For each of the equations, give the gradient of a line that is

Parallel to the graph
perpendicular to the graph
f(x)=2x-1

Since they're in arithmetic progression, the difference between consecutive terms is fixed.

[tex](x + 2) - (x - 1) = 3[/tex]

[tex]3x - (x + 2) = 2x - 2 = 3 \implies 2x = 5 \implies x = \dfrac52[/tex]

Then the first term is

[tex]x-1=\dfrac52 - 1 = \boxed{\dfrac32}[/tex]

and the fifth term is

[tex]3x + 3 + 3 = 3\cdot\dfrac32 + 3 + 3 = \boxed{\dfrac21}2[/tex]

Comparing the price of a 50000 mercedes to the price of a 40000 lexus The absolute price difference is 10000 while the relative price difference is 20%

Absolute difference refers to the gap between the prices. This implies the amount one has more than the other.

This could be solved by subtraction an is solves as follows:

price of a mercedes -  price of a lexus

= 50 000 - 40 000

= 10 000

Here, the price difference is expressed in percentage of the reference price being checked with. This is achieved using the formula below:

( price of a mercedes -  price of a lexus ) / price of a mercedes * 100

= (( 50 000 - 40 000 ) / 50 000 ) * 100

= (( 10 000 ) / 50 000 ) * 100

= ( 0.2 ) * 100

= 20%

Hence the absolute price difference is 10 000 and the relative price difference is 20%

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Answer:

1.) 3x + 7 = -x - 1

*collect like terms

3x + x = -1 - 7

4x = -8

x = -2

2.) 4x - 3 = 1 - 2x + 5

*collect like terms

4x + 2x = 1 + 5 + 3

6x = 9

x = 9/6

x = 3/2

3. 4x - 2 + x = 2x - 2

*collect like terms

4x + x - 2x = -2 + 2

3x = 0

x = 0/3

x = 0

4.) 3x - 4 + 1 = 5x - 5 - 2x

*collect like terms

3x - 5x + 2x = - 5 + 4 - 1

(this is a tricky one ... sorry I can't figure the answer)

Answer: B is correct answer

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

-x² + 7x + 5 is the domain of all real numbers.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².

we have to calculate (g - f)(x)

Which is equivalent to:

(g - f)(x) = g(x) - f(x)

Taking the two functions and substituting them into this expression, we get,

g(x) - f(x) = (7x + 5) - (x²)

simplifying the above function, we get

g(x) - f(x) = -x² + 7x + 5

Therefore, (g - f)(x) = -x² + 7x + 5.

We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.

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The function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

We are given the function:

y = 4 (3) x

Multiply 4 and 3, we get that:

y = 12 x

Now, subtract y from both the sides, we get that:

12 x - y = 0

We can see that the degree of each variable is 1 .

So, it will be a linear function.

Therefore, we get that, the function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

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Answer:

x<-27/4

​

Step-by-step explanation:

−4(2−x)1<−35

Multiply −4 and 1 to get −4.

−4(2−x) <−35

Use the distributive property to multiply −4 by 2−x.

−8+4x<−35

Add 8 to both sides.

4x<−35+8

Add −35 and 8 to get −27.

4x<−27

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

Answer:

[tex]\left[\begin{array}{ccc}-48&-60\\44&30\end{array}\right][/tex]

Step-by-step explanation:

0.5 X + 3A = B implies

X = 2(B-3A)

3A simply means multiplying each cell by 3

[tex]3A = \left[\begin{array}{ccc}12&24\\-33&-3\end{array}\right][/tex]

B-3A is a corresponding cell by cell subtraction

[tex]B-3A = \left[\begin{array}{ccc}-24&-30\\22&15\end{array}\right][/tex]

Finally multiply that by 2, result is at the top.

The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

What is Range of set?

The range is the set of possible output values, which are shown on the y-axis.

The function is given as;

y = -1/2 x + 3

Now, The values of x are given as;

x = 0, 2, 4, 6

Hence, The value of y are find as;

When x = 0

y = -1/2 * 0 + 3 = 3

When x = 2

y = -1/2 * 2 + 3

y = 2

When x = 4

y = -1/2 * 4 + 3

y = 1

When x = 6

y = -1/2 * 6 + 3

y = 0

Hence, All values of y are {3, 2, 1, 0}

So, The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

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Answer:

The fourth option

Step-by-step explanation:

Formula to find the area of a circle is [tex]\pi r^{2}[/tex]

[tex]\pi 7^2[/tex]

[tex]49\pi[/tex]

Answer:

y = 105

x = 31

Step-by-step explanation:

We have y and 75 as consecutive interior angles.
(Consecutive interior angles are are found between the two parallel lines and on the same side of the transversal)

Sum of two consecutive interior angles = 180°

so we have y + 75 = 180
y = 180-75 = 105

So y = 105

y and (3x+12) are opposite angles and are equal
So 3x+12 = y
3x + 12 = 105
3x = 105-12 = 93
x = 93/3 = 31

So x = 31

Based on Cameron's current music service fees, the number of songs that would make the new service a less expensive option is 101 songs

The expression for the new service assuming the number of songs is x is:

= 15 + 0.80x

The expression for Cameron's current service is:
= 0.95x

Equating them gives:

0.95x = 15 + 0.8x

0.95x - 0.8x = 15

0.15x = 15

x = 100 songs

The cost will be the same at 100 songs so the new service would be cheaper at 101 songs.

First part of question:

Cameron pays $0.95 per song with his current music service.

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The length of the rectangle according to the task content where the length of a rectangle is twice its width whose perimeter is; 84 feet is; 31.33.

According to the task content, it follows that the length of the rectangle is twice its width, If the perimeter is 84 feet.

Since the perimeter of the rectangle in discuss can be determined as follows;

Perimeter = 2(l + w)

where l = 2w.

Therefore,

94 = 2(2w + w)

47 = 3w

w = 47/3

w = 15.667.

Ultimately, the length of the rectangle in discuss is; 2w = 2× 15.667

= 31.33 feet.

Therefore, the length of the rectangle according to the task content where the length of a rectangle is twice its width whose perimeter is; 84 feet is; 31.33.

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Answer:

(2, -3)

Step-by-step explanation:

x= -3y-7    

5x+6y=-8  

1. Substitute x= -3y-7 into 5x+6y=-8 which becomes

5(-3y-7)+6y=-8

2. expand the brackets

-15y-35+6y=-8

3. simplify the equation

 -9y-35=-8

4. from this we can find the value of y by adding 35 on each side and then dividing by -9 on each side

-9y=27

y=-3

5. so, the value of y is -3 to find the value of x we just substitute the value of y (-3) into the x=-3y-7

x= -3(-3)-7

expand the brackets and simplify the expression

x=9-7

x=2

6. so the value of x=2

7. your final answer will be (2, -3)

The domain of the function is (0,∞) , {x|x>0}

and the range of the function is (−∞,∞),  {y|y ∈ R}

given the function is y = 3 log x

Set the argument in  log x greater than 0 to find where the expression is defined.

x > 0

The domain is all values of x that make the expression defined.

Interval Notation:

(0,∞)

Set-Builder Notation:

{x|x>0}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Determine the domain and range.

Domain: (0,∞) , {x|x>0}

Range :  (−∞,∞),  {y|y ∈ R}

Hence we get the required domain and range of the given function.

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Answer:

- 4 < x < -1

Step-by-step explanation:

Answer:

365 * 88 (^7) =  B=10

Answer: x=28/3=9.333

Step-by-step explanation:

Answer:

1/2 + 2/3 × 3/14

Step 1: you multiply first

= 2/3 × 3/14

= 6/42

= 7

Step 2: Now add

= 1/2 + 7

LCM = 14

= 1/2 + 7/1

= 1 + 14

2

= 15/2.

or 7.5

or 7½

If PQRS is a square & TR= 17, then

PR= 34

QS= 34

QT= 17

PQ= [tex]17\sqrt{2}[/tex]

A square in geometry is a two-dimensional plane figure having four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, however only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.

A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is another name for a rectangle with two sides that are opposite and the same length.

The following is a list of a square's most significant characteristics:

We know that,

Diagnose of a square are equal in magnitude and bisect each other.

So, In the given figure,

diagonals PR and QS are bisected at T.

RT = PT = 17

Hence,

PR=2RT=2*17=34

PR= 34

QS=34

[tex]QT=\frac{1}{2}QS = \frac{1}{2}*34 = 17[/tex]

QT=17

PQ = side of square

Let PQ= QR= a

In ΔPQR

[tex]PQ^{2} + QR^{2} = PR^{2}[/tex]

[tex]PQ^{2}+ PQ^{2} = 34^{2}[/tex]

[tex]2PQ^{2} = 34*34[/tex]

[tex]PQ = \sqrt{17*34} = 17\sqrt{2}[/tex]

PQ = [tex]17\sqrt{2}[/tex]

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Answer:

for question a)

yes it is a function

Step-by-step explanation:

more hours studied = higher score

Answer:

27

Step-by-step explanation:

Answer: Volume is calculated by lenght x width x height ,so you would say 6 x 4 x 4. Which is   96 cubic units !!!

Step-by-step explanation:

The growth factor for the annual rate of change of +12.5 % is 1.125.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 12.5 % = + 12.5 / 100 = + 0.125

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+ 0.125)

B = 1.125

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.125.

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Answer:

r = 10 mph

Step-by-step explanation:

3 hr. x rate = 2.5 hr x (rate + 2

r = 10 mph

Answer:

r = 10 mph

Step-by-step explanation:

Answer:

The top 2 and the bottom right!

Hope this helps!

The value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

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

The expression is given as

[ -2/3 x (-2/3) ] x ( -9/4)

Evaluate the expression in the bracket

So, we have

[ -2/3 x (-2/3) ] x ( -9/4) = [4/9] x ( -9/4)

Evaluate the product

[ -2/3 x (-2/3) ] x ( -9/4) = -1

Hence, the value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

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the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

We know that if a parabola has x-intercepts a and b, and a leading coefficient A, then the equation is:

f(x) = A*(x - a)*(x - b)

In this case the x-intercepts are x = -4 and x = 5, then we have:

f(x) = A*(x + 4)*(x - 5)

Now we use the fact that the parabola passes through the point (1, -40), then we have that:

f(1) = -40 =  A*(1 + 4)*(1 - 5)

        -40 = A*(5)*(-4) = A*-20

       -40/-20 = A = 2

Then the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

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Answer:

(0, -4)

Step-by-step explanation:

hope this helps!!! :))

Answer:

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

We have the following linear equation to represent given situation:

Solve it for x to get the average number of miles:

In linear equation, He ride 3 miles each day.

Variable: x = Constant distance distance traveled each day.

Equation : 10+4x= 22

What is a formula for linear equations?

Total distance needs to travel = 22 miles

Distance already traveled = 10 miles

He will ride bicycle for 4  more days.

Let x = Constant distance distance traveled each day.

Total distance = 10+4x

10+4x = 22

4x = 22 - 10

4x = 12

  x = 3

Hence, he rode 3 miles each day.

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