f(x) = x² + 7x +9

Find f(-7)

x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).

Given, two points (-5,0) and (-2,-3).

We are asked to find an equation of the line that passes through the given points.

As, we know

the equation of a line is

(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)

(y - 0)/(x - (-5)) = (0 - (-3))/(-5 - (-2))

y/(x + 5) = 3/-3

y/(x + 5) = -1

y = -(x + 5)

y = -x - 5

x + y + 5 = 0

Hence, x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).

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Answer:

Step-by-step explanation:

Cube Surface Area = 150 cm2

Cube Volume = ?

Ac = 6 a2

150 = 6a2

150/6 = a2

25 = a2

5 = a

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

Vc = a3

Vc = (5)3

Vc = 125 cm3

Answer:

Step-by-step explanation:

divide 150 by 6 and find the area of ​​one face of the cube, take the square root and find the side, side^3 and find the volume

150 : 6 = 25 cm² (area of ​​one face of the cube)

√25 = 5 (side of the cube)

5³ = 125 cm³ (volume of the cube)

The solution to the questions are:

From the question, we have the following parameters that can be used in our computation:

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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Answer:

7 yd

It's a 16 by 13 rectangle. Since 6 yd are already showing on the left side, you know 7yd remain to get 13 yd.

The equation that shows that angles angles formed by the diagonals and sides of the rhombus is x + y = z

The diagonals of rhombus intersect each other at 90 degrees

z =  angle formed at the diagonal = 90

x and y angle sides of the rhombus

applying the sum of angles of a triangle property

z + x + y = 180

where z = 90

90 + x + y = 180

x + y = 180 - 90

x+ y = 90

therefore x + y = z

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Answer:

5.1 units

Step-by-step explanation:

[tex]f(x)=5x-2\\f(3)=5(3)-2=13\\f(4)=5(4)-2=18[/tex]

[tex]\Delta x=1 unit=a\\\Delta y=5 units=b\\a^2+b^2=c^2\\(1)^2+(5)^2=c^2\\\sqrt26=c\\c=5.1 units[/tex]

In the information provided, cholesterol is high and accounts for 39% of the total. It may have a negative impact on heart health as well.

Cholesterol;-

Any member of the lipid class of chemical compounds is referred to as cholesterol. Sterols are a subclass of lipids.

All animal cells produce cholesterol, which is a structural component of animal cell membranes.

It may result in a number of issues, including obesity, heart disease, and stones. As its level is 39% in the amount provided, this is high.

Therefore, cholesterol looks to be a high-nutrient food.

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The variable y represents the range or output values of the function.

The range of a function is the set of output values of the function.

The given equation is y = mx + b.

Note that x is an independent variable, therefore, we substitute the values for x and calculate the value of y to that value of x.

Therefore, y denotes the range or output values of the function.

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Answer:

$602.50

Step-by-step explanation:

The monthly rent is $1,050.00.

If Yadira pays 3/5 ths of the rent, then her friend will pay 2/5 ths of the rent:

[tex]\implies \sf \dfrac{2}{5}\;of\;1050=\dfrac{2}{5} \times 1050=420[/tex]

Therefore, Yadira's friend pays $420 for rent.

If the monthly utilities average is $365, Yadira's friend's portion of the utilities will be half of the total:

[tex]\implies \sf \dfrac{1}{2}\;of\;365=\dfrac{1}{2} \times 365=182.5[/tex]

Therefore, Yadira's friend pays $182.50 for utilities.

So the total amount Yadira's friend will pay each month is:

[tex]\implies \sf Rent + Utilities=420+182.50=602.50[/tex]

Answer:

222-148=74 (people 3-2=1)

296-222=74 (people 4-3=1)

370-296=74 (people 5-4=1)

so 1/74 is the answer

Answer:

200

Step-by-step explanation:

a) The average wait time in the line = 13.33 minutes.

b) The average number of customer waiting on line = 4.67 minutes

What do you mean by average?

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

a) Values:

Arrival rate = 9 per hour

Service rate [tex]= \frac{60}{Service\ time}[/tex]

Service rate [tex]= \frac{60}{4.5} = 13.33[/tex]  minutes

b) Queue:

units in queue(LQ) = Arrival Time^2 / (Service rate* (Service rate - Arrival rate))

unit in queue(LQ) [tex]= \frac{ 9^2}{(13.33\times (13.33 - 9))}[/tex]

unit in queue(LQ) = 0.70

Time in Queue(WQ) = Arrival rate / (Service rate * (Service rate - Arrival rate))

time in queue (WQ) [tex]= \frac{9}{ (13.33 \times (13.33 - 9)}[/tex]

time in queue (WQ) = 4.67 minutes

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Line 1 and Line 2 are parallel because they have the same slope.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

Two lines are parallel if the slopes are the same.

The equation of line 1 is  y = 5x + 1

The slope of Line 1 is 5.

Let's find the slope of Line 2 using the equation.

2y - 10x + 3 = 0

Let's represent the equation in slope intercept form to locate the slope easily.

2y - 10x + 3 = 0

2y = 10x - 3

y = 10 / 2 x  - 3 / 2

y = 5x - 3 / 2

The slope of line 2 is 5

Therefore, Line 1 and Line 2 are parallel.

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The percentages are given as follows:

a) Failed, given that they completed the review: 15.38%.

b) Failed, given that they did not complete the review: 42.86%.

Considering these percentages, for item c, there is an inverse association between failing the exam and completing the exam review, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.

A proportion represents a fraction relative to a total amount, and this fraction, which is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

A percentage is one example of application of proportions, as it is the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.

For item a, we have that:

Hence the percentage is:

p = 10/65 x 100% = 15.38%.

For item b, we have that:

Hence the percentage is:

p = 15/35 x 100% = 42.86%.

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The solutions to each of the given exponential functions are;

1) g = 1.356

2) u = 1.725

3) x = 3

4) k = -5.288

5)  a = 4/3

6) z = 1.295

7) x = 13/2

8) v = -1.5286

9) y = 4.17

10) b = 1.2648

Exponential equations are usually in the form a^(x) = b^(y) . To solve exponential equations with same base, we normally make use of the property of equality of exponential functions .

1) 7^(g) = 14

gIn 7 = In 14

g = In 14/In 7

g = 1.356

2) 6^(u) = 22

u In 6 = In 22

u = In 22/In 6

u = 1.725

3) 7^(x - 2) = 7

7^(x - 2) = 7¹

Equating the exponents gives;

x - 2 = 1

x = 3

4) (0.66)^k = 9

k In 0.66 = In 9

k = In 9/In 0.66

k = -5.288

5) Exponential equation 8^a = 16

2^(3a) = 2⁴

Equating the exponents gives;

3a = 4

a = 4/3

6) The exponential equation 12^z = 25;

z In 12 = In 25

z = In 25/In 12

z = 1.295

7) The exponential equation 4^(x-5) = 8

2^(2(x - 5)) = 2^(3)

2x - 10 = 3

2x = 13

x = 13/2

8) (0.28)^v = 7

vIn 0.28 = In 7

v = In 7/In 0.28

v = -1.5286

9) 2^y = 18

y In 2 = In 18

y = In 18/In 2

y = 4.17

10) 17^b = 36

b In 17 = In 36

b = In 36/In 17

b = 1.2648

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-8)}) \implies y -0= -4 (x +8) \\\\\\ y=-4x-32\implies {\Large \begin{array}{llll} 4x+y=-32 \end{array}}[/tex]

Answer:

cost of each pencil [tex]= \frac{150}{x}[/tex]

The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.

Given that,

The table is

Input        Output

X               Y

1                 0

3                4

4                6

7                 p

20              q

We have to find the p and q values.

Take the points as

(x,y)=(1,0),(3,4),(4,6),(7,p) and (20,q)

Take the points (1,0) and (3,4)

Equation of the line is

y=mx+b

Where

The slope of the line is m, and the intercept is b.

Slope of the line is rise/run

m=4-0/3-1

m=4/2

m=2

Now,

y=mx+b

0=2(1)+b

2+b=0

b=-2

The equation of the line is y=2x-2.

Take the point(7,p)

p=2(7)-2

p=14-2

p=12

Take the point (20,q)

q=2(20)-2

q=40-2

q=38

Therefore, The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.

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To work to pay for the refurbished computer exists 89 hours.

Tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax reliefs.

Tax is defined as a mandatory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or national).

First estimate all the deduction

FICA = $10 per hour × 0.0765 = $0.77 per hr

Fed tax = $10 per hr × 0.12 = $1.2 per hr

State tax = $10 per hr × 0.08 = $0.8 per hr

Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour

Time required = $640 / $7.23 per hr

Time required = 89 hours

Therefore, the correct answer is option c) 89 hours.

The complete question is:

You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the refurbished computer?

a) 111 hours

b) 98 hours

c) 89 hours

d) 87 hours

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The icon to view the customary units in 11880 yields is 6.75 mi

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, rounding and choosing the appropriate number of significant digits may be necessary during the process.

To measure various parameters, various units of conversion are utilized.

Counting Length

Weighing Things

Evaluation of Capacity

Temperature Measurement

To better understand, we convert measurement units in mathematics.

For ease of understanding, the length of a table is measured in inches, whereas the length of a garden is measured in yards.

A finger's length cannot be expressed in kilometers.

Units of measurements are necessary to measure various quantities.

divide 11,880 yards length value by 1760 to get 6.75 miles

Therefore the icon to view the customary units in 11880 yields is 6.75 mi

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The value of y' by implicit differentiation, the value of y is [tex]y = \sqrt{5x +c}[/tex]

We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.

Given

The function is [tex]y^2 + 5 = 5x[/tex]

where x and y are variables..

On differentiating the equation, we have;

[tex]2yy' + 0 = 5[/tex]

on simplifying, we have

2yy' = 5

Now solve the equation explicitly for y and differentiate to get y' in terms of x.

2yy' = 5

Separate the variables

[tex]y^2 = 5x + c[/tex]

Taking square root on both the side

[tex]y = \sqrt{5x +c}[/tex]

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Answer:

21

Step-by-step explanation:

Do long division of 378 and 18.
The result of the division will be 21.
There will be 21 seashells on reach row for the science display.

If one plane can travel 10 miles per hour faster than another. The planes' speeds would be 435 miles per hour.

let s = speed of the slower plane

then

(s+10) = speed of the faster

time = distance /speed

495/s =510 /(s+10)

495s = 510s + 5100

Combine like terms

495 - 510s = 5100

15s = 5100

Divide both side by 15s

s = 5100/15

s = 425 mph  ( speed of the slower plane)

Speed of the fastest plane

(s+10)

425 +10

= 435 mph

Therefore  the speed of the fastest is 435 mph.

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Answer:

The correct answer is: 204.6

Step-by-step explanation:

(26 * 7.75) + (2/5 * 7.75) = 204.6

Answer:

[tex]\text{cosw}(\frac{1}{1-tanw} +\frac{sinw}{sinw-cosw} )[/tex]

Step-by-step explanation:

Assuming we're factoring.

1) Find the Greatest Common Factor (GCF).

GCF = [tex]\text{cosw}[/tex]

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]\text{cosw}(\frac{\frac{cosw}{1-tanw} }{cosw} +\frac{\frac{sinwcosw}{sinw-cosw} }{cosw} )[/tex]

3)  Simplify each term in parentheses.

[tex]\text{cosw}(\frac{1}{1-tanw} +\frac{sinw}{sinw-cosw} )[/tex]

Thanks.

Answer:

y=10x-15

Step-by-step explanation:

Use slope-intercept form: y=mx+b

M is your slope and B is your Y intercept

since your Y-intercept is negative, and adding a negative is just subtracting, you can just put -15 instead of +-15

If a sample consists of 1900 scores from sample no. 476th will be above the first quartile.

The three main methods for identifying the average value of a set of integers are mean, median, and mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.

The middle value in a list that is arranged from smallest to greatest is called the median.

The value that appears the most frequently on the list is the mode.

Given a sample consisting of 1900 scores.

∴ The no. of samples that would be above quartile is the next sample from (1/4)th of 1900 which is,

= (1/4)×1900 + 1.

= 475 + 1.

= 476.

So from sample no. 476th will be above the first quartile.

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The person that has the winning time is Alex.

From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.

It should be noted that in a race, the person that has the lowest time wins.

In this situation, the person with 8.625 seconds is the lowest.

Therefore, Alex wins.

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Answer: 24,000 ft.

Step-by-step explanation:

1in.(8)= 8 in.

SO: 3000ft.(8)= 24,000ft.

The 10th term of the series is 19.

Given series is an Arithmetic Progression (AP).

First term = a = 10

Difference = d = 11 -10

                        = 1

nth term = [tex]a_{n}[/tex] = a + (n-1)d

10th term = [tex]a_{10}[/tex] = 10 + (10 - 1)1

                        = 10 + 9*1

                        = 10 + 9

                        = 19

Hence, 10th term is 19.

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