Explain how you would solve the following system of equations using substitution. math step in your explanation, too!! This is the system that you should use: y= 4x -5 y = 3x -3

Answers

Answer 1

Answer:

[tex]x=2\\y=3[/tex]

Step-by-step explanation:

Solve by substitution method

[tex]y=4x-5\\y=3x-3[/tex]

First, solve [tex]y=4x-5[/tex] for [tex]y[/tex]:

Substitute [tex]4x-5[/tex] for [tex]y[/tex] in [tex]y=3x-3[/tex]

[tex]y=3x-3[/tex]

[tex]4x-5=3x-3[/tex]

[tex]4x-3x=5-3[/tex]

[tex]x=2[/tex]

Now that we have the value of x

substitute [tex]2[/tex] for [tex]x[/tex] in [tex]y=4x-5[/tex]

[tex]y=4x-5[/tex]

[tex]y=4(2)-5[/tex]

[tex]y=8-5[/tex]

[tex]y=3[/tex]

∴ The value of [tex]x[/tex] is [tex]2[/tex] and the value of [tex]y[/tex] is [tex]3[/tex]


Related Questions

A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]

Step-by-step explanation:

Given that,  

Point estimate = sample mean = [tex]\bar x[/tex] = 88.34  

sample standard deviation = s = 19.22  

sample size = n = 14  

Degrees of freedom = df = n - 1 = 13  

Critical value =[tex]t\alpha /2,[/tex] df = 1.771

 

Margin of error

[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]  

Margin of error = E = 9.10  

The 90% confidence interval estimate of the population mean is,  

[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]

What is 10+2
Please I need help

Answers

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Check the picture below

Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%

Answers

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50


The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?

Answers

Answer:

B. 28, 32, 36 millions

Step-by-step explanation:

Given:

P(t) = 24 + 0.4t

Where,

P(t) = population in millions

t = number of years

✔️Value of the population when t = 10:

Plug in t = 10 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(10)

P(t) = 24 + 4

P(t) = 28 million

✔️Value of the population when t = 20:

Plug in t = 20 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(20)

P(t) = 24 + 8

P(t) = 32 million

✔️Value of the population when t = 30:

Plug in t = 30 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(30)

P(t) = 24 + 12

P(t) = 36 million

The triangles are similar.


What is the value of x?


Enter your answer in the box.

x =

Answers

Answer:

x=12

Step-by-step explanation:

each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle

ex: 8*4=32 and 17*4=68

so we can assume that 15*4= 4x+12

60=4x+12

48=4x

x=12

Answer:

x = 12

Step-by-step explanation:

The triangles are similar so we can use ratios

4x+12      32

-------  = ------------

15             8

Using cross products

(4x+12) *8 = 15 * 32

(4x+12) *8 = 480

Divide each side by 8

(4x+12) *8/8 = 480/8

4x+12 = 60

Subtract 12 from each side

4x+12 -12 = 60-12

4x = 48

Divide by 4

4x/4 = 48/4

x = 12

4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?​

Answers

Answer:

12

Step-by-step explanation:

Which point is a solution to y equal greater than or less too
4x + 5?​

Answers

Answer:

4x+ 4

Step-by-step explanation:

Help please guys thanks

Answers

Answer:

5

Step-by-step explanation:

(625 ^2)^(1/8)

Rewriting 625 as 5^4

(5^4 ^2)^(1/8)

We know that a^b^c = a^(b*c)

5^(4*2)^1/8

5^8 ^1/8

5^(8*1/8)

5^1

5

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex] { {(625}^{2} )}^{ \frac{1}{8} } \\ { ({25}^{2 \times 2} )}^{ \frac{1}{8} } \\ {25}^{4 \times \frac{1}{8} } \\ {5}^{2 \times 4 \times \frac{1}{8} } \\ {5}^{ \frac{8}{8} } \\ {5}^{1} \\ = 5[/tex]

Question 4 of 10
If A = (-1,-3) and B = (11,-8), what is the length of AB?
A. 12 units
B. 11 units
C. 14 units
D. 13 units
SUBMIT

Answers

Step-by-step explanation:

AB = square root of [(xA-xB)^2+(yA-yB)^2]

AB=Squarerootof(-1-11)^2 +(-3-(-8))^2=Squarerootof(-12)^2+(5)^2)

AB=Squarerootof((144)+25)= Squarerootof(169)=13 the answer is 13 units

The choice D is the right one

Simplify
x * x^5 / x^2 * x

Answers

it’s x^3, i guess hope this helps

Is the answer right?

Answers

Answer:

one solution.. your answer is correct

Step-by-step explanation:

discriminate = 900 - (4*9*25)  = 0

thus only one solution

your answer is correct

Which of the following displays cannot be used to compare data from two different sets?

Answers

Answer:

Scatter plot charts are good for relationships and distributions, but pie charts should be used only for simple compositions — never for comparisons or distributions.

find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)

Answers

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]

If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?

Answers

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.

Answers

Answer:

48, 6

Step-by-step explanation:

The ratio of the pieces is 6 to 1

Add them together to get the total

6+1 = 7

Divide the total length by 7

56/7 = 8

Multiply the ratios by 8

6*8 = 48

 1*8 = 6

The peices are 48 and 6

Which one is greater 4.5% or 0.045

Answers

Answer:

They are equal

Step-by-step explanation:

4.5% is 0.045 in decimal form

Answer: They are equal

Step-by-step explanation:

I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent  (move it two spots to the right).

When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?

Answers

Answer:

55000×100/90

61,111.111

Solve for x and y…….

Answers

The shapes are the same size. Match the sides.

3x -1 = 17

Add 1 to both sides:

3x = 18

Divide both sides by 3:

X = 6

2y = 16

Divide both sides by 2

Y = 8

Answer: x = 6, y = 8

Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.

Answers

Answer:

1/4

Step-by-step explanation:

White = w

Black = B

Blue = b1

Tan = t

Wb1

Wt

Bbi

Bt

The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.

Answer:

1/4

Step-by-step explanation:

it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.

Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.

Answers

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).

Answers

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.

Answers

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the  flight.

This means that [tex]p = 0.905[/tex]

Also assume that the airline sells 200 tickets

This means that [tex]n = 200[/tex]

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]

Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{180.5 - 181}{4.15}[/tex]

[tex]Z = -0.12[/tex]

[tex]Z = -0.12[/tex] has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

[tex]p + 0.4522 = 1[/tex]

[tex]p = 1 - 0.4522 = 0.5478[/tex]

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Which of the following is a solution to 2sin2x+sinx-1=0?

Answers

Answer:

270 degrees

Step-by-step explanation:

If you plug in 270 in place of the x's, the function is true!

This is correct for Plate/Edmentum users!! Hope I could help :)

The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)

Answers

Answer:

30 clocks

Step-by-step explanation:

Set up an equation:

Variable x = number of clocks

1200 + 20x = 60x

Isolate variable x:

1200 = 60x - 20x

1200 = 40x

Divide both sides by 40:

30 = x

Check your work:

1200 + 20(30) = 60(30)

1200 + 600 = 1800

1800 = 1800

Correct!

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Describe the system of equations
How many solutions does this system have.

Answers

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?​

Answers

Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.

He wants to end up with a 44 mL solution, so

x + y = 44 mL

Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain

0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL

of acid.

Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives

0.04x + 0.15 (44 mL - x) = 5.28 mL

0.04x + 6.6 mL - 0.15x = 5.28 mL

1.32 mL = 0.19x

x ≈ 6.95 mL

==>   y ≈ 37.05 mL

Determine the domain and range of the graph

Answers

Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2

Answers

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1

Answers

9514 1404 393

Answer:

  (b)  x = 1

Step-by-step explanation:

A graph shows the solution to f(x) = g(x) is x = 1.

__

We want to solve ...

  g(x) -f(x) = 0

  x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0

  x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping

  (x^2 -1)(x +2) +11/3(x -1) = 0 . . . . .  . the difference of squares can be factored

  (x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor

  (x -1)(x^2 +3x +2 +11/3) = 0

The zero product rule tells us this will be true when x-1 = 0, or x = 1.

__

The discriminant of the quadratic factor is ...

  b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3

This is less than zero, so any other solutions are complex.

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