Which rule describes the translation below?

Answer:

Step-by-step explanation:

We only need two points to plot the graph of each equation.

[tex]y=-\dfrac{3}{2}x+2\\\\for\ x=0\to y=-\dfrac{3}{2}(0)+2=0+2=2\to(0,\ 2)\\\\for\ x=2\to y=-\dfrac{3}{2}(2)+2=-3+2=-1\to(2,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)[/tex]

Look at the picture.

Read the coordinates of the intersection of the line (solution).

Answer:

(-4,8)

Step-by-step explanation:

Given system of equations,

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

[tex]y=5x+28------(2)[/tex]

In equation (1), If x = 0, y = 2,

If y = 0,

[tex]-\frac{3}{2}x+2=0\implies -\frac{3}{2}x=-2\implies -3x=-4\implies x=\frac{4}{3}[/tex]

Join the points (0,2) and (4/3,0) in the graph we get the line (1),

In equation (2), if x = 0, y = 28,

If y = 0,

[tex]5x+28=0\implies 5x=-28\implies x=-5.6[/tex]

Join the points (0, 28) and (-5.6,0) in the graph we get the line (2),

Hence, by graph,

The intersection point of line (1) and (2) is (-4,8)

Which is the required solution.

Answer:

Option 2 is correct

[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]

Step-by-step explanation:

We can se ethat the given function is an exponential function.

The function is:

5^x

In order to compress the function the original function is multiplied a constant.

As the function is compressed by a factor of 1/2

The function will become:

g(x) = 1/2 * 5^x

Now the function is shifted to left which is a horizontal shift. For horizontal shift of n units, n is added to the power so the function will become:

[tex]g(x) = \frac{1}{2}5^{x+3}[/tex]

Then the function is shifted upwards two units, the vertical shhift is added to the whole function so the function will become:

[tex]g(x) = (\frac{1}{2})5^{(x+3)}+2[/tex]

Hence, Option 2 is correct ..

First we can rewrite the equation to,

[tex]x^2+2x-3=0[/tex]

Which factors to,

[tex](x+3)(x-1)=0[/tex]

And this leads towards two solutions,

[tex]x_1\Longleftrightarrow x+3=0\Longrightarrow x_1=-3[/tex]

and,

[tex]x_2\Longleftrightarrow x-1=0\Longrightarrow x_2=1[/tex]

The answer is A.

Hope this helps.

r3t40

Answer:

c

Step-by-step explanation:

Given

x² + 2x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = 3 + 1

(x + 1)² = 4 ( take the square root of both sides )

x + 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 1 from both sides )

x = - 1 ± 2, hence

x = - 1 - 2 = - 3 and x = - 1 + 2 = 1

Answer:

-2 >-4

This is true, so it is a solution

Step-by-step explanation:

2x+1> x-3

Subtract x from each side

2x-x+1> x-x-3

x +1 > -3

Subtract 1 from each side

x+1-1 >-3-1

x > -4

x =-2   Substitute this into the inequality

-2 >-4

This is true, so it is a solution

Answer:

The correct option is C.

Step-by-step explanation:

Given information: BCDE is a rectangular casing, DE = 3 cm and BE = 3 cm.

We need to find the smallest diameter of pipe that will fit the fiber optic line. It means we have to find the measure of DB.

The measure of all interior angles of a rectangle or square is 90°.

[tex]\angle DEB=90^{\circ}[/tex]

It means the DEB is right angled triangle.

According to the Pythagoras theorem:

[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]

In triangle DEB,

[tex](DB)^2=(DE)^2+(BE)^2[/tex]

[tex](DB)^2=(3)^2+(3)^2[/tex]

[tex](DB)^2=9+9[/tex]

[tex](DB)^2=18[/tex]

Taking square root both sides.

[tex]DB=\sqrt{18}[/tex]

[tex]DB=4.24264068712[/tex]

[tex]DB\approx 4.24[/tex]

Therefore the correct option is C.

Based on the information given, the smallest diameter will be C. 4.24 cm.

DB² = 3² + 3²

DB² = 9 + 9

DB² = 18

DB = ✓18

DB = 4.24

Therefore, the correct option is 4.24.

Learn more about diameter on:

https://brainly.com/question/1649593

Answer:

For every real number x, C expresses the solution to the inequality

Final answer:

To find the solution to the inequality x + 3 < 1, subtract 3 from both sides to get x < -2. The number line would have an open circle at -2 and be shaded to the left, indicating all numbers less than -2.

Explanation:

To solve the inequality x + 3 < 1, we need to find the value of x that makes the inequality true. We start by subtracting 3 from both sides of the inequality:

The number line for this inequality would have an open circle at -2 (since -2 is not included in the solution) and shade to the left of -2 to show that all numbers less than -2 are included. The reason we shade to the left is because those are the numbers that are less than -2, thus satisfying the inequality.

Answer:

29/12 > x

Step-by-step explanation:

–3(x + 2) > 4x + 5(x – 7)

Distribute

-3x -6 > 4x +5x-35

Combine like terms

-3x-6 > 9x -35

Add 3x to each side

-3x+3x-6 > 9x+3x -35

-6 > 12x-35

Add 35 to each side

-6+35 > 12x -35+35

29 > 12x

Divide each side by 12

29/12 > 12x/12

29/12 > x

Answer:

x = -8

Step-by-step explanation:

-4(2x+3) = 2x+6-(8x+2)

Distribute

-8x-12= 2x+6-8x-2

Combine like terms

-8x-12 = -6x+4

Add 8x to each side

-8x-12 +8x = -6x+4+8x

-12 = 2x+4

Subtract 4 from each side

-12-4 = 2x+4-4

-16 = 2x

Divide each side by 2

-16/2 = 2x/2

-8 =x

Answer:

.250

Step-by-step explanation:

4 is in the tenths place, if the number to the right of a number is five or higher you round the number up.

Answer:

Step-by-step explanation:

Math courses just love this kind of question. The only worse question would be something like -0.949 rounded to the nearest 1/10

Your question should round to 0.2.

The one I presented should round to -0.9

Answer:

See explanation

Step-by-step explanation:

Let x in be the base side length and y in be the height of the box. Since the base is a square, we have

[tex]S=x^2\Rightarrow x=\sqrt{S}[/tex]

The volume of the box is

[tex]V=S\cdot y\\ \\36=Sy\Rightarrow y=\dfrac{36}{S}[/tex]

The surface area of the box is

[tex]SA=2x^2+4xy\\ \\SA(S)=2S+4\cdot \sqrt{S}\cdot \dfrac{36}{S}=2S+\dfrac{144}{\sqrt{S}}[/tex]

The graph of the function SA(S) is shown in attached diagram.

Find the derivative of this function:

[tex]SA'(S)=(2S+144S^{-\frac{1}{2}})'=2-\dfrac{1}{2}\cdot 144\cdot S^{-\frac{1}{2}-1}=2-\dfrac{72}{S\sqrt{S}}[/tex]

Equate this derivative to 0:

[tex]2-\dfrac{72}{S\sqrt{S}}=0\\ \\2S\sqrt{S}=72\\ \\S\sqrt{S}=36\\ \\S^{\frac{3}{2}}=6^2\\ \\S=6^{\frac{4}{3}}[/tex]

So, the dimensions that produce a minimum surface area for this aluminum box are:

[tex]x=\sqrt{6^{\frac{4}{3}}}=6^{\frac{2}{3}} \ in\\ \\y=\dfrac{6^2}{6^{\frac{4}{3}}}=6^{\frac{2}{3}}\ in.[/tex]

Answer:

Let's evaluate each rental shop:

For one hour, the cost is $5 + $1.5 = $6.5. For ten hours the total cost is: $5 + 10×$1.5 = $20

For one hour, the cost is $6 + $1.25 = $7.25. For ten hours the total cost is: $6 + 10×$1.25 = $18.5

If Clara and her brother are thinking about renting a bike for an hour, Bargain Bikes is the best option. On the other hand, if they want to rent it fr several hours Frugal Wheels is the best option.

Answer:

8:7 and 64:49

Step-by-step explanation:

If the widths of two similar rectangles are 16 cm and 14 cm, the ratio of the areas are 8:7 and 64:49.

Answer:

6.32455532034 or just 6

Step-by-step explanation:

Answer:

2√10

Step-by-step explanation:

Find two numbers that multiply to forty, where one of them is a NON-PERFECT square. Those numbers would be 10 and 4. Take the square root of both and you will see that 2 comes from the 4, so that moves to the outside, and √10 stays the way it is because there is no perfect square to factor from this. With that being said, you have your answer.

I am joyous to assist you anytime.

Answer:

1 is not a function

2 is a function because you can write it (AS) f(x)=1/(2x).

Step-by-step explanation:

1) x^2+y^2=9 is a circle with center (0,0) and radius 3.

To get this all I did was compare to (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.

A circle is not a function.

You can solve solve for and see that you will get two values for y which is no go for a function.

Let's do that:

[tex]x^2+y^2=9[/tex]

Subtract x^2 on both sides:

[tex]y^2=9-x^2[/tex]

Square root both sides:

[tex]y=\pm \sqrt{9-x^2}[/tex].

2) 2xy=1

Divide both sides by 2x:

y=1/(2x).

This is a function only one y there.

Answer:

[tex]\frac{5}{2\sqrt{6} }[/tex]

Step-by-step explanation:

Since Θ is in fourth quadrant then cosΘ > 0, as is secΘ

Given

sinΘ = - [tex]\frac{1}{5}[/tex], then

cosΘ = [tex]\sqrt{1-(-1/5)^2}[/tex]

         = [tex]\sqrt{1-\frac{1}{25} }[/tex] = [tex]\sqrt{\frac{24}{25} }[/tex] = [tex]\frac{2\sqrt{6} }{5}[/tex]

Hence

secΘ = [tex]\frac{1}{\frac{2\sqrt{6} }{5} }[/tex] = [tex]\frac{5}{2\sqrt{6} }[/tex]

Answer:

[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]

The answer is the last one.

Step-by-step explanation:

If we are in quadrant 4, then x (cosine) is positive and y (sine) is negative.

Since cosine is positive, secant is positive because secant is the reciprocal of cosine.

So we already know the answer is not the 1st one or the 3rd one.

I'm going to use a Pythagorean Identity to find cosine value of theta.

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

Enter in -1/5 for [tex]\sin(\theta)[/tex]:

[tex]\cos^2(\theta)+(\frac{-1}{5})^2=1[/tex]

Simplify a bit:

[tex]\cos^2(\theta)+\frac{1}{25}=1[/tex]

Subtract 1/25 on both sides:

[tex]\cos^2(\theta)=1-\frac{1}{25}[/tex]

Write 1 as 25/25 so you have a common denominator on the right hand side:

[tex]\cos^2(\theta)=\frac{25}{25}-\frac{1}{25}[/tex]

[tex]\cos^2(\theta)=\frac{24}{25}[/tex]

Take the square root of both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{24}{25}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{24}}{\sqrt{25}}[/tex]

I will worry about simplifying the square root part when finding secant.

We said that cosine was positive because we were in the fourth quadrant.

[tex]\cos(\theta)=\frac{\sqrt{24}}{\sqrt{25}}[/tex]

Now recall that cosine and secant are reciprocals of each other:

[tex]\sec(\theta)=\frac{\sqrt{25}}{\sqrt{24}}[/tex]

Let's simplify the square part not.

Usually people hate the square root on both and also if you look at your choices none of the choice have square root on bottom.

So we are going to multiply top and bottom by [tex]\sqrt{24}[/tex]. I'm going to also write 5 instead of [tex]\sqrt{25}[/tex].

[tex]\sec(\theta)=\frac{5}{\sqrt{24}} \cdot \frac{\sqrt{24}}{\sqrt{24}}[/tex]

[tex]\sec(\theta)=\frac{5\sqrt{24}}{24}[/tex]

Now let's simplify the square root of 24.

We know 24 is not a perfect square, but 24 does contain a factor that is a perfect square. That factor is 4.

[tex]\sec(\theta)=\frac{5\sqrt{4}\sqrt{6}}{24}[/tex].

[tex]\sec(\theta)=\frac{5(2)\sqrt{6}}{24}[/tex]

[tex]\sec(\theta)=\frac{10\sqrt{6}}{24}[/tex]

Now both 10 and 24 share a common factor of 2 so let's divide top and bottom by 2:

[tex]\sec(\theta)=\frac{5\sqrt{6}}{12}[/tex]

The answer is the last one.

Answer: is there anyway U can give me a more zoomed in pic

Step-by-step explanation:

Answer:

The answer is 282

because 94 in 4 mins so you need to use multiple 94 x 3 the answer is 282.

Answer:

[tex]p=4[/tex]

[tex]x=\frac{-1}{2} \pm \frac{\sqrt{3}}{2}i[/tex]

Step-by-step explanation:

We are given (x+3) is a factor of [tex]x^3+4x^2+px+3[/tex], which means if were to plug in -3, the result is 0.

Let's write that down:

[tex](-3)^3+4(-3)^2+p(-3)+3=0[/tex]

[tex]-27+36-3p+3=0[/tex]

[tex]9-3p+3=0[/tex]

[tex]9+3-3p=0[/tex]

[tex]12-3p=0[/tex]

[tex]12=3p[/tex]

[tex]p=4[/tex]

So the cubic equation is actually [tex]x^3+4x^2+4x+3=0[/tex] that they wish we solve for [tex]x[/tex].

To find another factor of the given cubic expression on the left, I'm going to use synthetic division with that polynomial and (x+3) where (x+3) is divisor.  Since (x+3) is the divisor, -3 will be on the outside like so:

-3 |  1    4    4     3

   |       -3   -3    -3

     ---------------------

      1      1     1      0

So the other factor of [tex]x^3+4x^2+4x+3[/tex] is [tex](x^2+x+1)[/tex].

We must solve [tex]x^2+x+1=0[/tex].

Compare this to [tex]ax^2+bx+c=0[/tex].

We have [tex]a=1,b=1, \text{ and } c=1[/tex].

The quadratic formula is

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

Plug in the numbers we have for [tex]a,b, \text{ and } c[/tex].

[tex]x=\frac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex].

Simplify inside the square root while also performing the one operation on bottom:

[tex]x=\frac{-1 \pm \sqrt{1-4}}{2}[/tex]

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

Now our answer will include an imaginary part because of that sqrt(negative number).

The imaginary unit is [tex]i=\sqrt{-1}[/tex].

So our final answer is:

[tex]x=\frac{-1}{2} \pm \frac{\sqrt{3}}{2}i[/tex]

Final answer:

To find the value of p, substitute -3 into the polynomial since (X+3) is a factor, thus yielding p=3. With p known, the polynomial becomes [tex]x^3 + 4x^2 + 3x + 3[/tex] = 0, and can now be solved for x.

Explanation:

Finding the Value of p

Given the polynomial [tex]x^3 + 4x^2 + px + 3[/tex] and the fact that (X+3) is a factor, we can use polynomial division or synthetic division to find the value of p. Since (X+3) is a factor, when we substitute -3 for x in the polynomial, the result should be zero.

Substituting -3 into the polynomial yields:
[tex](-3)^3 + 4(-3)^2 + p(-3) + 3[/tex] = 0
-27 + 36 - 3p + 3 = 0
9 - 3p = 0.

Solving for p gives us:
3p = 9
p = 3.

Solving the Equation

Now that we know p, we rewrite the polynomial as [tex]x^3 + 4x^2 + 3x + 3 = 0[/tex] and use the fact that (X+3) is a factor to perform the division. The remainder of the division gives us a quadratic polynomial which we can solve using the quadratic formula or factoring.

Answer:

40,320

Step-by-step explanation:

First you have 8 movies to watch.

A day passes you have 7 left, then another day passes you have 6 left...

You do this until you have 1 movie left because by then you'd have watched 7 movies in 7 days of a week.

Take the product: 8 * 7 * 6 * 5...*2*1 = 8! = 40,320

Answer: C. 40,320

Step-by-step explanation:

Given : The total number of movies = 8

Also, in one week if you watch one movie a day , then the number of possible movies you can watch in next week must be 7.

Now, the number of ways to watch 8 movies taking 7 movies from is given by permutations :-

[tex]^8P_7=\dfrac{8!}{(8-7)!}\\\\=\dfrac{8!}{1!}=8\times7\times6\times5\times4\times3\times2\times1\\\\=40,320[/tex]

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

we know that

A function f(x) is even when

f(x)=f(-x) ----> the function is symmetry about the y-axis

A function is odd when

-f(x)=f(-x) ---> the function is symmetry about the origin

In this problem we have

f(x)=-5x

Verify if the function is even

For x=1 ----> f(1)=-5(1)=-5

For x=-1 ---> f(-1)=-5(-1)=5

so

f(x) is not equal to f(-x)

therefore The function is not even

Verify if the function is odd

we have

f(1)=-5

f(-1)=5

so

-f(1) is equal to f(-1)

-f(x)=f(-x)

therefore

The function is odd because it is symmetric about the origin.

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

Answer:

X =3 and x =6

Step-by-step explanation:

Just look at the line where they cross another line,

Answer:

B x=3 and x=6

Step-by-step explanation:

The zeros of the function are where the function crosses the x axis

Looking at the graph

This function crosses at x=3 and x = 6

Answer:

Graph C is your answer

Step-by-step explanation:

Draw the following graph using the easy coordinates, those are were y axis is zero, and the other were x axis is 0:

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

First point is (1,0) and the other (0,2)

The entire region that belongs to your graph is greater than drawn line.

Draw another graph using the same easy coordinates.

[tex]y=2x-1[/tex]

First point is (0.5,0) and the other (0,-1)

The entire region that belongs to your graph is lesser than the drawn line.

When you merge those graphs into one, you can clearly see that they correspond to the C answer.

Answer:

Graph A.

Step-by-step explanation:

The given inequalities are

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

[tex]y<2x-1[/tex]

The related equation of given inequalities are

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

[tex]y=2x-1[/tex]

The slope of line (1) is -2 and the y-intercept is 2.

The slope of line (2) is 2 and the y-intercept is -1.

Both related lines are dotted line because the points on the line are not included n the solution set.

Check each inequality by (0,0).

[tex]0>-2(0)+2\Rightarrow 0>2[/tex] False statement

[tex]0<2(0)-1\Rightarrow 0<-1[/tex] False statement

So, (0,0) is not included in the shaded area of any of these two inequities.

Therefore, graph A shows the solution to the system of linear inequalities.

Answer:

(a + 6b)(a - 4b)

Step-by-step explanation:

You want your midst term to result in 2ab, NOT -2ab.

I am joyous to assist you anytime.

Well,

[tex]x^6+1000=(x^2)^3+10^3[/tex]

From here we use [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex],

[tex](x^2+10)\boxed{(x^4-10x^2+100)}[/tex]

And the found our factor.

Hope this helps.

r3t40

Answer:

Option B

Step-by-step explanation:

Answer:

0.1469

Step-by-step explanation:

Given from the question;

Mean=8.4 hrs=μ

Standard deviation=1.8 hrs=δ

Sample size, n=40

Let  x=8.7

z=(x-μ)÷(δ÷√n)  

Find z(8.7)

z=(8.7-8.4)÷(1.8÷√40)

z={0.3×√40}÷1.8=1.05409

z=1.0541

Read from the  standard normal probabilities table

P(z>1.0541)

=0.1459

Final answer:

Using the Central Limit Theorem and standard error calculation, the probability that the mean rebuild time by 40 mechanics exceeds 8.7 hours is found to be approximately 0.1469.

Explanation:

To find the probability that the mean rebuild time for a 2005 Chevrolet Cavalier transmission by 40 mechanics exceeds 8.7 hours, given that the mean is 8.4 hours and the standard deviation is 1.8 hours, we will use the concept of the sampling distribution of the sample mean. Since the standard deviation of the population is known, we apply the Central Limit Theorem, which states that the distribution of the sample means will be approximately normal if the sample size is large enough (n>30 in this case).

First, calculate the standard error of the mean (SEM) using the formula: SEM = σ/√n, where σ is the standard deviation of the population and n is the sample size. Therefore, SEM = 1.8/√40 = 0.285.

Next, find the z-score that corresponds to a mean rebuild time of 8.7 hours using the formula: z = (X - μ)/SEM, where X is the value of interest (8.7 hours), and μ is the population mean (8.4 hours). Thus, z = (8.7 - 8.4)/0.285 = 1.05.

Finally, look up the z-score in a z-table or use a statistical calculator to find the probability that Z is greater than 1.05, which is approximately 0.1469.

Therefore, the probability that their mean rebuild time exceeds 8.7 hours is 0.1469.

Answer:

Making a fraction.

Step-by-step explanation:

Put the favored outcome as the numerator. Then, put the total number of outcomes as the denominator and boom, you have calculated probability. *Thumbs Up*

Answer:

8.45 kilometers

Step-by-step explanation:

Given

The distance from library to post office = 5.25 miles

We are given that one mile is equal to 1.61 kilometers

So to find the distance from the library to post office in kilometers we have to multiply 5.25 with 1.61

So,

The distance from library to post office in kilometers = 5.25*1.61

8.4525

Rounding off to nearest hundredth

8.45 kilometers ..

Answer:

The simplest form is 1/r^7 + 1/s^12

Step-by-step explanation:

The given expression is r^-7+s^-12.

Notice that the exponents of both the base are negative

So, we will apply the rule which is:

a^-b = 1/a^b

Which means that to change the exponent into positive we will write it as a fraction:

r^-7+s^-12.

= 1/r^7 + 1/s^12..

Therefore the simplest form is 1/r^7 + 1/s^12....

Answer:

The simplest form is 1/r^7 + 1/s^12

Step-by-step explanation: