What is the solution of the system?{4x−y=−38x+y=3Enter your answer in the boxes.
Answers
Solution:
Given:
[tex]\begin{gathered} 4x-y=-38 \\ x+y=3 \end{gathered}[/tex]Solving the system simultaneously by substitution method;
[tex]\begin{gathered} 4x-y=-38\ldots\ldots\ldots\ldots\ldots(1) \\ x+y=3\ldots\ldots\ldots\ldots\ldots\ldots.(2) \\ \\ \text{making y the subject of the formula from equation (2);} \\ x+y=3 \\ y=3-x\ldots\ldots\ldots\text{.}\mathrm{}(3) \\ \\ \text{Substituting equation (3) into equation (1);} \\ 4x-y=-38 \\ 4x-(3-x)=-38 \\ 4x-3+x=-38 \\ 4x+x=-38+3 \\ 5x=-35 \\ \text{Dividing both sides by 5;} \\ x=-\frac{35}{5} \\ x=-7 \\ \\ \text{Substituting the value of x into equation (3) to get y;} \\ y=3-x \\ y=3-(-7) \\ y=3+7 \\ y=10 \end{gathered}[/tex]Therefore, the solution of the system is;
[tex](x,y)=(-7,10)[/tex]Related Questions
what do you know one step equations x+7=15
Answers
We will see how to evaluate one step equations. The following equation is given as follows:
[tex]x\text{ + 7 = 15}[/tex]A one-step equation is accompained by a ( single mathematical operation ). A mathematical operation can be classified into:
[tex]\text{Multiplication , Division, Addition, Subtraction}[/tex]We can use either of the above mathematical operations to solve for the variable ( x ) given in the equation.
We see that a constant ( 7 ) is added to the variable ( x ). We need to isolate our variable ( x ) on the left hand side of the " = " sign. To do that we will seek help of a " Subtraction " operation.
We will subtract the constant ( 7 ) on both sides of the equation as follows:
[tex]\begin{gathered} x\text{ + 7 = 15 } \\ x\text{ + 7 - 7 = 15 - 7} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 8}} \end{gathered}[/tex]We have abotained a solution for the variable ( x ) using a single ( on-step ) mathematical operation as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 8}}[/tex]2 hours reading1 hour playing with friendsRate ? Ratio only ? Or a proportion?
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Answer:
[tex]\text{Ratio Only}[/tex]Explanation:
We get a rate when we consider how a quantity changes in relation to another
When we compare two quantities, we have a ratio
Equating two ratios, we have a proportion
From the question, we are comparing the number of reading hours to the number of playing hours
That means we have a ratio only
mmhey again um yea i looked at my notes but thats not really helpful :/
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We have the following:
Since the sides are equal, it means that all the angles are equal, we also know that the sum of the 3 angles within a triangle is always 180°, therefore
[tex]\begin{gathered} 5x+5x+5x=180 \\ \text{solving for x:} \\ 15x=180 \\ x=\frac{180}{15} \\ x=12 \end{gathered}[/tex]The value of x is 12
Which I two triangles are congruent? Complete the congruence statement.
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Answer:
∆vuw≈∆bca∆uvw≈∆cba∆vwu≈∆bacIf FG= 9x-2 and jk=3x+10, what value of x will make FG and JK congruent
Answers
ANSWER
x = 2
EXPLANATION
If we want FG and JK to be congruent, then we have to see which value of x makes:
[tex]FG=JK[/tex]true.
Which of the following Polynomial does not have real roots?
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Using the formula below
[tex]\begin{gathered} b^2-4ac \\ \text{Solving for the first option} \end{gathered}[/tex]For 2x²+4x+4, relataing it to the general form of a quadratic equation,
[tex]ax^2+bx+2=0[/tex]Where a, b, and c for the 2x²+4x+4 is given below,
[tex]\begin{gathered} a=2,b=4,c=4 \\ b^2-4ac=4^2-4(2\times4)=16-32=-16 \end{gathered}[/tex]Since b²-4ac is not supposed to be negative (i.e complex roots),
Answer is A
Which equation represents a line which is parallel to the line by – 7x = 24?:A) y=7/6x+3B) y=6/7x-2C) y=-7/6x-1D)y=-6/7x+7
Answers
We have the equation 6y-7x=24, and want to know what of the options represents a line parallel to that one.
First we need to write our equation in the form of the options:
[tex]\begin{gathered} 6y-7x=24 \\ 6y=7x+24 \\ y=\frac{7x+24}{6}=\frac{7x}{6}+\frac{24}{6} \\ y=\frac{7}{6}x+4 \end{gathered}[/tex]Now, we know that two lines are parallel if and only if they slopes are equal, so the slope of our line is 7/6 and the option that has the same slope is the option A.
So te correct answer is the option A
⦁ The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
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The part of the expression that represents the amount of tax Deborah will pay is 0.08(50h).
What part of the expression represents taxes?The given expression is known as a linear equation. A linear expression is an expression that has a single variable raised to the power of 1.
Tax is the compulsory amount levied by on goods and services. Tax is usually a percentage of the price of a good and service. Taxes increases the price of a good or service. The tax paid would increase with the total income earned.
Tax = tax percentage x total cost
Tax = 0.08 x (total hours worked x cost per hour)
Tax = 0.08 x (50 x h)
Tax = 0.08(50h)
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Find all values of y such that the distance between (5,y) and (-7,2) is 18.
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Find all values of y such that the distance between (5,y) and (-7,2) is 18.
Remember that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]substitute the given values
[tex]18=\sqrt[]{(y-2)^2+(5+7)^2}[/tex][tex]18=\sqrt[]{(y-2)^2+144}[/tex]squared both sides
[tex]18^2=(y-2)^2+144[/tex]solve for y
[tex]\begin{gathered} (y-2)^2=324-144 \\ (y-2)^2=180 \end{gathered}[/tex]take square root on both sides
[tex]\begin{gathered} y-2=\pm\sqrt[]{180} \\ y=2\pm\sqrt[]{180} \end{gathered}[/tex]simplify
[tex]y=2\pm6\sqrt[]{5}[/tex]A park volunteer Plans to work on pallet Stonewall for one hour every Monday one every Wednesday and three hours on Friday
Answers
Solution
For this case we can do the following:
Part a
we can select the points (0,0) and (2,10) and k is given by:
[tex]k=\frac{10-0}{2-0}=5[/tex]Part b
The equation is given by:
y= 8x
Part c
We can replace x= 16 in the equation and we got:
y= 8*16= 128 hours
Tracy wants to buy some food for her slumber party. Great Foods Grocery Store is selling 2 bags of potato chips for $6.50 and 5 two-liter sodas for $3.00. Best FoodsGrocery Store is selling 2 bags of potato chips for $5.00 and 3 two-liter sodas for $2.00. if p = potato chips and s= two-liter sodas, write a system of equations to model thisproblem2p=5.00 and 3s=2.006.50p + 3.00s= 7 and 5p +2s=52p=6.50 and 5s=3.002p + 5s 9.50 and 2p +39 7.00
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Answer:
[tex]\begin{gathered} \text{ The system that describes this problem:} \\ 2p+5s=9.50 \\ 2p+3s=7.00 \end{gathered}[/tex]Step-by-step explanation:
Let p be the potato chips
Let s be the two-liter sodas
Then, if Great Foods Grocery Store is selling 2 bags of potato chips for $6.50 and 5 two-liter sodas for $3.00:
[tex]2p+5s=9.50[/tex]For Best Foods Grocery Store:
2 bags of potato chips for $5.00 and 3 two-liter sodas for $2.00.
[tex]2p+3s=7[/tex]
Determine the linear equation of the vertical and horizontal line passing through the point (5,8).
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Given:
The horizontal and vertical line psses through the point (5,8).
To find:
Find the equation of vertical and horizontal line passing through the given point.
Equation of vertical line:
[tex]x=5[/tex]Equation of horizontal line:
[tex]y=8[/tex]Need help with finding the vertex and the Y intercept of the quadratic function and use them to graph the function for number 21
Answers
EXPLANATION
Given the function y=-2x^2 -12x -5
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=-2,\: b=-12,\: c=-5[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\left(-2\right)}[/tex][tex]\mathrm{Simplify}\colon[/tex][tex]x_v=-3[/tex]Plug in x_v=-3 to find the y_v value:
[tex]y_v=-2\mleft(-3\mright)^2-12\mleft(-3\mright)-5[/tex]Computing the powers and multiplying terms:
[tex]y_v=-18+36-5[/tex]Adding and subtracting numbers:
[tex]y_{v\text{ }}=13[/tex]Therefore, the parabola vertex is:
(-3,13)
Now, we need to compute the y-intercept
[tex]y\mathrm{-intercept\: is\: the\: point\: on\: the\: graph\: where\: }x=0[/tex][tex]\mathrm{Apply\: rule}\: 0^a=0[/tex][tex]0^2=0[/tex][tex]y=-2\cdot\: 0-12\cdot\: 0-5[/tex]Multiplying numbers:
[tex]y=-5[/tex]The y-intercept is at (0,-5)
In conclusion, the graph of the function is as follows:
Which answer describes the pattern in this sequence?12) 412, 1, 21OaddO multiply by 2o subtract 1multiply by12
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Answer:
The answer that describes the pattern in this sequence is;
[tex]\text{ multiply by }\frac{1}{2}[/tex]Explanation:
Given the sequence;
[tex]2,1,\frac{1}{2},\frac{1}{4},\ldots[/tex]The sequence shows a Geometric Progression.
The common ratio of the sequence would be;
[tex]\begin{gathered} r=\frac{1}{2}=\frac{\frac{1}{2}}{1}=\frac{\frac{1}{4}}{\frac{1}{2}} \\ r=\frac{1}{2} \end{gathered}[/tex]Therefore, the answer that describes the pattern in this sequence is;
[tex]\text{ multiply by }\frac{1}{2}[/tex]
[tex](1-(-1)*2)x^{2} -1[/tex]
Answers
Answer:
[tex]3x {}^{2} - 1[/tex]
Step-by-step explanation:
(1-(-1)×2) x² - 1
When there is a - in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses.
(1+1x2)x2-1
Any expression multiplied by 1 remains the same
(1+2) x²-1
Add the numbers
3x2-1
The data points on the scatter plot below show the amount of natural snow received and the amount of artificial snow made by a ski resort for each of 25 weeks. Draw the line of best fit for these data points. (It doesn't have to be the exact line of best fit. Just draw your best approximation.)
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We need to draw the line of best fit for the data points in the scatter plot.
One way of drawing this line is by leaving approximately the same amount of points above and below it:
Notice that the line has to follow the trend of the points: the amount of artificial snow made decreases as the amount of natural snow received increases.
In a raffle, one ticket will win a $930 prize, and the other tickets will win nothing. There are 500 in the raffle, each costing $6. If you buy a ticket, what is the expected profit?
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Question 7(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Two angles are complementary to each other. One angle measures 32°, and the other angles measure (12x-20) determine the value of x
O 64
O 6.5
32.5
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If the sum of (12x - 20)° + 32° = 180° then value of x is 14°.
What are supplementary and complementary angles?When the sum of the two angles is 180° they are said to be supplementary.
When the sum of the two angles is 90° they are said to be complementary.
Given, Two angles are complementary to each other.
One angle measures 32°, and the other angles measure (12x - 20)°.
∴ (12x - 20)° + 32° = 180°.
12x - 20° + 32° = 180°.
12x = 180° - 12°.
12x = 168°.
x = 14°.
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Which solution value satisfies the inequality x – 6 ≥ –7?Question 4 options:A)x = –7B)x = 0C)x = –5D)x = –2
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Let's solve the inequality:
[tex]\begin{gathered} x-6\ge-7 \\ x\ge-7+6 \\ x\ge-1 \end{gathered}[/tex]Hence any solution of the inequality has to be equal or greater than -1. From the list given we notice that the only value that fulfills this condition is x=0, therefore the correct option is B.
Describe two methods you could use to solve for `x` in `1.12^{x}=20`
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EXPLANATION:
Given;
We are given the following equation;
[tex]1.12^x=20[/tex]Required;
We are required to describe two methods which can be used to solve for x in this equation.
Step-by-step solution;
We can solve for the variable x by taking the natural log of both sides of the equation. This is shown below;
[tex]1.12^x=20[/tex]We take the natural log of both sides;
[tex]ln1.12^x=ln20[/tex]Next we apply the log rule;
[tex]\begin{gathered} If: \\ log_bx^a \\ Then: \\ alog_bx \end{gathered}[/tex]Therefore, our equation is now refined and becomes;
[tex]xln1.12=ln20[/tex]Divide both sides by ln(1.12);
[tex]x=\frac{ln(20)}{ln(1.12)}[/tex]A second method is to express it as a logarithmic equation;
[tex]1.12^x=20[/tex]We shall apply the log rule which is;
[tex]\begin{gathered} If: \\ log_bx=a \end{gathered}[/tex][tex]\begin{gathered} Then: \\ b^a=x \end{gathered}[/tex]For example;
[tex]\begin{gathered} If: \\ log_{10}100=2 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ 10^2=100 \end{gathered}[/tex]Therefore, for the equation given;
[tex]\begin{gathered} If: \\ 1.12^x=20 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ log_{1.12}20=x \end{gathered}[/tex]Note that both solutions can be simplified eventually with the use of a calculator.
ANSWER:
(1) By taking the natural log of both sides
(2) By expressing the equation as a logarithmic equation
The table shows the times Allison clocked in and out of work this week. Her employer rounds to the nearest quarter hour. How many total hours did she work?Time in. Time out8:03 am. 5:13 pm7:58 am. 4:49 pm7:46 am. 4:41 pm8:23 am. 4:50 pm7:31 am. 4:32 pmA) 44.25 hoursB) 45.5 hours C) 42.5 hours D) 44 hours
Answers
Answer:
A) 44.25 hours
Explanation:
To round time to the nearest quarter-hour, round those times within 7 minutes of a 15-minute mark to that 15 minutes.
Thus, the time in and time out are rounded to the nearest quarter-hour in the table below:
Next, add the differences:
[tex]\begin{gathered} Total=9:15+8:45+9:00:8:15+9:00 \\ =43hours+(15+45+15)minutes \\ =44\text{ hours 15 minutes} \\ =44+\frac{15}{60} \\ =44.25\text{ hours} \end{gathered}[/tex]She worked a total of 44.25 hours.
Option A is correct.
given f(x) = 5x-1 , evaluate f(5)= also solve f(x)=14 then x= ?
Answers
You have the following expression for f(x):
f(x) = 5x - 1
In order to find the value of f(5), replace x = 5 into the previous expression and simplify:
f(5) = 5(5) - 1 = 25 - 1 = 24
Hence, f(5) is 24
To determine the value of x when f(x) = 14, solve for x, as follow:
14 = 5x - 1 add 1 both sides
14 + 1 = 5x
15 = 5x divide by 5 both sides
15/5 = x
3 = x
x = 3
Hence, x = 3 when f(x) = 14
Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,-3). Find the coordinates ofvertex M.The coordinates are MOD.
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Given data:
The coordinate of first vertex is J(1, 4).
The coordinate of second vertex is K(5, 3).
The coordinate of third vertex is L(6,-3).
Assume the coordinate of M is (x, y).
The diagonal of the parallelogram intersect at the mid point, the mid point of the diagonal JL is,
[tex]\begin{gathered} a=\frac{1+6}{2} \\ =\frac{7}{2} \\ b=\frac{4-3}{2} \\ =\frac{1}{2} \end{gathered}[/tex]This is also the mid point of KM diagonal.
[tex]\begin{gathered} \frac{7}{2}=\frac{x+5}{2} \\ x=2 \\ \frac{1}{2}=\frac{y+3}{2} \\ y=-2 \end{gathered}[/tex]Thus, the coordinate of M is (2, -2).
9 Is the sentence correct? Select Yes or No. A. O Yes O No 2 3 B. O Yes O No c. > O Yes O No D. too O Yes O No 8 E. O Yes O No F.
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9 a) 1 /2 = 1/ 3 NO
b) 4/ 6 < 5/6 YES
c ) 5/ 6 > 5/8 YES
d) 4/8 < 7/8 YES
e) 3/3 = 3/ 8 NO
f) 1/4 < 3/4 YES
7. Elena wanted to find the slope and y-intercept of the graph of 25x – 20y = 100. Shedecided to put the equation in slope-intercept form first. Here is her work:-25x - 20y = 10020y = 100 - 25x5y = 5 - 2x-4She concluded that the slope isand the y-intercept is (0,5).a. What was Elena's mistake?b. What are the slope and y-intercept of the line? Explain or show your reasoning.
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The slope-intercept form for an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is the slope and (0,b) the y-intercept. Let's take the equation given by the question, operate and write it in slope-intercept form and see which was Elena's mistake. So we have:
[tex]25x-20y=100[/tex]We can substract 25x from both sides:
[tex]\begin{gathered} 25x-20y-25x=100-25x \\ -20y=100-25x \end{gathered}[/tex]Here we can see Elena's mistake. Instead of the equation I just wrote she got:
[tex]20y=100-25x[/tex]This doesn't have the negative sign in 20y. This was her mistake and answer to part a.
Now let's continue, we can divide both sides by -20:
[tex]\begin{gathered} -\frac{20y}{-20}=\frac{100-25x}{-20} \\ y=-\frac{100}{20}+\frac{25}{20}x \\ y=\frac{5}{4}x-5 \end{gathered}[/tex]Which means that the slope is 5/4 and the y-intercept is (0,-5).
Put the following equation of a line into slope-intercept form, simplifying all fractions. Žy 2x = 8 Answer: Submit Answer attempt 1 out of 2 Privacy Policy Terms of Service
Answers
We have the following:
the equation of a line into slope-intercep form is:
[tex]y=mx+b[/tex]now,
[tex]\begin{gathered} 2y-2x=8 \\ 2y=2x+8 \\ y=x+4 \end{gathered}[/tex]therefore, the answer is:
[tex]y=x+4[/tex]f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
Answers
f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
[tex]f\mleft(x\mright)=\frac{8x^{5}-7x^{4}-73x^{3}+23x^{2}-20x-5}{8x+1}[/tex]Determine whether each triangle is isosceles, equilateral, or can not be determined.
Answers
We have the following:
An isoceles triangle is that it has two equal sides and an equilateral triangle is that all sides are equal.
A.
It has two equal sides, therefore it is an isoceles triangle
B.
It has two equal sides, therefore it is an isoceles triangle
C.
It is not possible to determine since an angle of 60 ° does not determine the size of the other two angles
D.
It has two equal angles, which means that it has two equal sides, therefore it is an isoceles triangle.
(d) 8x + 3y = -45x + 2y = 6Solve the following simultaneous linear equation
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To solve the following simultaneous linear equation, we are going to solve for y on the first equation and replace it on the second as:
[tex]\begin{gathered} 8x+3y=-4 \\ 3y=-4-8x \\ y=\frac{-4-8x}{3} \\ y=\frac{-4}{3}-\frac{8x}{3} \end{gathered}[/tex]Replacing it on the second equation and solving for x, we get:
[tex]\begin{gathered} 5x+2y=6 \\ 5x+2(\frac{-4}{3}-\frac{8x}{3})=6 \\ 5x-\frac{8}{3}-\frac{16x}{3}=6 \\ 5x-\frac{16}{3}x=6+\frac{8}{3} \\ \frac{-1}{3}x=\frac{26}{3} \\ -x=26 \\ x=-26 \end{gathered}[/tex]Finally, replacing x on the first equation and solving for y, we get:
[tex]\begin{gathered} 8x+3y=-4 \\ 8(-26)+3y=-4 \\ 3y=-4+208 \\ 3y=204 \\ y=\frac{204}{3}=68 \end{gathered}[/tex]Answer: x = -26 and y = 68
To make subtraction of 5x - 16x/3, we can use the following equation:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{a\cdot d-b\cdot c}{b\cdot d}[/tex][tex]\begin{gathered} 5x-\frac{16x}{3}=\frac{5x}{1}-\frac{16x}{3}=\frac{5x\cdot3-1\cdot16x}{1\cdot3}=\frac{15x-16x}{3}=\frac{-1x}{3} \\ \end{gathered}[/tex]heights of men on a basketball team have a bell shaped distribution with the mean of 177 cm and a standard deviation if 5 cm. using the empirical rule, what is the approximate percentage of the men between 162 cm and 192 cm?
Answers
The variable
X: height of a basketball team
This variable has a bell shaped distribution (Normal distribution) with mean μ=177cm and a standard deviation of δ=5cm
The empirical rule states that
68% of the distribution is within one standard deviation away from the mean
[tex]\begin{gathered} \mu\pm\sigma=0.68 \\ 177\pm5 \\ (172;182) \end{gathered}[/tex]95% of the distribution is within two standard deviations away from the mean
[tex]\begin{gathered} \mu\pm2\sigma=0.95 \\ 177\pm2\cdot5 \\ (167,187) \end{gathered}[/tex]99.7% of the distribution is within three standard deviations away from the mean
[tex]\begin{gathered} \mu\pm3\sigma=0.997 \\ 177\pm3\cdot5 \\ (162,192) \end{gathered}[/tex]So, following the empirical rule, 99.7% of the men are between 162 cm and 192 cm