The diagram is not to scale.

Answer:

in the US, yes

in some other English-speaking countries, no

Step-by-step explanation:

"Standard form" depends on where you live. In the UK, the "standard form" of a quadratic equation is what is called "vertex form" in the US. That form is ...

3(x +1/3)^2 +29/3 = 0

In the US, the equation you show is in standard form.

Hello There!

Martha’s first step would represent “Associative Property Of Addition”

This basically means that you can add or multiply these numbers regardless of how they are grouped in a sequence.

Answer:

A

Step-by-step explanation:

The average rate of change is the change in attendance over change in time.

Δy / Δx

(333.7 - 298.3) / (5 - 2)

11.8

So the average rate of change is an increase of 11.8 thousand people per year.

The average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have to find the average rate of change from Year 2 to Year 5:

At year 2 the attendance = 298.3

At year 5 the attendance = 333.7

Average rate of change = (333.7-298.3)/(5-2)

= 11.8

Thus, the average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

Learn more about the rate of change here:

brainly.com/question/12786410

#SPJ2

Answer:

I think the answer is 4.5 if you subtract 75 from 129 and divide by 12?

After deducting the cost of materials, the remaining amount spent on labor was $54. By dividing this amount by the friend's hourly rate of $12, it is determined that Jared's friend worked for 4.5 hours on constructing the treehouse.

Jared is trying to calculate how many hours his friend worked on building a treehouse based on the total cost of the project. Jared spent $75 on materials and paid his friend $12 per hour for labor. The total cost for building the treehouse was $129.

To find out how many hours Jared's friend worked, we start by subtracting the cost of materials from the total cost:

Total cost of treehouse = $129

Cost of materials = $75

Total cost minus materials cost = $129 - $75 = $54

This $54 represents the total amount paid for labor. We can then divide this amount by the hourly rate to find the number of hours worked:

Hourly wage = $12

Labor cost / hourly wage = $54 / $12 = 4.5 hours

Therefore, Jared's friend worked for 4.5 hours on the treehouse.

Answer:

$33.00

Step-by-step explanation:

You find out how much the sale price is by subtracting 25% of 40 from 40:

40 - [(.25)(40)] and that equals 30.  So the sale price is $30.  Now if the tax is 10% (.1 in decimal form), we find the total cost by adding .1(30) to 30:

30 + [(.1)(30)] which is $33

Answer:

(1, 3)

Step-by-step explanation:

If the translation is ...

(3, 2) + (a, b) = (4, 5)

Then we can find (a, b) by subtraction:

(4, 5) -(3, 2) = (a, b) = (4-3, 5-2) = (1, 3)

Not the image of point (0, 0) will be ...

(0, 0) + (a, b) = image

(0, 0) + (1, 3) = (0+1, 0+3) = (1, 3)

The image of the point is (1, 3).

Answer:

  KM = 20

Step-by-step explanation:

If V is the midpoint of KM, then ...

  KV = VM

  2.5z = 5z -10

  0 = 2.5z -10 . . . . . . subtract 2.5z

  0 = z - 4 . . . . . . . . . divide by 2.5

  4 = z . . . . . . . . . . . . add 4

We know that V bisects KM, so KV is half the overall length. That is ...

  KM = 2·KV = 2·2.5z = 5z

Using the value of z we found, ...

  KM = 5·4 = 20

Answer:

192.53= original bill

Step-by-step explanation:

The bill you receive is equal to the original bill minus the prepaid amount

bill = original - prepaid

82.53 = original - 110

Add 110 to each side

82.53+110 = original-100+100

192.53= original bill

Answer:

For a. [tex]x=7[/tex]

For b. [tex]x=2[/tex]

Step-by-step explanation:

To solve this, we are using the intersecting secants theorem. The theorem says that if two secant segments intersect a circle from an exterior point, then the product of the measures of the exterior segment and the whole secant  is equal to the product of the measures of the other exterior segment and its whole secant.

Applying this to our circles:

For a.

[tex]5(5+x)=6(6+4)[/tex]

[tex]25+5x=6(10)[/tex]

[tex]25+5x=60[/tex]

[tex]5x=60-25[/tex]

[tex]5x=35[/tex]

[tex]x=\frac{35}{5}[/tex]

[tex]x=7[/tex]

For b.

[tex]4(4+x)=3(3+5)[/tex]

[tex]16+4x=3(8)[/tex]

[tex]16+4x=24[/tex]

[tex]4x=8[/tex]

[tex]x=\frac{8}{4}[/tex]

[tex]x=2[/tex]

We can conclude that the value of x in (a) is 7, and the value of x in (b) is 2

ANSWER

The discriminant is 384. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.

EXPLANATION

The given quadratic equation is:

[tex] - 3 {x}^{2} - 18x + 5 = 0[/tex]

We compare this equation to:

[tex]a {x}^{2} + bx + c = 0[/tex]

We have a=-3,b=-18, and c=5.

The discriminant of a quadratic equation is calculated using the formula:

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

We plug in the values to obtain:

[tex]D= {( - 18)}^{2} - 4( - 3)(5)[/tex]

[tex]D= 324 + 60[/tex]

Simplify:

[tex]D= 384[/tex]

The discriminant is greater than zero, hence there are two distinct real roots.

Since 384 is not a perfect square, the roots are irrational.

Answer:

D)

y > x + 4

y ≥ -3x - 2

Step-by-step explanation:

Blue line's boundary is above the line and dotted (>) so the equation: y > x + 4

Red line's boundary is above the line and solid (≥) so the equation: y ≥ -3x - 2

Answer

D)

y > x + 4

y ≥ -3x - 2

Answer:

D

Step-by-step explanation:

First put your numbers in order from least to greatest (These are negative numbers so that means that the smallest number is the one farthest away from zero)

-49, -43, -39, -18, -14, -12, -9

Mean is adding all the numbers together and dividing the sum by how many numbers there are in the data set

-49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184

There are seven numbers so divide -184 by 7:

-184 ÷ 7 ≈ 26.29

Median is the number in the middle. Take away the smallest number and the biggest number on each layer until you get to the middle

-49, -43, -39, -18, -14, -12, -9

       -43, -39, -18, -14, -12

              -39, -18, -14

                      -18 <-------------------Median

Mode is whatever number appears the most often in the data. In this case all the numbers appear only once so there is no mode

Range is subtracting the largest number by the smallest number

-9 - (-49) = 40

2. Data in order

13, 13, 13, 15, 21, 23, 25, 37

Outlier is the number that is a number that is rather far from the other number in the data

a. In this case the outlier is 37

b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160

160 ÷ 8 = 20

c. 13 + 13 + 13 + 15 + 21 + 23 + 25  = 123

123 ÷ 7 = 17.57

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Mean = 26.29

Median =  -18

Mode = 40

2 a.  37

2 b.  20

2 c.  17.57

Step-by-step explanation:

Mean = -49 + (-43) + (-39) + (-18) + (-14) + (-12) + (-9) = -184

There are seven numbers so divide -184 by 7:

-184 ÷ 7 ≈ 26.29

Median =

-49, -43, -39, -18, -14, -12, -9

       -43, -39, -18, -14, -12

              -39, -18, -14

                      -18

Mode =

-9 - (-49) = 40

2.

13, 13, 13, 15, 21, 23, 25, 37

Outlier is the number that is an odd number

a. In this case the outlier is 37

b. 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160

160 ÷ 8 = 20

c. 13 + 13 + 13 + 15 + 21 + 23 + 25  = 123

123 ÷ 7 = 17.57

Answer:

there could be 8 trucks to 10 cars

16 trucks to 20 cars

or just continuously multiply by 2

Step-by-step explanation:

Answer:

there could be 8 trucks to 10 cars

16 trucks to 20 cars

or just continuously multiply by 2

Answer:

  b ≈ 3.1

Step-by-step explanation:

The law of sines tells you ...

  b/sin(B) = c/sin(C)

Here, you have to find angle C based on the sum of the angles of a triangle being 180°.

 C = 180° - A - B = 180° - 69° - 32° = 79°

Multiplying the above law of sines equation by sin(B), you have ...

  b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707

  b ≈ 3.1 . . . . . rounded to tenths

Answer:

[tex]\displaystyle 3,1 ≈ b[/tex]

Step-by-step explanation:

First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:

[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]

Now that we have all three angles, we can solve for edge b

[the second edge], using the Law of Sines:

[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]

I am joyous to assist you at any time.

Step-by-step explanation:

[tex](4x - 2).6(2x + 7) \\ = (4x - 2)(12x + 42) \\ = 48 {x}^{2} + 168x - 24x - 84 \\ = 48 {x}^{2} + 144x - 84[/tex]

then

[tex]a = 48 \\ b = 144 \\ c = - 84[/tex]

Answer:

>,<,<,>,<

Step-by-step explanation:

The bigger side in the >/< Symbols mean that value is larger

Answer:

years worked: 14

at least 10 years: 73%

Step-by-step explanation:

The mean is found by adding the years of service and dividing by the number of employees. The total years of service is 417, so the average is ...

average years worked = 417/30 = 13.9 ≈ 14 . . . years

__

The percentage of employees that have worked there at least 10 years is found by counting the number with 10 or more years of service and dividing that count by the total number of employees. The result is then expressed as a percentage.

(10 years or over)/(total number) = 22/30 = 0.73_3 (a repeating decimal) ≈ 73%

_____

Comment on the working

A spreadsheet can be helpful for this. It has a function that can calculate the mean for you. Sorting the years of service into order can make it trivially easy to count the number that are 10 or more, or you can write a function that will do the count for you. (Also, less than 10 means the years are a single digit. There are 8 single-digit numbers in your list.) The hard part is copying 30 numbers without error.

The answers are: 14 years and 50%. 14 years is the population mean for the number of years worked, and 50 % of the employees worked for the company for at least 10 years.

To determine the answers, steps:

1. Calculate the Population Mean: Sum all the years worked and divide by the number of employees (30).

   [tex]Total\ years\ worked: 8 + 13 + 15 + 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13 + 12 + 1 + 14 + 14 + 17 + 16 + 7 + 27 + 18 + 24 = 412[/tex]

   [tex]Population\ mean =\frac{412}{30} \approx 14[/tex]

2. Calculate the Percentage of Employees who Worked At Least 10 Years: Count the employees who worked for 10 years or more, and divide by the total number of employees, then multiply by 100 to convert to percentage.

   [tex]Number\ of\ employees\ who\ worked\ at\ least\ 10\ years: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 15[/tex]

   [tex]Percentage = \frac{15}{30} * 100 = 50\%[/tex]

For this case we have the following system of equations:

[tex]y = x ^ 2-4x + 3\\y = -x + 3[/tex]

Matching we have:

[tex]x ^ 2-4x + 3 = -x + 3\\x ^ 2-4x + x + 3-3 = 0\\x ^ 2-3x = 0[/tex]

We solve by means of

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

Where:

[tex]a = 1\\b = -3\\c = 0[/tex]

Substituting:

[tex]x = \frac {- (- 3) \pm \sqrt {(- 3) ^ 2-4 (1) (0)}} {2 (1)}\\x = \frac {3 \pm \sqrt {9}} {2}\\x = \frac {3 \pm3} {2}[/tex]

Finally, the roots are:

[tex]x_ {1} = \frac {3-3} {2} = 0\\x_ {2} = \frac {3 + 3} {2} = \frac {6} {2} = 3[/tex]

Answer:

[tex]x_ {1} = 0\\x_ {2} = 3[/tex]

Answer:

Find the attached

Step-by-step explanation:

To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;

-5, -4, -3, 3, 4, 5

we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;

when x = -5, f(-5) =  |-5+2| - 3 = 0

when x = -4, f(-4) =  |-4+2| - 3 = -1

when x = -3, f(-3) =  |-3+2| - 3 = -2

when x = 3, f(3) =  |3+2| - 3 = 2

when x = 4, f(4) =  |4+2| - 3 = 3

when x = 5, f(5) =  |5+2| - 3 = 4

The graph of the function is as shown in the attachment below.

Answer:

Find the attached

Step-by-step explanation:

To graph the given function, we would need to obtain pairs of points (x, f(x)). We can let x be;

-5, -4, -3, 3, 4, 5

we simply substitute each value of x in the given function to obtain the value of the function corresponding to the given x value;

when x = -5, f(-5) =  |-5+2| - 3 = 0

when x = -4, f(-4) =  |-4+2| - 3 = -1

when x = -3, f(-3) =  |-3+2| - 3 = -2

when x = 3, f(3) =  |3+2| - 3 = 2

when x = 4, f(4) =  |4+2| - 3 = 3

when x = 5, f(5) =  |5+2| - 3 = 4

Explanation:

The sum of the measures of the interior angles of a triangle is 180°. Then the sum of the given angles is 180°:

m∠P +m∠Q +m∠R = 180°

(5x)° +(5x)° +(8x)° = 180°

18x = 180 . . . . . . . . . . . . . . . collect terms, divide by °

x = 10 . . . . . . . . . . . . . . . . . . divide by 18. This is your desired result.

Explanation:

The sum of the measures of the interior angles of a triangle is 180°. Then the sum of the given angles is 180°:

m∠P +m∠Q +m∠R = 180°

(5x)° +(5x)° +(8x)° = 180°

18x = 180 . . . . . . . . . . . . . . . collect terms, divide by °

x = 10 . . . . . . . . . . . . . . . . . . divide by 18. This is your desired result.

Answer:

6x is indeed the Greatest Common Factor.

Step-by-step explanation:

6x[3 - y² + 2y⁶]

ANSWER

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

EXPLANATION

The graph has a solid boundary line.

The region above the boundary line is shaded

Therefore the inequality sign involved is '≥'

The boundary line has equation

[tex]y = \frac{1}{4} x - 1[/tex]

We can now conclude that, the inequality graphed above is

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

Answer:

The answer is

Step-by-step explanation:

The inequality in the  graphed above is y≥1/4x-1

ANSWER

[tex]16\pi \: sq.in[/tex]

EXPLANATION

The area of a sector is calculated using the formula,

[tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]

The arc measure is given as 45°

The radius of the circle is 8 inches.

We substitute to obtain,

[tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]

[tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]

The answer is:

The correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°

Calculating the total area, we have:

[tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]

Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:

[tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

Have a nice day!

Answer:

  d. Distributive property

Step-by-step explanation:

The Distributive property of multiplication over addition is what allows you to multiply each of the terms in parentheses by the factor outside parentheses. It tells you ...

  a(b +c) = ab + ac

It works both ways, also allowing you to remove a common factor to outside parentheses.

Answer:

Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft

Step-by-step explanation:

we have

[tex]h(t)=-16t^{2}+150[/tex]

where

t ----> is the time in seconds after the ball is dropped

h(t) ----> he height in feet of a ball dropped from a 150 ft

Find h(2)

That means ----> Is the height of the ball  2 seconds after the ball is dropped

Substitute the value of t=2 sec in the equation

[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]

therefore

After 2 seconds, the height of the ball is 86.00 ft.

Answer:

Collin: about $401 thousand

Cameron: about $689 thousand

Step-by-step explanation:

A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...

[tex]P(t)=P_0(2^{t/d})[/tex]

In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.

In Collin's case, we have ...

P0 = 55,000, t = 43, d = 15

so his salary at retirement is ...

P(43) = $55,000(2^(43/15)) ≈ $401,157.89

In Cameron's case, we have ...

P0 = 35,000, t = 43, d = 10

so his salary at retirement is ...

P(43) = $35,000(2^(43/10)) ≈ $689,440.87

___

Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...

[tex]P(t)=P_{0}e^{kt}[/tex]

If we compare this equation to the one above, we find the growth factors to be ...

2^(t/d) = e^(kt)

Factoring out the exponent of t, we find ...

(2^(1/d))^t = (e^k)^t

That is, ...

2^(1/d) = e^k . . . . . match the bases of the exponential terms

(1/d)ln(2) = k . . . . . take the natural log of both sides

So, in Collin's case, the equation for his salary growth is

k = ln(2)/15 ≈ 0.046210

P(t) = 55,000e^(0.046210t)

and in Cameron's case, ...

k = ln(2)/10 ≈ 0.069315

P(t) = 35,000e^(0.069315t)

Answer:

The domain of g(x) is {xI x > -5} ⇒ first answer

Step-by-step explanation:

* Lets talk about the transformation at first

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* lets revise the meaning of the domain

- The domain is all values of x that make the function defined

- Find the values of x which make the function undefined

- The domain will be all the real numbers except those values

* Now we can solve the problem

∵ f(x) = √x

- f(x) translated 5 units to the left, then add x by 5

∴ f(x) ⇒ f(x + 5)

- f(x) translated 3 units up, then add f(x) by 3

∴ f(x) ⇒ f(x) + 3

- The function g(x) is created after the transformation

∴ g(x) = f(x + 5) + 3

∵ f(x) = √x

∴ g(x) = √(x + 5) + 3

- The function will be defined if the value under the square root

  is positive (means greater than 0)

∵ The expression under the square root is x + 5

∴ x + 5 > 0 ⇒ subtract 5 from both sides

∴ x > -5

- The domain will be all the real numbers greater than -5

∴ The domain of g(x) is {xI x > -5}

The domain of the function g(x), which is the function f(x) = square root of x translated left 5 units and up 3 units, is {x | x > -5}.

The original function f(x) has a domain of {x | x ≥ 0} because we cannot take the square root of a negative number. When the function is translated left 5 units, the new function, g(x), will start at x = -5 instead of x = 0, reflecting the domain shift due to translation. Therefore, the domain of g(x) is {x | x > -5}.

Answer: An obtuse angle is any angle greater than 90° and less than 180°

Step-by-step explanation:

Answer:

An obtuse angle is more than 90 degrees so anything above 90 degrees is obtuse while anything below is either an acute, strait, or right angle.

Step-by-step explanation:

Answer:

c The square of a number is equal to the product of 32 and that number.

Step-by-step explanation:

Let the number be w.

The square of the number is [tex]w^2[/tex]

The product (multiplication) of the number and 32 is [tex]32w[/tex]

The symbol = is read "is equal to"

[tex]w^2=32w[/tex]

The square of a number = The product of 32 and that number

The square of a number equals to The product of 32 and that number

We can conclude that the correct answer is c The square of a number is equal to the product of 32 and that number.

B is correct. I’ve noticed that you’ve posted a lot of questions like this, so here’s how I remember it. Soh-Cah-Toa

Soh stands for Sin=Opposite (the side opposite to the angle) over hypotenuse (the side opposite to the right angle)

Cah stands for Cos=Adjecent (the side next to the angle that is not the hypotenuse) over the hypotenuse

Toa stands for Tan=opposite over adjacent

Good luck! Hope I helped you understand.