Solve this system of equations by graphing. First graph the equations, and then type the solution.x+3y=6y=1/2x+7
Answers
Given the system of equations;
[tex]\begin{gathered} x+3y=6---(1) \\ y=\frac{1}{2}x+7---(2) \end{gathered}[/tex]We shall first of all re-arrange the equations in the slope-intercept form;
[tex]y=mx+b[/tex]Note that the second one has already been expressed in the slope-intercept form. For the first one we would now have;
[tex]\begin{gathered} x+3y=6 \\ 3y=-x+6 \\ \text{Divide both sides by 3;} \\ \frac{3y}{3}=-\frac{x}{3}+\frac{6}{3} \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]To plot this equations on a graph we take two extreme points. We can do this by finding the value of y when x = 0, and y when x = 0.
For the first equation, we would have;
[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ \text{When x}=0 \\ y=-\frac{1}{3}(0)+2 \\ y=0+2 \\ y=2 \\ \text{That means we have the point }(0,2) \\ \text{Also, when y}=0 \\ 0=-\frac{1}{3}x+2 \\ \frac{1}{3}x=2 \\ \text{Cross multiply this and you'll have;} \\ x=2\times3 \\ x=6 \\ We\text{ now have our second point, }(6,0) \end{gathered}[/tex]Hence, for the first equation we have the two points;
[tex]\begin{gathered} A(0,2) \\ B(6,0) \end{gathered}[/tex]For the second equation;
[tex]\begin{gathered} y=\frac{1}{2}x+7 \\ \text{When x}=0 \\ y=\frac{1}{2}(0)+7 \\ y=0+7 \\ y=7 \\ \text{This means we have the point }(0,7) \\ \text{Also, when y}=0 \\ 0=\frac{1}{2}x+7 \\ -\frac{1}{2}x=7 \\ \text{Cross multiply and you'll have;} \\ x=7\times(-2) \\ x=-14 \\ \text{That means we now have the second point which is }(-14,0) \end{gathered}[/tex]For the second equation we now have the points;
[tex]\begin{gathered} A(0,7) \\ B(-14,0) \end{gathered}[/tex]We can now input both sets of coordinates and our graph would come out as shown below.
The point of intersection as we can see is at where x = -6 and y = 4. Therefore;
ANSWER:
The solution to the system of equations as shown on the graph is;
[tex](-6,4)[/tex]
Related Questions
based on the side lengths given (a, b, and c), which triangles are right triangles????A. a=4, b=6, c=8B. a=6, b=8, c=10C. a=5, b=6, c=(square root of) 61D. a=6, b=9, c=12 PLEASE HELP!!
Answers
Explanation
From the question, a right-angle triangle must obey Pythagoras theorem. Therefore, we can see that
[tex]6^2+8^2=10^2\text{ also, }5^2+6^2=(\sqrt{61})^2[/tex]The rest of the values do not obey Pythagoras theorem. Therefore;
Answer: Option B and Option C
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.
#3) Ulices was charged $140 plus a pick up charge of $20 to ship 4 identical boxesbys Fast Ship. The pick up charge applies regardless of how many boxes are pickedup. What would have been the change to Ulices' account if he had shipped just 1box?
Answers
To determine the Ulices's account if he shipped just 1 box, calculate the charge for one box. To calculate the charge, compute the quotient between the charge for 4 boxes between 4 boxes, just as folow:
charge per one box = 140/4 = 35
Hence, for 1 box the charge is $35
Due to it is necessary to pay $20 idependenty of the number of boxex, you sum $20 to the cost for one box:
New Ulices's account = $35 + $20 = $55
Hence, Ulices's account would have been of $55
The functions f(x) and g(x) are shown on the graph.F(x)=x^2What is g(x)?A. g(x)= -x^2+3B. g(x)=(-x)^2-3C. g(x)=(-x)^2+3D.g(x)= -x^2-3
Answers
On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).
The original function is given as
[tex]f(x)=x^2[/tex]The function is reflected over the x-axis.
The rule for the reflection over the x-axis is given as
[tex]f(x)\to-f(x)[/tex]Applying this to the function, we have the new function to be
[tex]-x^2[/tex]The graph is also shifted downwards by 3 units.
This shift can be represented as
[tex]f(x)\to f(x)-3[/tex]Applying this to our function, we have the new function, g(x), to be
[tex]g(x)=-x^2-3[/tex]The correct option is OPTION D.
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
A department store is offering a promotion on candles. The promotion is "Buy 2 candles, get 40% off the 3rd Candle". If you are buying three of thesame candles with the same price, which two expressions below can be used to represent the cost of buying 3 candles.c+0.6c2.6cOc+c+0.4c2c +0.6c2.4c
Answers
Given:
it is given that a department store is offering a promotion on candles. The promotion is "Buy 2 candles, get 40% off the 3rd Candle".
Find:
we have to find the total cost of buying 3 same candles.
Explanation:
Let c be the cost of one candle.
Then 2c is the cost of two candles.
and, as per offer , the price of the third candle is 40% off.
if c is the price of one candle , then the cost of third candle is
c - (40% of c) = c - 0.4c = (1 - 0.4)c = 0.6c
Therefore, cost of third candle is 0.6c.
Now, the total cost of buying three same candles = 2c + 0.6c = 2.6c
Therefore, the options 2c + 0.6c and 2.6c are correct options
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
Yea I think and if it’s ok we
Answers
Explanation: To solve a derivate we can use a simple technique presented below
- First, we take the exponent and multiply it by the function. Second, we subtract a unit of the exponent. Let's visualize it better on the drawing below
Step 1: Now we can use the same concept to calculate all the derivates we need as follows
Final answer: So the final answers are
[tex]\begin{gathered} letter_{\text{ }}a=5x^4 \\ letter_{\text{ }}b=20x^3 \\ letter_{\text{ }}c=60x^2 \\ letter_{\text{ }}d=120x \end{gathered}[/tex].
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
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]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]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
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:
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.
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°
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
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 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
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]Abrha lives in an apartment and pays the following expenses each month: electric bill, $44.90; TV streaming service, $24.99; and rent, $625.85 Estimate his total expenses for the month by first rounding each value to the nearest tens place.
Answer: $700
Answers
Abrha will be spending $701 monthly, just by arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Abrha lives in an apartment,
electric bill, $44.90 = $50
TV streaming service, $24.99 = $25
Rent, $625.85 = $626
So the Total expenses will be (50+25+626) = $701 just by arithmetic operation
Hence Abrha will be spending $701 monthly.
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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.
If the product is 900, and the two of its three factors are 3 and 50, what is the third factor?
Answers
We have the multiplication of 3 factors, one of them unknown, that give 900 as a result.
We can write this as:
[tex]\begin{gathered} 3\cdot50\cdot x=900 \\ 150x=900 \\ x=\frac{900}{150} \\ x=6 \end{gathered}[/tex]The third factor is 6.
Use the Angle Bisector Theorem to set up an equation and solve for X.
1. AB is the Angle Bisector of 4CAD.
33° B (4x + 1)º A D
Answers
Step-by-step explanation:
what happens, if I cut something in half ?
not just into 2 pieces, but outright in half ?
a pizza or a cake ?
well, I get 2 identical pieces.
a bisector (bi = 2 or double, sector = part) splits an angle into 2 equal parts.
that means
33 = 4x + 1
from there we get
32 = 4x
x = 32/4 = 8
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
Which sequence of rigid motions will definitely work to take triangle RPQ onto triangle CAB?
Answers
RPQ to CAB transform
Rotation needed = RPQ using C as center ,an angle ACP
Translations= Line RC
Reflections= None
Then answer is
Option D)
Translate RPQ by the direct line segment RC
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:
Consider the polynomial
1/2a^4 + 3a³ + a.
1) What is the coefficient of the third term?
2) What is the constant term?
Answers
1) The coefficient of the third term is one.
2) The constant term is zero.
We are given a polynomial. A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive integer powers of variables. The polynomial is (1/2)a^4 + 3a³ + a. The polynomial has the variable "a". The polynomial has three terms. So, it is a trinomial. The third term of the polynomial is "a". The coefficient of the third term is 1. There is no constant term in the polynomial. So, we can say that the constant term is 0.
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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]
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
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 0.0692