The graph shows a linear relationship between x and y. What is the rate of change of
y with respect to x for this function?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2580\\ P=\textit{original amount deposited}\dotfill & \$2400\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 2580=2400[1+(\frac{r}{100})(1)] \implies \cfrac{2580}{2400}=1+\cfrac{r}{100}\implies \cfrac{43}{40}\implies \cfrac{100+r}{100} \\\\\\ \cfrac{4300}{40}=100+r\implies \cfrac{215}{2}=100+r\implies \cfrac{215}{2}-100=r\implies \boxed{\stackrel{\%}{7.5}=r}[/tex]

Answer:

7.5%

Step-by-step explanation:

The first step we need to do is to convert the measures from inches to feet (12 inches is 1 foot):

8 inches = 8/12 feet = 0.667 feet

6 inches = 6/12 feet = 0.5 feet

So the measures are 12.667 ft and 14.5 ft.

Now, to find the area of the rectangular living room, we just need to multiply these measures:

Since we expect a waste of 10%, we need to increase this area by 10%, that is, we multiply it by 110% or 1.1:

Since she cannot buy part of a square yard, we need to round up our answer (if we round down, the amount of carpet will not be enough). So rouding up, she will have to buy 203 in2 of carpet.

Answer:

First Choice:

(1.4)(0.18)²

Step-by-step explanation:

Using the negative exponent rule

[tex]\left(\dfrac{a}{b}\right)^{-1} = \dfrac{b}{a}[/tex]

we get

[tex]\left(\dfrac{5}{7}\right)^{-1} = \dfrac{7}{5}[/tex]

[tex]\dfrac{7}{5} = 1.4\\\\[/tex]

Therefore
[tex]\left(\dfrac{5}{7}\right)^{-1}\left(0.18\right)^2\\\\= (1.4)(0.18)^2[/tex]

The first thing we have to know is that 1 kilogram is equal to 1000 grams

if we have 5.4 kilograms

Multiply both sides of the equation by 20, the lowest common denominator of 4,5.

Multiply 5 and 12 to get 60.

Swap the sides so that all the terms of the variables are on the left side.

Divide both sides by 4.

Divide 60 by 4 to get 15.

The Confidence Interval for a Population Proportion is 0.69 ± 1.13

(-0.44 to 1.82)

Confidence Interval:

Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

Given,

n = 130 and

p= 0.69,

construct a 99% confidence interval.

Here we need to find the confidence interval.

According to the formula, the confidence interval is,

We know that,

Sample Size: 130

Sample Mean: 0.69

Confidence Level: 99%

99% Confidence Interval: 0.69 ± 1.13

(-0.44 to 1.82)

"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."

Margin of Error: 1.13

(to more digits: 1.13)

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The Vertex form of y= (x+9/2)² - 89/4 hence, vertex=(-9/2 , -89/4),

Given,y=x²+9x-2

Take out the leading coefficient.

y=(x²+9×x)-2

Complete the square.

y = (x² +(2×9/2) × x × (9/2)²) + (-2-(9/2)²)

Express the function in vertex form.

y=(x+9/2)² - 89/4

Hence the vertex form is y=(x+9/2)² - 89/4

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The most appropriate choice for LCM will be given by

After the year 2005, France and America will be in recession in the year 2029

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

France has a recession every 6 years.

America has a recession every 8 years.

Florence works out when France and America will both be in recession.

It will be possible in the year which is a common multiple of 6 and 8

In the year 2005, both France and America were in recession

France and America will both be in recession again after (LCM of 6 and 8) years

Now,

6 = 2 x 3

8 = 2 x 2 x 2

LCM of 6 and 8 = 2 x 2 x 2 x3

                          = 24

France and America will both be in recession again after 24 years  

After the year 2005, France and America will be in recession in the year (2005 + 24) = 2029

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Answer:

[tex]x + 53 + 86 = 63 \\53 - 86 = 33[/tex]

The solutions to the question are

The given parameters are:

Sides = 3

Fourth side = barn wall

Perimeter = 120 m

Next, we sketch the dog pen using the above parameters (see attachment)

Here, we have

P = 120m

Also, we have

P = 2x + y

This gives

2x + y = 120

Make y the subject

y = 120 - 2x

The area is calculated as

A = xy

So, we have

A = x(120 - 2x)

Hence, the area is A = x(120 - 2x)

See attachment for the graph of A = x(120 - 2x)

We have

A = x(120 - 2x)

Expand

A = 120x - 2x^2

Differentiate

120 - 4x= 0

So, we have

4x = 120

This gives

x = 30

Hence, the value of x that gives maximum area is 30

Recall that

y = 120 - 2x

So, we have

y = 120 - 2 * 30

Evaluate

y = 60

Hence, the dimensions is 30 by 60

From the graph, we have

x = 0 to 60

Hence, the domain of the function is 0 <= x <= 60

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Based on the fact that the data for the average CO₂ over the whole year was smoother than the daily and monthly level, the term for the phenomenon is called Smoothing.

Smoothing refers to a process in statistics where the messier points of a data distribution is removed. In other words, the data points that give the data set a varied distribution are removed so that the data set appears smoother.

There are several methods to engage in smoothing but most of them use averaging over a longer period of time. They would for instance, use the averages of a period over a month or weekly and convert it to an annual measure like the scatterplot of CO₂ for the year.

In conclusion, the fact that the average CO₂ scatterplot for the year was smoothly than monthly or daily is due to smoothing.

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Answer:

x = a/2 + 9/2

Step-by-step explanation:

Solve for x:

x^2 - 18 x + 81 = (x - a)^2

Expand out terms of the right hand side:

x^2 - 18 x + 81 = x^2 - 2 a x + a^2

Subtract x^2 - 2 a x + a^2 from both sides:

2 a x - 18 x - a^2 + 81 = 0

Collect in terms of x:

81 - a^2 + x (2 a - 18) = 0

Factor constant terms from the left hand side:

-(a - 9) (-2 x + a + 9) = 0

Divide both sides by -a + 9:

-2 x + a + 9 = 0

Subtract a + 9 from both sides:

-2 x = -a - 9

Divide both sides by -2:

Answer: x = a/2 + 9/2

The value of x in the similar triangles is x = 3.375

The triangles represent the given parameter

On the triangle, we have the following corresponding sides

AB to BC and AD to DE

This means that

AB : BC = AD : DE

Express as fractions

So, we have

AB/BC = AD/DE

Substitute the known values in the above equation

x/3 = x + 9/11

This gives

11x = 3x + 27

So, we have

8x =27

Divide

x = 3.375

Hence, the value of x is x = 3.375

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The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :

3x² + 16x + 5 = (3x + _)(x + _)

We need to solve the expression for finding out its factors.

y = 3x² + 16x + 5

y = 3x² + 15x + x + 5

y = 3x(x + 5) + 1(x + 5)

y = (3x + 1)(x + 5)

Therefore, the  roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

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Answer:

The Convention of 1818 was a treaty between the United States and Britain that set the 49th parallel as the boundary between British North America and the US across the West.Forty-Ninth ParallelCutting on the 49th parallel, on the right bank of the Moyie River, looking west, 1860.(courtesy North American Boundary Commission)The Convention of 1818 was a treaty between the United States and Britain that set the 49th parallel of latitude as the boundary between British North America and the US across the West. This remains the boundary today between the two nations.

hope that helps! Have a good day

Step-by-step explanation:

a distance on a coordinate grid is always the Hypotenuse of a right-angled triangle with the differences of the x coordinates and the y coordinates as the legs.

so, per Pythagoras

distance² = (x diff)² + (y diff)²

we have here a distance 17. 17² = 289.

to get integer coordinates the lengths of the legs must be integer numbers.

what 2 squared integer numbers can be added to get 289 ?

I found after subtracting 4, 9, 16, 25, 36, 49 and finally 64 (the squares of 2, 3, 4, 5, 6, 7, 8) that

289 - 64 = 225, which is also a square number (15²).

so, we get the possible integer coordinates of Q to be

(-4 + 8, 7 + 15) = (4, 22)

in this case the shorter leg has the length 8, and the longer leg the length 15.

the shorter leg is in this case horizontal, because it is the x coordinate difference. and Q is again as described (4, 22).

if we make the shorter leg vertical, that means it is the y coordinate difference. and Q is then

(-4 + 15, 7 + 8) = (11, 15)

Answer:

Step-by-step explanation:

6x-2x-8=12  

4x-8=12    (add 6x and -2x)

4x=20         (8+12=20)

x=5   (4 divide by 20 =5)

Answer:

1.) -4

2.) 3/5 and 6/10 are both equal to 0.6

Step-by-step explanation:

1.) 16(1/4 - 1/2)

For this one you can either distribute the 16 and solve or just subtract the fractions and solve.  I like the first method personally:

16/4 - 16/8

4 - 8

-4

2.) Fractions can be looked at as dividing the top (numerator) by the bottom (denominator).  If we put each of the answer choices into our calculator and divide, we get 3/5 and 6/10.  Note that 2/3 = 0.66, but that is not the same as 0.6.

The equation of line passing that has a slope of One-half and passes through point (2, –3) is y = 0.5x - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing that has a slope of One-half and passes through point (2, –3) is:

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

y + 3 = 0.5x - 1

y = 0.5x - 4

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The most appropriate choice for for linear equation will be given by -

Gain in weight of Max = 7.69 pounds

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let the gain in weight be x pounds

Weight of Max in the month of September = 3.04 pounds

Weight of Max today = 10.73 pounds

By the problem,

                          3.04 + x = 10.73

                                     x = 10.73 - 3.04

                                     x = 7.69

Gain in weight of Max = 7.69 pounds

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The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.

As per the question, we can write

The freezing point of seawater = −2 °C.

The freezing point of nitric acid = −42 °C.

We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;

The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid

The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.

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The  graphed piecewise function is conformed of two lines, it can be written as::

Notice that we have two lines that conform the piecewise function.

The linear equation in the left passes through the points (-8, 8) and (-1, 1), so the slope is:

m = (1 - 8)/(-1 + 8) = -7/7 = -1

Then it is something like:

y = -x + b

To find the value of b we use the point (-1, 1), we will get:

1 = -(-1) + b

1 - 1 = b

0 = b

Then the first line is:

y = -x   if x < -1.

The second line passes through points (-1, -3) and (4, 2), then the slope is:

m = (2 + 3)/(4 + 1) = 1

And we can see that it intercepts the y-axis at y = -1, so the linear equation here is:

y = x - 1

Finally, the piecewise function is:

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Given

s: silk flowers

r: ribbon

f: foam

v: vase

Procedure

s = 3r

r = 2f

v = 3f

s: silk flowers $24

r: ribbon $ 8

f: foam $ 4

v: vase $12

iven

adiius of circle = 3 ft

ind

rea and circumference of a circle

xplnanation

Circumference of a circle is given by

Area of circle =

inal ANnswer

ircumference =

Area =

The total number of different numbers which Toby could have picked according to the task content as given is; 1,000.

It follows from the task content that the number of different numbers which Toby could have picked given the conditions is to be determined.

On this note, since the required number is to be greater than 49,999 and must be a 5-digit number, the numbers which he could pick would range from;

49,999 - 99,999.

Hence, there are 5000 numbers in between.

Additionally, since the number must be a multiple of 5, the total number of multiples of 5 from 5,000 consecutive numbers is;

= 5,000/5

= 1000 different numbers.

Therefore, Toby could pick any of 1000 different numbers.

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[tex](x + \frac{1}{3} ) + (x + \frac{1}{5} ) = 1 \\ x + x + \frac{1}{3} + \frac{1}{5} = 1 \\ 2x(15) + \frac{1}{3} (15) + \frac{1}{5} (15) = 1(15) \\ 30x + 5 + 3 = 15 \\ 30x = 15 - 5 - 3 \\ 30x = 7 \\ \frac{30x}{30} = \frac{7}{30} \\ x = \frac{7}{30} [/tex]

ATTACHED IS THE SOLUTION

Answer:

250

Step-by-step explanation:

the radius of of circle V is 2

XZ is the diameter of circle Y (bigger circle)

UW is the diameter of circle V (smaller circle)

We are to find the radius of the smaller circle. To find the radius, we use the formula relating diamter to radius:

Diameter = 2(radius)

UW = 4, diameter =4

4 = 2(radius)

radius = 4/2

radius = 2

Hence, the radius of of circle V is 2