Final Answer:
The equation of the image after a dilation with a scale factor of 4, centered at the origin, is y = 8x + 8.
Explanation:
When a function undergoes dilation centered at the origin, each coordinate (x, y) is transformed to (kx, ky), where k is the scale factor. In this case, the original equation y = 2x + 2 is dilated by a factor of 4. Therefore, the new equation becomes y' = 4(2x + 2), which simplifies to y' = 8x + 8. The scale factor of 4 multiplies both the coefficient of x and the y-intercept, resulting in a steeper slope and a vertical shift.
In the original equation, the coefficient of x was 2, indicating a slope of 2. After the dilation, the coefficient becomes 8, indicating a steeper slope of 8. Additionally, the y-intercept of 2 is multiplied by 4, yielding a new y-intercept of 8. This transformation preserves the line's direction while magnifying its steepness and shifting it vertically. The equation y' = 8x + 8 represents the dilated image of the original line.
To summarize, the process involves multiplying both the coefficient of x and the y-intercept by the scale factor. This scaling maintains the line's direction while adjusting its steepness and vertical position. The resulting equation, y' = 8x + 8, accurately describes the image of the original line after dilation by a factor of 4 centered at the origin.
A bottle holds 8.2 ounces of liquid soap. Jesse used 0.2 of the soap in the bottle to clean the kitchen floor. How many ounces of soap did she use ?
Answer:
1.64 oz
Step-by-step explanation:
0.2 of the soap is 0.2 of 8.2 ounces which is
0.2 * 8.2 ounces
0.2 * 8.2 oz = 1.64 oz
She used 1.64 oz
0.2 is equal to 20% you can figure that out by multiplying 8.2 x20 and then diving that by 100
8.2x20=164
164/100=1.64
the world future society Predicts that by the year 2020, airplanes will be able to carry 1400 passengers. Today's biggest jets can carry 600 passengers. What will be the percent of increase of airplane passengers?
There will be 133.33% increase of airplane passengers.
Step-by-step explanation:
Present value of passengers = 600
Expected value of passengers by 2020 = 1400
Increase = Expected value - present value
Increase = 1400 - 600 = 800
Increase percentage = [tex]\frac{increase}{present\ value}*100\\[/tex]
[tex]Increase\ percentage=\frac{800}{600}*100\\\\Increase\ percentage=\frac{80000}{600}\\Increase\ percentage=133.33\%[/tex]
There will be 133.33% increase of airplane passengers.
Keywords: percentage, division
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The percent of increase in airplane passengers from 600 to 1400 is 133%, calculated using the formula for percentage increase.
To calculate the percent of increase of airplane passengers from 600 to 1400, we need to use the formula for percentage increase, which is: Percentage Increase = ((New Number - Original Number) / Original Number) imes 100%.
Following the formula:
Subtract the original number of passengers (600) from the new number (1400) to get the increase in passengers: 1400 - 600 = 800.Divide the increase (800) by the original number (600): 800 / 600 = 1.33 (or 133%).Multiply by 100 to get the percent in percentage form, which gives us the percent of increase: 133 imes 100% = 133%.Therefore, the percent of increase in airplane passengers from 600 to 1400 is 133%.
please help on this tysm ❤❤❤In the box, type in the number that will correctly complete the sentence.
Jane has a debt of $63. She owes equal amounts to seven different people. Her debt to each person can be expressed as Answer
dollars.
Answer:
9
Step-by-step explanation:
the answer is 9 because 7 goes into 63 evenly 9 times
Answer: $9
Step-by-step explanation:
$63 for 7 people
63 ÷ 7 = 9
So that means that one person gets $9
ALOT OF POINTS MUST EXPLAIN THE ANSWER IN WORDS
8. If 6x2 = 54, then x = ?
(1) 29.0 (2) 3.0 (3) 14.5
Answer:
3, -3
Step-by-step explanation:
6x^2=54
x^2=54/6
x^2=9
x=sqrt(9)
x=3, -3
Solve the problem.
If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be paid for the loan?
Answer:
Interest =$7540
Step-by-step explanation:
p=$13000
r=5.8%
t=10yrs
i=p*r*t/100
=13000*5.8*10/1000
=130*58
= $7540
Twice a number is added to the number and the answer is 78. Find the number.
Answer:
The number which satisfy the given statement is 26 .
Step-by-step explanation:
Given as :
Twice a number is added to the number and the resultant is 78
Let The number is x
Now, According to statement
Two times x + x = 78
Or, 2 × x + x = 78
Or, 3 x = 78
So , x= [tex]\frac{78}{3}[/tex]
∴ x = 26
I.e The number is 26
Hence The number which satisfy the given statement is 26 . Answer
show the decimal -3.4 on a number line. use trick marks to show the exact location between the two appropriate whole numbers.
Answer:
Step-by-step explanation:
Just draw a number line and label three numbers, -4, -3.4 & -3. Mark -3.4 in the number line.
Your friend was trying to complete this problem: There is a sale at the store and you have $50 to spend. Jeans cost $12 and shirts cost $8 If you buy 2 pairs of jeans and 3 shirts, will they have any money left over? if so how much? Their answer: No they will not have any money left because 2 pairs of jeans would cost $26 and 3 shirts would cost $24 and 26+24=50 so they would spend exactly the right amount. EXPLAIN their mistake! What did they do wrong? What should their answer have been?
Answer:
$48
Step-by-step explanation:
A pair of jeans= $12
Two pair of jeans= $12*2= $24
A shirt= $8
3 shirts= $8*3= $24
So it would be $24+$24= $48.
They made their mistake when calculating the cost of the jeans by getting $26 instead of $24.
Rewrite a. an = 19 - 7(n-1)
Solution for an=19-7(n-1) equation:
Simplifying
an = 19 + -7(n + -1)
Reorder the terms:
an = 19 + -7(-1 + n)
an = 19 + (-1 * -7 + n * -7)
an = 19 + (7 + -7n)
Combine like terms: 19 + 7 = 26
an = 26 + -7n
Solving
an = 26 + -7n
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Divide each side by 'n'.
a = 26n-1 + -7
Simplifying
a = 26n-1 + -7
Reorder the terms:
a = -7 + 26n-1
The sum of two numbers is 17 and their difference is 3 what are the two numbers
Answer:
10 and 7
Step-by-step explanation:
10 + 7 = 17
10 - 7 = 3
Answer:
your answer is 10 and 7.
Step-by-step explanation:
because if you add 10 and 7 you get 17. them if you subtract them the answer is 3.
2. Compare CH3Cl and CCl4. Explain why one is polar and one is nonpolar. Be sure to use
the term symmetry in your explanation.
Answer:
Step-by-step explanation:
CH3Cl is polar while CCl4 is non polar.
When we consider whether something is polar or not we have to consider the following:
-Molecular symmetry
-Polar bonds (based on Electronegativity)
-Whether or not all the bonds are equal in magnitude
So for CCl4:
-All of the bonds are equal, in that all the electronegativity differences (delta EN) are the same.
-There are polar bonds as the delta EN between Cl (EN = 3.0) and C (EN=2.5) is 0.5 which means the bond is polar covalent
But when we look at the symmetry of the molecule (by drawing the lewis structure) there are no lone pairs, meaning that the molecule is symmetrical and therefore, it is non polar.
For CH3Cl:
-There are polar bonds here whether between C-H or C-Cl like above, both delta EN are greater than or equal to 0.5
-But, all of the bonds are not equal in strength. Cl (3.0) atoms have much higher electronegativity values than H (2.1) and there for they will "pull" the electrons closer and polarize the molecule. Therefore, the differences in bonds causes this molecule to be asymmetrical, and hence polar.
CH3Cl is polar due to an uneven electron distribution and net dipole moment, due to the different atoms attached. In contrast, CCl4 is nonpolar because it's symmetrical with the dipole moments cancelling out.
Explanation:The compounds CH3Cl and CCl4 vary in their polarities due to their molecular geometry, leading to different symmetries. CH3Cl has a tetrahedral shape but is polar because of the presence of the electronegative Chlorine atom and three Hydrogen atoms, creating an uneven distribution of electrons and thereby, a net dipole moment. On the other hand, CCl4 is also tetrahedral, but it's nonpolar due to its symmetry. As it has four Chlorine atoms evenly distributed around the Carbon atom, the dipole moments cancel out each other leading to no net dipole moment.
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14+14p=21 solve for p
Answer: 0.5
Step-by-step explanation: In this problem, we're asked to solve the following equation for p. Let's first switch 14 and 14p around so we have 14p + 14 = 21.
To solve this equation for p, we must first isolate the term containing p which in this case is 14p.
Since 14 is being added to 14p, we need to subtract 14 from both sides of the equation.
14p + 14 = 21
-14 -14
On the left side of the equation, the positive 14 and negative 14 cancel each other out and we have 14p. On the right side of the equation, we hav 21 - 14 which gives us 7.
Now we have the equation 14p = 7.
Since p is being multiplied by 14, to get p by itself, we divide both sides of the equation by 14.
On the left side of the equation the 14's cancel and we are left with p. On the right side of the equation, 7 divided by 14 is 0.5 which is our answer.
Therefore, p = 0.5 which is the solution for our equation.
Remember, you can always check your solution by substituting a number in for a variable to make sure the equation is true.
Answer:
A. 1/2
Step-by-step explanation:
Took test got right on edge 2021
Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours. How long will it take them to finish the job together? It is not 3.333 hours
They both will finish the work in 3.07 hours
Step-by-step explanation:
Time taken by Rachel = 5 hours
Work done by Rachel in one hour = 1/5
Time taken by Carl = 8 hours
Work done by Carl in one hour = 1/8
Let x hours be the time taken by both to do work
Then 1/x will be the work done by both in one hour
So,
[tex]\frac{1}{5} + \frac{1}{8} = \frac{1}{x}[/tex]
Taking LCM
[tex]\frac{8+5}{40} = \frac{1}{x}\\\frac{13}{40} = \frac{1}{x}\\13x = 40\\x = \frac{40}{13}\\x = 3.07\ hours[/tex]
They both will finish the work in 3.07 hours
Keywords: Linear Equation
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Answer:
12 hrs
Step-by-step explanation:
X/30+x/48=1
common denominator
x/1440+x/1440
2x/1440=1
2x=1440
x=720
when you convert to hrs you get 12
Gail bought 5 pounds of oranges ans 2 pounds of bananas for $14. Her husband later bought 3 pounds of oranges ans 6 pounds of bananas for $18. What was the cost per pounds of the oranges and the bananas?
Answer:
Step-by-step explanation:
5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)
3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)
Let's use the elimination method. Multiply the first equation by -3:
-15r - 6b = -42
3r + 6b = 18
-----------------
12r = 24
Divide by 12:
r = 2
Answer:
The price per pound of the oranges is $ 2.
The price per pound of the bananas is $ 2.
Step-by-step explanation:
A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.
In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):
x: price per pounds of the orange y: price per pounds of the bananaThe price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)
The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)
Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:
[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]
One of the ways to solve a system of equations is through the substitution method. This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".
In this case, x is isolated from the first equation, obtaining:
5*x+2*y=14
5*x=14-2*y
[tex]x=\frac{14-2*y}{5}[/tex]
[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)
Replacing this equation (C) in the other equation you get:
[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]
Isolating the value of "y" you get:
[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]
[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]
[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]
[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]
[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]
[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]
y=2
Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.
Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:
[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]
[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]
[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]
x=2
Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.
9. Find the distance between the point P(-12,-2)
and Q(3,6).
Hint: a sketch is useful.
Answer:
Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
Step-by-step explanation:
Given points:
[tex]P(-12,-2)[/tex]
[tex]Q(3,6)[/tex]
To determine the distance between points P and Q.
Steps to be carried out:
1) Plot the points P and Q on graph.
2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]
3) Join PQ thus forming a right triangle POQ.
4) We can find the distance of sides OP and OQ by counting the units between the points.
OP=[tex]|-12-3|=|-15|=15\ units[/tex]
OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]
4)Now, we can apply Pythagorean theorem for triangle POQ.
[tex]PQ^2=OP^2+OQ^2[/tex] [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]
[tex]PQ^2=15^2+8^2[/tex]
[tex]PQ^2=225+64[/tex]
[tex]PQ^2=289[/tex]
Taking square root both sides:
[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]
[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.
∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
3/10 of an inch is equal to 7/8 of a mile. convert to unit rate and find how many inches are in 1 mile
Answer:
12/35 inches are in 1 mile.
Step-by-step explanation:
(3/10)/(7/8)=(3/10)(8/7)=24/70=12/35
1 mile=8/8
(8/8)(12/35)=1(12/35)=12/35
After a big snow storm, Joe and Jim decided to shovel driveways for money. Jim shoveled 3 less than twice as many driveways as Joe. They shoveled a total of 15 driveways. How many driveways did Joe (x) and
Jim (y) each shovel?
Answer:
Joe shoveled 6, Jill shoveled 9
Step-by-step explanation:
Answer:
Joe: 6
Jim: 9
Step-by-step explanation:
Joe: x
Jim: 2x - 3
x + 2x - 3 = 15
3x - 3 = 15
3x = 18
x = 6
- 5 = 1/(x + 12)
Solve the equation for y
Answer:
x=-61/5
Step-by-step explanation:
-5=1/(x+12)
x+12=-1/5
x=-1/5-12
x=-1/5-60/5
x=-61/5
Question 2 of 20 :
Select the best answer for the question.
2. Simplify (3a4 - 2a2 + 5a - 10) - (2a4 +
4a2 + 5a - 2).
O A. a4 – 6a² – 8
O B. a4 + 4a? + 10a - 12
O C. 5a4 + 4a3 + 3a? + 10a - 12
O D. a4 + 2a? + 10a - 12
Answer:
A
Step-by-step explanation:
(3a^4-2a^2+5a-10)-(2a^4+4a^2+5a-2)
a^4-6a^2-8
Given that point S is equidistant from the sides of triangle WXY, find the following measures.
SU - 5, 12, 13, or 18
M
m
Answer:
Step-by-step explanation:
5, 39, 24 just finished it
Answer:
[tex]SU=5\\\angle WXY = 24\°\\\angle SYW = 39 \°[/tex]
Step-by-step explanation:
According to the graph,
[tex]\angle WXT \cong \angle YXT[/tex]
So, [tex]m\angle YXT =12 \°[/tex]
By sum of angles we have
[tex]\angle WXY = \angle WXT + \angle YXT\\\angle WXY = 12 \° + 12\° = 24 \°\\\therefore \angle WXY 24\°[/tex]
By given, we know that
[tex]\angle UYS \cong \angle SYW\\\therefore \angle SYW = 39 \°[/tex]
By given, we know that side SU is a leg of the right triangle SUX, where the hypotenuse is 13 units, and the opposite angle is 12°. However, if you look closer, you would find that side ST is 5 units, and by GIven we know that ST = SU.
Therefore, SU = 5.
What is the value of the expression below? (6¼) x (6¼) x (6¼) x (6¼)
Answer:
6
Step-by-step explanation:
The expression [tex]6^{\frac{1}{4}}\times 6^{\frac{1}{4}}\times6^{\frac{1}{4}}\times6^{\frac{1}{4}}[/tex] can be simplified by applying power properties.Particulary, there is a property known as "power of a product property" that states that, when there is a product of a series of numbers that share the same base "a", [tex]a^n\times{a^m}\times{a^j}[/tex], the result of the multiplications is [tex]a^{m+n+j}[/tex].Then,in this particular case [tex]6^{\frac{1}{4}}\times 6^{\frac{1}{4}}\times6^{\frac{1}{4}}\times6^{\frac{1}{4}}[/tex] equals [tex]6^{\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} }=6^1=6[/tex]12k + 5k − 11m + 13m
To simplify the expression 12k + 5k - 11m + 13m, we can combine like terms by adding the coefficients of the like terms. The simplified expression is 17k + 2m.
Explanation:The expression 12k + 5k - 11m + 13m can be simplified by combining like terms. Like terms have the same variables raised to the same powers. In this expression, the terms 12k and 5k are like terms because they both have the variable k. Similarly, the terms -11m and 13m are like terms because they both have the variable m.
To simplify, we can add the coefficients of the like terms:
12k + 5k - 11m + 13m = (12 + 5)k + (-11 + 13)m
Therefore, the simplified expression is 17k + 2m.
Segment endpoints: (0,0) and (0,20) midpoint
Answer:
is is 20
Step-by-step explanation:
Factoring a Linear Binomial
Please include steps:
28 + 8v
Answer:
4(7 + 2v).
Step-by-step explanation:
The greatest common factor of 28 and 8v is 4 so we take 4 out:
28 + 8v
= 4(7 + 2v).
50 POINTS IF YOU ANSWER THIS QUESITON CORRECTLY. AND YOU CAN GET BRAINLIST IF YOU ANSWER QUESTION WITH EXPLANATION. :] 3. You purchase a car using a $25,000 loan with a 5% simple interest rate. (a) Suppose you pay the loan off after 4 years. How much interest do you pay on your loan? Show your work. (b) Suppose you pay the loan off after 2 years. How much interest do you save by paying the loan off sooner? Show your work.
Answer:
a) $25,261
b) $25,156
Step-by-step explanation:
I'm sorry but I don't know how to show my work because I just searched up "Car Loan Calulator" :|
So don't put me up for Brainlist
Review the image and two-column proof below. Which of the following represents a valid reason for statement #2? opposite angles of a parallelogram are equal opposite sides of a parallelogram are equal all three faces are congruent both bases of the prism are congruent
A valid reason is :opposite sides of a parallelogram are equal
Step-by-step explanation:
It is possible to notice that RUTS is a parallelogram where RU=TS and RS = UT.
When you introduce a diagonal RT you form triangles RUT and TSR.
∠URT = ∠STR ----alternate angles
∠UTR=∠SRT------alternate angles
RU║ST and RS║UT
RT=TR -----Common
ΔRUT ≡ ΔTSR by AAS theorem
hence RS=UT matching sides of congruent triangles
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Answer:
opposite sides of a parallelogram are equal
Step-by-step explanation:
got it right on odyssey
est
Complete the solution of the equation. Find the
value of y when x equals 0.
-7x + 3y = 30
Enter the correct answer
Answer:
[tex]y=10[/tex]
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
we have
[tex]-7x+3y=30[/tex]
so
For x=0
substitute the value of x in the linear equation and solve for y
[tex]-7(0)+3y=30[/tex]
[tex]3y=30[/tex]
Divide by 3 both sides
[tex]y=10[/tex]
Super easy word problem please help with question :(
Answer:
1. The required slope m, for the context is[tex]m = 1.08[/tex]
2. The y-intercept in the context is [tex]a = y = 1052[/tex]
3. The graph is on Desmos.
Step-by-step explanation:
Given:
[tex]a = 1.08\times t + 1052[/tex]
Where,
a is the speed of sound wave.
t is the air temperature.
This is a linear model type equation.
Can be represented in the slope intercept form which is equal to
[tex]y = mx + c[/tex]
Where,
m = Slope of the line.
c = y-intercept.
Now if we compare the given model by slope intercept formula we get
[tex]m = 1.08\\\\c = 1052[/tex]
So ,the slope in the context of the problem is [tex]m = 1.08[/tex].
and the y intercept in the context of the problem [tex]a = c = y = 1052[/tex]
For Sketching the graph we require two point
put t = 0
∴ a = 1052
Let A (1052, 0) be one point.
put a = 0
∴ t = -974.07
Let B (0, -974.07) another point.
So, the x intercept of the linear model is [tex]t = x = -974.07[/tex]
Here in the graph
X axis represent temperature in degree, Fahrenheit.(t)
Y axis represent Speed of sound wave in feet per second.(a)
Scale on both axes:
1 cm = 100 feet per second on y-axis
1 cm = 100 degree Fahrenheit on x-axis
solve for x
x- 2x (12 - 1/2) =2 (4-2x) +20
A.-14/9
B.-9/14
C.14/9
D.9/14
Answer:
A
Step-by-step explanation:
-22x=-4x+28
-18x=28
x=-28/18=-14/9