Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?

y – 2 = 3(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y – 3 = 2(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y + y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis. = 3(x – 2)
y + y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis. = 2(x – 3)\

Answer:

They would have the same amount of baseball cards after 9 weeks/in 10th week

Answer:

-5 = 2x + 11

Step-by-step explanation:

3x - 5 = 5x + 11

→ Minus 5x from both sides

-2x - 5 = 11

→ Add 5 to both sides

-2x = 16

→ Divide both sides by -2

x = -8

Answer:

D. all real numbers

Answer:

the variables given in 1, 2, and 3 are independent variables

Step-by-step explanation:

the x in a question would be the independent variable

the y is dependent because it depends on what you put in the x

The maximum volume of the box is the highest volume the box can have.

(a) A model function V(w)

The dimension of the cardboard is given as:

\(\mathbf{l =12}\)

\(\mathbf{w =8}\)

Assume the cut-out is x.

So, we have:

\(\mathbf{l =12 - 2x}\)

\(\mathbf{w =8 - 2x}\)

\(\mathbf{h = x}\)

Make x the subject in \(\mathbf{w =8 - 2x}\)

\(\mathbf{x = \frac{8 - w}{2}}\)

The volume of the box is calculated as:

\(\mathbf{V = lwh}\)

Substitute expressions for l and h

\(\mathbf{V = (12 - 2x) \times w \times x}\)

Substitute \(\mathbf{x = \frac{8 - w}{2}}\)

\(\mathbf{V = (12 - 2\times (\frac{8 - w}{2})) \times w \times \frac{8 - w}{2}}\)

\(\mathbf{V = (12 - (8 - w)) \times w \times \frac{8 - w}{2}}\)

\(\mathbf{V = (12 - 8 + w) \times w \times \frac{8 - w}{2}}\)

\(\mathbf{V = (4 + w) \times w \times \frac{8 - w}{2}}\)

So, we have:

\(\mathbf{V(w) = (4 + w) \times w \times \frac{8 - w}{2}}\)

Hence, the model of the function is: \(\mathbf{V(w) = (4 + w) \times w \times \frac{8 - w}{2}}\)

(b) The graph of the function and the model function

In (a), we have:

\(\mathbf{V = (12 - 2x) \times w \times x}\)

Substitute \(\mathbf{w =8 - 2x}\)

\(\mathbf{V = (12 - 2x) \times (8 -2x) \times x}\)

So, we have:

\(\mathbf{V(x) = (12 - 2x) \times (8 -2x) \times x}\)

See attachment for the graphs of V(x) and V(w)

(c) The roots of V(x)

From the graph of V(x), the roots are:

\(\mathbf{x = 0,4,6}\)

These values represent the possible cut-outs from the cardboard

(d) The maximum volume

From the graphs of V(x) and V(w), the maximum volume is:

\(\mathbf{Maximum = 67.60}\)

And the width of the cut-out is:

\(\mathbf{Width= 1.569}\)

Hence, the maximum volume is: 67.60 cubic inches, and the width of the cut-out is 1.569 inch

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Answer:

(a−9b)(a2+b)

Step-by-step explanation:

In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

Answer:

The correct answer is -9, 36, -9/2

Step-by-step explanation:

Answer:

d=18 feet

Step-by-step explanation:

The volume of a sphere is represented by the equation \(V=\frac{4}{3}\pi r\)³, where r is the radius. If the volume is 972\(\pi\),

\(972\pi =\frac{4}{3}\pi r\)³

Divide \(\pi\) from each side,

\(972=\frac{4}{3} r\)³

Multiply each side by 3/4 to get rid of the fraction,

\(r\)³\(=729\)

Using the cube root, we find that 729 is actually a perfect cube.

\(r=9\)

Now, the diameter is 2 times the radius, so

9×2=18

So, the measure of the diameter is 18 feet.

The value of the equation is A = ( 3y + 3x ) / 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( x + y ) ( 3/ 4 )   be equation (1)

On simplifying the equation , we get

A = [ 3 ( x ) + 3 ( y ) ] / 4

Now , on further simplification , we get

A = ( 3y + 3x ) / 4

Hence , the equation is A = ( 3y + 3x ) / 4

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Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

Step-by-step explanation:

b

It takes about 16 years to reach the population size of 22000.

Population growth is the term used to describe changes in population size over time, which can be either positive or negative. The population growth formula is \(P=P_0\times e^{rt}\). Here, P is the total population size after time t, P₀ is the initial population size, r is the rate of growth, and e is Euler's number (e=2.72).

Given the total population, after time t is 22000, the initial population is 10000, and the rate is  5%.

Then, the time is calculated as,

\(\begin{aligned}22000&=10000\times e^{(0.05\times t)}\\\frac{22000}{10000}&=e^{(0.05\times t)}\\\ln(2.2)&=0.05\times t\\t&=\frac{0.788}{0.05}\\&=15.76\\&\approx16\end{aligned}\)

The time it takes to reach a population size of 22000 is 16 years.

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The function f^(-1)(P) allows us to find the time at which the population reaches a certain value, given the growth model provided by f(t).This means that the population will be 20 million in approximately 34.657 years.

We set P equal to f(t):
P = 10e^(0.02t)
ln(P/10) = 0.02t
t = (1/0.02) ln(P/10)
t = 50 ln(P/10)
f^(-1)(P) = 50 ln(P/10).

This function gives us the time (in years) at which the population is equal to P million. So, for example, if we want to know when the population is 20 million, we can plug P = 20 into the formula:
f^(-1)(20) = 50 ln(20/10) = 34.657

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Answer

650

explanation:

multiply the length value by 10

Answer:

Step-by-step explanation:

(1/2)(1/2)=1/4

Answer:

y = -\(\frac{1}{2}\)x + 8

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes, so the equation so far is:

y = -\(\frac{1}{2}\)x + b

To find our b (y-axis intercept) we will plug in the points given

(equation) y = -\(\frac{1}{2}\)x + b

(plug-in) 6 = -\(\frac{1}{2}\)(4) + b

(multiply) 6 = -2 + b

(add 2 to both sides) 8 = b

(answer) b = 8

(plug-in b) y = -\(\frac{1}{2}\)x + 8

Based on the number of pounds of butter that Hall has and the number of cups needed per fasnachts, the number of fasnachts Hall will be able to make is 36 fasnachts

First, find out the number of cups of butter than Hall has:

= 9 pounds x 2 cups per pound

= 18 cups

Then, find out the number of 3/4 cups in this amount of butter:
= 18 cups / 3/4

= 18 x 4/3

= 24 cups

The number of fasnachts that Hall can make are:

= 24 x 1.5 frozen fasnachts per cup

= 36 fasnachts

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56.55

If you round that up it would be:

56.6

-Have a good day.

Answer:

4

Step-by-step explanatio

Answer: 4

Step-by-step explanation:

jiubpuunuibu

Answer:

-0.123

Step-by-step explanation:

...............

Answer:

top table

Step-by-step explanation:

consider some key coordinate points on the line

(- 2, 0 ) , (0, 3 ) , (2, 6 ) , (4, 9 )

these 4 points lie on the line and are included in the top table

To calculate the quarterly dividends received for 132 shares of Drius Security, we need to divide the yearly dividend by the number of quarters in a year (4) and then multiply it by the number of shares.

Quarterly dividend = (Yearly dividend / 4) * Number of shares Given: Yearly dividend = $12.11 Number of shares = 132 Calculating the quarterly dividends: Quarterly dividend = ($12.11 / 4) * 132 Quarterly dividend = $3.0275 * 132 Quarterly dividend ≈ $399.66 (rounded to two decimal places) Therefore, you would get paid approximately $399.66 in quarterly dividends for owning 132 shares of Drius Security. The answer is option d: $399.63.

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Answer:

the picture is the answer.

Step-by-step explanation:

this is a guess-and-check problem. So you'll have to start with the blank between 4 and 9.

The required proportional ratio is y = 0.08 x. gives Halona 23 minutes to move her 1.93 kilometers to her neighbor's house. As long as you move at a steady pace.

How many kilometers Halona can run in x minutes y expressed as a ratio. Then find y in percentage. The relationship between two or more proportional or inversely proportional sets of values, whether they are directly related or not, is called proportionality.

Here we have

Substitute k into the proportional equation.

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The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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