Expand the following expression.

5.9(21 - 3.54x)
A.
123.9x - 20.886
B.
26.9 - 9.44x
C.
20.886 + 123.9x
D.
123.9 - 20.886x

After the orchestra completed its program, there was a party to allow the patrons to mingle with the  musicians. Kayla’s Catering provided the food, drinks, and service for the party. There were two  hundred seven guests. Kayla charges $27.00 per guest for food and $10.00 per guest for drinks. To  that she adds $4.98 per guest for service. What was Kayla's total bill for catering the party?

The total bill for catering the party is $ 8689.86

Kayla’s Catering provided the food, drinks, and service for the party

Total number of guests = 207

Charge for food for 1 guest = $ 27

Charge for drink for 1 guest = $ 10

Charge for service for 1 guest = $ 4.98

To find: Kayla total bill for cater

Total bill = Total number of guests(Charge for food for 1 guest + Charge for drink for 1 guest + Charge for service for 1 guest)

[tex]Total\ bill = 207(27+10+4.98)\\\\Total\ bill = 207(37 + 4.98)\\\\Total\ bill = 207 \times 41.98\\\\Total\ bill = 8689.86[/tex]

Thus total bill for catering the party is $ 8689.86

The number of teachers required for the 425 students that enrolled at the school is 25.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

At Elmwood Middle School there are 4 teachers for every 68 students.

There are 425 students enrolled at the school.

Let the number of teachers be x required for the 425 students will be

[tex]\rm \dfrac{x}{4} = \dfrac{425}{68}\\\\x \ = \dfrac{425*4}{68}\\\\x \ = 25[/tex]

The number of teachers required for the 425 students that enrolled at the school is 25.

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Approximately 25 teachers are needed at Elmwood Middle School. So the correct option is c) 25.

To find out how many teachers are needed at Elmwood Middle School, we can set up a proportion using the given ratio of teachers to students.

Given:

- There are 4 teachers for every 68 students.

Let's set up the proportion:

[tex]\[\frac{\text{Number of teachers}}{\text{Number of students}} = \frac{4}{68}\][/tex]

We know there are 425 students enrolled at the school, so let's find out how many teachers are needed:

[tex]\[\text{Number of teachers} = \frac{4}{68} \times 425\][/tex]

[tex]\[\text{Number of teachers} = \frac{4 \times 425}{68}\][/tex]

[tex]\[\text{Number of teachers} = \frac{1700}{68}\][/tex]

[tex]\[\text{Number of teachers} \approx 25\][/tex]

So, approximately 25 teachers are needed at Elmwood Middle School.

Therefore, the answer is option C. 25.

The complete question is:

At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed? A. 17 B. 21 C. 25 D. 28

Answer:

3k+5a=45

Step-by-step explanation:

It says write an equation. It doesn't specify that you have to solve. That means you can use variables like (k) and (a).

That allows for more flexibility and the equation 3k+5a=45.

3k means that 3 dollars per ticket times (k) tickets equals the total price for kid's tickets

5a means that 5 dollars per ticket times (a) tickets equals the total price for adult's tickets

The equation to represent the cost based on the combination of kids' and adult tickets purchased by Larry is 3k + 5a = 45, where k represents the kids' tickets and a represents the adult tickets.

The problem can be translated into a simple algebraic equation where the number of kids' tickets (k) and the number of adult tickets (a) are the variables. Given the cost per ticket for each category (kids at $3 and adults at $5), we can define a equation where 3k + 5a = 45. This equation represents the cost distribution of the ten tickets that Larry purchased for the state fair, 3 multiplied by the number of kids' tickets plus 5 multiplied by the number of adult tickets.

Therefore, if Larry knows how many of each ticket he bought, he can insert the values for k and a into the equation to see if it equals to 45, the total amount of money he spent.

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y=-2/3x+5

Step-by-step explanation:

From the scattered plot, it is evident that the line of best fit will have a negative slope from the way the plots are aligned.

Selecting the line of best fit that will cut the y axis at +5, the points can be estimated as;

(5,1.5) and (3.5,2.5)

The slope can be found as;

m=Δy/Δx

m=2.5-1.5/3.5-5 =1.0/ -1.5 = -0.67

Finding the equation as;

m=Δy/Δx

-0.66 = y-2.5/x-3.5

-0.66(x-3.5) = y-2.5

-0.66x+2.3=y-2.5

-0.66x+2.3+2.5=y

-0.66x+4.7=y

⇒⇒  y= -0.66 x + 4.7

⇒⇒y= -2/3 x + 5

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Answer:

  A.  ∠ABC ≅ ∠DBE

Step-by-step explanation:

The whole proof is not shown, but in order to show the triangles similar, one would need to (a) show the sides are proportional, and (b) show the included angle is the same. The portion of the proof that is shown is on the way to showing side lengths are proportional. The missing part for showing triangle similarity is the congruence statement for angle B, as shown above.

__

Once the triangles are shown to be similar, additional work is needed to show DE║AC. At least one pair of corresponding "base" angles must be shown congruent, too.

Answer:

(x+7)/7 =y

Step-by-step explanation:

The first step is to switch the variables

x=7y-10

Add the 10 to both sides

x=7y-10

+10  +10

x+10=7y

Divide both sides by 7

(x+7)/7 =y

Answer:

the inverse function is (x + 10)/7

Step-by-step explanation:

y=7x-10

7x = y + 10

x = (y + 10)/7

therefore the inverse of the given function is (y + 10)/7

The value of x is [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]

Step-by-step explanation:

The equation is [tex]\frac{1}{x}-\frac{2}{3}=4 x[/tex]

Subtracting by [tex]4x[/tex] on both sides,

[tex]\frac{1}{x}-\frac{2}{3}-4 x=0[/tex]

Taking LCM,

[tex]\frac{3-12 x^{2}-2 x}{3 x}=0[/tex]

Multiplying by 3x on both sides,

[tex]-12 x^{2}-2 x+3=0[/tex]

Dividing by (-) on both sides,

[tex]12 x^{2}+2 x-3=0[/tex]

Using quadratic formula, we can solve for x.

[tex]\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}[/tex]

Taking out common term 2, we get,

[tex]\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}[/tex]

Thus, the value of x is  [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]

Answer:

I think 8

Step-by-step explanation:

9/2 and 5/8

here 8 is the LCM.

so, 9/2 × 4/4

5/8 × 1/1

which gives: 36/8 and 5/8

Answer:

It is 2

Step-by-step explanation:

Nothing can go into 2 and 8/4 is 2.

x° = 10°

Solution:

In the given figure the angle L represents 90°.

The center ray splits 90° into two angles.

(3x + 6)° + (5x + 4)° = 90°

⇒ 3x° + 6° + 5x° + 4° = 90°

Combine like terms together.

⇒ 3x° + 5x°+ 6° + 4° = 90°

⇒ 8x°+ 10° = 90°

Subtract 10° on both sides of the equation.

⇒ 8x°+ 10° – 10° = 90° – 10°

⇒ 8x° = 90° – 10°

⇒ 8x° = 80°

Divide by 8 on both sides of the equation.

⇒ x° = 10°

Hence, the value of x° = 10°.

Answer:

Step-by-step explanation:

6c + 5

term : 6c and 5....coefficient : 6......constant : 5

a coefficient is the number multiplied by the variable (the letter)....a constant is just a number with no variables (letters)

The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 and the constant is 5.

The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 because it is the number multiplying the variable c. The constant is 5 because it is a fixed value that does not involve any variables.

So the correct answer is option A: Term: 6c, coefficient: 6, constant: 5.

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Answer:

[tex]x=85\\ \\y=100\\ \\z=100[/tex]

Step-by-step explanation:

Angles with measures of [tex]95^{\circ}[/tex] and [tex]x^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]

[tex]x+95=180\\ \\x=180-95\\ \\x=85[/tex]

Angles with measures of [tex]80^{\circ}[/tex] and [tex]y^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]

[tex]y+80=180\\ \\y=180-80\\ \\y=100[/tex]

Find the measures of two remaining interior angles of the pentagon:

[tex]1. \ 180^{\circ}-62^{\circ}=118^{\circ}\\ \\2.\ 180^{\circ}-53^{\circ}=127^{\circ}[/tex]

The sum of the measures of all interior angles in the pentagon is

[tex](5-2)\cdot 180^{\circ}=540^{\circ},[/tex]

then

[tex]95^{\circ}+118^{\circ}+100^{\circ}+z^{\circ}+127^{\circ}=540^{\circ}\\ \\440^{\circ}+z^{\circ}=540^{\circ}\\ \\z^{\circ}=100^{\circ}[/tex]

Answer:

[tex]k=54[/tex]

Step-by-step explanation:

Find the coordinates of points M and N in terms of k. Solve the system of two equations:

[tex]\left\{\begin{array}{l}y=3x^2\\ \\y=-3x^2+k\end{array}\right.\Rightarrow \left\{\begin{array}{l}y=3x^2\\ \\y=-y+k\end{array}\right.\\ \\2y=k\\ \\y=\dfrac{k}{2}\\ \\\dfrac{k}{2}=3x^2\\ \\x^2=\dfrac{k}{6}\\ \\x=\pm\sqrt{\dfrac{k}{6}}[/tex]

Two points have the coordinates [tex]M\left(\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex] and [tex]N\left(-\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex]

Find the distance between M and N:

[tex]MN=\sqrt{\left(\sqrt{\dfrac{k}{6}}-\left(-\sqrt{\dfrac{k}{6}}\right)\right)^2+\left(\dfrac{k}{2}-\dfrac{k}{2}\right)^2}=\sqrt{4\dfrac{k}{6}}=\sqrt{\dfrac{2k}{3}}[/tex]

Since MN = 6, you have

[tex]\sqrt{\dfrac{2k}{3}}=6\\ \\\dfrac{2k}{3}=36\\ \\2k=108\\ \\k=54[/tex]

Answer:

b

Step-by-step explanation:

yes it b because it goes origion and it not a zero pair

Answer:

x = 5/4

y = 15/16

Step-by-step explanation:

We are given y = 3/4x

and 5/2x +2y = 5

Substituting the value y=3/4 x in second equation we get

5/2x + 2(3/4)x = 5

8/2x = 5

4x = 5

and so , x = 5/4

substituting value of x in y = 3/4x we get,

y = 3/4 (5/4)

So, y = 15/16

which are the required values of x and y on solving the two given equations.

The solution to the equation is (5/4, 15/16)

Given the system of equations

Substitute equation 1 into 2 to have:

5/2x  + 2(3/4x) = 5

5/2x + 3/2x = 5

8/2x = 5

4xx = 5

x = 5/4

Snce y = 3/4x

y = 3/4(5/4)

y = 15/16

Hence the solution to the equation is (5/4, 15/16)

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Answer:

See explanation!

Step-by-step explanation:

Let us first give some principle theory to aid our solution.

Considering two functions [tex]A(x)[/tex] and [tex]B(x)[/tex], in order to show that function

which is the inverse of [tex]y=ax[/tex].

Now let as solve our problem. We are given the following:

[tex]f(x)=3x-4\\g(x)=\frac{x+4}{3}[/tex]

Method A: Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x).

Let us take [tex][f(x)=y]=3x-4[/tex] and "exchanging" our variables we have

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

which is exactly the same with our given function of [tex]g(x)=\frac{x+4}{3}[/tex], so proved!

Method B: Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)

For this case we will use a simple input let us say [tex]x=1[/tex]. Thus taking the [tex]f(x)[/tex] function and plugging in we have:

[tex]f(x=1) = 3(1)-4\\f(1)=3-4\\f(1)=-1[/tex]

Now let us take the output of [tex]f(1)[/tex] which is [tex]-1[/tex] and use it the input to our second function of [tex]g(x)[/tex], so we have:

[tex]g(x=-1) = \frac{(-1)+4}{3}\\ \\g(-1)=\frac{3}{3}\\ \\g(-1)=1[/tex]

so the output of the second function is equal to the original input value of the first function, hence proved!

Method C: Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x.

Basically we are asked to prove that both [tex]f(g(x))=g(f(x))=x[/tex]

To do so, we just replace one function into the [tex]x[/tex] value of the other function as follow:

[tex]f(g(x))=3(\frac{x+4}{3} )-4\\\\f(g(x))=x+4-4\\\\f(g(x))=x[/tex]

Lets repeat now for the opposite as follow:

[tex]g(f(x))=\frac{(3x-4)+4}{3}\\ \\g(f(x))=\frac{3x}{3}\\ \\g(f(x))=x[/tex]

Hence proved!

[tex]\text{Solve for x:}\\\\-4x-6=-5y+9\\\\\text{Add 6 to both sides}\\\\-4x=-5y+15\\\\\text{Divide both sides by -4}\\\\\boxed{x=\frac{5}{4}y-\frac{15}{4}}[/tex]

Answer:

Yes

Step-by-step explanation:

I think because you didn't finish explaining the question, go check.
I can't understand what you are trying to ask.

A square with a whole number side length would have the same perimeter or area as the dog pen, assuming that the pen is rectangular.

If a square with a side length of s has the same perimeter as the dog pen, then we can write:

4s = 2(l + w) 2s = l + w

Since s is a whole number, l + w must be an even number. This means that both l and w must have the same parity (they must both be even or both be odd) for the equation to be true. However, if both l and w are even, then the ratio of l:w will not be a whole number, which means that a square with the same area as the dog pen cannot exist with whole number side lengths.

If a square with a side length of s has the same area as the dog pen, then we can write:

[tex]s^2[/tex]= lw

Since s is a whole number, we can express it as the product of two whole numbers:

s = ab

Substituting this into the equation for the area, we get:

[tex]a^2 b^2[/tex] = lw

This means that l and w must have at least two factors each that are perfect squares. However, if we assume that the dog pen is rectangular, then its dimensions cannot both have two factors that are perfect squares, which means that a square with the same area cannot exist with whole number side lengths.

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Note: The complete question is - Could a square with a whole number side length have the same perimeter as the dog pen? Could a square with a whole number side length have the same area as the dog pen?

The fraction 43/200 is evidently between 1/5 and 1/4 from equivalent fractions.

Im essence, since 43 lies between, 40 and 50;

The fraction 43/200 in turn lies between fractions 1/5 and 1/4.

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Answer:

2/3

Step-by-step explanation:

parallel lines have the same slope

given that a line has a slope of 2/3

a line that is parallel to this line would also have a slope of 2/3

ANSWER: $432

STEP-BY-STEP EXPLANATION:

The cost of the tablet is $360

Then Tabitha has to pay 20% sales tax.

The tax is the prices times 20%  plus the original price

360 ( 1+ 0.2)

360 (1.2)

=432

a = amount invested at 9%

b = amount invested at 11%

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{9\% of "a"}}{\left( \cfrac{9}{100} \right)a\implies 0.09a}~\hfill \stackrel{\textit{11\% of "b"}}{\left( \cfrac{11}{100} \right)b\implies 0.11b}[/tex]

we know she has a total of $40,000 to invest, so, if she invested "a" amount in one, the other quantity must be the slack left from 40,000 and "a", namely b = 40000 - a.

we also know that the yield or earned interest from both amounts is 4300, thus

[tex]\bf \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11b}~~=~~\stackrel{\textit{annual income from both}}{4300} \\\\\\ \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11(40000-a)}~~=~~4300 \\\\\\ 0.09a+4400-0.11a = 4300\implies -0.02a+4400 = 4300 \\\\\\ 4400=4300+0.02a\implies 100=0.02a\implies \cfrac{100}{0.02}=a\implies \boxed{5000=a} \\\\\\ \stackrel{\textit{we know that}}{b = 40000-a}\implies \boxed{b = 35000}[/tex]

To buy 78 cookies using packages of 13 or 39, you can either buy 2 packages of 39 or 5 packages of 13 and 1 additional cookie.

To find the number of ways you can buy 78 cookies using packages of 13 or 39, we need to consider the different combinations of packages.

Let's start with the largest package size, 39. If you buy 2 packages of 39, that's a total of 78 cookies. So one option is to buy 2 packages of 39.

Now let's consider the smaller package size, 13. If you buy 5 packages of 13, that's a total of 65 cookies. To reach a total of 78 cookies, you can buy 5 packages of 13 and 1 additional cookie.

Therefore, the total number of ways you can buy 78 cookies is 2 (using only packages of 39) or 1 (using 5 packages of 13 and 1 additional cookie).

Answer:

6(x+5)

Step-by-step explanation:

Answer: 6 x (x+5)

Step-by-step explanation: Since it is six times a number AND five, you want to do the addition equation first. To show this you place parentheses around a variable (x) plus 5. You add six in front of this because it comes first in the word problem.

Answer:

[tex]-5,-7[/tex]

It is Arithmetic.

Step-by-step explanation:

1) A sequence is geometric when it goes from a term to the next term by  multiplying by the same number, which is called "Common ratio" ([tex]r[/tex]).

2) A sequence is arithmetic when it goes from a term to the next term by  adding or subtracting a common value. This value is called "Common difference" and it is denoted with [tex]d[/tex].

Then, given the following sequence:

[tex]3, 1, -1, -3[/tex]

- Let's find out if it is geometric by dividing  each term by its previous one. Then:

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

Since there is no Common ratio, it is not a Geometic sequence.

- Now let's see if it is  arithmetic by subtracting each term by its previous one:

[tex]-3-(-1)=-2\\\\-1-1=-2\\\\1-3=-2[/tex]

You can idenfity that it has a Common difference:

[tex]d=-2[/tex]

Therefore, it is an Arithmetic sequence.

The next to terms are:

[tex]-3-2=-5\\\\-5-2=-7[/tex]

Answer:

16×4= 64

64.00+3.50

(16×4)+(64.00+14.00)

Step-by-step explanation:

First you have to find how much the tickets will cost per person then add 14.00 because of the one time person but there is four so time 3.50×4

Answer:

The three points for the line  y = -6x + 12 ...Red color line

point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)

point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)

point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)

The Graph is attached below.

Step-by-step explanation:

Given:

[tex]y = -6x +12[/tex]  ........... equation of a line

Let the points be point A, point B, and point C  

To Find:

point A( x₁ , y₁) ≡  ?

point B( x₂ , y₂) ≡ ?

point C(x₃ , y₃ ) ≡ ?

Solution:

For Drawing a graph we require minimum two points but we will have here three points.

For point A( x₁ , y₁)

Put x = 0 in the given equation we get

y = 0 + 12

y = 12

∴ point A( x₁ , y₁) ≡ ( 0 , 12)

For point B( x₂ , y₂)

Put y= 0 in the given equation we get

0 = -6x + 12

6x = 12

[tex]x=\dfrac{12}{6}=2[/tex]

∴ point B( x₂ , y₂)  ≡ (2 , 0)

For point C(x₃ , y₃ )

Put x = 1 in the given equation we get  

y = -6 × 1 + 12

y = 6

∴ point C(x₃ , y₃ )≡ (1 , 6)

Therefore,

The three points for the line  -2y = -x + 8 are

point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)

point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)

point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)

The Graph is attached below..

Answer:

After 3 months the total cost of each health club will be the same, and the total cost for each one will be US$ 55

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Club A = Membership fee of $ 16 + Monthly fee of $13

Club B = Membership fee of $ 22 + Monthly fee of $11

2. After how many months will the total cost of each health club be the​ same? What will be the total cost for each​ club?

For answering the question, we will use the variable x to be the number of months of membership of the two clubs, this way:

Club A = Club B

16 + 13x = 22 + 11x

13x - 11x = 22 - 16

2x = 6

x = 6/2 = 3

Substituting and proving x = 3:

16 + 13x = 22 + 11x

16 + 13 * 3 = 22 + 11 * 3

16 + 39 = 22 + 33

55 = 55

After 3 months the total cost of each health club will be the same, and the total cost for each one will be US$ 55

Answer:

The surface area of the prism is 252 square units

Step-by-step explanation:

we know that

The surface area of the prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the base of the prism

P is the perimeter of the base

L is the length or the height of the prism

step 1

Find the area of the triangular base B

The area of triangular base B is

[tex]B=\frac{1}{2}(8)(6)=24\ units^2[/tex]

The perimeter of the triangular base P is

[tex]P=8+6+10=24\ units[/tex]

we have

[tex]L=8.5\ units[/tex]

substitute the values in the formula

[tex]SA=2(24)+24(8.5)=252\ units^2[/tex]