Which of the following points is the intersection of the graphs given the equations y = x - 5 and y = 2x + 1?

A (1, 3)
B (-1, -4)
C (-2, -3)
D (-6, -11)

Answer:

Explanation:

The rotation of a point 180 degrees about the origin follows the rule:

That means that both the x-coordinate and the y-coordinate transform into their negative values.

So, - 3 transforms into - (-3) = 3, and - 2 transforms into - (-2) = 2.

The result is (-3, -2) → (3,2).

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:

-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:

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:

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:

Step-by-step explanation:

The solution of the system of equations is the coordinates of the intersection of the lines.

(1, -3)

Answer:

B.(1, -3)

Wherever the lines intersect is the solution. Hope this helps!

Step-by-step explanation:

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.

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:

[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:

[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:

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

Step-by-step explanation:

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

The area of the circle is found using the formula Area = PI x r^2

The area of a triangle is found using the formula Area = 1/2 x base x height.

Using the given dimensions:

Area of the circle = 3.14 x 3.8^2 = 45.3416 square units.

The area of the triangle is 1/2 x 5 x 10 = 25 square units.

To find the area of the unshaded part, subtract the area of the shaded triangle from the circle:

Area = 45.3416 - 25 = 20.3416

Round to two decimal places = 20.34

The answer is D. 20.34

D. 20.34

In this case, we must calculate first the Areas of the Triangle ([tex]A_{t}[/tex]), in square units, and the Circle ([tex]A_{c}[/tex]), in square units, later we subtract the Area of the former from the Area of the latter to determine the Area of unshaded region ([tex]A_{u}[/tex]), in square units. The Area formulas for each figure are, respectively:

Triangle

[tex]A_{t} = \frac{1}{2}\cdot b\cdot h[/tex] (1)

Circle

[tex]A_{c} = \pi\cdot r^{2}[/tex] (2)

Unshaded Area

[tex]A_{u} = A_{c} - A_{t}[/tex] (3)

Where:

[tex]h[/tex] - Height of the triangle.

[tex]b[/tex] - Base of the triangle.

[tex]r[/tex] - Radius of the circle.

If we know that [tex]h = 10[/tex], [tex]b = 5[/tex] and [tex]r = 3.8[/tex], then the area of the unshaded region is:

[tex]A_{t} = \frac{1}{2}\cdot (5)\cdot (10)[/tex]

[tex]A_{t} = 25[/tex]

[tex]A_{c} = \pi\cdot 3.8^{2}[/tex]

[tex]A_{c} \approx 45.365[/tex]

[tex]A_{u} = 45.365-25[/tex]

[tex]A_{u} = 20.365[/tex]

The correct answer is D.

Please see this question related to Area problems: https://brainly.com/question/16151549

[tex]3D-2E=3\left[\begin{array}{cc}5&5\\-3&7\\1&3\end{array}\right] -2\left[\begin{array}{cc}6&7\\2&-7\\0&5\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}15&15\\-9&21\\3&9\end{array}\right] -\left[\begin{array}{cc}12&14\\4&-14\\0&10\end{array}\right] \\\\3D-2E=\left[\begin{array}{cc}3&1\\-13&35\\3&-1\end{array}\right][/tex]

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:

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:

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:

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:

(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.

Answer:

The answer is 282

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

Answer:

situation 1 : flat rate of 50....1.50 per movie.....after 1 month her bill is 66.25

66.25 = 1.50x + 50

situation 2 : flat rate of 60....1.25 for every movie...

y = 1.25x + 60

both situations have a flat rate fee plus a charge for every movie. In situation 1, u can solve for x (the number of movies rented) because u know how much she was charged. However, in situation 2, without more information, u cannot solve this equation...what u would need to solve it would either be the number of movies rented or the total bill showing what she was charged. So basically, in situation 1, u are given more information then in situation 2.....enough information to be able to solve for the variable x...whereas, in situation 2, u are not given enough info to solve for a variable and get a numerical answer

BRAINLIEST PLEASE!!!!!

Answer: Situation 1 involves one independent variable that stands for the number of movies Melinda rented. Situation 1 gives a total for the monthly bill, but situation 2 does not give a total for the monthly bill. Because situation 2 leaves the total value out, it needs an additional variable. Therefore, situation 2 involves two variables—the number of movies Kimberly rented (the independent variable) and the monthly cable bill (the dependent variable). In this situation, we can’t solve for one variable without knowing the other.

Step-by-step explanation: ed.men.tum answer. DO NOT copy and paste!

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 ..

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:

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:

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:

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:

Answer:

parent funtion is most basic

Step-by-step explanation:i just took the test

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