Please answer question 5 and 6.

5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).

6.Graph the function.

The given expression is 4.9 x 10⁻¹¹.

What is a mathematical expression?

An expression, often known as a mathematical expression, is a limited collection of symbols that have been well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and groupings can all be represented by mathematical representations, which can also be used to indicate the logical syntax's sequence of operations and other features. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.

The given expression can be solved as follows

   (7x10⁻⁶)(7x10⁻⁶)

= (7x7) x (10⁻⁶x10⁻⁶)

= 49 x 10⁻¹²

= 4.9 x 10⁻¹¹

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A function is a relation in which each input value (x-value) has one and only one output value (y-value).

You have the following Linear function:

According to the explained in the problem, you must find an input value that gives you 13 as the output value. Knowing this, you can say that:

Substitute this value into the given function:

The final step is to solve for "x".

Therefore, the value of "x" so that the function has the given value 13, is:

Answer:

x = -5/f

Step-by-step explanation:

a) Divide both sides by f.

fx/f = -5/f

x = -5/f

Answer:

the answer is -5/f

Step-by-step explanation:

f(x)=fx

fx=-5

Divide both sides by f

fx/f =-5/f

x=-5/f

HOPE IT HELPED

Answer: [tex]f(x)=-4x+11[/tex] and [tex]f(x)=\frac{2}{3}x-8[/tex]

Step-by-step explanation:

All linear functions with unrestricted domains have a range of all real numbers.

In a absolute value graph the value of y is the same in -x and x.

To find the value of a you use one of the points (x,y) in the general form of absolute value:

( 1 , 8) x=1 f(x)= y=8

As:

You get:

Then:

The equation for the graph with points (1 , 8) and ( -1, 8) is:

Answer:

I believe the first one

Step-by-step explanation:

Brainliest pls?

The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.

In this problem we find a line segment whose endpoints are known and we need to determine the equation of the line perpendicular such that the segment is partitioned into two segments of equal length. Now we present the procedure. First, determine the coordinates of the midpoint:

M(x, y) = 0.5 · (8, - 1) + 0.5 · (4, - 9)

M(x, y) = (6, - 5)

Second, determine the slope of the line segment:

m = [- 9 - (- 1)] / (4 - 8)

m = (- 8) / (- 4)

m = 2

Third, calculate the slope of the bisector:

m' = - 1 / m

m' = - 1 / 2

Fourth, determine the intercept of the bisector:

b = y - m' · x

b = - 5 - (- 1 / 2) · 6

b = - 5 + 3

b = - 2

The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.

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Answer:

40 = (184*j) - 208 or 40 = 184j - 208

Original equation: y = x²

Tranformation rule:

horizontal translation c units leftt = f(x + c); so:

Modified equation: y = (x + 3)²

Answer:

4 6 3

_ 1 3 9

________

3 2 4

Step-by-step explanation:

you think of of a number

or use logic to answer it

The calculation for x=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .

In the question ,

it is given that x=0 ,

When x=0 in a point (x,y) means , that point lies on the y -axis , and it is called as the y intercept .

Y intercept is defined as the point where the graph of a line crosses the y-axis .

the point on the y-axis will be (0,y) ,

So , the graph will cross the y-axis when x=0 , and that point will be (0,y).

and the value of y will be called as the y intercept of the graph .

Therefore , the calculation for y=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .

The given question is incomplete , the complete question is

The calculation for x=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .

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Answer:

  120

Step-by-step explanation:

You want to find a number such that 50% of it is 60, using the formula R×B = A.

An amount is found by multiplying the rate by the base. That is described by the formula ...

  R × B = A

Here, we're given the amount and the rate, and we want to find the base. We can fill in the given numbers and solve for B.

  50% × B = 60

  B = 60/0.50 . . . . . . divide by the rate

  B = 120 . . . . . . . simplify

50% of 120 is 60.

ANSWER

10425

EXPLANATION

We want to multiply the numbers given by using product of parts.

To do this, we will split the number into hundred, tens and units. That is:

So that will be:

That is the answer.

Answer:

121 - 61 = 60 degrees

Step-by-step explanation:

Answer:

∠QPR=60

Step-by-step explanation:

∠SPQ-∠SPR=∠QPR

121-61=∠QPR

60=∠QPR

Givens.

• The diameter of the semi-circle is 9.25 yd.

• The other two sides of the triangle are 6.83 yd and 8.66 yd long.

First, find the perimeter of the semi-circle using the circumference formula.

Second, add the two sides of the triangle to the circumference of the semi-circle.

From the statement, we know that there are two possible scenarios:

A) Kira rolls the die and gets a face with a 1, 2, 3, 4, 5 or 6.

• The probability of this event is P(A) = 1/12.

• Kira will write the number of the face in this case.

B) Kira rolls the die and gets an edge.

• The probability for this event is 1/24.

• Kira will write the sum of the numbers that share the top edge.

• There are multiple values for the result of the sum.

We must take into account that:

• 1 and 5 are on opposite faces,

• 2 and 3 are on opposite faces,

• 4 and 6 are on opposite faces.

The possible values of the sum and the forms to get it are:

0. 3, = 1 + 2 → P(B'_1) = 1/24

1. 4, = 1 + 3 → P(B'_2) = 1/24

2. 5, = 1 + 4 → P(B'_3) = 2/24

3. 6, = 2 + 4 → P(B'_4) = 2/24

4. 7, = 1 + 6 = 2 + 5 = 3 + 4 → P(B'_5) = 3/24

5. 8, = 2 + 6 = 3 + 5 → P(B'_6) = 2/24

6. 9, = 3 + 6 = 4 + 5 → P(B'_7) = 2/24

7. 11, = 5 + 6 → P(B'_9) = 1/24

We have 8 possible results for the sum.

---------------------

Now, we want to know the value of the expected value of the numbers recorded by Kira.

By definition, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected value of the number recorded by Kira will be:

Where:

• A_i represents the result of event A_i and P(A_i) its probability,

• B_i represents the result of event B_i and P(B_i) its probability.

Using the data from above, we compute each of the sums.

A) For the first sum, we take into account that each event A_i has the same probability:

B) For the second sum, we use each of the values of the sum and the probabilities of each sum:

Summing the results of each sum, we get the following result for the expected value:

The expected value for the number recorded is 137/24 or approximately 5.71.

Answer: The answer is 10

Step-by-step explanation:

      Distribute 1(x-2)/5 = 1(x+6)/10

         x-2/5 = x+6/10

      Multiply by 10 on each side

         2(x - 2) = x + 6

          Distribute

          2x - 4 = x + 6

           Add 4 on each side

           2x= x + 10

           Subtract x

             x = 10

Answer: x=10

Step-by-step explanation:

1/5(x-2)=1/10(x+6)

Distribute and multiply first

(1/5*x) -(1/5*2)=(1/10*x) +(1/10*6)

1/5x-2/5=1/10x+6/10

We do not have the same denominators on both sides. 5 goes into 10 two times so we will multiply everything on the left by 2 to get a common denominator.

2/10x-4/10=1/10x+6/10

Subtract 1/10x from both sides

1/10x-4/10=6/10

Add 4/10 to both sides

1/10x=10/10

1/10x= 1

Multiply both sides by 10/1 (the fraction inverse) to get rid of the fraction.

(10/1)(1/10x) =(1)(10/1)

x= 10

Check work:

1/5(x-2)=1/10(x+6)

Substitute your answer for x

1/5(10-2)=1/10(10+6)

1/5(8)=1/10(16)

8/5=16/10

Simplify 16/10 by dividing by 2

8/5=8/5

using linear equation, Salma needs 10 number of visit to movie theater to get free movie ticket.

What is Linear equation?

A linear equation is one in which the variable's highest power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.

linear equation is given by y= mx + c

Salma has 30 rewards points just for signing up and 8.5 points for each visit. the equation became 30+8.5v=115

30+8.5v=115

8.5v=115-30

8.5v=85

v=10

therefore, she needs 10 number of visits to movie theater.

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let's take a looksie hmmmm a parabola opening downwards in vertex form using constants of "h" and "k" will be like

[tex]y = -(x+h)^2 +k\implies y = -x^2-2hx-h^2+k \\\\\\ \cfrac{dy}{dx}=-2x-2h\qquad \impliedby \textit{straight line with a negative slope}[/tex]

initial height = 6

Rate of growth = 3 inches per month

Table:

Month height 1

96+3(3) = 91

2 6 + 3 (2)=12

3 6+3 (3) = 15

Apply the formula:

H = H0 + rt

Where:

H0 = initial growth

r = growing rate

t= number of months

Replacing:

H(t) = 6 + (3 t)

The areas for this problem are given as follows:

3. 681.25 ft².

4. 193 m².

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For this problem, a rectangular deck of dimensions l = 18.75 ft and w = 15 ft is added, hence the area of the deck is:

A = 18.75 x 15 = 281.25 ft².

This area is added to the previous area, hence the total area is of:

A = 400 ft² + 281.25 ft² = 681.25 ft².

The figure is composed by:

The area of the triangle is half the base times the height, while the area of the rectangle was presented in the previous item, hence the total area of the figure is:

A = 10 x 18 + 0.5 x 13 x 2 = 180 + 13 = 193 m².

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The function family sketched is exponential function.

From the graph, we can find certain values of the function for certain x-values.

When x = 0, the function has value 1.

When x = 2, the function has value 4

When x = 3, the function has value 8.

When x = 4, the function has value 16

From this we can identify the function as the exponential function, f(x) = eˣ

because e⁰ = 1. i.e., exponential function has value 1 when x = 0 which satisfy the sketch of the function given.

Also the other options given as piecewise function, linear function and quadratic function.

A piecewise function will not have a continuous sketch, but here the sketch of the function is continuous. So it cannot be a piecewise function. A linear function will have the sketch as a straight line, but here it is not. So it is not a linear function. The function values given in the sketch does not satisfy the quadratic function also.

So the only option is the sketch is of the exponential function.

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The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.

a. D = P/64 is the solution to the formula's "d" subject.

b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.

A function can be defined as an expression, law or rule that shows the relationship between two variables.

Given the role as;

P = 64d

Where;

P stands for pressure in pounds per square foot.

The object's depth, d, is expressed in feet.

Now let's center the formula on the variable "d."

Both sides of the equation are divided by the variable "d64-based "'s coefficient. This is carried out so that the variable can stand on its own.

We have.

P/64 = 64d/64

d = P/ 64

If there is pressure, P is equivalent to 672 pounds per square foot.

When the value of the variable is inserted into the formula, we obtain;

d = P/64

Then,

d = 672/64

Discover the quotient.

d = 10. 5 ft.

Therefore,

The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.

a. D = P/64 is the solution to the formula's "d" subject.

b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.

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Answer:

12

Step-by-step explanation:

The original price is $414.

The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided. a fair deduction from a debt account, typically done in exchange for cash or quick payment.

Given Data

A DVD is discounted by 15% and then from the already discounted price, a further 20% discount is given.  

The price now is $300

x = 300 + 15% + 20%

x = 300 + [tex]\frac{15}{100}[/tex] + [tex]\frac{20}{100}[/tex]

x = 414

The original price is $414.

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Let's use the variables x, y and z to represent each of the three numbers.

If the sum of the three numbers is equal to 80, we have our first equation:

The first number is 8 more than the second, so:

The third number is 2 times the second, so:

Using these values of z and x in the first equation, let's solve it for y:

Now, calculating x and z, we have:

Therefore the first number is 26, the second number is 18 and the third number is 36.

(a) Amount of water in the first pool (In liters) = (817 + 19x) liters

Amount of water in the second pool (in liters) = 39x liters

(b) An equation to show when the two pools would have the same amount of water is 817 + 19x = 38x.

Given:

For the First Pool :

Initial amount of water in the Pool = 817 liters

Water is being added to the first pool at a rate of 19 liters per minute.

Amount of water added after x minutes = 19x

So, Total amount of water after x minutes = (817 + 19x) liters

For the Second Pool:

It was empty initially.

Water is being added to the second pool at a rate of 38 liters per minute.

Amount of water added after x minutes = 38x

So, Total amount of water after x minutes = 38x liters

Now to determine an equation to show when the two pools would have the same amount of water.

817 + 19x = 38x

38x - 19x = 817

19x = 817

x = 817/19

x = 43 minutes

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Okay, here we have this:

Considering the provided information, we are going to find the x- and y- intercepts and explain its meaning. So we obtain the following:

Since the x-intercept is the point where the Graph intersects the x-axis (y=0) and the y-intercept is the point where the Graph intersects the y-axis (x=0), we have that:

x-intercept=(300, 0)

y-intercept=(0, 16)

Since the y-axis represents the number of gallons, and the x-axis time, then the y-intercept indicates that when filling the tank it was left with 16 gallons, and the x-intercept indicates that when emptying the tank had traveled 300 miles.

The value of composite function (f о g) (-1) will be -1.

What is Composite function?

A composite function is a function that is written inside with another function and composition of functions is done by substituting one function into another function.

Given that;

The value of functions are;

f (x) = - 3x -1

And, g (x) = x² - 1

Now, All values of functions are;

f (x) = - 3x -1

And, g (x) = x² - 1

Composition of functions is calculated as;

Since, (f о g) (x) = f (g(x))

Substitute the value of function f(x) and g(x) in above equation;

(f о g) (x) = f (g(x))

              = f (x² - 1)

              = - 3(x² - 1) - 1

              = -3x² + 3 - 1

              = -3x² + 2

Put x = -1 in above equation we get;

(f о g) (-1) = - 3 (-1)² + 2

              = - 3 + 2

              = -1

So,  (f о g) (-1) = -1

Thus, The value of composite function (f о g) (-1) will be -1.

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