

So, we have:

59.50 + 5x < 70

Evaluate the like terms

5x < 10.5

Divide both sides by 5

x < 2.1

Hence, the number of gigabyte must be less than 2.1

Read more about linear inequalities at:

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Answer:

the answer is 14

Step-by-step explanation:

so first you subtract 8-  2 over 2 then =1 over 8 then subract 2 over 2

8 x 2 - 2 = 16 - 2 = 14 = 2 x 7 =  7

1 x 2  - 2  =   2   = 2   =  2 x 1  

then 1 x 2 = 2 =  7 over 1 next add 21 over 3 + 7 = 21 over 3 + 7 over 1 = 21 over 3 + 21 over 3 = 21 +21  over 3 =  42 over 3 =  3 X 14 over 3 x 1 = 14

hope this helps you have a good day

Answer:

put the cords on a chart

Step-by-step explanation:

Answer:

Slope: 50x

One point will be: (1,50)

Equation: y = 50x

Step-by-step explanation:

Answer:

The slope of the linear equation is *50

One point on the graph of the linear equation will be *(3, 150)

This linear equation can be written as *y – 150 = 50(x – 3)

Step-by-step explanation:

ttm

Answer:

23.14

Step-by-step explanation:

The semi circular region's diagram looks as if it is half of a circle, cut in half by its diameter.

So the circumference of a circle is 2πr or πd

This is half a circle, so the formula is πd/2

π9/2  =  14.137

However, that's only half of the circumference. That does not contain the diameter that is also included.

So if you add 9m to that you get 23.137

Answer:

There are five terms.

Terms in an expression contains variables and numbers. They are separated by any operators like addition and subtraction.

In this expression the terms are:

a^3,  3a^2b , -4ab, -11b and 7

As you can see, there are five terms in the expression

[tex] {n}^{2} - 11n + 10 = [/tex]

[tex](n - 1)(n - 10)[/tex]

.................................................

x y

1 16

2 12

3 8

5 0

Step-by-step explanation:

you have to substitute ever number on the X side in the equation to get the Y

for example 1 is under x so you will take

y=20-4(1)

y=20-4

y=16

The chairs in the auditorium illustrates an arithmetic sequence

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

We have the maximum number of rows to be 12.

So, the sigma notation would be:

[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

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Answer:

75%

Step-by-step explanation:

It's over 50% and it's definitely not 100%

Answer:

A

Step-by-step explanation:

You should always multiply before adding or subtracting. By saying "a product of 8 and 3," it means we multiplied them together first.

You should then add and subtract in the order in which they appear. Saying "five more" before "minus 2" means we did it in the right order.

By using the Pythagorean Theorem, we will see that the length of the missing side is 4 units.

We need to remember the Pythagorean Theorem, the sum of the squares of the cathetus is equal to the square of the hypotenuse.

In this case, the cathetus are x and 3, and the hypotenuse is 5, then we have:

x^2 + 3^2 = 5^2

x^2 = 25 - 9 = 16

x = √16 = 4

So the length of the missing side is 4 units.

If you want to learn more about right triangles, you can read:

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The file size sent in kilobytes was converted to bytes, the 4 kilobytes is equivalent to 80 bytes

Given Data

We are told that 1 kilobytes = is equivalent to 20 bytes

hence 4 kilobytes will be equivalent to x bytes

cross multiplying we have

4*20 = x

x = 80 bytes

Therefore, the file size is 80 bytes

Learn more about unit conversion here:

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Answer:

3.5

Step-by-step explanation:

The mean, or average, is calculated by adding up the scores and dividing the total by the number of scores

Answer:

H(t) = 50 - t/5

h(35)=50-35/5

=50-7

=43

h(35) = 43