Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is the number of years from today. p(t) = 3000 * (1.019) ^ t

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]

By solving the given equations, the values of x are 7 and -7.

So, |x| -7:

Now, solve for x as follows:

Then,

Therefore, by solving the given equations, the values of x are 7 and -7.

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Answer:

see below

Step-by-step explanation:

All the given equation have mod function in them .We know that, if

[tex]\longrightarrow |x| = y \\[/tex]

then ,

[tex]\longrightarrow x =\pm y \\[/tex]

1) |k| = 8

[tex]\longrightarrow k =\pm 8 \\[/tex]

__________________________

2)|x| = 7

[tex]\longrightarrow x = \pm 7\\[/tex]

__________________________

3) |a+2| = 8

[tex]\longrightarrow a + 2 =\pm \\[/tex]

[tex]\longrightarrow a = 8-2 \ or \ -8-2\\[/tex]

[tex]\longrightarrow a = 6 , -10 \\[/tex]

__________________________

4) |8a|/10 = 2

[tex]\longrightarrow |8a| = 20 \\[/tex]

[tex]\longrightarrow 8a =\pm 20\\[/tex]

[tex]\longrightarrow a =\pm\dfrac{20}{8} \\[/tex]

[tex]\longrightarrow a = \pm\dfrac{5}{2} \\[/tex]

___________________________

5)|-m+9| = 13

[tex]\longrightarrow -m+9 =\pm 13\\[/tex]

[tex]\longrightarrow m -9 =\pm 13\\[/tex]

[tex]\longrightarrow m = 13-9\ or \ -13-9\\[/tex]

[tex]\longrightarrow m = 4 , -22\\[/tex]

____________________________

6)|7-5x|=27

[tex]\longrightarrow 7-5x =\pm 27 \\[/tex]

[tex]\longrightarrow 5x -7 =\pm 27\\[/tex]

[tex]\longrightarrow 5x = 27 +7 \ or \ -27+7 \\[/tex]

[tex]\longrightarrow 5x = 34 \ or -20 \\[/tex]

[tex]\longrightarrow x =\dfrac{34}{5}, -4\\[/tex]

_____________________________

7)|2x+7|/5=5

[tex]\longrightarrow |2x+7|=25\\[/tex]

[tex]\longrightarrow 2x +7 =\pm 25 \\[/tex]

[tex]\longrightarrow 2x = 25-7 \ or \ -25-7\\[/tex]

[tex]\longrightarrow 2x = 18 \ or \ -32\\[/tex]

[tex]\longrightarrow x = 9 , -16 \\[/tex]

And we are done!

Remember that ordered pairs are written in the form:

To find it (-2,2) is a solution for the given equation, substitute x=-2 and y=2:

Since the expression -2=-3 is false, then the point (-2,2) is not a solution for the given equation.

Let's calculate the percentage of dogs in the animal group

The answer would be 40%.

Maryam's total percentage score on her exam is 71%.

Percentage is the ratio of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.

The first step is to determine the score on each paper.

Score on the first test = 65% x 120

(65 / 100) x 120  = 78

Score on the second test = 80% x 80

0.80 x 80 = 64

Total percentage score = (sum of scores / total score) x 100

Sum of scores = 64 + 78 = 142

Total score = 120 + 80 = 200

(142 / 200) x 100 = 71%

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Absolute value is the distance a number is from zero.

Because distance cannot be negative, an absolute value can never be a negative.

Therefore,

|x| = -5 has no solutions

Answer:

98 adult tickets

Explanation:

Part A

Let the number of children's ticket sold = c

Let the number of adult's ticket sold = a

Cost of a children's ticket = $7.75

Cost of an adult's ticket = $10.25

Total income from ticket sales = $1,585.75

An equation to represent this situation is:

Part B

If the number of children's ticket sold, c = 75

Then:

The number of adult tickets sold by the cinema is 98.

The simultaneous equations are:

Since, the unknown y has the same co-efficient across the two(2) equations, we can eliminate it directly.

Thus, we have:

To find y, substitute for x = -6 into any of the equations.

Thus, we have:

Hence, the correct option is option A

Looking at the diagram,

each small box represents one unit

The number of units from A to B is 4 units

The number of units from B to C is 3 units

Thus, the length of rectangle ABCD is 4 units and its width is 3 units.

The original coordinates are

A(0, 0)

B(0, 4)

C(3, 4)

D(3, 0)

If

The situation forms the right triangle above:

Where x is the length of the ladder.

Apply the Pythagorean theorem:

c^2 = a^2 +b^1

where:

c = hypotenuse = longest side = x

A &b = the other 2 legs of the triangle

Replacing:

x^2 = 60^2 + 15^2

Solve for x

x^2 = 3,600 + 225

x^2 = 3,825

x =√3,825

x = 61.85 ft

• Volume of pentagonal prism = area of base x height

Volume = 247 unis^3

height = 13 units

Replacing:

V = A x h

A = V / h

A = 247/13 = 19 units^2

The equation that can be used to determine the number of dogs that Julie has =

4× (number of chicken) = 64

An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.

The number of chicken owned by Julie = 16 chickens

The number of dogs = X

But she has 4× (number of chicken) = X

That is 4 × 16 = X

X= 64

Therefore the number of dogs that Julie has = 64 dogs.

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The volume of a sphere is given by:

The original sphere, with radius r=3, has volume:

The second sphere, with radius r=9, has volume:

To find how much the volume increased we substract the first volume to the second one:

Therefore the v

According to the given diagram the sum of ABD, DBE and EBC must be 90. Use this information to find the measure of DBE:

The measure of DBE is 24 degrees.

Given:

Required:

We need to find the solution by Vièta's theorem.

Explanation:

Compare 1st equation with

we get

Vièta's theorem is

now solve this equation and we get

because addition of 1 and 2 is 3 and multiplication is 2

Now for 2nd equation

apply Vièta's theorem

by this

because addition of 3 and -5 is -2 and multiplication is -15

With the help of the Pythagorean theorem, we know that we should buy 3 packages.

So, Pythagorean formula: c² = a² + b²

(Refer to the image of the kite attached below)

△1:

△2:

x₂ = x₁ = 19.2 in

△3:

△4:

Total: 19.2(2) + 15 + 2(12) + 20 + 2(23.3) = 144 in

Now,

So, we should buy 3 packages.

Therefore, with the help of the Pythagorean theorem, we know that we should buy 3 packages.

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Solution:

Given that a medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, this implies that

To evaluate the number of people that can be selected, we use the combination formula expressed as

In this case,

Thus, the question involves combination.

The point that belongs to the solution set is A( 4, 4)

Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.

They are mostly used to compare two numbers on the number line on the basis of their sizes.

Given the inequalities;

Make 'x' the subject from equation 1, we have;

x > 6 - y

substitute the value into equation 2, we have;

3( 6 - y) - 5y  ≤ 2

expand the bracket

18 - 3y - 5y ≤ 2

collect like terms

- 8y ≤ 2 - 18

- 8y ≤ -16

Make 'y' the subject of formula

y ≤ 2

Substitute the value in equation 3

x > 6 - 2

x > 4

Hence, the point is A( 4, 4)

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SOLUTION

What all graphs of proportional relationships have in common is a straight line.

This line is straight, no curves or bends. This straight line passes through the origin at an intersection of

Hence, the answer is "A straight line that passes through the origin and goes at a constant rate".

Given the equation of the line:

The given equation as the slope-intercept form: y = m * x + b

where m is the slope and b is the y-intercept

the y-intercept is the value of y when x = 0

By comparing the given equation with the slope-intercept form

So,

The slope = m = -2

The y-intercept = b = -1

the point of y-intercept = ( 0, -1 )

Answer:

3 or -3

Explanation:

Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:

8x² - 5 = 67

Now, we can solve the equation for x. Add 5 to both sides

8x² - 5 + 5 = 67 + 5

8x² = 72

Divide both sides by 8

8x²/8 = 72/8

x² = 9

Find the square root of both sides

x = √9

x = 3 or x = -3

Therefore, the number is 3 or -3

The answer is 5, 9, 10

Explanation:

Given the equation that models the number of passengers who can sit in a car expressed as 3x + 2y = 120

x is the number of adults

y is the number of children

The x-intercept is the point where y is zero i.e. the number of adults when there is no number of children.

when y = 0

3x + 2(0) = 120

3x = 120

x = 120/3

x = 40

This means that there will be 40 adults if there are no children

The y-intercept is the point where x is zero i.e. the number of children when there is no number of adults.

when x = 0

3(0) + 2y = 120

2y = 120

y = 120/2

y = 60

This means that there will be 60children if there are no adults

Given:

The objective is to find the solution of 2+2.

Since the required operation in the given question is addition.

So, the addition of 2 and 2 will be,

Hence, the answer is 4.

Given: the inequality is,

To solve the inequality,

The graph for the giev inequality is,

Since we have the original coordinates P(-6, 9), Q(3, 9), R(3, 3) & S(-6, 3) and the scale factor, we multiply each x-component and y-component of each point by 1/2 in order to get P'Q'R'S', that is:

P'(-3, 9/2)

Q'(3/2, 9/2)

R'(3/2, 3/2)

S'(-3, 3/2)

And those are our P'Q'R'S' coordinates after the scaling,

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The graphical solution for the two systems of equations are as follows:

CONCLUSION:

The solutions to the systems of equations are:

The value of x in the given quadratic equations is either -2.7 or -11.3.

A quadratic equation is a second-degree algebraic equation in x. ax² + bx + c = 0, where a and b are coefficients, x is the variable, and c is the constant term, is the quadratic equation in its simplest form.

Given first equation, y = x²- 6x + 4 second equation, y = x +1

Put the value of y in the first equation to get

x + 1 = x² - 6x + 4

Solving this equation

x² - 7x + 3 = 0

Using quadratic formula,

x = - b ± [tex]\frac{\sqrt{(b^{2}- 4ac)}}{2a}[/tex]

x = - 7 ±  [tex]\frac{\sqrt{(-7)^{2}- 4(3)}}{2}[/tex]

x = - 7 ± 4.3

Therefore in the given quadratic equations, the value of x can be either -2.7 or -11.3

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