Solve |3x - 4| = 15
a) {-19/3, 19/3}
b) {11/3, 19/3}
c) {-11/3, 19/3}

A ratio is the part divided by the whole. Johnny took 3 pieces of pizza when the whole pizza had 8. Johnny has 3/8 (3 out of 8) pieces of pizza, or .375 parts. To find that number, literally divide your part from your whole to get the decimal form.

Answer:

Part a) The vertex is the point (-2,-8)

Part b) The equation of the axis of symmetry is x=-2

Part c) The y-intercept is the point (0,-4)

Part d) The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a<0 then the parabola open downward (vertex is a maximum)

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

x=h ----> equation of the axis of symmetry

In this problem we have

[tex]y=x^{2}+4x-4[/tex]

This is the equation of a vertical parabola open upward

The vertex is a minimum

Part a)

what is the vertex of this function?

Convert the function into vertex form

[tex]y=x^{2}+4x-4[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+4=x^{2}+4x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y+4+4=(x^{2}+4x+4)[/tex]

[tex]y+8=(x^{2}+4x+4)[/tex]

Rewrite as perfect squares

[tex]y+8=(x+2)^{2}[/tex]

[tex]y=(x+2)^{2}-8[/tex] ----> equation in vertex form

The vertex is the point (-2,-8)

Part b) what is the equation of the axis of symmetry?

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

x=h ----> equation of the axis of symmetry

The vertex is the point  (-2,-8)

The x-coordinate of the vertex is -2

therefore

The equation of the axis of symmetry is x=-2

Part c) What is the y- intercept?

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=(0)^{2}+4(0)-4[/tex]  

[tex]y=-4[/tex]

The y-intercept is the point (0,-4)

Part d) Graph the line of symmetry. Plot the vertex and the point containing the y-intercept. Then plot another point on the graph and use the plotted points and the axis of symmetry to plot two more points. Draw the graph of the function through the points

To plot the function find the x-intercepts

we know that

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=(x+2)^{2}-8[/tex]

[tex](x+2)^{2}=8[/tex]

square root both sides

[tex]x+2=(+/-)2\sqrt{2}[/tex]

[tex]x=-2(+/-)2\sqrt{2}[/tex]

[tex]x1=-2(+)2\sqrt{2}=0.828[/tex]

[tex]x2=-2(-)2\sqrt{2}=-4.828[/tex]

the graph in the attached figure

Answer:

10 degrees

Step-by-step explanation:

115 degrees is the measure because angle 4 and angle 115 are transversal angles so yeah

For this case we have that by definition, the density is given by:

ρ =[tex]\frac {M} {V}[/tex]

Where:

M: It's the mass

V: It's the volume

The volume of a solid cone is given by:

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the data we have:

 [tex]V = \frac {1} {3} \pi * (4) ^ 2 * 21\\V = \frac {1} {3} \pi * 16 * 21\\V = 401.92 \ cm ^ 3[/tex]

On the other hand, we have that by definition, the density of the platini is given by:

[tex]21.45 \frac {g} {cm ^ 3}[/tex]

Substituting in the initial formula, we look for the mass:

[tex]M = 401.92 \ cm ^ 3 * 21.45 \frac {g} {cm ^ 3}\\M = 8621.184 \ g[/tex]

ANswer:

The mass of the platinum cone is 8621.2 grams.

To find the mass of a solid platinum cone with a height of 21 cm and a diameter of 8 cm, calculate the volume using the formula for a cone (⅓πr²h) and then multiply by platinum's density (21,450 kg/m³) to get approximately 30.342 kg.

Calculate the Mass of a Platinum Cone

To determine the mass of a solid cone made of platinum with a given height and diameter, we must first calculate its volume and then use the density of platinum to find its mass. The density of platinum is approximately 21,450 kg/m³. The volume of a cone is given by the formula ⅓πr²h, where r is the radius and h is the height. For our cone with a height (h) of 21 cm and a diameter of 8 cm, the radius (r) would be half of the diameter, so r = 4 cm = 0.04 m. Plugging the values into the formula, we get:

Volume (V) = ⅓π(0.04 m)²×21 cm = ⅓π(0.0016 m²)× 0.21 m = 0.0014136 m³.

To find the mass (m), we multiply the volume by the density of platinum (ρ):

Mass (m) = Density (ρ) × Volume (V) = 21,450 kg/m³ × 0.0014136 m³ = 30.342 kg.

Therefore, the mass of the solid platinum cone is approximately 30.342 kilograms.

Answer:

30°

Step-by-step explanation:

Given

BC=30°

Central abgle is equal to its arc

so <3=30°

Answer:

The answer is 30

Step-by-step explanation:

Answer:

interest earned= 12.47

the future value of an annuity= 162.47

Step-by-step explanation:

Given Data:

Interest rate,r= 4%

time,t = 2 years

monthly payment, P= 150

n= 12 as monthly

At the end of 2 years, final investment A= ?

As per the interest formula for compounded interest

A= P(1+r/n)^nt

Putting the values in above equation

= 150(1+0.04/12)^24

 = 162.47

Interest earned = A-P

                          = 162.47-150

                           = 12.47 !

Answer: She Is Not Correct The Answer Is 24

Step-by-step explanation: The answer is 24. This is because when you have order of operations, you always do parentheses first. (27-9) equals 18. Then multiply it by 3 so do 20 times 3 and then subtract 6 and you get 54. Then divide 54 by 9 and you get 6. 6+18 does not equal 42 so it would be the third one.

-HAVE A GREAT DAY-

Answer:

the answer is C.

Step-by-step explanation:

using pemdas you start with parenthesis,

(27-9)*3÷9+18=42

18*3÷9+18=42 .         use rules of multiplication and division

54÷9+18=42             divide again

6+18=42                  add

24=42

this is false because the numbers don't match up on the left and right side, so 24 is the real answer.

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

  y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

  x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

  x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

  substitute the three vertices of the feasible region in C and chose

  the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

The vertices of the feasible region are (0, 15), (10, 15), and (20, 5). The minimum value of the objective function C = 4x + 9y is 190 at the vertex (10, 15).

The feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied. To find the vertices of the feasible region, we need to find the intersection points of the lines formed by the given constraints. By solving the system of equations, we find that the vertices of the feasible region are (0, 15), (10, 15), and (20, 5).

To find the minimum value of the objective function C = 4x + 9y, we substitute the x and y values of each vertex into the objective function and determine which vertex gives the smallest value. By evaluating the objective function at each vertex, we find that the minimum value is obtained at the vertex (10, 15) with a value of 4(10) + 9(15) = 190.

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Answer:

Two distinct real solutions.

Step-by-step explanation:

Given the equation in the form [tex]ax^2+bx+c=0[/tex], you need to find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

For the equation [tex]-2x^2+5x-3=0[/tex] you can identify that:

[tex]a=-2\\b=5\\c=-3[/tex]

Then, substituting these values into the formula, you get that the Discriminant is:

[tex]D=5^2-4(-2)(-3)[/tex]

[tex]D=1[/tex]

 Since [tex]D>0[/tex], then [tex]-2x^2+5x-3=0[/tex] has two distinct real solutions.

The solutions of the equation 2x² = 18 are x = 3 and x = -3.

To find the solutions of the equation 2x² = 18, we need to solve for x.

We can start by dividing both sides of the equation by 2, which gives us x² = 9.

Next, we can take the square root of both sides to find the solutions. The square root of 9 is 3, so the solutions are x = 3 and x = -3.

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The equation 2x² = 18 has two solutions, x = 3 and x = -3, which can be determined both algebraically and graphically by observing the points where the parabola f(x) = 2x² - 18 intersects the x-axis.

The solutions of the equation 2x² = 18 can be found by first dividing both sides of the equation by 2, which simplifies to x² = 9. This is a standard quadratic equation which can be further solved by taking the square root of both sides. The solutions are x = 3 and x = -3. If we graph the related function, which is f(x) = 2x² - 18, we will see a parabola opening upwards with its vertex at the origin (0,0), and it will intersect the x-axis at the points (3,0) and (-3,0), representing our solutions.

To use a graph of the related function, we can plot the equation 2x² - 18 = 0 on a graph and find the x-values where the graph intersects the x-axis. These x-values correspond to the solutions of the equation.

ANSWER

[tex](x + 5i)(x - 5i) = 0 [/tex]

EXPLANATION

The given function is

[tex] {x}^{2} + 25 = 0[/tex]

The zeros of this function are;

[tex]x = \pm5i[/tex]

Or

[tex]x = - 5i \: and \: x = 5i[/tex]

[tex]x + 5i = 0\: and \: x - 5i = 0[/tex]

Hence the factored form is:

[tex](x + 5i)(x - 5i) = 0 [/tex]

If the equation were:

[tex] {x}^{2} - 25 = 0[/tex]

Then the factored form is

[tex](x + 5)(x - 5) = 0 [/tex]

Answer:

D) cylinder; radius = 6in.; height = 5 in.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

A solid figure is a three dimensional shape having length, width and height. Examples of three dimensional figures are prism, pyramid, cone, cylinder and so on.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

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For this case we must simplify the following expression:[tex](x ^ {\frac {3} {2}}) ^ 6[/tex]

We have that by definition of properties of powers that is fulfilled:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex]x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9[/tex]

ANswer:

Option D

Answer:

Discount Rate=17%

Step-by-step explanation:

We know the price and discount of the car. The formula for calculating the discount when rate is given is:

[tex]Discount=Listed\ price*discount\ rate[/tex]

We know two quantities out of three, so putting in the known values:

[tex]3000=18000*rate\\rate=\frac{3000}{18000}\\Rate=16.67%[/tex]

The rate rounded off to nearest percent will give us:

17 percent.

So the discount rate is 17% ..

When rounded to the nearest whole percent, the discount rate is 17%.

To calculate the rate of the discount for the Bucio family's new car purchase, we will use the formula for finding the percentage rate of a discount, which is:

Discount Rate = (Discount Amount / Original Price) x 100.

In their case, the car has an original list price of $18,000, and they are offered a discount of $3,000. Plugging these values into the formula gives us:

Discount Rate = ($3,000 / $18,000) x 100

Discount Rate = 0.1667 x 100

Discount Rate = 16.67%

When rounded to the nearest whole percent, the discount rate is 17%.

Answer:

[tex]\large\boxed{r=\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]y=rx\to r=\dfrac{y}{x}\\\\\text{From the table:}\\\\x=8,\ y=2\to r=\dfrac{2}{8}=\dfrac{1}{4}\\\\x=16,\ y=4\to r=\dfrac{4}{16}=\dfrac{1}{4}\\\\x=32,\ y=8\to r=\dfrac{8}{32}=\dfrac{1}{4}[/tex]

Answer:

D. h=7

Step-by-step explanation:

1               2            16

------ + ------------ = ----------

h-5        h+5          (h^2 -25)

1               2            16

------ + ------------ = ----------

h-5        h+5          (h-5)(h+5)

Since h^2 -25 factors in (h-5) (h+5)  ( it is the difference of squares)

We will multiply both sides by  (h-5) (h+5)  to clear the fractions

(h-5) (h+5)              2 (h-5) (h+5)            16 (h-5) (h+5)

------              + ------------                     = ----------

h-5                   h+5                                (h-5)(h+5)

Canceling like terms

 (h+5)              2 (h-5)             16

------              + ------------      = ----------

1                         1                          1

h+5 + 2(h-5) = 16

Distribute

h+5 + 2h -10 = 16

Combine like terms

3h-5=16

Add 5 to each side

3h-5+5 =16+5

3h =21

Divide each side by 3

3h/3 = 21/3

h = 7

Answer:

B. y=sin(x) and y=-1/2

Step-by-step explanation:

We have been given the following trigonometric inequality;

2sin(x)=>-1

The above inequality can be re-written as;

sin(x)=>-1/2

after dividing both sides by 2.

We can then formulate two separate equations, one containing the expression on the right hand side and the other containing the expression on the left hand side;

From the left hand side we form the following equation;

y = sin(x)

From the right hand side we form the following equation;

y = -1/2

Therefore, the above two equations can be graphed to help solve the given trigonometric inequality

Answer: B

y=sin(x) and y=-1/2

Step-by-step explanation:

Answer:

C ≈ 87.96in

Step-by-step explanation:

Answer:

each slice will be 1/36

Step-by-step explanation:

1/4 • 1/9 equals 3/36

Final answer:

Rebecca can divide ¾ of a cake into 9 pieces by finding the fraction of each piece relative to the whole cake, which is ⅛ or one-twelfth of the whole cake.

Explanation:

How to Divide a Cake into Equal Pieces

To divide ¾ of a cake into 9 equal pieces, Rebecca must consider how many pieces the whole cake can be divided into first. Since she has three-quarters of a cake, and she wants to make 9 pieces out of it, each piece will be one-ninth of the three-quarters of a cake. To find out the size of each piece relative to the whole cake, she divides ¾ by 9. This can be calculated as ¾ × ⅟, which simplifies to ⅛. This means that each piece of cake will be one-twelfth of the whole cake.

Understanding fractions such as halves, thirds, and quarters is useful in daily life and in solving problems like these. Knowing that a quarter is 25 cents makes it easier to grasp a quarter of a pie or cake. If you can visualize that two-thirds of a pie is more than half a pie, it helps when dividing portions or budgeting resources.

13 x 8= 104

hope this helps!

Answer:

ok friend so the answer is :) D

Step-by-step explanation:

because

Freq  =  1  / Period

Freq =  1 / 0.00024   =   4166.66 Hz  = 4167 Hz

:)

The frequency of the C8 note set by Adam Lopez is the inverse of its period of 0.00024 seconds. Calculating 1/0.00024 gives a frequency of 4166.67 Hz, which rounds to d) 4167 Hz.

The frequency of a musical note is the inverse of its period. The period is the amount of time it takes for one complete cycle of the sound wave. If Adam Lopez's record-setting C8 has a period of 0.00024 seconds, we can calculate the frequency as follows:

To the nearest hertz, the frequency of the C8 note is 4167 hertz.

The correct answer is D. 4167 hertz.

If P(3) stands for the probability of the number 3 getting rolled, since 3 was rolled 5 times (as shown on the graph) out of 50 (as mentioned in the question), the experimental probability would be: 5/50, which when simplified, is 1/10

The student is asked to calculate the experimental probability of rolling a 3, but the specific frequency Sarah rolled a 3 is not provided. Without this, we cannot compute the experimental probability. Generally, the method involves dividing the number of times a 3 was rolled by the total number of rolls.

The question asks for the experimental probability of rolling a 3 on a six-sided die based on the results Sarah obtained from her 50 rolls. However, the provided information does not include the actual frequency of rolling a 3 in her experiment. If we had that data, the experimental probability P(3) would be the number of times a 3 was rolled divided by the total number of rolls (50 in Sarah's case).

For example, if Sarah rolled a 3 ten times out of 50, then the experimental probability of rolling a 3 would be calculated as follows: P(3) = 10/50 = 1/5. Without the specific results of Sarah's rolls, we cannot determine the experimental probability from the information given in the question.

It’s hard to see the graph but from what I can see 15°

B is the correct answer

4y-7=2y-1

Subtract 2y from both sides

2y-7=-1

Add 7 to both sides

2y=6

Y=3

Answer:

• positive answer: 9

• negative answer: -6

Step-by-step explanation:

Since you know your multiplication tables, you are familiar with the fact 6·9 = 54. One of these factors is 3 larger than the other, so is the answer you seek.

The number is 9.

___

These multiplication problems often have negative solutions as well. Usually, the negative solution is the other factor of the pair, but with a minus sign. Here, that is -6:

(-6)(-9) = 54 . . . . . where -9 is 3 less than -6.

Answer:

9

Step-by-step explanation:

Let's break it down

" A number is multiplied "

Okay so we know that a number is being multiplied

" by the number 3 less than itself"

So whatever number it is, (lets use x) is being multiplied by a number (lets use y) 3 less then itself. So x - 3 = y and x·y = 54

So I started dividing all the numbers 1 - 9

54 ÷ 9 = 6

54 ÷ 8 = 6.75

54 ÷ 7 = 7.71~

54 ÷ 6 = 9

Then I stopped

Read the question again

"A number is multiplied by the number 3 less than itself. The result is 54."

A number - 9

Multiplied by the number 3 LESS then itself - 6

The result is 54 - 9 × 6 = 54

Hope that helps ^^

What the test is looking for is obviously x<=5 (the second one), but I'd actually say 0 is equal or less than x that is equal or less than 5, where x is a natural number.

You cannot have a negative quantity of books, nor can you have 4.3627272828 ones.

Answer:  The correct option is (B) [tex]x\leq 5.[/tex]

Step-by-step explanation:  We are given to write an inequality for the following situation :

"No more than 5 books are in your backpack".

Let the number of books in the backpack  be x.

The given situation implies that there will be either less than or equal to 5 books in the backpack.

Therefore, the required situation can be written as

[tex]x\leq 5.[/tex]

Thus, (B) is the correct option.

Answer: 3,658 miles

Step-by-step explanation:

118 x 31 = 3,658 miles

Multiply the daily value by the number of days to find the total.

Answer:

3,658

Step-by-step explanation:

So if Kellianna drives 118 Miles each day you would simply multiply the 118 x 31 (Days) = 3,658

Answer:

[tex]y=6\sqrt{3}[/tex]

Step-by-step explanation:

Using the Pythagoras theorem for triangle MTU,

[tex]TU^2+3^2=6^2[/tex]

[tex]TU^2+9=36[/tex]

[tex]TU^2=36-9[/tex]

[tex]TU^2=27[/tex]

[tex]TU^2=27[/tex]

From, triangle NTU,

[tex]y^2=TU^2+NU^2[/tex]

This implies that:

[tex]y^2=27+9^2[/tex]

[tex]y^2=27+81[/tex]

[tex]y^2=108[/tex]

[tex]y=\sqrt{108}[/tex]

[tex]y=6\sqrt{3}[/tex] units.

Answer:

The value of y=6√3 units.

Step-by-step explanation:

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