By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
A fighter plane, f, is told to intercept plane x which is 200 miles in front of f flying directly away from f at 500 mph. plane f is told it must intercept x in 6 minutes. how fast should f fly?
To intercept plane x, which is 200 miles in front and flying away at 500 mph, in 6 minutes, the fighter plane f should fly at 2500 mph.
Explanation:The question deals with the calculation of how fast the fighter plane (plane f) should fly in order to intercept plane x in the given time. This is essentially a problem in the physics concept of relative motion. Plane x is 200 miles away from f and is flying away at a speed of 500 mph. The fighter plane f has 6 minutes (or 0.1 hours) to intercept, which is the time needed to cover the distance between the planes. Recall the formula of velocity, v = d/t. Here, the distance d = 200 miles (distance between the planes), and t = 0.1 hours. Substituting these into the formula, we can calculate the necessary speed for plane f.
Additionally, since plane x is moving away from f at 500 mph, plane f must cover an additional 50 miles (500 mph * 0.1 hours) to intercept x. Therefore, the total distance f must cover is 250 miles (200 miles + 50 miles).
Substituting this into the formula of velocity, we find that f should fly at 2500 mph (250 miles / 0.1 hours) to intercept plane x in the allotted time.
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The fighter plane 'f' needs to fly at a speed of 2500 mph to intercept the escaping plane 'x' that is flying away at a speed of 500 mph and is currently 200 miles away.
Explanation:To solve this problem, we need to work with the concept of relative speed in the context of motion. Plane 'x' travels 500 miles per hour and the fighter plane 'f' needs to intercept Plane x in 6 minutes, which is 1/10th of an hour.
Since Plane x is 200 miles away, in the 1/10th of an hour, Plane x would have travelled an extra 50 miles (500 mph * 1/10), making the total distance Plane f needs to cover 250 miles (200 miles + 50 miles). To cover 250 miles in 1/10th of an hour or 6 minutes, Plane f needs to fly at a speed of 2500 mph (250 miles / 1/10 hr).
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The sum of the EXTERIOR angles of a pentagon equals 360°.
True
False
Answer:
TRUE
Step-by-step explanation:
sum of exterior angles of a pentagon equals 360°
hence,this statement is TRUE
what is the x for 3kx+24=9kx
The weight of water is 62 1/2 lb per cubic foot water that weighs 300 lb will fill how many cubic feet
The number of cubic feet will be 4.8
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given ,
The weight of water is 62 1/2 lb per cubic
Now,
Since, foot water that weighs = 300 lb
Hence, The cubic feet = 300/62.5
= 4.8
Thus, The number of cubic feet will be 4.8
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Final answer:
300 pounds of water will fill 4.8 cubic feet of space, calculated by dividing the total weight by the weight per cubic foot (300 lb / 62.5 lb/ft³).
Explanation:
The student is asking how many cubic feet of space would be filled by 300 pounds of water, given that water weighs 62 1/2 pounds per cubic foot. To find the answer, we divide the total weight of the water by the weight of water per cubic foot. In this case, we divide 300 lb by 62.5 lb/ft3 (since 62 1/2 pounds is the same as 62.5 pounds).
The calculation will be as follows:
Divide 300 lb by 62.5 lb/ft3.
300 lb / 62.5 lb/ft3 = 4.8 ft3.
Therefore, 300 pounds of water will fill 4.8 cubic feet of space.
Solve the equation−3=8x−4y for y
To solve the equation for y, rearrange the terms and isolate the variable y on one side of the equation.
Explanation:To solve the equation -3 = 8x - 4y for y, we need to isolate the variable y on one side of the equation. First, rearrange the terms:
8x - 4y = -3
Now, move the term with x to the right side by subtracting 8x from both sides:
-4y = -3 - 8x
Finally, divide both sides by -4 to solve for y:
y = (3 + 8x) / 4
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Calvin bought 20 pencils at $0.45 each. How much change did he get from a $10 bill?
Samuel pays $20 for a shirt that is on sale. If he saved $5, what is the percent of the discount?
Answer:
Step-by-step explanation:
So, If he saved $5 then we do $20 divided by $5 which gives 4 so now we split 100% into 4 pieces which gives us 25%.
If function f is defined by f x( ) = 3x2 − 5x + 4, what is f x( − 4) ?
The variance represents how the data is distributed around the mean
b. the variance is always equal to the mean squared (μ2)
c. the variance is negative whenever the mean of x is negative
d. the variance is the value of x that is most likely to occur in the data.
3. Which word choice supports the idea that the author has a positive point of view of rollerskating?
A.been around since the early 1700s
B.loved winter ice-skating
C.hard to roll
D.more popular
Answer The answer is B
Step-by-step explanation:
If sin theta = 12/13 and theta is an acute angle find cot theta
Answer:
cot θ = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
If sin θ = [tex]\frac{12}{13}[/tex] and 'θ' is an acute angle then we have to find the value of cotθ
From the figure attached.
y² + 12² = 13² [ by Pythagoras Theorem ]
y + 144 = 169
y² = 169 - 144 = 25
y = 5
Now cot θ = [tex]\frac{base}{Height}[/tex]
= [tex]\frac{y}{12}[/tex]
= [tex]\frac{5}{12}[/tex]
Therefore, cot θ =[tex]\frac{5}{12}[/tex] is the answer.
In a test of the microsort method of gender selection, 51 babies are born to couples trying to have baby boys, and 39 of those babies are boys. if the gender selection method has no effect of boys and girls find the mean and standard deviation for the number of boys born in groups of 51
Solve for the following equation 3+6z=13+6z
A.z=-5/6
B.z=2 2/3
C.infinitely many solutions
D.no solution
Answer:
D. No solution
Step-by-step explanation:
Since, if an equation after solving gives a true statement,
Then the equation has infinitely many solution,
While, after solving the equation,
We get, a false statement,
Then the equation has no solution,
Given equation,
3 + 6z = 13 + 6z
⇒ 3 = 13
Which is a FALSE statement,
Hence, the given equation has no solution.
OPTION D is correct.
what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
If KL = 2x, LM = 5x, and KM = 7, what is LM?
The perimeter of the square shown is 4(x+33) meters. What is the value of x if the perimeter is 28 meters
What is the range? Thanks
What is the value of the discriminant in the equation shown below? x^2-4x+10=0?
Answer:
The discriminant would be -24.
Step-by-step explanation:
Find the measure of each indicated angle
Answer:64
Step-by-step explanation:
36+84+x=180
x=180-120
x=60
right angle 90=x+y=60+y
y=90-60=30
y+86+?=180
30+86+?=180
?=180-116
?=64
A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. Which statement describes when the plans are based on the same number of aerobic exercise sessions?
A. Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
B. Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
C. Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
D. Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
A store sells a floor lamp for 73.99. The store is having a sale that reduces the lamps price by 35%.How much does the lamp cost during sale?
73.99 * 0.30 = 22.197 = $22.20
73.99 - 22.20 = 51.79
Lamp is $51.79
Write a complete two-column proof for following information.
Given: AB = 3y - 1, BC = 7y, AC = 29 Prove: AB = 8
its a normal line and the letters are in order ABC, B is kinda close to A
To prove AB = 8, we substitute the values given and show that the statement is false.
Explanation:To prove: AB = 8
Given: AB = 3y - 1, BC = 7y, AC = 29
Proof:
Since AB = 3y - 1 and AC = 29, we can substitute AC in place of AB in the equation AB = 3y - 1. This gives us 29 = 3y - 1.Simplifying the equation, we get 3y = 30.Dividing both sides of the equation by 3, we find y = 10.Substituting the value of y into AB = 3y - 1, we get AB = 3(10) - 1 = 30 - 1 = 29.Since AB = 29, we can see that AB is not equal to 8. Therefore, the given statement is false.Therefore, we cannot prove that AB = 8.
Please help!
Simplify (3/10)(-5/9).
A.) 1/6
B.) -1/6
C.) 77/90
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A rectangular fountain display has a perimeter of 400 feet and an area of at least 9100 feet. describe the possible widths of the fountain
What is the equation in slope intercept form of a line with a slope of 1/2 and y intercept of1?
What is the least common multiple of 12, 30 and 84?
Name the property the equation illustrates. 8 + 5.3 = 5.3 + 8 Inverse Property of Multiplication Inverse Property of Addition Associative Property of Addition Commutative Property of Addition
Answer:
The answer is : Commutative Property of Addition
Step-by-step explanation:
The communicative property of addition shows that "a + b = b + a".
The numbers can be written in any order, the result will be same.
The given terms are : 8 + 5.3 = 5.3 + 8
The solution for both are same; 13.3 = 13.3
So, this shows the commutative property of addition.
What is 30 divided by 1/2 ? A) 15 B) 20 C) 40 D) 60
15 points and brainliest -
E’F’G is the image of EFG under a dilation through point C.
What scale factor was used in the dilation?
A. -2
B. - 1/2
C. 1/2
D. 2
Answer:
For anyone else looking for the answer, the answer is actually, B. -1/2 I just did this test and got it right.