Which value of a makes the equation true?

Answer:

[tex]y = \frac{2}{3} x + 2[/tex]

Step-by-step explanation:

Start by finding the slope of the given line.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Slope of given line

[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]

[tex] = \frac{5 + 1}{ - 4} [/tex]

[tex] = \frac{6}{ - 4} [/tex]

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

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

[tex] - \frac{3}{2} m = - 1[/tex]

[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]

[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]

[tex]m = \frac{2}{3} [/tex]

[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]

Midpoint of given line

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

[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]

= (0, 2)

[tex]y = \frac{2}{3} x + c[/tex]

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].

There's something very off about this question.

In spherical coordinates,

x² + y² + z² = ρ²

so that

f(x, y, z) = 6 - (x² + y² + z²)

transforms to

g(ρ, θ, φ) = 6 - ρ²

When transforming to spherical coordinates, we also introduce the Jacobian determinant, so that

dV = dx dy dz = ρ² sin(φ) dρ dθ dφ

Since we integrate over a sphere with radius 4, the domain of integration is the set

E = {(ρ, θ, φ) : 0 ≤ ρ ≤ 4 and 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π}

so that the integral is

[tex]\displaystyle \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 - \rho^2) \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]

Computing the integral is simple enough.

[tex]\displaystyle = \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]

[tex]\displaystyle = 2\pi \int_{\phi=0}^{\phi=\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\phi[/tex]

[tex]\displaystyle = 2\pi \left(\int_{\phi=0}^{\phi=\pi} \sin(\phi) \, d\phi\right) \left(\int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \, d\rho\right)[/tex]

[tex]\displaystyle = 2\pi \cdot 2 \cdot \left(-\frac{384}5\right) = \boxed{-\frac{1536\pi}5}[/tex]

but the mass can't be negative...

Chances are good that this question was recycled without carefully changing all the parameters. Going through the same steps as above, the mass of a spherical body with radius R and mass density given by

[tex]\delta(x, y, z) = k - (x^2 + y^2 + z^2)[/tex]

for some positive number k is

[tex]\dfrac{4\pi r^3}{15} \left(5k - 3r^2\right)[/tex]

so in order for the mass to be positive, we must have

5k - 3r² ≥ 0   ⇒   k ≥ 3r²/5

In this case, k = 6 and r = 4, but 3•4²/5 = 9.6.

i think that the answer is 0 because f(2) means that you substitute 2 for x

2(2)=4

4-4=0

Answer:

in8− in4+ in2

Step-by-step explanation:

thats the aswer

Answer:

[tex]Understand \: how \: to \: work \: with \: negative \: bases \\ \: and \: negative \: exponents. \\

\bold{answer - } \\ {5}^{2} = 5 \times 5 = 25 \\ {5}^{ - 2} = \frac{1}{ {5}^{2} } = \frac{1}{25} = 0.04 \\ {( - 5)}^{2} = ( - 5) \times ( - 5) = 25 \\ - {5}^{2} = ( - 5) \times ( - 5) = 25 \\ \\ \bold \purple{hope \: it \: helps \: ♡}[/tex]

Answer:

£55

Step-by-step explanation:

50% is just another way to say 1/2. This means that 1/2 of £110 is £55.

Answer:

80

Step-by-step explanation:

1.To know this answer, we need to know some vocabulary that's used in t. Most people don't know how to solve questions if they have hard Vocabulary and what the question is Asking

Mean=The average of all his throws

It's asking us to calculate his total score  

2. Find Clues to help you solve word problems

Finding clues in Word Problems is a very important part a lot of people skip but this helps you solve the question easier

5 throws and Mean Score is 32 are the clues

3. Guess and check

The method to this thingy is called guess and check. There is another method which is slightly harder and i just don't want to do it.

Let's just say his scores were... 5, 6, 4, 5,10Add them up and you get 30Then 30/5

Let's try bigger numbers

20+25+20+20

If you like this method, you may try it another method is called work Backwards

5x32=160

Then divide 160 by 5 to double check and you get 32!!

========================================

Therefore, the answer s 160 as his total score

hope this gives you a clue to what we are doing and when you have a question like this, I really hope you understand the concept

Hope this helped (:

Answer:

See explanation

Step-by-step explanation:

Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)

G (-1, 3)  G' (-1.5, 4.5)

F (-2, -2)  F' (-3, -3)

G'x / Gx = -1.5/-1 = 1.5

G'y / Gy = 4.5 / 3 = 1.5

F'x / Fx = -3 / -2 = 1.5

F'y / Fy = -3 / -2 = 1.5

Answer:

[tex] \frac{2}{5} > \frac{1}{6} [/tex]

Answer: B. >

#CarryOnLearning

Answer:

80

Step-by-step explanation:

25 percent is equal to 1/4

1/4 of 80 is 20

Answer:

80

Step-by-step explanation:

Answer:

Step-by-step explanation:

Linear equations can have the form y = mx + b

where m is the slope of the line and equals Δy/Δx

and b is the y intercept.

Just for fun, let's choose the first and last sets of data points.

Δy = (275 - 135) = 140

Δx = (5 - 1) = 4

so slope m = 140/4 = 35    and the units on the slope would be $/month

Answer:

The slope of the line is 35

Step-by-step explanation:

We'll select [tex](1,135)[/tex] and [tex](2,170)[/tex] for this problem.

The slope is defined as the rate of change. Its formula is [tex]Slope=m=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}[/tex] where our two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

Therefore, we have [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{170-135}{2-1}=\frac{35}{1}=35[/tex] as our slope.

Answer:

8p - 11

Step-by-step explanation:

Got the same I-Ready question lol

a) The equation is therefore; x³ + 3x² + 2x = 336

b) Solving for the length, we get the length to be; x = 6.

c) All workings are as shown below;

According to the question;

In essence, the volume of the original prism is;

Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.

a) The equation is therefore;

b) Solving for the length, x is as follows;

By testing values and checking;

c) All workings are as shown above.

Read more on cubic equation:

https://brainly.com/question/8878887

Answer:

it is c

Step-by-step explanation:

Answer:

Simple Interest: A=P(1+rt)

A=15000(1+(0.1*4.2))

A=$21,300

Compound Interest:A=P(1+r/n)^nt

A=15000(1+0.1/4.2)^1*4.2

A=$64,500

Step-by-step explanation:

Factorization involves breaking down an expression.

The sum of cubes is given as:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

(a) Verify the formula

Expand the expression on the right-hand side

[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]

Collect like terms

[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]

[tex](a^3 + b^3) = a^3 + b^3[/tex]

The formula has been verified

(b) Factorized 8x^3+ 27

We have:

[tex]8x^3 + 27[/tex]

Express 27 as 3^3

[tex]8x^3 + 27 =8x^3 + 3^2[/tex]

Express 8 as 2^3

[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]

Rewrite as:

[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]

Given that:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

The expression becomes

[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]

[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]

(c)The other factor of 2^3 - b^3

By difference of cubes, we have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

So, the equation becomes

[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]

This gives

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

Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]

(c) Factor x^3 - 1

We have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

Express 1 as 1^3 in x^3 - 1

[tex]x^3 - 1 =x^3 - 1^3[/tex]

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes

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

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

Read more about factorization at:

https://brainly.com/question/43919

Answer:

5

Step-by-step explanation:

You divide your number by the denominator and then times it by the numerator

Answer:

The total number of batches of pancakes that Kim can make with  the model is 4 batches of pancake

Step-by-step explanation:

Number of cups of pancakes = 2/4

Number of cups of almonds to make a batch of pancakes = 1/8

Therefore, the batches of pancakes that she can make will be:

= 2/4 ÷ 1/8

= 2/4 × 8/1

= 4

In conclusion, the number of batches of pancakes that Kim can make with the cup of almonds is 4 batches.

56 + 8x

Area of Rectangle = Length x Width

Area of Rectangle = 8(7 + x)

113

Hope this helped you- have a good day bro cya)

A

Step-by-step explanation:

the origin, (0, 0)

For center of dilation Q, the image of a point A after dilation by a factor of k is ...   A' = kA + (k-1)Q Then for points A, A', and dilation factor k, the center of dilation can be found to be ...   (A' -kA)/(k-1) = Q

Here, that is ...   Q = ((-2, -2) -(1/2)(-4, -4))/(1/2 -1) = (0, 0)/(-1/2)  

Q = (0, 0) 

Answer:

a1=21

an=an-1+6

Step-by-step explanation:

Answer:

2 feet: $18

4 feet: $36

5 feet: $45

$81 = 4.5 feet

10 feet = $90

Step-by-step explanation:

2 feet: $18

4 feet: $36

18 + 18

5 feet: $45

18 + 18 + 9

$81 = 4.5 feet

81/18

10 feet = $90

18 + 18 + 18 + 18 + 18

Answer: c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

63 degrees

Step-by-step explanation:

The hint tells you that you can add the other 2 angles in the triangle to get the answer.

Answer:

72

Step-by-step explanation: