Answers
The image of the point P(x, y) = (4, 2) by means of a translation formula is point P'(x, y) = (- 1, 4).
What is the image of a given point after making a translation?
In this question we find the coordinates of a point set on Cartesian plane which is modified by using a translation, a kind of rigid transformation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that P(x, y) = (- 9, - 3) and P'(x, y) = (- 14, - 1), then the translation vector is:
T(x, y) = P'(x, y) - P(x, y)
T(x, y) = (- 14, - 1) - (- 9, - 3)
T(x, y) = (- 5, 2)
Then, the image of the point (4, 2) is:
P'(x, y) = (4, 2) + (- 5, 2)
P'(x, y) = (- 1, 4)
The image of the point (4, 2) by using a translation formula is (- 1, 4).
To learn more on translations: https://brainly.com/question/12463306
#SPJ1
Related Questions
After 5 years, Amanda's account earned $1500 in interest. If the interest rate (in decimal form) is 0.1, how much did Amanda initially
invest?
Answers
Amanda's starting capitalization is $3000.
Simple interest: What is it?Simple interest tells us how much interest will be charged on a loan.
Simple Interest = Principal x Interest Rate x Time" is the written formula.
Principal, rate of interest, and period make up the basic interest formula.
Rate (in decimal) Equals 0.1, as stated.
5 years is time.
$5000 with simple interest
As a result, 1500 = p (0.1). (5)
1500/0.5 equals the principal value
Principal is 3000.
Consequently, the first outlay is $3000.
To know more about simple interest, visit:
https://brainly.com/question/1173061
#SPJ9
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $438 million in ticket sales. If Singer B took in $22 million less than Singer A, how much did each tour generate?
Answers
To answer this question, we have that both singers generated $438 million in tickets sales.
Then, we can rewrite it in algebraic expressions as follows:
[tex]A+B=438[/tex]However, we know that singer B took in $22 million less than singer A:
[tex]B=A-22[/tex]Now, we can substitute this expression in the original one as follows:
[tex]A+A-22=438[/tex]And to solve this equation, we can add the like terms, and then add 22 to both sides of the equation as follows:
[tex]2A-22+22=438+22\Rightarrow2A=460\Rightarrow\frac{2A}{2}=\frac{460}{2}[/tex][tex]A=230[/tex]Then, to find the earnings of singer B, we have:
[tex]A+B=438\Rightarrow B=438-A[/tex]Then, B is equal to:
[tex]B=438-230\Rightarrow B=208[/tex]Then, we can check that A + B is:
[tex]A+B=230+208=438[/tex]And we can see that singer B took in $22 million less than singer A:
[tex]B=230-22=208[/tex]In summary, therefore, we can say that each tour generated:
Singer A generated $230 million in ticket sales and Singer B generated $208 million.
How much will a girl pay for a bag price at $15 if a discount of 10% is offered?
Answers
First, calculate how much is the discount equal to. Then, substract the discount from the original price to find the selling price.
Since the discount is 10%, find how much is 10% of $15 by multiplying 15 times 10/100:
[tex]15\times\frac{10}{100}=1.5[/tex]Then, 10% of 15 is equal to 1.5. Now, substract 1.5 from 15 to find the final price:
[tex]15-1.5=13.5[/tex]Therefore, the girl will pay $13.5. The answer is:
[tex]\text{ \$13.5}[/tex]The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
Answers
Answer:
The slopes are the same and the y-intercepts are different.
Explanation:
Given:
[tex]\begin{gathered} x+2y=8 \\ 2x+4y=12 \end{gathered}[/tex]Recall that the slope-intercept equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Let's go ahead and rewrite the first equation in slope-intercept form as seen below;
[tex]\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-\frac{1}{2}x+\frac{8}{2} \\ y=-\frac{1}{2}x+4 \end{gathered}[/tex]We can see from the above that the slope(m) of the first equation is -1/2 and the y-intercept(b) is 4.
Let's go ahead and rewrite the second equation in slope-intercept form as seen below;
[tex]\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-\frac{2}{4}x+\frac{12}{4} \\ y=-\frac{1}{2}x+3 \end{gathered}[/tex]We can see from the above that the slope(m) of the second equation is -1/2 and the y-intercept(b) is 3.
We can see from the above that, for the two equations, the slopes are the same, and the y-intercepts are different.
Question 9
1 pts
The price of gasoline has risen from $3.52/gallon last week to $4.31/gallon this week.
What is the percent change? Round answer to the tenths place.
Question 10
1 pts
Answers
Answer: 122.4% increase
Divide the new cost from the old
4.31 / 3.52 = 1.22443181818
Multiply by 100 to get a percent.
= 122.443181818%
= 122.4
You need to multiply by 100 to get the percent ….
=122.4
Sketch the graph of y= (x - 3)2 - 25, then select the graph that correspondsto your sketch.10140-1010101010111010HO-101010-20C.D.A.B.A. Graph AB. Graph BC. Graph CD. Graph D
Answers
Therefore,
[tex]\begin{gathered} when\text{ x=0} \\ y=(0-3)^2-25=9-25=-16 \end{gathered}[/tex]when x = 0, y =-16 we can confirm the graph is C.
Mr. Bowen used 2 gallons of paint on 1/3 of his fence. How many more gallons of
paint does he need to finish paining the entire fence?
Answers
Answer:
4
Step-by-step explanation:
→ Work out how much he needs in total
2 × 3 = 6
→ Minus how much he has used
6 - 2 = 4
Please help, picture attached
Answers
The measures of the unknown angles are as follows:
∠1 = 27∠2 = 97°∠3 = 56°∠4 = 27°∠5 = 56°How to find the measures of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles etc.
The parallel lines are line m and line l . The parallel lines m and l are cut by two transversals.
Therefore, the measures of the unknown angles are as follows:
∠1 = 27°(vertically opposite angles)
∠1 = ∠4(alternate angles)
∠4 = 27°
Alternate angles are congruent. Vertically opposite angles are congruent.
Therefore,
∠1 + ∠2 = 124
27 + ∠2 = 124
∠2 = 124 - 27
∠2 = 97°
∠3 = 180 - ∠2 - ∠1 (sum of angles on a straight line)
∠3 = 180 - 97 - 27
∠3 = 56°
∠5 = 180 - ∠4 - ∠2
∠5 = 180 - 97 - 27
∠5 = 56°
learn more on angles here: https://brainly.com/question/14684647
#SPJ1
Question 3 Cindy and Pam read their tavorite books, Cindy read for 4 hours and Pam read for 7 hours How much longer did Pam read than Cindy? A 23 hours 12 B 3 hours 31 hours D 12 5 12 hours Illuminate Education, Inc.
Answers
Let:
tc = Time that cindy read
tp = Time that pam read
How much longer did Pam read than Cindy? we need to find the difference, so:
[tex]\begin{gathered} tc=4\frac{3}{4}=\frac{19}{4} \\ tp=7\frac{2}{3}=\frac{23}{3} \\ so\colon \\ d=tp-tc=\frac{23}{3}-\frac{19}{4}=\frac{35}{12}=2\frac{11}{12} \end{gathered}[/tex]
Given ƒ(x) = − ½ (9 – 2x)
What is the value of f (15) ?
Answers
Answer: h of 15= -1/2(-21)= 10.5
Step-by-step explanation:
h(15)= -1/2(9-2(15))
h(15)=-1/2(9-30)
h(15)=-1/2(-21)
h(15)= 10.5
The picture I put in I understand girls more
Answers
Using long division:
19. Write ten-million (10,000,000) in scientific notation.
5
0105
01 x 106
01 x 107
01 × 108
Answers
Answer:
1 × 10⁷
Step-by-step explanation:
the correct answer is 1 × 10⁷
This question gettin me mad tight
The graph shows the value parent function
Which statement best describes the function?
A - the function is increasing when x > 0
B - the function is increasing when x< 0
C- the function is always increasing
D - the function is never increasing
Answers
Use exponential notation to simplify the given expressionsPresent your answer using only positive integer exponentsAswer the first one
Answers
We will use the next rule
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]Then
[tex]\sqrt[7]{x^6}\ast\sqrt[5]{x}=x^{\frac{6}{7}}\ast x^{\frac{1}{5}}=x^{\frac{6}{7}+\frac{1}{5}}[/tex][tex]x^{37/35}[/tex]P(-9,-4) Q(-7,-1) whats is PQ
Answers
Step-by-step explanation:
I assume the question is about the distance between both points.
2 points in the coordinate grid create a right-angled triangle :
their direct connection (distance) is the Hypotenuse (the baseline, it is the side opposite of the 90° angle), and the x and y coordinate differences are the legs.
so, we can use Pythagoras to get the distance.
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
so,
distance² = (-9 - -7)² + (-4 - -1)² = (-9 + 7)² + (-4 + 1)² =
= (-2)² + (-3)² = 4 + 9 = 13
distance = sqrt(13) = 3.605551275...
just in case, if you needed the line equation connecting these 2 points, I would assume the slope-intersect form
y = ax + b
"a" being the slope, "b" being the y-intersect (the y-value when x = 0).
the slope is always the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
using the 2 given points
x changes by +2 (from -9 to -7).
y charges by +3 (from -4 to -1).
the slope is
+3/+2 = 3/2
and our equation looks like
y = 3x/2 + b
now we use the coordinates of 1 point, e.g. (-7, -1), to get b
-1 = 3/2 × -7 + b = -21/2 + b
-1 + 21/2 = b
-2/2 + 21/2 = b
19/2 = b
our equation is then
y = 3x/2 + 19/2
or
y = (1/2)×(3x + 19)
Olivia picked 256 strawberries. She divided the strawberries evenly into 6
baskets. How many strawberries are in each basket? How many are left over
Answers
Answer:
42 strawberries in each backet with 4 left over
Step-by-step explanation:
256 divided by 6=42.6666667
42x6=252
256-252
Answer:
42 with 4 left over
Step-by-step explanation:
256/6
4 2
6. 256
4
24
16
12
4
What is 19.5 / 3 = decimal division
Answers
Answer:
6.5
Step-by-step explanation:
19.5 divided by 3 is 6.5
if you want to double check, you can multiply 3 by 6.5 and find it is 19.5
19.5/3= 6.5 decimal version
Express the relation below as a table. I’m confused some help would be nice
Answers
STEP-BY-STEP EXPLANATION
Given information
The following ordered pairs were provided in the question given
(11, -3)
(-20, 3)
(-17, 2)
Recall that, the general form of writing ordered pairs is (x, y)
Where,
x = input
y = output
For the above-ordered pairs
(11, -3) can be expressed as
x = 11 , and y = -3
(-20, 3)
x = -20, and y = 3
(-17, 2)
x = -17, and y = 2
The next step is to write the above-ordered pairs as a table
The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 30 hours. 1 day 24 hours 12 hours 12 hours (3 points) a 1 and 1 over 4. days b 1 and 1 over 2. days c 1 and 3 over 4. days d 2 days
Answers
54 hours is equivalent to 2 and 1 over 4 days. Because 1 day has 24 hours so we have to divide 54/24 to get the numeral of days which is equal to 2.25 days and .25 is equivalent to 1/4 of a day i.e., 2 1/4 days.
How is math operated in time?Time math entails learning how to tell time and converting it into seconds, minutes, hours, days, weeks, months, and years. Finding time math solutions can involve adding and subtracting to determine the amount of time elapsed or multiplying or dividing to convert time units. Time can be defined in mathematics as an ongoing and continuous sequence of events that occur in succession, from the past to the present to the future. Time is used to quantify, measure, compare, and even sequence events. Atomic clocks provide the most accurate measurement of time intervals the duration between two events. These clocks emit electromagnetic radiation, such as microwaves, at a precise frequency that causes the clock's atoms to jump from one energy level to another.
To learn more about time, refer to:
https://brainly.com/question/26714672
#SPJ9
Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80.
Answers
The scale drawing with length 0.0625m and width 0.05m.
What is scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.
When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.
Given:
length= 5m
width= 4m
and,
The scaled dimension = (Actual dimension) x (scale factor) ...(i)
scale factor =1/50
(1) The actual width = 4 m.
So, the width of the door on the scale drawing= 4x (1/80)= 0.05 m
(2)The actual length = 5 m.
So, the length of the door on the scale drawing= 5 x (1/80)= 0.0625 m
Hence, the scale drawing with length 0.0625m and width 0.05m.
Learn more about scale factor here:
https://brainly.com/question/18452571
#SPJ1
Watch help video The hypotenuse of a right triangle measures 20 cm and one of its legs measures 11 em. Find the measure of the other leg. If necessary, round to the nearest tenth oo Answer
Answers
We use pythagoras theorem
[tex]\text{hypothenus}^2=opposite^2+adjacent^2[/tex]Let y represent the other leg
[tex]\begin{gathered} 20^2=11^2+y^2 \\ 400=121+y^2 \\ y^2=400-121 \\ y^2=279 \\ y=\sqrt[]{279} \\ y=3\sqrt[]{31}\text{ cm} \\ y=16.70\text{ cm} \\ \end{gathered}[/tex]The measure of the other leg is 16.70 cm
Jordan Will hike the trail shown at a rate of 5mi/h. write a linear equation to represent the distance Jordan still has to walk after X hours. what does the Y-intercept of the equation represent?
Answers
using linear equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\text{time in hours} \\ y=dis\tan ce \\ m=5 \end{gathered}[/tex][tex]y=5x+31[/tex]The y - intercept which is equals to 31 represents the distance he still has to walk .
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right and 3 units up then the image is reflected on the x-axis. What are the coordinates of the final image?
Answers
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right.
A(-9 + 5 ,-7) B(-6 + 5,-2) C(-3 + 5 ,-6) = A ( -4, -7 ) , B ( -1 , -2 ) C ( 2 , -6 )
3 units up: A ( -4, -7 + 3 ) , B ( -1 , -2+ 3 ) C ( 2 , -6+ 3 )
The coordinates of the final image is = A( -4, -4 ) B ( -1 , 1 ) C ( 2 , -3)
If a gallon of paint weighs twelve pounds and seven ounces, what is the weight of a gallon of paint inkilograms? (Round to the nearest tenth.)Plan: Set up a plan or formula for solving the problem. (4 points)
Answers
Let:
Wlboz = Weight in lb + oz
Wkg = Weight in kg
The weight in kg is given by:
[tex]\begin{gathered} Wkg=12lb+7oz=12lb+0.4375lb=12.4375lb \\ Wkg=12.4375lb\times\frac{0.453592}{1lb}\approx5.6kg \end{gathered}[/tex]Answer:
5.6kg
I need help on #5 Please help me on my hw
Answers
Given:
The given problem is:
[tex](x+3)^2\ne x^2+9[/tex]Using the identity:
[tex](a+b)^2=a^2+b^2+2ab[/tex]Now substitute a = x and b = 3 in this identity:
[tex]\begin{gathered} (x+3)^2=x^2+3^2+2\times x\times3 \\ =x^2+9+6x \end{gathered}[/tex]Hence , the correct solution to the problem is:
[tex](x+3)^2=x^2+6x+9[/tex]Let sin 0= 4/9. Find the exact value of cos 0.
Answers
Statement Problem: Let;
[tex]\sin \theta=\frac{4}{9}[/tex]Find the exact value of;
[tex]\cos \theta[/tex]Solution:
In trigonometry, the ratio of the sine is defined as;
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]Thus,
[tex]\text{opposite}=4,\text{ hypotenuse=9}[/tex]By Pythagoras theorem, the square of the longest side (hypotenuse) is the sum of squares of the opposite and the adjacent sides.
[tex]\begin{gathered} (\text{hypotenuse)}^2=(\text{opposite)}^2+(\text{adjacent)}^2 \\ (\text{adjacent)}^2=(\text{hypotenuse)}^2-(\text{opposite)}^2 \\ (\text{adjacent)}^2=9^2-4^2 \\ (\text{adjacent)}^2=81-16 \\ (\text{adjacent)}^2=65 \\ \text{adjacent}=\sqrt[]{65} \end{gathered}[/tex]The ratio of the cosine is defined as;
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \end{gathered}[/tex]Hence,
[tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]Simplify.10(15 + n)50 + n0 150 + nO 150 + 10 n150 n
Answers
ANSWER
150 + 10n
EXPLANATION
We want to simplify:
10(15 + n)
To do this, we have to use the distributive property:
a(b + c) = a*b + a*c
Therefore:
10(15 + n) = (10 * 15) + (10 * n)
= 150 + 10n
That is the answer
Are 1 to 0.4 and 9 3.6 proportional?
Answers
The ratios 1 to 0.4 and 9 to 3.6 are proportional.
A ratio is a relationship between two objects that is expressed using numbers or amounts.
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Consider the ratio 1 to 0.4 and 9 to 3.6,
Let,
x = 1 to 0.4 = 1 : 0.4
= 1/0.4
= 10/4
= 5/2
Let, y = 9 to 3.6
y = 9 : 3.6
y = 9/3.6
y = ( 9 × 10 ) / 36
y = 10/4
y = 5/2
Therefore,
x = y
1 : 0.4 = 9 : 36
Hence, the ratios 1 to 0.4 and 9 : 3.6 are proportional.
Learn more about ratios here:
brainly.com/question/12024093
#SPJ1
The work of a student to solve a set of equations is shown below:Equation 1: m = 8 + 2n Equation 2: 4m = 4 + 4nStep 1: −4(m) = −4(8 + 2n)4m = 4 + 4nStep 2: −4m = −32 − 8n4m = 4 + 4nStep 3: −4m + 4m = −32 − 8n + 4nStep 4: 0 = −32 − 4nStep 5: n = − 8In which step did the student first make an error? (4 points)a. Step 1b. Step 2c. Step 3d. Step 4
Answers
Given:
m = 8 + 2n
4m = 4 + 4n
Let's follow the steps shown to find out the step with the error.
Step 1:
Multiply equation 1 by -4
-4(m) = -4(8 + 2n)
4m = 4 + 4n
Step 2:
-4m = -32 - 8n
4m = 4 + 4n
Step 3:
Use elimination method to simplify
-4m = -32 - 8n
4m = 4 + 4n
-4m + 4m = -32 + 4 -8n + 4n
This is where the student made the first error, because "4" was ommited.
This error led to subsequent errors in step 4 and 5
Step 4:
0 = -28 - 4n
Add 4n to both sides
0 + 4n = -28 - 4n + 4n
4n = -28
Step 5:
Divide both sides by 4
[tex]\begin{gathered} \frac{4n}{4}=\frac{-28}{4} \\ \\ n\text{ = -7} \end{gathered}[/tex]ANSWER:
The student first made an error in step 3.
your checking account is overdrawn by $120.22. you write a check for $80.25. what is the balance in your account???
Answers
The amount or balance left in the bank account is $39.97.
The amount of money held in a financial institution, such as a savings or checking account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.
The current balance in the bank account is $120.22.
The check was issued for $80.25.
Let x be the balance left in the account.
Then,
The balance left = Initial balance in the account - The amount for which the check was issued
x = Initial balance in the account - The amount for which the check was issued
x = $120.22 - $80.25
x = $39.97
The balance left in the bank account is $39.97.
Learn more about balance here:
brainly.com/question/27154367
#SPJ1
