Consider the following three systems of linear equations.(Please list what option it is.
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We transform System A into System B by converting equation A2 into equation B2. We transform System B into System C by converting equation B2 into equation C2.
We are given three systems of linear equations. The first system of linear equations is A1 : -2x + 7y = -5 and A2 : 4x - 3y = -23. The second system of linear equations is B1 : -2x + 7y = -5 and B2 : 11y = -33. The third system of linear equations is C1 : -2x + 7y = -5 and C2 : y = -3. To convert the system A to system B, we transform the equation A2 to equation B2. To convert the system B to system C, we transform the equation B2 to equation C2.
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Related Questions
write an extended proportion to indicate the proportional corresponding sides of the triangles
Answers
The correct extended proportion is:
[tex]\frac{MN}{RS}=\frac{MP}{RT}=\frac{NP}{ST}[/tex]Since the other two options have some non-correspondant proportions.
Find the quadratic function that y=f(x) that has the vertex (0,0) and whose graph passes through the point(-2,-8). Write the function in standard form
Answers
Given
The quadratic function that y=f(x) that has the vertex (0,0) and whose graph passes through the point(-2,-8)
Solution
Recall
[tex]y=a(x-h)^2+k[/tex][tex]\begin{gathered} Vertex\text{ =\lparen h,k\rparen} \\ \\ h=0 \\ k=0 \\ \\ y=a(x-0)^2+0 \\ y=ax^2 \end{gathered}[/tex]Given
Point (-2, -8)
[tex]\begin{gathered} x=-2 \\ y=-8 \\ -8=a(-2)^2 \\ -8=a4 \\ -8=4a \\ divide\text{ both sides by 4} \\ \frac{4a}{4}=-\frac{8}{4} \\ \\ a=-2 \end{gathered}[/tex]Now
[tex]\begin{gathered} y=a(x-h)^2+k \\ a=-2 \\ h=0 \\ k=0 \\ y=-2(x-0)^2+0 \\ y=-2(x)^2+0 \\ y=-2x^2 \end{gathered}[/tex]The standard form
[tex]y=ax^2+bx+c[/tex]Now
[tex]\begin{gathered} y=-2x^2+0x+0 \\ which\text{ is } \\ y=-2x^2 \end{gathered}[/tex]Checking with graph
The final answer
[tex]y=-2x^2[/tex]Alice fills up the gas tank of her car before going for a long drive . The equation below models the amount of gas , g , in gallons , in Alice's car when she has driven m miles . What is the meaning of 32 in the equation ?
Answers
Solution
For this case we have the following equation given:
[tex]g=15-\frac{m}{32}[/tex]We want to know what represent the 32 value
So then the answer is:
Total of miles that can cover the car with 15 gallons of gas
how to find arc for circles or angle indicated
Answers
Given data:
The given image of the circle.
The given diagram can be redrawn as,
Here, Triangle JOK is an isosceles triangle in which OJ and OK are radii, the expression for the angle sum property is,
[tex]undefined[/tex]i need help with this question parts 1 - 4
Answers
Given:
Given data points are (950,100) and (1000,40).
Required:
To find the linear model for this data.
Explanation:
The standard form of linear equation is
[tex]y=mx+b[/tex]Where
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{40-100}{1000-950} \\ \\ m=-\frac{60}{50} \\ \\ m=-\frac{6}{5} \end{gathered}[/tex]Now
[tex]y=-\frac{6}{5}x+b[/tex]Now we have to find b using the points (950,1000), we get
[tex]\begin{gathered} 1000=-\frac{6}{5}(950)+b \\ \\ 1000=-6\times190+b \\ \\ 1000=-1140+b \\ \\ b=1000+1140 \\ \\ b=2140 \end{gathered}[/tex][tex]y=-\frac{6}{5}x+2140[/tex]Final Answer:
[tex]y=-\frac{6}{5}x+2,140[/tex]A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred,George, Heather, and Ivan. Use the second row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). Theother six subjects will go into the control group. If the subjects are numbered through 9 alphabetically, what are the numbers of the three subjects selected? List thesubjects that will go in the treatment group.Line/Column(1)(2)(3)(4)177952454778618314079264955243209744831960479733397402669224773What are the numbers of the three subjects selected?{If not an answer please an explanation, I don’t understand how to get the numbers}
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The second row has the following numbers:
64955, 24320, 97448, 26692
We are interested in numbers from 0 to 9, then we are only interested in the first digit of the numbers, which are: 6, 2, 9, 2.
Student 2 is Brian
Student 6 is Fred
student 9 is Ivan
Use definitions of right-hand and left-hand limits to prove the limit statement.lim-1|x|X>0Since x approaches 0 from the left, x<0, (x = []).
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First we need to understand what |x| means or what values it repressents
[tex]|x|=\begin{cases}x,x\ge0 \\ \\ -x,x<0\end{cases}[/tex]|x| indicates the absolute value of x, this is, x is always going to be positive, for example,
when x = 1 -> |x| = 1 , but also when x = -1 , then |x| = 1
Since, in this case, we need to find the limit when X approaches 0 from the left we are going to use |x| = -x , for x<0
this is...
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}=\lim _{x\rightarrow0-}(-1)=-1[/tex]At this point we have proved the limit statement.
So, in order to answer the question in the lower part... x approaches to 0 from the left, x<0, |x| = -x
In the graph you can see, whenever X<0 the value of the funcion will be negative and when it approaches 0 it becomes -1
On the other hand, when the function approaches to 0 from the right, the value of the function is +1. This is a discontinuity
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}[/tex]This way we eliminate the absolute value, because, remember, when x<0, |x| = -x
A file that is 289 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to thenearest tenth.
Answers
Given:
289 megabytes
and 18.6% = 0.186
Therefore:
[tex]289\times0.186=53.754[/tex]Round to the nearest tenth: 53.8
Answer: 53.8 megabytes
What equation that represents the line that passes through the two points (5, 8) and (9, 2)?
Answers
The linear equation that passes through the two given points is:
7 = (-3/2)*x + 31/2.
What is the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Here the line passes through (5, 8) and (9, 2), then the slope is:
m = (2 - 8)/(9 - 5) = -6/4 = -3/2
So we have:
y = (-3/2)*x + b
To find the value of b, we can replace the values of one of the points in the equation, I will use (5, 8)
8 = (-3/2)*5 + b
8 = -15/2 + b
8 + 15/2 = b
31/2 = b
The line is: y = (-3/2)*x + 31/2
Convert.4,130 cm = M
Answers
ANSWER
41.3 m
EXPLANATION
1 meter is 100 centimeters. To transform from centimeters to meters, we have to divide by 100:
[tex]\frac{4,130}{100}=41.3[/tex]4,130 centimeters is 41.3 meters.
An experiment consists of rolling a dice. What is the probability of rolling anumber greater than 42 Express your answer as a fraction in simplest form.(Remember a dice has 6 sides numbering 1-6)O 1/2O 2/3O 1/3O 1/6
Answers
We have to calculate the probability of getting a number greater than 4 when rolling a six-side dice.
We can calculate this probability as the ratio between the "successes" (getting a number greater than 4) and the total possible outcomes.
In this case, the only outcomes greater than 4 are "5" and "6", so we have two successful outcomes.
The total number of outcomes is 6 (1, 2, 3, 4, 5 and 6).
Then, the probability is:
[tex]P(X>4)=\frac{\text{success}}{\text{total}}=\frac{2}{6}=\frac{1}{3}[/tex]Answer: 1/3
Knowledge check (probability) this is math not chemistry. I am looking at the tab
Answers
Answer:
5:13
Explanation:
Given that the probability of the box having a toy = 13/18
Therefore, the probability of the box not having a toy:
[tex]P(\text{ no toy\rparen}=1-\frac{13}{18}=\frac{5}{18}[/tex]The odds against an event is given as the ratio of the Number of unfavorable outcomes to number of favorable outcomes.
• Number of Unfavourable Outcomes = 5
,• Number of favourable Outcomes = 13
Thus, the odds against the box having a toy is 5:13.
given f(x) = x² + 4x -5find f(x) inverse
Answers
The function is given as
[tex]f(x)=x^2+4x-5[/tex]To find the inverse of the function ,
[tex]y=x^2+4x-5[/tex]Replace x with y.
[tex]x=y^2+4y-5[/tex]Now solve for y,
Add 4 and subtract 4 in the RHS.
[tex]x=y^2+4y-5+4-4[/tex][tex]x=y^2+4y-9+4[/tex][tex]x=(y+2)^2-9[/tex][tex]x+9=(y+2)^2[/tex][tex](y+2)^2=x+9[/tex][tex]y+2=\pm\sqrt[]{x+9}[/tex][tex]y=\sqrt[]{x+9}-2[/tex][tex]y=-\sqrt[]{x+9}-2[/tex]Hence the inverse of the function is
[tex]y=\sqrt[]{x+9}-2,-\sqrt[]{x+9}-2[/tex]a graph of a linear equation passes through (-2,0) and (0,-6)1. Use 2 points to sketch the graph of the equation2. is 3x-y=-6 an equation for this graph? (Yes or no question)3. Explain your reason of how you know
Answers
1) So we can graph the point and join the points with a line so:
2) we can rewrite the equation in the form slope intercept so:
[tex]\begin{gathered} 3x-y=-6 \\ y=3x+6 \end{gathered}[/tex]So the answer is NO
3) because the intercept with the y axis is -6 no 6 so for that reason we know that is not the function
which box and whisker plot has the greatest interquartile range?
Answers
Calculate each interquartile: subtract the upper quartile to the lower quartile
1. 9-7 = 2
2. 105-97 = 8
3. 17-7.5= 9.5
4. 7 -4 = 3
The greatest interquartile is 9.5 (option 3)
Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.7x + 7y = 281 4x + 4y = 16
Answers
Infinite number of solutions
Explanation:The given system of equations:
7x + 7y = 28........(1)
4x + 4y = 16.........(2)
Multiply equation (1) by 4
28x + 28y = 112..............(3)
Multiply equation (2) by -7
-28x - 28y = -112...............(4)
Add equations (3) and (4) together
0x + 0y = 0....................(5)
Since the right hand and left hand sides of equation (5) are equal, the equation has infinite number of solutions
Charles is 16 years older than his sister Michelle. In 8 years, he will be twice as old as Michelle. How old is each of them now?
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Charles is now 24 years old and Michell 8 years old
1) In this problem, let's turn that information into an equation so that we can solve it using Algebra.
2) The first equation is:
Charles: x+16
Michelle: x
After 8 years, since Charles is going to be twice older than Michelle, we'll have:
[tex]\begin{gathered} C=x+16 \\ M=x \\ --- \\ x+16+8=2(x+8) \\ x+24=2x+16 \\ x-2x=-24+16 \\ -x=-8 \\ x=8 \end{gathered}[/tex]Note that we equated the age of Charles plus 8 to the double of x, Michelle's age.
3) Let's now find the age of them now:
[tex]\begin{gathered} C=8+16 \\ C=24 \\ M=8 \end{gathered}[/tex]Plugging back into the first equations, we can see that Charles is now 24 yrs old and Michell 8 yrs old
For each question, use the following statements to write the compound statement anddetermine its truth value.P: Perpendicular lines intersect to form right angles.Q: All eagles are bald eagles.R: The capital of Texas is Houston.S: Congruent segments have equal length.Write the compound statement and determine its truth value: P V ~QPerpendicular lines intersect to form right angles or all eagles are bald eagles, falsePerpendicular lines intersect to form right angles or not all eagles are bald eagles; truePerpendicular lines intersect to form right angles or not all eagles are bald eagles; falsePerpendicular lines intersect to form right angles or all eagles are bald eagles: true
Answers
P:Perpendicular lines intersect and perpendicular lines form right angles. True
Q:
A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is 15/56,and the probability of selecting a black chip on the first draw is 5/8,find the probability of selecting the white chip on the second draw,given that the first chip selected was a black chip
Answers
Answer:
Explanations:
Probability is the likelihood or chance that an event will occur. Mathematically:
[tex]\text{Probability}=\frac{Expected\text{ outcome}}{total\text{ outcome}}[/tex]According to the question, we are told that the probability of selecting a black chip on the first draw is 5/8, this shows that the total number of chips is 8 since it was a first draw (all chips are intact).
If the probability of selecting a black chip and a white chip is 24/56 without replacement, then;
[tex]\text{Probability (a black and a white)=Pr(a black c}hip\text{)}\times Pr(white)[/tex]Substitute the given probability into the formula to have:
[tex]undefined[/tex]Would appreciate your help with this algebra question. Thank you!
Answers
The above function is to be used if the value of x is between 0 and 8. On the other hand, the function to be used when x ≥ 8 is -5x + 11.
Since the interval to be checked is from 2 to 7, we will be using the first function which is -2x + 4.
To determine the rate of change between those intervals, we have the formula below:
[tex]\text{rate of change = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]Let's solve f(x₂) first. Our x₂ = 7. Let's substitute the function above with x = 7.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(7)=-2(7)+4 \\ f(7)=-14+4 \\ f(7)=-10 \end{gathered}[/tex]Let's solve f(x₁) first. Our x₁ = 2. Let's substitute the function above with x = 2.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(2)=-2(2)+4 \\ f(2)=-4+4 \\ f(2)=0 \end{gathered}[/tex]So, we now have the value of f(x₂) = -10, and f(x₁) = 0. Let's use these values to the formula of the rate of change above.
[tex]\begin{gathered} \text{rate of change}=\frac{f(x_2)-f(x_1)^{}}{x_2-x_1} \\ \text{rate of change}=\frac{-10-0}{7-2} \\ \text{rate of change}=\frac{-10}{5} \\ \text{rate of change}=-2 \end{gathered}[/tex]Since the rate of change is a negative number, the function is decreasing over the interval [2, 7].
6. An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday? 8. Stan's Steakhouse has a server to cook ratio of 5 to 2. The total numbor of servers and cooks is 42. How many servers doos Stan's Steakhouse employ?
Answers
The ratio between the child tickets to adult tickets is 8 : 1
The child tickets are more by 147
Let us use the ratio method to solve the question
Child : Adult : difference
8 : 1 : 7 (8 - 1)
x : y : 147
By using cross multiplication
[tex]\begin{gathered} x\times7=8\times147 \\ 7x=1176 \end{gathered}[/tex]Divide both sides by 7 to find x
[tex]\begin{gathered} \frac{7x}{7}=\frac{1176}{7} \\ x=168 \end{gathered}[/tex][tex]\begin{gathered} y\times7=1\times147 \\ 7y=147 \end{gathered}[/tex]Divide both sides by 7 to find y
[tex]\begin{gathered} \frac{7y}{7}=\frac{147}{7} \\ y=21 \end{gathered}[/tex]The total number of tickets = 168 + 21 = 189
The total number of tickets is 189
Which mathematical property is demonstrated?5 • 7 • 4 = 5 • 4 • 7commutative property of additioncommutative property of multiplicationassociative property of additionassociative property of multiplication
Answers
What we can observe in equality is the commutative property of multiplication.
The answer would be Commutative Property of Multiplication
Given f(x)=x^2+4x+5, what is f(2+h)-f(2)/h equal to?A. h^2 + 8hB. 2x + h + 4C. 8 + hD. h + 4
Answers
ANSWER:
C. 8 + h
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]f\mleft(x\mright)=x^2+4x+5[/tex]We evaluate each case and obtain the following:
[tex]\begin{gathered} f(h+2)=\left(2+h\right)^2+4\left(2+h\right)+5 \\ \\ f(2+h)=4+4h+h^2+8+4h+5 \\ \\ f(2+h)=h^2+4h+4h+4+8+5 \\ \\ f(2+h)=h^2+8h+17 \\ \\ \\ f(2)=\left(2\right)^2+4\left(2\right)+5 \\ \\ f(2)=4+8+5 \\ \\ f(2)=17 \end{gathered}[/tex]We substitute each function evaluated to determine the final result, just like this:
[tex]\begin{gathered} \frac{f(2+h)-f(2)}{h}=\frac{h^2+8h+17-17}{h} \\ \\ \frac{f(2+h)-f(2)}{h}=\frac{h^2+8h}{h} \\ \\ \frac{f(2+h)-f(2)}{h}=h+8=8+h \end{gathered}[/tex]Therefore, the correct answer is C. 8 + h
Using the slope formula, find the slope of the line through the given points (2,-1) and (6,1)
Answers
Determine the slope of line pasing through points (2,-1) and (6,1).
[tex]\begin{gathered} m=\frac{1-(-1)}{6-2} \\ =\frac{1+1}{4} \\ =\frac{2}{4} \\ =\frac{1}{2} \end{gathered}[/tex]So slope of line is 1/2.
Find an equation of the line that goes through the points (7,8) and (4,-8). Write your answer in the form y=mx+b .y= x+ Preview m : ; Preview b : Write your answers as integers or as reduced fractions in the form A/B.Submit QuestionQuestion 2
Answers
For this question we will use the two points formula for the equation of a line:
[tex]y-8_{}=\frac{-8-8}{4-7}(x-7)\text{.}[/tex]Solving for y we get:
[tex]\begin{gathered} y-8=\frac{-16}{-3}(x-7), \\ y-8=\frac{16}{3}x-\frac{112}{3}, \\ y=\frac{16}{3}x-\frac{112}{3}+8, \\ y=\frac{16}{3}x-\frac{88}{3}. \end{gathered}[/tex]Answer:
[tex]y=\frac{16}{3}x-\frac{88}{3}.[/tex]Triangle ABC has vertices at A: (0,7), B: (0, 2), and C: (4,2). What is the perimeter in units?Round your answer to the nearest tenth (one decimal place).
Answers
Given that
A = (0, 7)
B = (0 2)
C = (4, 2)
[tex]undefined[/tex]predict adjusted wages in 1998 does this prediction require interpolation or extrapolating
Answers
The required interpolation in adjusted 2020 is 0.50
Explanation:We find the interpolation using the formula:
[tex]y=y_1+\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us choose these points as follows:
[tex]\begin{gathered} x_1=7.69 \\ x_2=7.87 \\ y_1=3.80 \\ y_2=5.15 \end{gathered}[/tex]So,
[tex]\begin{gathered} y=3.80+\frac{5.15-3.80}{7.87-7.69}(x-7.69) \\ \\ =3.80+\frac{1.35}{0.18}(x-7.69) \\ \\ =3.80+7.5(x-7.69) \\ y=7.5x-53.875 \end{gathered}[/tex]In adjusted 2020, we have x = 7.25, using this, we have:
[tex]\begin{gathered} y=7.5(7.25)-53.875 \\ =54.375-53.875 \\ =0.50 \end{gathered}[/tex]How do you use the distance formula to figure out the area of the triangle. I don't really know how to solve this problem or use distance formula
Answers
The Area of a Right Triangle
The area of any triangle of base B and height H is:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular, i.e, the angle between them must be 90°.
The trick here is to prove the triangle is right at the point (15, 5).
If two lines are perpendicular, the product of their slopes is -1.
Calculate the slope of the line that joins the vertices at (5, 15) and (15, 5):
[tex]\begin{gathered} m_1=\frac{5-15}{15-5} \\ m_1=-\frac{10}{10} \\ m_1=-1 \end{gathered}[/tex]Calculate the slope of the line that joins the vertices at (20, 10) and (15, 5);
[tex]\begin{gathered} m_2=\frac{5-10}{15-20} \\ m_2=\frac{-5}{-5} \\ m_2=1 \end{gathered}[/tex]It can be verified that m1 * m2 = -1, thus the lines are perpendicular and we can use the formula given above to compute the area.
Find the length of both lines with the formula of the distance:
[tex]\begin{gathered} L_1=\sqrt[]{(5-15)^2+(15-5)^2} \\ \text{Calculating:} \\ L_1=\sqrt[]{200} \end{gathered}[/tex][tex]\begin{gathered} L_2=\sqrt[]{(5-10)^2+(15-20)^2} \\ L_2=\sqrt[]{50} \end{gathered}[/tex]Apply the formula of the area:
[tex]\begin{gathered} A=\frac{\sqrt[]{200}\cdot\sqrt[]{50}}{2} \\ A=\frac{\sqrt[]{10000}}{2} \\ A=\frac{100}{2}=50 \end{gathered}[/tex]The area is 50 square units
points reflected over an axis graphically
Answers
The coordinate of the point N is (-6,2).
The point on reflection about x axis, the x -coordinate remain same and sign of y-coordinate changes.
Determine the coordinate of point N'.
[tex]N^{\prime}(-6,-1\cdot2)\rightarrow N^{\prime}(-6,-2)[/tex]Plot the point on the graph.
5. Find the equation of a line that is parallel to y = 2x + 8 and passes through (5, 1).
Answers
First, let's find the slope of the given line, comparing the equation with the slope-intercept form of a linear equation (y = mx + b, where m is the slope).
Looking at the equation, we have m = 2.
Since parallel lines have the same slope, so the slope of the parallel line is also m = 2.
Then, using the point (5, 1) in the equation, we have:
[tex]\begin{gathered} y=mx+b \\ 1=2\cdot5+b \\ 1=10+b \\ b=1-10 \\ b=-9 \end{gathered}[/tex]Therefore the equation is y = 2x - 9, and the correct option is 1.