What is the slope of the line?
-2
-1/2
1/2
2

Answer:

y - 11 = - 3(x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) is a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (- 2, 11)

m = [tex]\frac{11-5}{-2-0}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3

Use either of the 2 given points for (a, b)

Using (a, b) = (- 2, 11), then

y - 11 = - 3(x - (- 2)), that is

y - 11 = - 3(x + 2)

Answer:

Options A and B.

Step-by-step explanation:

An ellipse is represented by the equation [tex]\frac{(x+5)^{2}}{625}+\frac{(y-7)^{2}}{49}=1[/tex]

We have to find the foci of the given ellipse.

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

Then center of this ellipse is represented by (h, k) and foci as (c, 0) and (-c, 0).

And c is represented by c² = a² - b²

So we co relate this equation with our equation given in the question.

a = √625 = 25

b = √49 = 7

and c² = (25)² - (7)²

c² = 625 - 49 = 576

c = ±√576

c = ±24

Now we know center of the ellipse is at (-5, 7) so foci can be obtained by adding and subtracting x = 24 from the coordinates of the center.

Center 1 will be [(-5+24=19), 7] ≈ (19, 7)

Center 2 will be [(-5-24=-29), 7] ≈ (-29, 7)

Therefore, options A and B are correct.

Answer:

A and B

Step-by-step explanation:

Answer:

[tex]\sin( 115 \degree) = 0.906[/tex]

Step-by-step explanation:

The general point on a unit circle is given by

[tex]x = \cos( \theta) [/tex]

[tex]y = \sin( \theta) [/tex]

where

[tex] \theta = 115 \degree[/tex]

is the terminal side of the angle in standard position.

Therefore

[tex]x = \cos( 115 \degree) [/tex]

[tex]y = \sin(115 \degree) [/tex]

lies on this circle

This angle intersects the unit circle at

[tex]( - 0.423,0.906)[/tex]

Hence we must have

[tex] \cos( 115 \degree) = - 0.463[/tex]

[tex]\sin( 115 \degree) = 0.906[/tex]

Answer:

(-12,3)

Step-by-step explanation:

Since (6,3) is on the graph of f(x), then f(6)=3.

We want to see if we can use f(6)=3 to find a point on the graph of f(-1/2x).

If you compare -1/2x to 6, what must x be so they have the same value? x=-12.

If that wasn't obvious to you, just solve:

-1/2x=6

Multiply both sides by -2:

x=-12

So if we replace x with -12 in f(-1/2x) we get

f(-1/2*-12)

f(6)=3

And we were given this f(6)=3 so f(-1/2*-12)=3.

Answer:

h = 3+1.5x

Step-by-step explanation:

We start at a height of 3 inches

Then we growth at a rate if 1.5 inches per month, where x is the number of months

1.5x

Add them together

3+1.5x

The height is

h = 3+1.5x

Answer:

No this is not a solution

Step-by-step explanation:

Substitute the points in and see if the equation is true

-16 = 3(99) - -51

-16  = 297+51

-16 =348

False, so this is not a solution

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(500)(0.02)(3)\implies I=30~\hfill \stackrel{\textit{total amount in the account}}{500+30\implies 530}[/tex]

Answer:

[tex]\sqrt{7^{2}+5^{2}  }[/tex]

Step-by-step explanation:

Since the whole base of the triangle is 14, we can half it to find the base of one triangle which is 7.

Pythagoras Theorem states a² + b² = c²

In this case a² = 7 and b² = 5 so,

a² + b² = c²

a² = 7 and b² = 5

7² + 5² = c²

49 + 25 = c²

74 = c²

√74 = c

Answer:

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

Step-by-step explanation:

First we need to simplify your equation by grouping coefficients:

[tex]x^{2} +10x+23=0[/tex]

Now, there are two valid values for your variable, wich are determined by the following expressions:

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

We will call those expression as (eq1) and (eq2) in their respective order

In both scenarios the following is derived from your grouped equation.

[tex]a=1\\b=10\\c=23[/tex]

[tex]x1=\frac{-10+\sqrt{10^{2}-4*1*23 } }{2*1}\\x2=\frac{-10-\sqrt{10^{2}-4*1*23 } }{2*1}[/tex]

[tex]x1=\frac{-10+\sqrt{8 } }{2}\\\\x2=\frac{-10-\sqrt{8} }{2}[/tex]

We can simplify these expressions a little more by doing the following

[tex]x1=\frac{-10+2 \sqrt{2 } }{2}\\\\x2=\frac{-10-2\sqrt{2} }{2}[/tex]

The result is

[tex]x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}[/tex]

We can not simplify these expresions anymore

Answer:y=4x+11

Step-by-step explanation:

Substitute the coordinates in each of the above equations,

Then the left hand side of the equation should be equal to the right hand side of the equation.

By substituting the above coordinates in the second answer,

-1= 4(-3)+11

-1=-1

Answer:

b

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

According to the empirical rule:

So first we have to find how many standard deviations away from the mean are the given two values. This can be done by converting them into z scores.

The formula to calculate the z-score is:

[tex]z=\frac{\text{Data Value}-\text{Mean}}{\text{Standard Deviation}}[/tex]

Using the given values in above formula, we get:

For x = 2.3

[tex]z = \frac{2.3-2.9}{0.6}=-1[/tex]

For x = 3.5

[tex]z = \frac{3.5-2.9}{0.6}=1[/tex]

This means we have to tell how many data values are within one standard deviation of the mean. According to the empirical rule 68% of the values are between z= -1 and z = 1. So the answer is 68%

68% of students at the college have a GPA between 2.3 and 3.5.

The empirical rule states that for a normal distribution, 68% of the values falls within one standard deviation, 95% of the values falls within two standard deviation, and 99.7% of the values falls within three standard deviation.

Hence:

For a mean of 2.9 and a standard deviation of 0.6.

68% falls within 2.9 ± 0.6 = (2.3, 3.5)

68% of students at the college have a GPA between 2.3 and 3.5.

Find out more on empirical rule at: https://brainly.com/question/10093236

let's recall that, on the number line, for the positive side, the farther from zero, the larger the number, thus 100 is a much larger number than 10.

now, on the negative side of the number line, the farther from zero, the smaller the number, thus -1 is much much larger number than -1,000,000,000.

is -3 ≥ -15, is -3 larger or equals to -15, well, certainly is not equal but is certainly larger, yes.

Answer:

[tex]\Huge \boxed{10-N=8+N}[/tex]

Step-by-step explanation:

Difference: should be subtract.

N: should be a number.

Sum: Add

Therefore, the correct answer is 10-N=8+N.

Hope this helps!

Answer:

10-N=8+N

Step-by-step explanation:

10-N=8+N represents "the difference between ten and a number is the sum of eight and a number''.

You should go in order of PEMDAS:

P - parenthesis

E - exponents

M - multiplication

D - division

A - addition

S - subtraction

Answer:

see explanation

Step-by-step explanation:

The line with equation x = - 5

Is a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 5

Answer:

The correct answer is option 1)  (6,7)

Step-by-step explanation:

Points to remember

Mid point formula

Let (x₁, y₁) and (x₂, y₂) be the end points of a line segment, then the coordinates of the midpoint of the line segment is given by

[(x₁ + x₂)/2, (y₁ + y₂)/2]

To find the coordinates of B

Let A(x₁, y₁) =  (-4, 3), and M(1, 5)

Coordinates of B be (x₂, y₂)

We have,

[(x₁ + x₂)/2, (y₁ + y₂)/2] = (1, 5)

(x₁ + x₂)/2 = 1

(-4 + x₂)/2 = 1

-4 + x₂ = 2

x₂ = 2 + 4 = 6

(y₁ + y₂)/2 = 5

(3 + y₂)/2 = 5

3+ y₂ = 10

y₂ = 10 - 3 = 7

Therefore coordinates of B(6,7)

The correct answer is option 1)  (6,7)

Final answer:

The coordinates of point B, which lies diametrically opposite to A on circle M with a known center at (1, 5), are determined to be (6, 7).

Explanation:

Since segment AB is the diameter of circle M, and we know the coordinates of A (-4, 3) and center M (1, 5), we can find B by using the fact that the center of the circle is the midpoint of the diameter. The midpoint formula states that the midpoint M can be found using the following formulas:

Mx = (Ax + Bx) / 2

My = (Ay + By) / 2

Therefore, to find Bx and By, we can rearrange the formula:

Bx = 2Mx - Ax

By = 2My - Ay

Solving this gives us B as:

Bx = 2(1) - (-4) = 6

By = 2(5) - 3 = 7

So the coordinates of point B are (6, 7).

Answer:

Step-by-step explanation:

What he did at the end of the given equations is solve for x in x + 8y= 21

x = 21 - 8y                Substitute that result in the top equation.

7(21 - 8y) + 5y = 14  is the correct step To continue Remove the brackets

147 - 56y + 5y = 14   Combine

147 - 51y = 14             Add 51y to both sides.

147 = 51y + 14            Subtract 14 from both sides.

133 = 51y                   divide by 51

y = 2.61 rounded.

The incorrect step is underlined and italicized.

Answer:

21

Step-by-step explanation:

To find the greatest common factor between a set of numbers, you can list the factors of those numbers and find the largest one they each have in common.

A factor of a number is a number which can be multiplied against another number to get your original number.

Factors of 21: 1, 3, 7, 21

Factors of 63: 1, 3, 7, 9, 21, 63

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

21 is the greatest factor which all three have in common.

Answer:

21

Step-by-step explanation:

GCF of 21, 63 and 105

Break these numbers into prime factors

21 = 3*7

63 = 9*7 = 3*3*7

105 = 15*7 = 3*5*7

There is a 3, 7 in  all the terms

The largest number of 3's in the terms is 1

The largest number of 7's is 1

Multiply the largest number of terms together

3*7 =21

Answer:

graph 2

Step-by-step explanation:

It is partially written in Slope-Intercept Form [y = mx + b]. That 2 tells you to move up two units.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

The graph of f(x) +2 graph 3.

 since  y-intercepts is 2

The answer is option C

            slope(m)=tan∅=y axis/x axis.

Learn more about the straight lines here:-https://brainly.com/question/14323743

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Answer:

The x-intercepts are (5,0) and (7,0)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(6,-5)

substitute

[tex]y=a(x-6)^{2}-5[/tex]

Find the coefficient a

with the y-intercept (0,175) substitute the value of x and the value of y in the equation

For x=0, y=175

[tex]175=a(0-6)^{2}-5[/tex]

[tex]175=36a-5[/tex]

[tex]36a=180[/tex]

[tex]a=5[/tex]

substitute

[tex]y=5(x-6)^{2}-5[/tex]

Find the x-intercepts

Remember that the x-intercepts are the values of x when the value of y is equal to zero

For y=0

[tex]0=5(x-6)^{2}-5[/tex]

[tex]5(x-6)^{2}=5[/tex]

simplify

[tex](x-6)^{2}=1[/tex]

square root both sides

[tex]x-6=(+/-)1[/tex]

[tex]x=6(+/-)1[/tex]

[tex]x=6(+)1=7[/tex]

[tex]x=6(-)1=5[/tex]

therefore

The x-intercepts are (5,0) and (7,0)

Answer:

[tex]4(2+\sqrt{2})\text{ square unit}[/tex]

Step-by-step explanation:

Given function that shows the area of the opening,

[tex]A(\theta)=16 \sin\theta (\sin \theta + 1)[/tex]

If [tex]\theta = 45^{\circ}[/tex]

Hence, the area of the opening would be,

[tex]A(45^{\circ})=16 \sin 45^{\circ} (\cos 45^{\circ} + 1)[/tex]

[tex]=16\times \frac{1}{\sqrt{2}}\times (\frac{1}{\sqrt{2}}+1)[/tex]

[tex]=16(\frac{1}{2}+\frac{1}{\sqrt{2}})[/tex]

[tex]=8+\frac{16}{\sqrt{2}}[/tex]

[tex]=8+4\sqrt{2}[/tex]

[tex]=4(2+\sqrt{2})\text{ square unit}[/tex]

Answer:

[tex]5x^2 y^2[/tex]

Step-by-step explanation:

We need to use the properties shown below to solve this:

1. [tex]\sqrt[n]{x^a} =x^{\frac{a}{n}}[/tex]

2. [tex]\sqrt{x}\sqrt{x}  =x[/tex]

3.  [tex]\sqrt{x} \sqrt{y}=\sqrt{x*y}[/tex]

Area of a triangle is given by  1/2 * base * height, so we do that and simplify:

[tex]A=\frac{1}{2}(\sqrt{5x^3} )(2\sqrt{5xy^4} )\\A=\frac{1}{2}(5x^3)^{\frac{1}{2}}*2*(5xy^4)^{\frac{1}{2}}\\A=\sqrt{5}x^{\frac{3}{2}}*\sqrt{5}\sqrt{x} }  y^2\\A=\sqrt{5} \sqrt{5}x^{\frac{3}{2}} x^{\frac{1}{2}}y^2\\A=5*x^2y^2\\A=5x^2 y^2[/tex]

Answer:

Step-by-step explanation:

Later on in the course, I hope you are told that answers should not rely on diagrams.

Since you have to answer the question somehow, the answer (directly) is BCA. Since this is an appearance question (that's what the answer looks like), you can only state the answer, There really (in this case) is no what to offer a proof).

Answer:

[tex] \sqrt{2}[/tex]

Step-by-step explanation:

You can multiply by sqrt 6/sqrt 6 to get rid of the sqrt in the denominator. This leaves you with 2(sqrt 3)(sqrt 6)/sqrt 36. The sqrt's in the numerator can be multiplied to get 2(sqrt 18). The sqrt 36 can be simplified to just 6. Sqrt 18 can be split into sqrt 9 and sqrt 2. The sqrt 9 can be taken out and simplified as 3. 3x2=6. This leaves you with 6(sqrt 2)/6. The 6 in the numerator cancels the 6 in the denominator and just leaves sqrt 2.

Answer:

aaaaaaaaaaa

Step-by-step explanation:

Answer:

The correct option is 32

Step-by-step explanation:

The given expression is:

m∠1 = 3y – 6

m∠1= 90°

Now arrange the value of angle in the given equation:

3y-6=90

Move the constant to the R.H.S

3y= 90+6

3y= 96

Now divide both the terms by 3

3y/3=96/3

y=32

Thus the correct option is 32....

Answer:

x = 2.9.

Step-by-step explanation:

14.3 - 0.4x = 2.6x + 5.6​

14.3 - 5.6 = 2.6x + 0.4x

8.7 = 3x

x = 8.7 / 3 = 2.9 (answer).

Answer:

x=2.9

Step-by-step explanation:

14.3 -0.4x = 2.6x + 5.6​

Add .4x to each side

14.3 -0.4x+.4x = 2.6x+.4x + 5.6​

14.3 = 3x+5.6

Subtract 5.6 from each side

14.3 - 5.6 = 3x - 5.6

8.7 =3x

Divide each side by 3

8.7/3 = 3x/3

2.9=x

Answer:

A(x+2)(x-3)(x+6) where A is a constant.

If you want to change the order in that multiplication you can.

Read answer for my options on what your answer could look like.

Let me know the choices or if you have any questions.

Step-by-step explanation:

It says which like you have choices...

But I can give you several polynomials with those zeros.

By factor theorem if you have -6 is a zero then x+6 is a factor.

By factor theorem if you have -2 is a zero then x+2 is a factor.

By factor theorem if you have  3 is a zero then x-3 is a factor.

So a polynomial with those factors I mentioned is:

(x+6)(x+2)(x-3)

or

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

or

-12(x+6)(x+2)(x-3)

or

1.4(x+6)(x+2)(x-3)

and so on....

I guess you could also say

4(x+6)(x+2)(x-3)^3.

It didn't say it had to have this multiplicity of 1.

Anyways I think you are probably looking for an option that says something like this:

A(x+6)(x+2)(x-3)

where A is a constant.

Keep in mind multiplication is commutative so it could be written as

A(x+2)(x-3)(x+6) or something similar to that.

Answer:

(20+x)*2=x-6

40+2x=x-6

40=-x-6

46=-x

check:

x=-46

20-46*2=-46-6

-26*2=-52

-52=-52

x=-46

Answer:

x1=-14;x2=-26

Step-by-step explanation:

|x+20|=6

x+20=6

x+20=-6

Answer:

The correct answer is last option 78.5%

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r is the radius of circle

Area of square = a²

Where 'a' is the side length of square

To find the area of circle

Here r = 10 cinches

Area =  πr²

 =  3.14 * 10²

 = 3.14 * 100 = 314

To find the area of square

Here a = 20 inches

Area = a²

 = 20²

 = 400

To find the probability percentage

Probability = area of circle/Area of square

 = (314/400)*100

 78.5 %

Answer:

Step-by-step explanation:

2x3 out of 10x5+4x4+8x3.2x3(5x2+2x+4)

Answer:

2*5*5 +2*2*2*2 + 2*2*2*3

Step-by-step explanation:

Answer:

Hi there!

The answer to this question is: C. -3/2

Step-by-step explanation:

You first find the slope of the equation using the change of y over the change of x formula. You should get 2/3. Then it asks its perpendicular that is simply the negative reciprocal of the original slope. All you do is flip the fraction and make it negative, your final answer should be -3/2

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 3)

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

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] → C