Use the x-intercept method to find all real solutions of the equation.
x^3-11x^2+31x-21=0

Answer:

3rd group of possible answers is the correct set

Step-by-step explanation:

Each of the three points in the 3rd line of possible answers is a solution of the given equation, as can be verified by substitution:

If x = -2, y = -8(-2) = +16

If x = 3, y = -8(3) =  -24

If x = -4, y = -8(-4) = +32

Answer:

c

Step-by-step explanation:

Answer:

 √48 could not be M.

Step-by-step explanation:

M must be  between - 2 and 6, so:

a. √48 = 6.93 so this can't be M.

b.   √18 = 4.24 so this could be M.

c and d could also be M.

The coordinate of point M can be any of the given options.

To determine the possible coordinates of point M, we need to find the values between X (-2) and Y (6) on the number line provided. Starting from X (-2) and moving towards Y (6), the numbers that lie between them are -2, 0, 2, 4, and 6. We can see that all the given options for the coordinate of point M can be found on the number line. Therefore, none of the given numbers could not be the coordinate of point M.

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h = 12.

See the attached picture:

he has 84 hockey cards total

a. The series is

[tex]\displaystyle\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-4-\frac43-\frac4{3^2}-\frac4{3^3}-\cdots[/tex]

(first four terms are listed)

b. The series converges because this is a geometric series with [tex]r=\dfrac13<1[/tex].

c. Let [tex]S_N[/tex] be the [tex]N[/tex]-th partial sum of the series:

[tex]S_N=\displaystyle\sum_{n=1}^N-4\left(\frac13\right)^{n-1}[/tex]

[tex]S_N=-4-\dfrac43-\dfrac4{3^2}-\cdots-\dfrac4{3^{N-1}}[/tex]

Multiplying both sides by [tex]\dfrac13[/tex] gives

[tex]\dfrac13S_N=-\dfrac43-\dfrac4{3^2}-\dfrac4{3^3}-\cdots-\dfrac4{3^N}[/tex]

Subtracting this from [tex]S_N[/tex] gives

[tex]S_N-\dfrac13S_N=\dfrac23S_N=-4+\dfrac4{3^N}[/tex]

[tex]\implies S_N=-6+\dfrac6{3^N}[/tex]

As [tex]N[/tex] gets larger and larger [tex](N\to\infty)[/tex] the rational term converges to 0 and we're left with

[tex]\displaystyle\lim_{N\to\infty}S_N=\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-6[/tex]

Divide 7.8 by 1.18:

7.8 / 1.18 = 6.61 = 6.6 rounded to the nearest tenth.

When you divide scientific notation, subtract the exponents: 20 - 13  =7

The answer becomes 6.6 x 10^7

Division is one of the four fundamental arithmetic operations. The number of times the milk way is wider than the solar system is 6.61 × 10⁷.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that our solar system is 1.18 × 1013 meters in diameter, and the Milky Way galaxy is 7.8 × 1020 meters in diameter. Therefore, the number of times the milk way is wider than the solar system is,

Number of times = (Diameter of MIlky way)/(Diameter of Solar System)

                            = 7.8 × 10²⁰ meters/ 1.18 × 10¹³ meters

                            = 6.61 × 10⁷

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Answer:

Ella's Grade: 15

Minh's Grade: 16

Step-by-step explanation:

If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.

The number of boys in Ella's grade is 15 and Minh's grade is 16

Given that,

The ratio of  boys to girls in Ella's grade is 3:4

And the ratio of  boys to girls in Minh's grade is 4:5

The total number of girls is 20

Computation:

Let the number of boys be [tex]x[/tex]

So in the case of  Ella's,

[tex]\frac{3}{4}=\frac{x}{20}\\x=\frac{20\times3}{4}\\x=15[/tex]

And in case of Minh's,

[tex]\frac{4}{5}=\frac{x}{20}\\x=\frac{20\times4}{5}\\x=16[/tex]

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Answer:

23 Cards were given to your brother.

Step-by-step explanation:

12 + 24 = 36

36 - 13 = 23

Answer:

you gave him 23 cards

Step-by-step explanation:

12+24=36, 36-13=23

Answer: 6 teaspoons of sugar

Step-by-step explanation: Create a proportion

4 ounces of frosting = 2 teaspoons of sugar

8 ounces of frosting = 4 teaspoons of sugar

12 ounces of frosting = 6 teaspoons of sugar

To make 12 ounces of frosting, you would need 6 teaspoons of sugar.

To find out how much sugar is needed to make 12 ounces of frosting, we can set up a proportion using the given information. The recipe calls for 2 teaspoons of sugar for 4 ounces of frosting. We can set up the proportion: 2 teaspoons / 4 ounces = x teaspoons / 12 ounces.

To solve the proportion, we can cross multiply and divide. So, (2 teaspoons)(12 ounces) = (4 ounces)(x teaspoons). This simplifies to 24 = 4x. Dividing both sides by 4, we find that x = 6 teaspoons.

Therefore, you would need 6 teaspoons of sugar to make 12 ounces of frosting.

➷ The data set is not approximately periodic

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Answer:

Step-by-step explanation:

The given data doesn't show any periodic pattern, the change is not constant, and it doesn't simulate any simple pattern because the increase is like random, the first increase is for 1.35, the second is for 0.13, the third one is for 0.65, it doesn't show any periodic behaviour.

In addition, the variables involved aren't periodic, because it's about stocks, which it changes randomly.

Therefore, the right answer is the first option.

Answer:

Step-by-step explanation:

r = [tex]\frac{a_n}{a_{n-1}} = \frac{896}{3584} =  \frac{1}{4}[/tex]

Using the geometric series formula for the nth term:

[tex]S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} }  = 4777\frac{1}{2}[/tex]

Final answer:

The equation for the nth term of the geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The sixth term of the sequence is 14.

Explanation:

The given sequence is a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the equation for the nth term of the geometric sequence, we need to find the common ratio. We can do this by dividing any term in the sequence by the previous term.

For example, dividing the second term 896 by the first term 3584 gives us a common ratio of 1/4.

So, the equation for the nth term of the sequence is:

an = a1 × r(n-1)

where a1 is the first term and r is the common ratio.

To find the sixth term, we can substitute n = 6 into the equation:

a6 = 3584 × (1/4)(6-1)

a6 = 3584 × (1/4)5

a6 = 14

Graph of constant function is a horizontal line

It’s a horizontal line because all of the x’s must be different

Slope = (y2-y1)/(x2-x1)

Slope = (3-2)/(4-0)

Slope = 1/4

Answer:

[tex]\large\boxed{the\ slope=\dfrac{1}{4}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 2) and (4, 3). Substitute:

[tex]m=\dfrac{3-2}{4-0}=\dfrac{1}{4}[/tex]

Answer:

It can't be simplified.

Answer: form by math and can multiply two numbers or divide your choice

Step-by-step explanation:

To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.

Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.

Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.

Linda's daily savings: $1.55
Tyron's daily savings: $3.90

 Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x

We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)

Now, solve for x:

$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978

Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.

Answer:

16 pounds

Step-by-step explanation:

Total cereal she ate = 256 ounces

How many pounds she ate = ?

Given that (16 ounces = 1 pound)

Therefore, we have to divide the total ounces by 16 to calculate the cereal she ate in pounds = 256/16 = 16 pounds

Answer:

A. 16

Step-by-step explanation:

The second one should be it

I’m not sure bc I’m going off of my head

Factor out the common term 6

6(x^2 - 11x + 24) = 0

Factor x^2 - 11x + 24

6(x - 8)(x - 3) = 0

Solve for x;

x = 8,3

Answer:

Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Step-by-step explanation:

we know that

If cosine of angle theta is positive  then angle theta belong to the I or IV quadrant

and

If co secant of angle theta is negative then angle theta belong to the III or IV quadrant

therefore

angle theta belong to the IV quadrant (common solution)

Part 1) Find [tex]sin(\theta)[/tex]

we know that

[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]

we have

[tex]cos(\theta)=4/7[/tex]

substitute the value

[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex]

[tex]sin^{2}(\theta)=1-(16/49)[/tex]

 [tex]sin^{2}(\theta)=(33/49)[/tex]

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrant

Part 2) Find [tex]tan(\theta)[/tex]

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

we have

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex]

[tex]cos(\theta)=4/7[/tex]

substitute the values

[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex]

[tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Answer:

[tex]\frac{g}{8}-17[/tex] games

Step-by-step explanation:

Employees: 8

Sales last month: g

Average: [tex]\frac{totalGames}{Employees}[/tex]

To find out how many games Chris sold, we have to take the average and subtract 17.

[tex]\frac{g}{8}-17[/tex]

Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.

Answer:

g over 8 -17

Step-by-step explanation:

Answer:

You cant solve this without one more number.

Step-by-step explanation:

You need the length of the blue piece because it could be smaller or larger at this point. I may be wrong but unless I am missing something, and I totally might be if this is a kind of math I've never done, then please feel free to ignore me :) and have a lovely day!

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up → (x, y + n)

f(x) - n - shift the graph of f(x) n units down → (x, y - n)

f(x - n) - shift the graph of f(x) n units to the right → (x - n, y)

f(x + n) - shift the graph of f(x) n units to the left → (x + n, y)

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

(x, y) → (x - 3, y + 6)

x - 3 → shift the graph 3 units to the right

y + 6 → shift the graph 6 units up

Answer:

the right answer is left 3 units and up 6 units

Step-by-step explanation:

Answer:

The correct option is D) All real numbers.

Step-by-step explanation:

Consider the provided function.

Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.

Now consider the provided graph of the function.

The graph of the function is a straight line and function produces the positive and negative value of y.

By interpreting the graph it can be concluded the the range of the function is all real numbers.

Thus, the correct option is D) All real numbers.

Answer:

Step-by-step explanation:

A rectangular prism has 12 edges. In geometry, a prism is a solid figure with parallel ends or bases that are the same size and shape, with each side representing a parallelogram. The parallelograms in a rectangular prism are all rectangles.

The rectangular prism also has six faces, or flat sides. The surface area of a rectangular prism is determined by multiplying the length by the width of each of the six rectangles and by then adding the products together.

Answer:

The slope is undefined

Step-by-step explanation:

x = -4 is a vertical line.  Slope is defines as the change in y divided by the change in x.  

(change in y)/(change in x)

All the points on this line have the same x value, so the change in x is zero.  This means we have

(change in y)/0, which is undefined.

Answer:

UNDEFINED

Step-by-step explanation:

Any initial value set to equal x is considered an undefined rate of change [slope], which is a vertical line.

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

A diameter of a rhombus is an angle bisector. Therefore we have the equation:

[tex]3x-11^o=x+23^o[/tex]              add 11° to both sides

[tex]3x=x+44^o[/tex]                subtract x from both sides

[tex]2x=44^o[/tex]             divide both sides by 2

[tex]x=22^o[/tex]

Answer:

The area of the triangle = 31.5 feet² ⇒ answer (c)

Step-by-step explanation:

∵ Area of any Δ = 1/2 (side 1)(side 2)(sin the angle between them)

∴ The area of the Δ = 1/2 (b)(c) sin(∠A)

∵ b = 11 feet

∵ c = 10 feet

∵ m∠A = 35°

∴ Area of the Δ = 1/2 (11)(10) (sin(35)) = 31.547 feet²

∴ The area of the triangle = 31.5 feet²

∴ The answer is (c)

Answer:

This is correct, Carolyn will make $7.70 for each necklace but she loses $3.20 most likely for the suplices for the making of the necklace so she really earns $4.50.

Step-by-step explanation: