5x+2y=10 Does the relation represents a function

For direct variation, an increase or decrease in one variable leads to a proportional increase or decrease in the other variable

Given that y varies directly with x, we would introduce a constant of proportionality, k

The expresion becomes

y = kx

For x = 2 and y = 5,

5 = 2k

k = 5/2 = 2.5

The direct variation equation is

y = 2.5x

Given:

culver inc invested $635250 in a mine estimated to have 847000 tons of ore of uniform grade

So, the estimated cost per unit =

This means the cost = $0.75 per ton

Using the conversion factors, 454 grams of butter is used by the chef each day.

So, grams of butter used each day:

Then,

Therefore, using the conversion factors, 454 grams of butter is used by the chef each day.

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The correct question is given below:

A chef at a restaurant uses 19 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors

The point-slope form of the equation of a line is given to be:

where

The equation of the line is given to be:

This means that the slope is 5/2.

The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

Given,

The equation of the line: x - 4y = 20

The points which the line passes through, (x₁, y₁) = (8, 0)

We have to find the equation of the line parallel to the given line.

The formula for the slope intercept form:

(y - y₁) = m(x - x₁)

m is the slope of the line.

Lets find the slope of the line given.

x - 4y = 20

x = 20 + 4y

x - 20 = 4y

y = (x - 20) / 4

y = 1/4x - 5

Here, slope of the line is 1/4

Now, substitute the slope of the line and (x₁, y₁) in the slope intercept formula to get the equation of line parallel to the given line

(y - y₁) = m(x - x₁)

(y - 0) = 1/4(x - 8)

y = 1/4x - 8/4

y = 1/4x - 2

1/4x - y = 2

Therefore,

The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

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Though working with laws of exponents, when part of the exponential equations with the same base, the exponent need to be subtracted.

Since the Quotient of Powers rules is utilized to decrease the number of terms when parts like terms with exponents. In arrange to urge the solution, fair remove the exponents whereas dividing the terms with the same base is appropriate for exponents with the same bases. when powers are multiplied, for two whole numbers of the same bases the exponents are added, while when powers are divided for two whole numbers of the same bases, exponents are subtracted. When any number is raised to the power of zero it comes about in 1 is the zero exponent rule.

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For solving this exercise, we will use the formula of the Present or Current value, as follows:

Where:

PV = Present or Current Value

FV = Future Value

i = Interest or discount rate

n = Periods of time

Replacing with the values we know:

PV = 50,000 * 0.7894

PV = 39,470

Bob's Mom

The simplified form of the expression is a³ which is calculated by using the properties of exponents.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.

Typically, a superscript to the right of the base indicates the exponent. Then, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most succinctly, "b to the nth."

The given expression is a³(2a² + 4bc⁴)⁰.

From the properties of exponents we know that:

a⁰ = 1

Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1

Therefore the total value of the exponential expression is a³

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We are given the points (-1,7) and (3,-3) and we want to calculate the midpoint of the segment that joins this points. REcall that given points (a,b) and (c,d), the midpoint of the segment that joins the points is calculated by averaging each coordinate (that is,adding the coordinates and then dividing them by 2). So the midpoint would be

We know that

• Anne could run a mile in ,m, minutes.

• Now, time has decreased by 16%.

The following expressions represent the number of minutes She uses to run a mile now.

This expression represents 16% of m in fraction form.

This expressed represents 16% of m in decimal form.

Both expressions are equivalent because they refer to the same percentage 16%. That is 0.16 and 16/100 are equivalent to 16%

A mixed fraction exists one that is represented by both its quotient and remainder.

Product of -2 1/2 and -3 1/3 is  [tex]8\frac{1}{3}[/tex].

Product of 1 1/3 and -3 1/2  is [tex]-5\frac{5}{6}[/tex] .

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction exists, for example, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Product of -2 1/2 and -3 1/3 is  [tex]8\frac{1}{3}[/tex].

Product of 1 1/3 and -3 1/2  is [tex]-5\frac{5}{6}[/tex] .

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The most appropriate choice for equation of line in slope intercept form x intercept = 90

y intercept = 60

Domain = {0, 3, 6, 9, ....., 90}

Range = {0 , 2, 4,...., 88}

What is equation of line in slope intercept form?

Equation of line in slope intercept form is written as y = mx + c, where m is the slope of the line and c is the y intercept of the line.

The distance from origin to the point where the line cuts the x axis is the x intercept and the distance of origin to the point where the line cuts the y axis is the y intercept.

Here,

Selling price of one painting = $30

Selling price of x paintings = $30x

Selling price of y sculptures = $45

Selling price of y sculptures = $45y

Total revenue = $(30x + 45y)

By the problem,

                         30x + 45y = 2700

a)

For x intercept, y = 0

30x = 2700

x = [tex]\frac{2700}{30}[/tex]

x = 90

x intercept is $90

For y intercept, x = 0

45 y = 2700

y = [tex]\frac{2700}{45}[/tex]

y = 60

y intercept is 60

b)

In 30x + 45y = 2700

Since x represents the number of paintings sold and y represents the number of sculptures sold, then x and y has to be integers.

If x = 0 , y = [tex]\frac{2700}{45}[/tex] = 60

If x = 3, y = [tex]\frac{2700 -90}{45} = 58[/tex]

If x = 6, y =  [tex]\frac{2700 -180}{45} = 56[/tex]

If x = 9, y =  [tex]\frac{2700 -270}{45} = 54[/tex]

_______________________________

If x = 90 , y =  [tex]\frac{2700 -2700}{45} = 0[/tex]

Domain is the values of x

Domain = {0, 3, 6, 9, ....., 90}

Range is the values of y

Range = {0 , 2, 4,...., 88}

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Complete Question

The diagram with the questions have been attached below

Answer:

(3 1/3)·(y + (1 1/8)) = 6 11/12

(9/3 + 1/3)·(y + (8/8 + 1/8)) = 72/12 + 11/12

10/3·(y + 9/8) = 83/12

y + 9/8 = 83/12·3/10

y + 9/8 = 83/4·1/10

y + 9/8 = 83/40

y = 83/40 - 9/8

y = 83/40 - 45/40

y = 38/40

y = 19/20

Given data:

The given figure is shown.

For figure A, the expression for sin(A) is,

Thus, the value of angle A is 23 degrees.

(b)

The vaue of tan(A) is,

Thus, the value of A is 49 degrees.

(c)

The value of cos(A) is,

Thus, the value of A is 53 degrees.

(d)

The value of tan(A) is,

Thus, the measurement of angle A is 35 degrees.

The solution is written down, and the graph is drawb below

Given the following inequality:

We will solve the inequality as follows:

Divide both sides by 2

So, the solution to the inequality x = (-∞, 5]

So, x = 5 is a solution to the inequality

So, the answer will be yes; x = 5 is a solution.

We have to write 8.94 in fractional notation without simplification.

For decimal values, we can convert them to fractions taking into account the number of decimals they have.

In this case, 8.94 has two decimals. Then, we can multiply it by a fraction 100/100, as 100 has two zeros.

Then, we will get:

This works beacuse we multiply the number 8.94 by a number that will make it become an integer (without decimals). To keep the value of the fraction equal to the decimal number, we have to divide by the same factor (in this case, 100).

This fraction can be simplified.

Answer: the fractional notation, without simplification, of 8.94 is 894/100.

The slope of g(x) is -3 and the g(x) is reflected across the x-axis

The table of values is

x    f(x) = x   g(x) = -3x

0        0              0

1          1              -3

2         2             -6

From the question, we have the definition of the functions to be

f(x) = x and g(x) = -3x

Also, we have the following x values from the blank table of values

x = 0, 1 and 2

Next, we calculate f(x) and g(x) at these x values

For the function f(x), the values are

f(0) = 0, f(1) = 1 and f(2) = 2

For the function g(x), the values are

g(0) = 0, g(1) = -3 and g(2) = -6

The next step is to calculate the slope and the transformation

Recall that

f(x) = x and g(x) = -3x

Generally, the form of a linear equation is

y = mx

Where m is the slope

This means that the slope of g(x) is -3

Lastly, the negative sign in g(x) = -3x implies that the graph is reflected across the x-axis or the y-axis

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The bananas will last 2 days at the zoo (found by division).

According to the question,

We have the following information:

The elephants at the zoo eat [tex]3\frac{1}{6}[/tex] buckets of bananas each day. The zookeeper bought [tex]6\frac{1}{3}[/tex] buckets of bananas.

Now, first we will find the number of days taken in eating 1 bucket of bananas.

[tex]3\frac{1}{6}[/tex] buckets = 1 day

Now, we will convert this mixed fraction into simple fraction.

19/6 buckets = 1 day

1 bucket = 1/(19/6) days

1 bucket = 6/19 days

Now, we have the total number of buckets as [tex]6\frac{1}{3}[/tex].

Now, after converting this mixed fraction, we have:

19/3 buckets

1 bucket =  6/19 days

19/3 buckets = (6/19)*(19/3)

19/3 buckets = 2 days

2 is a whole number.

Hence, the given buckets of bananas will last 2 days.

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Answer:

54 inches

Step-by-step explanation:

There are 12 inches in 1 foot

12in = 1ft

There are 4 feet and 6 inches

If you break it down its 4×12

4 × 12 = 48

Add 6 inches

48 + 6 = 54

Therefore the answer would be 54 inches

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Based on the monthly payment of $1,100, it will take 16 years to liquidate the loan.

The number of periods is a function of the total payments that will be paid, given the compounding of the interest at 4.5% and the monthly payment of $1,100.

Using an online finance calculator, the total number of years is determined as follows:

I/Y (Interest per year) = 4.5%

PV (Present Value) = $150,000

PMT (Periodic Payment) = $-1,100

FV (Future Value) = $0

Results:

N (# of periods) = 191.328 months

= 16 years (191.328/12)

Sum of all periodic payments = $-210,460.39 (191.328 x $1,100)

Total Interest = $60,460.39

Thus, before the loan is paid off, it will take 16 years or 191 monthly payments.

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Let's begin by identifying key information given to us:

The population is represented by the equation:

We will compare the equation for the population with the general exponential growth equation, we have:

Comparing, we have:

Therefore, the rate of change is 7%. Hence, C is the answer

Step-by-step explanation:

to find 24 times 17 i multiply 20 times 17 and add it to 4 times 17?

Yes, that is one way of doing it:

Your method:

20 × 17 = 340

4 × 17 = 68

340 + 68 = 408

The typical way of solving is:

24 × 17 = 408

Both return the correct answer.

Answer:

24 times 17 = 408

But if you multiply:

20 times 17 = 340 Then add that to:

4 times 17 = 68

340 + 68 = 408

You would get the same answer so this is correct!

Step-by-step explanation:

Hope it helps! =D

Answer:

it would be 600

Given that BE is diameter and CD is perpendicular, we can deduct that arcs CE and DE are equal.

Therefore, arc DE is 45°.

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

We need to count the number of zeros in a number multiplied by a power of 10. Which is shown below:

The power of 10 will add a certain number of zeros, which is equal to the expoent of the power, in this case it's 7, but there is one more zero which is present in the "40", therefore the total number of zeros will be 8.

If two lines are perpendicular, then the product of their slopes is equal to -1.

If two lines are parallel, then their slopes are equal.

Write the equation of the lines P and Q in slope-intercept form by isolating y. Compare their slopes to see if they are either parallel or pependicular, or none.

The equation of a line with slope m and y-intercept b in slope-intercept form, is:

Line P:

Then, the slope of the line P is -2.

Line Q:

Then, the slope of the line Q is -2.

Since both lines have the same slope, then they are parallel.