Factor the polynomial by grouping : x^3+5x^2-6x-30

Answer:

y = 3x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 5)

m = [tex]\frac{5+1}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

the line crosses the y-axis at (0, - 1) ⇒ c = - 1

y = 3x - 1 ← equation of the line

Answer: Answer : Answer : 15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660,675,690,705,720,735,

Step-by-step explanation:

Step-by-step explanation:

-7(k-8)+2k Use distributive property.

-7k+56+2k Combine like terms.

-5k+56

Mother knows best :)

Answer:

C: 0.25  

Step-by-step explanation:

We will use conditional probability formula to solve our given problem.

[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,

[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.

[tex]P(\text{A and B})[/tex]= Probability of event A and event B.

[tex]P(A)[/tex]= Probability of event A.

Let us substitute our given values in conditional probability formula.

[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.

[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.

[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.

[tex]P(B|A)=\frac{0.05}{0.20}[/tex]

[tex]P(B|A)=\frac{1}{4}[/tex]

[tex]P(B|A)=0.25[/tex]

Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.

Answer:

probability that a randomly selected student plays a sport, given that the student is a senior is 0.25

Step-by-step explanation:

Let, A be an event that a student is senior.

Probability can be given as , p(A) = 0.20

B be the event where student plays a sport

Probability can be given as , p(B) = 0.15

We have given that the probability of a student is a senior and plays a sport is 0.05.

i.e p(A∩B) =  0.05

We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .

Use the formula: p(B/A) = p(A∩B) / p(A)

Plug corresponding values to get p(B/A).

p(B/A) = p(A∩B) / p(A)  = 0.05 /0.20

p(B/A) = 0.25 , this is the answer

Answer:

The answer my frind is D

Step-by-step explanation:

When you divide,

you must

blablabla

The first step in solving the equation 4x - 0.3 = 1.9 is to D) add 0.3 to both sides of equation, isolating the term with the variable 'x'.

The question is asking how to begin solving the equation 4x - 0.3 = 1.9 for the variable x.

This balances the equation and moves us closer to discovering what x is, so the correct option would be 'D. Add 0.3 to both sides of the equation'.

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Answer:

y = ⅗  

Step-by-step explanation:

  3x – 7/y = 1/3     Substitute the value of x

3×4 – 7/y = 1/3

  12 – 7/y = 1/3         Multiply each side by 3

36 – 21/y = 1             Subtract 36 from each side

      -21/y = -35          Multiply each side by y

         -21 = -35y        Divide each side by -35

            y = 21/35      Divide numerator and denominator by 7

            y = ⅗

=====

Check:

3×4 – 7/(⅗) = 1/3

  12 -7×5/3  = 1/3

    12 – 35/3 = 1/3

(36 – 35)/3 = 1/3

               1/3 = 1/3

He is buying one large tree, so subtract the cost of a large tree from the total:

1400 - 200 = 1200

He can spend 1200 on small trees.

Divide 1200 by the cost of a small tree to find how many small trees can be bought:

1200 / 150 = 8

He can buy 8 small trees.

Total number of trees = 8 small + 1 large = 9 total

Answer: 24% of all employees attend night school.

Step-by-step explanation: If 40% of all employees are men and 30% of the men attend night school, we can multiply 0.40 by 0.30 to get the percentage of men who attend night school: 12% or 0.12. To find the number of women who attend night school, multiply 0.20 by 0.60(assuming percentage of men and women add up to 100%) to get 12%. Add 12% and 12% to get 24% of all employees attend night school.

Answer:

Two complex roots.

Step-by-step explanation:

F(x)=2x^4 +5x^3 - x^2 +6x-1

is a polynomial in x of degree 4.

Hence F(x) has 4 roots.  There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.

Use remainder theorem to find the roots of the polynomial.

F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0

There is a change of sign in F from 0 to 1

Thus there is a real root between 0 and 1.

Similarly by trial and error let us find other real root.

F(-3) = -1 and F(-4) = 94

SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.

Other two roots are complex roots since no other place F changes its sign

Final answer:

The polynomial function has 4 complex zeros.

Explanation:

A polynomial function is a function of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, a_0 are constants and n is a non-negative integer. The number of complex zeros of a polynomial function is equal to its degree.

The given polynomial function is f(x) = 2x^4 + 5x^3 - x^2 + 6x - 1. The highest power of x in the function is 4, so the degree of the function is 4. Therefore, the function has 4 complex zeros.

The distance between the points (-3,-4) and (5,4) is approximately 11.31 units, and the distance between the points (-3,5) and (0,1) is exactly 5 units.

To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean Theorem, which is

d² = (x2 - x1)² + (y2 - y1)²

Let's calculate the distances for the given pairs of points.

Distance between (-3,-4) and (5,4)

d² = (5 - (-3))² + (4 - (-4))²

d² = (8)² + (8)²

d = 64 + 64 = 128

d = √128

≈ 11.31

Distance between (-3,5) and (0,1)

d² = (0 - (-3))² + (1 - 5)²

d² = (3)² + (-4)²

d = 9 + 16 = 25

d = √25

d = 5

Answer:

10 bracelets

Step-by-step explanation:

we need to convert 5 ft to inches

1 ft = 12 inches

multiply by 5

5 ft = 60 inches

60 inches of yarn, 6 inches per bracelet

60/6 = 10

10 bracelets

Answer:

I believe a) is your answer

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x+7)=36

Simplify: (Show steps)

2x+14=36

Answer:

352 ft is 3.34% of mi ;

2 mi is 3000% of 352 ft

Step-by-step explanation:

To calculate : 352 ft is ___% of 2 mi and 2 mi is ___% of 352 ft.

We can calculate first:

352 is x% of 2 mi.

Solve for x;

Use conversion:

1 mi = 5280 ft

2 mi = 10560 ft

x% of 10560 ft means [tex]\frac{x}{100} \times 10560 = 105.60 x[/tex]

then, our equation become;

352 = 105.6 x

Divide both sides by 105.6 we get;

x = 3.333333...

or

x ≈3.34

Similarly, for

2 mi is y% of 352 ft

Solve for y;

2 mi = 10560 ft

y% of 352 = [tex]\frac{y}{100} \times 352 = 3.52y[/tex]

then;

10560 = 3.52 y

Divide both sides by 3.52 we get;

[tex]y = \frac{10560}{3.52}[/tex]

y = 3000

Therefore; 352 ft is 3.34% of mi ; 2 mi is 3000% of 352 ft

Answer:

Long Beach, California, tax = 10.25%

Answer:

Slope of function A is 6 and slope of function B is 3. Slope of A is twice of slope of function B. The relationship between slopes is

[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]

Step-by-step explanation:

The function A is,

[tex]f(x)=6x-1[/tex]

It can be written as,

[tex]y=6x-1[/tex]

It is the slope intercept form like [tex]y=mx+c[/tex], where m is the slope. On comparing the function A with the slope intercept form, we get the value of slope of function A is 6.

[tex]m_{A}=6[/tex]

The graph of function B passing through the point (1,4), (-1,-2) and (-2,-5).

If a line passing through the points  and , then the slope of line is,

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

Choose any two points of function B. Let the function B is passing through the points (1,4) and (-1,-2).

[tex]m_{B}=\frac{-2-4}{-1-1}[/tex]

[tex]m_{B}=\frac{-6}{-2}[/tex]

[tex]m_{B}=3[/tex]

The slope of function B is 3.

Since slope of function A is 6 and the slope of function B is 3, so we can say that the slope of function A is twice of slope of function B.

[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]

The slope of Function A is 6 and the slope of Function B is 3. Therefore, the slopes of the two functions are not equal.

The equation representing Function A is f(x) = 6x - 1.

The graph representing Function B is a line passing through the ordered pairs (1, 4), (-1, -2), and (-2, -5).

To compare the slopes of the two functions, we can calculate the slope of each function and see if they are equal.

The slope of Function A is 6, and the slope of Function B can be found using the formula (y2 - y1)/(x2 - x1) by choosing any two pairs of ordered points.

For example, using (1, 4) and (-1, -2).

The slope of Function B is (4 - (-2))/(1 - (-1)) = 6/2 = 3.

Since the slope of Function A is 6 and the slope of Function B is 3, we can conclude that the slopes of the two functions are not equal.

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Answer:

1) [tex]\sqrt{-64}[/tex] is not a real number.

2) [tex]-\sqrt{25} =-5[/tex]

Step-by-step explanation:

1) The square root of a number is defined for real numbers if and only if the number under the square root sign is greater than or equal to zero.

This implies that [tex]\sqrt{-64}[/tex] is not a real number because [tex]-64\:<\:0[/tex]

2) [tex]-\sqrt{25} =-\sqrt{5^2} =-5[/tex].

The number under the square root sign is [tex]25[/tex], which is greater than zero. Note that the negative sign is not inside the square root sign, it is outside it.

The value √-64 is not a real number, and -√25 is a real number.

√-64 and -√25 involve taking the square root of negative numbers, which results in complex numbers because real numbers do not have square roots of negative values.

Let's evaluate both:

√-64:

The square root of -64 is denoted as √(-64). In the realm of complex numbers, it's represented as 8i, where 'i' stands for the imaginary unit. So, √-64 = 8i.

-√25:

The square root of 25 is 5, and when you add a negative sign in front of it, you get -5. So, -√25 = -5.

In summary, √-64 is not a real number, and it is equal to 8i in the realm of complex numbers, while -√25 is a real number and equal to -5.

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plug in the number of years for where x is

34,000(.84)ˣ

and then do

.84ˣ

and then when you get that answer, multiply by 34,000

Answer:

Area = 18

Step-by-step explanation:

We know that a square has side lengths of s

We can use the Pythagorean theorem to find s

a^2 + b^2 = c^2

We know that the hypotenuse or c = the length of the diagonal or 6

Substituting in what we know

s^2 + s^2 = 6^2

2s^2 = 36

Divide each side by 2

2s^2/2 = 36/2

s^2 = 18

Take the square root of each side

sqrt(s^2) = sqrt(18)

We only have to take the positive square root since it is a length

s = sqrt(9) sqrt(2)

s= 3sqrt(2)

The side length of the square is 3sqrt(2)

To find the area, we multiply the side  by the side or s^2

s^2 =  (3sqrt(2))^2

From above

s^2 = 18

Answer:

Cauchy problem

Step-by-step explanation:

If you are talking about 'initial value problem', it is when talking about differential equations, an initial value problem is called a Cauchy problem by some authors as well. This is an ordinary differential equation together with a specified value which is called the initial condition. I really hope this helps!

The initial value is also known as the y intercept

The initial value, also known as the y-intercept or constant term, is a fundamental concept in mathematics, particularly in linear equations or functions. It represents the starting point or baseline on a graph, indicating the value of  x is zero.

The y-intercept is where a line intersects the y-axis and serves as a reference for the function's behavior, influencing its direction and movement on the coordinate plane.

Hence we can say that The initial value is also known as the y intercept

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Answer:

Current value of house is $106000

Step-by-step explanation:

We are given

A house valued at $100000

gains 6%in value

so,

current value = past house value + gain(%) * (past house value)

past house value =100000

gain(%)=6%

so, we can plug value

Current value is

[tex]=100000+\frac{6}{100}\times 100000[/tex]

[tex]=106000[/tex]

Answer:

1 in 65 chances.

Step-by-step explanation:

Answer: 83485

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

Explanation:

The formula we will use is

A = P*(1+r)^t

with

A = final amount = unknown (what we want to find)

P = starting amount = 24000

r = growth rate in decimal form = 0.12

t = number of years elapsed = 11 (since we go from 2014 to 2025)

Plug those values mentioned into the formula. Then use a calculator to simplify

A = P*(1+r)^t

A = 24000*(1+0.12)^11

A = 24000*(1.12)^11

A = 24000*3.47854999334551

A = 83485.199840292

A = 83485

The investment will be worth about 83485 dollars

5

180°-(90°+68°)=180°-158°=22°

6

180°-22°=158°

Answer:

22° and 158°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles in the triangle from 180

∠5 = 180° - (90 + 68)° = 180° - 158° = 22°

∠5 and ∠ 6 form a straight angle, thus the angles are supplementary

∠6 = 180° - ∠5 = 180° - 22° = 158°

Answer:

D) x = 14

Step-by-step explanation:

x/2 = 7

We want to isolate x

We can multiply by 2 on each side.

2 * x/2 = 7*2

x = 14

Answer:

14

Step-by-step explanation:

Well if you simplify or divide how ever you want to say it, it will be simplified to 7.

Answer:

400 yd  

Step-by-step explanation:

There are 2 ft of ribbon for 1 doll.

For 600 dolls,

Ribbon = 600 × 2/1

Ribbon = 1200 ft

=====

Convert feet to yards

1 yd = 3 ft

Ribbon = 1200 × 1/3

Ribbon = 400 yd

[tex]p\%=\dfrac{p}{100}\\\\4\%=\dfrac{4}{100}\\\\\dfrac{9}{x}=\dfrac{4}{100}\to\boxed{B.}[/tex]

The slope-intercept form for the line that passes through the point (8,7) and has a slope of -3/4 is y = -3/4x + 13. We found this by substituting the given slope and point into the slope-intercept equation and solving for b, the y-intercept.

We're working on a mathematics problem here that involves the slope-intercept form of a line, which is usually written as y = mx + b. Here, m represents the slope of the line and b is the y-intercept, the point where the line intercepts the y-axis.

To write an equation for this line, we're given that the line passes through the point (8,7) and has a slope (rise over run) of negative 3/4, a negative value indicating the line decreases as it moves to the right.

We can substitute the slope and the given point into the slope-intercept equation to solve for the y-intercept: 7=(-3/4)*8+b, this simplifies to: 7=-6+b, and finally b=7+6 which gives us 13.

Therefore, the slope-intercept equation for this line with a slope of -3/4 and passing through the point (8,7) is y = -3/4x + 13.

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Final answer:

The equation of the line passing through the point (8,7) with a slope of negative 3/4 is y = -3/4x + 13 in slope-intercept form.

Explanation:

To write an equation for a line in slope-intercept form given a point and a slope, we use the formula y = mx + b, where m is the slope and b is the y-intercept. For a line that passes through the point (8,7) with a slope of negative 3/4, we first input the slope into the equation, getting y = -3/4x + b. We then substitute the x and y values from the point (8,7) into the equation and solve for b: 7 = -3/4(8) + b. This simplifies to 7 = -6 + b, and adding 6 to both sides gives us b = 13. Thus, the equation of the line in slope-intercept form is y = -3/4x + 13.

Answer:

10 miles

Step-by-step explanation:

Thinking process:

The distance that Maria rides: 4 miles

Total time by Maria = 2.5 hrs

The friend   = 2hrs