The difference between two-fifth of a number and 9 is 7. Find the number.

Answer:

Step-by-step explanation:

Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.

A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.

Synthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...

  p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment

And dividing the cubic by (x -1) gives ...

  p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment

The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.

The rewrite of p(x) is ...

  p(x) = (x +4)(x +3)(x -1)(x -2)

The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.

We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2

The y-intercept is +24, the constant in the polynomial.

With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.

A graph is seen in the first attachment.

Answer:

9 square megameters

Explanation:

Given:

We want to find out how many square megameters are in 9,000,000 square kilometers.

Multiply both sides of the equation by 9,000,000.

There are 9 square megameters in 9,000,000 square kilometers.

Answer:

114 cm^2; x = 6: it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense

Step-by-step explanation:

for the first one the area of a trapezoid is [tex]\frac{1}{2} h(b_{1} +b_{2})[/tex]

so

first find the height of the triangle

8^2 + h^2 = 10^2

64 + h^2 = 100

h^2 = 36

h = 6

so

the height is 6

now plug it in

[tex]\frac{1}{2} * 6 (25 + 13)[/tex]

[tex]\frac{1}{2} * 6(38)[/tex]

114 cm is the first answer

for the second one you can add all of them together and set them equal to 27

x - 1 + 2x - 4 + 3x - 4 = 27

6x - 9 = 27

6x = 36

x = 6

that is the second answer

it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense

The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,

-68% of data within 1 standard deviation.

-95% of data within 2 standard deviation

-99.7 of data within 3 standard deviation.

In our case the mean is

and the standard deviation is

then, the empirical formula imply that

and

then, the answer is 14 minutes to 34 minutes

Answer:

D

Step-by-step explanation:

The birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%

(a)In England, from 1961 to 1994, the birth rate fell by 26.1%

We need to find the birth rate in England in 1994

Birth rate in 1961 is 17.6

Birth rate in 1994 = 17.6 - 17.6 x26.1/100

= 17.6 - 17.6 x261/1000

= 17.6 - 4.6

= 13

(b) In Wales, the birth rate also fell.

The birth rate in 1961 is 17.0

The birth rate in 1994 is 12.2

Percentage fall is 100 x (17.0 - 12.2)/17.0

Percentage fall is 28.23 %

Therefore, the birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%

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Given:

The speed of the beetle is, s = 9 km/h.

The objective is to convert the speed into centimeters per second.

Explanation:

Since, it is known that,

Conversion;

Then, the speed can be converted as,

Hence, the the converted value is 250 cm/s.

Answer:

see explanation

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2

Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )

P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )

R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )

S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )

Answer: 11

Step-by-step explanation:

Let the number be x.

[tex]9x+30=140-x\\\\10x=110\\\\x=11[/tex]

Answer:

{1, 3, 5, 7}

Step-by-step explanation:

U = {1, 2, 3, 4, 5, 6, 7, 8}

P = {2, 4, 6, 8}

P'= {1, 3, 5, 7}

Answer:  [-4, 0] which is choice A

=====================================================

Reason:

lowest point is when y = -4

highest point is when y = 0

The range is any value of y between these values, including the endpoints themselves. We say the range is [tex]-4 \le y \le 0[/tex] which condenses to the interval notation [-4, 0]

Use square brackets to include the endpoints.

If there were open holes at the highest and lowest points, then we would use curved parenthesis instead.

The salesman A must make 150 order to make the same amount of salesman B .

In the question ,

it is given that ,

Salesman A gets paid $300 per month

for every sale salesman A get $8 .

let the number of sales made by salesman A be "x" .

So, amount made by salesman A = 300 + 8x

Salesman B earns per month = $1500 .

To make the amount earned by both the salesman same ,

300 + 8x = 1500

8x = 1500 - 300

8x = 1200

x = 1200/8

x = 150

Therefore , The salesman A must make 150 order to make the same amount of salesman B .

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Using the model Carter will find parts A, B and C b to be

Part A = 26 tens

Part B = 13

Part C = 13 ones

A model is a representation in form of shape used for to achieve a desired aim. Models are choose with respect to the importance

The given model is a rectangle

Subtracting 13 from 273 to give 260. This  can be arranged in tens by doing

= 260 / 10

= 26

Hence, A is 26 tens

Representing the C part in place value we have 13 ones

Since B = C, we have B = 13

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Answer:

Twenty-three and seven-ninths

Step-by-step explanation:

Might not be correct I don't really remember how to do this

Answer:

Well your answer is down below

Step-by-step explanation:

First as a Inequality −3(2x−5)<5(2−x)

Step 1: Simplify both sides of the inequality.

−6x+15<−5x+10

Step 2: Add 5x to both sides.

−6x+15+5x<−5x+10+5x

−x+15<10

Step 3: Subtract 15 from both sides.

−x+15−15<10−15

−x<−5

Step 4: Divide both sides by -1.

−x−1<−5−1 x>5

So your answer is x>5

hope this helps

~~Wdfads~~

x+119°=180°(Co-interior angles are supplementary m || n)

[tex]x = 180 - 119 \\ x = 61[/tex]

y=119°(alternate angles are equal m ||n)

GOODLUCK.

37 inches total, but 35 with just December, January, and February (depending on the definition of winter)

Answer:

[tex]\frac{17}{4}[/tex]

Step-by-step explanation:

Replace y with 3/2 and solve for x

2x + 3(3/2) = 13

2x + 9/2 = 13  Subtract 9/2 from both sides

2x = [tex]\frac{13}{1}[/tex] - [tex]\frac{9}{2}[/tex]

2x = [tex]\frac{26}{2}[/tex] - [tex]\frac{9}{2}[/tex]

2x = [tex]\frac{17}{2}[/tex]  Divide both sides by 2

x = [tex]\frac{17}{2}[/tex] ÷ [tex]\frac{2}{1}[/tex]

x = [tex]\frac{17}{2}[/tex] x [tex]\frac{1}{2}[/tex]

x = [tex]\frac{17}{4}[/tex] o r4 [tex]\frac{1}{4}[/tex] or 4.25

11. The amount he pays in annual state income tax is $1,497.

13. The amount that will be paid for tax will be $2000.

14. The amount he pays in annual state income tax is $707.50.

11. Given;

Annual earnings = $57,900

State tax rate = 3%

Amount earned in exemption = $8,000

Taxable Income = Annual Income - Exemptions

Igor's taxable income = $57,900 - $8,000 = $49,900

Taxable Income × Tax rate = Amount paid as tax

The amount he pays is therefore; $49,900 × 3% = $1,497

13. The amount that will be paid as tax will be:

= 4.6% × $43500

= $2000

Therefore, the amount is $2000.

12. a) We can see that the exemptions for a married person are $4000 and $2000 per dependent. Since there are 2 dependents, therefore:

Amount for exemptions = $4000 + (2 dependents × $2000 per dependent)

Amount for exemptions = $4000 + $4000 = $8000

Amount for exemptions = $8000

b) Taxable wages = Annual gross pay - Exemptions

Taxable wages = $63840 - $8000 = $55840

Annual state income taxes = Taxable wages × State tax rate

Annual state income taxes = $55840 × 4% = $2233.6

14. The amount he pays in annual state income tax is $707.50.

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Answer:

$107125.80

working out:

50000x1.115^7=107125.8 (rounded)

We were given that:

For P

Answer: False

Step-by-step explanation: The two lines do not overlap so they do not intercept.

The principal amount is $99,055.82.

When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.

Given:

Amount = 120,000

r = R/100

r = 2.4/100

r = 0.024 per year,

Then, solve the equation for P

P = A / [tex](1 + r/n)^{nt}[/tex]

P = 120,000.00 /[tex](1 + 0.024/12)^{(12)(8)[/tex]

P = 120,000.00 / [tex](1 + 0.002)^{(96)[/tex]

P = $99,055.82

Hence, the principal amount is $99,055.82.

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The relation which represents a function is the mapping diagram.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).

In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.

Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.

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The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.

Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.

Note that the regression equation is usually given as:
ŷ = bX + a; where

y = dependent variable

b  = Slope/coefficient

X  = Independent Variable
a = Constant/ Intercept.

Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.

From the graphing calculation, we have:

The sum of X = 21

The sum of Y = 33.39

Mean X = 3

Mean Y = 4.77

Sum of squares (SSₓ) = 28

Sum of products (SP) = 22.96

Recall that the regression equation is given as:
ŷ = bX + a;

Where;

b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]

Hence,

b = 22.96/28

= 0.82

a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31

hence,

ŷ =  0.82X + 2.31.

Lets find Y if x = 10

y = 0.82 (10) + 2.31 [plugging in the value]

= 8.2 +2.31

= 10.51

Let's find X where Y = 10

10 =  0.82X + 2.31. [Plugging in the value]

collect like terms over the equation sign

10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X

X = 9.37804878049
X [tex]\approx[/tex] 9.38

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define what happens when a function is shrunk vertically

When the factor is greater than 1, the condition that satisfies the function is to multiply by 1.4

When the graph is verticcally shrunk, this means that the function is multiplied by 1.4

Hence, the function becomes:

STEP 2: Define what happens when the graph is shifted left by 3 units.

If the function is shifted left by 3 units, this implies that we add 3 units to the x of the function.

This gives:

The resulting coordinate of △ D'E'F' is translated by the vector is

(-1, -2),  (3,-4), and (1, -7)

Given the vertices of ∆DEF are D(2,5), E(6,3), and F(4,0).

we are asked to graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7)​.

If the coordinate of the vertices is translated by the vector (-3, -7), the resulting coordinates of △ D'E'F' will be expressed as:

D'= (2-3, 5 - 7) = (-1,-2)

E' = (6 - 3, 3 - 7) = (3, -4)

F' = (4 -3 , 0 - 7) = (1, -7)

Hence we get the required coordinates of the translated image.

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The formula for the Volume(V) of the cylinder is given as,

Given:

Therefore,

Hence, the volume of the cylinder is

Answer: $17

Step-by-step explanation:

$425 divided by 25

Answer:

Her hourly rate is $17/hr.

Step-by-step explanation:

We can figure this out by taking the total dollars ($425) and dividing it by how many hours she spent working (25). 425 divided by 25= 17. Therefore, her hourly rate is 17$/hr.

To convert from radical form to exponential in fractional form, we can follow:

Firstly, notice that 9 is the same as 3 squared:

Now, we can apply the change:

Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:

So, the expression in the simples form and fractional exponent is: