If a⋅b+c⋅d=12, and a,b,c and d are all integers greater than 1, how many values are possible for a, if a, b, c, and d are not necessarily distinct?

Answer:

there is a 16% percent decrease

Step-by-step explanation:

percent of change = (new value - original value) ÷ original value

= (357 - 425) / 425

= -68/425

= -0.16

there is a 16% percent decrease

To calculate the merit increase based on your annual review score, we can use the given information that merit increases start at 0.5% for a score of 2.6 and increase by 1% every 0.4 points.

First, we need to determine the difference between your score and the starting score of 2.6:

3.4 - 2.6 = 0.8

Next, we divide this difference by 0.4 to determine the number of 0.4-point intervals:

0.8 / 0.4 = 2

Since each 0.4-point interval corresponds to a 1% increase, we multiply the number of intervals by 1% to find the total increase:

2 * 1% = 2%

Therefore, you will be receiving a merit increase of 2%.

Answer:

It's weight. A is right.

Answer:

A) Weight

Step-by-step explanation:

Think about what "pull of gravity" means. What force pulls you toward the center of the earth because of gravity? Weight of course.

Answer:

(1) The slope of the line having y = 5 as its equation is zero ⇒ (C)

(2) The slope of the line having x = -4 as its equation is undefined ⇒ (B)

Step-by-step explanation:

Let us use the rules above to solve the question

(1)

∵ The equation of the line is y = 5

→ That means the line is horizontal

∴ The line is a horizontal line

∵ The slope of the horizontal line = zero

∴ The slope of the line having y = 5 as its equation is zero

(2)

∵ The equation of the line is x = -4

→ That means the line is vertical

∴ The line is a vertical line

∵ The slope of the vertical line is undefined

∴ The slope of the line having x = -4 as its equation is undefined

Complete question is;

Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.

V(0) = 2 means that the value of the bank account when it is opened is $2000

V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000

V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening

Answer:

Statement 1: True

Statement 2: False

Statement 3: False

Step-by-step explanation:

We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.

This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000

From this little explanation, it's clear that only statement 1 is correct.

Answer:

the answer is   9.879

The equation of the graph g(x)  is \(3^{x-6}\)

What is a graph ?

A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;

In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.

The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

If the graph of the function  f(x) = 3^x is translated 6 units to the right , then the function becomes

g(x) = f(x - 6)

     = \(3^{x-6}\)

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Answer:

I believe it's true

Step-by-step explanation:

I hope this helps

Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: y + 3 ≥ 2 and y + 3 < 6

To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:

y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:

2 ≤ y+3 and y + 3 < 6

Combine the two:

2 ≤ y+3 < 6

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The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

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Answer: 11:23

Step-by-step explanation: because that is the simplest terms

Answer:

17

Step-by-step explanation:

204/12

= 17

Answer:

17 pounds

Step-by-step explanation:

1/12 = x/204

204/12 = 17

Hey there!

y = mx

mx = y

3(5) = y

3 + 3 + 3 + 3 + 3 = y

6 + 6 + 3 = y

12 + 3 = y

15 = y

Thus, your answer is: y = 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

s=d/t

s=18/30

s=3/5km/h

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.

Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,

x / y = (1/2) / (1/3)

x / y = 3/2                        ...1

x + y = 5                          ...2

From equations 1 and 2, then we have

(3/2) y + y = 5

(5/2) y = 5

y = 2 quart

Then the value of 'x' is given as

x + 2 = 5

x = 3 quart

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer: 27 x 1/3

Step-by-step explanation: 27/1 x 1/3 = 9 orchards per store

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

John manages 27 apple orchards in North Georgia. He wants to split the orchards into thirds so that he can open 3 local stores.

Then the number of orchards in each store will be

⇒ 27 / 3

Then the expression can be written as,

⇒ 27 x (1/3)

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

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The amount of money that Marie will have in her account in 7 years is equal to $10,350.

Given the following data:

Interest rate = 2% = 0.02.

Simple interest = $10,000.

Time = 7 years.

Conversion:

Interest rate = \(\frac{0.02}{4}\) = 0.005.

Mathematically, simple interest is given by this formula:

\(I=PRT\)

Where:

Substituting the given parameters into the formula, we have;

\(I=10000 \times 0.005 \times 7\)

I = $350.

Amount of balance;

\(A=I+P\\\\A=350+10000\)

A = $10,350.

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Answer: somewhere in the 17000s

Step-by-step explanation:

Just did the test

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Given:

The function is

\(f(x)=x^3-2\)

The secant line passing through (-4,f(-4)) and (2,f(2)).

To find:

The equation of the secant line.

Solution:

We have,

\(f(x)=x^3-2\)

At x=-4,

\(f(-4)=(-4)^3-2\)

\(f(-4)=-64-2\)

\(f(-4)=-66\)

At x=2,

\(f(2)=(2)^3-2\)

\(f(2)=8-2\)

\(f(2)=6\)

The secant line passes through the points (-4,-66) and (2,6). So, the equation of the secant line is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-(-66)=\dfrac{6-(-66)}{2-(-4)}(x-(-4))\)

\(y+66=\dfrac{6+66}{2+4}(x+4)\)

\(y+66=\dfrac{72}{6}(x+4)\)

On further simplification, we get

\(y+66=12(x+4)\)

\(y+66=12x+48\)

\(y=12x+48-66\)

\(y=12x-18\)

Therefor, the equation of the secant line is \(y=12x-18\).

Answer:

(1) y = 4d + 50

(2) y = 6d + 24

(3) 4d + 50 = 6d + 24

(4) Jane and Ellis will have $102 saved in 13 days.

Step-by-step explanation:

(1) This situation represents a linear equation.

⭐What is a linear equation?

Let's substitute the values of m and b into the slope-intercept form equation.

Jane saves $4 MORE every day, which is a constant additive amount. Thus, 4 = m.

Jane INITIALLY saves $50 into the savings account. Thus, 50 = b

\(y = 4d + 50\)

(2) This situation represents a linear equation.

⭐What is a linear equation?

Let's substitute the values of m and b into the slope-intercept form equation.

Ellis saves $6 MORE every day, which is a constant, additive amount. Thus, 6 = m.

Ellis INITIALLY saves $24 into his savings account. Thus, 24 = b.

\(y = 6d + 24\)

(3) To find at what day Ellis and Jane will have the same amount of money in their savings account, you need to set their equations equal to each other.

\(y = 6d + 24\\y = 4d + 50\\4d + 50 = 6d + 24\)

(4) First, you need to find at what day they will have the same amount of money in their savings account:

\(4d + 50 = 6d + 24\)

\(26 = 2d\)

\(13 = d\)

Then, you need to substitute that day into one of the equations and solve for y, the amount of money.

I am choosing the equation for Ellis, but you can also choose the equation for Jane:

\(y = 6d + 24\)

\(y = 6(13) + 24\)

\(y = 78 +24\)

\(y = 102\)

❗❗❗A lot of people may stop at this point and say that Jane and Ellis will both have $102 on the 13th day, but you should also substitute the value of d into both equations to avoid a careless error and losing marks❗❗❗

Equation for Jane:

\(y = 4d + 50\)

\(y = 4(13) + 50\)

\(y = 52 + 50\)

\(y = 102\)

✔️We avoided a careless error by confirming that d = 13✔️

∴ Jane and Ellis will both have $102 on the 13th day

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The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.

The reciprocal of the divisor 5 1/5 divided by 1/10

To the reciprocal of the divisor.

Equation: 5 1/5 divided by 1/10

1st: Flip the 1/10 to become 10/1

2nd: Change division to multiplication

New equation: 5.1/5.10/1

⇒ 50/5

       ⇒ 10.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

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If the correlation coefficient is 4, the percentage of variation in the dependent variable explained by the estimated regression equation is 16%.

The correlation coefficient is a measure of linear association between two variables, usually denoted by r. A correlation coefficient of 4 indicates a strong positive linear relationship between the two variables.

A correlation coefficient of 4 does not give any indication as to the percentage of variation in the dependent variable explained by the estimated regression equation. To find this percentage, we must use the coefficient of determination, denoted by r2.

The coefficient of determination is the square of the correlation coefficient and can be interpreted as the percentage of the variance in the dependent variable that is explained by the estimated regression equation.

Hence, in this case, r2 would be 16, indicating that the estimated regression equation explains 16% of the variance in the dependent variable.

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The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

yes

Step-by-step explanation:

it is a many to one function

could you vote me brailiest plz, im trying to level up. thx :)

Answer:

Relation

Step-by-step explanation:

This is a relation and not a function.

Because, in (8, 14) and (14, 14) range values are repeated.

Answer:

90 degree and 55 degree

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Question 6

\(\left(\frac{-7-2}{2}, \frac{-10-3}{2} \right)=(-4.5, -6.5)\)

Question 7

\(\left(\frac{-4+8}{2}, \frac{-3+2}{2} \right)=(2, -0.5)\)

Answer:

6

Step-by-step explanation:

h=3(12/6)

There are 48 ways to order this model of car. The correct option is A

We need to multiply the number of options for each feature to get the total number of ways to order this particular car:

   4 color choices

   2 options (manual or automatic) for the transmission

   Audio system: 6 choices

We can multiply these figures in order to find the total number of ways by applying the counting principle to multiplication:

4 × 2 × 6 = 48

Therefore, there are 48 ways to order this model of car.

Therefore, The correct option is A

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