A line passes through points (0,k) and (2,0) and has a slope of -1.5.
What is the equation of the line?
What is the y-intercept?
What is the value of k?

Answer:

The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min

Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min

Step-by-step explanation:

\(\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}\)

The surface area of a sphere of radius r is given by:

\(\\S = 4\pi r^2\\\)

The rate of change of surface area is given by
\(\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\\)

\(\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}\)

We are given that \(\text{$\dfrac{dr}{dt}$}\) = 70 cm/min and asked to find rate of change of S when r = 40 cm

Substituting these values into the equation for \(\dfrac{dS}{dt}\)
\(\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min\)

In absolute values

Find the area of the base \(A=64\pi\).

Multiply area of the base by height to get volume

\(V=20\cdot64\pi=4021.24\)

Hope this helps.

Answer:

Peat's Pizza is is the one Tina should order from.

Step-by-step explanation:

If 4-pizzas from Peat's Pizza is 26 dollars, and she wants to order the 4 pizza special, Multiply 26 and 10 to get $260. Now if she wanted to order 4 times from Pizza Palace, which costs 75 dollars for 10 pizzas, Multiply the cost, 75, and the amount of times you want to order, to get the total cost. (Please tell me if I'm wrong! I'm trying to identify what I can.)

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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The mathematical model that represents the general price movement of mortgages is:     ΔPM = f(Δk, ΔPrin, ΔC)

Where ΔPM is the change in the price of the mortgage, Δk is the change in the required rate of return, ΔPrin is the change in the principal payment, and ΔC is the change in the interest payment.

This means that the change in the price of a mortgage is a function of the change in the required rate of return, the change in the principal payment, and the change in the interest payment.

The securities that are issued to financial institutions to increase liquidity in the secondary mortgage market by financing the origination of mortgages are:

Financial institutions may also receive private-label pass-through securities, although these are not guaranteed by government entities like Ginnie Mae, Freddie Mac, or Fannie Mae.

They are not backed by the government, but by private institutions, which can make them riskier.

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Answer:

y=-1

Step-by-step explanation:

14-(.5*30) same as dividing 30 by 2

14-15=-1   combine

Answer:

Step-by-step explanation:

Y=1

It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.

also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.

dunno if I explained it very well

The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is the inequality as -

x - 2y² < 12

The given inequality is -

x - 2y² < 12

2y² - x < - 12

2y² < x - 12

y² < (x/2) - 6

\($y < \pm\sqrt{\frac{x}{2}-6 }\)

\($y < \sqrt{\frac{x}{2}-6 }\)        

and

\($y < -\sqrt{\frac{x}{2}-6 }\)

Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.

Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

d

Step-by-step explanation:

The value of f(x) when x is 3 is 15

A Function in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For example, if f(x) = x² +2x +5 , the value of f(x) when x is 2 is calculated as;

f(x) = 2² + 2(2) + 5

f(x) = 4 +4+5

= 13

This done by substituting the given value of x into the expression.

Similarly , if f(x) = 5x, the value of f(x) when x is 3 is calculated as;

f(x) = 5(3)

f(x) = 15

therefore the value of f(x) when x is 3 is 15

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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Answer:

the oldest sister spent 2.70$ (given)

the middle sister spent 10.80$

and the youngest sister spent 7.12$

Step-by-step explanation:

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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The length of the hypotenuse of the triangle is b = x√2 units

Given data ,

Let the triangle be represented as ΔABC

And , the triangle is a 45 - 45 - 90 triangle

So , the two legs are congruent to one another and the non-right angles are both equal to 45 degrees

And , the sides are in the proportion x : x : x√2

Now , the length of the sides of the triangle are

The measure of base BC = a units = x

The measure of height AB = c units = x

So , the measure of the hypotenuse of the triangle is = x√2 units

Hence , the triangle is solved and hypotenuse AC = x√2 units

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hello

in the first question, we were asked 5 units to the left of 4

sice we are moving left, it would be negative value of 5

in the second question, we are moving 5 units right from point 4

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

2 cups you need to fill the jug to 4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

It depends on the size and markings of the jug.

If we assume that the jug is divided into equal intervals and each interval represents an equal volume,

then we can say that filling the jug to the second interval means that the jug is 1/2 full.

To fill the jug to the fourth interval, we need to fill the remaining 2 intervals, which means we need to add another 2 cups of liquid.

So, the answer is 2 cups.

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Answer:

Equation of line is \(\mathbf{y=-3x+3}\)

Option A is correct.

Step-by-step explanation:

We need to write an equation that represents the line that passes through the point (-1, 6) and has a slope of -3.

The equation will be of slope-intercept form: \(y=mx+b\)

where m is slope and b is y-intercept

We are given slope m =-3, we need to find y-intercept b

Finding y-intercept

using slope m=-3 and point (-1, 6)

\(y=mx+b\\6=-3(-1)+b\\6=3+b\\b=6-3\\b=3\)

So, y-intercept b is 3

Now the equation of line having slope m= -3 and y-intercept b = 3 is

\(y=mx+b\\y=-3x+3\)

Equation of line is \(\mathbf{y=-3x+3}\)

Option A is correct.

Answer:

a or the first one

Step-by-step explanation:

y=-3x+3

Step-by-step explanation:

A. 36÷3=12 $12 per ticket

B. 8.25÷3=2.75 $2.75 per ice-cream cone so do 2.75×2=5.50 $5.50 for 2 ice creams

C. 0.99÷3=0.33 $0.33 per banana so do 0.33×5=1.65

$1.65 for 5 bananas

HOPE THIS HELPS

The simplified expression based on tej values given is 3a⁴b + 4a³b³.

An expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.

It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:

a²b(3a² +4ab²) = 3a⁴b + 4a³b³

Therefore, the simplified expression is 3a⁴b + 4a³b³.

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Answer:

ujjjhhhggokkkkbfdxfghhhhbb

Answer: -26/15

Step-by-step explanation:

8+7 cause f(x) is 8

Answer:

Hey!!!!

the answers are 2, 6, 3, 12, 4, 1

Please read the explanation... it always helps..

Step-by-step explanation:

Alrighty... let's begin....

A factor is any number that you can multiply by another number to get a product

So choose the numbers you can mutiply by another number to get twelve... which are...  2, 6, 3, 12, 4, 1

if you are wondering why twelve well... 12 x 1 = 12

i hope this helps!!!!

Answer:

yes

Step-by-step explanation:

(1:2)x2=9/18

yes the ratios 9:18 and 1:2 equivalent

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

We need to check whether the ratios 9:18 and 1:2 are equivalent.

Equivalent ratios are the ratios that are the same when we compare them.

Two or more ratios can be compared with each other to check whether they are equivalent or not.

Here the two ratios are 9:18 and 1:2

We can write 9:18 as fraction 9/18

When we simplify it we get 1/2

Hence, yes the ratios 9:18 and 1:2 equivalent

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The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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SOLUTION

The given angle in radian is:

The angle is converted as follows:

The correct answer is 75 degree

Let's define:

y: new value

x: previous value

Given that the value of x is decreased by 40%, then:

Choice B represents the situation

Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units