The new function after the parent function f(x)=2^(x) is horizontally shrunk by a factor of two, translated right by 10 and translated 5 units down is f(x) = 2^((x-10)/2) - 5.
- Horizontal shrink by a factor of two: This means that the x-value of each point on the graph will be divided by 2. To achieve this, we can multiply the x-value inside the function by 1/2, or divide it by 2. So, the function becomes
f(x) = 2^((x/2))
- Translation right by 10: This means that the entire graph will shift 10 units to the right. To achieve this, we can subtract 10 from the x-value inside the function. So, the function becomes
f(x) = 2^((x-10)/2)
- Translation 5 units down: This means that the entire graph will shift 5 units down. To achieve this, we can subtract 5 from the entire function. So, the function becomes
f(x) = 2^((x-10)/2) - 5
Therefore, the new function is f(x) = 2^((x-10)/2) - 5
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f(x)=x^4−19x^3+135x^2+2 - Fias the toe crical nambers a,b of f′ (that is. the values at which f′′′ is zero or undetined) and lat thoir euact values in the fiet colume of the tibie below (n ancendeng order, a
Local Minima is 5 and 80
The critical numbers, a and b, of f'(x)=x^4−19x^3+135x^2+2 can be found by setting the derivative f'(x) = 0 and solving for x.
The derivative is: f'(x) = 4x^3 − 57x^2 + 270x
By setting the derivative equal to 0, we get:
4x^3 − 57x^2 + 270x = 0
Solving for x, we get:
x = 0, x = 5, x = 9
The critical numbers of f'(x) are 0, 5 and 9. The second derivative f''(x) is undefined at x = 0, so this is a local maximum point, while x = 5 and 9 are local minimum points.
Table:
Critical number | Second derivative (f''(x)) | Value
0 | Undefined | Local Maximum
5 | -80 | Local Minimum
9 | 80 | Local Minimum
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7. Use a half-angle identity to find each exact value. a. sin 195 b. cos 165
8. Find the following: a. cos θ/2 given sin θ = - 4/5 with 180º < θ < 270º. b. cot θ/2, given tan θ = - √5 / 2 with 90° < θ < 180°.
The exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.
To find the exact value of sin 195 and cos 165 using a half-angle identity, we need to use the following formulas:
sin(x/2) = √[(1-cosx)/2] and cos(x/2) = √[(1+cosx)/2]
For sin 195, we can use the half-angle identity for sine:
sin(195/2) = sin(97.5) = √[(1-cos195)/2] = √[(1+0.9063)/2] = √(0.9532) = 0.9763
For cos 165, we can use the half-angle identity for cosine:
cos(165/2) = cos(82.5) = √[(1+cos165)/2] = √[(1-0.2588)/2] = √(0.3706) = 0.6088
For question 8, we can use the given values and the half-angle identities to find the exact values of cos θ/2 and cot θ/2.
For cos θ/2 given sin θ = -4/5 with 180º < θ < 270º, we can use the half-angle identity for cosine:
cos(θ/2) = √[(1+cosθ)/2] = √[(1+√(1-sin^2θ))/2] = √[(1+√(1-(-4/5)^2))/2] = √[(1+√(1-(16/25)))/2] = √[(1+√(9/25))/2] = √[(1+(3/5))/2] = √(0.8) = 0.8944
For cot θ/2 given tan θ = -√5/2 with 90° < θ < 180°, we can use the half-angle identity for cotangent:
cot(θ/2) = (1+cosθ)/sinθ = (1+√(1-sin^2θ))/sinθ = (1+√(1-(1/tan^2θ)))/(1/tanθ) = (1+√(1-(1/(-√5/2)^2)))/(-√5/2) = (1+√(1-(4/5)))/(-√5/2) = (1+√(1/5))/(-√5/2) = (1+(1/√5))/(-√5/2) = (1-(1/√5))/(-√5/2) = -0.2764
Therefore, the exact values are sin 195 = 0.9763, cos 165 = 0.6088, cos θ/2 = 0.8944, and cot θ/2 = -0.2764.
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Ms.lang borrows $2,300 for 30 months at 13% interest per year. How much interest will ms.lang pay? What is the total amount she will repay?
Answer:
The formula to calculate simple interest is:
I = Prt
Where I is the interest, P is the principal amount borrowed, r is the interest rate per period, and t is the time period.
Using this formula, we can calculate the interest Ms. Lang will pay as follows:
I = Prt
I = 2300 * 0.13 * (30/12)
I = $975
Therefore, Ms. Lang will pay $975 in interest over the 30-month period.
To calculate the total amount she will repay, we need to add the interest to the principal amount borrowed:
Total amount = Principal + Interest
Total amount = $2300 + $975
Total amount = $3275
Therefore, Ms. Lang will repay a total of $3275, which includes the $2300 principal and $975 interest.
now, we're assuming this is on a simple interest rate, so hmm say a year has 12 months, so 30 months will just be 30/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2300\\ r=rate\to 13\%\to \frac{13}{100}\dotfill &0.13\\ t=years\to \frac{30}{12}\dotfill &\frac{5}{2} \end{cases} \\\\\\ I = (2300)(0.13)(\frac{5}{2}) \implies I = 747.5~\hfill \underset{ \textit{amount to be repaid} }{\stackrel{ 2300~~ + ~~747.5 }{\text{\LARGE 3047.5}}}[/tex]
Hellllllllllllllllp meeeeeeeeeeeee
Answer: Option B is the correct answer
Step-by-step explanation:
Area of lateral surface = 3 x Area of rectangle
The rectangle is of 5 inches wide and 14 inches long.
Area of rectangle = 5 x 14 = 70 square inches
Area of lateral surface = 3 x Area of rectangle
Area of lateral surface = 3 x 70 = 210 square inches
Option B is the correct answer.
Find the relative maxima and minima, if any, of the function or
DNE. f(x) = x + 9/x + 5
The relative maxima.
To find the relative maxima and minima of the function f(x) = x + 9/x + 5, we need to first find the derivative of the function.
The derivative of f(x) is f'(x) = 1 - 9/x^2.
Next, we need to set the derivative equal to zero and solve for x to find the critical points.
1 - 9/x^2 = 0
9/x^2 = 1
x^2 = 9
x = ±3
So, the critical points are x = 3 and x = -3.
To determine if these are relative maxima or minima, we need to use the second derivative test.
The second derivative of f(x) is f''(x) = 18/x^3.
Plugging in x = 3, we get f''(3) = 18/27 = 2/3, which is positive. This means that x = 3 is a relative minima.
Plugging in x = -3, we get f''(-3) = 18/-27 = -2/3, which is negative. This means that x = -3 is a relative maxima.
Therefore, the relative maxima is at x = -3 and the relative minima is at x = 3.
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A blue print of a house has a scale of 1. 5 in 5 feet would a ping pong table that is 9 feet by 5 feet fit in a space that has a drawing dimensions of 3 inches and 4. 8 inches if so how much space in feet square will remain after the table is put in the room
There will be about 111.25 square feet of space remaining in the room after the ping pong table is put in.
First, we need to convert the scale of the blueprint to a real-world scale. Since the scale is 1.5 in 5 feet, we can write this as:
1.5 inches : 5 feet
To convert this to a ratio that we can use, we can divide both sides by 1.5 inches:
1 inch : 3.33 feet
Now we can use this ratio to convert the dimensions of the room from the blueprint to real-world dimensions:
3 inches x 3.33 feet/inch = 9.99 feet
4.8 inches x 3.33 feet/inch = 15.96 feet
So the room is approximately 10 feet by 16 feet.
Next, we need to see if the ping pong table will fit in the room. The table is 9 feet by 5 feet, which means it needs at least a space of 9 feet x 5 feet = 45 square feet. To convert this to the scale of the blueprint, we can use the inverse of the ratio we calculated earlier:
1 foot : 1/3.33 inches
So the table needs at least a space of 9 feet x (1/3.33 inches/foot) = 27 inches by 5 feet x (1/3.33 inches/foot) = 15 inches on the blueprint.
The space in the room is 3 inches x 4.8 inches on the blueprint, which is equivalent to 3 inches x (1/1.5 inches/foot) = 2 feet and 4.8 inches x (1/1.5 inches/foot) = 1 foot 7.8 inches in real-world dimensions.
Since the table will fit on the blueprint, we can now calculate the remaining space in the room. The total area of the room is approximately 10 feet x 16 feet = 160 square feet.
The area taken up by the ping pong table is approximately 9 feet x 5 feet = 45 square feet, or 27 inches x 15 inches on the blueprint. To convert this to square feet, we can use the ratio we calculated earlier:
27 inches x (1/12 feet/inch) x 15 inches x (1/12 feet/inch) = 3.75 square feet
So the remaining space in the room is approximately 160 square feet - 45 square feet = 115 square feet - 3.75 square feet
= 111.25 square feet.
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Use simple interest to find the ending balance.
$36,000 at 6.3% for 4 years
Answer:
$45072
Step-by-step explanation:
I = Prt
I = 36000(6.3/100)(4)
I = 9072
ending balance = 36000 + 9072
= 45072
60 students went on a school trip to the zoo. 32 of the students bought a packed lunch
From the given information provided, the number of students who brought a packed lunch and did not visit the gift shop is 32.
The number of students who brought a packed lunch and did not visit the gift shop can be calculated by subtracting the number of students who visited the gift shop from the number of students who bought a packed lunch:
32 - 0 = 32
A frequency tree is a visual representation of data that shows how the total number of individuals or items is distributed among different categories or groups. It is commonly used in statistics and probability to organize and analyze data in a hierarchical structure.
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If k is a real number, then the vectors(1,k),(k,3k+18)are linearly independent precisely whenk=a,b, wherea=,b=, anda
The vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.
If k is a real number, then the vectors (1,k), (k,3k+18) are linearly independent precisely when k≠a,b, where a=-18 and b=1/3. This is because for the vectors to be linearly independent, the equation c1(1,k) + c2(k,3k+18) = (0,0) should only have the trivial solution of c1 = c2 = 0. If k = a or k = b, then there will be nontrivial solutions for c1 and c2, making the vectors linearly dependent.
To find the values of a and b, we can set the equations for the x and y components equal to 0 and solve for k:
c1 + c2k = 0
c1k + c2(3k+18) = 0
From the first equation, we can solve for c1 in terms of c2 and k:
c1 = -c2k
Substituting this into the second equation:
-c2k^2 + c2(3k+18) = 0
c2(-k^2 + 3k + 18) = 0
Since c2 cannot be 0, we can divide both sides by c2 and solve the quadratic equation for k:
-k^2 + 3k + 18 = 0
(k-1/3)(k+18) = 0
So k = 1/3 or k = -18. Therefore, the vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.
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Darcy gave her beauty technician a $4.80 tip. The tip was 5% of the cost of the procedure. Write an equation to find b, the cost of the procedure.
Therefore , the solution of the given problem of equation comes out to be required equation is 0.05b = 4.80 .
How do equations operate?Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection integer between each sign part and the number of lines. The significance of a symbol usually contradicts itself.
Here,
The following equation can be set up to represent the circumstance if x is the procedure's cost:
=> 5% of x = $4.80
The percentage must first be divided by 100 to become a decimal before we can answer for x:
=> 0.05x = $4.80
Then, by dividing both lines by 0.05, we can separate out x:
=> x = $96
Consequently, the process will cost you $96. It is possible to confirm that the gratuity is 5% of $96:
=> 5% of $96 = 0.05 × $96 = $4.80
So, the solution is:
=> 0.05b = 4.80
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The owner of a beverage company wants to determine whether two of his machines are filling bottles with the correct amount of liquid. He randomly selects 20 bottles filled by each of the two machines and measures the number of ounces that the bottles contain. The histograms below show the data. If the machines are designed to dispense between 5 and 6 ounces into a bottle, which machine appears to be doing a better job? Explain how you determined your answer.
Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.
What is histogram?The most common graph for displaying frequency distributions is a histogram.
To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.
Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.
Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.
This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.
Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.
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Your question seems incomplete, the probable complete question is:
Mr. Ling is adding a pond in the shape of a semicircle in his backyard. What is the area of the pond? Use 3.14 for n. Round to the nearest
hundredth if necessary.
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ft²
Check Answer
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The area of the pond after rounding to the nearest hundredth is 39 feet²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
To find the area of a semicircle, we need to first find the radius of the pond.
Let's assume the diameter of the pond is 10 feet.
Since a semicircle is half of a circle, the radius of the pond is half the diameter, which is 5 feet.
Now we can use the formula for the area of a semicircle, which is:
A = (1/2)πr²
where A is the area and r is the radius.
Plugging in the values, we get:
A = (1/2) × 3.14 × 5²
A = 39.25
Rounding to the nearest whole number, the area of the pond is approximately 39 square feet.
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∟A= 7x + 24° , ∟B = 3x + 92° Solve for x and then find the measure of ∟A:
∟A=_____°
Measure of ∟A is 119°
To solve for x, we must use the fact that the angles have the same measure, so ∟A = ∟B.
Substitute 7x + 24° for ∟A and 3x + 92° for ∟B and set them equal to each other:
7x + 24° = 3x + 92°
Subtract 3x from both sides:
7x - 3x = 92° - 24°
4x = 68°
Divide both sides by 4 to solve for x:
x = 17°
Now that we have x, we can substitute 17° for x into the original equation for ∟A to find its measure:
∟A = 7x + 24°
∟A = 7(17°) + 24°
∟A = 119°
Therefore, the measure of ∟A is 119°.
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Help me. giving brainliest!!!
Answer: 709 milliliters
Step-by-step explanation:
It is just the sum of the numbers so,
236 + 473 = 709
709 milliliters
Hope this helps!
Answer:
709 millimeters
Step-by-step explanation:
Add it up 236 = 473 = 709
100 POINTS!! I posted 2 math questions worth 50 points! Please help! :)
Where are the questions?
need help by tonight please help me
Keith who runs a daycare center bought 14 gallons of paint to do up the classroom how many classrooms can he get painted in all if each room requires 7/4 gallons of paint
Answer:
Keith bought 14 gallons of paint, and each classroom requires 7/4 gallons of paint.
To find how many classrooms can be painted, we can divide the total amount of paint by the amount of paint needed per classroom:
14 ÷ (7/4) = 8
Therefore, Keith can paint 8 classrooms in total.
The quotient of x and 3 plus 24 PLEASE HELP
Answer:
(24 divided by 3) + x
Step-by-step explanation:
i did it
I REALLY NEED HELP ON THESE QUESTIONS!
The surface areas of these cylinders are 75.39 cm, 835.76 cm, 1324.11 cm, and 3543.71 cm.
How to calculate the surface area of a cylinder?The surface area of a cylinder can be calculated by using the formula 2π r h + 2π r², which means we need the radius and the height to calculate the area. Let's now use this formula to know the area of each cylinder:
Cylinder 1:
2π 2 4+ 2π 2² = 75.39 cm
Cylinder 2:
2π 7 12+ 2π 7² = 835.76 cm
Cylinder 3:
2π 8.2 17.5+ 2π 8.2² = 1324.11 cm
Cylinder 4:
2π 12 35 + 2π 12r² = 3543.71 cm
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Helpppp pleasee ill give everything please see the photo (find the missing angle. Round to the nearest degree
Answer:
64.15°
Step-by-step explanation:
here
theta = 64.15°
( solution in picture)
The cargo bed of a commercial truck is shaped like a rectangular prism. The dimensions are shown. Billy has 80 cubic meters of mulch to take to his house. How many trips will he have to make until all the mulch is at his house?
Answer:
We need to find out how many trips Billy needs to make to transport 80 cubic meters of mulch. Since we know the dimensions of the cargo bed, we can find its volume and then divide the total volume of mulch by the volume of the cargo bed to find the number of trips.
The volume of the cargo bed is:
V = l × w × h
where l is the length, w is the width, and h is the height. Using the dimensions given in the diagram, we get:
V = 4 m × 2.5 m × 1.5 m = 15 cubic meters
Now we can divide the total volume of mulch by the volume of the cargo bed to find the number of trips:
Number of trips = total volume of mulch / volume of cargo bed
Number of trips = 80 cubic meters / 15 cubic meters ≈ 5.33
Since Billy cannot make a fractional number of trips, he will need to make 6 trips to transport all the mulch to his house.
LetP(x)=10x5−35x4+22x3+13x2+4x+4. (a) Use the Rational Roots Theorem to find all possible rational roots ofP(x). LetP(x)=10x5−35x4+22x3+13x2+4x+4. (b) Find all roots ofP(x)
The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.
To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.
We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.
In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.
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if tan t = 11/7 and 0≤ t≤????/2 find sin t, cost, csc t, sect, and cott. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter √2. sin t = cos t = csc t = sec t = cot t =
The hypotenuse is sqrt(11^2 + 7^2) = sqrt(170). Then, sin t = 11/sqrt(170), cos t = 7/sqrt(170), csc t = sqrt(170)/11, sec t = sqrt(170)/7, and cot t = 7/11.
Since we know that tan t = 11/7, we can use the Pythagorean identity (sin^2 t + cos^2 t = 1) to find the other trigonometric functions. First, we will find sin t and cos t:
tan t = 11/7 = opposite/adjacent = sin t/cos t
sin t = 11*cos t
cos t = 7*sin t
Substituting the second equation into the first equation:
sin t = 11*(7*sin t)
sin^2 t = 121*sin^2 t
121*sin^2 t - sin^2 t = 0
120*sin^2 t = 0
sin^2 t = 0/120
sin^2 t = 0
sin t = 0
Since sin t = 0, cos t = 1. Now we can find the other trigonometric functions:
csc t = 1/sin t = 1/0 = undefined
sec t = 1/cos t = 1/1 = 1
cot t = 1/tan t = 1/(11/7) = 7/11
So, the values of the trigonometric functions are:
sin t = 0
cos t = 1
csc t = undefined
sec t = 1
cot t = 7/11
Note: Another way to find the values of the trigonometric functions is to use the Pythagorean Theorem to find the hypotenuse of the right triangle with sides 11 and 7.
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The box plots display the math scores for two 7th grade math classes. which statement is best supported by the information in the box plots? A, the range for Mrs. Morales‘s class is greater than the range for Mr. Florez‘s class  B, the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales‘s class C, the median score for Mrs. Morales’s class is equal to the median for Mr. Flores’s class  D, the interquartile range for Mr. Flores‘s class is greater than the interquartile range for Mrs. Morales‘s class 
Therefore, the best statement supported by the information in the box plots is statement B, "the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales's class."
What is box plot?A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of numerical data. It displays the five-number summary of a dataset, which includes the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.
Here,
From the box plots, we can make the following observations:
A) The range for Mrs. Morales's class appears to be 100-50 = 50.
The range for Mr. Florez's class appears to be 95-55 = 40.
Therefore, statement A is not supported by the information in the box plots.
B) The box plot for Mr. Flores's class is more symmetrical than the box plot for Mrs. Morales's class, which is skewed to the left.
Therefore, statement B is supported by the information in the box plots.
C) The median score for Mrs. Morales's class appears to be between 70 and 75.
The median score for Mr. Florez's class appears to be between 75 and 80.
Therefore, statement C is not supported by the information in the box plots.
D) The interquartile range for Mrs. Morales's class appears to be between 60 and 80, which is a range of 20.
The interquartile range for Mr. Florez's class appears to be between 65 and 85, which is also a range of 20.
Therefore, statement D is supported by the information in the box plots.
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The average length of an official chess table in the International Chess Federation is 110 centimeters (cm)
with a tolerance of 16.5 cm. If c is the length of the chess table and V is the variation from 110 cm, the
function V(c) = |c-110| can be used to find the amount of variation.
Complete the statements by typing decimal values in the blank spaces.
Answer:
1. What is the maximum length of a chess table that is still within the tolerance limit?
To find the maximum length of a chess table that is still within the tolerance limit, we add the tolerance to the average length:
110 cm + 16.5 cm = 126.5 cm
Therefore, the maximum length of a chess table that is still within the tolerance limit is 126.5 cm.
2. What is the minimum length of a chess table that is still within the tolerance limit?
To find the minimum length of a chess table that is still within the tolerance limit, we subtract the tolerance from the average length:
110 cm - 16.5 cm = 93.5 cm
Therefore, the minimum length of a chess table that is still within the tolerance limit is 93.5 cm.
Step-by-step explanation:
Martina can run 3 miles without stopping. Last year she could run 3,640 yards witho stopping. How many more feet can Martina
Martina can run 4,920 more feet this year compared to last year.
Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.
First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.
1 mile = 5,280 feet
1 yard = 3 feet
So, 3 miles = 3 x 5,280 feet = 15,840 feet
And, 3,640 yards = 3,640 x 3 feet = 10,920 feet
Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.
15,840 feet - 10,920 feet = 4,920 feet
Therefore, Martina can run 4,920 more feet this year compared to last year.
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What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14-37
The intersection set, A∩ B, of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 } is equals to the { 6, 14}.
For any two sets A and B, the intersection, A∩ B (read as A intersection B) lists all the elements that are present in both sets, and are the common elements of A and B. The intersection of sets is denoted by the symbol '∩'. It is subset of both of sets, A and B. For example, if Set A = {1,2,3,4,5} and Set B
= {3,4,6,8}, A ∩ B = {3,4}.
Here, we have two sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14 }
The common elements in sets A and B
= { 6,14 }
Therefore, the intersection of A and B,
A ∩ B = { 6, 14}.
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Complete question:
What is the intersection of the sets A = {2, 5, 6, 14, 16} and B = {1, 3, 6, 8, 14}?
2. Kim, Doug, and Conner all run on the cross country team. In the last race Doug finished first, Kim finished 3 minutes after Doug, and Conner finished with a time that was twice Doug’s time.
a. What is the sum of their times?
b. What property or properties did you use?
c. Evaluate the expression if Doug ran the race in 27 minutes.
a) The sum of their times is of 4x + 3.
b) The property used is the combination of like terms, which we use to add the terms with the variable x.
c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.
How to obtain the expression?Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:
D = x.
Kim finished 3 minutes after Doug, hence:
K = D + 3
K = x + 3.
Conner finished with a time that was twice Doug’s time, hence:
C = 2x.
Then the total time is given as follows:
T = D + K + C
T = x + x + 3 + 2x
T = 4x + 3.
If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:
T = 4 x 27 + 3
T = 111 minutes.
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Need help with dilation & reflection! asap would be great :)
The value of image of coordinates of triangle ABC are,
A' = (4, - 4)
B' = (5 - 1)
C' = (1, - 3)
And, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,
D' = (- 15, 6)
E' = (- 12, 12)
F' = (- 6, 12)
G' = (- 9, 6)
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Reflect the triangle ABC across the line y = x
And, Dilate DEFG by a scale factor of 3 about (- 5, 5).
Now,
We know that;
The rule of reflection across the line y = x is,
(x, y) → (y, x)
Thus, The value of coordinates of triangle ABC are,
A = (- 4, 4)
B = (- 1, 5)
C = (- 3, 1)
Hence, The image of coordinates of triangle ABC are,
A' = (4, - 4)
B' = (5 - 1)
C' = (1, - 3)
And, The coordinates of DEFG are,
D = (- 5, 2)
E = (- 4, 4)
F = (- 2, 4)
G = (- 3, 2)
Hence, After dilate DEFG by a scale factor of 3 about (- 5, 5) is,
D' = (- 5x3, 2x3) = (- 15, 6)
E' = (- 4x3, 4x3) = (- 12, 12)
F' = (- 2x3, 4x3) = (- 6, 12)
G' = (- 3x3, 2x3) = (- 9, 6)
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i need help with finding the domain and range for this will give brainliest
For the given function we have:
domain [0, 76,867] and range [$0, $12,375,587]
How to find the domain and range?We know that x represents the number of people in atendance, then:
R(x) = 161*x
Represents the revenue.
The domain is the set of possible inputs, and it will go between 0 and 76,867 (total number of seats).
The range will go between:
R(0) = 161*0 = 0
R(76,867) = 76,867*161 = 12,375,587
Then the domain is all the integers in [0, 76,867] and the range is [$0, $12,375,587]
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