Which equation represents a line which is parallel to the line y = 3x - 8x + y = 18x - 3y = -123x + y = 6y - 3x = 7
Answers
Parallel equations have the same slope. First, let's identify the slope of the given equation, which is in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the given equation with this form, we have m = 3, so the slope is 3.
Now, let's identify the slope of each option:
[tex]\begin{gathered} x+y=18\\ \\ y=-x+18\\ \\ m=-1 \end{gathered}[/tex][tex]\begin{gathered} x-3y=-12\\ \\ 3y=x+12\\ \\ y=\frac{1}{3}x+4\\ \\ m=\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} 3x+y=6\\ \\ y=-3x+6\\ \\ m=-3 \end{gathered}[/tex][tex]\begin{gathered} y-3x=7\\ \\ y=3x+7\\ \\ m=3 \end{gathered}[/tex]Therefore the correct option is the fourth one: y - 3x = 7.
Related Questions
(2x + 2x + 3) - (x2+2x+1) =O A. x2 + 2O B. x2 + 4x + 2O c. x²+4O D. x2 + 4x + 4
Answers
We are given the following difference of polynomials:
[tex](2x^2+2x+3)-(x^2+2x+1)[/tex]Let's group tohether similar terms in order to solve it, and remember that the "-" sign affects every element inside the parentheses. With this, we rewrite the opperation as follows:
[tex](2x^2-x^2)+(2x-2x)+(3-1)=x^2+0+2=x^2+2[/tex]And so, the result is
[tex]x^2+2[/tex]How do i use gauss’s approach to find the sum of 8+ 14+ 20+26+…..+62
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Gauss's approach consists of a method to find the sum of the first N natural numbers:
[tex]1+2+\cdots+(N-1)+N=\frac{N\cdot(N+1)}{2}\text{.}[/tex]1) To use Gauss's approach, we write the sum of the problem as:
[tex]\begin{gathered} 8+14+20+26+\cdots+62 \\ =2\cdot4+2\cdot7+2\cdot10+2\cdot13+\cdots+2\cdot31 \\ =2\cdot(4+7+10+13+\cdots+31) \end{gathered}[/tex]2) Now, we
Write an equation for the line that passes through (-2,13) and whose slope is undefined. Give an answer in standard form.
Answers
To get the equation of the line in standard form is given by
[tex]y=mx+c[/tex]The slope of a line can be positive, negative, zero, or undefined.
When the line is exactly vertical, it does not have a defined slope
Since we have the coordinates through which the line passes: (-2,13)
where
x=-2 and y=13
Therefore, since the slope is undefined,
x = -2 will be the equation of the line
It can also be expressed as x+2=0
Part 1How many people ordered quesadillas and chili con queso but did not order nachos?. How many people ordered just nachos?L. If a person is chosen at random, what is the probability that they ordered chili con queso?. If a person is chosen at random, what is the probability that they did not order any of these items?. Given that a person ordered nachos, what is the probability that they also ordered quesadillas?. Given that a person ordered quesadillas and chili con queso, what is the probability that they also ordered nachos?. If a person is chosen at random, what is the probability that they ordered at least 2 of the items?
Answers
Given The Venn diagram represents the number of people who ordered quesadillas, chili, and nachos.
We will find the following:
1) How many people ordered quesadillas and chili con queso but did not order nachos?
As shown, we will find the intersection between quesadillas and chili con queso
So, the answer will be: 9 people
2) How many people ordered just nachos?
So, the answer will be: 22 people
3) If a person is chosen at random, what is the probability that they ordered chili con queso?
The number of people who ordered chili con queso = 5
The total number of people = 5 + 15 + 22 + 9 + 11 + 2 + 19 + 21 = 104
So, the probability will be = 5/104 = 0.048
4) If a person is chosen at random, what is the probability that they did not order any of these items?
The number of people who did not make order = 21
So, the probability will be = 21/104 = 0.20
5) Given that a person ordered nachos, what is the probability that they also ordered quesadillas?
The number of people who ordered nachos and quesadillas = 2 + 11 = 13
So, the probability will be = 13/104 = 0.125
6) Given that a person ordered quesadillas and chili con queso, what is the probability that they also ordered nachos?
The number of people who ordered the 3 kinds = 11
So, the probability = 11/104 = 0.106
7) If a person is chosen at random, what is the probability that they ordered at least 2 of the items?
The number of people who ordered 2 items only = 2 + 15 + 9 = 26
So, the probability will be = 26/104 = 0.25
Given f (x) = 2 (x – 3) – .2x. What is the value of f(-10)?
Answers
Answer:
f(-10)=-24
Explanation:
Given that:
[tex]f(x)=2(x-3)-0.2x[/tex]To evaluate f(-10), we substitute x with the value -10.
Therefore:
[tex]\begin{gathered} f(-10)=2(-10-3)-0.2(-10) \\ =2(-13)+2 \\ =-26+2 \\ =-24 \\ f(-10)=-24 \end{gathered}[/tex]The value of f(-10) is -24.
Find the x-intercept of the line represented by the equation -7x+5y=70
Answers
Answer:
(-10, 0)
Explanation:
The x-intercept is the point where the graph crosses the x-axis. It occurs when y = 0, so we need to replace y by 0 and solve for x
-7x + 5y = 70
-7x + 5(0) = 70
-7x + 0 = 70
-7x = 70
-7x/(-7) = 70/(-7)
x = -10
Then, the x-intercept is the point (x, y) = (-10, 0)
Therefore, the answer is
(-10, 0)
Solve for p p+5=15math is wonderful but I'm not good at it.................
Answers
The initial expression is:
p + 5 = 15
To solve for p, we need to substract 5 on both sides as:
p + 5 - 5 = 15 - 5
p + 0 = 10
p = 10
Answer: p = 10
I need help with this practice problem solving The subject is trig
Answers
Explanation
Given
[tex]\begin{gathered} |P|=\frac{3}{4}x+2 \\ |Q|=2x+1 \\ |P+Q|=\frac{2}{3}x-2 \end{gathered}[/tex]We know that, from Cauchy inequalities
[tex]|P|+|Q|>|P+Q|[/tex]Therefore;
[tex]\begin{gathered} \frac{3}{4}x+2+2x+1>\frac{2}{3}x-2 \\ \frac{3}{4}x+2x+3>\frac{2}{3}x-2 \\ \text{Multiply through by 12} \\ 12(\frac{3}{4}x+2x+3)>12(\frac{2}{3}x-2) \\ 9x+24x+36>8x-24 \\ 33x+36>8x-24 \\ 33x-8x>-36-24 \\ 25x>-60 \\ x>-\frac{12}{5} \\ \end{gathered}[/tex]From the above, we will find the x values for the given inequalities
[tex]\begin{gathered} \text{For }\frac{3}{4}x+2>0 \\ \frac{3}{4}x>-2 \\ x>-\frac{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{For }2x+1 \\ 2x>-1 \\ x>-\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{For }\frac{2}{3}x-2>0 \\ \frac{2}{3}x>2 \\ x>3 \end{gathered}[/tex]The range that satisfies the above inequality is
Answer:
[tex](3,0)[/tex]Let g be the piecewise defined function shown.g(x)= x + 4, −5 ≤ x ≤ −12 − x, −1 < x ≤ 5Evaluate g at different values in its domain.I don't understand why g(0)=2 because 0 can fit into both domain values.ex. -5 ≤ 0 ≤ 1 -1 < 0 ≤ 5
Answers
Given:
[tex]g(x)=\left\{ \begin{aligned}x+4,-5\le x\le-1 \\ 2-x,-1For the domain values, we have:For −5 ≤ x ≤ −1
Lets take all range of values of x
g(-5) = x + 4 = -5 + 4 = -1
g(-4) = x + 4 = -4 + 4 = 0
g(-3) = x + 4 = -3 + 4 = 1
g(-2) = x + 4 = -2 + 4 = 2
g(-1) = x + 4 = -1 + 4 = 3
For −1 < x ≤ 5
Lets take all range of values of x
g(0) = 2 - x = 2 - 0 = 2
g(1) = 2 - x= 2 - 1 = 1
g(2) = 2 - x= 2 - 2 = 0
g(3) = 2 - x= 2 - 3 = -1
g(4) = 2 - x= 2 - 4 = -2
g(5) = 2 - x= 2 - 5 = -3
Billy takes out a $2,400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate? Give your answer as a percentage to the nearest tenth of a percent. Do not include the percent symbol in your answer.
Answers
To calculate the total interest payable, we use the formula
I=Prt
where:
I = simple interest
P = $2,400
r = 0.08
t = 18/12
Then I = 2,400 x 0.08 x 1.5 = 288
Therefore the total amount he receives at loan drawdown is $2,400 − $288 =$2,112.
Now to calculate the effective interest rate we use the formula
A=P(1+rext).
where
A = $2,400
P = $2,112
t = 1.5
re = effective interest rate
so we have: 2,400 = 2,112(1 + 1.5xre)
finally we solve for re and we obtain
re = 9.1
suppose that you drive 30000 miles per year and gas averages $4 per gallon complete part A and B
Answers
Problem says you drive 30,000 miles per year and gas averages $4 per gallon.
a. If you own a hybrid car averaging 30 miles per gallon, then annually you will consume the next amount of gallons:
[tex]30,000\text{miles x}\frac{1gallon}{30miles}=1,000gallons[/tex]And you will pay for 1000 gallons:
[tex]1000\text{gallons}\frac{4dollars}{1gallon}=4000\text{ dollars}[/tex]But, if you own a SUV averaging 9 miles per gallon, you'll consume the next amount of gallons:
[tex]30,000\text{miles x}\frac{1gallon}{9miles}=3,333.3gallons[/tex]And you will spend in fuel:
[tex]3333.3\text{gallons}\frac{4dollars}{1gallon}=13333.3\text{ dollars}[/tex]Thus, if you own a hybrid car, you will save in annual fuel expenses:
[tex]13333.3-4000=9333.3\approx9333dollars[/tex]b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 4.8% compounded monthly, at the end of four years you will save:
The formula is:
[tex]A=\frac{P\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{(\frac{r}{n})}[/tex]Where A is the balance in the account after t years, P is the amount you deposit each month, r is the annual interest rate in decimal form and n is the number of compounding periods in one year (12 as it is monthly).
Then, if you save annually $9333, each month you save $9333/12=$777.75
At the end of 4 years, you will save then:
[tex]\begin{gathered} A=\frac{777.75\lbrack(1+\frac{0.048}{12})^{12\cdot4}-1\rbrack}{(\frac{0.048}{12})} \\ A=\frac{777.75\lbrack(1+0.004)^{48}-1\rbrack}{(0.004)} \\ A=\frac{777.75\lbrack(1.004)^{48}-1\rbrack}{(0.004)} \\ A=\frac{777.75\lbrack1.2112-1\rbrack}{(0.004)} \\ A=\frac{777.75\times0.2112}{(0.004)} \\ A=41066.5\approx41067 \end{gathered}[/tex]After 4 years you will save $41067
Sketch a graph of x−y=−4Find the midpoint between (−1,4) and (−4,1)
Answers
Solution:
Given the equation:
[tex]x-y-=-4[/tex]To sketch the graph of the above equation,
step 1: Evaluate the value of y, when x equals zero
Thus,
[tex]\begin{gathered} x-y=-4 \\ when\text{ x=0, we have} \\ 0-y=-4 \\ \Rightarrow y=4 \end{gathered}[/tex]step 2: Evaluate the value of x, when y equals zero.
Thus,
[tex]\begin{gathered} x-y=-4 \\ when\text{ y=0, we have} \\ x-0=-4 \\ \Rightarrow x=-4 \end{gathered}[/tex]step 3: Plot the obtained points in steps 1 and 2 on a graph.
Thus, the points are
[tex]\left(0,4\right?\text{ and \lparen-4,0\rparen}[/tex]The graph of the equation is as shown below:
MIdpoint: The midpoint (x,y) between two points is expressed as
[tex]\begin{gathered} \lparen x,y)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right? \\ where \\ \lparen x_1,y_1)\text{ and \lparen x}_1,y_1)\text{ are the coordinates of the endpoints} \end{gathered}[/tex]Given the points (-1,4) and (-4,1), we have
[tex]\begin{gathered} x_1=-1 \\ y_1=4 \\ x_2=-4 \\ y_2=1 \end{gathered}[/tex]Thus, the midpoint of the points (-1,4) and (-4, 1) is evaluated as
[tex]\begin{gathered} \lparen x,y)=\left(\frac{-1+\left(-4\right)}{2},\frac{4+1}{2}\right? \\ =\left(\frac{-1-4}{2},\frac{4+1}{2}\right? \\ =\left(-\frac{5}{2},\frac{5}{2}\right? \\ \Rightarrow\left(x,y\right)=\left(-2.5,\text{ 2.5}\right? \end{gathered}[/tex]Hence, the midpoint between (−1,4) and (−4,1) is (-2.5, 2.5).
Which inequality is true? A. 3π > 9B. π + 8 < 11C. π/2 > 2D. 2π - 1 < 5
Answers
3π ≈ 9.42
9.42 > 9
This is true. Therefore, A is the correct choice
12357:23Westin is comparing the triangles below.H Н4 cm27G117°8 cmF117LKSave and ExitNextSubmitMark this and return
Answers
Answer:
The last option: The angle in the listed order do not correspond.
Explanation:
The two triangles are similar because they share two angles (117 and 27) and their corresponding sides (8 cm and 4 cm) are in a ratio. The similarity statement is
[tex]\text{HGF}\sim\text{JLK}[/tex]the order of the similarity statement above indicates that
H = J
G = L
F = K
and
[tex]\begin{gathered} GH\sim JL \\ GF\sim LK \\ HF\sim JK \end{gathered}[/tex]However, Westin writes
[tex]\text{HGF}\sim\text{LJK}[/tex]which suggests that H = L and G = J and that is not true.
Therefore we conclude the westin's statement is false since it doesn't given the angles in correct order.
what is the number of pi
Answers
the number pi is a irrational number and its value is 22/ 7 or 3.14 approx.
What is the horizontal shift as well as the horizontal stretch/shrink of the function t(x)=4 cos((pi/12)x)+8?
Answers
Explanation:
We were given the function:
[tex]t\left(x\right)=4cos\left(\left(\frac{\pi}{12}\right)x\right)+8[/tex]Graphically:
We are to determine its horizontal shift & its stretch/shrink. This is shown below:
Horizontal Shift:
[tex]\begin{gathered} \text{From the general form of the sinusoidal function, we have:} \\ y=A\cos[B(x-C)]+D \\ where: \\ A=amplitude \\ \frac{2\pi}{B}=period \\ C=Phase(horizontal)\text{ }shift \\ D=Vertical\text{ }shift \end{gathered}[/tex]Comparing the general form with the function given unto us, we have:
[tex]C=0[/tex]There is no horizontal shift
Horizontal stretch/shrink:
If we have:
Rita started the day with rapps. Then she deleted 5 apps and still had twice as many apps as Cora has Write an equation that represents the number of apps each girl has
Answers
Rita has:
[tex](r-5)\text{ apps}[/tex]Cora has:
[tex]\frac{1}{2}(r-5)\text{ apps}[/tex]Explanation:Rita started the day with r apps
She deleted 5, and has
[tex]r-5[/tex]Then she still has twice as many apps as Cora, so Cora app is:
[tex]\frac{1}{2}(r-5)[/tex]Determine f^-1(2) given the following: f(1 = -3f(2) = -2f(-1) = 2f(3) = -1
Answers
We assume that the function is as follows:
[tex]f^{-1_{}}(2)=?[/tex]Then, we have that:
[tex]f^{-1}(x)=\frac{1}{f(x)}[/tex]Thus, if we have that:
[tex]f(2)=-2\Rightarrow f^{-1^{}_{}}(x)=\frac{1}{f(x)}\Rightarrow f^{-1}(2)=\frac{1}{f(2)}=\frac{1}{-2}\Rightarrow f^{-1}(2)=-\frac{1}{2}[/tex]Therefore, the value for the function is f^-1(2) = -1/2 or
[tex]f^{-1}(2)=-\frac{1}{2}[/tex]I need help with this word problem I suck at word problems
Answers
We have the given equation that represents the distance D from home after x hours of driving:
a)
To graph the equation, we use the distance on the y-axis and the hours on the x-axis.
We need to find the points:
When x=1,
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(1) \\ D=1500 \\ \text{Hence, we have the point (1,1500)} \end{gathered}[/tex]When x=2,
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(2) \\ D=1400 \\ \text{Hence, we have the point (2,1400)} \end{gathered}[/tex]When x=3
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(3) \\ D=1300 \\ \text{Hence, we have the point (3,1300)} \end{gathered}[/tex]When x=4
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(4) \\ D=1600-400 \\ D=1200 \\ \text{Hence, we have the point (4,1200)} \end{gathered}[/tex]When x= 5
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(5) \\ D=1100 \\ \text{Hence, we have the point (5,1100)} \end{gathered}[/tex]Plot the points to get the graph.
b) The slope is given by the rate of change, in this case, the range of change is 100 because this number depends on x. where x represents the number of hours.
c) If Jim is driving after 6 hours, then, we need to replace x = 6 on the distance equation.
Hence:
[tex]\begin{gathered} D=1600-100x \\ D=1600-100(6) \\ D=1000 \end{gathered}[/tex]Therefore, after 6 hours Jim is 1000km far away from home.
Jinkie's Jumpin' Junkfood's "Jammin' Jazzy Candy Bar normally sells for $15.Right now they are selling at o 40% discount. Oliver also has a coupon that allowshim to take 30% off the sale price at the register. How much does Oliver pay?
Answers
Solution:
Selling price = $15
At discount of 40%, Jinkie's Jumpin' Junkfood's sells for;
[tex]\begin{gathered} 15-(15\times0.4)=15-6 \\ 15-(15\times0.4)=9 \end{gathered}[/tex]But Oliver also has a coupon worth 30% discount off the same price at register;
[tex]\begin{gathered} 9-(9\times0.3)=9-2.7 \\ 9-(9\times0.3)=6.3 \end{gathered}[/tex]Thus, Oliver pays $6.3
Complementary events are:always, never, sometimes. Choose one that is exclusive
Answers
Answer;
Always
Explanation;
Firstly, we have to understand what it means for two events to be complementary
When two events are complementary mathematically, it means that for one to occur, the other must not occur.
An example of this is fact that it will rain at a moment, and it will not rain at that same moment in time. Only one of these two can occur at that particular point in time
Now, mutually exclusive events are events that are disjoint in happening. What this mean is that these two events cannot and will not happen at the same time
So, we can see that when two events are complementary, then they are mutually exclusive
So, the correct choice of answer here is that they are always mutually exclusive
Expand: (2f-1) to the second power
Answers
To expand the expression: (2f-1) to the second power
[tex]\begin{gathered} (2f-1)^2=(2f-1)(2f-1) \\ =2f(2f-1)-1(2f-1) \\ =4f^2-2f-2f+1 \\ =4f^2-4f+1 \end{gathered}[/tex]What is 4.01 - 2.95 =............. SHOW WORK
Answers
Given: An expression-
[tex]4.01-2.95[/tex]Required: To determine the solution to the expression.
Explanation: The subtraction steps are as follows-
Carrying a 1 from left to right as 1 can't be subtracted from 5. After carrying one, we have 11 minus 5, which gives 6.
But we cannot take 1 from zero, so we take one from 4 and it becomes ten but we have 1 in the previous step. So now we have 9 minus 9 which gives 0.
4.Jonathan deposite $8,000.00 cd accont that pays 2.4% interest compound quarterly. What is his balance after 9 months (3 quarters)
Answers
A = P(1 + r/n)^(nt)
P is the principal, in this case $8000
r is the iterest rate, in this case 2.4%, in decimal numbers, so 0.024
n is the number of cycles, 1 per quarter
t is the time, in this case 3 quarters
using the formula:
A = 8000(1 + 0.024/1)^((1) (3)) = 8000(1.024)^3
A = 8000 (1.07374) =8589.9345
So the answer is $8,589.93
Round 4265 to the nearest hundred
Answers
4300
Explanation:The given number is 4265
This can be written as:
4 thousand
2 hundred
6 tens
5 units
Therefore, since 6 is greater than 5, change 6 and 5 to zero and 1 to 2.
4265 rounded to the nearest hundred becomes 4300
what is p-21=34P -21 equals 34
Answers
The given expression is : p - 21 = 34
Smplify the equation for p :
p - 21 = 34
Add 21 on both side :
p - 21 + 21 = 34 + 21
p = 55
p = 55
Answer : p = 55
plete the following: Find the locus of points whose: - abscissa is one-half the square of the ordinate.
Answers
Let y be the ordinate and x be the abcissa.
One half the square of the ordinate is written algebraically as:
[tex]\frac{1}{2}y^2[/tex]Since the abcissa is one half the square of the ordinate, then:
[tex]x=\frac{1}{2}y^2[/tex]Which is the equation of a parabola.
Rhonda has an extra credit project to make a rectangular prism with the volume of at last 24 in? If the area of her base in which to the possible ogs, of her prism in order to meet her teacher's requirements? A Oh=4 в Ohев CO4 DOns 8
Answers
Let's begin by identifying key information given to us:
The volume of rectangular prism (at least) = 24 in^3
Area of the base = 6 in^2
The volume of a rectangular prism is given by:
[tex]\begin{gathered} V\le A\cdot h \\ V=24in^3 \\ A=6in^2 \\ \text{h=?} \\ 24\le6\cdot h \\ 24\le6h\Rightarrow6h\ge24 \\ 6h\ge24 \\ h\ge\frac{24}{6}=4 \\ h\ge4 \end{gathered}[/tex]To have a rectangular prism of at least 24 in^3, the height must be greater than or equal to 4
Therefore, A (h >= 4) is the correct answer
Which exponential equation is equivalent to this logarithmic equation?log_(x)5+log_(x)12=7A. 7^x=17B. 7^x=60C. x^7=60D. x^7=17
Answers
We are given the following equation:
[tex]\log _x5+\log _x12=7[/tex]we will use the following property of logarithms:
[tex]\log _ab+\log _ac=\log _a(bc)[/tex]Applying the property:
[tex]\log _x(5\times12)=7[/tex]Now we will use the following property:
[tex]\log _ab=c\rightarrow b=a^c[/tex]Applying the property:
[tex]5\times12=x^7[/tex]Solving the operation:
[tex]60=x^7[/tex]And thus we get the exponential equivalent of the equation.
HELP ME PLEASEEEEEEEEEEEEE
Answers
Answer:
A
Step-by-step explanation:
Lets treat this linear inequality as a linear equation first and simplify it and "solve" for x.
-3x+12 ≤ 15
Subtract 12 on both sides
-3x≤3
Now divide -3 on both sides. However, don't fall into the trap many fall into. When dividing or multiplying an inequality by a negative number, you must switch the sign direction.
x≥-1