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In this Multiplication in Algebra question, The expression '80 (1/4) x' is equivalent to '20x'. When the constant 80 multiplies with the fraction 1/4, the product then multiplies with the variable 'x' resulting in a simplified expression '20x'.

The given mathematical expression 80 (1/4) x can be simplified using the rules of multiplication in algebra.

Here the number 80 multiplies with the fraction 1/4 and then by the variable 'x'.

To carry out this operation, first multiply 80 by 1/4 which equals to 20, and then multiply this by 'x', so your final result would be 20x. Hence, the expression 80 (1/4) x is equivalent to 20x.

Learn more about Multiplication in Algebra here:

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The probable question may be:

Which is equivalent to 80 (1/4) x

Answer:

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

Step-by-step explanation:

Given y = f(x), then

y = f(x) + c represents a vertical translation

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Here the translation is 4 units down ⇒ c = - 4, thus

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

The equation of a line y = 2/3x moved 4 units down would be y = 2/3x - 4.

In the case of a vertical translation, the equation of a line y = mx + b is altered by adding or subtracting a constant value, which moves the line up or down on the coordinate plane. For example, with the given equation of a line, y = 2/3x, to translate it 4 units down, we subtract 4 from y. Therefore, the equation for the vertical translation would be y = 2/3x - 4.

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The answer would be 2. Angle PQR = Angle SQT

Hope it helps :)

Answer is 2 for sure Goodluck.

Answer:

585$

Step-by-step explanation:

multiply 55 by 5, then multiply 20 by 8, last multiply 25 by 6 and add each of the totals to one another.

The mean ticket price is 5.85

Answer:

C

Step-by-step explanation:

This is saying sum 5 and a number and multiply the result by 4

let n be the number then 5 + n is the sum, and

4(5 + n) is 4 times the resultant sum

Answer:

[tex]P=0.735[/tex]

Step-by-step explanation:

Call A to the event in which Nathan is allergic to penicillin

So

[tex]P (A) = 0.75[/tex]

[tex]P (A') = 1-P (A) = 0.25[/tex]

Call B the event in which the skin test predicts correctly.

So:

[tex]P (B) = 0.98\\P (B ') = 1-P (B) = 0.02[/tex]

We look for the probability that Nathan is allergic to penicillin and the test predicts it.

This is [tex]P (A\ and\ B)[/tex].

[tex]P (A\ and\ B) = P (A)*P (B)\\\\P (A\ and\ B) = 0.75 * 0.98\\\\P (A\ and\ B) = 0.735[/tex]

Answer:

v=9i+3j

Step-by-step explanation:

The given vector, v has initial point at P1 = (−5, −2) and terminal point at P2 = (4, 1).

The vector v is found by subtraction the initial point from the terminal point.

v=<4,1>-<-5,-2>

v=<4--5,1--2>

v=<9,3>

We write v as multiples of the basis vectors to obtain:

v=9i+3j

Answer:

y=-4x-17

Step-by-step explanation:

You want to find the equation for a line that has a slope of -4 and a y-intercept of -17.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

All you really have to do here is

replace m with -4, which is the slope you gave, and

replace b with -17, the y-intercept you gave,

in the equation y=mx+b.

The equation of the line that has a slope of -4 and a y-intercept of -17 is:

y=-4x-17.

It would be A.

All of the others include “Natural Numbers” -5 is not a natural number. A natural number is a counting number like 1,2,3,4,5.

Answer: I believe your answer is A.

hope you get 100%! ^.^

Check the picture below.

Answer:

The correct answer is last option.

m<AEB = 140

Step-by-step explanation:

From the figure we can see  rectangle.

It is given that, m<ADE = 70°

To find the value of m<AEB

From the figure we get Triangle ADE is isosceles triangle

<DAE = 70°

Therefore m<AED = 180 - (70 + 70) = 40°

<AED and <AEB  are linear pairs

Therefore m<AEB = 180 - m<AED

 = 180 - 40 = 140

The correct answer is last option

140

Answer:

z = [tex]-\frac{2}{5}[/tex] or - 0.4

Step-by-step explanation:

8+2z = 6 - 3z

2z = 6 - 8 - 3z

2z + 3z = - 2

5z = -2

z = [tex]-\frac{2}{5}[/tex] or - 0.4

Answer:

a. 1/27

Step-by-step explanation:

When dividing exponents and the base is the same, we subtract them

x^a/ x^b = x^(a-b)

3^3/3^6

3^(3-6)

3^(-3)

The negative exponent means it is in the denominator

1/3^3

1/27

Answer:

C

Step-by-step explanation:

Find the height (h ) above eye level and add 5 to give height from floor level.

Since the triangle is right use the tangent ratio to find h

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{5}[/tex]

Multiply both sides by 5

5 × tan60° = h, hence

h ≈8.66

The height is 8.66 + 5 = 13.66 ≈ 14 ft ( to nearest foot )

Answer:

Graph B

Step-by-step explanation:

We are given 4 graphs.

We need to find the function graph which is positive of the entire interval [-3, -2]

It is a closed interval. So it is inclusive of -3 and -2

In these interval the graph of y value must be in positive region.

By looking at the graph, the graph B has positive y-values in the entire interval [-3, -2]

Therefore, the answer is Graph B)

Answer:

Graph 2 represents that the  function is positive for the entire interval [-3, -2].                      

Step-by-step explanation:

We are given four different graphs for different functions. We have to find the graph that is positive for the entire interval [-3,-2].

We make the following observation from the given graphs.

Thus, function in graph 2 is positive for the entire interval [-3, -2].

Answer:

b

Step-by-step explanation:

Also got B if you it’s not right let me know send me a comment and I will try to help with the best of my ability

Answer:

O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.

Step-by-step explanation:

We are given Speed = 3.00 · 10^8 meters per second.

And Distance = 3.54.10^7 metwers

We need to find time.

We know that,

Distance = Speed * Time

3.54.10^7 = 3.00 · 10^8 * Time

Time = 3.54.10^7 / 3.00 · 10^8

Time = 1.18 X 10^7-8

Time = 1.18 x 10^-1

Time = 0.118 seconds.

So, O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.

I would go with answer D here just because it is the only option over 13, and the hypotenuse is always larger than the other sides. Im not positive on the math behind it though tbh.

ANSWER

(-1,2)

EXPLANATION

The given quadratic expression is:

[tex]f(x) = {x}^{2} + 2x + 3[/tex]

The coefficient of the quadratic term is already 1.

So we add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 2x + 1 - 1+ 3[/tex]

We factor the first three terms to obtain

[tex]f(x) =(x + 1)^{2} + 2[/tex]

This is now in the form:

[tex]f(x) = a({x - h)}^{2} +k[/tex]

where (h,k) which is equal to (-1,2) is the vertex.

The first number is the X coordinate and the second number is the Y coordinate.

Looking left to right the lines intersect at X = 1

Looking up and down they intersect at Y = -3

The answer is C. (1,-3)

Answer:

Step-by-step explanation:

The equation of a circle in the standard form:

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

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2-12y-15=0[/tex]

Convert into a standard form using

[tex](a-b)^2=a^2-2ab+b^2\qquad(*)[/tex]

[tex]x^2+\underbrace{y^2-2(y)(7)+7^2}_{(*)}-7^2-15=0\\\\(x-0)^2+(y-7)^2-49-15=0[/tex]

[tex](x-0)^2+(y-7)^2-64=0[/tex]           add 64 to both sides

[tex](x-0)^2+(y-7)^2=64[/tex]

The center (0, 7)

The radius: r = √64 = 8

Answer:

x = 0, y = 7

Step-by-step explanation:

Solving a system of equations using substitution requires one side to be equal to a variable present in the equation, in this case x or y. We should simplify the equation using elimination before substituting to reduce the chance of error.

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. These equations arew already aligned for us.

                  3x - 10y=-70

             -   4x +9y = 63

                  -x + y = 7

Now, for substitution, the equation must be set to a variable.

                  -x + y = 7

                  y = x + 7

Next, plug the equation in where applicable in another equation.

                  4x +9(x + 7) = 63

                  4x + 9x + 63 = 63

                  13x = 0

                  x = 0

The final step of substitution is to plug the known variable into an equation to find the other variable.

                  3(0) - 10y=-70

                  0 - 10y = -70

                  10y = 70

                  y = 7

I guarantee you this answer is correct, I worked it out using other methods and graphing prior to submitting this answer.

Answer:

x = 0 , y = 7

Step-by-step explanation:

[tex]3x - 10y = - 70..............(1) \\ 4x + 9y = 63...................(2) \\ (1) \times 4 \\ 12x - 40y = - 280...........(3) \\ (2) \times 3 \\ 12x + 27y = 189...........(4) \\ (4) - (3) \\ 67y = 469 \\ \\ y = \frac{469}{67} \\ y = 7 \\ put \: y = 7 \: into \: (1) \\ 3x - 10(7) = - 70 \\ 3x - 70 = - 70 \\ 3x = - 70 + 70 \\ 3x = 0 \\ x = \frac{0}{3} \\ x = 0[/tex]

You will have to use trig to solve this:

The side you have is adjacent to the known angle

The side you are looking for is opposite the known angle

^^^This means you need to use tan:

tan(24) = [tex]\frac{x}{12}[/tex]

.445222 = [tex]\frac{x}{12}[/tex]

^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x

5.3 ≈ x

Hope this helped!

so we know the point E is on the circle, thus the distance NE is really the radius of the circle hmmm what would that be?

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad E(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-1-(-6)]^2+[1-(-2)]^2}\implies r=\sqrt{(-1+6)^2+(1+2)^2} \\\\\\ r=\sqrt{5^2+3^2}\implies r=\sqrt{34}\implies r\approx 5.83 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad H(\stackrel{x_2}{-10}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NH=\sqrt{[-10-(-6)]^2+[-7-(-2)]^2} \\\\\\ NH=\sqrt{(-10+6)^2+(-7+2)^2}\implies NH=\sqrt{(-4)^2+(-5)^2} \\\\\\ NH=\sqrt{41}\implies NH\approx 6.4\impliedby \begin{array}{llll} \textit{units away from the center}\\ \textit{is outside the circle} \end{array}[/tex]

recall the radius is about 5.83, anything shorter than that is inside the circle, anything longer than that is outside it.

Answer:

outside the circle

Step-by-step explanation:

trust me. i did it on khan academy

Answer:

y-axis

Step-by-step explanation:

Answer:

The answer to the question

The correct answer is B

This is the assumption method ;)

Take all tickets to be adult tickets

$9 x 553 = $4977

Then..... $4977 - $3936 = $1041

The difference between the child and adult ticket is $3, so divide $1041 by $3

$1041 divided by $3 = 347

347 is the number of child tickets sold

347 x $6 = $2082

So 553 - 347 = 206 ( no. of adult tickets )

206 x $9 = $1854

Child tickets sold : 347

Adult tickets sold : 206

:0 ITS MAGIC IM SO SMART

Answer:

347 child tickets and 206 adult tickets are sold

Step-by-step explanation:

Let x be the no. of child tickets sold

Let y be the no. of adult tickets sold

A ticket office sold 553 tickets one day.

Equation becomes : [tex]x+y=553[/tex] ---A

Cost of 1 child ticket = $6

Cost of x child tickets = 6x

Cost of 1 adult ticket= $9

Cost of y adult tickets = 9y

Now we are given that the receipts totaled $3936.

So, Equation becomes : [tex]6x+9y=3936[/tex] ---B

Plot A and B

[tex]x+y=553[/tex] ---Green

[tex]6x+9y=3936[/tex] ---Purple

Intersection point = (x,y)=(347,206)

Refer the attached figure

Hence 347 child tickets and 206 adult tickets are sold

move parentheses by 6. 12x+110=6x+600

move variable to its left side and change its term 12x+110-6x=100

collect like terms and subtract 12 the divide both sides by 6.

answer 81.666666666666

Answer:

[tex]x = 230/3\\[/tex]

Step-by-step explanation:

Step 1:  Distribute

12x + 110 = 6(x + 100)

12x + 110 = (6 * x) + (6 * 100)

12x + 110 = 6x + 600

Step 2:  Subtract 6x from both sides

12x + 110 - 6x = 6x + 600 - 6x

6x + 110 = 600

Step 3:  Subtract 110 from both sides

6x + 110 - 110 = 600 - 110

[tex]6x = 490[/tex]

Step 4:  Divide both sides by 6

[tex]6x / 6 = 490 / 6[/tex]

[tex]x = 490 / 6[/tex]

[tex]x = (460/2) / (6/2)[/tex]

[tex]x = 230/3[/tex]

Answer:  [tex]x = 230/3\\[/tex]

Answer:

[-5, -3]

Step-by-step explanation:

Just find the *median* of each coordinate.

Step-by-step explanation:

[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\\dfrac{9!}{9-32}=\dfrac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{-23}=-\dfrac{362880}{23}[/tex]