Answer:
(-7, 5)
Step-by-step explanation:
You want to know the image of the point (-4, -6) after reflection in the x-axis and translation 3 left and 1 down.
Composition of transformationsThe composition ...
[tex]T_{-3,-1}\circ r_{\text{x-axis}}[/tex]
is interpreted to mean reflection in the x-axis occurs first, then translation by (-3, -1).
That is, a composition of transformations is evaluated right to left.
ReflectionReflection in the x-axis moves a point from below the x-axis to the same distance above the x-axis. That is, the sign of the y-coordinate changes:
(-4, -6) ⇒ (-4, 6) . . . reflection in the x-axis
TranslationThe translation vector is added to the coordinates of the point:
(-4, 6) +(-3, -1) = (-4-3, 6-1) = (-7, 5)
The image of the point is located at (-7, 5).
Expand and simplify 4(2x - 1) + 3(2x + 5)
Answer:
14x+11
Step-by-step explanation:
Let L be the line that passes through the points with coordinates (1,1) and (-1,3).
(a) Determine the equation (in the form y = mx + b) of the line L.
(b) Determine the equation of the line K that passes through the (0, -1) and is perpen-
dicular to the line L.
(c) Find the coordinates of the point at which the lines and K intersect.
(a). The equation of the line L in the form of y = mx + b is y + 2x = 0.
(b). The equation of the line K that passes through the point (0, -1) and is perpendicular to the line L is y = 2x - 1.
(c). The intersection of the lines and K is located at a location with the coordinates (0,-1).
Define equation of line.The equation of a line has the usual form axe + by + c = 0. Here, x and y are the variables, a and b are the coefficients, and c is the constant term. You may also find and see the equation of a line in the slope-intercept form, point-slope form, two-point form, intercept form, and normal form.
The formula of slope is given by m = (y₂-y₁)/(x₂-x₁).
Here, m is the slope of the line.
(x₁, y₁) and (x₂, y₂) are the two points of the line.
Now put the value of x₁, y₁, x₂, y₂ in
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
m = [tex]\frac{3-1}{-1-1}[/tex]
m = 2/-1
m = -2
The slope of the line perpendicular is:
mₐ = - 1/m
mₐ = -1/-2
mₐ = 2
(a) The equation (in the form y = mx + b) of the line L.
(y-y₁) = m(x-x₁)
(y-1) = -2(x-1)
y-1 = -2x-1
y = -2x
y + 2x = 0
(b) The equation of the line K that passes through the (0, -1) and is perpendicular to the line L.
x = 0 and y = -1
y = mx + b
y = 2x + b
-1 = 2×0 + b
-1 = b
b = -1
Substituting the above in y = mx + b to get:
y = mx + b
y =2x + (-1)
y = 2x - 1
(c) The coordinates of the point at which the lines and K intersect.
y = 2x - 1
y+2x+1=0
(2x-1)+2x+1=0
4x =0
x = 0, y = -1
The intersection of the lines and K is located at a location with the coordinates (0,-1).
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Type an equation for the following pattern.
Can you please help me
Answer:1=a
2=b
3=c
Step-by-step explanation:
What are the coordinates for the image of the figure E(0,4), F(2,2), G(0,0), D(-4,3) if it has been dilated with a scale factor of 1/4
Answers:
E ' = (0, 1)
F ' = (0.5, 0.5)
G ' = (0, 0)
D ' = (-1, 0.75)
Notes: 0.5 = 1/2 and 0.75 = 3/4
================================================
Explanation:
Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25
For instance, the point E(0,4) moves to E ' (0, 1) since
x coordinate: 0*0.25 = 0y coordinate: 4*0.25 = 1Do the same for the other points.
Can someone help wit this problem I’m confused on it
Answer:
1/9
Step-by-step explanation:
When the quantities are proportional, you are able to find the constant of proportionality by y/x. If you take each one of the y's listed and divide it by x, you will get 1/9.
For example 1 2/9 ÷11
1 2/9 is the same at 9/9 + 2/9 or 11/9
[tex]\frac{11}{9}[/tex] ÷ 11 is the same as [tex]\frac{11}{9}[/tex] ÷ [tex]\frac{11}{1}[/tex] To divide with fractions, you multiply by the reciprocal.
[tex]\frac{11}{9}[/tex] x [tex]\frac{1}{11}[/tex] The 11 can cancel out and we are left with [tex]\frac{1}{9}[/tex]
Answer: r = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
y = rx
finding r (substitute y and x):
5 = r x 45
5/45 = r
r = [tex]\frac{5}{45} = simplify = \frac{1}{9}[/tex]
checking:
rx = y
[tex]\frac{1}{9}[/tex] x 11 = 1 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{9}[/tex] = 1 [tex]\frac{2}{9}[/tex]
convert mixed fraction into improper fraction
[tex]\frac{11}{9}[/tex] = [tex]\frac{11}{9}[/tex]
correct
A spherical tank has a capacity of 750 gallons. Using the fact that one gallon is about 0.1337 , find the radius of the tank to the nearest hundredth of a foot.
The radius of the spherical tank of capacity 750 gallons to the nearest hundredth is 2.88 ft.
How much s a gallon?
In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L[1] (231 cubic inches); and the US dry gallon ("usdrygal"), which is defined as 18 US bushel (exactly 4.40488377086 L).
Given data: 1 gallon ≈ 0.1337 ft³
Then, 750 gallons = 0.1337 x 750 ≈ 100.275 ft³
We know, Volume of sphere, [tex]V=\frac{4}{3}\pi r^{3}[/tex]
then, r = [tex]\sqrt[3]{\frac{3}{4\pi }V }[/tex]
= [tex]\sqrt[3]{\frac{3}{4\pi } 100.275}[/tex]
= [tex]2.88 ft.[/tex]
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An urn contains twenty chips, numbered 1 through
20. Two are drawn simultaneously. What is the probabil-
ity that the numbers on the two chips will differ by more
than 2?
The probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that an urn contains twenty chips, numbered 1 through 20. Two are drawn simultaneously.
Number of favorable outcomes = ( 4 - 2 ) , ( 3 - 1 ) , ( 6 - 4 ) , ( 10 - 8 ), ( 11 - 9 ), ( 7 - 5 ), ( 14 - 12), ( 15- 13 ) , ( 18 - 16 ), ( 19 - 17 ) = 10
Number of samples = 20
Probability = Number of favorable outcomes / Number of sample
Probability = 10 / 20
Probability = 1 / 2
Therefore, the probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).
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-10/17 divided by (-15/17)
Answer:
0.66
Step-by-step explanation:
Evalute f(x) = x² + 1 for f(10)
Answer:
101
Step-by-step explanation:
Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.
Hope this helps!
A passenger train's distance traveled is monitored over time. The results are displayed in this table.
Time (h)
2
3
4
5
Distance traveled (mi)
60
120
180
240
300
What is the constant of proportionality of this proportional relationship?
Enter your answer in the box.
Answer:
Step-by-step explanation:
60
On a map of the Thunderbird Country Club golf course, 1.5 inches equals 15 yards. How
long is the 15th hole if the map shows 17.5 inches?
175 yards long is the 15th hole if the map shows 17.5 inches.
hole = c yards
1.5 / 15 = 17.5 / c
1.5 c = 15 * 17.5
1.5 c = 262.5
c = 175 yards
A length unit equal to 36 inches, or 3 feet (see foot), in the United States Customary System, or 0.9144 metre in the International System of Units. A cloth yard is 37 inches long, and it was also the standard length for arrows.
The yard is an English unit of length that equals 3 feet or 36 inches in both the British imperial and US customary measurement systems. Since 1959, it has been standardized as 0.9144 meter by international agreement. One mile is equivalent to 1,760 yards. The survey yard in the United States is slightly longer.
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write in a number in which the value of the 8 is ten times greater than the value of the 8 in 8304?
Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.
Which number has the value of the 8 is ten times greater than the value of the 8 in 8304?It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.
It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.
Hence, an example of a number that is ten times greater is; 10 × 80,000.
Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.
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Jasmine received a $140 paycheck from her job at the supermarket today. If she spends $10 every day at Starbucks, in how many days will she have exactly $30 left? Represent and solve this problem by creating a table graph and equation.
Anumeha is mowing lawns for a summer job. For every mowing job, she charges an initial fee of $10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for instance, is $35
Let y represent Anumeha's fee (in dollars) for a single job that took x hours for her to complete.
The equation that can represent the fee for x hours is y = 10 + 5x.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
We have,
Initial fee = $10
Let the constant fee for each hour of work = M
Fee for 5 hours of work = $35
Every mowing job for 5 hours = Initial fee + constant fee for 5 hours
$35 = $10 + M x 5
35 = 10 + 5M
25 = 5M
M = 5
So,
If y represents Anumeha's fee (in dollars) for a single job that took x hours for her to complete.
We can write an equation as:
y = 10 + 5x
Thus the equation that can represent the fee for x hours is y = 10 + 5x.
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-Solve the system. y - 10=3x
(2y=6x+20
infinite solutions
no solution
(10,40)
(2,13)
Step-by-step explanation:
[tex]y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20[/tex]
you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.
(LOTS OF POINTS ANSWE FAST) multiply (5 4/7) (-2 2/5)
Answer:
-13 13/35
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation: Just took it
Factor 2x² + 8x - 90 completely.
O a
Ob
OC
Od
(2x +9)(x - 5)
(2x-9)(x - 5)
2(x + 9)(x - 5)
2(x-9)(x - 5)
A
Please helppp
Factors of the polynomial 2x² + 8x - 90 is Option (c) 2(x + 9)(x - 5).
What is Factorization?Factorization is the method used to discover the factors of a given value or mathematical statement. A factor is an integer that is multiplied by another to create the original number. For instance, 2, 3, 6, 9, and 18 are the factors of 18. Likewise, in the case of polynomials, the factors are the polynomials that are multiplied to create the initial polynomial.
Given Equation: 2x² + 8x - 90
Step 1: Pull out like factors from the equation
⇒ 2x² + 8x - 90 = 2 • (x² + 4x - 45)
Step 2: Factorize by splitting the middle term of the equation (x² - 4x - 45)
⇒ x²+ 9x - 5x - 45
Step 3: Take Common factors from the two pairs of the equation
⇒ x(x + 9) - 5(x + 9)
Step 4: Rewrite the polynomial in factored form
⇒ 2(x + 9)(x - 5)
Therefore the factorization result is 2(x + 9)(x - 5).
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I need help! Can someone help me with these problems please!
Regarding the average rate of change of the function, it is found that:
a) 245 habitants per year between 1998 and 2001.
b) The average rate of change was of -328.5 habitants per year between 2002 and 2004.
c) The rate of population increase was greater between 1998 and 2001.
d) The rate of population decrease was greater between 2002 and 2004.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
In 1998 the population was of 856.In 2001 the population was of 1591.Hence the rate is:
(1591 - 856)/3 = 245.
The average rate of change was of 245 habitants per year between 1998 and 2001.
For item b, we have that:
In 2002 the population was of 1483.In 2004 the population was of 826.Hence the rate is:
(826 - 1483)/2 = -328.5.
The average rate of change was of -328.5 habitants per year between 2002 and 2004.
Hence:
c) The rate of population increase was greater between 1998 and 2001.
d) The rate of population decrease was greater between 2002 and 2004.
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Yossi used to have a square garage with 250 ft 2 of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answer:
5√10 ≈ 15.81 ft5√15 ≈ 19.36 ft22.47%Step-by-step explanation:
You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.
Side lengthThe area of a square is given by the formula ...
A = s²
Solving for the side length (s), we find ...
s = √A
The side length of a square with 250 ft² area is ...
s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length
The area of a square that has 50% more area is ...
(250 ft²) × (1 +50%) = 375 ft²
The side length of that square is ...
√375 ft = 5√15 ft ≈ 19.36 ft . . . side length
Percentage changeThe percentage change can be found from ...
percentage change = ((new value)/(old value) -1) × 100%
= ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%
The percentage increase in the length of one side is about 22.47%.
A tower has a revolving restaurant 785 feet above the ground. The restaurant makes a
complete revolution every 90 minutes. While a visitor was at the tower, the restaurant
rotated through 82°. How long was the visitor at the tower?
The visitor was at the tower for ______
minutes.
Answer:
1 revolution is 360 degrees
1 hour = 60 minutes
360/60 = 6
so it rotates 6 degrees every minute
135/6 = 22.5 minutes
cual es el resultado de y=−2x+5
Answer:3
Step-by-ste
la respuesta es 3 porque si sumas -2x a 5 pues -2 es. un numero negativo y 5 es positivo restas 5-2 y obtienes 3
The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation’s central office during the year. A random sample of 25 clerical workers reveals the following: Absenteeism: days, days. 12 clerical workers were absent more than 10 days. Construct a 95% confidence interval estimate for the mean number of absences for clerical workers during the year. Interpret. (Assume that the population is normally distributed)
The 95% confidence interval estimate for the mean number of absences for clerical workers during the year is (8.132, 11.268).
What is confidence interval?It should be noted that the mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given a = 0.05, Z(0.025) = 1.96 (from standard normal table).
The 95% confidence interval will be:
xbar +/- Z*s/vn
= 9.7 +/- 1.96*4/✓(25)
= (8.132, 11.268)
Therefore, the 95% confidence interval is (8.132, 11.268).
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A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
find the value of x.
find length of the longest side.
Step-by-step explanation:
perimeter=s+s+s
p=x/2+x-5+x-2
13=x/2+x-5+x-2
26=x+x+x-10-4
26=3x-14
26+14=3x
3x/3=40/3
x=13.3cm
b.
x/2=6.65
x-5=8.3
x-2=11.3
longest side=11.3cm
Please help me! I have a fe of this for me to finish my homework! Please
I=Prt. You borrow $10,000 from the bank at a 8% rate for 5 years. Find
the simple interest you will pay on this loan.
Answer:14 000
Step-by-step explanation:
Simple interest formula: A=P(1+in)
A= amount after interest is added
P= initial amount (10000)
i= interest rate (8%)
n= number of periods (5 years)
Now substitute what you have into the simple interest formula:
A=P(1+in)
A=10000(1+(8/100)(5))
A= 14 000
The reason why 8 is divided by 100 is that 8 is a percentage. Unless you have a percentage function on your calculator, I'd strongly encourage you to ALWAYS divide your percentages by 100.
what is an equivalent fraction for 6/10
Answer:
3/5, 9/15 - some equivalent fractions for 6/10
Suppose a deep sea diver dives from the surface to 206 feet below the surface. He then dives down 18 more feet. Use integers to represent this situation. Then find the diver's present depth. (Simplify)
Answer:
Step-by-step explanation:
You are buying a house and will borrow $330,000 on a 25-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.15 percent. Alternatively, she tells you that you can “buy down” the interest rate to 3.8 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points
What is the desired annual percentage rate for the borrower?
The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%
difference in interest rate=4.15%-3.8%
difference in interest rate=0.35%
We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point
number of points required to buy down interest=1 point*0.35%
number of points required to buy down interest=0.350
In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%
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4 friends buy 16 pizzas. Each pizza is cut into
12 pieces. Each person eats the same number
of pieces.
How many pieces does each person eat?