Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9? y = 2x3 + x2 + 3x +5 y =9 y = 2x3 + x2 y = 3x + 14 y = 2x3 + 4x2 – x + 5 y = –3x2 + 4x + 9 From least to greatest, what are the roots of the polynomial equation?

Answer:

ST = √353 or 18.79

I can add a step-by-step explanation if you want me to.

The length of ST is approximately 18.79 units.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

We are given that;

Points= S (-1,8), and T (7,-9)

Now,

x1​=−1

y1​=8

x2​=7

y2​=−9

Substituting these values into the formula, we get:

d=(7−(−1))2+(−9−8)2​

d=(8)2+(−17)2​

d=64+289​

d=353​

d= 18.79

Therefore, by the distance the answer will be 18.79 units.

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Answer:

  $2.50

Step-by-step explanation:

Jake's total expenditure is ...

  total = admission + c × (number of tickets)

  36 = 13.50 + 9c . . . an equation to solve

  4 = 1.50 +c . . . . . . . divide by 9

  2.50 = c . . . . the cost of one ticket

Each ticket cost Jake $2.50.

Answer:

(- 9, 0) and (8, 0)

Step-by-step explanation:

To find the x- intercepts let f(x) = 0, that is

(x - 8)(x + 9) = 0

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 8 = 0 ⇒ x = 8

The x- intercepts are x = - 9 and x = 8

Answer:

C

Step-by-step explanation:

(4√6)/(5√6)

= 6^(¼) ÷ 6^(1/5)

= 6^(1/4 - 1/5)

= 6^[(5-4)/20]

= 6^(1/20

When dividing roots, multiply them together: 4 x 5 = 20

Invert the product: 1/20

Raise the number under the root by that

Answer = 6 ^ 1/20

Answer:

60 feet

Step-by-step explanation:

The height, h (in meters), of the object launched from a platform is represented by the equation

[tex]h=h(x)=-5x^2+20x+60[/tex]

where x is the time (in seconds) passed after the launch.

The time of launch is [tex]x=0[/tex] (0 seconds passed after the launch)

Substitute [tex]x=0[/tex] to find the height:

[tex]h=h(0)=-5\cdot 0^2+20\cdot 0+60=60\ feet[/tex]

See explanations below on solving simultaneous equations by elimination.

Step-by-step explanation:

In solving simultaneous equations by elimination, you make one side of the variables equal and eliminate that side by either addition or subtraction, then solve the remaining variable whose value is then used in one of the equations to find the other variable. For example;

(i)   4x - 2y= 10

(ii)  x+ y =4

Making the x variable part equal to eliminate x

1(4x-2y=10)--------multiply by 1

4(x+y=4) ---------multiply by 4

4x -2y =10

4x+4y=16

Apply subtraction to eliminate the x variables

0 +6y =6

6y=6

y=6/6 = 1

Use the value of y =1 in the equation x+y= 4

x+y=4

x+1=4

x=4-1 = 3

x= 3,  and y=1

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Step-by-step explanation:

[tex]12\times(2+2^3)\qquad\text{use PEMDAS}\\\\\text{first power}\\\\=12\times(2+8)\\\\\text{next addition in parentheses}\\\\=12\times10=120[/tex]

Answer:

The stage directions describe how characters react to Helen.

Step-by-step explanation:

In the given scene, the different characteristics of Helen as well as how other characters react when they see Helen is depicted in the scene. Other characters in the scene react differently to Helen when they come in contact with her. This is the main objective of the stage direction. It shows the interaction between Helen and others.

The stage directions represent the additions of the meaning to the play in terms of the stage directions describe how characters react to Helen.

The following information should be considered:

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Answer: Angle A = 120° and angle C = 45°

Step-by-step explanation: The first thing to note at the back of our minds is that the sum of the interior angles of a triangle equals 180°. Given that the three angle are available, we can start by adding them all together. Hence,

{12x + 12} + 15 + {3x + 18} = 180

12x + 12 + 15 + 3x + 18 = 180

By collecting like terms, we arrive at,

12x + 3x + 12 + 15 + 18 = 180

15x + 45 = 180

Subtract 45 from both sides of the equation

15x = 135

Divide both sides of the equation by 15

x = 9

At this point, we can now substitute for the value of x = 9 in the expressions representing angles A and C.

Angle A = 12x + 12

= 12(9) + 12

= 108 + 12

= 120

Angle A = 120°

Angle C = 3x + 18

= 3(9) + 18

= 27 + 18

= 45

Angle C = 45°

Answer:

KE = 6250 Joule.

Step-by-step explanation:

Every moving body has kinetic energy and it is given by the expression

[tex]KE = \frac{1}{2}mv^{2}[/tex]

where the moving body has m as the mass and v as the velocity.

If m is in Kg and v is in meter/sec, then KE will be expressed in Joule.

Now, in this case, m = 500 and v = 5 meter/sec.

So, [tex]KE = \frac{1}{2} \times 500 \times (5)^{2} = 6250[/tex] Joule. (Answer)

Step-by-step explanation:

Since f is a linear function then its graph must be a line

to draw a line ,all you need is plotting two points.

f(0)=1/2(0)+2=0+2=2 then the line passes through the point (0,2)

f(2)=1/2(2)+2=1+2=3 then the line passes through the point (2,3)

look ok at the photo below for the graph.

Answer:

11,356

Step-by-step explanation:

We multiply 5,678 by 2 because the word 'twice' is the same as multiplying by 2

Answer:

The choices Kyle has are option D.)  {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}

Step-by-step explanation:

The choices available to Kyle either of the models 4, or 5 or 6 and each model can have a protective case which can be either red(R) or blue(B) or camo(C).

So Kyle can have model 4 in red protective case, 4R, or model 4 in blue protective case(4B), or model 4 in camo protective case (4C) or

Kyle can have model 5 in red protective case, 5R, or model 5 in blue protective case(5B), or model 5 in camo protective case (5C) or

Kyle can have model 6 in red protective case, 6R, or model 6 in blue protective case(6B), or model 6 in camo protective case (6C).

So the choices Kyle has are option D.)  {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}

Answer:

D

Step-by-step explanation:

Answer:

-1/5m-4/5

Step-by-step explanation:

2/5m-4/5-3/5m

2/5m-3/5m-4/5

-1/5m-4/5

Answer:

5000

Step-by-step explanation:

Answer: t = 2698

Step-by-step explanation: Subtract 14 from 2712 to get the value of t

Answer:

They ate 7/8 of a pizza altogether.

Step-by-step explanation:

So, you know Mrs. Rivera ate 3/8 of a pizza and Ms. Carter ate 4/8 of a pizza.

You add 3/8 + 4/8 and you get 7/8.

The ate 7/8 of a pizza altogether.

The quantity of pizza  that Mrs. Rivera and Ms. Carter ate altogether is equal to [tex]\frac{7}{8}[/tex]

Given the following data:

To calculate how much (quantity) pizza  they ate altogether:

A fraction can be defined as a numerical quantity that isn't a whole number.

Hence, a fraction is simply a part of a whole number.

In this exercise, we would add up the two fractions, so as to calculate how much (quantity) pizza  they ate altogether.

[tex]Total \;quantity = \frac{3}{8} + \frac{4}{8}[/tex]

Lowest common multiple (LCM) = 8

[tex]Total\;quantity = \frac{4\;+\;3}{8} \\\\Total\;quantity = \frac{7}{8}[/tex]

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Answer:

16

Step-by-step explanation:

Using the Remainder theorem

f(x) divided by (x + h) then the remainder is the value of f(- h)

here the divisor is (x + 3), thus remainder is f(- 3)

remainder = 5(- 3)² + 9(- 3) - 2 = 5(9) - 27 - 2 = 45 - 29 = 16

Answer:

Step-by-step explanation:

㏒(6)-㏒(2)=㏒(6/2)=㏒ 3

The expression log(6) – log(2) in form of log(c) is log(12).

Logarithms are another way of writing exponents in mathematics. A number's logarithm with a base equals another number. Exponentiation is the inverse function of logarithm.

A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other numbers. It is the simplest way to express enormous numbers.

We have to write the expression log(6) – log(2) in form of log(c).

Using product property for logarithms

log a + log b= log (ab)

Here, a= 6 and b= 2 then

ab = 6 . 2= 12

Thus, the required form of log(6) – log(2) is log(12).

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Answer:

y=3/4x+6

Step-by-step explanation:

y-y1=m(x-x1)

y-6=3/4(x-0)

y-6=3/4(x)

y-6=3/4x

y=3/4x+6

Answer:

K = 3

a = 6

Step-by-step explanation:

F is directly proportional to a

That’s F = Ka

K is the constant

Divide both sides by a to get the constant k

K = F/a

When F = 24 and a =8

K = 24/8

= 3

When F = 18

a = ?

F = Ka

18 = 3 x a

18 = 3 x a

Divide both sides by 3

18/3 = 3 x a /3

6 = a

a = 6

Answer:

[tex]g(15)=93.8\%[/tex]

see the explanation

Step-by-step explanation:

Let

x ----> the number of years since 2008,

g(x) ----> the percent of people 25 years and older who have completed at least high school

we know that

[tex]g(x)=0.008x^2+0.42x+87.5[/tex]

so

For x=15 years since 2008

substitute

[tex]g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%[/tex]

That means

In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%

Final answer:

To find g(15), we substitute x with 15 in the function g(x) = [tex]0.008x^2 + 0.42x + 87.5[/tex], yielding g(15) = 95.6%. This means that in 2023, it's projected that 95.6% of people 25 and older will have completed high school according to the given quadratic trend.

Explanation:

The student is asking for the evaluation of the function g(x) = [tex]0.008x^2[/tex] + 0.42x + 87.5 at x = 15, which represents the number of years since 2008. To find g(15), we need to substitute x with 15 in the given function:

g(15) = 0.008(15)2 + 0.42(15) + 87.5

Calculating the value step by step:

152 = 225

0.008 × 225 = 1.8

0.42 × 15 = 6.3

1.8 + 6.3 + 87.5 = 95.6

Therefore, g(15) = 95.6.

In words, this means that if the trend described by function g(x) continues, then in the year 2023 (15 years after 2008), 95.6% of people aged 25 and older will have completed at least a high school education. This is a projection of graduation rates over time.

Answer:

Step-by-step explanation:

50

The ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e.  [tex]\mathbf{\dfrac{2}{3}}[/tex]

A ratio of two integers a and b can be represented into a fraction as numerators and denominators.

[tex]\mathbf{\dfrac{a \to numerator}{b \to denominator}}[/tex]

To recognize and determine the ratio of the whole numbers in their lowest terms, we will multiply both the numerator and the denominator by 10.

i.e.

[tex]\mathbf{=\dfrac{1.00}{1.50}}[/tex]

[tex]\mathbf{=\dfrac{1.00\times 10}{1.50 \times 10}}[/tex]

[tex]\mathbf{=\dfrac{10}{15}}[/tex]

DIvide both the numerator and denominator by 5;

[tex]\mathbf{=\dfrac{2}{3}}[/tex]

Therefore, we can conclude that the ratio of the whole numbers in its lowest term is ratio $2 to $3 i.e.  [tex]\mathbf{\dfrac{2}{3}}[/tex]

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Answer: $9.8 per hour

Step-by-step explanation:

If Dave works for 5 hours at double time, then he gets paid for 10 hours of work. If he earned $98 for 10 hours of work, all you need to do is divide the amount of money earned by the hours of work. [tex]\frac{98}{10}[/tex]=9.8 dollars per hour.

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

I had this question on a test and i made an 100%

Answer:

75 sides when the interior angle is 175.2

Step-by-step explanation:

these problems are all done the same way. Subtract the interior angle from 180 and divide the result into 360

360/(180 - 175.2)

360 / 4.8

75 sides

Answer:

Step-by-step explanation:      

2(20x30)+ 2(8x30) + 2(20x8)                                                                                                      -                                                                                                                                                                                                                                               I                                                                                                                                                                                                                >          1200 + 480 + 320=                                                                                                       2000                                                                                                                                  hope this helps :D

The material required for making a new cereal box with new dimensions is 2000 sq. cm. This is obtained by calculating the total surface area of the box with new dimensions.

It is given that,

The Outstanding O's cereal box has been redesigned with the new size and shape

The new dimensions are,

L=20 cm

W=8 cm

H=30 cm

To get the required material, the surface area of the box with new dimensions is to be calculated.

So,

S.A=2(LW + WH + LH)

     =2(20×8+8×30+30×20)

     =2(160+240+600)

     =2(1000)

     =2000 sq. cm

Therefore, the material required for the new box is 2000 sq. cm

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The sample space for odd numbers between 20 and 30 is {21, 23, 25, 27, 29}. These are integers that are not wholly divisible by 2.

The sample space is a term used in mathematics, specifically in statistics and probability, to describe all possible outcomes of an experiment. In this case, the experiment is to find all odd numbers between 20 and 30. An odd number is an integer that is not exactly divisible by 2. The odd numbers between 20 and 30 are: 21, 23, 25, 27, and 29. Therefore, the sample space you are looking for is {21, 23, 25, 27, 29}.

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