The original point (-6, -9) is shifted 1 unit to the left and 5 units down to reach the new position (-7, -14).
To find the image point after translating the point (-6, -9) left 1 unit and down 5 units, we subtract the translation values from the coordinates of the original point.
For the horizontal translation (left 1 unit), we subtract 1 from the x-coordinate:
New x-coordinate = -6 - 1 = -7
For the vertical translation (down 5 units), we subtract 5 from the y-coordinate:
New y-coordinate = -9 - 5 = -14
Therefore, the image point after the translation is (-7, -14).
This means that the original point (-6, -9) is shifted 1 unit to the left and 5 units down to reach the new position (-7, -14).
This translation is a geometric operation commonly used in mathematics and computer graphics to move objects or points in a coordinate plane.
1. The scatterplot below shows the fuel efficiency (in
miles per gallon) and weight (in pounds) of
twenty subcompact cars.
91
3000
(a) Is there a clear explanatory variable and
response variable in this setting? If so, tell
which is which. If not, explain why not.
Car weight
(b) Does the scatterplot show a positive association, negative association, or neither? Explain why this
makes sense.
(c) How would you describe the form of the relationship?
(d) Which of the following is closest to the correlation between car weight and fuel efficiency for these
20 vehicles? Explain.
r=-0.9
r=-0.6
r=0 r=0.4
(e) There is one "unusual point" on the graph. Explain what is "unusual" about this car.
(
What effect would removing the “unusual point” have on the correlation? Justify your answer.
(g) If we converted the car weights to metric tons (1 metric ton -2,205 pounds). How would the
correlation change? Explain.
The explanatory variable is the car's weight, with fuel efficiency as the response variable; a likely negative association may exist, possibly linear or non-linear; a correlation like r=-0.9 or r=-0.6 is plausible; an 'unusual point' could be an outlier affecting the correlation; removing it might strengthen or weaken the correlation; converting weights to metric tons wouldn't alter the correlation.
(a) In this context, the explanatory variable is the car's weight (in pounds) and the fuel efficiency (in miles per gallon) is the response variable. This is because we are typically interested in determining the effect of a car's weight on its fuel efficiency.
(b) Based on the context, a scatterplot might show a negative association between the car's weight and its fuel efficiency. This would make sense as heavier cars often require more fuel to operate efficiently, leading to lower miles per gallon.
(c) The form of the relationship between car weight and fuel efficiency can vary. For instance, it could be linear (indicating a constant rate of change) or non-linear (indicating a rate of change that varies with weight).
(d) Without viewing the scatterplot it's not possible to definitively answer this, but based on the proposed negative relationship, a correlation of r=-0.9 or r=-0.6 would be plausible. Correlations range from -1 to 1, and a negative sign indicates an inverse relationship.
(e) An 'unusual point’ could be an outlier on the scatterplot that doesn't model the relationship between car weight and fuel efficiency like the rest of the data. This could be due to factors unique to this car, such as a highly efficient engine that gets more miles per gallon despite its weight
(f) Depending on the unique characteristics of the 'unusual point', its removal could either increase or decrease the correlation. If this point were causing the correlation to be weaker, its removal would cause the correlation to strengthen, and vice-versa.
(g) Converting the car weights to metric tons wouldn't change the correlation between weight and fuel efficiency. Correlation is unitless and depends only on the relationship between variables, not the scale they're measured on. Thus, while the specific values for weight would change, the strength, direction, and form of the relationship between weight and fuel efficiency would remain the same.
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Please help and explain I’m very confused thank you
Answer:
31° = x
Step-by-step explanation:
According to the Supplementary Angles Theorem, 123° and that acute angle right up against it, form a straight angle, so you do this:
[tex] - 123 + 180 = 57[/tex]
Now that the second angle measure is found, according to the Triangular Interior Angles Theorem, the sum of the interior angles of all triangles add up to 180°:
180° = 57° + 92° + x°
|________|
180° = 149° + x°
-149° - 149°
________________
31° = x
I am joyous to assist you anytime.
Please answer with a detailed explanation. Thank you!
Answer:
This answer is 8
Step-by-step explanation:
It actually is very simple. For this question you do not even need the g(x) equation to continue, so put it aside for now. F(x) means that whatever number that will take the place of x will be used in this equation. If f(x)=3x-1, then f(3)=3(3)-1
This happens because the 3 in f(3 tells you to substitute x for 3 in the equation. ) So just plug in 3 for x and solve to get the answer 8.
Answer:
This answer is 8
Step-by-step explanation:
Please help
Use p(x)=x^2+4x+9. Find a polynomial r(x) such that p(x)+r(x)=2x^2-6x+14.
Find a polynomial s(x) such that p(x)+s(x)=2x^2+14
Find a polynomial t(x) such that p(x) + t(x) has degree 2 and p(x) * t(x) has degree 3.
This box holds 4 crates of eggs each holds 6 dozen eggs how many eggs are in a eggs are in the box when it is full.
Each crate holds 6 dozen eggs.
1 dozen = 12 eggs.
Multiply 12 by 6 to get the total number of eggs per crate:
6 x 12 = 72 eggs per crate.
The box holds 4 crates, multiply the number of each in a crate by the number of crates:
72 eggs x 4 crates = 288 total eggs.
6(k-5)<-6, solve for k
Answer:
k > 4
Step-by-step explanation:
Answer:
k< 4
Step-by-step explanation:
6(k-5)<-6
divid by : 6 (k-5)<-1
add : 5 k<-1+5
k< 4
Malik stops at the grocery store to buy a bag of diapers and 2 cans of formula. He spends a total of $37. The next week he stops and buys 2 bags of diapers and 5 cans of formula for a total of $87. How much does a bag of diapers cost? How much is one can of formula?
Answer:
The cost of one bag of diapers is $11 and the cost of one can of formula is $13
Step-by-step explanation:
Let
x -----> the cost of one bag of diapers
y ----> the cost of one can of formula
we know that
[tex]x+2y=37[/tex] -----> equation A
[tex]2x+5y=87[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (11,13)
see the attached figure
therefore
The cost of one bag of diapers is $11 and the cost of one can of formula is $13
Final answer:
The cost of one bag of diapers is $11, and the cost of one can of formula is $13, as determined by solving a system of two linear equations that describe Malik's purchases.
Explanation:
The student is presented with a system of linear equations based on the purchases made by Malik at different times. The purchases involve a bag of diapers and cans of formula, with the total amounts spent being provided. This information can be turned into a system of equations to solve for the price of one bag of diapers and the price of one can of formula.
Let D represent the cost of one bag of diapers and F represent the cost of one can of formula. From the given information, we can construct the following equations:
D + 2F = $37 (Equation 1: One bag of diapers and two cans of formula cost $37)
2D + 5F = $87 (Equation 2: Two bags of diapers and five cans of formula cost $87)
Now, let's solve this system of equations using the method of substitution or elimination. For simplicity, let's use the elimination method:
Multiply Equation 1 by 2, so it can be arranged to eliminate D:
2D + 4F = $74
Subtract Equation 1 modified from Equation 2:
(2D + 5F) - (2D + 4F) = $87 - $74,
which simplifies to F = $13.
Now plug the value of F back into Equation 1:
D + 2($13) = $37,
D + $26 = $37,
therefore D = $37 - $26,
D = $11.
Therefore, the cost of a bag of diapers is $11, and the cost of one can of formula is $13.
What is the relationship between the independent and dependent variable?
Answer: Direct proportion because as the time goes up the distance goes up
if 3 pizzas serve 12 people, how many pizzas are needed for a pizza party with 68 people
Answer:
17
Step-by-step explanation:
if 3 pizzas serve 12 people then 17 pizzas can serve 68 people.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, 3 pizzas serve 12 people.
Assuming y = kx.
12 = 3k.
k = 4.
Now,
68 = 4x.
x = 17
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Look at the unit circle shown below.
Which statement is TRUE? A The x-coordinate of P corresponds to cosθ , which has a period of 2π . B The x-coordinate of P corresponds to cosθ , which has a period of π . C The y-coordinate of P corresponds to cosθ , which has a period of 2π . D The y-coordinate of P corresponds to cosθ , which has a period of π .
Answer:
A is true.
Step-by-step explanation:
Cos θ = adjacent / hypotenuse = x/1 = x.
Cosθ has a period pf 2π.
Answer:
The correct option is A.
Step-by-step explanation:
Draw a perpendicular form point P on x-axis.
Radius of unit circle is 1 . It means in triangle OPA
Hypotenuse = OP = 1 units
Adjacent= OA = x
Perpendicular = PA = y
In a circle angled triangle,
[tex]\cos \theta = \frac{adjacent}{hypotenuse}[/tex]
In triangle OPA,
[tex]\cos \theta = \frac{x}{1}[/tex]
[tex]\cos \theta =x[/tex]
The x-coordinate of P corresponds to cosθ.
The period of a unit circle is 2π.
Therefore, the correct option is A.
A driveway is in the shape of a rectangle 3.0 meters wide by 5.0 meters long. What is its perimeter?
Answer: I believe the answer is 18 meters
Step-by-step explanation:
Answer:
The perimeter would be 16.
Step-by-step explanation:
3.0+3.0=6
5.0+5.0=10
10+6=16
The value of the 6 in 5426.37 is 1/10 of the value of the 6 in which number
A. 4643.92
B. 6129.83
C. 2371.67
D. 1565.44
Answer:
D
Step-by-step explanation:
the value of 6 in 5426.37 is 6 which is 1/10 of 60 so the answer is 1565.44
How do you solve |x-4| is less than or equal to 2?
Answer:
|x - 4| ≤ 2
-2 ≤ x - 4 ≤ 2
2 ≤ x ≤ 6
Classify each number below as an integer or not.
Answer:
1. yes
2. no
3. yes
4. no
5. yes
Step-by-step explanation:
The method i use is if the number is not a fraction than it is an integer. besides 6 for some reason.
Here is the catch if the fraction can be simplified into a whole number than it is an integer.
The area of a rectangular rug is 18.7 Square yards the width of the rug is 2.75 yards Isabell found the length of the rug by dividing its area by its width what is the length in yards of the rug?
Thank you so much for helping me Have a blessed night/day!
What is 7ab(2a+4b-6)
Answer:
[tex]14a^{2}b[/tex] + [tex]28ab^{2}[/tex] - 42ab
Step-by-step explanation:
The expression 7ab(2a+4b-6) simplifies as 14a^2b + 28ab^2 - 42ab by distributing 7ab to each number within the parentheses.
Explanation:This question involves distribution which is a property in Mathematics. To simplify the expression
7ab(2a+4b-6), you need to distribute or multiply 7ab with each number within the parentheses. When we do this step-by-step:
7ab times 2a = 14a2b7ab times 4b = 28ab27ab times -6 = -42abSo, the expression 7ab(2a+4b-6) simplifies as 14a2b + 28ab2 - 42ab.
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Factor the following expression
10x^5+5x^3-14x^2-7-
Answer:
C. (5x^3-7)(2x^2+1)
Step-by-step explanation:
Given expression is,
10x^5+5x^3-14x^2-7
=10x^5-14x^2 + 5x^3 - 7 (By the commutative property)
=2x^2(5x^3-7)+5x^3-7 (Taking 2x^3 common from first two terms )
=(5x^3-7)(2x^2+1) (Taking 5x^3-7 common from both terms)
\implies 10x^5+5x^3-14x^2-7=(5x^3-7)(2x^2+1)
Hence, Option C is correct
If it is known that a+b/a−b =c, find the following.
3a+3b/2a−2b
Answer:
[tex]\frac{3}{2}[/tex] c
Step-by-step explanation:
Given
[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator
= [tex]\frac{3(a+b)}{2(a-b)}[/tex]
= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] = [tex]\frac{3}{2}[/tex] c
Darelene has 3/4 lb. of almonds. She needs to share it equally among 6 freinds. How many will each freind be given ( please show step by step explanation)
Answer:
1/8 lb. of almonds for each of her 6 friends
Step-by-step explanation:
So i'm doing this in school too. This is how I would do it.
She has 3/4 lb. of almonds, and she needs to split it with 6 friends.
So what you would do is do 3/4 ÷ 6/1
To divide one fraction by another, invert (turn upside-down) the second fraction, then multiply. Cancelling by a common factor of 3 gives 1 /8.
I hope this helps!
HELP ASAP PLZ !! Is triangle MNP a dilation of triangle JKL? Explain why or why not.
To confirm if triangle MNP is a dilation of triangle JKL, one must examine the ratios of the corresponding sides. In a dilation, a figure's size changes but its shape and the angles between its sides remain the same, and the lengths of the sides remain proportional. Without the specific measurements, it's not possible to definitively say if MNP is indeed a dilation of JKL.
Explanation:To determine if triangle MNP is a dilation of triangle JKL, we need to examine the ratios of the corresponding sides. Dilation in mathematics is a transformation that alters the size of a figure without changing its shape or the angles between its sides. In a dilation, the lengths of the sides are proportional.
For example, if triangle MNP has sides that are twice as long as the corresponding sides of triangle JKL, then MNP is a dilation of JKL by a factor of 2.
If the sides of triangle MNP do not maintain the same proportionality with triangle JKL, then triangle MNP is not a dilation of triangle JKL. Therefore, without concrete values or further details, it's difficult to definitively answer whether MNP is a dilation of JKL.
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A reasonable estimate for 597 x 52 is
Answer: 30,000
Step-by-step explanation: Round 597 to nearest hundred and 52 to nearest ten.
Final answer:
To estimate 597 x 52, round 597 to 600 and 52 to 50, then multiply to get 600 x 50 = 30,000. Therefore, a reasonable estimate is 30,000.
Explanation:
The student has asked for a reasonable estimate for 597 x 52. To provide an estimate, we can round numbers to simplify the multiplication. In this case, we can round 597 to 600 and 52 to 50. Now, let's multiply these rounded numbers.
First, multiply 6 by 50, which equals 300.Then, since we rounded up to the hundreds, we recall that 600 is 10 times greater than 60, so we must multiply 300 by 10, which equals 3000.Therefore, a reasonable estimate for 597 x 52 is 30,000.
What is the solution to this equation?
7x – 3(х – 6) = 30
A.x= 12
B.х = 6
C. х = 3
D. x= 9û
Answer:
x = 3
Step-by-step explanation:
[tex]7x-3(x+6)=30[/tex]
Isolate the variable by dividing each side by factors that don't contain the variable.
5k - 7 > 5k + 8
guys I really need help!!
Answer:
Step-by-step explanation:
Can you draw two triangles each having two 45° angles and one. 90° angle that are not similar justify her answer
No, you cannot draw two triangles each having two 45° angles and one 90° angle that are not similar. All 45-45-90 triangles are similar by definition because they have the same shape, i.e., their angles are the same (two 45° angles and one 90° angle). These similar figures can differ in size, but not in shape.
Explanation:No, it is not possible to draw two triangles each having two 45° angles and one 90° angle that are not similar. Let's break this down.
All triangles that have two 45° angles and one 90° angle are called 45-45-90 triangles. In a 45-45-90 triangle, the angles are always the same, so they are always similar by the definition of similar figures. Similar figures have the same shape, but not necessarily the same size. Their corresponding angles are congruent (the same) and their corresponding sides are in proportion.
Since all 45-45-90 triangles have the same angles - two 45° angles and one 90° angle - they are all similar to each other, regardless of their size. The size of the triangle does not matter, because the definition of similar figures is based on the shape, not the size. Hence, it is impossible to draw two 45-45-90 triangles that are not similar.
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Is 4x-3=2x+13 a true statement?
Answer:
It is ture.
4x-3=2x+13
2x-3=13
2x=16
x=8
Ellie colors 20% of the total shapes on her paper. She colors 10 shapes. Enter the number of shapes on Ellie's paper.
Answer:
50 shapes
Step-by-step explanation:
If 20% is 10 shapes, then 30% would be 15, 40% would be 20, and so forth. when you get to 100%, the answer would be 50 shapes because the numbers of shapes is half the percentage. For example, 5% is 2.5 shapes, 10% is 5 shapes, 60% is 30 shapes.
CAN EXPLAIN FURTHER
would appreciate brainliest, but I am content with just giving you an answer :)
a television with a 5:4 screen shows an image with a ratio of 20:12 which creates a letter boxed image. What percent of the screen area is occupied
Answer: [tex]75\%[/tex]
Step-by-step explanation:
You know that the ratio of the television's screen is [tex]5:4[/tex] . This ratio can be also written as the following fraction:
[tex]\frac{5}{4}[/tex]
The television shows an image with a ratio of [tex]20:12[/tex] which can be also written as a fraction:
[tex]\frac{20}{12}[/tex]
Set up the following proportion and solve for "x":
[tex]\frac{20}{x}=\frac{5}{4}\\\\x=\frac{4*20}{5}\\\\x=16[/tex]
Now, in order to find the percent of the screen area occupied make the following division:
[tex]\% occupied=\frac{12}{16}*100=75\%[/tex]
is 0.9 repeating a rational or irrational number
Answer:
rational
Step-by-step explanation:
it is rational
a rational number is that which is non-terminating (a number which cannot be terminated) and repeating . So 0.99999…. aquires both repeating and non-terminating property . Hence it is a rational number .
A student has these scores on their assignments. The teacher is considering dropping a
lowest score.
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a) What effect does eliminating the lowest value, 0, from the data set have on the mean
and median?
b) Would there be more of a significant change on the IQR or Standard Deviation?
Explain why.
The answers are shown below:
What is mean and median?The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.
Given data:
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9
= 700/9
= 77.777
Median without '0' = 80
Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70
Median with '0' = 80
b)standard deviation= 18.121673811445. (without '0')
standard deviation with 0 = 28.982753492379
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Solve for C: S = C+RC
Answer:
factoring c is the best way to solve this
Step-by-step explanation:
S = C ( 1 + R )
C = S/( 1 + R )
The equation after solving is C = S / (1 + R).
To solve for C in the equation S = C + RC, we can factor out C on the right side:
S = C + RC
S = C(1 + R)
Then, we can divide both sides by (1 + R) to isolate C:
S / (1 + R) = C
Therefore, the solution is:
C = S / (1 + R)
For example, if S = 100 and R = 0.1, then C would be:
C = 100 / (1 + 0.1)
C = 100 / 1.1
C = 90.9090909090909
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