Solve this absolute value equation and show all work.

1) 9 + |2x - 3| = 7

2) 3 + |2x - 4| = 15

y=2x-10

x=2y-10

x+10=2y

x+10/2=y

final answer: y=(x+10)/2

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{2}x+5}[/tex]

Step-by-step explanation:

[tex]f(x)=2x-10\to y=2x-10\\\\\text{we exchange each other x and y}\\\\x=2y-10\\\\\text{solve for y}\\\\2y-10=x\qquad\text{add 10 to both sides}\\\\2y=x+10\qquad\text{divide both sides by 2}\\\\y=\dfrac{1}{2}x+5[/tex]

Answer: $186.25

Step-by-step explanation:

To find the original price of the Digital Media Player before the 20% reduction, you can follow these steps:
1. Understand the discount:
A 20% reduction means the item is sold for 80% of its original price (100% - 20% = 80%).
2. Set up the equation to represent this situation:
Let the original price be \( P \). If the player is marked down by 20%, then it is now being sold for 80% of its original price. So we can write the following equation:
\[ 0.80 \cdot P = 149 \]
3. Solve for \( P \) (the original price):
To find the original price, divide the reduced price by 0.80 (which represents the 80% it is now being sold for).
\[ P = \frac{149}{0.80} \]
4. Calculate the result:
\[ P = \frac{149}{0.80} \]
\[ P = 186.25 \]
So the original price of the Digital Media Player was $186.25.

if your teacher allows the pi symbol then your answer is 2513. if your teacher requires you to use 3.14 for pi then your answer is 2512. basically you use the Pythagorean theorem to find the height, and then plug the height (24) and the radius which is half the diameter (10) into the equation to find the volume of the cone. if you have any other questions about it please ask! hope this helps:)

Answer:

D, B

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

In the first triangle, for angle A, 11 is the adjacent leg, 60 is the opposite leg, and 61 is the hypotenuse.  Therefore:

sin A = 60/61 = 0.98

cos A = 11/61 = 0.18

tan A = 60/11 = 5.45

So the correct answer is D.

In the second triangle, for angle Y, 16 is the adjacent leg and 65 is the hypotenuse.  To find the sine, we need to know the opposite leg.  So first, use Pythagorean theorem to find the opposite leg.

c² = a² + b²

65² = 16² + b²

4225 = 256 + b²

b² = 3969

b = 63

So the sine of Y is:

sin Y = 63 / 65

Answer B.

1. From the given right angle triangle, the adjacent side of angle A is 11 units.

The hypotenuse is 61 units.

We use the cosine ratio to get:

[tex] \cos(A) = \frac{adjacent}{hypotenuse} [/tex]

We substitute to obtain;

[tex]\cos(A) = \frac{11}{61} [/tex]

[tex]\cos(A) = 0.18[/tex]

[tex]A=\cos^{ - 1} (0.18)[/tex]

The correct choice is D.

2. From the given right triangle,

[tex]XZ^2 + {16}^{2} = {65}^{2} [/tex]

[tex]XZ^2 + 256 =4225[/tex]

[tex]XZ^2 =4225 - 256[/tex]

[tex]XZ^2 =3969[/tex]

Take positive square root

[tex]XZ=\sqrt{3969}[/tex]

[tex]XZ=63[/tex]

[tex] \sin(Y) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin(Y) = \frac{63}{65} [/tex]

The correct answer is B

Answer:

Choice c.

Step-by-step explanation:

The domain of a rational function is found where the denominator of the fraction is equal to 0.  These are the values that are NOT allowed.  We have to factor the denominator completely to find these values that make the denominator equal 0.  In other words, our denominator right now is:

[tex]x(x^2-16)[/tex]

we set each factor equal to 0:

x = 0 or

[tex]x^2-16=0[/tex]

The left side of that quadratic is the difference of perfect squares, so it factors into the 2 binomials:

(x + 4)(x - 4)

Setting each of those equal to 0 we can solve for the values of x that are not allowed:

If x + 4 = 0, then

x ≠ 4.

If x - 4 = 0, then

x ≠ -4

So the domain for this rational function is:

{x I x ≠ ±4, x ≠ 0},

which is c.

Answer:

30

Step-by-step explanation:

The population mean can be estimated with the sample average, so add up all the ages and divide by how many there are.

(19 + 27 + 25 + 21 + 44 + 22 + 45 + 34) / 8

29.625

Rounded to the nearest whole number, the average age is 30.

Answer:

The correct answer option is C. [tex]4\sqrt{3}[/tex].

Step-by-step explanation:

We are given an equilateral triangle which is divided into two equal halves and that makes two right angled triangles with known measures of angles.

We are to find the length of the altitude of the triangle. For that we can use the trigonometric ratios.

[tex]sin 60 = \frac{a}{8}[/tex]

[tex]\frac{\sqrt{3} }{2} =\frac{a}{8}[/tex]

[tex]a= \frac{\sqrt{3} }{2} \times 8[/tex]

[tex]a = 4\sqrt{3}[/tex]

Therefore, the correct answer option is C. [tex]4\sqrt{3}[/tex].

Answer:

The correct answer option is C. . \

Answer:

infinite number of solutions

Step-by-step explanation:

Given

8(x - 3) = 8x - 24 ← distribute left side

8x - 24 = 8x - 24

The expressions on both sides are equal

Hence any real value of x is a solution

That is there are an infinite number of solutions

To find the vertex of a parabola given an equation, you can use the formula x = -b/2a to find the x-coordinate and then substitute it back to find the y-coordinate.

The equation of the parabola is given as y = -1/4x² + 4x - 19. To find the coordinates of the vertex, we use the formula x = -b/2a to find the x-coordinate, and then substitute it back into the equation to find the y-coordinate.

Here, a = -1/4 and b = 4. Plugging these values into x = -b/2a, we get x = -4/(2×(-1/4)) = 4. Substituting x = 4 back into the equation gives us y = -1/4(4)² + 4(4) - 19 = -1.

Therefore, the coordinates of the vertex of the parabola are (4, -1).

Answer:

2196

Step-by-step explanation:

3^2 = 9

9+3^7 = 2196

ANSWER

21

EXPLANATION

The given by binomial expression is:

[tex]( {x}^{2} + y)^{7} [/tex]

Comparing this to

[tex](a+ b)^{n} [/tex]

We have:

[tex]n = 7[/tex]

[tex]a = {x}^{2} [/tex]

[tex]b = y[/tex]

The coefficient of the (r+1)th term is given by:

[tex] \binom{n}{r} [/tex]

We want to find the coefficient of the third term:

[tex]r + 1 = 3[/tex]

[tex]r = 2[/tex]

Therefore the coefficient is:

[tex]\binom{7}{2} = 21[/tex]

The coefficient of the third term is 21.

Answer:

54 degrees I think is correct

Answer:

31,2

Step-by-step explanation:

we can represent the numbers with two variables, x and y.

So the difference of them is 29.

x-y=29

Their sum is 33.

x+y=33

we can find the answer with a system of equations.

[tex]\left \{ {{x-y=29} \atop {x+y=33}} \right.[/tex]

x=29+y                    x=31        S{31,2}

y+29+y=33

2y=4

y=2

Answer:

x=31, y=2. (31, 2).

Step-by-step explanation:

x-y=29

x+y=33

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

x=y+29

y+29+y=33

2y+29=33

2y=33-29

2y=4

y=4/2

y=2

x-2=29

x=29+2

x=31

Answer:

[tex]\frac{\sqrt{17} }{7}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sinx = [tex]\sqrt{1-cos^2x}[/tex]

Note that ([tex]\frac{4\sqrt{2} }{7}[/tex])² = [tex]\frac{32}{49}[/tex]

sinΘ = [tex]\sqrt{1-(32/49)}[/tex]

        = [tex]\sqrt{\frac{17}{49} }[/tex] = [tex]\frac{\sqrt{17} }{7}[/tex]

Answer:

31.9 degrees

Step-by-step explanation:

tan(A) = 5.1/8.2

A = tan^-1 (5.1/8.2) = 31.9 degrees

The measure of angle A is 31.1 degrees.

To find the measure of angle A, we can use the following trigonometric function:

tan(A) = opposite over adjacent

In this case, the opposite side is 5.1 and the adjacent side is 8.2. Plugging these values into the formula, we get:

tan(A) = 5.1 / 8.2

A = tan⁻¹(5.1 / 8.2)

A ≈ 31.1 degrees

Therefore, the measure of angle A is 31.1 degrees (rounded to one decimal place).

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D) because in functions the input X can have only one output Y

Answer:

d.(-3,-2),(1,6) and (2,3)

Step-by-step explanation:

We are given that the set of ordered pairs shown represents a function f

{(-5,3),(4,9),(3,-2),(0,6)}

We have to find that which three ordered pairs could be added to the set so that function remains same.

Function: It is mapping between  elements of two sets A and B and every element of set A is uniquely mapped with each element of set B.

Or We can say that there is only one image of each element .

In the function

Image of -5 is 3 ,image of 4 is 9 ,image of 3 is -2 and image of 0 is 6.

a.(-3,-2),(4,0),(0,-1)

There is image of 0 is -1

It is not possible because two images of one element is not possible.

Hence, option a is false.

b.(1,6),(2,3) and (-5,9)

There is image of -5 is 9

Image of -5 is 3 in given function

Two  images one elements is not possible .Hence, option b is false.

c.(4,0),(0,-1) and (-5,9)

It is false because image of 4 is 0 and image of -5 is 9 which is not possible.

Hence, option C is false.

d.(-3,-2),(1,6) and (2,3)

Image of -3 is -2

Image of 1 is 6

Image of 2 is 3

It is true because every element have different image and function remain same.

Therefore, option D is true.

Answer:

302 m³

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = [tex]\frac{1}{3}[/tex] πr²h

where r is the radius and h the height

Consider the right triangle from the vertex of the cone to the midpoint of the base and the radius

with hypotenuse = 10 cm

h² + 6² = 10²

h² + 36 = 100 ( subtract 36 from both sides )

h² = 64 ( take the square root of both sides )

h = [tex]\sqrt{64}[/tex] = 8

Hence

V = [tex]\frac{1}{3}[/tex] π × 6² × 8

  = [tex]\frac{1}{3}[/tex] π × 36 × 8

   = [tex]\frac{36(8)\pi }{3}[/tex] ≈ 302 m³

Ted's debt can be expressed as 2w - 28

Data;

This is a mathematical expression written to represent word problems.

Given that Ted's debt is 14 less than half of Mike's debt and Mike's debt is represented as w.

Let x represent Ted's debt

[tex]x = \frac{w}{2} - 14\\ x = 2w -28[/tex]

The expression can be written as 2w - 28

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Answer:

40 mph and 68 mph

Step-by-step explanation:

Let x mph be the speed of the slower car, then 2x-12 mph is the speed of the faster car.

In 6 hours the faster car got to San Diego, so it travels the distance

[tex]6\cdot (2x-12)=12x-72\ miles.[/tex]

By that time the slower car was 168 miles away from the destination, so the slower car travels the distance

[tex]12x-72-168=2x-240\ miles[/tex]

It takes the slower car 6 hours to travel 12x-240 miles, so

[tex]6x=12x-240\\ \\6x-12x=-240\\ \\-6x=-240\\ \\6x=240\\ \\x=40\ mph.[/tex]

Now,

[tex]2x-12=2\cdot 40-12=80-12=68\ mph[/tex]

Triangle XYZ is a right triangle.

What value should f be to yield 90 degrees?

6(3f - 15)°.

Let f be 8, 10, 12, 15.

When f = 10, we get 90 degrees for angle Z.

Z = 6(3•10 - 15)

Z = 6(30 - 15)

Z = 6(15)

Z = 90

Answer: Choice B.

okay so your answer would be  B.)  f=10

It intersects both nappes of the double napped cone, but does not go through the vertex. This weird intersection will create a conic curve that is called the...

The cross-section that is obtained on slicing the double napped cone such that it does not pass through the vertex of the cone is:

                                Hyperbola.

We know when a plane intersects only one nape of a double napped cone then the cross section that is obtained is either a parabola, ellipse or a circle.

But when it passes through both the napes of a double napped cone then the cross-section obtained is a hyperbola.

               Hence, the answer is Hyperbola.

Answer:

f(x) = 3x - 3

Step-by-step explanation:

Plug into TI-83/84 calculator.

Hit STAT

Hit EDIT

X-Values go in for L1

Y-Values go in for L2

Hit STAT

Scroll over to CALC

Hit #4 for LinReg (Finds line of best fit)

Enter all the way through

A is your slope

B is your y-intercept

Answer:

[tex]f(x)=3x-3[/tex]  

Step-by-step explanation:

Data : (-2,-9), (0,-3), (1,0), (3,6), (5,12)

Using technology , Plot the points on the calculator .

(Refer the attached figure)

Or

First calculate the slope of given points

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]   ---A

[tex](x_1,y_1)=(-2,-9)[/tex]

[tex](x_2,y_2)=(0,-3)[/tex]

Substitute values in A

[tex]m = \frac{-3-(-9)}{0-(-2)}[/tex]

[tex]m = \frac{-3+9}{2}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m = 3[/tex]

[tex](x_1,y_1)=(1,0)[/tex]

[tex](x_2,y_2)=(3,6)[/tex]

Substitute values in A

[tex]m = \frac{6-0}{3-1}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m = 3[/tex]

Since the slopes are same .

So, the the given data is a linear function.

Now to obtain the equation for data we will use two point slope form.

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]   ---B

[tex](x_1,y_1)=(-2,-9)[/tex]

[tex](x_2,y_2)=(0,-3)[/tex]

Substitute values in B

[tex]y+9= \frac{-3-(-9)}{0-(-2)}(x+2)[/tex]  

[tex]y+9= \frac{6}{2}(x+2)[/tex]  

[tex]y+9=3(x+2)[/tex]  

[tex]y+9=3x+6[/tex]  

[tex]y=3x+6-9[/tex]  

[tex]y=3x-3[/tex]  

So, [tex]f(x)=y=3x-3[/tex]  

Thus Option B is true .

Hence the required equation is  [tex]f(x)=3x-3[/tex]  

Answer:

-2log3x - 3.

Step-by-step explanation:

Reflecting over the x axis gives  - log 3x.

A vertical stretch gives the function  -2log3x.

Finally a shift down 4 units gives the function -2log3x - 3.

Answer:

[tex]g(x)=-2log3x -3[/tex]

Step-by-step explanation:

In order to stretch a function you need to multiply by a factor, in this case is two.

In order to shift your function vertically, you need to add or subtract a number, adding you shift up, subtracting you shift down. That's why wee subtract the 3 units, because it says 'shifting down'.

This is a secant-tangent problem.

(Whole)(outside) = (tangent)^2

(x + 12)(x) = 8^2

x^2 + 12x = 64

x^2 + 12x - 64 = 0

In this quadratic equation, we see that a = 1, b = 12 and c = -64.

Plug those values into the quadratic formula and solve for x.

Answer:

x = 4

Step-by-step explanation:

Given a secant and a tangent drawn from an external point to the circle, then

The square of the measure of the tangent is equal to the product of the external part and the entire secant, that is

x(x + 12) = 8²

x² + 12x = 64 ( subtract 64 from both sides )

x² + 12x - 64 = 0 ← in standard form

with a = 1, b = 12 and c = - 64

Using the quadratic formula to solve for x

x = ( - 12 ± [tex]\sqrt{12^2-(4(1)(-64)}[/tex] ) / 2

  = ( - 12 ± [tex]\sqrt{144+256}[/tex] ) / 2

  = ( - 12 ± [tex]\sqrt{400}[/tex] ) / 2

x = [tex]\frac{-12-20}{2}[/tex] or x = [tex]\frac{-12+20}{2}[/tex]

x = - 16 or x = 4

However x > 0 ⇒ x = 4

Answer:

I'm not 100% sure on this but I think it would be C- 8.1

Step-by-step explanation:

Answer:

(24) is the homogeneous mixture

Answer:

Option 2 - 0.682

Step-by-step explanation:

Given : Expression [tex]\sin 43^\circ[/tex]

To find : Use the calculator to find the following expression to the nearest thousandth?

Solution :

Step 1 - Write the expression

[tex]\sin 43^\circ[/tex]

Step 2 -  Using calculator we find the value of [tex]\sin 43[/tex] in degrees.

[tex]\sin 43^\circ=0.6819[/tex]

Step 3 - Convert to the nearest thousandth

[tex]0.6819\approx 0.682[/tex]

Therefore, The value of the given expression is [tex]\sin 43^\circ=0.682[/tex]

So, Option 2 is correct.

Range is subtracting the biggest value and the smallest value of the data. For this set of data the range is:

9 - 3 -------------------------------> 6

Mode is the number that appears most often. In this set of data no number appears more than twice so mode is not applicable

Median is the middle of the numbers when ordered from least to greatest. For this set of the data the median is:

3  4  6  8  9

    4  6  8  

        6

Mean is adding all the number together then dividing the sum by how many numbers there are in the data. For this data the mean is:

(3 + 4 + 6 + 8 + 9) ÷ 5

(30) ÷ 5 ------------------------------------> 6

As you can see the range, median, and mean all have the value of 6

Hope this helped!

The range, median and mean of this data all have the value 6.

Mean- The average value of a data set is the same as the mean.

Mode-  The mode is the number that appears the most frequently in a data set.

Range-  In a frequency distribution, range is the difference between the highest and lowest observation.

Median- The median of a data collection is the number in the middle.

Range of the given data set = Highest value - Lowest value

Range of the given data set  = 9 - 3 = 6

Mean of the given data set = Sum of observations / total observations

Mean of the given data set = (3 + 4 + 6 + 8 +9)/5

Mean of the given data set  = 30 / 5 = 6

Mode of this set = All the numbers are there only once

Median of this data set = Out of the given five observations, 3rd term is the middle value which is equal to 6.

Hence median, mean and range of this data have the value 6.

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Answer: Option C.

Step-by-step explanation:

The volume of a sphere can be calculated with this formula:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

You can observe in the figure that the value of the radius of this sphere is:

[tex]r=4\ units[/tex]

Then you can substitute this radius into the formula [tex]V=\frac{4}{3}\pi r^3[/tex].

Therefore, the volume of the sphere shown in the figure is:

[tex]V=\frac{4}{3}\pi (4units)^3[/tex]

[tex]V=\frac{256}{3}\pi \ units^3[/tex]

Answer:

c

Step-by-step explanation:

it’ll be a rectangle if im not mistaken

It would be a rectangle. Brainliest please!!

Answer:

50

Step-by-step explanation:

Divided $225 divided by $15 which equal $15 then divided $750 divided by 15 which equal $50.

Thelma and Laura need to mow at least 65 lawns to make a profit of $750 after accounting for the $225 cost of the lawnmower. They must charge $15 per lawn to meet this goal.

Let's define x as the number of lawns mowed. Thelma and Laura charge $15 per lawn mowed, so the total money they make through mowing lawns is $15x. They initially spent $225 for a lawnmower, and they want to make a profit of at least $750. Profit is calculated as revenue (money made) minus costs, so we have the inequality $15x - $225 >= $750. Simplify this inequality to get x >= 65. Therefore, they need to mow at least 65 lawns in order to make their desired profit.

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Answer:

an equation

Step-by-step explanation:

A mathematical statement that two expressions are equal is called an equation.

The word "equation" comes from the same root as "equality"...  so is two sides of an expression are of equal values, they form an equation, like A = B.

When both sides of a statement are not equal to each other, that is an inequality, meaning NOT equal, like A > B.

We have to fill the given statement. The term "equal" represent by sign "=" which shows that two expression are connected.

The given statement is correctly filled with equation.

Given:

The statement is given.

The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.

Whereas if the two equation are not equal then it is known as inequality.

Thus, the given statement is correctly filled with equation.

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