Solve the multi-step equation. Type in your solution (ie, x=3, 4=7, 5=5).

6x+7= 2(3x+5)+9

[tex]\it \dfrac{3}{5}:x=\dfrac{3}{4} \Rightarrow x=\dfrac{3}{5}:\dfrac{3}{4}=\dfrac{\not3}{5}\cdot\dfrac{4}{\not3}=\dfrac{4}{5}[/tex]

[tex]\it So,\ \ \dfrac{3}{5}\ divided\ by\ \dfrac{4}{5}\ is\ \dfrac{3}{4}[/tex]

a) To find the company's revenue and costs if it sells 2000 shirts, we can substitute 2000 for x in the given revenue and cost functions:

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Revenue: r(x) = 10x, so r(2000) = 10(2000) = $20,000

Costs: c(x) = 3x + 9000, so c(2000) = 3(2000) + 9000 = $15,000

b) The profit function, p(x), is the difference between the revenue function and the cost function. So, the profit function for this company is:

p(x) = r(x) - c(x) = 10x - (3x + 9000) = 7x - 9000

c) To find the company's profit in 2012, when it sold 5000 shirts, we substitute 5000 for x in the profit function:

p(5000) = 7(5000) - 9000 = $20,000

So, the company had a profit of $20,000 in 2012 when it sold 5000 shirts.

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The annual interest rate on the loan is 0.02 or 2%.

To find the annual interest rate on the loan, we need to use the formula for simple interest:

I = Prt

where:

I is the interest,

P is the principal (the amount of the loan),

r is the annual interest rate (expressed as a decimal),

t is the time in years

We know the following information:

I = $240

P = $4000

t = 3

We can use this information to set up the equation and solve for r:

240 = 4000 * r * 3

240 = 12000r

r = 240/12000

r = 0.02

Therefore, the annual interest rate on the loan is 0.02 or 2%.

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According to the given information in the question the average rate of change is 3.

Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.

The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.

The formula R = D/T, or rate of change equals the distance travelled, can be used to address rate of change problems in general.

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Answer:

use the graph

Step-by-step explanation:

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔDEF and ΔEGF,

∠F=∠F (Reflex property)

EF=EF (Reflex property)

∠DEF=∠EGF=90°

By AA similarity, ΔDEF ~ ΔEGF

So, DF/EF = EF/GF

12/x = x/2

x²=12×2

x=2√6 units

Therefore, the value of x from the given figure is 2√6 units.

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Answer:

2 5$ bills

1 10$  bill

5 2$ bills

Step-by-step explanation:

Answer:

390,000

Step-by-step explanation:

The function f(x)=2x-3 is not surjective.

The surjective function is defined with reference to the elements of the range set, such that every element of the range is a co-domain.

A surjective function is a function whose image is equal to its co-domain, and every element y can be mapped from element x so that f(x) = y.

it suffices to give an example of y∈Z such that f(x)=y has no solutions. Just pick y=−2 and derive that

f(x)=−2⟺2x−3=−2⟺2x=1

and it should be quite clear that this has the unique solution x=0.5 over Q so no solutions for Z.

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Answer: 1 apple = 3 bananas

Step-by-step explanation:

10 bananas = 2 pineapples

which means

5 bananas = 1 pineapple eq_i

1 pineapple = 2 bananas + 1 apple eq_ii

Using eq_i and eq_ii, we conclude

1 apple = 3 bananas ... answer



hope that helps...

Answer:

1. x = 9

2. (10, -4)

4. (-4, -6)

5. (4, -1)

Step-by-step explanation:

1. Since we know that y = 3x + 27, we can substitute that into y = 4x + 18.

3x + 27 = 4x + 18

9 = x

x = 9

Continue the processes of setting both equations of a system to a specific value, and then substituting it into the other equation.

The length of the diagonal KM is 8√(2) inches.

The area of a square is given by the formula: area = side^2.

So, if the area of square JKLM is 64 square inches, then we know that:

64 = side^2

To find the diagonal KM, we can use the Pythagorean Theorem. The diagonal KM is the hypotenuse of a right triangle where the legs are the side of the square.

So the formula is KM = √(side^2 + side^2)

Substituting in the known area of the square, we have:

KM = √(64 + 64)

KM = √(128)

KM = 8√(2)

Therefore, the length of the diagonal KM is 8√(2) inches.

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KM = √(side^2 + side^2)

Substituting in the known area of the square, we have:

KM = √(64 + 64)

KM = √(128)

KM = 8√(2)

The ordered pair that describes the location of M'' will be (5, -1).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

Point M is located at (−5, 1) on the coordinate plane. The coordinate after the reflection over the y-axis is given as,

M' = (-x, y)

M' = (- (-5), 1)

M' = (5, 1)

The coordinate after the reflection over the x-axis is given as,

M" = (x, -y)

M" = (5, -1)

The ordered pair that describes the location of M'' will be (5, -1).

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The maximum area of the cargo space in a Mac truck is 32 sq ft.

What is Area of Rectangle?

The area of a rectangle can be calculated by multiplying its length and width.

          [tex]Area \ of\ Rectangle = length * breadth[/tex]

The maximum area of the cargo space in a Mac truck can be calculated by finding the area of a rectangle. To find the area of a rectangle, you multiply the length by the width.

In this case, the length of the floor of the cargo space is 4' and the width is 8', so:

Area = 4' x 8' = 32 sq ft

So, the maximum area of the cargo space in a Mac truck is 32 sq ft.

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Answer:

20 cars

Step-by-step explanation:

He wants 4500

He makes 1700 salary

4500-1700=2800

Now you need to divide the remaining 2800 needed by the 140 he gets per car he sells

2800÷140=20

So he needs to sell 20 cars

Q.7 ...

[tex]tsa \: of \: cuboid \: = 2(lb + bh + lh) \\ = 2(4 \times 3 + 3 \times 5 + 5 \times 4) \\ = 2(12 + 15 + 20) \\ = 2(47) \\ = 94 \: square \: units \: ...[/tex]

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Answer: I CANR

Step-by-step explanation:

Answer:

24+56 is equivalent to 80.

It is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
(a)

(a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)²

LHS,
= a²(c² + d²)  + b² (c² + d²)
= a²c² + a²d² + b²c² + b²d²
= a²c² + b²d² + 2abcd + b²c² + a²d² - 2abcd
= (ac + bd)² + (bc - ad)²
= RHS

Thus, it is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².

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Answer:

y = 8

Step-by-step explanation:

The angle represented by (8x - 31)° = angle represented by (6x + 3)° since they are alternate interior angles

8x - 31 = 6x + 3

=> 8x-6x = 3 + 31

2x = 34

x = 17

Angles (8x - 31) and (5y + 35) are adjacent linear angles - they lie on the same straight line. their sum must equal 180

8x - 31 + 5y + 35 = 180

Plugging x = 17

8(17) -31 + 5y + 35 = 180

5y + 140 = 180

5y = 180 - 10 = 40

y = 40/5 = 8

Alex paid 64.48

price of sweatshirt which alex bought  :  59.99

sales tax                                                   :  4.499

total price alex paid is                               64.48

calculation of salex tax

price of sweatshirt              :59.99.

sales tax                               :4.499          

{59.99 x 7.5% } = 4.49

Alex paid 64.48  

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Answer:

x = 77°

Step-by-step explanation:

When an angle has its vertex on a circle, the arc that gets cut by sides is double the angle.

So arcDF is double angleEFD.

angleEFD = 74°

arcDF = 148°

arcFH is double angleD.

angleD = 29°

arcFH = 58°

All the arcs of the circle all add up to 360°

arcDF + arcFH + arcDH = 360°

148° + 58° + arcDH = 360°

206 + arcDH = 360°

subtract 206

arcDH = 154°

Again, the arc is double the angle, or the angle is half the arc.

arcDH = 154°

angleDFH = 77°

x = 77°

see image.

Answer: 6 Goats and 5 Ducks

Hope this helps :)

Step-by-step explanation:

6 goats (4 legs) = 24 legs

5 ducks (2 legs) = 10 legs

6 * 4 = 24

5 * 2 = 10

24 + 10 = 34

6 + 5 = 11

Answer:

6 goats and 5 ducks

Step-by-step explanation:

Given: g+d=11

Goats have 4 legs. Ducks have 2 legs. For total of 34 legs.

Use the word problem to create equation: 4g+2d=34

We can solve for either, we'll solve for g(goat) first:

4g+2d=34

2d=34-4g

d=17-2g

Plug what we found for d into other equation:

g+d=11

g+(17-2g)=11

-g+17=11

-g=-6

g=6

Plug what we found for g into equation to solve for d(duck):

g+d=11

6+d=11

d=5

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Answer: 5/3

Step-by-step explanation:

1 2/3 ÷ 3/4

= 5/4 ÷ 3/4

= 5/4 * 4/3

= 5/3  3/4 cups

No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

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Answer:

Answer in attached photo.

Step-by-step explanation:

Solution is in the attached photo, do note this question tests on finding the area of shapes.

Let the number of student tickets be [tex]s[/tex] and the number of adult tickets be [tex]a[/tex].

[tex]\begin{cases} 5.50s+9.50a=703 \\ s+a=98 \end{cases}[/tex]

We can draw a quadrilateral ABCD with sides AB, BC, CD, and AD having lengths of 2.4 cm, 4.3 cm, 3.1 cm and 2 cm respectively. The diagonal BD has a length of 3.9 cm.

Step 1: Draw a line segment AB with length 2.4 cm.

Step 2: Draw a line segment BC with length 4.3 cm.

Step 3: Draw a line segment CD with length 3.1 cm.

Step 4: Draw a line segment AD with length 2 cm.

Step 5: Draw the diagonal BD with length 3.9 cm.

Step 6: Connect the endpoints of the line segments AB, BC, CD, and AD to form a quadrilateral ABCD.

We can construct a quadrilateral ABCD given the given dimensions. To begin, we will draw a line segment AB with a length of 2.4 cm. This will be the first side of our quadrilateral. Next, we will draw a line segment BC with a length of 4.3 cm. This will be the second side of our quadrilateral. After that, we will draw a line segment CD with a length of 3.1 cm. This will be the third side of our quadrilateral. Then, we will draw a line segment AD with a length of 2 cm. This will be the fourth side of our quadrilateral. Finally, we will draw the diagonal BD with a length of 3.9 cm. To complete the quadrilateral, we will connect the endpoints of the line segments AB, BC, CD, and AD. This will form a quadrilateral with the given dimensions. The quadrilateral ABCD will have side lengths of 2.4 cm, 4.3 cm, 3.1 cm, and 2 cm respectively. The diagonal BD will have a length of 3.9 cm. Our quadrilateral ABCD is now constructed and ready to use.

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Answer:

22 students

Step-by-step explanation:

Answer:

Answer in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note we will use x,y and z to be the 3 consecutive natural numbers. Do also note in this case, since the three numbers are consecutive, they have a difference of 1 between each other.

Answer:

22 miles

Step-by-step explanation:

trust