The image of (-6, -2) after dilation by a scale of 4 is (-24, -8)
Explanation:The image of (-6, -2) after dilation by a scale of 4 is
(-6*4, -2*4)
= (-24, -8)
When simplified, what is the value if i2 = −1?
Solution:
Given:
[tex]\begin{gathered} \sqrt[]{-128} \\ \\ \text{also,} \\ i^2=-1 \end{gathered}[/tex]To simplify, we break the radical down into bits.
[tex]\begin{gathered} \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{128} \\ To\text{ simplify }\sqrt[]{128}\text{ , we split it into a number that is a p}\operatorname{erf}ect\text{ square and another number,} \\ \text{Hence,} \\ \sqrt[]{128}=\sqrt[]{64\times2}=\sqrt[]{64}\times\sqrt[]{2} \\ \text{This means,} \\ \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{64}\times\sqrt[]{2} \\ \text{But recall that;} \\ i^2=-1 \\ \text{Taking the square root of both sides,} \\ i=\sqrt[]{-1} \\ \text{Substituting it in the expression below,} \\ \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{64}\times\sqrt[]{2} \\ \sqrt[]{-128}=i\times8\times\sqrt[]{2} \\ \sqrt[]{-128}=8i\sqrt[]{2} \end{gathered}[/tex]Therefore, the simplified form is;
[tex]8i\sqrt[]{2}[/tex]Perform the following operationand express the answer inscientific notation.5.7365x10-5 = 3.4891x10-8[ ? ]x10?)Coefficient (green)Exponent (yellow)Enter
Both numerator and denominator have 5 significant figures, then the quotient will have 5 significant figures too.
a car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km write an equation for the cost y birr in terms of the distance X driven , if the car is leased for 5 days.
The equation for the cost y birr in terms of the distance X driven is y = 20 + 2x.
When the car is leased for 5 days, the cost is 100 + 2x.
How to calculate the value?From the information, the car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km.
The equation for the distance x will be:
= 20 + (2 × x)
= 20 + 2x.
When the car is leased for 5 days, this will be:
= 5(20) + 2x.
= 100 + 2x
= 100 + 2x
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If a number is raised to a power of 2, it is A. CubbedB. Powered C. Squared
If we raise a number to a power of 2, we can represent the result graphically as shown below (where n is the number to be raised to a power of 2)
This is a square of side equal to n.
Therefore, the answer is option C, squared.
Translate the figure 1 unit right and 4 units up.Draw a vector from the origin 1 unit right and 4 units up.I need help pls
We want to translate the figure 1 unit right and 4 units up. This means we are going to add +1 to each x cordinate and +4 to each y cordinate.
To do this, the coordinates of the figure will change as follows:
(-9, -4) = (-9 + 1, -4 + 4) = (-8, 0) (starting point)
(-6, -9) = (-6 + 1, -9 + 4) = (-5, -5)
(-5, -5) = (-5 + 1, -5 + 4) = (-4, -1)
(-1, -5) = (-1 + 1, -5 + 4) = (0, -1)
(-2, -1) = (-2 + 1, -1 + 4) = (-1, 3)
(-9, -4) = (-9 + 1, -4 + 4) = (-8, 0) (ending point)
Now, we have to plot these new cordinates:
The figure has been translated
ok Find the distance from M to N on the coordinate plane if M(-5,8) and N(9,-2).
The above formula is used to find the distance betweent two points on the coordinate plane
let x1 = -5
let y1 = 8
let x2 = 9
let y2 = -2
inputing the following values in the above equation
[tex]\sqrt[]{(-5-9)^2+(8-(-2)^2}[/tex][tex]\sqrt[]{(-14)^2+(8+2)^2}[/tex][tex]\sqrt[]{(-14)^2+10^2}[/tex][tex]D=\sqrt[]{196\text{ + 100}}\text{ }[/tex][tex]\sqrt[]{296}[/tex][tex]undefined[/tex]What is the equation of the line of best fit for the following data? Round theslope and y-intercept of the line to three decimal places.ху2258.7.109111113
Answer:
Explanation:
The equation o
Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
With the first term being 28 and the difference being 2, this geometric progression is finite because 28 is divided by 14 and then that number is divided by 2 and so on.
What is geometric progression?
A mathematical sequence known as a geometric progression (GP) is one in which each succeeding term is generated by multiplying each preceding term by a fixed number, or "common ratio." This progression is also referred to as a pattern-following geometric sequence of numbers. A geometric progression is a series in which each term can be obtained by multiplying or dividing the term before it by a predetermined amount. Infinite GP sum refers to the total number of terms in an infinite GP. S_ = a/(1 - r), where an is the first term and r is the common ratio, is the formula for calculating the sum of an infinite geometric progression.
Here,
This is geometric progression with first term 28 and difference 2 and this is finite GP as 28 is divided by 14 then 14 is divided by 2 so on as the definition of GP says, "a series of numbers with a fixed ratio between each and the previous one (e.g., each subsequent number is increased by a factor of 3 in the progression 1, 3, 9, 27, 81 )".
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PLEASE HELP ME ASAP!!!! I NEED YOU!
2. Consider the linear expression.
3.2a - 1 - 4 1/3 + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please answer question in this format:
(expression)
= (next step)
= (next step)
= (next step)
= (answer)
1) 3.2a , a and 1 , 4 1/3 , 7 are the like terms in the expression.
2) 2.2a + 1.66 is the simplified linear expression
What is linear expression ?The greatest power of a variable in a linear equation is always equal to 1. A one-degree equation is another name for it. A linear equation with one variable is typically expressed as Ax + B = 0. Here, the variables x and A and B are constants and coefficients, respectively.
Calculation1 ) Merger of similar items 3.2a , a
and 1 , 4 1/3 , 7
2 ) 3.2 a -1 - 4 1/3 + 7 -a
= 3.2a - a - 1 - 4 1/3 + 7
= 2.2a + 6 - 13/3
= 2.2a + 6 - 4.34
= 2.2a + 1.66
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use the distributive property to evaluate the expression (3+6)(-8)
We have the following:
The distributive property of multiplication over addition can be used when multiplying a number by a sum.
[tex]\begin{gathered} \mleft(3+6\mright)\mleft(-8\mright)=9\cdot-8 \\ -72=-72 \end{gathered}[/tex]549 vehicles in 9 acres. How many in 1 acre?
We have that there are 549 vehicles in 9 acres, we want to know how many are in 1 acre. We see that those quantities are proportional and therefore:
[tex]v=\frac{549\cdot1}{9}\Rightarrow v=61[/tex]We will have that there are 61 vehicles in 1 acre.
what is the slope formula (-12,-2) and (18,4) ?
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In thie case we have:
[tex]\begin{gathered} m=\frac{4-(-2)}{18-(-12)} \\ =\frac{4+2}{18+12} \\ =\frac{6}{30} \\ =\frac{1}{5} \end{gathered}[/tex]therefore the slope between this points is 1/5.
What would the Outputs be when the Inputs are 1,7,-3, and -5 if the function is Y=x
The function is:
[tex]y=x[/tex]This means that the output of the function is equal to the input. So when the inputs are 1,7,-3 and -5. The outputs will also be 1, 7, -3 and -5.
Which of the following equations describes the graph? (options included)
So,
Given a quadratic equation of the form:
[tex]y=ax^2+bx+c[/tex]There's some important facts we could use to determine which options are not correct.
First fact: the y - intercept of the graph is the number c. So, if our graph intercepts at y=1, that means that c=1.
For that reason, option A is not correct, because c=1.
Second fact: the sign of the number "a", will determine the concavity of the graph. This is, in other words:
That means that if "a" is positive, the graph will has the form of the left, and if "a" is negative, it will take the form of the right side.
Based in this, we can see that our graph has the form of the left side, so "a" has to be positive.
For that reason, options A and C are incorrect.
Now we should pick between B or D.
The third fact, is that, when the sign of "b" is negative, our graph seems to be moved to the right.
When the sign of b is positive, the graph seems to be moved to the left.
As you can see, our graph seems to be moved to the right, so the sign of b should be negative.
For these reasons, the appropiate answer is D.
[tex]y=\frac{1}{2}x^2-2x+1[/tex]
Need help with relationship between measures of two given angles
Note that in the picture we are asked about the angles QRW and RWQ. This two angles are part of the the same triangle. So we can ignore the rest of the image and focus only on the triangle that contains both. We have the following
Using this information, we can see that the measure of the three sides of the triangle are different. This means that the triangle is a scalene triangle. This type of triangles have the property that the measure of each angle is different from the other. So, we know that the measure of angles QRW and RWQ are different.
To dig deeper in the problem, we will use the sines law for triangle, which states the following. If we have a triangle of the form
Then, we have the following
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]In this case, we have c=45 and a=47, so we have
[tex]\frac{\sin A}{47}=\frac{\sin C}{45}[/tex]where A is the angle RWQ and C is the angle QRW, if we multiply both sides by 45, we get
[tex]\sin C=\frac{45}{47}\cdot\sin A[/tex]In this case, we have that 45/47 < 1. Since angles A and C are less than 180° degrees, the sine of this angles is a positive number, so we have that
[tex]\sin C=\frac{45}{47}\cdot\sin A<\sin A[/tex]Note also that angles A and C should have a measure less than 90°. Over this interval, the sine function is an increasing function, which means that if sin(C)So we have that the measure of angle QRW is less than the measure of angle RWQ.
True or False. Given the following vectors:a=(3,4,-2)b=(2,-7,1)c=(-6,5,4)The value of a +cxb is (36,18,30)
Answers
False
Explanation
Given vectors:
a = (3, 4, -2)
b = (2, -7 ,1)
c = (-6, 5, 4)
What to find:
The value of a + c x b
Step-by-step solution:
c x b = (-6, 5, 4) x (2, -7, 1)
c x b = (-12, -35, 4)
a = (3, 4, -2)
Therefore, a + c x b = (3, 4, -2) + (-12, -35, 4)
a + c x b = (-9, -32, 2)
Thus, (-9, -32, 2) ≠ (36, 18, 30)
Hence the answer is False
He cosed that the system has an esse number of solutions. Which is the BEST evaluation of Alfred's conclusion
At for any positive value of the corresponding value of is negative, which means the system has no solution
08 Nescored both equations describe lines that have infinitely many solutions
00 scored if the st equation is moped by a and added to the second equation, the result is 136, which leads to exactly one solution
00 escorect if the fest equation is multiplied by 4 and subtracted from the second equation, the result is 3a8y--14, which means the
system has an inte number of solutions SO HELP
Answer: 08
Step-by-step explanation:
For the experiment, determine the two given events are independent. The answers are guessed on a twenty-question multiple-choice test. The events are "the first question is correct" and "the second answer is correct". Are the two events independent or not independent?
Two events are independent when one of the events happen and the result does not affect on the result for the second event.
In this case if we have multiple-choice answers on the test the probability of having the correct answer for both of them is the same, however if we get the first one correct it does not mean that we will have the second answer correct.
For this reason the events are independent.
Super Yoga Program has two plans, basic plan and trial plan. In basic plan, you will pay $20 per month as a membership fee and $8 per each session. In trial plan, you pay $12 per each session.a. If you go to Yoga sessions 4 times in a month, which plan is better for you? Explain.b. If you go to Yoga sessions 8 times in a month, which plan is better for you? Explain.c. If you go to Yoga sessions n times in a month, express the total cost of basic plan as an expression.d. If you go to Yoga sessions n times in a month, express the total cost of trial plan as an expression.
ANSWER:
a. trial plan
b. basic plan
c. 20 + 8n
d. 12n
STEP-BY-STEP EXPLANATION:
a.
We calculate the price in each case, like this:
[tex]\begin{gathered} p_b=20+8\cdot4=52 \\ p_t=12\cdot4=48 \end{gathered}[/tex]Therefore, if you go 4 times a month, the trial plan is better.
b.
We calculate the price in each case, like this:
[tex]\begin{gathered} p_b=20+8\cdot8=84 \\ p_t=12\cdot8=96 \end{gathered}[/tex]Therefore, if you go 8 times a month, the basic plan is better.
c.
Let n be the number of times you go per month, the cost expression of basic plan would be:
[tex]p_b=20+8n[/tex]d.
Let n be the number of times you go per month, the cost expression of the trial plan would be:
[tex]p_t=12n[/tex]May you solve the system of linear equations by graphingm?
We shall begin by plotting the graph of the equations given which are;
[tex]\begin{gathered} y=\frac{1}{3}x+6 \\ y=-\frac{2}{3}x+3 \end{gathered}[/tex]The black line shows the graph of y = [1/3]x + 6
The red line shows the graph of y = [-2/3]x + 3
The solution to these system of equations is at the point (-3, 5)
which of the following numbers is a power of 10 options 1010 500 1000 or 20
Answer
Answer = 1000
Explanation
A power of 10 would be a number that can result from multiplying 10 by itself a number of times.
And from the options, we can see that only
1000 = 10 × 10 × 10
Hope this Helps!!!
Carter plays 5/8 of a basket ball game. The basket ball game is 40 minutes long. Which if the following shows how to find the number of minutes carter plays?how do we do it?
Answer:
C.
Explanation:
The number of minutes played by Carter is given below:
[tex]\begin{gathered} \text{Multiply the fraction of time Carter played by the total time of a basketball game:} \\ =\frac{5}{8}\times40 \\ =\frac{5\times40}{8} \\ =25 \end{gathered}[/tex]Hence, C is the correct option
Jane is a software saleswoman. Her base salary is $1500, and she makes an additional $110 for every copy of English isFun she sells.Let P represent her total pay (in dollars), and let N represent the number of copies of English is Fun she sells. Write anequation relating P to N. Then use this equation to find her total pay if she sells 29 copies of English is Fun.
You know that "P" represents her total pay (in dollars) and "N" represents the number of copies of English is Fun Jane sales.
According to the information given in the exercise, Jane makes $110 for every copy of English is Fun, then you can set up the following expression for this:
[tex](110)(N)=110N[/tex]Knowing that her base salary is $1500, you can conclude that her total pay "P" will be the sum of her base salary and the amount of money she makes for every copy she sells. Based on this, you can write the following equation relateion "P" to "N":
[tex]P=1500+110N[/tex]If Jane sales 29 copies of English is Fun, then:
[tex]N=29[/tex]Substituting this value into the equation and evaluating, you get:
[tex]\begin{gathered} P=1500+(110)(29) \\ P=1500+3190 \\ P=4690 \end{gathered}[/tex]The answers
- Equation:
[tex]P=1500+110N[/tex]- Solution:
[tex]P=4690[/tex]Her total pay if she sells 29 copies of English is Fun, is $4690
The aquarium has 6 fewer yellow fish than green fish. 40% of the fish are yellow. How many green fish are in the aquarium? Show your work.
The total number of green fish are in the aquarium is 18.
What is called the linear equation?A linear equation is just an algebraic equation of the form y=mx+b, where the slope is m and b is the y-intercept, and just a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."T = Total fishes in aquarium.
G = Green fishes
Y = Yellow fishes
Thus, the linear equation for all fishes are-
T = G + Y ...eq 1
The aquarium has 6 fewer yellow fish than green fish.
G = Y+6 Put in eq 1
T = (Y+6) + Y
T = 2Y+6
40% of the fish are yellow = 0.4.
Y = 0.4×T
T = 2×(0.4×T) + 6
Solve for total fishes
T = 0.8T + 6
0.2T = 6
T = 30
Solve for Green fishes.
G = 0.6×T (given)
G = 18
Thus, the number of green fish are in the aquarium is 18.
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i have the first answer but keep getting the second one wrong please help!!
Kenyan = k
$3.50 per pound
Sri Lankan = s
$5.60 per pound
6lbs of blend
$28.35
s+k = 6
3.50k + 5.60s = 28.35
where:
k = lbs of kenyan
s = lbs of Sri Lankan
Solve the system
s+k = 6
3.50k + 5.60s = 28.35
solve the first equation for s:
s = 6-k
Replace in the second equation:
3.50k + 5.60 (6-k) = 28.35
3.50k + 5.60(6)+ 5.60(-k) = 28.35
3.50k + 33.6 - 5.60k = 28.35
3.50k - 5.60k = 28.35-33.6
-2.1k= -5.25
k= -5.25/-2.1
k= 2.5 lbs
Replace k on any equation and solve for s
s+k= 6
s+ 2.5 = 6
s= 6-2.5
s= 3.5 lbs
I am having a little bit of trouble on this (help)
Answer:
D
Step-by-step explanation:
We should use ratio.
AB is 5
DE is 10
AB/DE = 1/2
BC is 12 and EF is 24
BC/EF=1/2
AC is 13 and DF is 26
AC/DF= 1/2
So we can write the equation like D choice.
Write the slope-intercept form of the equation of the line described. 11.) through: ( 1 , 2 ) , perpendicular to Y= -1/5x +2
We would like to find the equation of the line that passes through the point (1.2) and is perpendicular to the line y=-1/5 x +2, and write in slope intercept form. To do this first we have to remeber that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]and that to find it we need a point and the slope. In this case we have the point but we don't know the slope yet. To find the slope we notice that the line has to be perpendicular to the line y=-1/5 x +2. We need to remember that two lines are perpendicular if and only if
[tex]m_1m_2=-1[/tex]where m1 and m2 are the slopes of the lines.
The line y=-1/5 x +2 is wirtten in the slope-intercept form:
[tex]y=mx+b[/tex]from this we notice that its slope is -1/5, then using the relation for perpendicular lines we have that
[tex](-\frac{1}{5})(m)=-1[/tex]Solving for m we have that
[tex]\begin{gathered} m=\frac{-1}{-1}(5) \\ =5 \end{gathered}[/tex]So, our line passes through the point (1,2) and has an slope equal to 5. Plugging this values on the equation for a line we have
[tex]\begin{gathered} y-2=5(x-1) \\ y-2=5x-5 \\ y=5x-5+2 \\ y=5x-3 \end{gathered}[/tex]so the equation of the line we were looking for is y=5x-3. (Notice that it is already written in the adequate form).
Name an angle supplementary to
Supplementary angles are angles that add up to 180 degrees.
To find the supplementary angle to ∠EOD, we find the angle with ∠EOD that makes up a straight line.
Looking at the figure, EC is a straight line and both ∠EOD and ∠DOC fall on this line. These two angles make up 180 degrees.
Thus,
The one supplementary angle to ∠EOD is ∠DOC.
AnswerBWrite an equivalent expression for each expression without drawing a diagram: a) (x + 2)(x+6) b.) (x + 5)(2x + 10)
7. What equation is represented by this illustration?OOOOOOOOO A 2x + 4 = 8x +1OB. 42 - 2 = 2 - 8O 0.42 +2 = 8O D.4.2 + 2 = 2 +8
We have 4 x's and 2 "units" in the left side. We know that this is equal or equivalent to one X and 8 units, pictured in the right side.
So we can write the left side as: 4x+2
And the rigth side as: x+8
As both sides are equal, we can write:
[tex]4x+2=x+8[/tex]The answer is Option D: 4x+2=x+8