Choose the correct simplification of (4x3 + 3x2 − 6x) − (10x3 + 3x2). Select one: a. 6x3 + 6x b. −6x3 − 6x2 − 6x c. −6x3 − 6x d. 6x3 + 6x2 + 6x

Answer:

S and T

Step-by-step explanation:

I put R&T, that's wrong. It's S and T.

The pair of spheres are congruent is S and T.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

As, per the given figure,

Figure R having a radius 3.

Figure S is having a radius 4

Figure T is having radius 4

So, by considering the property of congruence figure S and T will be congruent spheres.

Learn more about congruence here:

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The graph is attached.

To find the graph that shows the solution to the system of linear inequalities below, we need to find the axis intercepts and consider the given conditions for both inequalities.

So, solving we have:

First inequality: Blue line and area.

[tex]y\leq -3x+2[/tex]

Finding the x-axis intercept, making "y" equal to 0.

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

[tex]0=-3x+2\\\\3x=2\\\\x=\frac{2}{3}=0.66[/tex]

So, the x-axis intercept is located at the point (0.66,0)

Finding the y-axis intercept, making "x" equal to 0.

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

[tex]y=-3*0+2=2[/tex]

So, the y-axis intercept is located at the point (0,2)

Also, we can see that since the coefficient of the linear term is negative (-3) the line is decreasing (line with negative slope).

Now, that we already know the axis intercepts, we need to remember that the inequality is given by the following expression:

[tex]y\leq -3x+2[/tex]

The less or equal inequality symbol means that the solution region of the inequality is under the function.

Second inequality: Red line and area.

[tex]y>2x-3[/tex]

Finding the x-axis intercept, making "y" equal to 0.

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

[tex]0=2x-3\\\\2x=3\\\\x=\frac{3}{2}=1.5[/tex]

So, the x-axis intercept is located at the point (1.5,0)

Finding the y-axis intercept, making "x" equal to 0.

[tex]y=2x-3[/tex]

[tex]y=2*0-3=-3[/tex]

So, the y-axis intercept is located at the point (0,-3).

Also, we can see that since the coefficient of the linear term is positive (-3) the line is increasing (line with positive slope).

Now, that we already know the axis intercepts, we need to remember that the inequality is given by the following expression:

[tex]y>2x-3[/tex]

The greater inequality symbol means that the solution region of the inequality is above the function.

Hence, since we have a system of linear inequalities, the solution to the whole system is located between the solution region of the given inequalities.

The graph is attached, the solution to the system of linear inequalities is represented by the shaded area (light purple area).

Have a nice day!

The solution to the inequality is attached. It is the side that is dark green as shown in the graph.

Inequality

Inequality is an expression used to show the non equal comparison of two or more numbers and variables.

Given the inequalities:

y < -3x + 2   (1)

y > 2x - 3    (2)

Plotting the graph using the online geogebra tool.

The solution to the inequality is attached. It is the side that is dark green as shown in the graph.

Find out more on inequality at: https://brainly.com/question/24372553

Answer: Its (5,-2)

Step-by-step explanation: When you reflect across the x-axis the y value changes.

x = original price, or 100%

if we take off 25% from 100% what's left is 75%, that's the discounted price.

let's then take 10% of that.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of "x"}}{\left( \cfrac{75}{100} \right)x\implies 0.75x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{10\% of 0.75x}}{\left( \cfrac{10}{100} \right)0.75x\implies 0.075x}~\hfill \stackrel{\textit{total percent savings}}{0.75x-0.075x\implies 0.675x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{changing that to percent format}}{0.675\cdot 100\implies 67.5\%}[/tex]

Final answer:

The system of equations y = 1/4x + 2 and 3y = -3/4x - 6 represents two distinct parallel lines with the same slope but different y-intercepts, thus the system has no solution.

Explanation:

To find the solution to the system of equations y = 1/4x + 2 and 3y = -3/4x - 6, we need to check if they have a common solution, indicating the point where they intersect, or if they are parallel, which would mean they have no solution, or if they are the same line, which would translate into infinitely many solutions.

First, simplify the second equation by dividing every term by 3, which gives y = -1/4x - 2. Now we can see that the coefficients of x and the constant terms in both equations are multiples of one another but with opposite signs, which means the lines are parallel and have the same slope but different y-intercepts. Therefore, these two equations represent two distinct parallel lines that never intersect.

The correct answer is that there is no solution to this system of equations because the lines are parallel and will never meet.

Answer:

k = 4.

Step-by-step explanation:

An arithmetic sequence has a common difference.

So for this to be arithmetic:

k + 3 - (k - 1) = 3k - 1 - (k + 3)

k + 3 - k + 1 = 3k - 1 - k - 3

3 + 1 = 2k - 4

4 + 4 = 2k

k = 4.

The sequence is  3, 7, 11.

1. The given absolute value inequality is:

[tex] |x| \: > \: 5[/tex]

This implies that;

[tex] - x \: > \: 5 \: or \: x \: > \: 5[/tex]

We the first inequality by -1 and reverse the sign to get:

[tex]x \: < - \: 5 \: or \: x \: > \: 5[/tex]

The correct answer is

C. { x|x < -5 or x > 5}

2. The given inequality is:

[tex] |4x - 8| \: < \: 12[/tex]

This implies that,

[tex] - (4x - 8) \: < \: 12 \: or \: (4x - 8) \: < \: 12[/tex]

Divide through the first inequality by -1 and reverse the sign

[tex]4x - 8\: > \: - 12 \: or \: 4x - 8\: < \: 12[/tex]

Group similar terms:

[tex]4x \: > \: - 12 + 8 \: or \: 4x \: < \: 12 + 8[/tex]

Simplify:

[tex]4x \: > \: - 4\: or \: 4x \: < \: 20[/tex]

Divide both sides by 4

[tex]x \: > \: - 1\: or \: x \: < \: 5[/tex]

If

[tex]S=1+2+\cdots+(n-1)+n[/tex]

then it's also true that

[tex]S=n+(n-1)+\cdots+2+1[/tex]

so that

[tex]2S=(1+n)+(2+(n-1))+\cdots+((n-1)+2)+(n+1)=n(n+1)\implies S=\dfrac{n(n+1)}2[/tex]

For any integer [tex]n[/tex], [tex]n(n+1)[/tex] is even. We have [tex]5\mid S[/tex] if either [tex]5\mid n[/tex] or [tex]5\mid(n+1)[/tex]. This means [tex]n[/tex] must satisfy either [tex]n\equiv0\pmod5[/tex] or [tex]n\equiv4\pmod5[/tex], in which case we have a general solution of

[tex]n=5k[/tex]

or

[tex]n=5k-1[/tex]

where [tex]k[/tex] is any integer.

Final answer:

Strategic voting leads to the Pepsi candidate winning the election for Soft Drink commissioner, despite the strong preference for Coca-Cola among the voting population.

Explanation:

The Pepsi candidate wins in a landslide in the election for Soft Drink commissioner, despite there being a strong preference for Coca-Cola among the voting population because of the concept of strategic voting. Strategic voting occurs when voters strategically choose a candidate who they believe has a better chance of winning, rather than their preferred choice. In this scenario, it is possible that the supporters of the Coca-Cola party split their votes among the four candidates, while the supporters of the Pepsi candidate remained united, resulting in the Pepsi candidate winning by a large margin.

Answer:

[tex]\frac{81}{3}[/tex]

Step-by-step explanation:

Given the direct variation equation

y = kx ← k is the constant of proportionality

then for

y = [tex]\frac{81}{3}[/tex] x

k = [tex]\frac{81}{3}[/tex]

Answer:

[2, -10]

Step-by-step explanation:

Simply plug in 2⃣ for every "x" you see, evaluate, then you will arrive at your answer.

Answer:

5.87

Step-by-step explanation:

29.35/x=100/20

(29.35/x)*x=(100/20)*x       - we multiply both sides of the equation by x

29.35=5*x       - we divide both sides of the equation by (5) to get x

29.35/5=x

5.87=x

x=5.87

Answer:

$5.87

Step-by-step explanation:

20% = 20/100 = 1/5

hence 20% tip,

= 20% of the total cost

= 1/5 x $29.35

= $5.87

well, this is an OCTAgon, OCTA = 8.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=30\\ p=\stackrel{8\times 12}{96} \end{cases}\implies A=\cfrac{1}{2}(30)(96)\implies A=1440[/tex]

Answer:

20,001,030,001

For this case we must express the following phrase in numerical form:

"twenty billion, one million thirty thousand and one as a number"

twenty billion is equivalent to [tex]20,000,000,000[/tex]

one million equals [tex]1,000,000[/tex]

thirty thousand equals [tex]30,000[/tex]

one equals 1

Then, we can express:

[tex]20,001,030,001[/tex]

Answer:

20,001,030,001

Answer:

16

Explanation:

Area of Triangle = 1/2(B*H)

Height - 4

Base - 8

8 * 4 = 32

32 / 2 = 16

Answer:

1+i

Step-by-step explanation:

The explicit formula for the compound interest geometric tell us: If P1 is invested at an interest rate of i per year, compounded annually, the future value Pn at the end of the nth year is:

[tex]Pn=P1(1+i)^{(n-1)}[/tex]

For example if you have $10 at 5% at an interest rate of 5% per year.

Then if you want to know the amount of money at the end of the 2, 3 and 4 year, you have:

n=1 year P1=10

n=2 year

[tex]P2=10(1+(5/100))[/tex]

[tex]P2=10(1+(5/100))^{(2-1)}[/tex]

[tex]P2=10(1+(5/100))^{(1)}[/tex]=10,5

n=3 year

[tex]P3=10(1+(5/100))*(1+(5/100))[/tex]

[tex]P3=10(1+(5/100))^{(3-1)}[/tex]

[tex]P3=10(1+(5/100))^{(2)}[/tex]=11.025

n=4 year

[tex]P4=10(1+(5/100))*(1+(5/100))*(1+(5/100)) [/tex]

[tex]P4=10(1+(5/100))^{(4-1)}[/tex]

[tex]P4=10(1+(5/100))^{(3)}[/tex]= 11.57625

Answer:

Domain f(x) = R - {1}

As it is a rational expression, the denominator cannot be zero.

Now the function holds all real values except 1 for which the denominator will become zero which is undefined.

Therefore the domain will be all real numbers except 1.

Answer:

-20 + 48i

Step-by-step explanation:

(4 +6i)^2 (Perfect square)

= (4)^2 + 2(4)(6i) + (6i)^2

= 16 + 48i + 36i^2

= 16 + 48i - 36    (i^2 = -1)

= -20 + 48i

Answer:

[tex]-20+48 \text{i}[/tex]

Step-by-step explanation:

Note that

[tex](4+6i)^2=4^2+2\cdot(4\cdot6i)+(6\cdot i)^2=16+48i+36i^2=16+48i-36\\\\=(36-13)+48i=-20+48i[/tex]

and we are done.

Answer:

6x³ - 4x² + 4x

Step-by-step explanation:

The additive inverse is the value added to make the expression equal to zero.

Given

- 6x³ + 4x² - 4x , then the additive inverse is

- ( - 6x³ + 4x² - 4x)

= 6x³ - 4x² + 4x

The additive inverse of the polynomial is 6x³ - 4x² + 4x.

Given: Polynomial

-6x³ + 4x² - 4x

Additive inverse of the polynomial is the polynomial when added to the original polynomial gives the sum zero.

Let, the additive inverse of the given polynomial be P.

⇒ P + -6x³ + 4x² - 4x = 0

⇒ P = 6x³ - 4x² + 4x

Therefore, the additive inverse of the given polynomial is 6x³ - 4x² + 4x.

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I believe the answer is 286 since the equation is 250(1.07) t

this tells me that 250= original size and 1.07= growth of the bacteria and t for time or hour in this case

250x(1.07) 2

267.5x(1.07)

286.225 = 286

the slope intercept form is y=mx+b

since the line intersects at (0,3) b= 3

since the slope is 0 m= 0

so the equation would be y=0x+3 or y=3

Answer:

y=3

Step-by-step explanation:

Hi there!

We are given that a line contains the point (0, 3), and has the slope 0

We want to find the equation of this line, in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

The y intercept is the point that intersects the y axis; at this point, the value of x is 0

The point (0, 3) we were given is actually the y intercept of this line (the value of x at this point is 0!)

We can therefore, plug it into the formula.

We can just plug in the y value as b into the equation.

Here's the equation so far:

y=mx+3

Now we need to find m.

As the the slope of the line is 0, it means that if we plug 0 in as m, then we can find the equation of the line.

So substitute 0 as m

y=0x+3

This can also be written as y=3

Hope this helps!

See more on finding the equation of the line from a slope and a point here (n.b. the answer is written in a different format, but the logic is still the same): https://brainly.com/question/14358313

For this case we have that by definition of trigonometric relations of rectangular triangles, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]Cos (A) = \frac {3} {4.24} = 0.707547169811\\Cos (B) = \frac {3} {4.24} = 0.707547169811[/tex]

So:

[tex]\frac {Cos (A)} {Cos (B)} = \frac {0,707547169811} {0,707547169811} = 1[/tex]

Answer:

[tex]\frac {Cos (A)} {Cos (B)} = 1[/tex]

Answer:

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](x2,y2)=(-7,4)[/tex]

[tex](x1,y1)=(2,-3)[/tex]

Substitute the values

[tex]m=\frac{4+3}{-7-2}[/tex]

[tex]m=\frac{7}{-9}[/tex]

[tex]m=-\frac{7}{9}[/tex]

therefore

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values

Answer:

C

Step-by-step explanation:

Answer:

C. f(x)=3(1/2)^x

Step-by-step explanation:

standard form of a function is f(x)=ab^x

a should be 3, or the y value where the x value is 0

the b value is 1/2 because that's the rate of change

To convert 25/38 to a percentage, divide 25 by 38, multiply by 100, and round to the nearest tenth, resulting in 65.8%.

To convert 25/38 to a percentage, you divide 25 by 38 and then multiply the result by 100.

The calculation would look like this:

Divide 25 by 38: 25 ÷ 38 = 0.6578947368

Multiply the result by 100 to get the percentage: 0.6578947368 × 100 = 65.78947368%

Round the result to the nearest tenth of a percent: 65.8%

Therefore, 25/38 as a percentage rounded to the nearest tenth of a percent is 65.8%.

Final answer:

To express 25/38 as a percentage, divide 25 by 38 and then multiply the result by 100. The answer is approximately 65.8%.

Explanation:

To express 25/38 as a percentage, you can divide 25 by 38 and then multiply the result by 100.

25 ÷ 38 ≈ 0.6578947368421053

0.6578947368421053 × 100 ≈ 65.8

Therefore, 25/38 as a percentage, rounded to the nearest tenth of a percent, is approximately 65.8%.

Answer:

6 since 8(3/4)=6

Step-by-step explanation:

(x^8)^(3/4)

=x^(8*3/4) by one of the law of exponents

=x^(8/4 *3)

=x^(2 *3)

=x^6

The system of linear inequalities which is represented by the  graph is:

        y>x-2 and    y<x+1

The first inequality--

It is a dotted line which passes through (-1,0) and (0,1) and the shaded region is below the line.

first we find the equation of line:

The equation of a line passing through (a,b) and (c,d) is given by:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Hence,

(a,b)=(-1,0) and (c,d)=(0,1)

Hence, the equation of line is:

[tex]y-0=\dfrac{1-0}{0-(-1)}\times (x-(-1))\\\\i.e.\\\\y=\dfrac{1}{1}\times (x+1)\\\\i.e.\\\\y=x+1[/tex]

Also, the inequality is strict since the line is dotted.

Hence, the inequality is given by: y<x+1

The second inequality --

is a dotted line which passes through (0,-2) and (2,0)

and the shaded region is above the line.

The equation of line is given by:

  y=x-2

and the inequality is strict.

Hence, the inequality is given by:

        y>x-2

Answer:

(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)

Step-by-step explanation:

It almost look like someone possibly meant to write a perfect cube there instead of 51... but we can still factorize this... it just won't be as pretty.

The formula for factoring a difference of cubes is

u^3-v^3

=(u-v)(u^2+uv+v^2).

So the answer here is

(2y)^3-(cubert(15)x)^3

=(2y-cubert(15)x)(4y^2+2cubert(15)xy+cubert(15^2)x^2)

cubert means cube root of

The thing I'm cube rooting is the thing in ( ) next to the cubert.

Make sure you actually write the symbol for cube root instead of my notation.

Answer:

2/3

Step-by-step explanation:

-5/12 ÷ -5/8

Copy dot flip

-5/12 * -8/5

The 5's cancel

-8/-12

Divide the top and bottom by -4

2/3

Answer:

2/3

Step-by-step explanation:

-5/12 divided by -5/8

To solve this you need to change the division sign to a multiplication sign.Then find the reciprocal of the second fraction. It should look like this.

-5/12*-8/5

Then you multiply straight across

5*8=40

5*12=60

40/60

This can be simplified to 2/3

Answer:

Option D. (0, 2)

Step-by-step explanation:

we have

[tex]f(x)=2(3)^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate of change

In this problem

a=2 ---> the initial value ( value of the function when the value of x is equal to zero)

b=3

b=1+r ----> 3=1+r ----> r=2 ---> r=200%

Remember that

The initial value of the function is equal to the y-intercept

The initial value is the point (0,2)

therefore

The y-intercept is the point (0,2)