Mathematics College


(08.03 MC)
A system of equations is shown below:

y = 3x – 7
y = 2x + 1

What is the solution to the system of equations? (1 point)


A. (8, 17)

B. (–8, 17)

C. (–8, –17)

D. (8, –17)

Answers

Answer 1

Answer:

(8, 17)

Step-by-step explanation:

Here you have two functions equalling y.

To find x, we set these two functions equal to one another, which eliminates y:  

3x - 7 = 2x + 1.

Find x.  To do this, subtract 2x from both sides, obtaining x - 7 = 1.

Next, add 7 to both sides:  x = 8.

Finally, find y.  Do this by subbing 8 for x in either of the two given equations.

Working with the 2nd equation:  y = 2(8) + 1 = 17

Thus, the solution is (8, 17).

Answer 2

I believe the answer is (8 , 17)

Related Questions

Which of the numbers below are whole numbers?Check all that apply. A. 9747.25 B. 0.7832 C. 918 D. 0 E. 46245.7 F. 484.857

Answers

I'm pretty sure it's C and D
whole number is an integer;  number without fractions; or without decimal.
whole numbers: { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

so answer

C. 918
D. 0

When a certain type of thumbtack is​ flipped, the probability of its landing tip up​ (U) is 0.54 0.54 and the probability of its landing tip down​ (D) is 0.46 0.46. Suppose you flip two such​ thumbtacks, one at a time. The probability distribution for the possible outcomes of these flips is shown below. a. Find the probability of getting 0​ ups, 1​ up, or 2 ups when flipping two thumbtacks. b. Make a probability distribution graph of this.

Answers

Part A. In probability and statistics, there is an equation for repeated trials. This is useful for situations like tossing a coin or rolling a dice. Each possible result of a situation has its own probability of p. You want to find the total probability of getting 'r' number of successes out of 'n' trials. The equation is

P = n!/r!(n-r!) * p^(n-r) * q^r, where
n is the number of trials; in this case n=2
r is the number of times an event can happen successfully
p is the probability of that success
q is the probability of failing; note that p+q=1

The p for ups is 0.54, while q is 0.46. When r=0 ups
P = 2!/0!(2-0!) * (0.54)^(2-0) * (0.46)^0
P = 0.2916

The same thing is done to r=1 and r=2. The complete table is shown below

     r            P
    0         0.2916
    1         0.4968
    2         0.2116

When you graph r against P, you will get a probability distribution graph as shown in the picture (Part B).

A spinner is divided into 10 equal sections numbered 1 through 10. If the arrow is spun twice, what is the probability the first number will be a 2 and the second number will be a 4?

Answers

The probability of spinning 2 then 4: [tex]\( \frac{1}{10} \times \frac{1}{10} = \frac{1}{100} \).[/tex]

To find the probability that the first spin results in a 2 and the second spin results in a 4, we need to determine the probability of each event and then multiply them together because the spins are independent.

1. Probability of spinning a 2 on the first spin:

  Since there is 1 section labeled '2' out of 10 sections in total, the probability of spinning a 2 on the first spin is [tex]\( \frac{1}{10} \)[/tex].

2. Probability of spinning a 4 on the second spin:

  Similarly, there is 1 section labeled '4' out of 10 sections in total, so the probability of spinning a 4 on the second spin is also [tex]\( \frac{1}{10} \)[/tex].

Now, to find the probability of both events happening (the first spin resulting in a 2 and the second spin resulting in a 4), we multiply the probabilities of each event:

[tex]\[ P(\text{first spin = 2}) \times P(\text{second spin = 4}) \][/tex]

[tex]\[ = \frac{1}{10} \times \frac{1}{10} \][/tex]

[tex]\[ = \frac{1}{100} \][/tex]

So, the probability that the first spin results in a 2 and the second spin results in a 4 is [tex]\( \frac{1}{100} \)[/tex].

two similar triangles have areas of 18 and 32 find the ratio of their perimeters

Answers

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{s^2}{s^2}=\cfrac{18}{32}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{18}{32}\implies \cfrac{s}{s}=\sqrt{\cfrac{18}{32}} \\\\\\ \cfrac{s}{s}=\cfrac{\sqrt{18}}{\sqrt{32}}\implies \cfrac{s}{s}=\cfrac{\sqrt{9\cdot 2}}{\sqrt{16\cdot 2}}\implies \cfrac{s}{s}=\cfrac{\sqrt{3^2\cdot 2}}{\sqrt{4^2\cdot 2}}\implies \cfrac{s}{s}=\cfrac{3\sqrt{2}}{4\sqrt{2}} \\\\\\ \cfrac{s}{s}=\cfrac{3}{2}[/tex]

Graphs of exponential functions

For both y= 8× and y= (2/7)×, what would be the equation of the horizontal asymptote for those two?

Answers

Both graphs approach the x-axis as x gets large either in the positive direction or the negative direction. An equation for the x-axis is  y = 0.

0.02 is 10 times 0.2

Answers

It is false.
10*0.2 = 2

0.02 is actually a tenth of 0.2
False, because .2 is quite times .02 not .02 is 10 times .02.

In a school, the probability that a student takes environmental science and geography is 0.72.The probability that a student takes technology is 0.25. What is probability that a student takes geography given that the student is taking environmental science?

Answers

I believe it would be 0.75

If not that the only other thing I could think of would be 0.03, but it says he is already taking environmental science.

How much would $500 invested at 6% interest compounded monthly be worth after 4 years? Round your answer to the nearest cent

Answers

1) Compound interest formula:
[tex]A = P(1+ \frac{r}{n}) ^{nt}[/tex]**
**A = amount, P = principal amount, r = rate, n = # of times interest is compunded every year, t = time(in years)
2) Plug numbers in
[tex]A = (500)(1+ \frac{0.06}{12}) ^{(12)(4)}[/tex]
3) Solve
A = 635.24458054

Hope this helped! Good Luck!

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00  is $635.24.

Compound Interest

Given Data

Principal p = $500Rate  r = 6%Time t = 4 years

A = P + I where

P (principal) = $500.00

I (interest) = $135.24

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 500.00(1 + 0.06/12)(12)(4)

A = 500.00(1 + 0.005)(48)

A = $635.24

Learn more about compount interest here:

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What is the estimate of 2616

Answers

[tex]Hundreds:[/tex] [tex]2,600 [/tex]
[tex]Tens:[/tex] [tex]2,620 [/tex]
[tex]Thousands:[/tex][tex]3,000 [/tex]

[tex]good \\ luck \\ on \\ your \\ assignment \\ \\ \\ \\ enjoy \\ your \\ day! \\ \\ \\ \\ MeIsKaitlyn[/tex]

Which fraction has a value that's equal to 7/8?

Answers

21/24 is the answer that have the value that's equal to 7/8
Four options are given for this question, which are: 15/8, 49/64, 56/8 and 21/24.
7/8 = 0.875
15/8 = 1.875
49/64 = 0.7656
56/8 = 7
21/24 = 0.875.
The fraction that has a value that corresponds with that of 7/8 is 21/24, therefore, 21/24 is the correct option.

what is the vertex of y=3x^2+6x+5

Answers

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llcclll} y = &{{ 3}}x^2&{{ +6}}x&{{ +5}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]

Who wanna help me ??

Answers

It's 33.7, or 34 if you round it, you can find x by doing tan32 which would equal x/51, tan32=x/51, and solve for x

Which expression is equivalent to (3b + 2r) + (4b + r)?

Answers

I think it should be 7b+3r
It would be 7b+ 3r. 
Since you have to distribute them. you would add 4 with 3 which is seven and 2 with a. A is a number but since you dont know, it is a one. So it would be B
Hopefully this helps!:)
Dont for get to like and rate!

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution. 1-6i is a zero of f(x) = x^2-2x^3+38^2-2x+37

Answers

The Complex conjugate root theorem states that if a-bi is a solution, so is a+bi, and vice versa. Therefore, 1+6i is another solution

The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 35 cubic inches when it's base area is 15 square inches and it's height is 7 inches. What is the volume of a pyramid with a base area of 36 square inches and a height of 5 inches?

Answers

V ~ base_area * height

Take ratios:

V2/V1 = base_area_2 * h2 / base_area_1 / h1 = 36 * 5 / 15 / 7 = 12/7,

V2 = 12/7*v1 = 12*35/7 = 60 cubic inches.

Check but it gives a round solution ...

Evaluate the expression for s = 11 and v = 8.

(s – v)2


A. 113
B. 6
C. 9
D. 57

Answers

Answer:

C. 9

Step-by-step explanation:

s=11

v=8

(11-8)²

(3)²

9

If compact discs cost $15.89 each, how much does one compact disc cost with 6% sales tax?

Answers

 6% = 0.06

 if you want to know the total price including the tax

 multiply 15.89 x 1.06 = 16.84

If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

If compact discs cost $15.89 each.

Then the cost of each disc after 6% sales tax will be

→ 1.06 × $ 15.89

→ $ 16.84

If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.

More about the percentage link is given below.

https://brainly.com/question/8011401

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Determine the scale factor of the function f(x)=1/3root x

Answers

Please be clear with the expressions.
Here we assume 
f(x)=(1/3) sqrt(x)

A scale factor is a multiplier applied to a parent function.
If the parent function is f(x), and
g(x)=a*f(x), then a is a scale factor.

Assuming the parent function is sqrt(x), and f(x)=(1/3) sqrt(x)
then the scale factor is  (1/3).
[note]
if f(x) is a cube root, then write
f(x)=cube root(x), or f(x)=x^(1/3).
the exponentiation sign ^ is very useful.
Im taking the test right now and got it wrong lol.. for anyone needing help the answer is NOT 3. just to narrow it down for you 

The equation y = 30x + 40 represents the line of best fit showing Ted’s earnings in terms of the number of hours he works as a plumber. If x is the number of hours he works and y is Ted’s earnings, which statement describes this situation correctly? Ted’s initial charge is $30, and his hourly charge is $40. Ted’s initial charge is $40, and his hourly charge is $30. Ted does not charge an initial amount, and his hourly charge is $40. Ted does not charge an initial amount, and his hourly charge is $70.

Answers

Ted’s initial charge is $40, and his hourly charge is $30. 

Answer:  Ted’s initial charge is $40, and his hourly charge is $30.

Step-by-step explanation:

We know that the general equation of a line in intercept form is given by :-

[tex]y=mx+c[/tex], where m is the slope of the line and c represents the y-intercept of the function.

The given function :-The equation [tex]y = 30x + 40[/tex] represents the line of best fit showing Ted’s earnings in terms of the number of hours he works as a plumber.

Here, Slope =30

The y-intercept = 40

If x is the number of hours he works and y is Ted’s earnings.

Then by comparing the general equation of line in intercept form,  the initial amount charged by Ted =y-intercept = $ 40

His hourly charge = Slope = $ 30

Which equation represents the average of the x-intercepts for 4x^2-24x+20

Answers

number of x intercepts in this equation is 2 because max power in the function is 2. number of x intercepts is determined by "highest power".

let x1 represent first x intercept and
let x2 represent second x intercept

Formula for finding average of x intercepts is logicaly:
Avg = (x1 + x2)/2

we want to find x1 and x2
4x^2 - 24x + 20 = 0
x^2 - 6x + 5 = 0


x1 = 5
x2 = 1

Avg = 3

Evaluate ,where e is the solid that lies between the cylinders x^2+y^2=1 and x^2+y^2=16, above the xy-plane, and below the plane z=y+4

Answers

Final answer:

To evaluate the solid e which lies between two cylinders and a plane, one would typically set up a triple integral in cylindrical coordinates. This involves translating the given boundaries from rectangular coordinates into cylindrical coordinates to account for the radial, angular, and vertical dimensions of the solid.

Explanation:

This question pertains to the evaluation of a solid, denoted as e, that is located between the two cylinders x^2 + y^2 = 1 and x^2 + y^2 = 16. These cylinders are located above the xy-plane and below the plane z = y + 4. The evaluation of such a solid requires the application of integral calculus. Typically, in such cases we would set up a triple integral by converting rectangular coordinates into cylindrical coordinates (r, theta, z).

Given the specifics of the solid, the radial path r would vary between sqrt(1) and sqrt(16), which is between 1 and 4. The angular path theta would cover the full circle, thus varying between 0 and 2π. The z-coordinate would be bounded below by the xy-plane (0) and above by the plane z = y + 4.  Please note that you would need to convert the z-boundary into cylindrical coordinates as well.

Learn more about Triple Integrals in Cylindrical Coordinates here:

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Holly wants to save money for an emergency. Holly invests $1,100 in an account that pays an interest rate of 8.75%. How many years will it take for the account to reach $6,400

Answers

I believe it would be 3.5 years or 3 1/2 years

Answer:

20.99 years . plato

Step-by-step explanation:

It costs $145 for 10 people to attend a concert. How much does it cost a group of 8 people?

Answers

It would cold $116 for 8 people to attend a concert.

$145/10 = $14.50
$14.50 * 8 = $116.00

Answer:

$145/10 = $14.50

$14.50 * 8 = $116.00

Step-by-step explanation:

Pat writes all the 7-digit numbers in which all the digits are different and each digit is greater than the one to its right (so the tens digit is greater than the units, the hundreds greater than the tens, and so on). For example, 9,865,320 is one of the numbers that Pat writes down.
One of Pat's numbers is chosen at random. What is the probability that the middle (thousands) digit is a 5?

Answers

There are many ways to solve this problem.  I will show two.  I invite interested readers to present other answers, most probably more elegant ones. 

(A) Solve by cases.
Because of the nature of the problem, the first digit can only begin with 6,7,8 or 9.
Case 6: 1 way
If it begins with a "6", there is only one way, namely consecutively, 6543210.
Case 7: 7 ways
If it begins with a 7, there is one way, consecutively, 7654321.
Since it finishes with a 1, a variation could be that one of the six following digits could have a gap with the previous, such as
7543210, or 7643210...  There are 6 ways to do this.
total = 1+6 = 7 ways.
Case 8: 28 ways
consecutively=1 way
one digit skips 1 with previous digit=6 ways (e.g. 8654321...)
one digit skips 2 with previous digit=6 ways (e.g. 8543210,8743210...)
two digits skip 1 with previous digit=C(6,2) ways = 6*5/(2*1)=15 ways
total = 1+6+6+15 = 28 ways
Case 9: 64 ways
consecutively=1 way
one digit skips 1 with previous digit=6 ways
one digit skips 2 with previous digit=6 ways
one digit skips 3 with previous digit=6 ways
two digits skip 1 with previous digit=(6*5/(2*1))=15 ways
one digit skips 1 and one digit skips 2 with previous = 6*5=30 ways
total=1+6+6+6+15+30=64 ways

Grand total = 1+7+28+64 =120 ways.


(B) by computer program
The easiest way is to write a program and solve it to give a total of 120.
An example program could be:count:0;for x1:6 thru 9 do (    for x2:5 thru x1-1 do (        for x3:4 thru x2-1 do(            for x4:3 thru x3-1 do(                for x5:2 thru x4-1 do(                    for x6:1 thru x5-1 do(                        for x7:0 thru x6-1 do(                            count:count+1                            )                        )                    )                )            )        )    )$print(count)$
Output shows 120 ways.

What's the value of 4 in the number 745

Answers

Because 4 is in the tens place in the number 745, the value is equal to
4*10=40

Final answer: 40
Hello, the "4" is in the tens place
Good luck!

Factor and simplify the algebraic expression.

3x^-4/3 +6x^1/3

Thanks in advance if you can help me!

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\\\ and\qquad a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\[/tex]

[tex]\fb 3x^{-\frac{4}{3}}+6x^{\frac{1}{3}}\implies 3\cdot \cfrac{1}{x^{\frac{4}{3}}}+6x^{\frac{1}{3}}\implies \cfrac{3}{x^{\frac{4}{3}}}+6x^{\frac{1}{3}}\impliedby LCD=x^{\frac{4}{3}} \\\\\\ \cfrac{3+(6x^{\frac{1}{3}})(x^{\frac{4}{3}})}{x^{\frac{4}{3}}}\implies \cfrac{3+6x^{\frac{1}{3}+\frac{4}{3}}}{x^{\frac{4}{3}}}\implies \cfrac{3+6x^{\frac{5}{3}}}{x^{\frac{4}{3}}}\implies \cfrac{3+6\sqrt[3]{x^5}}{\sqrt[3]{x^4}}[/tex]

that'd be hmmm a kinda simplification of it, not sure if I could call it a simplified version, more like an expansion though.

a tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shawdow. what is the height of the tree?

Answers

First you need to set up the ratios.

x/9=6/4
(with hights on top, and shadows on bottom)

then you need to cross multiply and divide.
4x=54
      /4
x=13.5

Consider the partially completed​ one-way anova summary table. source sum of squares degrees of freedom mean sum of squares f between 270 within 18 total 810 21 what is the sum of squares within for this anova​ procedure?

a. 620

b. 390

c. 540

d. 680

Answers

The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The sum of squares within for this ANOVA​ procedure is 680. The answer is letter D.


A telephone pole cast a shadow that is 37 m long find the height of the telephone pole if a statue that is 33 cm tall cast a shadow 83 cm long ?

Answers

By similar triangles we know:

h1/x1=h2/x2

p/37=33/83  multiply both sides by 37

p=1221/83 m

p≈14.71 m (to nearest hundredth of a centimeter)

Answer:

The height of the telephone pole is 14.711 m (Approx) .

Step-by-step explanation:

Let us assume that the height be x .

Let us assume that the shadow  be y .

(As the shadow is always proportional to the height .)

Thus

[tex]x\propto y[/tex]

y = kx

Where k is the constant of proportionality .

As given

if a statue that is 33 cm tall cast a shadow 83 cm long .

y = 83 cm

x = 33 cm

Put in the equation y = kx .

83 = 33k

[tex]k = \frac{83}{33}[/tex]

As given

A telephone pole cast a shadow that is 37 m .

Let us assume that the height of the telephone pole be z .

As

1m = 100cm

37m = 3700 cm

y = 3700 cm

x = z

Put in the equation  y = kx .

3700 = zk

[tex]k = \frac{3700}{z}[/tex]

Compare the value of k .

[tex]\frac{3700}{z} = \frac{83}{33}[/tex]

[tex]\frac{3700\times 33}{83} =z[/tex]

[tex]\frac{122100}{83} =z[/tex]

z = 1471.1 cm(Approx)

As

[tex]1\ cm = \frac{1}{100}\ m[/tex]

[tex]1471.1\ cm = \frac{1471.1}{100}\ m[/tex]

                       = 14.711 m (Approx)

Therefore the  height of the telephone pole is 14.711 m (Approx) .

The scores of a high school entrance exam are approximately normally distributed with a given mean m = 82.4 and standard deviation = 3.3. What percentage of the scores are between 75.8 and 89?

Answers

mean, m=82.4
standard deviation, sigma=3.3
Need proportion of sample between 75.8 and 89.

first calculate Z-scores of 75.8 and 89
Z(75.8)=(75.8-82.4)/3.3=-2
Z(89)=(89-82.4)/3.3=2

So
P(75.8<X<89)
=P(-2<Z<2)
=P(Z<2)-P(Z<-2)
=0.9772-0.0227
=0.9545


The percentage of the scores are between 75.8 and 89 can be calculated using z-scores.

The percentage of the scores between 75.8 and 89 is 95%.

Given:

The mean is [tex]m=82.4[/tex].

The standard deviation is [tex]\sigma =3.3[/tex].

Calculate the Z- score for 75.8.

[tex]Z(75.8)=\dfrac{(75.8-82.4)}{3.3} \\Z(75.8) = -2[/tex]

Calculate the Z- score for 89.

[tex]Z(89)=\dfrac{(89-82.4)}{3.3}\\Z(89)=2[/tex]

Calculate the percentage of the scores are between 75.8 and 89.

[tex]P(75.8<X<89)=P(-2<Z<2)\\P(75.8<X<89)=P(Z<2)-P(Z<-2)\\[/tex]

Refer the z-table, put the value,

[tex]P(75.8<X<89)=0.9772-0.0227\\P(75.8<X<89)=0.9545[/tex]

Thus, the percentage of the scores between 75.8 and 89 is 95%.

Learn more about z-score here:

https://brainly.com/question/13299273

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