The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.

 y = 2/3x + 7  is slope-intercept form of the equation .

What exactly does slope intercept mean?

the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept

      2x-3y = -9

      3y = 2x + 9

         y = 2/3x + 9/3

          y = 2/3x + 3

compare equation y = mx + c  

  slope = 2/3  

to find c put x = -3 and y = 5

     y = mx + c  

      5 = 2/3 * (-3) + c

      5 = -6/3  + c

        c = 5 + 2  = 7

put the final equation together

           y = 2/3x + 7

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The image of the point after the transformation is (2, -7)

The given parameters are:

Point =  (-1, 3)

Transformation rule:

D₂ o T 4.-5

The above means that

When these transformations are combined, we have

(x, y) = (2x + 4, 2x - 5)

So, the mathematical representation of this transformation is

(x, y) = (2x + 4, 2x - 5)

Substitute the equation Point =  (-1, -3) in the equation (x, y) = (2x + 4, 2x - 5)

So, we have the following equation

(x, y) = (2(-1) + 4, 2(-1) - 5)

Evaluate the product

(x, y) = (2, -7)

Hence, the image is (x, y) = (2, -7)

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Problem

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?

Solution

For this case we can set up the following notation

x= number of cheeseburgers

y= small fries

4x +5y= 2310

3x + 2y= 1330

From the first equation we can solve for x and we got:

x= 577.5 - 5/4 y

And now we can replace this into the second equation and we got:

3(577.5 -5/4 y) +2y= 1330

And we can solve for y:

1732.5 - 15/4 y + 2y = 1330

-7/4 y = -402.5

y= 230 cal

And solving now for x we have:

x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal

The angle A is given 72 degree and angle C is given 90 degree.

The side b is 5.

Then the right triangle is given

Use the property , the sum of the angles of the property is the 180 degree.

Then the angle B is 18 degree.

Then to determine side a , use the tan trigonometric function.

The side a is 15.38.

Now to determine the side c, use the trigonometric function sin .

The side c is 16.18.

The first equation given in the question as, y = 1^x is not exponential.

What do you mean by exponential?

A mathematical function with the form f (x) = a^x is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental no., or roughly 2.71828, is the most often used exponential function on regular basis.

The equation, y = 1^x is not an exponential because for any integer value of x, y always equals to zero. Which makes it simple equation and not an exponential equation.

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2.

The reason for 2 is 'the angles are vertical'.

3. In the diagram below, we can identify the alternate interior angles more easily

Therefore, Therefore, the statements of the third step are

Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.

The standard score for the given X value is -0.06

Standard Score

Standard score or Z - Score is inversely varies with the standard deviation and directly varies with the difference of the raw score and the mean score.

The formula to calculate standard score is

z - score = (X - μ)/σ

Where

Z = standard score

x = observed value

μ = mean of the sample

σ = standard deviation of the sample

Given,

Here we have the value of X = 83, μ=88.1 and σ=87.

Now, we need to find the standard score for this values and we have also round off the result to two decimal places.

Apply the given values on the z-score formula, then we get,

z-score = (83 - 88.1)/87

When we simplify the numerator, then we get,

z - score = -5.1/87

After the division of these numbers we get the value of z-score as,

z - score = -0.0586

When we round off the result into two decimal place then we get the value of standard score as -0.06.

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If we apply the first discount the shoes would have a price of:

To this pice we make the 20% discount, then:

Therefore, after the discounts the price would be $84

Calculate the given division, as shown below

First, let's see the progression of the sequence of numbers

As you can see from the second term the sequence continues with a constant change of -13 which means d=-13.

The answers will be the expressions inside the red square box in each case.

Answer:

[tex]8.808 \times 10^{-6}[/tex]

Step-by-step explanation:

Given expression:

[tex](2.6 \times 10^{-6})+(3.2 \times 10^{-2})(1.94 \times 10^{-4})[/tex]

The grouping of numbers by parentheses in a different way does not affect their product.  Also, changing the order or position of the product of two numbers does not change the end result.

[tex]\implies (2.6 \times 10^{-6})+(3.2 \times 1.94 \times 10^{-2} \times 10^{-4})[/tex]

Multiply the numbers 3.2 and 1.94:

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2} \times 10^{-4})[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2-4})[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-6})[/tex]

Factor out the common term 10⁻⁶:

[tex]\implies 10^{-6}(2.6+6.208)[/tex]

Add the numbers 2.6 and 6.208:

[tex]\implies 10^{-6}(8.808)[/tex]

[tex]\implies 8.808 \times 10^{-6}[/tex]

Scientific notation is written in the form a × 10ⁿ , where 1 ≤ a < 10 and n is any positive or negative whole number.  Therefore, the final answer is in scientific notation.

Answer:

A

Step-by-step explanation:

Adding the equations,

[tex]2y=10 \implies y=5 \\ \\ \therefore 2x+3(5)=1 \implies x=-7[/tex]

1. The lower limit of this confidence interval is $587.13.

2. The upper limit of this confidence interval is $841.25.

The lower limit describes the lowest price that entry-level road bikes will cost.

The upper limit refers to the highest price that entry-level road bikes can command.

Using the lower and upper limits, Randy can confidently estimate the range of the asking price of the used entry-level road bikes.

N = 14

Mean price, µ = $714.19

Sample deviation = $184.56

Confidence interval = 99%

The z-score of 99% confidence interval = 2.576

The margin of error = z-score x (standard deviation/√n)

= 2.576 x ($184.56/√14)

= $127.06

Lower Limit =  µ - margin of error

= $714.19 - $127.06

= $587.13

Upper Limit = µ + margin of error

= $714.19 + $127.06

= $841.25

Thus, Randy can estimate that the price of used entry-level road bikes is $714.19 ±$127.06 at a 99% confidence level.

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Answer: 36

One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.

Therefore, the number of elements in the sample space would be:

There would be 36 elements in the sample space.

ANSWER

EXPLANATION

We want to write the equation of the circle in vertex form:

The first step is to group the x terms and y terms together and take the constant to the right-hand side of the equality sign:

Now, complete the square for the x terms:

Repeat the process for the y terms:

That is the equation of the circle in vertex form.

The value of the composite function (g ° h)(0) is equivalent to zero.

A function that is composed of further functions, each of which serves as the input to the next.

Given the function below;

g(x) = 5x

h(x) = √x

Determine the composite function (g o h)(x)

(g o h)(x) = g(h(x))

(g o h)(x) = g(√x)

g(√x) = 5√x

Substitute the value of x to have:

(g o h)(0) = 5√0

(g o h)(0) = 0

This gives the required value

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Simplify the equation 4x+9y = -9 in slope-intercept form of equation.

So slope of line is -4/9 and int

Let's define first the variables.

let H be the number of bags of the type that cost 3.25 and P the number of bags of the type that cost 2.75.

since they sold a total of 156 bags we have that H+P=156

and from the other condition we obtain 3.25H+2.75P=455

now we can solve the system of equations.

from the first equation H=156-P

substituing the previous equality in the second one we obtain:

now that we have P, we can replace it in the first equation obtaining that H=50

then the answer will be that they sold 50 bags of $3.25 and 106 bags of $2.75

parallel lines have the same slopes. Therefore,

Y can be found below

[tex] \sqrt{ \frac{4 {x}^{2} }{3y} } \\ = \frac{ \sqrt{4 {x}^{2} } }{ \sqrt{3y} } \\ = \frac{ \sqrt{4 } \times \sqrt{ {x}^{2} } }{ \sqrt{3y} } \\ = \frac{2x }{ \sqrt{3y} } [/tex]

ATTACHED IS THE SOLUTION

Answer:

The image is the answer

Step-by-step explanation:

Given:

Radius of the cirle = 11 ft

Angle = 150 degrees

π = 3.14

Let's find the area of the sector of the cicle.

To find the area of the sector, apply the formula:

Where:

π = 3.13

θ = 150 degrees

r = 11

Thus, we have:

Solving further:

Therefore, the sector area of the circle is 158.3 square feet.

ANSWER:

158.3 square feet.

we have the following:

where d is distance, t is time and v is velocity, replacing:

therefore, the distance is 13.2 miles

Answer:

378

Step-by-step explanation:

Start with prime factoriazation

18 = 2 * 3 * 3

54 = 2 * 3 * 3* 3

63  = 3 * 3 * 7

2 * 3 * 3 * 3 * 7 = 378  

Answer:

Numere prime:37,377,769,1243,1999

Sunt numere prime deoare au ca divizori doar 1 si ei insusi

To simplify the expression

-0.26v + v - 0.07

we will only add the ones with variable v

0.74v -0.07

The correct option is

0.74v - 0.07

The value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The linear equation one variable is:

−0.28x − 15.3 = 1.92

-0.28x = 1.92 + 15.3

-0.28x = 17.22

x = -17.22/0.28

x = -61.5

Thus, the value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

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Answer:

its B -61.5

Step-by-step explanation:

i attched pictures to show you

$6,50,000 is the cost of the goods sold.

By dividing a company's cost of sales, or cost of goods sold, by its inventory turnover, one can determine how well it uses its inventory (COGS).

The number of times inventory is sold or used over a given time frame, like a year, is referred to as the inventory turnover in accounting. It is calculated to determine whether a company has an excessive amount of inventory in relation to its level of sales.

Inventory turnover is the count of times a company's stock is sold during the course of a month, a quarter, or (most frequently) a year of business.

We should apply the following formula to calculate the cost of goods sold:
Cost of goods sold / inventory equals inventory turnover.
Rearranging the equation and replacing the unknown values results in:

Inventory plus inventory turnover equals cost of goods sold.
Price of items sold = $5,000,000 divided by 13
$6,50,000 is the cost of the goods sold.

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The number that should go in the gap to factorise the given expression is 2

From the question, we are to determine the number that should go in the gap in order to factorise the given expression.

The given expression is

6x + 14

To determine the number that should go in the gap,

First we will factorize the given expression

6x + 14

The greatest common factor (GCF) of 6 and 14 is 2

Thus,

We can factor out 2 as follows

2(3x + 7)

The factored form of the expression is 2(3x + 7)

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The equation is

Therefore x<-2. The number line representation is