Mathematics College

The answer to this problem

Answers

Answer 1

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does the problem want:

⇒use the substitution method

⇒ to solve the problem

Let's substitute y's value from the second equation to our first equation

[tex]2x-y=8\\y=x-3\\\\\rm \hookrightarrow 2x-(x-3)=8\\\rm \hookrightarrow 2x-x+3=8\\\rm \hookrightarrow x=8-3=5[/tex]

Now substitute the x's value into the first equation

[tex]y=x-3\\x=5\\\\\rm \hookrightarrow y=(5) - 3 =2[/tex]

The solution is (5,2)

Answer: (5,2) or (B)

Hope that helps!

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Related Questions

2. Fruit snacks are 12 packs for $3.60. How much would it cost for just 1 pack? Hint:
Think of $3.60 as 360 cents.

Answers

Answer:

$0.3 or 30 cents

Step-by-step explanation:

if 12 pack=$360,

1 pack = ?

therefore,$360×1pack ÷ 12 packs=$30

=$30

Rob Herndon, an accountant with Southwest Airlines, wants to retire 50% of
Southwest Airlines bonds by 2028. Calculate the payment Rob needs to make
at the end of each year at 5% compounded annually to reach his goal of paying
off $430,000 in 10 years.

Answers

For Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

What is a future value?

A future value refers to a value on a future date based on an assumed growth rate of interest over some period.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

Data and Calculations:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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what value of x will make ONM similar to SRQ by the SAS similarity theorem?

Answers

The triangles will be congruent by SAS if x = 25 , Option C is the correct answer.

What is a Triangle ?

A triangle is a polygon with three sides , angles and vertices.

Two triangles are given , in the figure

They have an angle equal to each other ,

For the Triangle to be congruent by SAS , two sides of the triangles must be proportional along with the angle included must be equal.

The two sides will become proportional when x = ?

8/10 = 20 /x

On solving this

x = 25 ,

Therefore the triangles will be congruent by SAS if x = 25.

The complete question is

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?

A) 16

B) 20

C) 25

D) 50

The figure is attached with the answer.

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The area of rectangle is 2356 square meters. The length is 38 meters. What is the width?

Answers

Answer:

62 meters

Step-by-step explanation:

So the area of a rectangle can be defined as: [tex]A = wl[/tex] where A=area, w=width, l=length. So if we plug in the known values we can solve for the unknown, which in this case is the width. So let's plug in the known values:

[tex]2356 m^2 = 38 m * w[/tex]

Divide both sides by 38 m

[tex]62 m = w[/tex]

your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?

Answers

Answer:

Step-by-step explanation:

It would be better to purchase onions at 1.99 per pound

What is the volume of the composite figure?

Answers

The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid = 4,050 ft³.

How to Find the Volume of a Composite Figure?

The composite figure shown is composed of a square pyramid and a rectangular prism. To find the volume of the composite figure, find the volume of the square pyramid and the volume of the rectangular prims respectively.

Volume of the square pyramid = 1/3(B)(h), where:

Base area (B) = (l)(w) = (15)(15)

Base area (B) = (l)(w) = 225 ft³.

h = 9 ft

Volume of the square pyramid = 1/3(225)(9)

Volume of the square pyramid = 675 ft³.

Volume of the rectangular prism = (length)(width)(height)

Volume of the rectangular prism = (15)(15)(15)

Volume of the rectangular prism = 3,375 ft³.

The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid

The Volume of the composite figure = 3,375 + 675

The Volume of the composite figure = 4,050 ft³.

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y=10^x +6
find the inverse

Answers

[tex]y=10^x+6\\10^x=y-6\\x=\log_{10}(y-6)\\\\f^{-1}(x)=\log_{10}(x-6)[/tex]

Translate (5, 1) to the right 3 units.
Then reflect the result over the y-axis.
What are the coordinates of the final point?

Answers

Answer:

Step-by-step explanation:

Answer

When you translate either left or right, the x coordinate is the one that you change. To go right when you are dealing with a point, you must add the amount you are asked to go right. So when you go right 3 units, add 3 to the 5.

(5 + 3,1) = (8,1)

when going across the y axis, you are still only changing the x coordinate.

All you need do is put a minus sign in front of the x coordinate. So your final answer is (-8,1)

Reciprocal of 3 4/7 that would help

Answers

Answer:

fraction form: 7/25

Decimal form: 0.28

Step-by-step explanation:

brainliest!!!!

Question 3(Multiple Choice Worth 1 points)
(06.05 LC)
Given the following functions f(x) and g(x), solve f[g(7)].
f(x) = 4x + 21
g(x)=2x+2
16
49
85
784

Answers

Answer:

C.) 85

Explanation:

Given following:

f(x) = 4x + 21g(x) = 2x + 2

While solving these function questions, go from right to left.

Steps:

f[g(7)]f[2(7) + 2]f[16]4(16) + 2185

Identify the underline place 75.733

Answers

The underlined place is tenths.

Rounding off o the tenth place = 75.7.

What is the Nearest Tenth?

The tenths of a number is the first digit after a decimal point. To round off a number to the nearest tenth, if the number next to the tenth digit is not up to 5, let it be assumed as 0.

The underlined place is the tenths. Rounding 75.733 to the nearest tenth would give us: 75.7. This is because the next digit close to 7 is 3. It is not up to 5.

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Please help! I will give you lots of points!!!

Directions: construct the bisector of the following figures.

Note: please draw them out each on a piece of paper or laptop. Thank you!

Answers

A bisector is the required line that divides a given line or an angle into two equal parts. The required construction of the bisectors is shown in the attachment to this answer.

Bisection is the process in which a given line or angle is divided into two equal parts by constructing the required bisector. Thus the steps to bisect the given arcs are stated below:

For figure 1:

Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.Repeat the same process using point B as the center and the same radius as that used in A.Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector.

For figure 2:

Open the compass to any radius, using point M as the center draw arcs on the reverse side of the given arc MN.Repeat the same process using point N as the center and the same radius as that used in M.Join the intersections of the arcs on the reverse sides of arc MN by a line. Thus the required bisector.

For figure 3:

For figure 4:

NB: The point of intersection of the bisectors in relation to arc AC is the radius of the given arc.

The required constructions are attached to this answer.

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At the beginning of the week, you have $1250.33 cents in your checking account. During the week you spend $184.59 on food, $645.50 on rent and $112.11 on clothing. You get paid $323.89 during this week. How much money will be in your bank account at the end of the week?

Answers

Answer:

ending balance = $623.02

Step-by-step explanation:

Amounts you spend get subtracted from your bank balance. Amounts you earn get added.

Bank balance

Your ending balance is ...

ending balance = beginning balance - expenses + earnings

ending balance = $1250.33 -(184.59 +654.50 +112.11) +323.89

ending balance = $623.02

This circle is centered at the origin, and the length of its radius is 4. What the equation of the circle? 150 ė O A.2.1 4 O B. (x-4)² + (x-4)² = 16 O C. x² + y² = 4² O D. x² + y² = 4

Answers

Answer:

Step-by-step explanation:

The formula for the equation of a circle is [tex](x-a)^2+(y-b)^2=r^2[/tex].

Since the center of this circle is (0,0) and the radius is 4, the equation will be [tex]x^2+y^2=4^2[/tex]

Have a nice day!

Devon had 40 video games. He sold 2/5 of them at $500 each.

(a) How many video games does he have left?

(b) of the remaining video games, he sold 3/8 of them for $ 7200 altogether and kept the rest for himself

(I) How many video games did Devon keep for himself?

(ii) what was the selling price of a video game?

(c) Calculate the total amount of the money he received from the sale of the video games.

Answers

Using proportions, it is found that:

a) He has 24 videogames left.

b - I) He kept 15 videogames for himself.

b - II) The selling price of a videogame was of $800.

c) He received $15,200 from the sale of the videogames.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Item a:

He has 3/5 of 40 videogames left, hence:

3/5 x 40 = 3 x 8 = 24.

He has 24 videogames left.

Item b:

He kept 5/8 of the 24 videogames, hence:

5/8 x 24 = 5 x 3 = 15.

He kept 15 videogames for himself.

He also sold 9 videogames for $7,200, hence the selling price of one of them is:

7200/9 = $800.

Item c:

Earned $7,200 plus 500 for 16, hence:

T = 7200 + 500 x 16 = $15,200.

He received $15,200 from the sale of the videogames.

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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 195, x = 126; 95% confidence

Answers

Using the z-distribution, the 95% confidence interval for the population proportion is (0.5791, 0.7133).

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The other parameters are given as follows:

[tex]n = 195, \overline{p} = \frac{126}{195} = 0.6462[/tex]

Hence the bounds of the interval are:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6462 - 1.96\sqrt{\frac{0.6462(0.3538)}{195}} = 0.5791[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6462 + 1.96\sqrt{\frac{0.6462(0.3538)}{195}} = 0.7133[/tex]

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there are 5 trur or fales questions on an exam. how many different ways can a student do the exam if it is forbidden to leave the answer blank

Answers

Answer:

32 different ways.

Step-by-step explanation:

There are 2 combinations for each question, and there are 5 questions. Therefore there are [tex]2\times2\times2\times2\times2[/tex] = 32 different ways the student could do the exam.

Have a nice day!

Is finding a car's depreciation over a 10 year period considered as univariate or bivariate?

Answers

Determining a car's depreciation over a ten year period is considered a bivariate.

What is a bivariate?

A Bivariate data is made up of two variables that are observed against each other. In determining the deprecation of a car, the cost of the car is observed against the passage of time and the depreciation factor.

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how do you simplify 7v3 . 10uv5 . 8uv3

Answers

The simplification form of the provided expression is 560v¹¹u⁴ after using the property of the exponent.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The complete question is:

How do you simplify:

[tex]\rm 7v^3\cdot \:10u^3v^5\cdot \:8uv^3[/tex]

By using the property of the integer exponent:

[tex]\rm =560v^3u^3v^5uv^3[/tex]

[tex]\rm =560v^{11}u^4[/tex]

= 560v¹¹u⁴

Thus, the simplification form of the provided expression is 560v¹¹u⁴ after using the property of the exponent.

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100 POINTS!! Find the indicated angle or side. Give an exact answer.
Find the measure of angle A in degrees.

Answers

Answer:

A = 120

Step-by-step explanation:

To find angle A we will need to use the law of cosines, since we know the three sides of the triangle.

a^2=b^2+c^2−2*b*c*cosA

(2 sqrt(13)) ^2 = 6^2 + 2^2 + 2 * 6 * 2 cos A

4*13 = 36 + 4 - 24 cos A

52 = 40- 24 cos A

12 = -24 cos A

-1/2 = cos A

Take the inverse cos of each side

cos^-1(-1/2) = cos^-1(cos A)

120 = Cos A or 240 = Cos A

A cannot be greater than 180 so A = 120

Answer:

A = 120°

Step-by-step explanation:

We can use the cosine rule to solve for angle A, since lengths of all sides are known:

[tex]a^2 = b^2+ c^2 - 2(b)(c) \space\ cos A[/tex]

where a, b, and c are the sides opposites angles A, B, and C respectively.

∴ a = 2√3 , b = 6, c = 2

• Rearranging the formula to make A the subject:

[tex]2(b)(c) \space\ cos A = b^2 + c^2 -a^2[/tex]

⇒ [tex]cos A = \frac{b^2 + c^2 -a^2}{2(b)(c)}[/tex]

⇒ [tex]A = cos^{-1}(\frac{b^2 + c^2 -a^2}{2(b)(c)} )[/tex]

• Now we can substitute the values into the equation to calculate the value of angle A:

[tex]A = cos^{-1}(\frac{6^2 + 2^2 -(2\sqrt{13})^2}{2(6)(2)} )[/tex]

⇒ [tex]A = cos^{-1} (-\frac{1}{2} )[/tex]

⇒ A = 120°

In order for the parallelogram to be a rhombus, x=[?]. (9x+31) 32
HELP NEEDED ASAP

Answers

X = 3

Explanation:

In a rhombus, the diagonals are perpendicular, creating four congruent right triangles.

Because the value of all three angles within any given triangle will add up to 180°, we can easily simplify the equation.

First, we’ll need to add our given angles. Which are 32° (as can be seen on the graph) and 90° (because any pair of perpendicular lines create four right angles and this triangle includes one of them).

32° + 90° = 122°

Next, we’ll subtract 122 from 180 to find the remaining angle measure

180 - 122 = 58

Then, we’ll subtract 31 with the subtraction property of equality

58 - 31 = 27

Right now, our equation looks like:

27 = 9x

In order to simplify this equation further, we must use the division property of equality to get x on its own.

27/9 = 9x/9

3 = x

What is the primary importance of benefits 1and 2 as discussed in "the pros and cons of patents"?

Answers

Benefits 1 and 2 in the 'Pros and Cons of Patents' significantly throws light on the opportunity of owning a market, and securing funds respectively.

What is the primary importance of benefits 1 and 2?

Benefit 1 of 'Pros and Cons of Patents' is about the possibility of owning a market.

Since the US government will protect your creation for 20 years, you will essentially control the market for that product during that time. For instance, Eli Lilly invented Prozac in 1987 and had the monopoly for 14 years until 2001.

Benefit 2 of 'Pros and Cons of Patents' concerns around attracting and accumulating the sources of funding and investors.

If an invention is not protected, no one will put their money at risk The only way an invention can ensure a return is through patent protection since investors don't care about good intentions; they only care about money.

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Answer:

According to the article, patents allow inventors to “own the market” for their ideas, meaning the US government has deemed the idea original and protected the idea from being reproduced by others for 20 years. This makes the idea more marketable, which allows the inventor to attract investors. These benefits support the idea that patents promote invention.

Step-by-step explanation: edmentum sample answer

2. If G (4,3) was translated (x, y) → (x-7, y +3), where is G' located?

Answers

Answer:

the location of point G would be at G(-3,6)

Step-by-step explanation:

x=4

so 4-7 =-4

and y=3

so 3+3= 6

therefore, (x-7,y+3) = (-3,6)

Two shops, Lidal and Oldi, sell the same brand of toilet rolls but with different package sizes.
Calculate the price per roll for each shop.
Write which shop is the best value for money in the comment box.
lidal:8 for 2.80
oldi:9 for 3.24

Answers

The price per roll for Lidal and Oldi shop is 0.35 and 0.36 respectively.

Therefore Lidal shop is the best value for money.

Given,

Lidal shop:

8 rolls costs 2.80

∴ one roll costs = 2.80/8

= 0.35

Oldi shop:

9 rolls costs 3.24

∴ one roll costs = 3.24/9

= 0.36

Hence we get the per price for the shops as 0.35 and 0.36

we can see that for lidal shop if per roll it is 0.35 then if a person wants to buy 9 rolls then it will cost him 3.15, whereas in the case of oldi shop the price for 9 rolls is 3.24.Therefore, lidal shop is the best value for money.

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Which is the graph of y = 2 – square root of x?

On a coordinate plane, a curved line approaches the grid line at (3, 2.3), crosses the y-axis at (0, 1.5) and ends at (negative 2, 0).

On a coordinate plane, a curved line approaches the grid line at (negative 3, 2.3), crosses the y-axis at (0, 1.5) and ends at (2, 0).

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

Answers

The graph of [tex]y = 2 - \sqrt x[/tex] is (c) a curved line that passes through points (0,2) and (3,0.3)

How to determine the graph

The function is given as:

[tex]y = 2 - \sqrt x[/tex]

The above function is a square root function.

This means that the domain is [tex]x \ge 0[/tex]

The domain implies that options (a) and (b) are false, because they include negative x values

For option (c); set x= 0 and 3

[tex]y = 2 - \sqrt 0 = 2[/tex]

[tex]y = 2 - \sqrt 3 = 0.3[/tex]

This means that the graph of [tex]y = 2 - \sqrt x[/tex] is a curved line that passes through points (0,2) and (3,0.3)

Answers

Answer:

(-1,1) (-4,1) (-4,3)

Step-by-step explanation:

literally mirror shape A to the y-axis

the original cordinates:

(1,1) (4,1) (4,3)

would now be

(-1,1) (-4,1) (-4,3) because it's reflected

a washer and dryer cost 750 combined the washer cost $50 more than the dryer what is the cost of the dryer?

Answers

Answer:

350$ for dryer

Step-by-step explanation:

x = cost of dryer
x + 50 = cost of washer

750 = x + (x + 50)
750 = 2x + 50
700 = 2x
350 = x

PLS HELP WILL MARK BRAINLYEST

graph y=0.4x

Answers

Answer:

B, C, E

Step-by-step explanation:

Answer:

B,C,E

Step-by-step explanation:

The equation tells you that .4 is the slope (which is the rate of change). So B and C are both correct, if we look at E, we can put it on a graph and check if it is!

The director of a health clinic has a quarterly budget of $600,000. She
would like to allocate this budget to maximize the number of patient visits, P, which is
given as a function of the number of doctors, D, and the number of nurses, N, by
[tex]P=1000D^0^.^6N^0^.^3[/tex].

A doctor’s quarterly salary is $40,000; nurses is $10000.

Maximize the number of patient visits given the pay constraints.

Find the value of the LaGrange multiplier and interpret its meaning in this
problem.

Answers

The meaning of this problem is that with 7 nurses they can only hire D=13.25

What is the meaning of this problem.?

Generally, the equation for the model is mathematically given as

[tex]P=1000D^{0.6}N^{0.3}[/tex]

Therefore,

[tex]dv/dD=0.6*1000*D^{0.4}N)^{0.3}[/tex]

[tex]dv/dD=600* \frac{N6.1}{D6.1}=0[/tex]

Also

[tex]dv/dN=300* \frac{N6.8}{N6.7}=0[/tex]

Equations 1 and 2

[tex]300* \frac{D6.8}{N6.7}=600* \frac{N6.1}{D6.1}[/tex]

.sub D=(60N)/4

[tex]300* \frac{((60N)/4)6.8}{N6.7}=600* \frac{N6.1}{((60N)/4)6.1}[/tex]

N=6.67

N=7

solve for D

D=(60(7))/4

D=13.25

In conclusion, with 7 nurses they can only hire D=13.25

Answers

The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).

What is the rewritten form of the expression?

The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;

2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)

= log {(x+3)²(x-2)^5}/(x-7)³(x²)