Answers
The system of equations we have is:
[tex]\begin{gathered} -3x-2y=-7 \\ x+4y=1 \end{gathered}[/tex]And we need to check if the point (3,-1) is a solution.
Step 1. Identify the values of x and y from the point.
In a point, the first number represents the x-value, and the second number represents the y-value. So in point (3,-1) 3 is the x-value, and -1 is the y-value:
[tex]\begin{gathered} x=3 \\ y=-1 \end{gathered}[/tex]Step 2. Substitute the x and y-value into the first equation and check that the result is equal to -7.
The first equation is:
[tex]-3x-2y=-7[/tex]Substituting x=3 and y=-1:
[tex]-3(3)-2(-1)=[/tex]Solve the operations:
[tex]-9+2=-7[/tex]Since we get -7 as the result, (3,-1) is a solution for the first equation. But we still need to check if the point is a solution for the second equation.
Step 3. Substitute the x and y values into the second equation and check that the result is 1.
The second equation of the system is:
[tex]x+4y=1[/tex]Substituting x=3 and y=-1:
[tex]3+4(-1)=[/tex]Solving the operations:
[tex]3-4=-1[/tex]The result we get is -1, not 1. Thus, since the point (3,-1) is not a solution for the second equation, it is also not a solution to the system of equation.
Answer: False
Related Questions
Write the equation of the line that passes through the points `(1,\ -2)` and `(4,\ 4)`.
Answers
m=6/3
m=2
y=2x+b
4=2(4)+b
4=8+b
b=-4
y=2x-4
Which of the following equations does the graph below represent?
Answers
Answer:
The answer is -3x + 6y = 36
Step-by-step explanation:
1. Write 250 metres as a fraction of a kilometre.
Answers
Answer:1/4 or 0.25/1
Step-by-step explanation:
In 1 kilometer there are a thousand meters. So 250 is a quarter of 1000 which makes the fraction 1/4 or 0.25/1 whichever you need.
what 93 by the power of 7
Answers
The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
''93 to the power of 7''
Now,
Solve the expression as;
93 to the power of 7 = 93⁷
= 93 × 93 × 93 × 93 × 93 × 93 × 93
= 60,170,087,060,757
Thus, The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
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3(8 – 4x) < 6(х – 5)
Answers
the inequality equation is
3(8 - 4x) < 6(x -5)
open the parentheses
3*8 - 3*4x < 6*x - 6*5
24 - 12x < 6x - 30
collect the like terms
24 + 30 < 6x + 12x
54 < 18x
divide both sides by 18
54/18 < 18x/18
3 < x
x > 3
The answer is x > 3
2. The scale from the real Eiffel Tower to the scale model is 15 ft to 3 in. What is the unit rate?
Answers
Ok, so
If the scale from the real Eiffel Tower to the scale model is 15 ft to 3 in, the unit rate will be:
[tex]\frac{15ft}{3in}=5\frac{ft}{in}[/tex]This means that, in the scale:
5 ft = 1 in.
Then, the unit rate is 5.
nearest thousandth in 67directions: use a calculator to approximate each to the nearest thousandth subject: 2.2C evaluating common and natural logarithms
Answers
EXPLANATION
Given the expression:
ln 67:
Solving the operation with a calculator gives us the following result:
ln 67 = 4.204692619...
Thus, rounding to the nearest thousandth will give us:
= 4.205
So, answer to point 1) is D) 4.205
1. What is the x intercept of the graph y=x-32. What is the y intercept of the graph y=x-33. What is the x intercept of the graph y=4x+24. What is the y intercept of the graph y=4x+2
Answers
1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.
You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.
-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)
-Replacing the equation of the function by y=0:
[tex]\begin{gathered} y=x-3 \\ 0=x-3 \\ 0+3=x-3+3 \\ 3=x \end{gathered}[/tex]The x-intercept has coordinates at (3,0)
2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.
You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.
-Looking at the graph, the red line crosses the y-axis at the point (0,-3)
-Replace the equation with x=0
[tex]\begin{gathered} y=x-3 \\ y=0-3 \\ y=-3 \end{gathered}[/tex]The y-intercept is (0,-3)
3. The equation y=4x+2 is represented in the graph by the blue line
As before, you have to identify the point where the line crosses the x-axis.
-From the graph:
-Replace the equation with y=0 and calculate the corresponding value of x:
[tex]\begin{gathered} y=4x+2 \\ 0=4x+2 \\ 0-2=4x+2-2 \\ -2=4x \\ -\frac{2}{4}=\frac{4x}{4} \\ -\frac{1}{2}=x \end{gathered}[/tex]The x-intercept is (-1/2,0)
4. The y-intercept is the point where the blue line crosses the y-axis.
-You can identify it from the graph:
-Or replace the equation with x=0 and determine the corresponding value of y
[tex]\begin{gathered} y=4x+2 \\ y=4\cdot0+2 \\ y=2 \end{gathered}[/tex]The coordinates of the y-intercept are (0,2)
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y = 10x - 8
Step-by-step explanation:
The slope is "m", or how much the y-value changes on a line when the x-value changes by one.
The y-intercept is the y value of the line when it is intersecting the y-axis, or when the x-value is 0.
To find the slope, take 2 points from the graph and plug into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x\\_1}[/tex]
I'll use (0, -8) and (1,2).
Plug into the formula.
[tex]\frac{2--8}{1-0}[/tex]
[tex]\frac{10}{1}[/tex]
10
Slope = 10
To find the y-intercept, look at the table. What is the y-value when the x-value is equal to 0?
-8
y-intercept: -8
Slope-Intercept form:
y = mx + b
m: slope
b: y-intercept
y, x: leave as variables
y = 10x - 8
help please which one is it
Answers
The function B has a greater rate of change.
What is rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Therefore, rather than the size of each change individually, it is the rate—or the acceleration or deceleration of changes. In finance, rate of change is employed to comprehend price returns and spot trend momentum.
First to find the rate of change for function A.
Rate of change = [tex]\frac{0-5}{2.5-1.5} = \frac{-5}{1}=-5[/tex]
Function A has rate of change is -5.
Now consider, the second equation
y = -4.5x + 15
Since, the slope is rate of change for the equation.
So, function B has rate of change of -4.5
Now compare the rate of change for both the functions A and B
-5 < -4.5
Therefore, function B have greater rate of change.
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Find the value of each variable. I need help solving this
Answers
Answer:
y = 75; z = 75
Step-by-step explanation:
105 and z are a linear pair and that means they add up to 180
they are on a straight line which is why they are a linear pair
105 + z = 180
subtract 105 to both sides
z = 75
now add all of the remaining sides and subtract that from 360 because a quadrilaterals angles add to 360
75 + 89 + 95 = 259
360 - 259 = y
360 - 259 = 101
y = 101
these are your answer
Answer:
y=95
z=105
Step-by-step explanation:
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Which scatterplot shows the weakest negative linear correlation?
On a graph, points are grouped closely together and increase.
On a graph, points are grouped closely together in a line and increase.
On a graph, points are grouped closely together and decrease.
On a graph, points are grouped closely together in a line and decrease.
Answers
The scatterplot shows the weakest negative linear correlation is On a graph points are grouped closely together and increase. Option A.
The scatterplot showing the weakest negative linear correlation is the following scatterplot. The dots are scattered along the decreasing trend line. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that an increase in one variable tends to increase the other variable.
A negative correlation means that as one variable increases the other tends to decrease. Plotted points indicate correlations between variables if any. The scatterplot above is an example of a weak negative correlation. In this graph, y values decrease as x values increase, but the pattern does not resemble a straight line.
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How would I approach this problem? I’m not sure how to solve measurements
Answers
To identify the mass of the solute, subtract the total mass by the mass of the graduated cylinder.
Thus, we have the following:
[tex]20.6g-2.55g=18.05g[/tex]To obtain the concentration of the solution, divide the obtained mass by the total volume and then simplify.
Thus, we have the following:
[tex]\frac{18.05g}{74.79mL}=\frac{1805g}{7479mL}\approx0.241g\cdot mL^{-1}[/tex]AB bisects LDAC and
m/DAB = 37°. What is
m/DAC?
Answers
The value of the angle m∠DAC is 74° as AB bisects ∠DAC .
We know from the properties of angles that the angle bisector will bisect the angle into two equal parts.
∠DAC is bisected by the straight line AB. This forms two angles ∠DAB and ∠BAC .
∠DAC =∠DAB + ∠BAC
now, ∠DAB = ∠BAC
given that ∠DAB = 37
Hence m∠BAC = 37
now,
∠DAC = ∠DAB + ∠BAC
m∠DAC = 37° + 37°
m∠DAC = 74°
A line that divides an angle into two equal angles is known as an angle bisector in geometry. A device that splits an object or form into two equal halves is referred to as a "bisector." A ray that divides a given angle into two identical segments of the same length is called an angle bisector.
Therefore the value of m∠DAC is 74° .
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what is the sum of the first five terms in this series?(picture of problem below)
Answers
Provided information:
We know the first 4th terms of the series:
[tex]6,-\frac{6}{3},\frac{6}{9},-\frac{6}{27}[/tex]We can express this series in summation notation as:
[tex]\sum_{i\mathop{=}1}^n\frac{6}{(-3)^{i-1}}[/tex]Therefore, the 5th term of the series is:
[tex]\frac{6}{(-3)^{5-1}}=\frac{6}{(-3)^4}=\frac{6}{81}[/tex]Now, we have to add the first five terms:
[tex]6+(-\frac{6}{3})+\frac{6}{9}+(-\frac{6}{27})+\frac{6}{81}[/tex]The next step is to convert all fractions to have the same denominator, so:
[tex]\begin{gathered} 1st:6*\frac{81}{81}=\frac{486}{81} \\ 2nd:-\frac{6}{3}*\frac{27}{27}=-\frac{162}{81} \\ 3rd:\frac{6}{9}*\frac{9}{9}=\frac{54}{81} \\ 4th:-\frac{6}{27}*\frac{3}{3}=-\frac{18}{81} \end{gathered}[/tex]Now, they have the same denominator, it remains the same and we just need to add the numerators:
[tex]\frac{486-162+54-18+6}{81}=\frac{366}{81}[/tex]And now, let's simplify the fraction by dividing the numerator and denominator by 3:
[tex]\frac{\frac{366}{3}}{\frac{81}{3}}=\frac{122}{27}[/tex]The answer is A. 122/27
consider the following system of equations with the solution (1, 8). which system of equations would have the same solution?
Answers
Replacing x=1 in the equations to verify if the value of y is equal to 8, we have:
A.
y= 5*(1) + 3 = 8 (Multiplying and adding) (It is correct as the result for y is equal to 8)
y= 9*(1) - 1 = 8 (Multiplying and subtracting)(It is correct as the result for y is equal to 8)
B
y= 4*(1) + 2 = 6 ≠ 8 (Multiplying and adding) (It is not correct as the result for y is not equal to 8)
C
y= -2*(1) + 10 = 8 (Mulitplying and subtracting) (It is correct as the result for y is equal to 8)
y= 8*(1) + 1 = 9 ≠ 8 (Multiplying and adding) (It is not correct as the result for y is not equal to 8)
D.
y= 7*(1) -5 = 9 ≠ 8 (Multiplying and subtracting) (It is not correct as the result for y is not equal to 8)
The answer is the option A.
Solve 5(4m + 1) − 2m = −13.
Answers
Answer:
Step-by-step explanation
5(4m+1)-2m=-13
20m+5-2m=-13
20m-2m=-13-5
18m=-18
m=-1
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{5(4m+1)-2m=-13 } \end{gathered}$}[/tex]
Apply the multiplicative law of distribution.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{20m+5-2m=-13 } \end{gathered}$}[/tex]
Combine as terms.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m+5=-13 } \end{gathered}$}[/tex]
Rearrange the unknown terms to the left side of the equation.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-13-5 } \end{gathered}$}[/tex]
Calculate the sum or difference.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-18 } \end{gathered}$}[/tex]
Divide both sides of the equation by the coefficient of the variable.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-\frac{18}{18} } \end{gathered}$}[/tex]
Solve for the common factor.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-1 \iff } \end{gathered}$}\boxed{\boxed{\bf{Answer}}}[/tex]
A telephone plan consists of a monthly fee of $15 plus 20 cents per minute for long distance calls are made. Write an equation for the total monthly cost C, when n minutes are used for long distance calls.
Answers
a)Using the given information we can set the following equation:
[tex]C=0.20n+15[/tex]b) The graph of the linear equation above for up to and including 200 minutes is as follows:
Which corresponds to option B.
c) If n=40 then:
[tex]C=0.20\cdot40+15=8+15=23[/tex]Then the total monthly cost is $23.
d) If C=30, solving the first equation on the board for n we get:
[tex]\begin{gathered} 30=0.20n+15 \\ 0.20n=15 \\ n=75 \end{gathered}[/tex]Then the number of minutes is 75.
Page 5.26, Problem 3: A baseball team had 80 players show up last year and this year had 96 players show up for tryouts. Find increase in players from last year to this year. Your answer.
Answers
In order to determne the increse in the number of players, estimate the percentage increase. Proceed as follow:
First, calculate the difference in the number of player:
96 - 80 = 16
next, determine what is the associated percentage of such difference:
(16/80)(100) = 20%
Hence, the percentage increase was of 20%
Which is the graph of the linear inequality y >-x-3
Answers
Answer:
The correct graph is shown below.
Hope this helps!
1. What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.(a) Show your work.(b) is the product of 3x-4 and 5x² - 2x + 6 equal to the product of 4 - 3x and 5x² - 2x + 6? Explain
Answers
SOLUTIONS
(a) What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.
[tex](3x-4)(5x^2-2x+6)[/tex][tex]\begin{gathered} 3x(5x^2-2x+6)-4(5x^2-2x+6) \\ 15x^3-6x^2+18x-20x^2+8x-24 \\ collect\text{ like terms} \end{gathered}[/tex][tex]15x^3-26x^2+26x-24[/tex]The product is
[tex]15x^3-26x^2+26x-24[/tex][tex](4-3x)(5x^2-2x+6)[/tex]The product will be
[tex]\begin{gathered} 4(5x^2-2x+6)-3x(5x^2-2x+6) \\ 20x^2-8x+24-15x^3+6x^2-18x \\ -15x^3+26x^2-26x+24 \end{gathered}[/tex]The product of 4 - 3x and 5x² - 2x + 6 will be equal to the -1 multiply be the product of 3x - 4 and 5x² - 2x + 6, thus the two product are same
Checking
[tex]\begin{gathered} -1(-15x^3+26x^2-26x+24) \\ 15x^3-26x^2+26x-24 \end{gathered}[/tex]Hence the two answer are the same.
Find the measures of the numbered angles in the isosceles trapezoid shown below.
Answers
First, notice that since we have an isosceles trapezoid, the base angles will be equal, then:
[tex]\measuredangle3=60\degree[/tex]next, we have that the angles adjacent to opposite bases are supplementary, then we can write the following equation:
[tex]\measuredangle2+\measuredangle3=180[/tex]using the fact that the measure of angle 3 is 60 degrees, we can find the measure of angle 2:
[tex]\begin{gathered} \measuredangle2+60=180 \\ \Rightarrow\measuredangle2=180-60=120 \\ \measuredangle2=120 \end{gathered}[/tex]then, since angles 1 and 2 are also base angles, they are equal. Therefore, the measure of the anlges is:
[tex]\begin{gathered} \measuredangle1=120 \\ \measuredangle2=120 \\ \measuredangle3=60 \end{gathered}[/tex]Use the expression x^2 + 10x − 13 to answer the following questions.Part A: What numeric expression should be added in order to complete the square for the given expression?Part B: What expression is equivalent to the given expression after completing the square?Select two answers: one for Part A and one for Part B.
Answers
Given the expression below
[tex]x^2+10x-13=0[/tex]The general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]Using the completing the square method,
[tex]\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}[/tex]Where b =10 from the given equation
[tex]\begin{gathered} \text{Addding (}\frac{b}{2})^2\text{ to both sides} \\ ie\text{ (}\frac{10}{2})^2=5^2=25 \\ \text{Add 25 to both sides} \end{gathered}[/tex][tex]x^2+10x+25=13+25[/tex]For part A, the numerical value to be added is 25
Hence, for part A, the answer is 25-25
By completing the square
[tex]\begin{gathered} x^2+10x+25=13+25 \\ (x+5)^2=38 \\ (x+5)^2-38=0 \end{gathered}[/tex]Hence, for part B, the answer is (x+5)²-38
Simplify four fourths over nine
Answers
The simplification of four fourths over nine written as 4/4 ÷ 9 is given by 1/9
How to simplify fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
Given: four fourths over nine
= 4/4 ÷ 9
= 1 ÷ 9
= 1/9
Or alternatively
4/4 ÷ 9
multiply by the reciprocal of 9= 4/4 × 1/9
= (4 × 1) / (4 × 9)
= 4/36
= 1/9
In conclusion, the fraction four fourths over nine is simplified as 1/9
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The graph shows the function f(x). Which equation represents f(x). F(x)=-3 square root x. F(x) = -3 square root x - 1. F(x) = 3 square root -x - 1. F(x) = 3 square root - x
Answers
The graph given is has the cubic function as the parent function.
The cubic function is shown below:
I need help
What is 15% off of 10$
Answers
Answer: $8.50
hope this helps :)
im not the nest at math but im pretty sure that is what is is.
Step-by-step explanation:
penelope had 1/2 of her birthday cake leftover so she decided to take it to work. she shared her birthday cake equally among herself and four of her co workers. what fraction of the cake did each person get?
Answers
In a circle with radius 0.9, an angle intercepts an arc of length 3.6. Find the angle inradians to the nearest tenth.
Answers
SOLUTION
Given the question on the question tab;
[tex]\begin{gathered} radius\text{ r=0.9} \\ angle\text{ }\theta=? \\ Length\text{ of arc=3.6} \end{gathered}[/tex][tex]\begin{gathered} Length\text{ of arc =}\theta r \\ 3.6=0.9\theta \\ \theta=\frac{3.6}{0.9} \\ \theta=4.0 \end{gathered}[/tex]
The angle is 4.0
I don’t know how to solve this I would love some help and explanations oh now to solve it please
Answers
Given the point-slope equation
[tex]y+1=\frac{2}{3}(x-8)[/tex]Simplify as shown below
[tex]\begin{gathered} y+1=\frac{2}{3}x-8\cdot\frac{2}{3}=\frac{2}{3}x-\frac{16}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{16}{3}-1=-\frac{19}{3} \\ \Rightarrow-\frac{2}{3}x+y=-\frac{19}{3} \end{gathered}[/tex]The answer is -2x/3+y=-19/3. Write -2/3 in the first gap, 1 in the second gap, and -19/3 in the third one.
How to multiply fractions
[tex]\begin{gathered} \frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d} \\ \Rightarrow8\cdot\frac{2}{3}=\frac{8}{1}\cdot\frac{2}{3}=\frac{8\cdot2}{1\cdot3}=\frac{16}{3} \end{gathered}[/tex]How to add fractions,
[tex]\begin{gathered} \frac{a}{b}+\frac{c}{d}=\frac{\text{ad+cd}}{bd} \\ \Rightarrow-\frac{16}{3}-1=-\frac{16}{3}-\frac{3}{3}=\frac{-16\cdot3-3\cdot3}{3\cdot3}=\frac{-48-9}{9}=-\frac{57}{9}=-\frac{19}{3} \end{gathered}[/tex]Answer:
2x + -3y = 19
Step-by-step explanation:
In this question, they already gave you the equation of the line. But it is in point-slope form. We just need to rearrange the equation to look like:
Ax + By = C
A and B and C should be positive or negative whole numbers. So let's get rid of the fraction first.
y + 1 = 2/3 (x - 8)
You could use distributive property on the right side, but that is just going to make two terms have fractions. Instead, let's multiply both sides by 3 and get rid of the fraction.
3(y + 1) = 3• 2/3(x-8)
3(y + 1) = 2(x - 8)
Now use distributive property.
3y + 3 = 2x - 16
We need x and y on the left and plain numbers on the right.
3y + 3 = 2x - 16
Subtract 3
3y = 2x - 19
Subtract 2x
3y - 2x = -19
Rearrange the x and y terms, put x in the lead.
-2x + 3y = -19
This is almost standard form. The A is supposed to be positive. So change the sign of ALL the numbers. A is 2, the B is -3 and the C is 19. Those are the numbers that go in the blanks on your question.
what is the converted fraction of 110/17
Answers
Answer:
6 8/17
Step-by-step explanation:
17 x 6 is 102 so that can go into 110
Then you do 110-102 to find how many are left over 110-102= 8 so there are 8 left over so that goes into the numerator so the answer is 6 8/17 The denominator stays the same unless you can simply but in this case you can’t.