What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?
2x + 6

2x − 6

2x + 4

2x − 4, r = 1

Answer:

AAS

Step-by-step explanation:

Triangle congruence or congruent triangles are defined as triangles that are similar in size and shape. The corresponding sides of the triangle if are equal, then the corresponding angles will be equal.

In the given question, the two angles and non-included sides of one triangle are congruent to the corresponding two angles and sides of the other triangle.

The given congruency explains the AAS congruency theorem.

The AAS theorem can be explained as:

1. AAS stands for Angle-angle-side.

2. It states that for the triangle having two pairs of congruent angles and a non-common side is congruent to the corresponding side and angles, then triangles are said to be congruent.

Thus, the given example shows the AAS congruent theorem.

To know more about congruency, refer to the following link:

https://brainly.com/question/19258025

Answer:

50%

Step-by-step explanation:

The percent increase is found by first finding the difference between the two values and then dividing that difference by the original amount.  Then to get the percentage, multiply by 100.  For us, that looks like this:

[tex]\frac{1.8-1.2}{1.2}[/tex]

Do the subtraction to get

[tex]\frac{.6}{1.2}[/tex]×100

And that comes out to 50%.

recall that

1² = 1

1⁴ = 1

1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

[tex]\bf \cfrac{d^2-1}{d^2-d}\div \cfrac{d+1}{d-1}\implies \cfrac{d^2-1}{d^2-d}\cdot \cfrac{d-1}{d+1}\implies \cfrac{\stackrel{\stackrel{\textit{difference of}}{\textit{squares}}}{d^2-1^2}}{d(d-1)}\cdot \cfrac{d-1}{d+1} \\\\\\ \cfrac{\begin{matrix} (d+1) (d-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{d~~\begin{matrix} (d-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{d-1}{\begin{matrix} d+1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\implies \cfrac{d-1}{d}[/tex]

ANSWER

x=36.08 units

EXPLANATION

From the given right triangle,x is adjacent to the 49° angle.

The hypotenuse of the right triangle is 55 units.

Recall the mnemonics SOH-CAH-TOA

We use the cosine ratio,

[tex] \cos(49 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(49 \degree) = \frac {x}{55} [/tex]

Solve for x,

[tex]x = 55\cos(49 \degree) [/tex]

x=36.0832

Rounding to the nearest hundredth,we have

x=36.08

Answer:

Step-by-step explanation:

The formula for this is

x° = [tex]\frac{1}{2}[/tex](major arc - minor arc)

The measure around the outside of a circle is 360°.  We have the minor arc as 120°.  So the major arc is 360 - 120 = 240.  Fitting that into the formula:

x° = [tex]\frac{1}{2}[/tex](240 - 120)

x° = [tex]\frac{1}{2}[/tex](120)

x° = 60

Answer:

The answer is -4.

Step-by-step explanation:

-5(3n+4)=40

-15n -  20 = 40

15n = 60

-4.

Answer:

C

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant.

Using the distance formula

[tex]\sqrt{(x-4)^2+(y-1)^2}[/tex] = | y - 5 |

Squaring both sides

(x - 4)² + (y - 1)² = (y - 5)² ← distribute the factors in y

(x - 4)² + y² - 2y + 1 = y² - 10y + 25 ( subtract y² - 10y + 25 from both sides )

(x - 4)² + 8y - 24 = 0  ( subtract (x - 4)² from both sides )

8y - 24 = - (x - 4)² ← add 24 to both sides )

8y = - (x - 4)² + 24 ( divide both sides by 8 )

y = - [tex]\frac{1}{8}[/tex] (x - 4)² + 3

Hence

f(x) = - [tex]\frac{1}{8}[/tex] (x - 4)² + 3 → C

the answer is....... 56%

A. 56%

First, find the number in the cell that is in the row “Hiked” and the column “Poison ivy rash”. There is only one that matches this description, and it contains the number 0.56.

To convert a decimal number to a percentage, multiply it by 100, or move the decimal point two places to the right, which is essentially the same thing. This gives you 56, which means the answer is 56%.

Answer:

Fertilizer B produced a 15% greater yield

Step-by-step explanation:

Mean yield fertilizer A = 20.2

Mean yield fertilizer B = 23.2

Thus, 23.2 − 20.2

20.2

= 0.1485 ≈ 0.15 or 15%

Answer : The correct option is, (B) Fertilizer B produced a 15% greater yield

Step-by-step explanation :

First we have to calculate the total yield of potato with fertilizer A.

Total yield of potato with fertilizer A = (27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19) kg

Total yield of potato with fertilizer A = 202 kg

Now we have to calculate the total yield of potato with fertilizer B.

Total yield of potato with fertilizer B = (28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 21) kg

Total yield of potato with fertilizer B = 232 kg

Now we have to calculate the percent yield.

[tex]\text{Percent yield}=\frac{232-202}{202}\times 100[/tex]

[tex]\text{Percent yield}=14.85\% \approx 15\%[/tex]

From this we conclude that, the fertilizer B produced a 15% greater yield.

Hence, the correct option is, (B) Fertilizer B produced a 15% greater yield

Answer:

It's D.

Step-by-step explanation:

That would be D.

-24 + 24 = 0.

Answer:

The correct option is D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.

Step-by-step explanation:

Consider the provided information.

We need to find Which situation results in the final value of zero.

Option A) E the temperature after a decrease of 5°F from a temperature of -5°F.

Decreasing means we need to subtract 5°F from the existing temperature.

E=-5°F-5°F=-10°F

Hence, now the temperature is -10°F.

Therefore, it is not the correct option.

Option B) The height of an airplane after taking off from ground level and rising 1000 feet.

If the airplane was at the ground level then we consider the height of the airplane was 0 feet above the ground.

After taking off it is rising 1000 feet above the ground level that means the overall rising is 1000 feet.

Therefore, it is not the correct option. As final value is not 0.

Option C) See the amount of money received and change after making a $10 purchase with the $20 bill.

If you purchase something which cost you $10 and you are purchasing it with the $20 bill.

The money you will received is: $20-$10=$10

Which is not 0.

Therefore, it is not the correct option.

Option D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.

The previous position of the object was 24 m below sea level

It can be written as -24m as the distance is below sea level.

Now the object Increasing 24 m, therefore,

-24+24=0

Hence, the final value is zero.

Therefore, the correct option is D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.

Answer:

FG=13

Step-by-step explanation:

We can make an equation that looks like this:

EF+FG=EG

Then, we can substitute in the numbers we know:

12+FG=25

Then solve:

FG=25-12

FG=13

Hope I helped soz if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Trademark ~Potato. 2019.

Answer:

FG = 13

Step-by-step explanation:

We can write

EF + FG = EG ← substitute values

12 + FG = 25 ( subtract 12 from both sides )

FG = 25 - 12 = 13

Answer:

Find the attached

Step-by-step explanation:

Graphing a system of equations can easily be done using modern technology graphing tools. Desmos graphing tool is the most widely used tool for this purpose.

The system of equations will be solved graphically. The point of intersection will be the solution if needed.

The attachment below shows the graph of the system of equations;

y=-1/2x+4 and x+2y=8

From the attachment below, we notice that the two lines are coincident. This is to mean that the two equations represent the same line.

The answer is:

The correct option is:

B) 15

To solve the problem, we need to use the Pythahorean Theorem. We know that we can use the theorem since we are working with a right triangle as we can see in the picture.

So, we are given the following information:

[tex]Hypothenuse=c=25units\\\\Opposite=b=20units[/tex]

Now, using the Pythagorean Theorem, we have:

[tex]c^{2}=a^{2} +b^{2} \\\\25^{2}=a^{2}+20^{2}\\\\a^{2}=25^{2}-20^{2}=225\\\\a=\sqrt{225}=15[/tex]

Hence, we have that the correct option is:

B) 15

Have a nice day!

Answer:

999

Step-by-step explanation:

Regrouping used to be called borrowing. Since no single column can have a digit larger than 9, then you would have the number 999 where you would never have to "borrow", or "regroup

Final answer:

A three-digit number that requires no ungrouping for subtraction should have each digit greater than the corresponding digit in the number being subtracted. For example, subtracting 234 from 453 requires no ungrouping because each digit in 453 is greater than the corresponding digit in 234.

Explanation:

The student's question pertains to the process of subtraction without requiring ungrouping, also known as regrouping or borrowing, when subtracting from a three-digit number. To avoid ungrouping, the number we subtract from should have each digit larger than the corresponding digit of the number being subtracted. For simplicity, let's consider subtracting a three-digit number of the form XYZ, where X, Y, and Z are individual digits. To ensure there's no need for ungrouping, the number from which we are subtracting should have each place value (hundreds, tens, and ones) greater than or equal to those in XYZ.

For example, if we take the number 453 and subtract 234 from it, no ungrouping is needed because 4 is greater than 2, 5 is greater than 3, and 3 is greater than 4. Hence, any three-digit number with digits greater than those of the subtrahend in the corresponding place values would satisfy the condition of needing no ungrouping to subtract from. By following this rule, the process of subtraction becomes straightforward without the complication of borrowing across place values.

The equation [tex]\(4x^2 + 20x + 25 = 0\)[/tex]  rewritten by completing the square is [tex]\((x + \frac{5}{2})^2 = \frac{25}{4}\)[/tex] , and the solutions are (x = 0) and (x = -5).

Sure, let's complete the square for the given quadratic equation [tex]\(4x^2 + 20x + 25 = 0\).[/tex]

1. First, let's divide the entire equation by 4 to simplify the coefficients:

[tex]\[x^2 + 5x + \frac{25}{4} = 0\][/tex]

2. Now, let's focus on completing the square for the quadratic term[tex]\(x^2 + 5x\).[/tex] To do this, we need to add and subtract the square of half of the coefficient of (x):

[tex]\[x^2 + 5x + \left(\frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 + \frac{25}{4} = 0\][/tex]

3. Simplify the expression inside the parentheses:

[tex]\[x^2 + 5x + \frac{25}{4} - \frac{25}{4} + \frac{25}{4} = 0\][/tex]

4. Combine like terms:

[tex]\[x^2 + 5x + \frac{25}{4} - \frac{25}{4} = 0\][/tex]

5. Now, we have a perfect square trinomial on the left side:

[tex]\[\left(x + \frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 = 0\][/tex]

6. Finally, let's simplify:

[tex]\[\left(x + \frac{5}{2}\right)^2 - \frac{25}{4} = 0\][/tex]

7. To isolate \(x\), add \(\frac{25}{4}\) to both sides:

[tex]\[\left(x + \frac{5}{2}\right)^2 = \frac{25}{4}\][/tex]

8. Now, take the square root of both sides:

[tex]\[x + \frac{5}{2} = \pm \sqrt{\frac{25}{4}}\][/tex]

9. Simplify the square root:

[tex]\[x + \frac{5}{2} = \pm \frac{5}{2}\][/tex]

10. Subtract[tex]\(\frac{5}{2}\)[/tex]  from both sides to solve for (x):

[tex]\[x = -\frac{5}{2} \pm \frac{5}{2}\][/tex]

11. Simplify further:

[tex]\[x = -\frac{5}{2} + \frac{5}{2} \text{ or } x = -\frac{5}{2} - \frac{5}{2}\][/tex]

12. This gives us the solutions:

[tex]\[x = 0 \text{ or } x = -5\][/tex]

So, the equation [tex]\(4x^2 + 20x + 25 = 0\)[/tex] rewritten by completing the square is[tex]\((x + \frac{5}{2})^2 = \frac{25}{4}\),[/tex] and the solutions are (x = 0) and (x = -5).

Complete question:

Rewrite the equation by completing the square 4x^2+20x+25=0

(x+__)^2=___

Answer:

The solution to this system is (-2,1)

Step-by-step explanation:

The given system of equations is;

[tex]-3x-4y=2[/tex]...eqn1

and

[tex]-5=5x+5y[/tex]....eqn2

We make y the subject of the second equation to get:

[tex]-5y=5x+5[/tex]

[tex]\implies y=-x-1[/tex]...eqn3

We put eqn3 into eqn1 to get;

[tex]-3x-4(-x-1)=2[/tex]

We expand to get:

[tex]-3x+4x+4=2[/tex]

[tex]-3x+4x=2-4[/tex]

Simplify both sides to get:

[tex]x=-2[/tex]

Put x=-2 into eqn3

[tex]\implies y=--2-1[/tex]

[tex]\implies y=1[/tex]

The solution to this system is therefore (-2,1)

Answer:

[tex]\dfrac{4000\pi}{3}[/tex] ft³

Step-by-step explanation:

First, let's figure out how to get the volume of a sphere from its surface area. If r is the radius of our sphere, then

The formula for a sphere's surface area is [tex]A = 4\pi r^2[/tex]

The formula for a sphere's volume is [tex]V=\frac{4}{3}\pi r^3[/tex]

So to get from area to volume, we have to divide the area by 3 and then multiply it by r. Mathematically:

[tex]V=\frac{A}{3}r[/tex]

Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area - [tex]400\pi[/tex] ft² - so we can use the area formula to find that radius:

[tex]A=4\pi r^2=400\pi\\r^2=100\\r=10[/tex]

And now that we have our radius, we can put it into our volume formula to find

[tex]V=\frac{A}{3} r=\frac{400\pi}{3}(10)=\frac{4000\pi}{3}[/tex] ft³

Answer:

a. -0.9

Step-by-step explanation:

The closer you get to 1, either positive or negative, the stronger the correlation

-.9 is closest to -1, so it has the strongest negative correlation

.9 cause it basically has the highest absolute value.

Answer:

[tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

cosx = [tex]\sqrt{1-sin^2x}[/tex]

note that ([tex]\frac{\sqrt{23} }{12}[/tex] )² = [tex]\frac{23}{144}[/tex]

cosΘ = [tex]\sqrt{1-\frac{23}{144} }[/tex] = [tex]\sqrt{\frac{121}{144} }[/tex] = [tex]\frac{11}{12}[/tex]

Answer:

Part 1) Sin ϴ = 5/13, Cos ϴ = 12/13, Tan ϴ = 5/12

Part 2) Sin A = 4/5, Cos A = 3/5,Tan A = 4/3  

Step-by-step explanation:

we know that

In a right triangle

The function sine of an angle is equal to divide the opposite side to the angle by the hypotenuse

The function cosine of an angle is equal to divide the adjacent side to the angle by the hypotenuse

The function tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

Part 1)

Find the Sin ϴ

Sin ϴ=5/13

Find the Cos ϴ

Cos ϴ=12/13

Find the Tan ϴ

Tan ϴ=5/12

Part 2) we know that

In the right triangle ABC

Applying the Pythagoras Theorem

Find the hypotenuse AB

[tex]AB^{2}=6^{2}+8^{2}[/tex]

[tex]AB^{2}=100[/tex]

[tex]AB=10\ units[/tex]

Find the Sin A

Sin A=8/10=4/5

Find the Cos A

Cos A=6/10=3/5

Find the Tan A

Tan A=8/6=4/3

Answer:

Question 1: Sin ϴ = 5/13, Cos ϴ = 12/13, Tan ϴ = 5/12

Question 2: Sin A = 4/5, Cos A = 3/5,Tan A = 4/3  

Step-by-step explanation:

Here's proof showing that one of the questions is right. Hope this helps!

Answer:

Last Option moved [tex]\frac{\pi}{2}[/tex] units right

Step-by-step explanation:

If we have a function f(x) and we want to move it horizontally then we make the transformation:

[tex]y = f (x + h)[/tex]

If [tex]h <0[/tex] then the graph of f(x) moves horizontally h units to the right

If [tex]h> 0[/tex] then the graph of f(x) moves horizontally h units to the left.

In this case we have the function [tex]y = tan (x)[/tex] and the transformation is performed to obtain [tex]y = tan(x- \frac{\pi}{2})[/tex]

Notice that in this transformation

[tex]h <0 = -\frac{\pi}{2}[/tex]

Then the graph of [tex]y = tan (x)[/tex] moves horizontally [tex]\frac{\pi}{2}[/tex] to the right

The graph of y = tan ⁡(x − π / 2) has moved π / 2 units right compared to y = tan ⁡x.

The graph of y = tan ⁡(x − π / 2) compared to the graph of y = tan ⁡x has moved π / 2 units right.

The function y = tan ⁡(x − π / 2) is obtained by shifting the graph of y = tan ⁡x horizontally to the right by π / 2 units. The minus sign in (x − π / 2) indicates a rightward shift.

So, the correct answer is that the graph of y = tan ⁡(x − π / 2) has moved π / 2 units right.

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Answer:

24 degrees

Step-by-step explanation:

A Ferris wheel is in the shape of a circle. Having 15 seat buckets means that the circle will be divided into 15 sections. Keep in mind that we are assuming that the seat buckets are equally spaced.

We know that:

Degrees in one circle: 360 degree

Dividing in 15 sections:

[tex]=\frac{360}{15}\\=24\ degrees[/tex]

So the angle of measurement between the seat buckets is 24 degrees ..

Answer: 29 Hours of Work

Step-by-step explanation: Let's start by working backwards.. We know that Ken makes 5 dollars an hour, and he worked 40 hours. 5 * 40 = 200, and 400-200 = 200. This means that Kim has to work 200/7 hours, or (approximately) 29 hours of work.

Answer:

90

Step-by-step explanation:

DM=1/4 of MBND

a circle =360

360÷4=90

Answer:

for the first question it would be A. 4+8+16+32 because infinite series are such as :

9,18,36,72,144,288

10,20,40,80,160,

so basically its multiplying *2

I cant do #2 without seeing the formula

Answer:

B The length is 5 inches, the width is 2 inches, and the height is 14 inches.

Step-by-step explanation:

The equation that desribes the volume of a party-favor bag is

[tex]x^3+6x^2-27x-140=0.[/tex]

The solutions of theis equation can be found among divisors of -140. The divisors are:

[tex]\pm1, \pm2, \pm4, \pm5, \pm 7,\pm 10, \pm 14, \pm 20, \pm 35, \pm 70, \pm 140.[/tex]

Note that

[tex]5^3+6\cdot 5^2-27\cdot 5-140=125+150-135-140=275-275=0,[/tex]

so

[tex]x=5[/tex]

is the solution of the equation.

Hence,

the length is 5 inches, the width is 5-3=2 inches and the height is 5+9=14 inches.

Answer:

B. The length is 5 inches, the width is 2 inches, and the height is 14 inches.

Step-by-step explanation:

After calculating the total involuntary deductions for FICA, Federal withholding, and State withholding, we subtract this total from the gross pay to determine the amount available for housing and fixed expenses, which is $2023.63.

To find out how much you are allowed for housing and fixed expenses, we first need to calculate the total involuntary deductions. This is done by applying the given percentages to the gross pay.

For the FICA it would be: $2759.00 * 7.65% = $211.16

Federal withholding would be: $2759.00 * 12% = $331.08

And for the State withholding: $2759.00 * 7% = $193.13

You'll then add all the deductions together: $211.16 + $331.08 + $193.13 = $735.37

The final step is to subtract the total deductions from the gross pay: $2759.00 - $735.37 = $2023.63

Hence, you are allowed $2023.63 for housing and fixed expenses.

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To calculate the amount allowed for housing and fixed expenses, subtract the involuntary deductions from the gross pay which is $2,023.19

To calculate the amount allowed for housing and fixed expenses, we need to subtract the involuntary deductions from the gross pay. First, calculate the FICA deduction by multiplying the gross pay by 7.65% (0.0765). Next, calculate the federal withholding by multiplying the gross pay by 12% (0.12). Finally, calculate the state withholding by multiplying the gross pay by 7% (0.07). Subtract the sum of these deductions from the gross pay to find the amount allowed for housing and fixed expenses.

Gross pay: $2,759.00

FICA deduction: $2,759.00 x 0.0765 = $211.60

Federal withholding: $2,759.00 x 0.12 = $331.08

State withholding: $2,759.00 x 0.07 = $193.13

Amount allowed for housing and fixed expenses:

$2,759.00 - $211.60 - $331.08 - $193.13

= $2,023.19

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Answer:

A) y = sin(x) +1

Step-by-step explanation:

The centerline of the function is at +1, so choices B and D are eliminated.

The function value is at the centerline at x=0, so choice C is eliminated.

The appropriate choice is A:

y = sin(x) +1

Answer:

Step-by-step explanation:

Given is a graph whichis symmetrical about y =1 and periodical with period 2pi

Amplitude is 1

Since amplitude is 1,

sinx has coefficient 1

Since symmetrical about y =1

we have[tex]y=sinx +1[/tex]

There is no horizontal shift and also x has coefficient 1 since period = 2pi

In other words, this graph given is obtained as a transformation of y=sinx vertically up by 1 units.

Hence equation would be

y=sinx +1

Answer:

For Ashley, p=10d+0

For Carly, p=8d+40

Step-by-step explanation:

Ashley: The slope is 10 (pages) times how many days have passed.

Her y-intercept is 0 because that is how many pages she read before starting.

P is the y-value because solving the equation (putting a number in for how many days it's been) will give you the number of pages she read.

Carly: The slope is 8 (pages) times how many days have passed.

Her y-intercept is 40 because that is how many pages she read before starting reading 8 per day.

System of equations to represent the situation, using d for days and p for pages are (p = 10d) and (p = 8d + 40) and this can be determined by using the given data.

Given :

The following steps can be used to determine the system of equations:

Step 1 - According to the given data, Ashley reads 10 pages per day. So, the slope of the linear equation that represents this situation is 10 and it is given by:

p = 10d

where 'p' is the number of pages and 'd' is the total number of days.

Step 2 - According to the given data, Carly reads 8 pages per day, but she started early and is already on page 40. So, the slope of the linear equation that represents this situation is 8 and it is given by:

p = 8d + 4

For more information, refer to the link given below:

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Step 1 - According to the given data, Ashley reads 10 pages per day. So, t Ste           he slope of the linear equation that represent this situat

Answer:

A

Step-by-step explanation:

Pick a letter that's easy to count. I chose Q, because it has a tail below the baseline that makes them easy to spot.

Not C or D — too many quarters

Not B — too many nickels

It is often easier to find the correct answer choice by eliminating the bad choices, then seeing if what is left is consistent with the problem statement.

Choice A seems to have the right numbers of pennies and dimes (along with quarters and nickels).