If p - q = 4 and p² - q² = 24, what is the value of p + q?

Answer:

6 + (-15)

Step-by-step explanation:

6 - 15 would also be written as 6 + (-15). If you distribute the '+' into the '-15', you would get the negative 15.

1 * -15 = -15

So, 6 + (-15) would be the equivalent addition expression​.

Hope this helps.

Answer: The axis of symmetry is x=3.

Answer:

[tex](-\infty,-9)\cup(-9,\infty)[/tex]

Step-by-step explanation:

The domain of a rational function is all real numbers except for when the denominator equals 0.

So, to find the domain restrictions, set the denominator to 0 and solve for x.

We have the rational function:

[tex]s(y)=\frac{7y}{y+9}[/tex]

Set the denominator to 0:

[tex]y+9=0[/tex]

Subtract 9:

[tex]y\neq-9[/tex]

So, the domain is all real numbers except for -9.

In other words, our domain is all values to the left of negative 9 and to the right of negative 9.

In interval notation, this is:

[tex](-\infty,-9)\cup(-9,\infty)[/tex]

And we're done :)

Answer:

b. none

Step-by-step explanation:

All the other answers have the number 8 in it which the equation does not have.

Answer:

first week = m miles

second week = 6 miles less than triple the number of miles they ran the

first week.

Triple of the number of miles they ran the first week = 3 * m = 3m

Therefore = 3m - 6

Answer: -4

Step-by-step explanation: f(x)= 3x - 5 | f(x) = -17

If you write the equation in this form: -17 = 3x-5 Than add +5 to each side and divide it by 3 you'll get x=-4 Which is definitely the answer.

Answer:

n= 3 and n = -3

Step-by-step explanation:

In general

|n| = a <=> n = a or n= -a (for n and a are real numbers)

Answer:

50

Step-by-step explanation:

Given

there is 1 water station at every 0.3 KM

If there are n water stations at every 0.3 KM

then KM covered by them = n*0.3 = 0.3n

given that total KM covered is 15 km

Thus,

0.3n = 15

=> n = 15/0.3 = 50

Thus, there are 50 water stations.

Answer:

-7× 2 +3= 17

-7×0+3=3

-7×5+3= -32

The required evaluated values of f(x) = -7x+3 would be 17, 3, -32 respectevily when substitute the values  x = -2, x = 0, and x = 5.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been the given expression:

f(x) = -7x+3

To determine the evaluated values of  g(x) = 3x when x = -2, x=0, and x=5

We have to substitute x with the given number.

⇒f(x) = -7x+3

Substitute the value of x = -2 in the f(x) = -7x+3

⇒ f(-2) = -7× 2 +3

⇒ f(-2) = 17

Substitute the value of x = 0 in the f(x) = -7x+3

⇒ f(0) = -7×0+3

⇒ f(0)  =3

Substitute the value of x = 5 in the f(x) = -7x+3

⇒ f(5) = -7×5+3

⇒ f(5) = -32

Hence, the required evaluated values of f(x) = -7x+3 would be 17, 3, -32 respectevily when substitute the values  x = -2, x = 0, and x = 5.

Learn more about the algebraic expression here :

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Answer:

b

Step-by-step explanation:

Answer:

The equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.

Step-by-step explanation:

Market equilibrium occurs in those markets in which the quantity demanded by consumers equals the quantity supplied by firms. In this state, the equilibrium point has its corresponding equilibrium quantity and price. That is, the equilibrium point is that point where, for a given price, the quantity supplied is equal to the quantity demanded.

The supply and demand curves represent the quantities that consumers are willing to buy and producers are willing to sell at that price respectively.

Being:

Since when the market reaches equilibrium, the quantity demanded equals the quantity supplied and x representing the quantity demanded in units of thousand, then:

[tex]\frac{50 - p}{6}=\frac{p-14}{6}[/tex]

Solving, you get:

[tex]6*\frac{50 - p}{6}=p-14[/tex]

50 - p= p -14

50 - p +14 = p

50 +14= p + p

64= 2*p

[tex]p=\frac{64}{2}[/tex]

P=32 dollars

This value is the equilibrium price. Replacing this value in the demand and supply equation, the equilibrium quantity is obtained, which should be the same for both cases:

So, the equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.

In its graphical representation, the equilibrium point can be seen as that point where the supply and demand curves intersect. You can see this in the attached image, where the blue line represents the supply and the red line the demand.

Answer:

D

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 12 when x = 6, thus

- 12 = 6k ( divide both sides by 6 )

- 2 = k

y = - 2x ← equation of variation

When y = - 4, then

- 4 = - 2x ( divide both sides by - 2 )

2 = x → D

Answer:

Step-by-step explanation:

[tex]x^3 \times y^4\\\\x = 3\\y =0 \\\\(3)^3\times 0^4\\\\3^3\times\:0^4\\\\\mathrm{Apply\:rule}\:0^a=0\\0^4=0\\\\=3^3\times\:0\\\\\mathrm{Apply\:rule}\:0\times\:a=0\\=0[/tex]

Answer:

We need to calculate [tex]x^3*y^4[/tex] for x = 3 and y = 0.

First thing we do is replacing x and y on [tex]x^3*y^4[/tex]:

[tex]3^3*0^4[/tex]

Now, we only need to solve it:

[tex]3^3*0^4[/tex] = [tex]27 * 0[/tex] = [tex]0[/tex]

Remember that [tex]3^3 = 3*3*3[/tex]

Answer:

Linear Function

Step-by-step explanation:

Given

The table showing values of x and y

Required

Determine the type of function

To determine the type of function, the table represents;

One will need to determine the table equation.

Start by solving for the slope;

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

When x - 0; y = 0 and When x = 80; y = 60.

This gives

[tex]m = \frac{0 - 60}{0 - 80}[/tex]

[tex]m = \frac{- 60}{- 80}[/tex]

[tex]m = \frac{3}{4}[/tex]

The formula is determine as follows;

[tex]y - y_1 = m(x - x_1)[/tex]

When x - 0; y = 0; m = 3/4; This gives

[tex]y - 0 = \frac{3}{4}(x - 0)[/tex]

[tex]y = \frac{3}{4}(x - 0)[/tex]

Open Bracket

[tex]y = \frac{3}{4}x - 0[/tex]

[tex]y = \frac{3}{4}x[/tex]

The above is an example of a linear equation.

Hence; option B answers the question

Step-by-step explanation:

A)y=8

B)k=10

5y=72-32

5y=40

y=8

1/2k+24=29

k+48=58

k=58-48

k=10

Answer:

2j²/5

Step-by-step explanation:

We know that j has to be squared so j², and to find 2/5's of that number we need to multiply it by 2/5.

j²×(2/5)

Now to simplify it we can multiply the j² to the numerator.

2j²/5

Answer:

Ok so...

Mean: 68.76

Median: 72

Range: 85

Step-by-step explanation:

Answer:

Yeah

Step-by-step explanation:

Hope that helped

Answer:

3 or 4

Step-by-step explanation:

Answer:

6 m and 18 m

Step-by-step explanation:

There are 2 similar triangles in the diagram

lamppost/ lamppost's shadow/ line from end of shadow to top of lamppost

Nick/ Nick's shadow/ line from end of shadow to top of Nick

Therefore the ratios of corresponding sides are equal.

Note the shadow of the lamppost = 12 + x, thus

[tex]\frac{6}{2}[/tex] = [tex]\frac{12+x}{x}[/tex] ( cross- multiply )

6x = 2(12 + x) = 24 + 2x ( subtract2x from both sides )

4x = 24 ( divide both sides by 4 )

x = 6

Thus

Nick's shadow is 6 m long

Lamppost's shadow is 12 + 6 = 18 m long

If a < b, then dividing both sides by a positive number will not flip the inequality sign. The inequality flips if you divide both sides by a negative number.

So if a < b, then a/3 < b/3 as well.

Answer:

5ft

Step-by-step explanation:

because you divide the quotent the the base and the reslut is divided by the top left and the left

Answer:

The value is 4

Step-by-step explanation:

This is because the value of an absolute number is always positive so the absolute value of 4 would remain 4.

Answer: 4

Step-by-step explanation: The absolute value is how far a number is away from 0

So, there are 3 more "parts" of students than of adults (5 - 2), right?

Those 3 parts are made up of 12 people.

12/3 = 4 people per part

2(4) = 8 adults

5(4) = 20 students

Answer:

2/5=8

Step-by-step explanation:

Answer:

[tex]x > 3[/tex]

Step-by-step explanation:

[tex]x - 5 > - 2 \\ x > - 2 + 5 \\ x > 3[/tex]

First you collect like terms

Then you add

Answer:

[tex]t \leq 63[/tex]

Step-by-step explanation:

Quotient of two numbers also means the result of the two numbers after division.

If the quotient of a number t and 4.2 is at most 15., this can be expressed using the inequality;

[tex]\dfrac{t}{4.2}\leq 15[/tex] (note that at most 15 means that the highest value we can have is 15 after taking the quotient of the number hence the reason of the inequality sign.)

On solving the inequality for the variable t

[tex]\dfrac{t}{4.2}\leq 15\\\\multiply \ both \ sides \ by \ 4.2\\\\\dfrac{t}{4.2}* 4.2\leq 15 * 4.2\\\\t \leq 63[/tex]

Hence t is at most 63

Answer:

y = 393.75

Step-by-step explanation:

Proportions:

84 ⇔ 16

y   ⇔ 75

y = 75*84/16

y = 393.75

Answer:

-3/5

Step-by-step explanation:

-8/15 + (-1/15) = -8/15 - 1/15 = -9/15 = -3/5

Answer:

c. Square Root

If you want me to explain, let me know!

Answer:

$10,700

Step-by-step explanation:

The total cost of the boat if Jacob makes all of his payments on time is $10,300

The total cost of the boat is the sum of the total amounts paid less the amount refunded for swift payment

Total amount paid = $800 + ($275 x 36) =

$800 + $9900 = $10,700

Amount refunded = 400

Total cost = $10,700 - $400 = $10,300

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