Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?

Without further context or diagrams, it's challenging to determine the radii of the stated circles. In general, properties of the equilateral triangle and the relationship between the radius of the circle and the side of the triangle are used in these geometrical problems. More details would permit applying these principles to reach a solution.

Based on the information provided, it appears that there might be some missing context or diagrams for this question. Without further elucidation on Amanda's particular design, it would be difficult to accurately determine the radius of the 'large circle' and the 'smaller circles'.

Generally, in such geometric problems which have circles inside an equilateral triangle, one often uses properties of the equilateral triangle and relations between the radius of the circle and side of the triangle. For instance, in an equilateral triangle, where a circle fits exactly inside the triangle (incircle), the radius could be found by the formula (side of equilateral triangle) / (2*sqrt(3)). Similarly, when a circle is drawn outside the triangle (circumcircle), encompassing it, the radius is calculated as (side of equilateral triangle) / sqrt(3).

However, without additional context or a clear diagram, it's impossible to apply these principles to solve Amanda's challenge.

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We are gonna use the formula y=mx+b

Then, B= 10 T=25

So, the final equation is: 10b+25t(greater than or equal to) 175

An inequality that models how much Liz earns from babysitting and tutoring is 10b+25t≥175.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let b represent the number of hours Liz babysits. Let t represent the number of hours she spends tutoring.

Given Liz babysits for $10 per hour and tutors for $25 per hour. She wants to make at least $175 each week. Therefore, the inequality can be written as,

($10 × b) + ($25 × t) ≥ $175

10b + 25t ≥ 175

Hence, an inequality that models how much Liz earns from babysitting and tutoring is 10b+25t≥175.

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No, this is not an appropriate question to ask because it doesn't give the person who is taking the survey a variety of options. Also looking at this questionnaire the business will not get the exact answer they want.

if the business wants to have a much more precise feedback on their product then the appropriate question to ask would be.

On a scale of 1 to 10 how much would you rate our product?

This question will give the audience a wider range of answers and they are more likely to give a more honest opinion than if you ask them if they like the product a little or a lot. On the other hand this question will also benefit the company as they can easily find the average of the feedback given.

Answer:

D

Step-by-step explanation:

The question is on asymptotes of a hyperbola

General equation for a hyperbola is; (x-h)² /a² - (y-k)²/b² =1

given  y²/36 - x²/121 =1

then h=0 and k=0 thus  Center of hyperbola= (0,0) at the origin.

b²=36,b⇒6   a²=121, a⇒11

Vertices of hyperbola v=( h+a, k) and (h-a, k) = (11,0) and (-11, 0)

Equation of asymptotes is given by;

y=k ± b/a (x-h) and we have found that a=11 and b=6

hence y=0 ± 6/11(x-0)

y=6/11 x and y= -6/11 x

Answer: Option D

[tex]y=\frac{6}{11}x[/tex]

and

[tex]y=-\frac{6}{11}x[/tex]

Step-by-step explanation:

We know that the general equation of a hyperbola with transverse vertical axis has the form:

[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2} =1[/tex]

Where the point (h, k) are the coordinates of the center of the ellipse

2b is the length of the transverse horizontal axis

2a is the length of the conjugate axis

The asymptotes are lines to which the hyperbola graphic approaches but never touches.

The asymptotes have the following equation

[tex]y -y_1=\±m(x-x_1)\\\\[/tex]

Where

[tex]m=\frac{a}{b}\\\\y_1 = h\\\\x_1 = k[/tex]

In this case the equation of the ellipse is:

[tex]\frac{y^2}{36} -\frac{x^2}{121}=1[/tex]

Then

[tex]h=y_1= 0\\\\k =x_1= 0[/tex]

[tex]m = \frac{\sqrt{36}}{\sqrt{121}}[/tex]

The asymptotes are:

[tex]y -0=\±\frac{\sqrt{36}}{\sqrt{121}}(x-0)\\\\[/tex]

[tex]y=\±\frac{6}{11}x[/tex]

see the attached image

Answer:

The area of the base of the cylinder is [tex]14.5\ in^{2}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of cylinder

h is the height of the cylinder

In this problem we have

[tex]V=174\ in^{3}[/tex]

[tex]h=12\ in[/tex]

Substitute in the formula  and solve for B

[tex]174=B(12)[/tex]

Apply the division property of equality

[tex]B=174/(12)=14.5\ in^{2}[/tex]

Answer:14.5

Step-by-step explanation: just did it

Answer:

A.

Line

Step-by-step explanation:

In geometry a straight line is defined as the shortest distance between any two given points. Using the concept of locus, a Line is defined as the locus of all points that are equidistant from two given points.

On the other hand, the locus definition of a circle is the locus of a point that moves at a fixed distance from a center point. This fixed distance is called the radius of the circle.

Final answer:

The correct answer to the student's question is a circle, as it is the locus of all points equidistant from two coinciding points, which are special case foci of an ellipse.

Explanation:

The locus of all points that are the same distance from two given points is called a perpendicular bisector, but this is not one of the options provided. Among the given options, the correct answer is a circle. Thinking geometrically, if the two given points are the foci of an ellipse, the locus of points equidistant to the foci would indeed be a circle, specifically when the foci coincide at the center of the circle. This characteristic relates closely to the definition of an ellipse as provided, which is a closed curve wherein the sum of the distance from the foci to any point on the curve is constant. However, this definition does not fully match the question's condition of being the same distance from the two points, which is a special case of an ellipse where the foci are at the same place, thus forming a circle.

Final answer:

Ryan invested £300 in a simple interest account with a 4% annual rate to achieve a £24 increase over 2 years.

Explanation:

Understanding Simple Interest Calculations

Ryan's investment scenario involves calculating simple interest, which is straightforward and doesn't compound over time. To find the principal amount Ryan invested, we can use the simple interest formula:

I = PRT

Where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years. Given that the interest (£24) accrued over 2 years at a rate of 4%, we can set up the equation:

£24 = P * 0.04 * 2

Rearranging the equation to solve for P gives us:

P = £24 / (0.04 * 2)

So, the principal amount Ryan invested would be £300. This is the amount that, when increased by a 4% simple interest rate over 2 years, resulted in a £24 increase in value.

Answer:

Option c.

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

y=sin^-1 (-1/2x)   on the interval -5 ≤ x ≤ 5

Looking at the graph, we can tell that the correct option is

Option c.

Answer:

2

Step-by-step explanation:

We should put π in place of [tex]\theta[/tex] and 6 in place of [tex]h(\theta)[/tex] in the equation given and then do algebra to find the value of [tex]a[/tex]. Steps are shown below:

[tex]h(\theta)=aSin(\theta-\frac{\pi}{2})+4\\6=aSin(\pi-\frac{\pi}{2})+4\\6=aSin(\frac{\pi}{2})+4\\6=a(1)+4\\6=a+4\\a=6-4\\a=2[/tex]

The answer is 2

Note: the value of [tex]Sin(\frac{\pi}{2})[/tex]  is 1

Answer:

There is a strong negative relationship between x and y

Step-by-step explanation:

we know that

The correlation coefficient r measures the direction and strength of a linear relationship. It can take a range of values from +1 to -1.

Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship

In this problem

The correlation coefficient for the data is −0.9847

therefore

Is a strong negative correlation

Answer:

D.. Just took . the test

Step-by-step explanation:

Final answer:

To find the length of a 90° arc with a circle radius of 10 miles, multiply the radius by π/2. The arc length is calculated to be approximately 15.71 miles.

Explanation:

The radius of a circle is 10 miles, and we're asked to find the length of a 90° arc. The length of an arc can be calculated using the formula arc length = (central angle in radians) × radius. Since there are 2π radians in a 360° circle, a 90° angle corresponds to π/2 radians. Therefore, the arc length for a 90° arc on a circle with a 10-mile radius would be (π/2) × 10 miles.

Calculating the arc length, we get:

arc length = (π/2) × 10 miles

arc length = 5π miles

Using the approximate value of π (3.14159), the arc length would be roughly:

arc length = 5 × 3.14159 miles

arc length = 15.70795 miles

Hence, the length of a 90° arc for a circle with a 10-mile radius is approximately 15.71 miles.

For this case we have that by definition, the slope point equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

By definition, if two lines are perpendicular, the product of their slopes is -1. That is to say:

[tex]m_ {1} * m_ {2} = - 1\\If\ it\ tells\ us: m_ {1} = - \frac {3} {2}:\\- \frac {3} {2} * m_ {2} = - 1\\m_ {2} = \frac {2} {3}[/tex]

Substituting:

[tex]y = \frac {2} {3} x + b[/tex]

We substitute the point to find "b":

[tex]3 = \frac {2} {3} 6 + b\\3 = 4 + b\\b = 3-4\\b = -1[/tex]

Finally:

[tex]y = \frac {2} {3} x-1[/tex]

Answer:

[tex]y = \frac {2} {3} x-1[/tex]

[tex]\bf \cfrac{5}{\sqrt{30}}\cdot \cfrac{\sqrt{30}}{\sqrt{30}}\implies \cfrac{5\sqrt{30}}{(\sqrt{30})^2}\implies \cfrac{5\sqrt{30}}{30}\implies \cfrac{\sqrt{30}}{6}[/tex]

Answer:

the answer is d

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

21.63

use the Pythagorean theorem.

a^2+b^2=c^2

Answer:

FE = 30°

Step-by-step explanation:

arc FGC = arc FG + arc GB + arc BC

220° = 90° + arc GB + 70° . . substitute known values

60° = arc GB . . . . . . . . . . . . . subtract 160°

__

External angle A is half the difference of arcs EG and GB:

30° = (1/2)(arc FE +90° -60°) . . . substitute known values

60° = arc FE + 30° . . . . . . . . . . . multiply by 2 and simplify

30° = arc FE . . . . . . subtract 30°

_____

The key to this problem is the relationship between external angle A and the measures of the arcs it subtends.

1) The caterpillar was already at 4.5 feet so 4.5 will be added. If it crawls upwards 38 of an inch every minute and the amount of minutes is not specified, this will be represented as 38x. That means the answer is C. f(x) = 38x + 4.5

2) Substitute the known values into the equation. There are 7 people at $8.25 a person, which is a total of $57.75 I used 7 because he invites 6 friends, plus himself. He only has $50 on his gift card, so he won't have enough to cover the cost. The answer is A.

3) They start out with 40lbs and recieve 120 more. They have 160lbs in total. If they sell 8lbs a day for 5 days, thats 8*5 or 40lbs total. 160 - 40 = 120lbs left after 5 days. I'd say the answers are A, B, and D.

4) I think the answer would be C because 1,500 is used to find the number of grams of isotope present after t years. The number of grams can't be 1,500. I hope that makes sense because I'm not sure how to explain it.

5) The growth factor is 2 (2x, x being the number of hours). Multiply by 15 because the lab has 15 of them. The answer is B. f(x) = 15 * 2x

I hope this helps you! I'm sorry if I got any of them wrong!

Answer:

x = 4.

Step-by-step explanation:

log(x + 6)- log(x - 3) = 1

Using the law log a - log b = log a/b:

log (x + 6)/ (x - 3) = 1

Removing logs:

(x + 6)/ (x - 3) = 10

x+ 6 = 10x - 30

9x = 36

x = 4 (answer).

Answer:

Step-by-step explanation

[tex]log (x+6) - log (x-3) = 1 \\log \frac {x+6}{x-3} = log \ e\\x+6 = e(x-3)\\(1-e)x = -(e+3)\\x=\frac{e+3}{e-1}[/tex]

Step 1: on LHS the difference of two logs, is equal of the log of the division, on RHS, 1 is the log of the base, whatever the base is.

Rest is a 1st grade equation, isolate x, divide.

From the definition of conditional probability:

[tex]P(R_1\mid Q)=\dfrac{P(R_1\cap Q)}{P(Q)}[/tex]

By the law of total probability,

[tex]P(Q)=P(Q\cap R_1)+P(Q\cap R_2)+P(Q\cap R_3)[/tex]

[tex]P(Q)=P(Q\mid R_1)P(R_1)+P(Q\mid R_2)P(R_2)+P(Q\mid R_3)P(R_3)[/tex]

[tex]P(Q)=0.42[/tex]

Since

[tex]P(R_1\cap Q)=P(Q\mid R_1)P(R_1)[/tex]

we end up with

[tex]P(R_1\mid Q)=\dfrac{0.03}{0.42}\approx0.0714[/tex]

if the cone has a diameter of 12, thus its radius is half that, namely 6.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=20 \end{cases}\implies V=\cfrac{\pi (6)^2(20)}{3}\implies V=240\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill V\approx 753.98~\hfill[/tex]

The volume of cone is 240π m³.

The mathematical term "volume" indicates the amount of three-dimensional space that an object or closed surface occupies. The volume is measured in cubic units like m³, cm³, in³, and so on.

Volume is also sometimes referred to as capacity.

Given diameter of cone = 12m

radius = diameter/2 = 12/2 = 6m

height of cone = 20m

volume of cone is given by 1/3πr²h

where r = radius and h = height

volume = 1/3 x π x (6)² x 20

volume = 240π m³

Hence the volume is 240π m³.

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Answer:

Step-by-step explanation:

[tex]\frac{1}{2}x+\frac{1}{5}y = 2 \mid 5x + 2y = c[/tex]

First let's multiply the 1st equation by 10.

[tex]5x + 2y = 20 \mid 5x + 2y = c[/tex]

So, we can see that the equations have the same coefficients and that implies  they are equal.

So the equation has no solutions for. [tex]c \in R \setminus{20}[/tex]

The given system of linear equations has no solutions only when c is different than 20.

A system of linear equations has no solutions only when both lines are parallel.

Remember that two lines are parallel if the lines have the same slope and different y-intercept.

In this case, our lines are:

(1/2)*x + (1/5)*y = 2

5x + 2y = c

Writing both of these in the slope-intercept form, we get:

y = 5*2 - (5/2)*x

y = c/2 - (5/2)*x

So in fact, in both cases, we have the same slope.

And the only condition to not have any solution is to have:

c/2 ≠ 5*2 = 10

c/2 ≠ 10

c ≠ 10*2 = 20

c ≠ 20

So if c is any value different than 20, the system has no solution.

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The standard form of the equation of the ellipse is,[tex]\frac{x^2}{7} +\frac{y^2}{14} =1[/tex]. It is obtained by the dividing complete equation by 196.

If the major axis is a units long and the minor axis is b units long, and the ellipse is centered on (0,0). The equation for that ellipse is:

[tex]\rm \frac{x^1}{a^2} +\frac{y^2}{b^2} =1 \\\\\[/tex]

The given equation is;

28x²+14y²=196

Divide the complete equation by 196;

[tex]\rm \frac{28x^2}{196} +\frac{14y^2}{196} =\frac{196}{196} \\\\ \frac{x^2}{7} +\frac{y^2}{14} =1[/tex]

Hence, the standard form of the ellipse is represented as,[tex]\frac{x^2}{7} +\frac{y^2}{14} =1[/tex]

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Answer:

  96 or better

Step-by-step explanation:

Brenda has scored relative to her desired average +2, -1, and -4 points, or a total of -3 points. To ensure her average is 93, she must score at least 3 points above her desired average: 96 or better.

Answer:

A. 7

Step-by-step explanation:

you bring down the 1 and multiply it by -2 then -2 goes to add with 2, which makes it 0. Then 0 x -2 is 0. 0 then goes to add with -3, then -3 comes down. -2 x -3 is 6. 6+1 is 7.

The remainder in the synthetic division problem is 7.

To find the remainder using synthetic division, follow these steps:

Step 1: Write the coefficients of the polynomial in descending order, including placeholders for missing terms. In this case, the polynomial is given as:

[tex]1x^3 + 2x^2 - 3x + 1[/tex]

Step 2: Since we are dividing by (x + 2), change the sign of the divisor and set it equal to zero to find the value we'll use in the synthetic division.

x + 2 = 0

x = -2

Step 3: Set up the synthetic division table:

       -2  |   1   2   -3   1

Step 4: Perform the synthetic division:

Bring down the first coefficient:         1

Multiply -2 by 1:                             -2

Add the result to the next coefficient:   2 - 2 = 0

Multiply -2 by 0:                              0

Add the result to the next coefficient:   -3 + 0 = -3

Multiply -2 by -3:                            6

Add the result to the next coefficient:   1 + 6 = 7

Step 5: The last entry in the synthetic division row (7 in this case) is the remainder.

The remainder in the synthetic division problem is 7.

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Explanation:

Rearrange 0 = x + 2 + x^2 into x^2 + x + 2 = 0

Note that we have something in the form ax^2 + bx + c = 0

where a = 1, b = 1, c = 2

Plug these three values into the discriminant formula

d = b^2 - 4ac

d = 1^2 - 4*1*2

d = 1 - 8

d = -7

The discriminant for the quadratic equation 0 = x squared + x + 2, using the formula b squared - 4ac, and substituting the values a = 1, b = 1 and c = 2, is -7.

The question is asking for the value of the discriminant for the quadratic equation 0 = x2 + x + 2. The discriminant is part of the quadratic formula and its value can be computed using the formula b2 - 4ac. In this equation, a = 1, b = 1, and c = 2. By substituting these values into the formula, we get: (1)2 - 4 * 1 * 2 = 1 - 8 = -7. Therefore, the value of the discriminant for the given equation is -7.

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ANSWER

P(X=4 or X=1)=0.2

EXPLANATION

From the table, the probability that X=4 is P(X=4)=0.15

and the table, the probability that X=1 is P(X=1)=0.05

We want to find P(X=4 or X=1)

Recall that

P(X=4 or X=1)=P(X=4)+P(X=1)

We substitute the given probability values to obtain:

P(X=4 or X=1)=0.15+0.05

P(X=4 or X=1)=0.2

Answer: 0.2 is the answer

Step-by-step explanation:

hope this helps :]

The answer is -- 36

Answer:

the answer is 36

Step-by-step explanation:

While 50 miles per hour so 50 multiplied by 4 will give you 200 miles

The second vehicle traveling at 60 miles per hour traveling for 8 hours so multiply 60 x 8 and you will get 480

280 miles farther the second car travels.

Given:

Find:

Solution:

So, as it is given that one car traveled 50 miles per hour for 4 hours that means it travels 50*4 miles = 200 miles.

So, this car travels 200 miles.

Now, the second car traveled 60 miles an hour for 8 hours which means it travels 60*8 miles = 480 miles.

So, the second car travels 480 miles.

Now, for getting how farther the second car traveled we have to subtract the miles traveled by the first car from the second car.

Therefore, second car travels farther = 480 - 200 = 280 miles.

Hence, the second car travels 280 miles farther from the first car.

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Answer:

3/10

Step-by-step explanation:

Answer:

the answer to that is 1/10

Step-by-step explanation:

ANSWER

[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]

EXPLANATION

The given polynomials are:

[tex]G = - 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} [/tex]

and

[tex]P = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} [/tex]

We want to subtract these two polynomials.

[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} - (- 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} )[/tex]

Expand the right hand side to obtain:

[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} + 3 {w}^{4} - 2 {w}^{2} {z}^{2} - 5z^{4} [/tex]

Group the similar terms:

[tex]P-G = 8 {w}^{4} + 3 {w}^{4}- 3{w}^{2} {z}^{2} - 2 {w}^{2} {z}^{2} - 5z^{4} + z^{4}[/tex]

Combine the similar terms to get:

[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]

Answer:

The unit vector u is (-5/√29) i - (2/√29) j

Step-by-step explanation:

* Lets revise the meaning of unit vector

- The unit vector is the vector ÷ the magnitude of the vector

- If the vector w = xi + yj

- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w

- The unit vector u in the direction of w is u = w/IwI

- The unit vector u = (xi + yj)/√(x² + y²)

- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j

* Now lets solve the problem

∵ v = -5i - 2j

∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29

- The unit vector u = v/IvI

∴ u = (-5i - 2j)/√29 ⇒ spilt the terms

∴ u = (-5/√29) i - (2/√29) j

* The unit vector u is (-5/√29) i - (2/√29) j