Evaluate A^2-B^2 for A=3 and B=-4.

Answer:

[tex]\fbox{\begin{minipage}{16em}Option D: y = (4/7)x + 8 is correct\end{minipage}}[/tex]

Step-by-step explanation:

(1) A typical form of equation of a line is:

[tex]y = Mx + b[/tex]

with, [tex]M[/tex] is slope and [tex]b[/tex] is y-intercept.

(2) Another straight line has equation in form of:

[tex]y = Nx + c[/tex]

with [tex]N[/tex] is slope and [tex]c[/tex] is y-intercept

(3) If these two lines are perpendicular, according to the property of two perpendicular lines on the two-dimensional plane, we have:

[tex]M[/tex] x [tex]N[/tex] = -1

(4) Transform the given equation of original line into typical form:

      [tex]7x + 4y = -24\\[/tex]

<=> [tex]4y = -7x - 24[/tex]

<=>  [tex]y = (\frac{-7}{4})x - \frac{24}{4}[/tex]

<=> [tex]y = (\frac{-7}{4})x - 6[/tex]

=> [tex]M = \frac{-7}{4}[/tex]

=> [tex]N = \frac{-1}{M} = \frac{-1}{\frac{-7}{4} } = \frac{-4}{-7} = \frac{4}{7}[/tex]

=> Option D: [tex]y = (\frac{4}{7})x + 8[/tex] is correct (Slope = [tex]\frac{4}{7}[/tex])

Hope this helps!

:)

Answer:

-1/4

Step-by-step explanation:

Multiplicative inverse is another word for reciprocal

It is the number you multiply by to get 1

-4 * x = 1

Divide each side by -4

x = 1/-4

x = -1/4

Answer:

- 1/4

Step-by-step explanation:

- 4 * x = 1

= - 1/4

Hope this helps!

Answer:

(4x-1)(4x-1)

(x-6)(x+5)

(3x-7)(3x+7)

(3x-1)(x+6)

Step-by-step explanation:

yes

Answer:

m<1=120

Step-by-step explanation:

A linear pair adds up to 180 degrees.

So <1+<2=180

Let <2=X, that would make <1=2X because <1 is 2 times more.

So substitute that into the equation.

2x+x=180.

Combine like terms and get 3x=180

Divide both sides by 3 and get x=60.

Substitute that into <1 and get <1=120

a= 34 degrees

b= 28 degrees

c= 62 degrees

Step-by-step explanation:

First you know that b is 1/2 of 56 degrees or 28.

The triangle with the a in it is isoceles because the two sides are both radii.

In the triangle the top angle = 112 because it is a centeral angle to the 112 arc.

Angle a and opposite to a are equal and then have to be 34 degrees to equal 180.

We know two arc lengths are 112 and 56 and the one with angle a has to be 34x2 or 68.

a whole circle equals 360.

360-56-68-112 = 124

Angle c = 1/2 of 124, or 62 degrees

Answer:

Between 1997 and 2004, Baffin Bay’s polar bear population  

decreased

.

528 is about  

25

percent of 2074.

Step-by-step explanation:

Answer:

decreased

25

Step-by-step explanation:

Answer:

x=40

Step-by-step explanation:

The 2 angles are opposite each other. Therefore, they are vertical angles. This means the 2 angles are equal. So, we can set them equal to each other.

120=3x

We want to find out what n is. In order to do this, we have to get n by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

x is being multiplied by 3. The opposite of multiplication is division. Divide both sides by 3.

120/3=3x/3

120/3=x

40=x

x is equal to 40.

Answer:

40

Step-by-step explanation:

i had this a while ago

Answer:

The price before the increase was £21.20

Step-by-step explanation:

Now, let the former price before the increment be £x

The increment would be 22-x

Mathematically, the percentage increment = difference between the prices/old price * 100%

Thus, we have(

(22-x)/x * 100 = 4

100(22-x) = 4x

2200-100x = 4x

100x + 4x = 2200

104x = 2200

x = 2200/104

x = 21.154

which is x = 21.2 to the nearest penny

Answer:

21.15

Step-by-step explanation:

22 × 10 = 220

100%+4%=104

104 ÷ 10 = 10.4

220 ÷ 10.4 =21.15384615

To the nearest penny it would be 21.15

Answer:

option c. 10.2%

Step-by-step explanation:

Number of visitors to Alec's website in February = 1,544

Number of visitors to website in March = 1,386

Number of decreasing members = 1544 - 1386 = 158 visitors

decrease percentage = [tex]\frac{\text{number of decreasing members}}{\text{number of previous members}}\times 100[/tex]

                                    = [tex]\frac{158}{1544}\times 100[/tex]

                                    = 10.233 ≈ 10.2%

percentage decrease of the number of visitors is 10.2%.

Option c. is the answer.

Answer:

0.25

Step-by-step explanation:

As a decimal, 0.25

As a fraction, 1/4

As a percentage, 25%

Answer:

0.25

Step-by-step explanation:

1/4

= 1*25/4*25

= 25/100

(Multiplying to both numerator and denominator doesn't change the value)

Now to write 25/100 as a decimal

The decimal point goes two places to the left in 25

(Since 100 has 2 zeroes so two values back)

25/100 = .25

= 0.25

Answer:

So you can divide by 2 for the picture. 4/2 = 2

So you can get 2 x 2 picture. The ratio would be 1

if you have a variable it would always be

x by x.

If you want to cover whole wall multiply by 4/3 on the 4 x 4 picture

The original needs to be scaled up by a factor of 75.

Given that, reproducing a 4 cm × 4 cm picture on a 3 m × 3 m wall.

We need to find what ratio we should use.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We know that 1 m=100cm, then 3 m=300 cm.

The picture on the wall is (300 cm)/(4 cm) = 75 times as large in each dimension as the original.

Therefore, the original needs to be scaled up by a factor of 75.

To learn more about the ratio visit:

https://brainly.com/question/13419413.

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c will prove that b is parallel

Answer:

The government loses $1000 per tax payer, according to the following function:

[tex]y(x) = -1000*x[/tex]

Where "y" is the total money earned by the government and "x" is the number of tax payers.

Step-by-step explanation:

Let's call the monetary balance of the government after one year "y", where "x" is the number of tax payers. Since each tax payer, "x", pays a total of $1500 every year, but the government spends $2500 with each one of them, then we can build a function "y(x)", with the value of collected tax being positive while the cost of each tax payer is negative, as shown below:

[tex]y(x) = 1500*x - 2500*x\\y(x) = x*(1500 - 2500)\\y(x) = -1000*x[/tex]

The government loses $1000 per tax payer.

Answer:

It's B. (2x+5) (x+4)

Answer:

b

Step-by-step explanation:

2x²+13x+20

You can just try all the answers if you'd like and see which one equals 2x²+13x+20.

Using FOIL for all of them:

a. (2x-5)(x-4) = 2x²-8x-5x+20 = 2x²-13x+20

b. (2x+5)(x+4) = 2x²+8x+5x+20 = 2x²+13x+20

c. (2x+2)(x+10) = 2x²+20x+2x+20 = 2x²+22x+20

d. is obviously not correct since we already have an answer.

Our answer is b. (2x+5)(x+4)

Answer:

1/3

Step-by-step explanation:

plug in 0 for x

0 * anything = 0 (cancels out the -2/9) and you're left with 1/3

Answer:

$ 11

Step-by-step explanation:

A game costs $ x.

Two games costs 2x.

50 + 2x = 72

2x = 72 - 50

2x = 22

x = 11

Answer: 9/4a^2|b^3|c^4

Step-by-step explanation:

81/16

Square root(81) = 9

Square root(16) = 4

9/4

Since 4 is the index of the radical, all of the exponents divide by 4

(index 4)a^8 = a^2

(index 4)b^12 = b^3

(index 4)c^16 = c^4

Now put the variables together to get the answer:

9/4a^2|b^3|c^4

Answer: £225

Step-by-step explanation:

Amount shared = £750

Let Sarah's share = y

Therefore,

Caroline's share = 3y

Bridget's share = 2(3y) = 6y

Mathematically,

y + 3y + 6y = £750

10y = £750

y = £750/10

y = £75

Caroline's share = 3y

Caroline's share = 3 × £75 = £225

Caroline's share is £225

Answer:

5.657

Step-by-step explanation:

Root 2=1.41421

1.41421 x 4 = 5.657

Answer:7^-2

Step-by-step explanation:

7^-1(7^5/7^6)=7^-1*7^(5-6)=7^-1*7^-1=7^(-1-1)=7^-2

Answer:

5

Step-by-step explanation:

The square root of a number is basically that number multiplied by itself.

for example, the square root of 4 is 2 because 2 x 2 is 4

the square root of 25 is 5 because 5 x 5 = 25

Answer:

root 25 = 5

Step-by-step explanation:

because when we will do the prime factorisation then at your left side 5x5 will come aand at right side will come so, 5x5 = 25 .

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Answer:

245/999

Step-by-step explanation:

0.245bar = n

1000 n - n = 245

999n = 245

n = 245/999

Answer:

31.6227766

Step-by-step explanation:

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Answer:

10,000 nickels

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Slope equation is (y2-y1)/(x2-x1)

(-1-4)/(2-3)

-5/-1

5

Answer:

D

Step-by-step explanation:

A is not true because from the graph, they make less money at $13 compared to $10 even though 13 > 10. B isn't true either because when the app price is more than $7 the profit decreases, not increases. D is true because the y-coordinate of the vertex (which is the maximum in this case) is about 40 million, and if we know the maximum already we know that C is false because 40 ≠ 7.

The solution to the inequality shown is -4 < n ≤ 5

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

From the inequality, we can see that:

n > -4 as well as n ≤ 5

Combining this two inequalities gives:

-4 < n ≤ 5

The solution to the inequality shown is -4 < n ≤ 5

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

Answer:

(- 2, 0 )

Step-by-step explanation:

Given

y = 2x² + 2x - 4

To find the x- intercepts let y = 0, that is

2x² + 2x - 4 = 0 ( divide through by 2 )

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

x- intercepts are x = - 2, x = 1, that is

(1, 0 ) and (- 2, 0 )

The other x- intercept is (- 2, 0 )

Answer:

18x = 90

x = 5

Step-by-step explanation:

Since it is a 90° angle, you can use 11x + 7x = 90

18x = 90

Answer:

32p

Step-by-step explanation:

Times between 8pm and 11.30 are:

8pm,9pm,10pm,11pm,11.30pm

Costs for associated times:

8pm: 12p

9pm: 12p

10pm : 12p

11pm: 8p

11.30 pm: 4p

Total/sum = 32p

Answer:

32P

Step-by-step explanation: