If f(x)= x³+4x² - 15-18 and a + 1 is a factor of f(x), then find all of the
zeros of f(x) algebraically?

Answer:

10x^2 + 47.2x - 84.18

Step-by-step explanation:

You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible

As a result, the cone's volume is equal to three times its radius √343/π .

The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.

So with respect to the information provided to us :

Height of a cone =3* radius of the base

let height be h and radius be r

h=3r

The Formula for volume of cone is:

V=1/3hπr²

Putting the value we get:

343=1/3*π*r²*3r:

r= √343/π

Therefore ,

the volume of the cone whose height is three times its radius is:

√343/π

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Answer:

the  next year population is 122,689      

Step-by-step explanation:

The computation of the next year population is as follows:

= This year population × increase percentage

= 119,000 × (1 + 0.031)

= 119,000 × 1.031

= 122,689

Hence, the  next year population is 122,689

The above formula is applied so that the correct value of the population could come

and the same is relevant

The expression gives the cost of fuel for this journey is option H mp / 100 fx

Given,

The total distance of a car journey = m miles

One kilometer = x miles

The amount of petrol needed to travel a distance of f kilometers = 1 liter

Cost of the fuel = p pence/ liter

Now we have to find the expression which gives the cost of fuel for this journey in pounds.

1 pound = 100 pence

So,

The distance in miles we can travel with 1 liter of petrol = fx

Total liter of petrol needed for the journey = m/fx

Total cost of petrol for the journey = mp / fx100

That is,

The expression gives the cost of fuel for this journey is option H mp / 100 fx

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The question is incomplete. Completed question is given below:

A car journey is m miles long.

One kilometre is equivalent to x miles.

The car uses one litre of fuel to travel a distance of f kilometres.

Fuel for the car costs p pence per litre.

Which of the following expressions gives the cost of fuel for this journey, in pounds?

(There are 100 pence in one pound.)

A. 100fmpx

B. 100fmp/x

C. 100mpx/f

D. 100mp/fx

E. fmpx/100

F. fmp/100x

G. mpx/100f

H. mp/100fx

123°

180°-57°=<6=123°

Answer:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome

Answer:

The answer is really option A. x^2 - x +2-5/x-1

Step-by-step explanation:

I just took the test and got it right :)

The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.

The variance's positive square root is the standard deviation. One of the foundational strategies in statistical analysis is standard deviation. The term "standard deviation," often shortened as "SD," tells us how far a value deviates from the mean value. It is represented by the symbol "."

Given that : The mean birth weights of infants born at an area hospital in the month of April is 128 oz. with a standard deviation of 10.2 oz.

So let's look at this and see what the correct interpretation of a standard deviation is, which is the distance between each person's actual way of being born and a braille and the main way it was, which is typically about 10 points two oh. From this, we can deduce what the question Act is. The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.

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     The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

     Then, add or subtract 50% from the first total and then, I believe, add (or it might be the other way around) to get your actual total. We would want it because it shouldn't affect the cost of the first machine. I'm sorry, but I haven't done any math in a long. use a calculator if necessary

    Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price + profit margin = selling price.

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The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]

The inverse of a matrix is given by

[tex]A^{-1} = \frac{1}{|A|} adjA[/tex]                   ...(1)

Now, determinant of matrix A is

|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]

= (3)(2) - (2)(1)

= 6 - 2

= 4

Now, adjoint A will be

[tex]A_{11}[/tex] = 3

[tex]A_{12}[/tex] = -1

[tex]A_{21}[/tex] = -2

[tex]A_{22}[/tex] = 2

AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]

Now, substituting the values of |A| and AdjA in equation (1), we get

[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]        

Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

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Answer:

11

Step-by-step explanation:

If you input the number and then solve, you should get that #=#

2(11)+9=4(11)-13

22+9=44-13

31=31

Answer: 11

Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31

Answer:

Step-by-step explanation:

The attached graph is NOT a function, since it doesn't pass the vertical line test.

If a vertical line cuts the graph more than once, then this relation is not a function.

Answer:

y = 12x + 18

Step-by-step explanation:

Equation of line in slope-intercept form: y =mx +b

Here, m is the slope and b is the y-intercept.

  m = 12

Substitute m =12 in the above equation,

        y = 12x + b

This line passes through (-2,-6). So, plugin the point in the above equation.

       -6 = 12*(-2) + b

      -6 = -24 + b

-6 + 24 = b

         b = 18

Equation of the line:

         [tex]\sf \boxed{\bf y = 12x + 18}[/tex]

By 6.2 miles per hour, Sheri commutes more quickly.

We are given that,

John travels to work = 20km/hr

Sheri travels to work = 500m/min converting this into km/hr we get ,

1.61km/hr or 1 mile

John travels to work at the following rate:

[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]

Sheri travels work at the following rate:

[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]

Computing the difference between the two,

18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr

thus, by 6.2 miles per hour, Sheri commutes more quickly.

What are conversions in maths?

An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.

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The robot will take 0.15 hours to complete one task.

What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.

Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.

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Given,

To find g(f(-2)). we first find the value of f(-2).

The value of f(-2) is,

So now to find the value of g(f(-2)),

So the value of g(28) is,

So the value of g(f(-2)) is 51.

Answer:

x = 9

Step-by-step explanation:

given g(x) = - x and g(x) = - 9 , the equate right sides

- x = - 9 ( multiply both sides by - 1 )

x = 9

Answer:

u = 115

Step-by-step explanation:

35 = u/5 + 12

35 - 12 = u/5

(35 - 12) * 5 = u

u = (35 - 12) * 5

u = 115

Answer:

72 and 12

Step-by-step explanation:

substitute x = 3 into the expressions

2(x + 3)²

= 2(3 + 3)²

= 2(6)²

= 2 × 36

= 72

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

3(x - 1)²

= 3(3 - 1)²

= 3(2)²

= 3 × 4

= 12

The length of the pole is 19.15 feet.

The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.

Given:

Angle made by straight road = 15°

Angle of elevation of the sun = 57°

Length of the shadow = 75 feet

∠ACB = 90° - 57° = 33°

∠CAB = 57° - 15° = 42°

Using Sine Law to find BC i.e.length of the pole.

[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]

[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]

[tex]BC= \frac{75sin 42}{sin 33}[/tex]

BC ≅ 19.15 feet (to the nearest hundredth.)

Hence, the approximate length of the pole is 19.15 feet.

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The temperature in the evening is 79.5 degrees Fahrenheit.

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

Jesse recorded a temperature in the morning of 75 degrees Fahrenheit

The temperature increased by [tex]4\frac{1}{2}[/tex] degrees Fahrenheit in the afternoon

75 +  [tex]4\frac{1}{2}[/tex] =[tex]\frac{159}{2}[/tex]

=79.5 degrees Fahrenheit

Before decreasing by 2.6 degrees Fahrenheit in the evening. The temperature in the evening is 79.5 degrees Fahrenheit.

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The smallest possible number of students in the algebra class is 13.

Let n≥5 be the number of students.

The sum of their scores must be at least 5×100 + (n - 5).

Simultaneously, we must achieve the mean 76, which is equivalent to achieving the mean sum 76n.

As a result, we have a sufficient precondition on n: we should have 5×100 + (n - 5) ≤ 76n.

This can be reduced to 200 ≤ 16n. This is true for the smallest integer n = 13.

To complete our solution, we must now determine how 13 students might have scored just on test.

We have 13×76 = 988 points to distribute to them. Because five 100s equal 500, we must distribute the remaining 488 points as among remaining eight students.

This can be accomplished, for example, by awarding each of them 61 points.

Thus, the smallest possible number of students in the class is 13.

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Step-by-step explanation:

2x+(-8x) +5-5

-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know

Coordinates of PQRSTU

P = (-2, -6)

Q = (-4, -6)

R = ((-4, -2)

S = (2, -4)

T = (2, -8)

U = (0, -10)

They changed to ABCDEF

A = (4, 4)

B = (2, 4)

C = (2, 8)

D = (8, 6)

E = (8, 2)

F = (6, 0)

Transformations used = (x + 6, y + 10)

Answer:

Step-by-step explanation:

x = 39

C. 39 Cars

22) 68

24) 90

26) 158

a) The x-intercepts of y=f(x) is (-3,0) (4,0)

b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.

Here to determine the x-intercept put y=0,

Given f(x)=(x-4) (x+3)

a) y=(x-4) (x+3)

Replacing y by 0 we get,

(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)

b) y = -2(x-4) (x+3)

Replacing y by 0 we get,

-2(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)

Replacing y by 0 we get,

(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0

By solving the above equation

(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0

-1/2x=4 and -1/2x=-3

x=-1/8 and x=1/6

Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) y=(-(x+1)-4) (-(x+1) +3)

Replacing y by 0 we get,

(-(x+1)-4) (-(x+1) +3) =0

By solving the above equation

(-(x+1)-4) =0 and (-(x+1) +3) =0

-(x+1) =4 and -(x+1) =-3

x=-5, 2

Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

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The likelihood or probability that she will give the first student a blue calculator and the second student a yellow calculator is 6.6%.

The math teacher Mrs. Piatt has six black, nine yellow, and two blue calculators.

Therefore, the total number of calculators is 17.

The probability that she hands out a blue calculator to the first student is:

P₁ = Number of blue calculators/ Total number of calculator

P₁ = 2/17

Now, as a calculator is handed out to a student. Then the remaining number of calculators is 16.

Therefore, the probability that the second student gets a yellow calculator will:

P₂ = Number of yellow calculators/ Total number of calculators.

P₂ = 9/16

Therefore, the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second will be:

P = P₁ × P₂

P = 2/17 × 9/16

P = 18/272

P = 0.06617647058

P = 6.6%

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The scientific notation is 6.3 × [tex]10^{-3}[/tex]

The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])

Calculate the product or quotient

=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])

Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]

=63 × [tex]10^{-2-2}[/tex]

=63 ×[tex]10^{-4}[/tex]

= 6.3 × [tex]10^{-3}[/tex]

Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].

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The expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .

In the question ,

two expressions are given as

8x²+3(x²+y) and 7x²+7y+4x²-4y .

Simplifying the first expression

we get ,

= 8x²+3(x²+y)

= 8x² + 3x² + 3y

adding the like terms , we get

= 11x² + 3y

Simplifying the second expression

we get ,

= 7x²+7y+4x²-4y

adding and subtracting the like terms ,

we get

= 11x² + 3y

We can see that both the expressions are giving the final answer  as 11x² + 3y  .

hence , both the expressions are equivalent .

Therefore , the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .

The given question is incomplete , the complete question is

Are the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y equivalent ? Explain your reasoning .

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