Translate each description into an algebraic expression. Then, evaluate the expression
using the value shown in the box for the variable.
EXAMPLE: the quotient of 112 and a added to 25 = (112 + a) + 25 = 53
a = 4
w = 10
b=3
x = 11
c = 9
y = 7
d=2
z = 5
1. the difference of 100 and the product of y and 12 =
2. b times the sum of 15 and 37 =
3. 27 added to the product of z and 12 =
4. 135 divided by the product of c and 5 =
5. w to the second power times the quotient of 12 and 4 =
6. 12 times d divided by the difference of 25 and 19 =
7. the product of x and 5 added to 13 =

A percentage is a way to describe a part of a whole. The amount Emily shared is $30.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,

15% of $200

= 0.15 × $200

= $30

The amount Emily shared is $30.

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Answer:

[tex]\textsf{E.} \quad y\:dy=xe^x\:dx[/tex]

Step-by-step explanation:

Given equation:

[tex]ye^{-x}\dfrac{dy}{dx}=x[/tex]

Divide both sides by [tex]e^{-x}[/tex]:

[tex]\implies \dfrac{ye^{-x}}{e^{-x}}\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]

[tex]\implies y\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]

Multiply both sides by [tex]dx[/tex] :

[tex]\implies y\:\dfrac{dy}{dx}\cdot dx=\dfrac{x}{e^{-x}}\cdot dx[/tex]

[tex]\implies y\:dy=\dfrac{x}{e^{-x}}\:dx[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:[/tex]

[tex]\implies y\:dy=xe^x\:dx[/tex]

Answer: E

Step-by-step explanation:

[tex]ye^{-x} \frac{dy}{dx}=x\\\\y \frac{dy}{dx}=xe^{x} \\ \\ \boxed{y dy=xe^{x} dx}[/tex]

The linear equation is y = (1/7)*x + 11/7.

The general linear equation is:

y = a*x + b

Where a is the slope.

Here we know that a = (1/7), then the line is:

y = (1/7)*x + b

We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.

Replacing that, we get:

1 = (1/7)*(-4) + b

1 + 4/7 = b

7/7 + 4/7 = b

11/7 = b

So the linear equation is:

y = (1/7)*x + 11/7.

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The equation of the linear function of the line is: y = 1/7x + 11/7.

A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:

1 = 1/7(-4) + b

1 = -4/7 + b

1 + 4/7 = b

11/7 = b

b = 11/7

Plug in the values of m and b into y = mx + b:

y = 1/7x + 11/7

The equation of the linear function is: y = 1/7x + 11/7

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Answer:

45

Step-by-step explanation:

Answer:

3/4 = -3* 2*(c-

I hope it helps!

if it does pls mark me brainliest answer

The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

Sales revenue $43,189.84

(7,796 units × $5.54)

Less Cost of goods sold $17,852.84

[($22,900/10,000)×7,796]

Gross profit $25,337

( $43,189.84-$17,852.84)

Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

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The coordinates of the vertices of the reflected image are (-3,4)  (0,4) (-3, 2) (0,2).

Reflection is a mathematical transformation of a shape by moving the vertices of the shape across a line of reflection.

Analysis:

coordinates of the shape before transformation are: (-3, 0) (0,0) (-3, -2) 0, -2)

Across the line of transformation, the corresponding vertices(old and new) must be equal distance from the line of reflection.

Also for reflection on y-axis only y-coordinates are affected.

so for point(-3, 0) 0 is 1 unit away from y = 1 so the other coordinate 1 unit away from y = 1 is y = 2 making the new point (-3, 2) same as others .

Find the image in the attached file below.

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The expression for YYY is (d) (x >= 50) && (x <= 100)

The instruction is given as:

If (YYY) {

// Output "50, 51, ..., 99, 100"

}

The value of x is given as:

x = 50 to 100 (inclusive)

This means that:

x must be greater than or equal to 50 AND x cannot exceed 100

The keyword AND is represented as &&.

So, the condition is:

x >= 50 && x <= 100

Hence, the expression for YYY is (d) (x >= 50) && (x <= 100)

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An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,

(6⁻¹⁰/6⁻⁴)

= 6⁻¹⁰ × 6⁴

= 6⁽⁻¹⁰⁺⁴⁾

= 6⁻⁶

= 1/6⁶

Hence, the correct options are A and C.

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Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

Answer:

Option (C)

Step-by-step explanation:

The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.

So, this means that adding 1 to this, the range matches with option C.

It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .

It is given that

Jeremy is reading a 60-page book.

The time taken to read  20 pages is 30 minutes

Then it can be written as 20:30 = 2:3

The rate of reading is same so To read the rest 40 pages is given by

40:x

40: x = 2:3

40*3/2 = x

x = 60 minutes

Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.

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Answer:

54 degrees!

Step-by-step explanation:

its a right triangle so we know 2 out of the 3 angles

so 36 + 90 = 126

180 - 126 = 54!

hope this helps :)

Answer:

s = 17units

Step-by-step explanation:

For this problem, we are trying to find a specific unknown side length.

We're actually given some extraneous information (information that is not needed to solve the problem):  It isn't necessary to know that BC is 5.

If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.

It isn't clear if the diagram you were provided gives ∠ABD as a right angle,  if it only gives ∠CBD as a right angle, or if it gives both as a right angle.  Below, we prove that it doesn't matter, because regardless, both must be right angles.

Is Triangle ABD a "right triangle"?

Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary.  Since they are supplementary, their measures add to 180°.  Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle.  Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.

Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).

Pythagorean Theorem

Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.

The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle.  (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b.  The only thing that is required is that "c" be the length of the hypotenuse)

In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs.  Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]

[tex]64 +225 =s^{2}[/tex]

[tex]289 =s^{2}[/tex]

Applying the square root property...

[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]

[tex]s=17 \text{ or } s=-17[/tex]

Final Solution

We discard the negative solution we obtained, since s represents the length of the side of a triangle.

s = 17units

Answer:

17

Step-by-step explanation:

Answer:

x = $1 & y = $2.

Each doughnut cost $1 and hot chocolate cost $2.

Answer:

I don't see the equation options.  See below for a predicted equation.

y= (2/3)x + 4

Step-by-step explanation:

The points are (-3,2), (0,4), and (3,6).  I will assume they lie in a straight line.

Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

m, the slope, is also known as the "Rise/Run."

Pick any two points.  I'll use (0,4) and 3,6)

Rise = (6-4) = 2

Run  = (3-0) = 3

Slope = 2/3

The equation becomes y = (2/3)x + b

B is easy in this case.  Point (0,4) tells us that y = 4 when x = 0 (the definition of b).

The equation is y= (2/3)x + 4

See the attached graph.

The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)

The complete question is added as an attachment

From the attached image, we have the following coordinate

B = (-2, 4)

When the triangle is rotated by 270 degrees, the rule of rotation is:

(x, y) ⇒ (y, -x)

For point B, we have:

B' = (4, 2)

Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)

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Answer:

17 in.

Step-by-step explanation:

There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.

The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,

4x + 1 - 1 ≥ -8

4x ≥ -8

x ≥ -2

Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.

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Answer:

See below

Step-by-step explanation:

To construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.

Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle.  The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.

To construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).

So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.

Finding a point that is equidistant from two given points

Set the compass to any radius that is larger than half the distance between the two endpoints.  If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.

Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice.  If uncertain, draw the entire circle.  Keeping the radius saved.

With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times.  If it doesn't intersect two times, the radius chosen at the beginning was too small.  Start the entire process over with a larger radius.

These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.

Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.

Steps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):

Note:  Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three.  So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.

Answer:

Formula for a linear sequence is

Tn=a+(n-1)d

where Tn is the nth term

a is the first term

n is the number of term

d is common difference

Triangles FGH and ABC are congruent because of the: AAS congruence theorem.

The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.

In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.

Therefore, both triangles are congruent because of the AAS congruence theorem.

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Answer:

4.5-1.4=3.1

Step-by-step explanation:

Hope this answers your question!

If not, I am sorry.

Step-by-step explanation:

9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....

[tex]...[/tex] :)..

Answer: 10

The arc length of the semicircle is

a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10

As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.

So,

(42/180)(5a+10)=a+4

42(5a+10)=180(a+4) [multiply both sides by 180]

210a+420=180a+720 [distributive property]

30a+420=720 [subtract 180a from both sides]

30a=300 [subtract 420 from both sides]

a=10 [divide both sides by 30]

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

Given the log function expressed as:

log(x-3) + logx=1

According to the law of logarithm, addition becomes product to have:

log x(x -3) = log₁₀10

x² - 3x = 10

x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0

x = -2 and 5

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

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Answer:

x = -2

y = 4

Step-by-step explanation:

To solve the system of equations, you want to plug one equation into the other and then simplify. You can do this by setting one equation equal to a variable (like in the first equation), and then substituting the function into the variable into the second equation.

First Equation: y = -2x

Second Equation: 5x - 7y = -38

5x - 7y = -38                                <----- Second equation

5x - 7(-2x) = -38                           <----- Plug first equation into "y"

5x + 14x = -38                              <----- Multiply -7 and -2x

19x = -38                                      <----- Add 5x and 14x

x = -2                                           <----- Divide both sides by 19

Now that you know the value of one variable, you can use it to find the value of the second variable. This can be done by plugging x = -2 in to one of the equations.

y = -2x                                         <----- First equation

y = -2(-2)                                      <----- Plug -2 in "x"

y = 4                                            <----- Multiply -2 and -2

To use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive

Additive inverse is simply changing the sign of a number and then adding it to the original number to get an answer that is equal to 0.

The additive inverse of a  number is another number

The additive inverse of number 3 is - 3

For an expression that uses subtraction, to use the additive inverse, change the sign of the number to positive

Thus, to use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive

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