Solve the linear system using the elimination method 2x-5y=-3, -x+2y=3

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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The distance from Ferris, to Dunlap, to Butte is given by

15 mi + 20 mi = 35 mi

Now, let us find the direct distance from Ferris to Butte.

Since this is a right-angled triangle, we can apply the Pythagorean theorem.

Where a and b are the shorter sides and c is the longest side.

The direct distance from Ferris to Butte is 25 mi

The difference between the longer and the direct distance is given by

Difference = 35 mi - 25 mi = 10 mi

Therefore, the direct distance from Ferris to Butte is 10 mi shorter than the distance Jashayne found.

Answer:

Circumference: 12π + 8 cm,

Area: 48 ( cm )^2

Step-by-step explanation:

This figure is composed of circles, squares, and semicircles. As you can see, the squares indicate that each semicircle should have ( 1 ) the same area, and ( 2 ) the same length ( circumference ). It would be easier to take the circumference of the figure first, as it is composed of arcs part of semicircles the same length.

Circumference of 1 semicircle = \(\frac{1}{2}\)( πd ) =  \(\frac{1}{2}\)π( 4 ) = 2π ( cm )

Circumference of Figure (composed of 6 semicircles + 2 sides of a square),

We know that 6 semicircles should be 6 \(*\) 2π, and as the sides of a square are equal - if one side is 4 cm, the other 3 are 4 cm as well. Therefore the " 2 sides of a square " should be 2

Circumference of Figure = 6 \(*\) 2π + 2 = 12π + 8 ( cm )

_____________

The area of this figure is our next target. As you can see, it is composed of 3 semicircles, and the area of 3 semicircles subtracted from the area of 3 squares. Therefore, let us calculate the area of 1 semicircle, and the area of 1 square first.

Area of 1 semicircle = 1/2π\(r^2\) = 1/2π\((2)^2\) = 2π ( cm ),

Area of 1 square = ( 4 cm )( 4 cm ) = 16 ( \(cm^2\) )

So, the area of the figure should be the following -

Area of Figure = 3 \(*\) 2π + 3( 16 - 2π ) = 48 ( cm )^2

Answer:

Hamburger = $6

Hotdog = $4

Step-by-step explanation:

136 - 14(2) = 108

108 / 13 + 14 = 4

If a hamburger is 2 dollars more than you would just add 2 to this

La ecuación lineal está dada por y = (5/4)x + (1/2)

Una ecuación lineal tiene la forma:

y = mx + b

donde y, x son variables, m es la tasa de cambio y b es el intercepto en y.

Dada la ecuación:

5x/2y-1=2​

Para resolver la ecuación, primero multiplique en cruz:

5x = 4y - 2

4y = 5x + 2

y = (5/4)x + (1/2)

La ecuación lineal está dada por y = (5/4)x + (1/2)

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Answer:

B) 352

Step-by-step explanation:

45% = 0.45

640 x 0.45= 288

288 is how many students walked to school

So to find how many took the bus to school

640- 288= 352

Answer:

0

Step-by-step explanation:

say that you have 0 bottles of ketchup and you get 0 more bottles of ketchup every hour you work. not only does it make no sense but if you work zero hours you will end up with 0 ketchup bottles

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

t = 15

Step-by-step explanation:

t - 12 = 3

t = 3 + 12

t = 15

Answer:

a) Q1= 144.10

Median = 150

Q3=155.90

b) The 99 percentile would be:\(a=150 +2.33*8.75=170.39\)

And represent a value who accumulate 99% of the values below

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

\(X \sim N(150,8.75)\)  

Where \(\mu=150\) and \(\sigma=8.75\)

Part a

Lets begin with the first quartile:

\(P(X>a)=0.75\)   (a)

\(P(X<a)=0.25\)   (b)

We can find the quantile in the normal standard distribution and we got z=-0.674.

And we can apply the z score formula and we got:

\(z=-0.674<\frac{a-150}{8.75}\)

And if we solve for a we got

\(a=150 -0.674*8.75=144.10\)

The median for this case is the mean \(Median =150\)

For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:

\(a=150 +0.674*8.75=155.90\)

Part b

We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.

And we can apply the z score formula and we got:

\(z=2.33<\frac{a-150}{8.75}\)

And if we solve for a we got

\(a=150 +2.33*8.75=170.39\)

And represent a value who accumulate 99% of the values below

Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r

Answer:

A Circle

Step-by-step explanation:

Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

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Answer:

Explanation:

If V is the centroid of triangle PQR, then;

P

Answer:

the solution to the equation is m = 28/3, or approximately 9.3333

Step-by-step explanation:

To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:

3m/2/3 = 7

(2/3) * (3m/2/3) = (2/3) * 7

3m/2 = 7 * (2/3)

3m/2 = 14/3

Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:

(2) * (3m/2) = (2) * (14/3)

3m = 28/3

Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:

(3m) / 3 = (28/3) / 3

m = 28/3

Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.

Answer:

Maybe m = 14/9

Maybe m = 14

Step-by-step explanation:

It is not clear what you mean by the fraction on the left side.

Do you mean

3m/(2/3) = 7  ?

If so:

3m = 7 × 2/3

3m = 14/3

m = 14/9

Do you mean

(3m/2)/3 = 7   ?

If so:

3m/2 = 21

m = 21 × 2/3

m = 14

Do you mean something else?

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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Answer:

x has to be greater than 0

Step-by-step explanation:

It basically shows you that based on the inequality sign.

Answer:

x solved is 0 < x

and graphing it on the number line

-1  0  1

    O->

Step-by-step explanation:

So, solving for x is easy you divide the 2 from 2x onto the other side and 0/2 is 0 meaning 0 < x, the < stays the same as you divided with a positive and it would start at 0 and the line would go to the right as 0 is less than x. if you have to it would be a open circle with a dotted line if deltamath makes you do that too.

The most appropriate choice for functions will be given by -

f (x) - (-g(x)) =  f(x)  + g(x) holds for  f(x)=3x-7-and g(x) = -2x+5.

f (x) - (-g(x)) =  f(x)  + g(x) holds for every functions

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

For f(x) - (-g(x))

-g(x) = -(-2x  + 5)

       = 2x - 5

f (x) - (-g(x)) = (3x - 7) - (2x - 5)

                      3x - 7 - 2x + 5

                       x - 2

For f(x)  + g(x)

f(x)  + g(x) = (3x - 7) + (-2x + 5)

                = 3x - 7 - 2x + 5

                = x - 2

So f (x) - (-g(x)) =  f(x)  + g(x) holds here

Since addition and subtractions can be done on functions,

f (x) - (-g(x)) =  f(x)  + g(x) holds for every functions.

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The best estimate of the number of times that Lou is on time to class follows a binomial distribution and is equal to 24.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The number of times that Lou is on time to class follows a binomial distribution, where the number of trials (classes) is n=32 and the probability of success (Lou being on time) is p = 75% = 0.75.

The expected number of times that Lou is on time to class can be calculated as:

E(X) = n × p = 32 × 0.75 = 24

Therefore, the best estimate of the number of times out of 32 that Lou is on time to class is 24, using the binomial distribution.

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Answer:

Thanks

Step-by-step explanation:

Thanks

d = 8

Divide both sides of the equation by the same term

Answer:

d = 8

Step-by-step explanation:

Step 1: Divide both sides by 12.

Therefore, the solution is 8.

Answer:

(5x-2)=3x4

Step-by-step explanation:

add that's in the () first

Answer: .

Step-by-step explanation:

Answer:

B. 14,525

Step-by-step explanation:

If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:

$35 x 415 = $14,525

Therefore, the answer is B. $14,525.

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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