After applying the translation (x - 1, y - 3), the vertices of the triangle originally at (-4, 5), (0, 0), and (4, 5) will move to new locations (-5, 2), (-1, -3), and (3, 2).
Explanation:The question is about translation in mathematics, specifically in geometry. A translation is a function that moves every point a constant distance in a specific direction. If we have a point at coordinates (x, y), a translation of the form (x - a, y - b) will shift that point a units to the left and b units down:
The point (-4, 5) will shift to (-4 - 1, 5 - 3) = (-5, 2)The point (0, 0) will shift to (0 - 1, 0 -3) = (-1, -3)The point (4, 5) will shift to (4 - 1, 5 - 3) = (3, 2).So, the vertices of the triangle after the translation (x - 1, y - 3) will be (-5, 2), (-1, -3), and (3, 2).
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Solve 81^x = 27^x+2
X=1
X=2
X=5
X=6
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot.
What is the probability that a randomly selected car with no 4-wheel drive has third row seats?
0.3
0.4
0.7
0.8
Probability measures to determine the possibility of an event. In this case, the events are cars with no 4 wheels and cars with third row seats.
The probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
Let:
[tex]A \to[/tex] A car with no 4-wheel drive
[tex]B \to[/tex] A car that has third row seats
The probability that a randomly selected car with no 4-wheel drive has third row seats is represented as:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
From the 2-way table, we have the following parameters:
[tex]n(A\ n\ B) = 12[/tex]
[tex]n(A) = 40[/tex]
So, the probability is:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
[tex]P(B|A)= \frac{12}{40}[/tex]
[tex]P(B|A)= 0.3[/tex]
Hence, the probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
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algebra- you make a large pot of soup. You freeze the soup in small and medium containers. A small container holds 4 ounces and a medium container holds 6 ounces. The soup can fill 6 small containers and 10 medium containers.
A.Write an equation in standard form that models the possible combinations of small and medium containers that the soup can fill.
B. Graph the equation from part (a)
C. Find four possible combination.
A. Let us say that:
s = number of small containers
m = number of medium containers
From the given data, the total volume of soup is:
total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces
So the equation is:
4s + 6m = 84
B. We rewrite the equation explicit to one variable, here we choose s:
4s = 84 – 6m
s = 21 – 1.5m
Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.
C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:
21 small containers, 0 medium containers
15 small containers, 4 medium containers
9 small containers, 8 medium containers
3 small containers, 12 medium containers
Landon babysits and works part time at tge water park over the summer. onw week, he babysat for 3 hours and worked at the water park for 10 hours and made 109$. the next week he babysat for 8 hours and worked at the water park for 12 hours and made 177$. how much does London make per hour at each job ?
1 define your variables ,- what are you solving for
2 set up equations - using the information given
3 solve the system using your method of choice
Answer:
Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.
Step-by-step explanation:
Let the amount made per hour in dollars for babysitting be = x
Let the amount made per hour in dollars at water park be = y
As per the condition, the equations form:
[tex]3x+10y=109[/tex] .......(1)
[tex]8x+12y=177[/tex] ......(2)
Multiplying (1) by 8 and (2) by 3, and subtracting (2) from (1), we get
[tex]44y=341[/tex]
=> y = 7.75
And [tex]3x+10(7.75)=109[/tex]
=> [tex]3x+77.5=109[/tex]
=> [tex]3x=109-77.5[/tex]
=> [tex]3x=31.5[/tex]
x = 10.5
Therefore, Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.
Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
which graph represents a circle with equation x2 + y2 = 9
Answer: The correct option is (B). Its image is attached below.
Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:
[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
Center, (h, k) = (0, 0) and radius, r = 3 units.
We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.
We see that the graph of the circle is same as the one provided in option (B).
Thus, option (B) is CORRECT.
You parents gave you $50 to take your brother and sister to the movies. Your ticket cost $7.25 and your siblings cost $4.25. If you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
Adults: 7.25
Seniors: 6.00
Children under 8: 4.25
Answer:
You bring home $14.25 with you.
Step-by-step explanation:
First we add the money spent in movie tickets and snacks.
Your ticket = $7.25
Brother's ticket = $4.25
Sister's ticket = $4.25
Soda and popcorn = $20.00
Total = 7.25 + 4.25 + 4.25 + 20.00 = $35.75
Your parents gave you = $50.00
You spent = $35.75
Balance = 50.00 - 35.75 = $14.25
You bring home $14.25 with you.
A bakery has prepared 320 ounces of bread dough. a machine will cut the dough into a loaf. the amount of d dough left after m minutes is given by the function d (m)=-5m+320. how many minutes will it take the machine to use all the dough? find a reasonable domain and range for this situation.
A. how many minutes will it take the machine to use all the dough?
We are given the formula:
d (m) = - 5 m + 320
To find for the value of m when all dough is used, we set d (m) = 0:
0 = - 5 m + 320
m = 320 / 5
m = 64 minutes
B. The domain is time and time can never be negative so it always starts at zero, so at time = 0, the range d (m) is:
d (m) = - 5 (0) + 320
d (m) = 320
The other domain and range is already described in (A.), when all dough is used up.
So the pair of reasonable domain and range is:
(0, 320), (64, 0)
Which gas is plotted using the y-axis on the right?
If the sum of six consecutive even integers is 390 what is the smallest of the six integers
how do i factor x^3+3x^2
find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)
Answer:
24 unit
Step-by-step explanation:
Given,
The vertices of the triangle ABC are,
A (1,1), B (7,1), and C (1,9),
By the distance formula,
[tex]AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}[/tex]
[tex]BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}[/tex]
[tex]CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}[/tex]
Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit
Find the measures of an angle and its complement if one angle measures 24 degrees
use the image above to write a conjecture about regular polygons and lines of symmetry
Using the formula for volume of a cone, express r in terms of V, h and pi
The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,
V = (1/3)(pi)(r^2)h
Dividing both sides of the equation by (1/3)(pi)(h) will give us,
3V/(pi)(h) = r^2
Taking the square-root of both sides,
r = sqrt(3V/(pi)(h))
Answer:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Step-by-step explanation:
We are given the following information in the question.
Using the formula for volume of cone, we have to express r in terms of V, h and pi.
Formula:
[tex]\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}[/tex]
Now, we have to evaluate r, the radius of cone.
Rearranging the terms, we have,
Working:
[tex]V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}[/tex].
Thus, r in form of V, h and pi can be written as:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Answer for 14 and 15 only
what 3 digits are in the ones/units period 4,083,817
what times what equals 108
12 times 9 = 108, 18 times 6 = 108, 27 times 4 = 108 and 36 times 3 = 108.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given that, what times what equals 108,
Below is a list of all the different ways that what times what equals 108.
12 times 9 equals 108
18 times 6 equals 108
27 times 4 equals 108
36 times 3 equals 108
54 times 2 equals 108
108 times 1 equal 108
Hence, 12 x 9 = 108. 18 x 6 = 108. 27 x 4 = 108. 36 x 3 = 108.
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There are multiple pairs of numbers that multiply to 108, such as 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, and 9 × 12. Therefore, any pair of these factors will correctly answer the question.
To determine what times what equals 108, we need to identify the factors of 108.
1 × 108 = 108
2 × 54 = 108
3 × 36 = 108
4 × 27 = 108
6 × 18 = 108
9 × 12 = 108
There are multiple pairs of numbers that, when multiplied together, equal 108. Therefore, any of these factor pairs are valid answers to the question.
For example, 9 times 12 or 6 times 18 are pairs that satisfy this condition.
Suppose a coin is tossed 12 times and there are three heads and nine tails. how many such sequences are there in which there are at least five tails in a row?
Lee works at a job where her pay varies directly with the number of hours she works. Her pay for 6.5 hours is 49.40. Write a direct variation equation relating lee's pay x to the hours worked y. Then find her pay if she works 25 hours in a week
Final answer:
The direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x. Lee's pay for working 25 hours in a week is $190.
Explanation:
Let's define the direct variation equation:
y = kx
We can substitute the information given in the question:
When x = 6.5, y = 49.40
49.40 = 6.5k
k = 49.40 / 6.5
k = 7.60
Therefore, the direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x.
To find Lee's pay if she works 25 hours, we can substitute x = 25 into the equation:
y = 7.60(25)
y = 190
Lee's pay for working 25 hours in a week is $190.
What key would you use is 10 students chose cartoons
Find the distance between A (0,1) and B (-4,6) to the nearest tenth
Isa's calculator displays a number as 7.3579 E8. What is this number in standard form? Enter your answer in the box.
∠E∠E and ∠F∠F are vertical angles with m∠E=9x+12m∠E=9x+12 and m∠F=3x+24m∠F=3x+24 .
What is the value of x?
Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F
Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24
Subtract both sides of the equation by 3x
6x + 12 = 24
Subtract 12 from both sides
6x = 12
Divide both sides by 6
x = 2
This should be your answer. Have an awesome day! :)
Elizabeth bought 4 drinks and some nachos. The nachos cost $6, and she spent a total of $18. How much did each drink cost? Use d to represent the cost of each drink. A. ; each drink cost $4. B. ; each drink cost $6. C. ; each drink cost $2. D. ; each drink cost $3.
Answer:
D. ; each drink cost $3
Step-by-step explanation:
Given that Elizabeth bought 4 drinks and some nachos.
Total amount spent = [tex]18[/tex]$
She can buy only in integers the drinks i.e.1,2,or 3
Nachos also she can buy 1,2...
If x is the no of nachos and d the cost of drink, we get
[tex]6x+4d=18[/tex]
If x=1, d =3
x=2, d = 1.50
d=3, d=0 (which is not possible)
Hence d can take values either as 3 or 1.50
Out of the options given 3 is only there.
D. ; each drink cost $3
twenty-two pencils cost $0.60 less than $5 what is the cost per pencil?
Karli's shadow is 60 inches long. A nearby fire hydrant casts a shadow 40 inches long. If Karli is 48 inches tall, what is the height of the fire hydrant?
Solve 6e^(x)-4e^(-x)=5. Solve for x and please describe how you got your answer.
For the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x, where a is a constant and a>1
It is given that,
6eˣ-4e⁻ˣ=5
Multiplying complete equation by eˣ
eˣ(6eˣ-4e⁻ˣ)=5(eˣ)
6(eˣ)(eˣ) - 4(e⁻ˣ)(eˣ) =5(eˣ)
6e²ˣ-4 = 5(eˣ)
6e²ˣ-5eˣ -4 = 0
Suppose y = eˣ
6y² - 5y -4 = 0
After solving the equation we get y = 4/3 and y = -1 / 2.As a result,
eˣ = 4/3
x = log(4/3)
x = 0.29
Thus, for the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
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?/48=7/8 what is the numerator
An auditor performs attribute sampling to test for proper cancellation of payment vouchers. in a sample population of 100, two vouchers are missing the proper cancellation, while one simply cannot be located. the error rate of the sample is