What is the value of y

The domain and range of this linear function f(x) = 4x – 8 is: A. domain: {x | x is a real number}; range: {y | y > –8}.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain refers to the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

In conclusion, the domain of this linear function consist of all real numbers while the range comprises the set of all real numbers on the y-axis that are greater than negative eight (-8).

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Answer:

its a

Step-by-step explanation:

The equation of the line with the given slope and the y-intercept.

slope = 1/5; y-intercept = -5 is y = 1 / 5 x - 5

The equation of a line can be described as follows:

y = mx + b

where

Therefore,

slope of the line = 1 / 5

y-intercept = - 5

Hence, the equation of the line can be represented as follows:

y = 1 / 5 x - 5

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the answer is x= -48

solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!

Answer:

This is not an arithmetic sequence because -15 + 7 = -8, not 8.

The amount of petrol consumed in one hour will be 200 liters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

In 45 minutes, an automobile uses 150 gallons of gasoline.

Consequently, the rate of gasoline consumption in liters per minute will be

= 150 / 45

= 10 / 3  Liters per minute

We are aware that an hour is made up of 60 minutes.

The amount of gasoline that will be used in an hour will then be

= (10 / 3) x 60

= 10 x 20

= 200 liters

Thus, 200 liters of gasoline will be burned in an hour.

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Answer:

there the vehicle uses 250 litres

Step-by-step explanation:

[tex]150 = 45[/tex]

[tex]x = 75[/tex]

[tex]x = 75 \div 45 \times 150[/tex]

[tex]x = 250litres[/tex]

The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented  as - 96a + 84b + 32x + 24y

Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

Therefore, the equivalent expression of  −12(8a − 7b) + 8(4x + 3y) can be solved as follows:

−12(8a − 7b) + 8(4x + 3y)

open the bracket

−12(8a − 7b) + 8(4x + 3y)

- 96a + 84b + 32x + 24y

Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y

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The angles are given below

What is an angle?

An angle is a symbol in Euclidean geometry created by two rays, called the flanks of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are placed in the plane having the rays. Angles are also generated when two planes overlap. These are termed as dihedral angles. An angle defined by two overlapping curves is the angle of both the rays falling tangent to the individual curves at their place of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius.

(a) angle a = 112° (alternate angles)

angle b = angle a = 112° (vertically opposite angles)

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The interest rates required to get a total amount of $2,420 from compound interest on a principal of $2,000 compounded 1 times per year over 2 years is 10% per year.

The interest on savings that is calculated on both the initial principal and the interest accrued over time is known as compound interest.

The concept of compound interest, also known as "interest on interest," is thought to have first appeared in Italy in the 17th century. It will accelerate the growth of a sum more quickly than simple interest, which is calculated only on the principal sum.

Money is multiplied more quickly through compounding, and the more times it is compounded, the higher the compound interest will be.

Using the formula A = P(1 + r/n)^nt

Solving for rate r as a decimal

r = n[(A/P)^(1/nt) - 1]

r = 1 × [(2,420/2,000)^{1/(1)(2)} - 1]

r = 0.1

Then convert r to R as a percentage

R = r × 100

R = 0.1 × 100

R = 10%/year

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By the degfinition of a congruent triangle, the statement that was made that ∆JOL and ∆IOM are congruent triangles is false.

The two triangles are said to be congruent triangles based on the fact that all of their corresponding sides are the same and said to be equal. Then all of the corresponding sides of the angles would also have an equa; measure.

The definition that I have given above says that the congruent triangles are those that have the same shapes and also have the same sizes. The corresponding sides of the angles and the sides would also be the same.

In the diagram that we have here, we can see that IOM and JOL do not have the same size. Hence the congruent law is not correct. To be congruent it would have to be that the the corresponding sides are the same and there is the equality in the angles of the triangles.

Since this property is not in the shape we would have to conclyde that the statement is wrong. They are not congruent triangles.

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The height of the triangular prism is calculated as: 12 cm.

The volume of a right-triangular prism = 1/2(base of triangular face)(height of triangular face)(length of the triangular prism).

Given the following:

Plug in all the values into the volume formula for the triangular prism:

750 = 1/2(5)(h)(25)

750 = (1 × 5 × h × 25)/2

750 = (125h)/2

Multiply both sides by 2

750 × 2 = (125h)/2 × 2 [multiplication property of equality]

1,500 = 125h

Divide both sides by 125

1,500/125 = 125h/125 [division property of equality]

12 = h

h = 12 cm

Thus, the height of the prism that has a base of the triangle measuring 5cm, a prism length of 25 cm., and a volume of 750 cubic cm is determined as 12 cm.

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Completing the checkbook register using the transactions done on the checking account at Really Awesome Bank shows that the ending balance was $298.12.

A checkbook register records transactions with a bank for a checking account.

The transactions of a checking account include withdrawals or payments, deposits, and bank charges if any.

Check   Date        Description          Payments         Deposit,       Balance

No.                                                   Withdrawal (-)     Credit (+)  

           August 1  Initial deposit                                  $200.00      $200.00

101       August 2 Groceries (Shaw’s)      $59.94                               140.06

           August 2 Parking fee                   $12                                    128.06

           August 4 Paycheck                                         465.00         593.06

102     August 6  Electricity                     $47.50                             545.56

103     August 6  Pants                            $70.56                             475.00

104     August 7  Bike, Helmet, Gloves $188.42                             286.58

         August 11  Paycheck                    $287.50                            574.08

        August 11   Savings account        $250.00                            324.08

        August 12  Luch (Red Robin)         $25.96                             298.12

August 2 – $59.94 ($57.91 x 1.035%)

August 4 – $465 ($15.50 x 30)  (15.50/hr for 30 hours)

August 6 – $70.56 (3 x $25.98 x 85% x 1.065)

August 7 – $188.42 ($165 + $35.12 + $10.99 x 85% x 1.05)

August 11 – $287.50 (15.50 x 25 - $100)

August 12 – $25.96 (24.61 x 1.055)

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The most appropriate choice for cost function and average cost function will be given by -

[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]

The number of flashdrive is very large, the average cost will come down to as low as $6.

What is cost function and average cost function?

Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.

Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.

Here,

C(x) = 17000 + 6x

[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]

        [tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]

        =   [tex]\frac{17000}{x}+6[/tex]

[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]

                    = 0 + 6

                    = 6

This means as the number of flashdrive is very large, the average cost will come down to as low as $6

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Complete Question

The cost​ (in dollars) for manufacturing a particular flashdrive is 17000 + 6x ​, where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per​ flashdrive, denoted by ​, is found by dividing​ c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]

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From the figure the shaded parts are two: the quadrant part and the sector part. The solution shows that:

area of the shaded part of the quadrant = area of the shaded part of the sector = ( pi * r^2) / 4 - bh/2

given data

ACD is a sector of a circle

From the figure we deduce that arc AC with line O is a quadrant of a circle. Hence the area of the shaded part of the quadrant is:

= area of a circle /4 - area of the right angle triangle

where area of a circle = pi r^2

area of triangle =  1/2 * base * height = bh/2

Area of the shaded part of the quadrant

= ( pi * r^2) / 4 - bh/2

base AO = radius of the circle = height CO

this forms an isosceles triangle and base angles of an isosceles triangle are equal. < A = < C = x

< A + < C + 90 = 180

x = 45 degrees

area of sector

= ∅/360 * pi*r^2  

= (45 / 360) * (pi*r^2)

= (pi * r^2) / 4

area of the shaded part of the sector = area of sector - area of the right angle triangle

= (pi * r^2) / 4 - bh/2

Comparing both sides that shows that the tow shaded parts are equal hence the shaded part of the quadrant is equal to the shaded part of the sector

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The additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

For the given question,

The money invested by Ms. May at 7% rate of interest is $8,000.

Let 'x' be the money invested at the rate of 4%.

The interest for the total annual income is 5%.

Thus,

7%of 8,000 + 4% of x = 5%(8,000 + x)

8,000×0.07 + 0.04×x = 0.05(8,000 + x)

On solving,

560 + 0.04x = 400 + 0.05x

0.01x = 160

x = 16,000

Thus, the additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

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The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros

Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.

Simple interest = principal × rate × time

= 14,000 × 0.01 × 12

= 1,680 Euros

In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.

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The surface area of the solid cuboid 7m 6m and 3m. total surface area of cuboid is 162 [tex]m^{2}[/tex].

A cuboid is a six-sided solid known as a hexahedron in the geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces. A cuboid is a convex polyhedron with the same polyhedral graph as a cube in mathematics.

A cube with six square faces, a rectangular prism, rectangular cuboid, or a rectangular box with six rectangle faces are special situations. In both circumstances, the faces of the cube and the rectangular prism come together at a right angle.

total surface area of cuboid

= 2(lb+bl+lh)

=2(7×6+6×3+3×7)

=2(81)

=162 [tex]m^{2}[/tex]

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2 grams = 2000 milligrams

Conversion between different units of measurement of the same quantity is called as conversion of units.

The process of conversion depends on the specific situation and the precision and accuracy of measurement.

Conversions from one unit to another should be exact, without changing the precision of the first. This is sometimes called soft conversion. It does not involve changing of the physical configuration of the unit being calculated.

'g' is the same as grams and similarly 'mg' is the same as milligrams.

Thus, when asked to convert 2 g to mg, as in the given question,

first multiply the value in grams by the conversion factor '1000'.

So, 2 grams = 2 × 1000 = 2000 milligrams.

A gram is larger unit than a milligram.

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The expression 5^8/ 5^2 is equal to  5×5×5×5×5×5. Option C

An algebraic expression can be defined as a  are mathematical expression with a minimum of two terms containing variables, factors, constants and coefficients.

An exponential function is simply defined as a function in which its value is a constant that is raised to the power of a variable or number.

It is a relation or expression that takes the form y = aˣ  in mathematics, where x is a independent variable.

Given the expression as;

⇒ 5^8 / 5²

⇒ 5^8-2

⇒ 5^6

⇒ 5×5×5×5×5×5

Hence, the value is 5×5×5×5×5×5

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The complete question;

Which of the following expressions is equal 5^8/ 5^2 to?

A.5×5×5

B. 1/5×5×5×5

C. 5×5×5×5×5×5

D.3

The graph that correctly represent the experiment that was graphed with the function  t(m) = 0.2m + 6 is the first option with points

given data

t(m) = 0.2m + 6

information deduced from the graph

examining the graph shows that first graph have the intercept as 6

using the points to calculate slope we have

= (y2 - y1) / (x2 - x1 )

= (6 - 0) / (0 - -30)

= 6 / (0 + 30)

= 6 / 30

= 0.2

Since the points are same with the given information we can conclude that the first option has the graph of the given function

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One possibility for resolving the inequality is (20, 60) in which x represents the number of tacos sold, and y the number of burritos sold

When graphing inequalities, the dependent variable, or y, is placed on the left side of the equation, while the other variables are placed on the right side.

The parameters are as follows:

Hudson has enough ingredients to make 90 tacos.

Each taco costs $3 to purchase.

Each burrito costs $7 to purchase.

Hudson must sell $420 worth of tacos and burritos per day.

x = number of tacos sold

y = the number of burritos sold

We need to graphically represent and solve the system of inequalities, and to identify one possible solution

The inequalities in the system are as follows:

x + y ≤ 90

3·x + 7·y ≥ 420

We have the following graphs to plot the above inequalities:

y ≤ 90 - x

y ≥ 420/7 - 3·x/7

y ≥ 60 - 3·x/7

The vertices of the feasible region's triangle are as follows from the inequality graph:

(0, 90), (0, 60), and the third vertex is found as follows for accuracy;

90 - x = 60 - 3·x/7

x = 52.5

y = 90 - x

∴ y = 37.5 at the vertex

The third vertex is (52.5, 37.5)

Therefore, the feasible region's vertices are (0, 90), (0, 60), and (52.5, 37.5), and one possible solution within the feasible region is (20, 60)

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The missing side length that is represented by x in the triangles that are similar is: B. 5.

According to the similarity theorem, the corresponding side lengths of two triangles that are similar have the same ratio and are therefore proportional to each other.

The two triangles are considered similar to each other, this means that their corresponding side lengths would be proportional to each other and would have the following equal ratio:

45/9 = 25/x

Cross multiply

(45)(x) = (9)(25)

45x = 225

Divide both sides by 45

45x/45 = 225/45

x = 5

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If each player loses 5 points for each second that he or she finishes after the first-place finisher.  the players in order from greatest to least number of points is: player 4, player 2, player 1, player 4.

Payer 1 :

Player 1 = 3(31) - 5(8)

Player 1 = 93 - 40

Player 1 = 53 points

Player 2 :

Player 2 = 3 (18)

Player 2 = 54 points

Player 3:

Player 3 = 3(24) - 5(3)

Player 3 = 72 - 15

Player 3 =  57 points

Player 4:

Player 4 = 3(27) - 5(6)

Player 4 = 81 -30

Player 4 = 51 points

Now list the players in order from greatest to least number of points.

Player 3 = 57 points

Player 2 = 54 points

Player 1 = 53 points

Player 4 = 51 points

Therefore the player based on ranking is: player 4, player 2, player 1, player 4.

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Answer: 48300

Step-by-step explanation:

23 % of 3.000.000 is [tex]\frac{3.000.000*23}{100} = 690.000[/tex]

So, 690.000 have college degree.

7 % of 690.000 is [tex]\frac{690.000* 7}{100} = 48.300[/tex]

So, 48.300 people have advanced degree.

Answer: 495

Step-by-step explanation:

Lower bound of 2.6 is 2.5

An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, notably in order theory. To determine a rounded number's upper and lower bounds: Determine the place value of the claimed level of accuracy. By two, multiply this place value. Find the upper bound by adding this amount to the provided value, and the lower bound by deducting this amount from the given value.

Given Data

2.6 to the lower bound

Bound of 2.6 is 2.5 to 2.7

Lower bound of 2.6 is 2.

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Answer:

The answer is -10/9

Step-by-step explanation:

10*x=(-1.111...*10 .) second equation

10x=-11.111....

subtruct second equation from the first equation

10x=10*-11.111.

-

x=-1.1111.

9x=10

x=10/9

A graph of the relationship between Sam’s age and Matt’s age has been plotted in the graph shown in the image attached below.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In order to solve this word problem, we would assign variables to Sam and Matt's age, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

x = 5 + y

Re-arranging the algebraic equation, we have;

y = x - 5

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Answer:

x = 7

Step-by-step explanation:

To get rid of the x^2, do the opposite of x^2: radicals, or square roots.

x^2 = 121

x = √121

Think about what number can multiply by itself to get 121...

7 • 7 or 7^2 = 121

So, in x^2 = 121, x = 7.

x^2 = 121

x = √121

7 = √121

7 = 7 ✔

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The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.

The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.

A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables

The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index

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