I have a quiz tomorrow and I need to figure out how to solve a linear equation using a graph ASAP. Can you please help me?
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SOLUTION
The given equations are
[tex]\begin{gathered} x+y=18 \\ y=x+12 \end{gathered}[/tex]The graph of the equations are shown:
Notice that the line intersect at (3,15)
Therefore, the solutions of the system of equations are
[tex]x=3,y=15[/tex]
Related Questions
Heidi purchased a used car. She made a down payment of 1504. This was 16% of the purchase price, what’s the price of the used car. I need to see the steps to solve this problem
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We have
1504 represents 16%
? represents 100%
In order to calculate the 100% and find the price of the car, we will do the operation
[tex]\frac{1504\times100\text{ \%}}{16\text{ \%}}=\frac{150400}{16}=9400[/tex]ANSWER
$9400 is the price of the used car
help with math problems graphs
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To fill the table we need to notice that Ali drives 5000 miles per year, then for the distance after a number of years we multiply the mileage for the number of year, then we have that the table will be:
2-10,000
5-25,000
8-40,000
The graph of the points is shown below:
Enter the coordinates to plot points on the graph of
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Given: A function g(x)
[tex]g(x)=-\frac{3}{8}x^3[/tex]Required: To find two points on the graph of the given function.
Explanation: To find the points on the graph, first put x=1 to get,
[tex]g(1)=-\frac{3}{8}[/tex]Now at x=2,
[tex]g(2)=-3[/tex]Also, we can find more points as
[tex]\begin{gathered} g(-1)=\frac{3}{8} \\ g(-2)=3 \end{gathered}[/tex]Now plotting the graph with points we get the following graph
Final Answer: The two points on the graph are (2,-3) and (-2,3)
how to solve this problem?
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To calculate the lateral area of the prism you must start finding the perimeter of the base of the prism to do that we must analyse the triangles base
by definition the lateral area of a triangular prism is the area of the sides of the prism without the base and top faces
the perimeter will be
[tex]\begin{gathered} 8+8+5 \\ 21 \end{gathered}[/tex]the height of the prism will be 9
the lateral area will be
[tex]\begin{gathered} (21)\cdot9 \\ 189 \end{gathered}[/tex]8÷2(2+2)what is the anwer
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To find the answer of this question, follow the
Solve the following system of equations graphically on the set of axes below.y = -3x - 5x - y = -3Plot two lines by clicking the graph.
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y = -3x - 5 Eqn(1)
x - y = -3 Eqn(2)
First we are going to isolate y on each equation to find some points to plot the graphs.
Eqn(1)
As it is not needed to isolate y, we find some points to plot.
x y
0 -3(0) - 5 = -5
1 -3(1) - 5 = -8
-1 -3(-1) - 5 = -2
Points for plotting: (0,-5), (1,-8), (-1,-2)
Eqn(2)
Isolating y, we have:
x = y - 3 (Subtracting y from both sides of the equation)
x + 3 =y (Adding 3 to both sides of the equation)
Then, we find some points to plot
x y
0 (0) +3 = 3
1 (1) +3 = 4
-1 (-1) +3 = 2
Plotting the equations we have:
Based on the graph the solution would be: x=-2 and y=1, as it is the intersection point.
Nina worked 12 hours on Monday, 7 hours on Wednesday, and 7 hours on Friday.Here gross pay for all 3 days was $236.21. What was her hourly rate?Round answer to a hundredths place. If answer does not have a hundredths placethen include zeros so that it does have a hundredths place
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First, find the total amount of time that Nina worked. Then, divide the gross pay over the total amount of time (measured in hours) that Nina worked to find the hourly pay rate.
Since Nina worked 12 hours on Monday, 7 hours on Wednesday and 7 hours on Friday, the total amount of time that Nina worked was:
[tex]12+7+7=26[/tex]Since her gross pay was $236.21, divide 236.21 over 26 to find the hourly rate:
[tex]\frac{236.21}{26}=9.085[/tex]Since the last nonzero digit of the number 9.085 is a 5, round it up to the hundredths place.
Therefore, the hourly rate is equal to 9.09 dollars per hour.
Jacob is a high school basketball player. In h particular game, he made some two point shots and some three point shots. Jacob made a total of 14 shots altogether and scored a total of 36 points. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.
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Let:
x = number of two point shots made
y = number of three point shots made
Jacob made a total of 14 shots altogether, therefore:
[tex]x+y=14[/tex]and scored a total of 36 points:
[tex]2x+3y=36[/tex]As you can see from the graph, the solution is (x,y)=(6,8)
Therefore:
He made 6 two point shots and he made 8 three point shots
Two parallel lines are cut by a transversal as shown below.Suppose =m∠3132°. Find m∠5 and m∠8.
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The angle 3 is given 132 degree.
ExplanationTo determine the angle 5 and angle 8.
Use the property that the sum of the corresponding interior angles is 180 degree.
[tex]\angle3+\angle8=180\degree[/tex]Substitute the values
[tex]\begin{gathered} 132\degree+\angle8=180\degree \\ \angle8=180\degree-132\degree \\ \angle8=48\degree \end{gathered}[/tex]And also from the figure,
The sum of angle 8 and 5 is 180 degree.
[tex]\begin{gathered} \angle8+\angle5=180\degree \\ \angle5=180\degree-48\degree \\ \angle5=132\degree \end{gathered}[/tex]Answer
Hence the angle 5 is 132 degree and angle 8 is 48 degree.
Solve. Show your work.log6(2x – 4) + 11 = 13
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ANSWER
x = 20
EXPLANATION
To solve this equation, first, we have to subtract 11 from both sides,
[tex]\begin{gathered} \log_6(2x-4)+11-11=13-11 \\ \\ \log_6(2x-4)=2 \end{gathered}[/tex]Then, there is the property of logarithms that states that if we raise the base of a logarithmic expression to the expression, the result is the argument of the logarithm,
[tex]a^{\log_a(b)}=b[/tex]So, the next step is to raise 6 to each side of the equation,
[tex]\begin{gathered} 6^{\log_6(2x-4)}=6^2 \\ 2x-4=36 \end{gathered}[/tex]Then, add 4 to both sides,
[tex]\begin{gathered} 2x-4+4=36+4 \\ 2x=40 \end{gathered}[/tex]And divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{40}{2} \\ \\ x=20 \end{gathered}[/tex]Hence, the solution is x = 20.
what is the sum of the positive even factors of 12?
Answers
24
Explanation:We need to state the positive factors of 12
They are: 1, 2, 3, 4, 6, 12
Then we take out the positive even factors of 12
They are: 2, 4, 6, 12
The sum of the positive even factors of 12 = 2+4+6+12
The sum of the positive even factors of 12 = 24
I need help with figuring out the rate of change
Answers
Explanation
Step 1
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
[tex]\text{rate of change=}\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]then select the 2 poitns of the line, Let
P1(5,60)
p2(12,72)
Step 2
replace
[tex]\begin{gathered} \text{rate of change=}\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{72-60}{12-5}=\frac{12}{7} \\ \text{rate of change=12/7} \end{gathered}[/tex]I hope this helps you
et y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by thequation 1200 + 10x = y.Answer the questions below.lot that a change can be an increase or a decrease.or an increase, use a positive number. For a decrease, use a negative number.
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The change in the total cost for each book printed is $10.
The cost to get started ( before any books are printed) is $1200
Step - by -step Explanation
What to find?
• The change in the total cost for each book printed.
,• The cost to get started ( before any books are printed).
Given:
The given equation is 1200 + 10x = y
where x is the number of xopies of book printed and y is the total cost of publishing the book .
b) To obtain the cost to get started;
Substitute x = 0 into the given equation.
1200 + 10(0) = y
1200 = y
Hence, the cost to get started is $1200
a) To find the cost for each book;
Put x =1 in the given equation.
1200 + 10(1) = y
1210 =y
Change in cost for each book printed is 1210 - 1200 = 10
Hence, the change in the total cost for each book printed is $10.
sorry it is blurry but this is what it say in ABC, centroid D is on the median AM AD=x+4 and DM=2x-4 Find AM
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The measure of AM is 12
Here, we are to find the measure of AM
Mathematically, the centroid divides the median on which it lies into 2 parts
These parts are usually in the ratio 1 to 2
What this mean is that if we multiply the smaller side by 2, we get the larger side
That would proceed as follows;
[tex]\begin{gathered} 2(2x-4)\text{ = x + 4} \\ 4x\text{ - 8 = x + 4} \\ \\ 4x-x\text{ = 8 + 4} \\ \\ 3x\text{ = 12} \\ \\ x\text{ = }\frac{12}{3} \\ \\ x\text{ = 4} \end{gathered}[/tex]Now, the length of the median is the sum of the two parts
Mathematically, that would be;
[tex]\begin{gathered} AM\text{ = x + 4 + 2x-4} \\ \\ AM\text{ = 3x} \\ \\ \text{Substituting x =4} \\ \\ AM\text{ = 3(4) = 12} \end{gathered}[/tex]Segment GH is shown below with its midpoint marked as M. Construct the line that passes through M and is perpendicular to GH. Leave all construction marks. Plot a point on the line you drew and mark it as K.Draw in HK and GK. What rigid body motion could be used to map angle GMK onto angle HMK? Explain why HK and GK must be congruent.
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We are given the line segment GH, and we are asked to construct a perpendicular line that passes through the midpoint of GH, M. To do that, we need to place a compass in point G and draw a circle of radius GH, that is we place the end of the compass at point H. Then we need to place the compass at point H and draw a circle of radius GH, that is the other end of the compass must be at point G. It looks like this:
Now we draw a line joining the points where the two circles intercept, like this:
The resulting line is perpendicular to GH and passes through the midpoint M. We mark one of the endpoints of the new line as K. When joining HK and GK we get the following:
To map triangle GMK into triangle HMK we would have to do a reflection (which is a rigid motion) across the line KM.
GK and HK are congruent or they have the same measure because triangles GMK and HMK are right tringles since lines KM and GH are perpendicular, moreover, since M is a midpoint that means that segments GM and MH have the same length and since both triangles share the side KM, that means that sides GK and KH must also be the same.
Tony van four and a half miles and 1/2 hours wait an equation for the distance in Miles why that she's when an x hours
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2)
Given data:
The given distance is d= 4/5 miles.
The given time is t = 1/5 hours.
The speed can be calculated as,
[tex]\begin{gathered} s=\frac{d}{t} \\ =\frac{(\frac{4}{5}\text{ miles)}}{\frac{1}{5}\text{ hour}} \\ =4\text{ miles/hour} \end{gathered}[/tex]The expression for the distance in x hours is,
[tex]y=4x[/tex]Thus, the expression for the distance is y=4x.
Write the area of the rectangle as the product of length x width and also as a sum of the areas of the box
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Area as product
= ( a+ 8) • (5a) =
Area as sum
= a•5a + 8•5a
= 5a^2 + 40a
Speedy carz rents cars for a $45 flat fee and $0.75 per mile driven. Affordable autos rents cars for $1.25 per mile plus a $24 flat fee. How many miles must be driven on these rental cars so that the costs of both companies are the same? How much money will it cost when this number of miles are driven?
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Speedy Carz :
Flat fee: $45
Cost per mile: $0.75
x= number of miles
Cost of Speedy Carz= 0.75x+45
Affordable autos;
Flat fee: $24
Cost per mile: $1.25
Cost of Affordable autos: 1.25x+24
If both costs are the same:
Cost of Speedy Carz=Cost of Affordable autos
So:
0.75x+45=1.25x+24
Solve for x:
45-24 = 1.25x-0.75x
21= 0.5x
21/0.5=x
x= 42 miles
To calculate the cost when that number of miles are driven, replace x on any equation:
0.75x+45
0.75(42)+45
31.5+45
$76.5
AIden was asked to find the product of 24 5 and 77 His werk is shown below Estimate: 25 x 200 Actual: 24.5x 7.7- 1,886.5
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The product of 24.5 and 77
the work will be as following
at first find the product of 245 and 77, then put the decimal point after one digit
so,
so, the product of 245 and 77 is 18865
Put the decimal after one digit
So, the product of 24.5 and 77 is 1,886.5
A baseball pitcher allowed 3 runs in 9 innings. At that rate, how many runs would he allow in 36 innings?
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ANSWER
12 runs
EXPLANATION
We have that the baseball pitcher allowed 3 runs in 9 innings.
Let the number of runs he allowed in 36 innings be x.
This means that:
3 runs = 9 innings
x runs = 36 innings
Cross-multiply:
=> 3 * 36 = 9 * x
Divide both sides by 9:
[tex]\begin{gathered} x\text{ = }\frac{3\cdot\text{ 36}}{9} \\ x\text{ = }12\text{ runs} \end{gathered}[/tex]Therefore, at this rate he would allow 12 runs
The weekly revenue for a product is given by R(x)=216x−0.033x2, and the weekly cost is C(x)=9000+108x−0.066x2+0.00002x3, where x is the number of units produced and sold.(a) How many units will give the maximum profit?(b) What is the maximum possible profit?
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First, we need to find an equation for the profit. The profit is the difference between the revenues R(x) and the costs C(x).
We already know the expressions for R(x) and C(x), so we just need to write R(x) - C(x):
[tex]P(x)=R(x)-C(x)[/tex][tex]P(x)=216x-0.033x^2-(9000+108x-0.066x^2+0.00002x^3)[/tex]Now we can work the parenthesis:
[tex]P(x)=216x-0.033x^2-9000-108x+0.066x^2-0.00002x^3[/tex]Simplifying like terms:
[tex]P(x)=108x+0.033x^2-0.00002x^3-9000[/tex]To find the maximum profit we need to calculate the values of x that make the derivative of P(x) = 0.
First, we calculate the derivative:
[tex]P^{\prime}(x)=108+2\cdot0.033x-3\cdot0.00002x^2[/tex][tex]P^{\prime}(x)=108+0.066x-0.00006x^2=0[/tex]Solving the second-grade equation we obtain that the values making the equation above 0 are 2000 and -900. We can discard -900 as it is a negative number.
Then we have that
a) The number of units that will give the maximum profit is x = 2000.
Now to calculate the maximum possible profit we just need to estimate the profit when 2000 units are produced. That is obtained then by calculating P(2000):
[tex]P(2000)=108\cdot(2000)+0.033\cdot(2000)^2-0.00002\cdot(2000)^3-9000[/tex][tex]P(2000)=179000[/tex]With this we have finally that:
b) The maximum possible profit is 179000.
A quadrilateral had vertices J(-7,-2) K(0,4) and M(2,-4). What is the most precise name for the quadrilateral?
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The quadritaletral has :
J(-7, -2)
K(0,4)
M(2,-4)
There are three coordinates and the maximum number of lines draw by three coordinates are three
So, the quadrilateral has three sides
and the quadrilateral which have three sides are called Triangle and it show as:
Answer: Triangle
Show that x = 4 is not a solution to the equation: 5(x+3) = 12.
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5 ( X + 3 ) = 12
5 x + 15 = 12
5 x = 12 -1 5
5x = -3
Divide both sides by 5 ,
x = -3 /5
It shows that x = 4 is not the solution to the equation.
Answer:
Step-by-step explanation:
5(4+3)=12
5(7)=12
35=12 not true
Please mark brainliest hopes this help
write an expression that is equivalent to each original expression use expressions in the box below not all Expressions will be used
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The first expression is
[tex](7\times6)+(7\times y)[/tex]since there is 7 in both parenthesis, we can factorize 7, then we can write
[tex](7\times6)+(7\times y)=7(6+y)[/tex]Second expression.
In this part, we have
[tex]y(6+7)[/tex]by applying the distributive law, this expression is equivalent to
[tex]y(6+7)=y\times6+y\times7[/tex]Third expression.
We have in this part:
[tex](6\times y)+(6\times7)[/tex]similarly to the first question, we can factorize 6, then we obtain
[tex](6\times y)+(6\times7)=6(y+7)[/tex]Fourth expression.
We have in this part:
[tex]y(6+y)[/tex]by applying the distributive law, this expression is equivalent to
[tex]\begin{gathered} y(6+y)=y\times6+y\times y \\ \sin ce\text{ y times y is } \\ y^2 \\ \text{then we have} \\ y(6+y)=y\times6+y^2 \end{gathered}[/tex]reasonable domain and range I really need help solving this problem
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First we need to identify which one is our independent variable (x) and which is our dependent variable (y).
The independent variable is the number of t-shirts. So x will correspond to the number of t-shirts sold.
The domain is the possible values for x, so here, since the coach has 4 t-shirts for sale, the possible values for x are 0, 1, 2, 3, and 4:
[tex]d\colon\left\lbrace 0,1,2,3,4\right\rbrace [/tex]The dependent variable is the raised money, because it dependes in the number of t-shirts sold.
Since he already has $50, if he sells 1 more at $12, he will have
50+12=62
If he sells 2 more:
50+2(12)=50+24=74
If he sells 3 more:
50+3(12)=50+36=86
If he sells all of the 4:
50+4(12)=50+48=98
The range is the possible values for y.
So, the possible values for the dependent variable y according to the number of T-shorts sold is:
[tex]r\colon\left\lbrace 50,62,74,86,98\right\rbrace [/tex]Answer: A.
explain the following incomplete sentence is the number 1 Prime
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yes, 1 is a prime number.
the number 1 can only be divided by it own, so it is a prime number
or we can say that the number 1 has only 1 factor that is 1 , so it is a prime number
Find 2 rational numbers greater than 1/4 whose product is less than 1/4
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A rational number is a number that can be expressed as the ratio of 2 integers
The rational number, 1/3 is greater than 1/4
The product of 1/3 and 1/3 is
1/3 * 1/3 = 1/9
1/9 is less than 1/4
The rational numbers are 1/3 and 1/3
I need help to find the indicated operation:h(x)= x^3-xg(x)= 4x-4Find (h+g)(-4)
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Solve;
[tex]\begin{gathered} g(n)=2n-2 \\ h(n)=n^2+3n \\ \text{Therefore, (g x h) is;} \\ (2n-2)(n^2+3n) \\ =\lbrack2n\times n^2\rbrack+\lbrack2n\times3n\rbrack-\lbrack2\times n^2\rbrack-\lbrack2\times3n\rbrack \\ =2n^3+6n^2-2n^2-6n \\ \text{Collect like terms and you'll have,} \\ =2n^3+4n^2-6n \\ \text{Therefore} \\ (g\mathrm{}h)(n),\text{ now becomes} \\ (2n^3+4n^2-6n)\times n \\ =2n^4+4n^3-6n^2 \end{gathered}[/tex]A square pyramid has a height that is 8 centimeters long and a base with sides thatare each 9 centimeters long. Find the volume of the pyramid.648 cm3O 324 cmO 162 cm3O 216 cm3Question 105 pts
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The answer is 216cm³
To solve this, we use the formula for the volume of a square pyramid.
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]Where B is the area of the square base and h is the heigh of the pyramid
Let's calculate B. The area of a square is one of it's sides squared. The side of the base are 8cm long. Then:
(8cm)²=81cm²
Now we use the formula:
[tex]undefined[/tex]Probability of independent eventsA spinner has 10 equally sized sections, 7 of which are gray and 3 of which are blue. The spinner is spun twice. What is the probability that the first spin landson gray and the second spin lands on blue?Write your answer as a fraction in simplest form.
Answers
Thouse events are independent, so we can calculate them separately and the final rpobability will be the product of them.
[tex]P(A\, and\, B)=P(A)\cdot P(B)[/tex]The first event, say A, is of landing on gray. Since 7 out of the 10 are gray, the probability is:
[tex]P(A)=\frac{7}{10}[/tex]Th second event, B, is of landing on blue. Since 3 out of the 10 are blue, the probability is:
[tex]P(B)=\frac{3}{10}[/tex]So, the probability of both is:
[tex]P(A\, and\, B)=P(A)\cdot P(B)=\frac{7}{10}\cdot\frac{3}{10}=\frac{21}{100}[/tex]