Solve the system of equations 2x - 3y = 4 and 9x - 8y = - 26 by combining the
equations.
Answers
[tex]\sf \Large \boxed{\sf +}\\ \sf \Large \boxed{\sf +}\\\\ \sf \Large \boxed{\sf 11x+-11y=-22}\\\\ 2x+9x-3y-8y=4-26\\Combine\\11x-11y=-22\\Simplify\\x-y=-2\\x=y-2\\Plug\ the\ value\ in\ the\ equation\\2(y-2)-3y=4\\2y-4-3y=4\\-y-4=4\\-y=8\\y=-8\\Solve\ for\ x\\9x-8(-8)=-26\\9x+64=-26\\9x=-90\\x=-10[/tex]
Related Questions
How many ways can a president, Vice President and treasure be selected from a club that has 24 members?
Answers
The Solution:
Given:
selecting 3 ( president, Vice president, and Treasurer) from 24 members.
Required:
Find the number of ways.
[tex]^{24}C_3=\frac{24!}{(24-3)!3!}[/tex][tex]=\frac{24!}{21!\times3!}=\frac{24\times23\times22}{3\times2}=4\times23\times22=2024\text{ ways}[/tex]Answer:
2024 ways
A high school guidance counselor determined the following information regarding students and their likelihood of playing a sport and/or having a part-time job:30% of students play a sport. 65% of students have a part-time job. Of those students who play a sport, 50% have a job.What is the probability a person has a job, if they don't play a sport?
Answers
Conditional Probability
Given two events A and B (not excluding), the probability that A occurs given that B has occurred is called a conditional probability and is calculated as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A∩B) is the probability that A and B occur simultaneously and P(B) is the probability that B occurs.
Now with the given data, we must find the values of the required probabilities.
30% of the students play a sport (S), this means that:
70% of the students don't play a sport (NS).
65% of the students have a job.
Note that there could be students who both play sports and have a job.
Of the 30% of the students who play a sport, 50% have a job. This means that:
15% of the students play a sport and don't have a job
15% of the students play a sport AND have a job
65% - 15% = 50% of the students have a job and don't play a sport
That last number is the numerator of the equation given above:
P(A∩B) = 0.5
The event B corresponds to students that don't play a sport (NS), thus:
P(B) = 0.7
Thus we have:
[tex]P(A|B)=\frac{0.5}{0.7}=\frac{5}{7}[/tex]The required probability is 5/7 or 0.7143
Write a linear equation in standard form for the line that goes through (4,4)and (8,3)
Answers
The standard equation of a line has the form:
y=mx+b
Where m is the slope of the line and b is the intercept.
The only thing we need to determine the equation of a line is two points, in this case, we have the points (4,4) and (8,3). Then, from the first point we know that when x equals 4 y equals 4 and from the second point we know that when x equals 8 y equals 3, we can express this with the standard formula of a line, like this:
4=m*4+b and 3=8*m+b
subtraction the second expression from the second one, we get:
4-3=m*4+b-8*m-b, we can cancel b and then we have:
4-3=m*4-m*8, we can subtract 3 from 4 in the left side and 8*m from 4*m from the right side and then:
1= -4*m , we can divide both sides by -4 and then:
m= -1/4
Now that we know the value of the slope, we only need to specify the value of b, we can do this by replacing the value of m in the expression 4=m*4+b of the first point and then solve for b, like this;
4=m*4+b, m=-1/4, then:
4= 4*(-1/4)+b, then:
4= -1+b, then, adding -1 in both sides we have:
4+1=b, then:
b=5
And the standar form of the line would be:
y=(-1/4)*x+5
write the following equation in a function form.x-3y=-9
Answers
the given equation is
x - 3y = -9
-3y = -9 - x
-3y = - (9 + x )
3y = 9 + x
y = x/3 + 3
so the answer is
y = x/3 + 3
Would love for an expert to verify my solutions:High school trig.
Answers
The entered responses are correct
Explanation:Write out the points from the given information to see the nature of the ellipse as follows:
[tex]\begin{gathered} x=4\cos\frac{\pi}{2}=0 \\ \\ y=3\sin\frac{\pi}{2}=3 \\ \\ (x,y)=(0,3) \end{gathered}[/tex][tex]\begin{gathered} x=4\cos\pi=-4 \\ \\ y=3\sin\pi=0 \\ \\ (x,y)=(-4,0) \end{gathered}[/tex][tex]\begin{gathered} x=4\cos\frac{3\pi}{2}=0 \\ \\ y=3\sin\frac{3\pi}{2}=-1 \\ \\ (x,y)=(0,-1) \end{gathered}[/tex]The answers to choose from are -40, 130, 53, -63, -140, 265, 234
Answers
First we need to know how to convert radians to degrees
[tex]d=\text{r}\cdot\frac{180}{\pi}[/tex]where r is the measure in radians and d is the measure in degrees
for A.
r=53pi/36
[tex]d=\frac{53\pi}{36}\cdot\frac{180}{\pi}=265[/tex]the measure in degrees is 265°
for B.
r= 13pi/18
[tex]d=\frac{13\pi}{18}\cdot\frac{180}{\pi}=130[/tex]the measure in degrees is 130°
for C.
r=-7pi/20
[tex]d=-\frac{7\pi}{20}\cdot\frac{180}{\pi}=-63[/tex]the measure in degrees is -63°
for D.
r=-2pi/9
[tex]d=-\frac{2\pi}{9}\cdot\frac{180}{\pi}=-40[/tex]the measure in degrees is -40°
Select the correct answer,
Which coordinate pair is the best estimate of the point of intersection in this graph?
5
3
2
-1
3
- 1
-2
-3
-4
Answers
ANSWER:
A. (1.5, 0.75)
STEP-BY-STEP EXPLANATION:
We locate the point in the Cartesian plane as follows:
The United States Postal Service delivers about 2⁴ * 3 * 5³ pieces of mail each second. There are 2⁸ x 3⁴ x 5² seconds in 6 days. How many pieces of mail does the United States Postal Service deliver in 6 days write your answer as an expression involving three powers.
Answers
To get to the answer, we'll have to multiply the pieces of mail delivered each second by the amount of seconds in 6 days. This is,
[tex]\begin{gathered} (2^4\times3\times5^3)\times(2^8\times3^4\times5^2)^{} \\ \rightarrow2^4\times3\times5^3\times2^8\times3^4\times5^2^{} \end{gathered}[/tex]Using power properties,
[tex]2^4\times3\times5^3\times2^8\times3^4\times5^2\rightarrow2^{12}\times3^5\times5^5[/tex]Therefore,
[tex]2^{12}\times3^5\times5^5[/tex]pieces of mail are delivered by the United States Postal Service in 6 days.
2 + aIf f(a) =5for what value of a does f(a) = fo?
Answers
Answer
Option A is correct.
The value of a for which f(a) is (1/10) is
a = -(3/2)
Step-by-step Explanation
f(a) is given as
[tex]f(a)=\frac{2+a}{5}[/tex]We are then told to find the value of a for which f(a) = (1/10)
Recall that
f(a) = (2 + a)/5
So, we just equate this definition of the function to (1/10)
[tex]\begin{gathered} f(a)=\frac{2+a}{5}=\frac{1}{10} \\ \frac{2+a}{5}=\frac{1}{10} \\ \text{Cross multiply} \\ 10\times(2+a)=1\times5 \end{gathered}[/tex]10(2 + a) = 5
20 + 10a = 5
Subtract 20 from both sides
20 + 10a - 20 = 5 - 20
10a = -15
Divide both sides by 10
(10a/10) = (-15/10)
a = -1.5 = -(3/2)
Option A is correct.
Hope this Helps!!!
Walter went to Japan for a business trip. Walter converted $ 900 US into 80,514 Yen at the local bank. Walter spent 53,944 Yen on this trip and returned with the remaining Yen to the US.Find the remaining amountRound answer to the nearest whole dollar.
Answers
$297
Explanation:Amount taken for the trip = $900 US
Converting to Yen, amount = 80,514 Yen
Amount spent = 53,944 Yen
Amount remaining + Amount spent = Total amount for the trip
Amount remaining + 53944 = 80514
Amount remaining = 80514 - 53944
Amount remaining = 26570 Yen
We need to convert back to US dollars:
if 80,514 Yen = $900 US
let 26570 Yen = y
Cross multiply:
[tex]\begin{gathered} y(80514\text{ Yen) = \$900 (}26570\text{Yen)} \\ y\text{ = }\frac{\text{ \$}900\text{ }\times\text{ }26570}{80514} \end{gathered}[/tex][tex]y\text{ = \$297.00}[/tex]The remaining amount aftert the trip is $297 (nearest whole dollar)
Use the distributive property of operations and choose the correct equivalent expression for 15 - 21p1(5 - 2p)15(5 - 7p)3(5 - 7p)None of these answers are correct.3(5 - 21p)
Answers
According to the given data we have the following:
15 - 21p
correct expression?
To find the correct expression we need to check which expression is the correct one by multiplying the number which is outside of parentesis to the numbers inside of the parentesis.
Therefore,
15 - 21p
The right option in this case is:
3(5 - 7p)
3 times 5 is=15
3 times -7=21
Therefore 3(5 - 7p)= 15 - 21p
Hello, the three problems below is what I need help with.Use the given functions solve:f(x)= 6x+7. g(x)= -2x-4. h(x)= -3x/4Answer:1. f(x-2)2. g(7x+1)3. h(-12)
Answers
Explanation
you have to replace the values in each function
Step 1
[tex]\begin{gathered} f(x)=6x+7 \\ f(x-2)=6(x-2)+7=6x-12+7=6x-5 \\ f(x-2)==6x-5 \\ \end{gathered}[/tex]Step 2
[tex]\begin{gathered} g(x)=-2x-4 \\ g(7x+1)=-2(7x+1)-4 \\ g(7x+1)=-14x-2-4 \\ g(7x+1)=-14x-6 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} h(x)=\frac{-3x}{4} \\ h(-12)=\frac{-3\cdot-12}{4} \\ h(-12)=\frac{36}{4} \\ \\ h(-12)=9 \end{gathered}[/tex]I hope this helps you
Can you help me with this assignment
Answers
since the line that is wanted is parallel to the one given means that it has the same slope as this one.
1. write the line given in the slope-intercept form
[tex]\begin{gathered} 6x-5y=15 \\ -5y=15-6x \\ 5y=6x-15 \\ y=\frac{6}{5}x-3 \end{gathered}[/tex]2. after having the slope find the y-intercept using the point given (5,4)
[tex]\begin{gathered} y=\frac{6}{5}x+b \\ 4=\frac{6}{5}\cdot(5)+b \\ 4=6+b \\ 4-6=b \\ -2=b \end{gathered}[/tex]3. rewrite the equation
[tex]y=\frac{6}{5}x-2[/tex]Hi I need help with this question, please and thank you
Answers
real part = 8
imaginary part = -√245
Explanation:[tex]\begin{gathered} \text{Given:} \\ 8\text{ - }\sqrt[]{-245} \end{gathered}[/tex][tex]\begin{gathered} \text{For a complex number:} \\ a\text{ + bi} \\ a\text{ = real part} \\ b\text{ = imaginary part} \end{gathered}[/tex]since we can't find square root of a negative number, we will introduce the complex number:
i² = -1
[tex]\begin{gathered} 8-\sqrt[]{-245}\text{ = 8-}\sqrt[]{245i^2} \\ =\text{ 8-i}\sqrt[]{245} \\ \\ \text{writing in the form of real and imainary number:} \\ \text{8-}\sqrt[]{245i}\text{ = 8 + (i}\times\text{-}\sqrt[]{245}) \end{gathered}[/tex][tex]\begin{gathered} \text{real part = 8} \\ \text{imaginary part = -}\sqrt[]{245} \end{gathered}[/tex]which of the following is used to determine spread/variability in a data set? (select all that apply) (standard deviation, median, mean, IQR)
Answers
Answers: IQR and standard deviation
Explanation:
Consider the following compound inequality. 2x+3_<5 or 4x+1>17A)Solve the inequality for x.B) Graph the compound inequality. C) Enter the solution in interval notation.
Answers
step 1
Solve the first inequality
[tex]2x+3\leq5[/tex][tex]\begin{gathered} 2x\leq5-3 \\ 2x\leq2 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval (-infinite,1]
step 2
Solve the second inequality
4x+1>17
4x>16
x>4
the solution for the second inequality is the interval (4, infinite)
therefore
the solution of the compound inequality is
(-infinite,1] U (4, infinite)
In a number line, the solution is
At x=1 is a closed circle and at x=4 is an open circle
find all real zeros of the function g(x)=-4(x-1)2(x+7)3
Answers
Answer:
1 or -7
Step-by-step explanation:
i hope this is what you were looking for
need help converting the point slope form equation to slope intercpt form(y-1)=1/2(x-6)(y+10)=1/3(x+9)
Answers
The standard form of the slope intercept equation is written as
y = mx + b
Where m = slope and b = intercept
[tex]\begin{gathered} (y\text{ - 1) = }\frac{1}{2}(x\text{ - 6)} \\ \text{Firstly, open the parentheses} \\ y\text{ - 1 = }\frac{1}{2}\cdot\text{ x - }\frac{1}{2}\cdot\text{ 6} \\ y\text{ - 1 = }\frac{1}{2}x\text{ - }\frac{6}{2} \\ y\text{ - 1 = }\frac{1}{2}x\text{ - 3} \\ \text{Isolate y} \\ y\text{ = }\frac{1}{2}x\text{ - 3 + 1} \\ y\text{ = }\frac{1}{2}x\text{ - 2} \end{gathered}[/tex]You can earn 5 coins A club's first meeting was attended by 12 people. The second meeting was attended by 4 times as many people as the first meeting. How many people attended the second meeting?
Answers
The first meeting had 12 people. Since, the second meeting is 4 times as many as the first meeting then we multiply the number of people in the first meeting by 4.
4 x 12 = 48
Therefore, there are 48 people who attended the meeting.
How do you quickly find and graph functions for: f(x)=300-25x
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
f(x) = 300 - 25x
Step 02:
graph function:
You only need 2 points to graph a line:
point 1:
x = 0:
y = 300 - 25x
y = 300 - 25(0)
y = 300
( 0 , 300)
point 2:
y = 0:
y = 300 - 25x
0 = 300 - 25x
25x = 300
x = 300 / 25
x = 12
( 12 , 0)
Graph:
That is the full solution.
1. The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation? A) The total number of students at the school in 2000.B) The average number of students per classroom in 2000.C) The estimated increase in the average number of students per classroom each year.D) The estimated difference between the average number of students per classroom in 2010 and in 2000.
Answers
Given the equation:
y = 0.56x + 27.2
The equation above represents the average number of students per classroom at a Central High school from 2000 to 2010.
Where,
x represents the number of years since year 2000
y represents the average number of students per classroom
Also, 27.2 represents the number of students at the school in 2000.
Since the equation is in slope intercept form: y = mx + b, where m is the slope.
This means that 0.56 represents the slope and slope can be simply defined as the average rate of change.
Therefore, the statement that best describes the number 0.56 in the equation is the estimated increase in the average number of students per classroom each year.
ANSWER:
C) The estimated increase in the average number of students per classroom each year.
A truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1:4:3 if there are 76 tomato juice bottles, then how many juice bottles in total are there?
Answers
Answer: Total number of juice bottles is 152
The truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1 : 4: 3
There are 76 tomato juice bottle
Let the number of grapefruit bottle = x
Let the number of pineapple juice bottle = y
1: 4 : 3 = x : 76: y
To find the number of juice bottles, we will need to establish a proportion
[tex]\begin{gathered} 1\text{ : 4 = x : 76} \\ \frac{1}{4}\text{ = }\frac{x}{76} \\ \text{Introduce cross multiply} \\ 1\cdot\text{ 76 = 4 }\cdot\text{ x} \\ 76\text{ = 4x} \\ \text{Divide both sides by 4} \\ \frac{76}{4}\text{ = }\frac{4x}{4} \\ x\text{ = }\frac{76}{4} \\ x\text{ = 19} \end{gathered}[/tex]To calculate for y, we will still need to establish a proportion
[tex]\begin{gathered} 4\text{ : 3 = 76 : y} \\ \frac{4}{3}\text{ = }\frac{76}{y} \\ \text{Introduce cross multiply} \\ 4\cdot\text{ y = 76 x 3} \\ 4y\text{ = 228} \\ \text{Divide both sides by 4} \\ \frac{4y}{4}\text{ = }\frac{228}{4} \\ y\text{ = }\frac{228}{4} \\ y\text{ = 57} \end{gathered}[/tex]Since, x is the number of grapefruit bottles, then the number of grapefruit bottles in the truck is 19 bottles
Since, y is the number of pineapple bottles, therefore, the number of pineapple bottle is 57 bottles
Total number of juice bottles in the lorry = 19 + 76 + 57
The total number = 152 juice bottles
Which of the following ordered pairs is a solution to the equation 2x+4y=16? Select all that apply.Select all that apply:(11,−10)(−12,10)(4,2)(6,1)(−8,−6)
Answers
Answer:
[tex]\begin{gathered} (x,y)\Rightarrow(-12,10) \\ (x,y)\Rightarrow(4,2) \\ (x,y)\Rightarrow(6,1) \end{gathered}[/tex]Explanation: The plot of this equation along with ordered pairs is:
Therefore the answer is:
[tex]\begin{gathered} (x,y)\Rightarrow(-12,10) \\ (x,y)\Rightarrow(4,2) \\ (x,y)\Rightarrow(6,1) \end{gathered}[/tex]A quality control inspector has drawn a sample of 20 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection? Round your answer to four decimal places.
Answers
The binomial distribution is
[tex]\begin{gathered} P(X=k)=(nbinomialk)p^k(1-p)^{n-k} \\ k\rightarrow\text{ number of successful trials} \\ n\rightarrow\text{ total number of trials} \\ p\rightarrow\text{ probability of a trial being successful} \\ (nbinomialk)=\frac{n!}{(n-k)!k!} \end{gathered}[/tex]Therefore, in our case, the distribution is
[tex]n=20,p=20\%=0.2[/tex]And we are interested in the probability of k=0 (0 defective bulbs) and k=1 (1 defective bulb). Thus,
[tex]P(X=0)=(20binomial0)(0.2)^0(0.8)^{20}=1*1*0.8^{20}=0.8^{20}[/tex]Similarly,
[tex]P(X=1)=(20binomial1)(0.2)^1(0.8)^{19}=20*0.2*(0.8)^{19}=4*0.8^{19}[/tex]Hence,
[tex]P(X\leq1)=P(X=0)+P(X=1)=0.8^{20}+4(0.8)^{19}\approx0.0692[/tex]The probability of the 20 bulbs including 1 or fewer defective bulbs is 0.0692, the answer is 0.0692Amelia had a total of 1,260 marbles and table tennis balls. She had 40 fewer marbles than table tennis balls.How many table tennis balls did she have?
Answers
Let 'x' represent number of marbles
Let 'y' represent number of table tennis balls
Amelia had a total of 1,260 marbles and table tennis balls,
The mathematical representation is,
[tex]x+y=1260\ldots\ldots\text{.}.1[/tex]She had 40 fewer marbles than table tennis balls.
The mathematical representation is,
[tex]x=y-40\ldots\ldots\ldots2[/tex]Substitute x = y - 40 from equation 2 into equation 1 to solve for y
[tex]\begin{gathered} y-40+y=1260 \\ y+y=1260+40 \\ 2y=1300 \\ \frac{2y}{2}=\frac{1300}{2} \\ y=650\text{ table tennis balls} \end{gathered}[/tex]Hence, she has 650 marbles.
Find the slope of the line that passes through (10,8) and (1,12)
Answers
1) To find out the slope, we need to plug into this formula those points:
2) So the measure of how steep is that line is given by the slope of m=-4/9
And the line has a decreasing orientation since this slope is < 0.
3) Hence, the slope is m= -4/9
Solve for b.
42 = 42 +9b
Answers
Answer:
b=0
Step-by-step explanation:
42=42+9b
We move all terms to the left:
42-(42+9b)=0
We add all the numbers together, and all the variables
-(9b+42)+42=0
We get rid of parentheses
-9b-42+42=0
We add all the numbers together, and all the variables
-9b=0
b=0/-9
b=0
Answer:
b = 0
Step-by-step explanation:
42 - 42 = 42 + 9b - 42
0 = 9b
9b = 0
9b/9 = 0/9
b = 0
~ LadyBrainiac
Seventh grade M.12 Simple interest E7Y Trisha has $74,430 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will she earn in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $ Submit
Answers
Given:
The initial balance = P = $74,430
Interest rate per year = r = 10% = 0.1
The interest is not compounded, so it is a simple interset
Time = t = 1 year
So,
[tex]I=P\cdot r\cdot t=74430\cdot0.1\cdot1=7443[/tex]So, the answer is I = $7,443
A recipe for cookie call for 2/3 of cups of sugar per batch.Colin and Rae used 5 1/3 cups of sugar to make multiple batches of cookies.how many batches dish she make??
Answers
Given
Cookie needs 2/3 of cups of sugar per batch
Colin and Rae
5 1/3 cups of sugar
Procedure
[tex]\begin{gathered} \frac{5\text{ 1/3}}{2/3} \\ \frac{\frac{16}{3}}{\frac{2}{3}}=\frac{16}{2}=8 \end{gathered}[/tex]
The answer would be 8
If there are 25 people in a room and 15 chairs, how many different seating arrangements are possible?A)3268760B)7.41x10^11C)4.27x10^18D)4.27x10^19
Answers
We will investigate the counting principles that are used for cases of probability evaluation.
There are two possible types of counting principles.
Combinations:
It gives us the total number of possible selections that you can make "given" - " for " something. It is a simple selection process between the subejct and an object. The notation used for determining the number of selections/combinations is expressed as:
[tex]^nC_r[/tex]Where,
[tex]\begin{gathered} n\colon\text{ Total number of subjects} \\ r\colon\text{ Total number of ob}\imaginaryJ ects \end{gathered}[/tex]Then we can use the calculator infused functions of " C " combinatorics!
Permutations:
It gives us the total number of possible arrangements comprised of selections and shuffling that you can make "given" - " for " something. It is a simple selection and shuffling process of subject and object. The notation used for determining the number of selections/combinations and re-shuffling is expressed as:
[tex]^nC_r\cdot\text{ r!}[/tex]The above means that to determine arrangements we first need to find the number of combinations " C " between the subject and object then we will re-shhuffle the order of each combination paired with an object!
We are given the following:
[tex]\begin{gathered} \text{Subject : people} \\ \text{Object : chairs} \end{gathered}[/tex]The corresponding variables are:
[tex]\begin{gathered} n\text{ = 25} \\ r\text{ = 15} \end{gathered}[/tex]We are to determine the total number of possible arrangements that are possible. Hence, we are looking at the case of permutations that involves the selection and re-shuffle process.
The total number of arrangements can be made as such:
[tex]\begin{gathered} ^{25}C_{15}\cdot15! \\ 4.27\cdot10^{18}\text{ possible arrangements} \end{gathered}[/tex]