A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
b. What information can you use to determine the domain and range?

Answer:

$640

Step-by-step explanation:

3 checks at $120 each = 3 x 120 = $360

This will reduce the balance so we should treat it as -360

2 paychecks at 240 = 2 x 240 = $480

This will increse the balance so we should treat it as +480

Net balance = 520 - 360+480=640

Balance = $640

Function f(x) to represent the 10-point bonus. f(x) = x+10

Function g(x) to represent the 9% increase. g(x) = X +0.09x

                                                                     g(x) = 1.09x

Use a composite function to find your grade if the 10-point bonus is applied before the 9% increase.

(g.f)x = g(f(x))

  f(75) = 85

 g(85) = 92.65

Use a composite function to find your grade if the 9% increase is applied before the 10-point bonus.

(f.g)(x) = f(g(x))

g(75) = 1.09(75) = 81.75

f(x) = 81.75+10 = 91.75

You would want 10 point bonus applied  before percentage increase. the 10 point bonus is flat increase.

whereas the percentage increased larger if multiplying by  a bigger number  your grade would be almost 1% higher with is option

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The solution (B) x=79.

Rewriting the equation to find the solution -

(x+2)³/₄=27

Raising both sides of the equation with exponent ⁴/₃

((x+2)³/₄)⁴/₃ = 27⁴/₃

Cancelling the exponents on Left Hand Side of the equation. Writing the value on Right Hand Side of the equation in exponent form

x + 2 =  (3³)⁴/₃

Cancelling 3 on Right Hand Side of the equation

x + 2 = 3⁴

Solving Right Hand Side of the equation

x + 2 = 81

Shifting 2 to Right Hand Side of the equation

x = 81 - 2

Performing subtraction on Right Hand Side of the equation

x = 79

Hence, the solution is (B) x=79.

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Answer:

no solution or -3=4

Step-by-step explanation:

Step-by-step explanation:

when lines are parallel gradiant should be the same in both equations

or m in y=mx+c

A)

1. y=-3x-6

2. y=-3x+6

therefore A is parallell

B)

1. y=44x+7/2

2.y=2/3x-17

therefore not parallel

c)

1. y=8x/7-17/7

2. y=-23x/21+30/21

therefore not parallel

d)

1. y=-8x/7+6

y=-7x/8-12

therefore not parallel

might have missed something-am tired. let me know if you have an issue.

Answer:

30°, 45° and 105°

Step-by-step explanation:

2 + 3 + 7 = 12 parts

180/12 = 15 degrees each part

First angle (2 parts)

2(15) = 30°

Second angle (3 parts)

3(15) = 45°

Third angle (7 parts)

7(15) = 105°

Hope this helps

Answer:

t=−7/6

I hope this helps.

Answer:

Step-by-step explanation:

Given:-

–2g2h2

To solve the given expression, we'll substitute g with -5 and h with 2:-

[tex]\sf -2\left(-5\right)2\left(2\right)2[/tex]

Apply the following rule :- (a) = a

Now, we can follow the PEMDAS order of operations:-

Multiply:-

Multiply -2 * -5 = 10:-

Multiply 10 * 2 = 20:-

Multiply 20 * 2 = 40

and finally multiply 40 * 2 = 80!

Therefore, your answer is 80!

_____________________

Hope this helps!

Have a great day!

Answer:

80

Step-by-step explanation:

give hope brainliest

Answer:

C.

Step-by-step explanation:

Answer:

C.

D.

Step-by-step explanation:

For right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A right angle triangle is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

If a right triangle has a line of symmetry then two sides of triangle will have same length and two angles are equal.

For a triangle to have a line of symmetry, it must be an isosceles triangle, meaning two of it’s sides and two of it’s angles must be the same.

From there it follows that for a right triangle to have a line of symmetry it must be an isosceles right triangle, meaning it must either have two 90-degree angles, or two identical non-90-degree angles.

Hence for right triangle has a line of symmetry two sides of the triangle have the same length and two angles of the triangle have the same measure.

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The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression, log (2x - y) = 1

Applying exponential on both sides, we get,

e^(log 2x - y) = e^1

2x - y = e

To Check Results,

Taking logarithm both sides,

log (2x - y) = log e

log (2x - y) = 1

Thus, the answer is verified.

Take expression, log (x + y) = 3 log 2

Applying exponential on both sides, we get,

e^(log (x + y) = e^(3 log 2)

x + y = e^(log 8)

x + y = 8

To Check Results,

Taking logarithm both sides,

log (x + y) = log 8

log (x + y) = 3 log 2

Thus, the answer is verified.

Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.

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Problem 37

We subtract 1 from all three parts to isolate the variable x.

-5 < x+1 < 4

-5-1 < x+1-1 < 4-1

-6 < x < 3 is the final answer

========================================================

Problem 40

Let's isolate the 3x portion first. To do this, we add 1 to all three sides.

2 < 3x-1 ≤ 6

2+1 < 3x-1+1 ≤ 6+1

3 < 3x ≤ 7

Then we divide all parts by 3 to fully isolate x.

3/3 < 3x/3 ≤ 7/3

1 < x ≤ 7/3 is the final answer

The equation of the straight line passing through the point (3, 3)

which is perpendicular to the line y=-1/2x-4 is y= 2x-3

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation for a straight line is y = mx + c. (1)

The line is parallel to the equation y=-1/2 x-4 ....(2),

meaning that the value of m in equation (1) is 2 y = 2x + c

The needed line has the equation y= 2x-3 since it goes through the point (3,3) where 3=2(3)+c provides c=-3.

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For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

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Applying the sine ratio, the length of CD is calculated as: 12.687 cm.

The sine ratio is stated as:

sin ∅ = opposite length / hypotenuse length of a right triangle.

Use the Pythagorean theorem to find BC:

BC = √(AC² - AB²)

AC = 12 cm

AB = 6 cm

Plug in the values

BC = √(12² - 6²)

BC = √(144 - 36)

BC = √108

Find the length of CD using the sine ratio:

∅ = 55

Opposite length = BC = √108

Hypotenuse length = CD

Substitute

sin 55 = √108/CD

(CD)(sin 55) = √108

CD = √108/sin 55

CD ≈ 12.687.

Therefore, applying the sine ratio, the length of CD is calculated as: 12.687 cm.

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14. Constant of variation, k = 3/2

15. The graph does not represent a direct variation.

16. Constant of variation, k = 1/4

17. Constant of variation, k = 1

A direct variation is a proportional relationship where variable x varies directly with variable y. The equation of a direct variation is modelled by the equation below:

y = kx.

k is the constant of proportionality of the relationship between x and y. It is also referred as the unit rate. On a proportional or direct variation graph, it can be determined by using any point on the graph (x, y) to find k.

k = y/x.

All graphs that represent direct variations passes through the origin (0, 0). The coordinate of the constant of proportionality of a direct variation graph is (1, k), where the constant of variation = k, and x = 1.

14. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 3/2

15. The graph does not pass through the origin (0, 0), so it does  represent a direct variation.

16. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1/4

17. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1

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The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.

Two triangles are said to be congruent if all their corresponding sides and angles are congruent. This means that the triangles have equal angles and equal sides.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

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For x = 80 and y = 130, l and m will be parallel to j and n respectively.

If two lines are parallel, then the sum of the interior angles is supplementary.

Thus, if m || n, then (x - 30) and (x + 50) will be supplementary

⇒ (x - 30) + (x + 50) = 180

x - 30 + x + 50 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Thus, if x = 80, then k will be parallel to l

Now, if m || n, then y and (x - 30) must be supplementary

⇒ (x - 30) + y = 180

x - 30 + y = 180

we found that x = 80

⇒ 80 - 30 + y = 180

50 + y = 180

y = 180 - 50

y = 130

Thus, if y = 130 then, k will be parallel to l.

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The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5

Let us assume that one spends x hours doing homework on a typical weekday. Then we can write

The inequality expression for a slow weekend is given as;

X ≥ 2

In the same vein, the inequality expression for a busy weekend is given as;

X ≤ 5

Pooling the two inequalities expression we have;

2 ≤ x ≤ 5

Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b

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The distance being proportional to the time Hector walked 2 km in 18 minutes.

Two variables are proportional if they can be written in the form ak=b where k is the proportionality constant.

Here the proportionality constant is speed.

Speed is defined as the distance covered in unit time. The unit of speed can be written as kilometer per hour, miles per hour or meters per second.

The distance is proportional to the time walked therefore:

1.5/2=13.5/T₁

or, T₁=18

Similarly:

1.5/4.5=13.5/T₂

or, T₂=40.5 minutes

again,

1.5/5=13.5/T₃

or, T₃=45 minutes.

Hence the total time taken to complete the distances 2,4.5 and 5 is given by 18,40.5 and 45 minutes.

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Answer:

1. 9/10 x 3 = 93/10

2. 9/8

Espero que esto ayude a tener un buen día!

Step-by-step explanation:

=5(2,47y)+5(-2,03)

=12.35y-10,15

Answer:

One number is -6 and the other number is 7.

Step-by-step explanation:

Let x be one of the numbers and y be the other number.

So 8x + 5y = -13.

Also, x + y = 1

These two equations are the algebraic version of the words in the problem.

We need to solve this system of equations. You may be studying solving systems of equations using substitution or elimination method or even matrices. I will show you here using elimination method, sometimes called addition or subtraction method.

We need to multiply x+y=1 by -5.

-5(x + y = 1)

-5x - 5y = -5

We can stack the two equation and add them together to eliminate one of the variables.

8x + 5y = -13

-5x - 5y = -5

___________ Add.

3x = -18

3x = -18 Now divide by 3.

x = -6

Put thus value back into one of the original equations.

x = -6

x + y = 1

Substitute.

-6 + y = 1

Add 6.

y = 7

When one number is -6 and the other number is 7, then both equations will be true.

Answer:

If y varies directly as x and y= 64 when x=4 find x when y=48

x=3

Answer:

gdjsgsghdbdgdjdnvshskdndhdhdhdbbdbdhdhdhd

Because the squared equation can have negative roots.

If the equation you're given already includes the squared variable (and you don't multiply by the variable yourself), then you don't need to worry about the extraneous root. Both solutions will be correct because the variable was already squared.

You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive. That means that, if you square a variable (especially for variables on both sides of the equation, which can easily hide a negative) or a negative number, you should always do a quick plug-in and check.

Because the squared equation can have negative roots.

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The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.

Hence, option D) -7/4 is the correct answer.

Given the expression in the question;

12.5 - 31/2 + 1 1/4

First, convert the mixed fraction into an improper fraction.

1 1/4 = ( 1×4 + 1 )/4 = ( 4 + 1 )/4 = 5/4

Now, rewrite the expression as;

12.5 - 31/2 + 5/4

Find the common denominator

( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )

( 12.5/1 × 4/4 ) - ( 31/2 × 2/2 ) + ( 5/4 × 1/1 )

Perform the multiplication operation

50/4 - 62/4 + 5/4

Now, combine the numerators over the common denominator.

( 50 - 62 + 5 )/4

( -12 + 5 )/4

( -7 )/4

-7/4

The the simplified form of the given expression 12.5 - 31/2 + 1 1/4 is -7/4.

Hence, option D) -7/4 is the correct answer.

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The expression of the statement is 1.06x

Expressions are mathematical statements that are represented by variables, coefficients and operators

The statement is given as

The price of an item plus 6% sales tax

Let the price of the item be x

So, we have the sales tax amount to be

Sales tax amount = x * 6%

Evaluate the product

So, we have

Sales tax amount = 0.06x

So, the total amount is

Total = x + 0.06x

Evaluate the sum

So, we have

Total = 1.06x

Hence, the expression of the statement is 1.06x

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