Answer:
60 and -60
Hope this helps! :)
Quadrilateral ABCD has coordinates A (0, 2), B (3, 4), C (4,2), D (3,0). Determine the coordinates of the vertices of A'B'C'D' after a translation along vector < 2, -3>.
The coordinates of the vertices of A'B'C'D' after a translation will be ( 2, -1 ), ( 5, 1), ( 6, -1), and ( 5, -3) respectively.
What is translation?The translation is the action of moving the image's position relative to the coordinate system. The points are translated on a coordinate plane.
Given that quadrilateral, ABCD has coordinates A (0, 2), B (3, 4), C (4,2), and D (3,0).
The translation of the points will be done as below:-
A(0, 2) ⇒ ( 2, -1 )
B (3, 4) ⇒ ( 5, 1)
C (4,2) ⇒ ( 6, -1)
D (3,0) ⇒ ( 5, -3)
Therefore, the coordinates of the vertices of A'B'C'D' after a translation will be ( 2, -1 ), ( 5, 1), ( 6, -1), and ( 5, -3) respectively.
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Write in Interval form/notation
Answer: (-∞, -1] and (0, 2)
Step-by-step explanation:
Can't compare f(x) = x+1 when x<=0 with g(x)=x+1 when x>-1 since the functions are equal between -1<x<=0.
Compare f(x) = 3 when x>0 with g(x)=x+1 when x>-1
g(x) can't be greater than or equal to f(x):
g(x)<f(x)
x+1<3
x+1-1<3-1
x<2 and x>0 ==> 0<x<2
0<x<2 ==> (0, 2) ==> x is between 0 and 2 not including 0 and 2.
Compare f(x) = x+1 when x<=0 with g(x)=2x when x<=-1. Both equations have common x-values at x<=-1.
g(x)<f(x)
2x<x+1
2x-x<x-x+1
x<1 and x<=-1 ==> x<=-1
x<=-1 ==> (-∞, -1] ==> x is between -∞ and -1 not including -∞ but including -1.
(-∞, -1] and (0, 2)
A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?
Probability of 0.79 and would not warrant a refund
Probability of 0.21 and would not warrant a refund
Probability of 0.79 and would warrant a refund
Probability of 0.21 and would warrant a refund
The probability of 0.21 and would not warrant a refund. Therefore, option A is the correct answer.
Given that, mean depth =0.98 mm, standard deviation =0.35 mm.
What is a standard deviation?In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
We are given that the distribution of tire tread is a bell-shaped distribution that is a normal distribution.
Formula: [tex]Z_{score}=\frac{x-\mu}{\sigma}[/tex]
Here, P(depth less than 0.70 mm)
P(x < 0.70)
Then, P(x < 0.70)=P(z<(0.70-0.98)/0.35)
=P(z<(-0.8)
Calculating from the normal z table, we get P(z<(-0.8)=0.212
≈0.21
Thus, the probability of 0.21 and would not warrant a refund. Therefore, option A is the correct answer.
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there is 1/3 of an apple pie left after the bake sale. Four people would like to share it equally. what portion of the original pie will each person get?
Answer:
Each person would get 1/12 of the original pie
Step-by-step explanation:
3×4=12 1/3÷4=1/12
Ana's gymnastics
scores were posted on the scoreboard in order from highest to lowest score. One digit in her floor score is not visible. List all the possible digits for the missing number.
15/ Finley's vault score is 15.050. How does
The digits for the missing number are 1, 2, 3, 4.
The difference between her vault score and her uneven bar score is 0.367
How to illustrate the information?The floor score must be higher than 15.133 and lower than 15.500
The missing digit must be an integer.
Then all the possible scores are: 15.166 , 15.266 , 15.366 and 15.466
Because 15.166 > 15.133 and 15.466 < 15.500
Then all the possible digits are 1 , 2 , 3 , 4
The difference between her vault score and her uneven bar score is
= 15.500 - 15.133
= 0.367
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Ana’s gymnastics scores were posted on the scoreboard in order from highest to lowest score. One digit in her floor score is not visible. List all the possible digits for the missing number.
Vault- 15.500
Floor- 15._66
Uneven Bars- 15.133
Beam- 14.200
What is the difference between her vault score and her uneven bar score?
Use the following commission schedule to find the total graduated commission in Problems 5–8. Chart is in picture. Show work
Please help
Using proportions, the commissions are given as follows:
5. a. $200. b. $0. c. $0. d. $200.
6. a. $250. b. $200. c. $0. d. $490.
7. a. $250. b. $800. c. $300. d. $1350.
8. a. $250. b. $800. c. $1250. d. $2300.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item 5, the amount is less than $5,000, hence there is a single commission of 5%, as follows:
0.05 x 4000 = $200.
Hence the amounts are:
a. $200. b. $0. c. $0. d. $200.
For item 6, the commissions are divided as follows:
5% of the first $5,000: 0.05 x 5000 = $250.8% of the next $3,000: 0.08 x 3000 = $240.For a total of $490, as 250 + 240 = 490.
Hence the amounts are:
a. $250. b. $200. c. $0. d. $490.
For item 7, the commissions are divided as follows:
5% of the first $5,000: 0.05 x 5000 = $250.8% of the next $10,000: 0.08 x 10000 = $800.10% of the final $3,000: 0.1 x 3000 = $300.For a total of $1,350, as 250 + 800 + 300 = 1350.
Hence the amounts are:
a. $250. b. $800. c. $300. d. $1350.
For item 8, the commissions are divided as follows:
5% of the first $5,000: 0.05 x 5000 = $250.8% of the next $10,000: 0.08 x 10000 = $800.10% of the final $12,500: 0.1 x 12500 = $1,250.For a total of $2,300, as 250 + 800 + 1250 = 2300.
Hence the amounts are:
a. $250. b. $800. c. $1250. d. $2300.
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The blood types of 700 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type. If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
If a person from this group is selected at random, the probability that this person has type AB blood is 0.0928
How to solve for the probabilityFrom the question we have the total number of persons that there blood types have been collected as 700.
The number of people that have the AB blood type is given as 65.
Hence the probability would be
65 / 700
= 0.0928.
What is probability?This is the term that is used in the field of mathematics to refer to the likelihood of something occurring. It tells us of the chances that may be present that would show that a certain phenomenon would occur.
Hence the probability is 0.0928
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Hans went to a store and bought 3 items. Each item costs the same. He spent $21. How much did each item cost?
Answer:
$7
Step-by-step explanation:
If the total spending is $21, and he bought 3 items, we have to divide 21 by 3 and that makes 7
Hope it helped!
Answer:
7
Step-by-step explanation:
because each item is the same
let the item be 3x=21(given)
so x=21/3
therefore x = 7
come on this is easy
A list of facts from which a c conclusion can be drawn
Answer:
fjfj dhfj dh. hfhc hfh hfh hfh hfh hcdh
Triangle PQR with vertices P(-4, 0), Q(-6, -3), and R(-5,-5):
a) reflection in the line x = -2
b) dilation with scale factor of 3 using (-1, -4) as the center
a) reflection in the line x = -2 is P'Q'R' is shown.
b) The coordinates of image P'Q'R' are
(-12, 0), (-18, -9), R(-5,-5) respectively.
What is defined as the dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.Part a) reflection in the line x = -2
When the triangle PQR with the coordinates P(-4, 0), Q(-6, -3), and R(-5,-5) made a reflection along the x = -2, the coordinates of the image are obtained as;
See the graph; image triangle P'Q'R';
P' = (0, 0)
Q' = (2, -3)
R' = (1, -5)
Part b) dilation with scale factor of 3 using (-1, -4) as the center.
Let the coordinates are;
(x, y) ---> (kx, ky); where k is the scale factor i.e, 3.
This can be written as; (3x, 3y).
For the point P(-4, 0).
The image of P' = (-4×3, 0×3) = (-12, 0)
For the point Q(-6, -3)
The image of Q' = (-6×3, -3×3) = (-18, -9)
For the point R(-5,-5)
The image of P' = (-5×3, -5×3) = (-15, -15)
Therefore, the image with the dilation of scale factor of 3 is P'Q'R' are
(-12, 0), (-18, -9), R(-5,-5) respectively.
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use each graph to determine an equation of the circle in (a) center radius form and (b) general form
The graph to determine an equation of the circle in
(a) center radius form
(b) general form
(x -3)² +(y -1)² = 4 . . . . center-radius form
x² +y² -6x -2y +6 = 0 . . . . general form
The "center-radius" form is
(x -h)² +(y -k)² = r² . . . . . . . circle with center (h, k) and radius r
The graphed circle has its center at (3,1) and a radius of 2. Putting these numbers into the above form gives the equation
(x -3)² +(y -1)² = 4 . . . . center-radius form
Expanding the parentheses, we get
x² -6x +9 +y² -2y +1 = 4
Subtracting 4, and putting in general form, the equation becomes ...
x² +y² -6x -2y +6 = 0 . . . . general form
a graph (inclusive of a sequence of one or greater factors, strains, line segments, curves, or areas) that represents the variant of a variable in assessment with that of one or greater other variables. the gathering of all factors whose coordinates fulfill a given relation (inclusive of a function)
A graph of a function is a unique case of a relation. within the modern foundations of mathematics, and, generally, in set theory, a function is clearly same to its graph. however, it is regularly useful to look functions as mappings, which consist no longer best of the relation among enter and output, but additionally which set is the domain, and which set is the codomain. as an instance, to mention that a characteristic is onto (surjective) or not the codomain have to be taken under consideration
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m = -7.6, y-intercept
(0,2/5)
Answer:12
Step-by-step explanation:
cuz yes
Place the numbers in order from least to greatest.
= 0.059
0.11
0.09
0.0099998
0.111
The order of numbers from least to greatest :
0.0099998 < 0.059 < 0.09 < 0.11 < 0.111 .
Given, numbers 0.059 , 0.11 , 0.09 , 0.0099998 , 0.111 .
Ascending order : When the set of numbers are to be arranged in least to greatest order.
Descending order : When the set of numbers are to be arranged in greatest to least order.
Now the numbers are to be arranged in ascending order.
Least number : 0.0099998
Second least number : 0.059
Third least number : 0.09
Fourth least number : 0.11
Greatest number : 0.111
Thus the order of numbers in ascending order will be least to greatest .
0.0099998 < 0.059 < 0.09 < 0.11 < 0.111
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Find the unit price.
$6.42 for 3 pounds
Answer:
$2.14 per pound
Step-by-step explanation:
To find this: do 6.42 divided by 3, will give you the unit price
Mrs Rama uses three types of fruit juice for a party. The ratio of the amount of watermelon juice to the amount of apple juice is 4: 9. The Ratio of the amount of apple juice to the amount of orange juice is 27: 14. Find the ratio of the amount of watermelon juice to the amount of apple juice to the amount of orange juice in its simplest form
the ratio of the amount of watermelon juice to the amount of apple juice to the amount of orange juice in its simplest form is 12 : 27 : 14.
The ratio of the amount of watermelon juice to the amount of apple juice = 4 : 9
This can also be written as:
4 × 3 : 9 × 3
12 : 27
The ratio of the amount of apple juice to the amount of orange juice = 27 : 14
Now, the ratio of the amount of watermelon juice to the amount of apple juice to the amount of orange juice will be:
Ratio = 12 : 27 : 14
Therefore, the ratio of the amount of watermelon juice to the amount of apple juice to the amount of orange juice in its simplest form is 12 : 27 : 14.
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A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 1, 4, 6. The second column is labeled y with entries 9, 0, negative 7, negative 1.
What is the range of the given function?
{x | x = –5, 1, 4, 6}
{y | y = –7, –1, 0, 9}
{x | x = –7, –5, –1, 0, 1, 4, 6, 9}
{y | y = –7, –5, –1, 0, 1, 4, 6, 9}
The range of the given function is B. {y | y = –7, –1, 0, 9}
How to illustrate the information?It should be noted that ee usually denote independent variable as x and dependent variable as y.
The range of a function is basically the set of all resulting y-values.
Given the first column is labeled x with entries - 5, 1, 4, 6. The second column is labeled y with entries 9, 0,-7, -1.
Then, the range of the given function = values in second columns
i.e. Range={y | y = –7, –1, 0, 9} [Arranged in order].
In conclusion, the correct option is B.
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Which expression is equivalent to 12(5 - 4x)?
Answer:
12x
Step-by-step explanation:
12(5-4x)=60-48x
=12x
W contains the top movies of 2014 according to Time Magazine. If W= {The Grand Budapest Hotel, Boyhood, The LEGO Movie, Lucy, Goodbye to Language, Jodorowsky's Dune, Nightcrawler, Citizenfour}, how many subsets does W contain?
Answer:
256
Step-by-step explanation:
The number of subsets of a set with n elements is 2^n.
Mickey bought lunch for his fellow office workers on Monday. He spent $24.20 on 3 hamburgers and 2 fish sandwiches. Chloe bought lunch on Tuesday and spent $23.60 for 4 hamburgers and 1 fish sandwich. What is the price of 1 hamburger, and what is the price of 1 fish sandwich?
The price of 1 hamburger is $4.6 and 1 fish sandwich is $5.2
Calculations and ParametersLet 1 hamburger be x
Let 1 fish sandwich be y
Thus, we have:
3x + 2y= 24.20...... eq 1
4x + y= 23.60........ eq 2
Let's use the substitution method here:
Make y the subject formula in eq 2
y= 23.60 - 4x......... eq 3
Put the value of y into eq 1
3x + 2(23.60 - 4x) = 24.20
3x + 47.2 - 8x = 24.20
-5x + 47.2 = 24.20
Exchange values to eliminate the negative symbol
5x = 47.2- 24.20
5x= 23
x= 4.6
Put the value of x into eq 3
23.60- 4(4.6)
y= 23.60-18.4
y= $5.2
Therefore, the price of 1 hamburger is $4.6 and 1 fish sandwich is $5.2
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what would be the answer to this (9-3×2)²
144?
9
Step-by-step explanation:
PEMDAS
inside parentheses we have 3*2 = 6
9-6 =3
3^2 = 9
Katie is selling lemonade for $1.50 per cup. She
decides to put them on sale for $0.90. What percent
discount did she give on her lemonade?
Answer:
60 percent
Step-by-step explanation:
just do 90/150, and yo get 60 percent
write the equation of the line that passes through the points (1, 7) and (-3, -1)
Answer:
y = 2x + 5
Step-by-step explanation:
The slope is
[tex]\frac{-1-7}{-3-1}=2[/tex]
Substituting into point-slope form, we get the equation to be
[tex]y-7=2(x-1)[/tex]
which rearranges into slope-intercept form as:
[tex]y-7=2x-2 \\ \\ y=2x+5[/tex]
7. Apply Star A is 12 billion years old. Star B is in the same cluster. About how old is Star B? Why?
Star B is roughly 12 billion years old as star A.
What is the time?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.In the situation given in the question where start A is 12 billion years old and star B is from the same cluster as star B.
It is completely possible that star B is also approximately 12 billion years old as in a cluster of stars many many stars form together or in a very small gap of time.So, it is completely possible that star B is roughly 12 billion years old.Therefore, star B is roughly 12 billion years old.
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When multiplying a number by 10 move the decimal to the right. When multiplying a number by .01 move the decimal to the left. Why
The reason why multiplying a number by 10 moves the decimal to the right is because the number is increasing. When the decimal moves left when multiplied by 0.01, the number is decreasing.
What happens when you multiply by powers of 10?When you multiply by powers of 10 which are positive, the number that is being multiplied will see its decimal move to the right. This is to show that the number is now increasing in value.
When you multiply by 0.01 however, the number will decrease and so the decimal will have to move left to show that the value of the number has decreased. For instance, 50 x 0.01 becomes 0.5.
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(NEED HELP FAST!! 100 POINTS!!) The selling price of a used car is $8850. Trade in allowance is $1500. Tax is 8%. Tag fee is $130. Title fee is $35. Finance charges are 9.5% annual simple interest. What is the total price of the financed amount? What are the total finance charges? What are the monthly payments if the vehicle is financed for 3 years? What is the total deferred price of the car?
The total price of the financed is $7,973
The total finance charges are $2,272.31
The monthly payment if the vehicle is financed for 3 years is $284.59
What is the impact of trade-in allowance on selling price?
The trade-in allowance on the car's selling price reduces the total amount the car dealer would charge a tax of 8% on.
selling price net of trade in allowance=$8850-$1500
selling price net of trade-in allowance=$7,350
the selling price plus sales tax=$7350*(1+8%)
the selling price plus sales tax=$7,938.00
total cost including title fee =$7,938+$35
total cost including title fee=$7,973
finance charges for 3 years=$7,973*9.5%*3
finance charges for 3 years=$2,272.31
monthly payment=($7,973+$2,272.31)/36
monthly payment=$284.59
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What is the sum of the 22 solutions of the equation x^2-4x-45=0x
2
−4x−45=0 ?
The solution for the equation x² – 4x – 45 = 0 is (x – 9) (x + 5)
Given,
Quadratic equation = x² – 4x – 45
We can solve this by using quadratic formula.
Equations of the form ax² + bx + c = 0 can be solved using quadratic formula.
Here the equation is in the form of above mentioned:
x² – 4x – 45 = 0
Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Substitute the values in the formula,
x = [tex]\frac{-(-4)(+-)\sqrt{(-4)^{2}-4(-45) } }{2}[/tex]
x = [tex]\frac{4(+-)\sqrt{16 -4(-45)} }{2}[/tex]
x = [tex]\frac{4(+-)\sqrt{16+180} }{2}[/tex]
x = [tex]\frac{4(+-)\sqrt{196} }{2}[/tex]
x = [tex]\frac{4(+-)14}{2}[/tex]
Now, solve the equation for:
x = [tex]\frac{4+14}{2}[/tex] = [tex]\frac{18}{2}[/tex] = 9
Next, solve the equation for:
x = [tex]\frac{4-14}{2}[/tex] = [tex]\frac{-10}{2}[/tex] = -5
According to ax² + bx + c = a(x - x₁) (x - x₂),
Here, x₁ is 9 and x₂ is -5
So,
x² - 4x - 45 = ( x - 9) (x - (-5))
That is,
x² - 4x - 45 = (x - 9) (x + 5)
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Is the sqrt3 greater than the sqrt of 10/2
The square root of 3 is not greater than the square root of 10/2.
This is because the square root of 3 is 1. 73 and the square root of 10/2 is 2. 24
What is the square root of a number?The square root of a number can be defined as the factor that when multiplied by itself gives the original number.
The square root is represented with the symbol " √"
From the information given, we are to determine which is greater between the square root of 3 and the square root of 10/2
The expression is represented as;
√ 3
√10/2
Now, let's simply the square root
√3
Find the square root
= 1. 73
√10/2
Find the quotient of 10/2 first, then substitute the value to find the square root, we have;
10/ 2
5
Find the square root of 5
√5 = 2. 24
We can see that the square root of 3 is not greater than the square root of 10/2
Thus, the square root of 3 is not greater than the square root of 10/2
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If a man walks six feet per second, how many minutes will it take for to
walk 5400 feet?
[tex] \large \bf \implies{15 \:minutes}[/tex]
Step-by-step explanation:In this question speed remain same
[tex] \bf \longrightarrow{Apply \: \frac{d_1}{d_2} = \frac{t_1}{t_2} }[/tex]
[tex] \bf \longrightarrow{\frac{6}{5400} = \frac{1}{t_2} }[/tex]
[tex] \bf \longrightarrow{t_2 = 900 \: second}[/tex]
Convert this second into minutes
[tex] \bf \longrightarrow{1min = 60sec} \\ \bf \longrightarrow{1sec = \frac{1}{60} min} \\ \bf \longrightarrow{ \frac{900}{60} = 15min}[/tex]
Therefore, A man take 15 minutes to walk 5400 feet.Please help me gemotry
Answer:
45°
Step-by-step explanation:
59 + x + 80 + 49 + x = 180 the sum of the interior angles of a triangle equal 180 Combine the like terms
2x + 188 = 180 Subtract 1588 from both sides
2x = -8 divide both sides by 2
x = -4 Now plug this in for A
49 + x
49 -4 = 45
If the point (4,1) is a point on the graph of f, then f( __ )____.