Answers
Answer:
The graph in the attached figure ( is the third option)
Step-by-step explanation:
we have the compound inequality
[tex]-18> -5x+2\geq -48[/tex]
Divide the compound inequality in two inequalities
[tex]-18> -5x+2[/tex] -----> inequality A
[tex]-5x+2\geq -48[/tex] -----> inequality B
Step 1
Solve inequality A
[tex]-18> -5x+2[/tex]
[tex]-18-2> -5x[/tex]
[tex]-20> -5x[/tex]
Multiply by -1 both sides
[tex]20<5x[/tex]
[tex]4<x[/tex]
Rewrite
[tex]x > 4[/tex]
The solution of the inequality A is the interval ------>(4,∞)
Step 2
Solve the inequality B
[tex]-5x+2\geq -48[/tex]
[tex]-5x\geq -48-2[/tex]
[tex]-5x\geq -50[/tex]
Multiply by -1 both sides
[tex]5x\leq 50[/tex]
[tex]x\leq 10[/tex]
The solution of the inequality B is the interval -----> (-∞,10]
therefore
The solution of the compound inequality is
(4,∞) ∩ (-∞,10]=(4,10]
All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)
The solution in the attached figure
Related Questions
please help anyone.
Answers
Answer:
- [tex]\frac{27}{7}[/tex]
Step-by-step explanation:
Given
f(x) = [tex]\frac{3}{x+2}[/tex] - [tex]\sqrt{x-3}[/tex]
Evaluate f(19) by substituting x = 19 into f(x)
f(19) = [tex]\frac{3}{19+2}[/tex] - [tex]\sqrt{19-3}[/tex]
= [tex]\frac{3}{21}[/tex] - [tex]\sqrt{16}[/tex]
= [tex]\frac{1}{7}[/tex] - 4
= [tex]\frac{1}{7}[/tex] - [tex]\frac{28}{7}[/tex] = - [tex]\frac{27}{7}[/tex]
why is .3 repeating a rational number
Answers
Answer:
.333333... can be expressed as 1/3.
Step-by-step explanation:
A rational number is defined as:
any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
aka, any number that you can express as a fraction.
Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.
If you didn't know this, don't worry. You'll get it soon enough.
Hope this helped!
find the perimeter of a triangle with side lengths of 16.3 CM 18.75 cm and 24.2 centimeters.
Answers
Answer:
59.25 cm
Step-by-step explanation:
The perimeter means the sum of all the sides of a figure.
The perimeter of a triangle would be sum of all 3 sides (triangle has 3 sides).
The measure oof 3 sides are given, so we just need to add them to get the perimeter.
Perimeter = 16.3 + 18.75 + 24.2 = 59.25 cm
To find the perimeter of the triangle, add the side lengths of 16.3 cm, 18.75 cm, and 24.2 cm to get a total of 59.25 cm. The formula used is simple addition of all side lengths.
To find the perimeter of a triangle, you need to add up the lengths of all its sides. The side lengths given are 16.3 cm, 18.75 cm, and 24.2 cm.
First, add the length of the first side: 16.3 cm + 18.75 cm = 35.05 cm.Second, add the length of the second side to the sum: 35.05 cm + 24.2 cm = 59.25 cm.Therefore, the perimeter of the triangle is 59.25 cm.
Mellisa is an expert scuba diver.she's down in the Pacific Ocean, looking for a rare type of sunfish. At one point, she is 29 meters below the surface of the water.
A. As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters. What is her final depth at the end of the 12 minutes?
B. Later in her dive, Mellisa is at a depth of 40 meters. She decides to rise toward the surface very slowly. Every minute, she rises 2 meters. If she does this for eight minutes, what is her depth?
Answers
Answer:
A. 14 meters
B. 24 meters
Step-by-step explanation:
A. Mellisa starts at 29 meters deep, then rises 15 meters. So her final depth is 29 − 15 = 14 meters.
B. Melissa starts at 40 meters deep, then rises 2 m/min for 8 minutes. That means she rises a total distance of 2 × 8 = 16 meters. So her final depth is 40 − 16 = 24 meters.
Answer:
At one point, Mellisa is 29 meters below the surface of the water.
A.
As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters.
So, her final depth at the end of the 12 minutes = [tex]29-15=14[/tex] meters
B.
Mellisa is at a depth of 40 meters. Every minute, she rises 2 meters.
So, in 8 minutes she will rise [tex]2\times8=16[/tex] meters
Her depth will be = [tex]40-16=24[/tex] meters
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.
File ATTACHED
THANK YOU
Answers
Answer:
Part 1) [tex]f(x)=\frac{2x-1}{x+2}[/tex] -------> [tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]
Part 2) [tex]f(x)=\frac{x-1}{2x+1}[/tex] -------> [tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]
Part 3) [tex]f(x)=\frac{2x+1}{2x-1}[/tex] -----> [tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]
Part 4) [tex]f(x)=\frac{x+2}{-2x+1}[/tex] ----> [tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]
Part 5) [tex]f(x)=\frac{x+2}{x-1}[/tex] -------> [tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]
Step-by-step explanation:
Part 1) we have
[tex]f(x)=\frac{2x-1}{x+2}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{2x-1}{x+2}[/tex]
Exchange the variables x for y and t for x
[tex]x=\frac{2y-1}{y+2}[/tex]
Isolate the variable y
[tex]x=\frac{2y-1}{y+2}\\ \\ xy+2x=2y-1\\ \\xy-2y=-2x-1\\ \\y[x-2]=-2x-1\\ \\y=\frac{-2x-1}{x-2}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]
Part 2) we have
[tex]f(x)=\frac{x-1}{2x+1}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{x-1}{2x+1}[/tex]
Exchange the variables x for y and t for x
[tex]x=\frac{y-1}{2y+1}[/tex]
Isolate the variable y
[tex]x=\frac{y-1}{2y+1}\\ \\2xy+x=y-1\\ \\2xy-y=-x-1\\ \\y[2x-1]=-x-1\\ \\y=\frac{-x-1}{2x-1}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]
Part 3) we have
[tex]f(x)=\frac{2x+1}{2x-1}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{2x+1}{2x-1}[/tex]
Exchange the variables x for y and t for x
[tex]x=\frac{2y+1}{2y-1}[/tex]
Isolate the variable y
[tex]x=\frac{2y+1}{2y-1}\\ \\2xy-x=2y+1\\ \\2xy-2y=x+1\\ \\y[2x-2]=x+1\\ \\y=\frac{x+1}{2(x-1)}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]
Part 4) we have
[tex]f(x)=\frac{x+2}{-2x+1}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{x+2}{-2x+1}[/tex]
Exchange the variables x for y and t for x
[tex]x=\frac{y+2}{-2y+1}[/tex]
Isolate the variable y
[tex]x=\frac{y+2}{-2y+1}\\ \\-2xy+x=y+2\\ \\-2xy-y=-x+2\\ \\y[-2x-1]=-x+2\\ \\y=\frac{-x+2}{-2x-1} \\ \\y=\frac{x-2}{2x+1}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]
Part 5) we have
[tex]f(x)=\frac{x+2}{x-1}[/tex]
Find the inverse
Let
y=f(x)
[tex]y=\frac{x+2}{x-1}[/tex]
Exchange the variables x for y and t for x
[tex]x=\frac{y+2}{y-1}[/tex]
Isolate the variable y
[tex]x=\frac{y+2}{y-1}\\ \\xy-x=y+2\\ \\xy-y=x+2\\ \\y[x-1]=x+2\\ \\y=\frac{x+2}{x-1}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]
Answer:
Step-by-step explanation:
Find the sum (4s/ s2-2s+1)+(7/s2+2s-3)
Answers
Answer:
It would be 7/2s, however if you want to solve it completely, you do 7 ÷ 2. It would give you 3.5 so, s = 3.5.
Which function describes this graph?
—
10
А. y = (х – 4 )(х - 4)
В. у = х2 - 2x +6
оооо
ос. у = х2 + 8х +12
D. у = (х-2)(х – 6).
Answers
Answer:
C. y = x2 + 8x + 12
Step-by-step explanation:
To find x intercept/zero, substitute y = 0
0 = x^2 + 8x + 12
x^2 += 8x + 12 = 0
x^2 + 8x + 12 = 0
Solve the quadratic equation
ax^2 + bx + c = 0 using x = -b±[tex]\sqrt{b^2 -4ac[/tex] / 2ax = -8±[tex]\sqrt{8^2 -4(1)(12)[/tex] / 2(1)x = -8±[tex]\sqrt{8^2 -4(12)[/tex] / 2(1)
any expression multiplied by 1 remains the same
x= -8±[tex]\sqrt{8^2 - 4(12)[/tex] / 2(1)
Evaluate the power
8^2
write the exponentiation as a multiplication
8(8)
multiply the numbers
64
x = -8±[tex]\sqrt{64 - 4(12)[/tex] / 2(1)
multiply the numbers
x = -8±[tex]\sqrt{64 - 48[/tex] / 2(1)
any expression multiplied by q remains the same
x = -8±[tex]\sqrt{64-48[/tex] /2
subtract the numbers
x = -8±[tex]\sqrt{16[/tex] / 2
calculate the square root
x= -8± 4 / 2
x= -8 + 4 / 2
x= -8 - 4 / 2
simplify the expression
x = -2
x = -8 - 4 / 2
x = -2
x = -6
final solutions are
x1 = -6, x 2 = -2
On an average work day, 160 cars go through a toll booth per hour.The driver of each car pays a $1.50 toll how much money is collected in toll in 8 hours
Answers
Your question asks how much money was collected at the toll for a period of 8 hours.
Answer: $1,920To find the answer, we would need to gather some important information from the question.
Important information:
160 cars go through the toll per hourEach car pays $1.50With the information above, we can solve the problem.
First, let's find how much money the toll makes in one hour. To find this, we need to multiply 1.50 by 160 cars, since the toll costs $1.50 and 160 cars go through it per hour.
[tex]1.50*160=240[/tex]
The toll makes $240 per hour.
Now, since we need to find how much the toll makes in 8 hours, we need to multiply 240 by 8.
[tex]240 * 8=1,920[/tex]
When you're done solving, you should get 1,920.
This means that the toll makes $1,920 in 8 hours.
I hope this helps!Best regards,MasterInvestorRafeal has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answers
Answer:
60 different votes.
Step-by-step explanation:
This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:
5P3 = 5*4*3 = 60 possibilities.
There are 60 different votes!!!
Answer: 60 different votes are possible
Step-by-step explanation:
We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.
The formula for permutations is:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Where n is the number of bands you can choose and you choose 3 of them.
Then we calculate:
[tex]5P3 =\frac{5!}{(5-3)!}\\\\5P3=\frac{5!}{2!}\\\\5P3 = 60[/tex]
Finally, the number of possible votes is 60
(05.03)Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon. Pentagon with square measuring 8 inches by 5 inches and two triangles with heights of 7 inches and 6 inches.
72.5 in2
75.5 in2
83 in2
96 in2
Answers
Answer:
83 square inches
Step-by-step explanation:
Let's find the answer, you can see the attached file for clarity.
Because we have a rectangle measuring 8 inches by 5 inches, we can use the area of the rectangle as follows:
A1=base*height=(8 inches)*(5 inches)=40 square inches
Now, because we have a triangle over the square side of 8 inches long, we can divide the triangle into 2 rectangle triangles, each of them with a base of 4 inches and a height of 7 inches, obtaining:
A2=2*(base*height/2)=2*(4 inches)*(7 inches)/2=28 square inches
Doing the same for the other triangle we get 2 triangles with a base of 2.5 inches and a height of 6 inches, obtaining:
A3=2*(base*height/2)=2*(2.5 inches)*(6 inches)/2=15 square inches
The addition of all areas is:
A=A1+A2+A3=40 square inches + 28 square inches + 15 square inches
A=83 square inches.
In conclusion we have an area of 83 square inches.
Answer:
83
Step-by-step explanation:
Jenny and Hanan are collecting clothes for a clothing drive. Hanan collected 1/2 as many bags of clothes as Jenny did. If Jenny collected 3/ 4 of a bag of clothes, what portion of a bag of clothes did Hanan collect?
Answers
Answer:
Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes
Step-by-step explanation:
Let
x ------> amount of clothing bag that Jenny collected
y ------> amount of clothing bag that Hanan collected
we know that
[tex]y=\frac{1}{2}x[/tex] -----> equation A
[tex]x=\frac{3}{4}[/tex] -----> equation B
Substitute equation B in equation A
[tex]y=\frac{1}{2}(\frac{3}{4})[/tex]
[tex]y=\frac{3}{8}[/tex]
therefore
Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes
Which statement best applies to the slope of the line below?
A the slope is negative
B. the slope is zero
C.the slope is positive
D. the line has no slope
Answers
Answer:
D it is a horizontal line . . .horizontal lines do not have a slope
Step-by-step explanation:
Answer:
B. the slope is zero
Step-by-step explanation:
The line shown is a horizontal line. Horizontal lines have zero slope.
Vertical (up and down) lines do not have a slope ( or what we usually call undefined slope)
Write the equation of the line shown in the graph. Please help.
Answers
On this line, for all y-values, the x-value will always be -3.
Since it is a vertical line it has no run, only a rise. This makes the slope undefined.
This said, the equation for this line is x = -3
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of "c" in the quadratic equation 3x 2 + 5x + 7 = 0?
Answers
Answer:
7
Step-by-step explanation:
The quadratic equation looks like:
ax + by + c = 0
"c" is the variable that stands for the "constant", or the number that does not have an extra variable attached, and so is "unchanging". In this case, your answer is 7, which is the constant of the equation. Once defined, the number cannot be changed.
~
A cashier has 54 bills, all of which are $10 or $20 bills. The total value of the money is $910. How many of each type of bill
does the cashier have?
Answers
x = 37 = number of $20 bills
54-x=54-37=17=number of $10 bills
Answer:
the number of $10 bills = 17
the number of $20 bills = 37
Step-by-step explanation:
Let x be the number of $10 bills and y be the number of $20 bills
Total bills = 54
So [tex]x+y= 54[/tex]
Total value of money is $910
[tex]10x+20y= 910[/tex]
now we solve for x and y
Solve the first equation for y
[tex]x+y= 54[/tex]
[tex]y=54-x[/tex]
Now replace y in second equation
[tex]10x+20y= 910[/tex]
[tex]10x+20(54-x)= 910[/tex]
[tex]10x+ 1080-20x= 910[/tex]
[tex]1080-10x= 910[/tex]
Subtract 1080 from both sides
[tex]-10x= -170[/tex]
Divide both sides by -10
x= 17
[tex]y=54-x[/tex]
Replace x with 17
[tex]y=54-17=37[/tex]
the number of $10 bills = 17
the number of $20 bills = 37
find the radius of a circle with a diameter of 40 in
Answers
Answer:
20 in
Step-by-step explanation:
The radius is half the diameter.
You are given the diamter is 40 in.
So the radius is half of 40 in.
Half of 40 in means what is 40 in divided by 2.
Half of 40 in or 40 in ÷ 2 is 20 in.
The radius is 20 in.
Answer: 20 inches
Step-by-step explanation: A radius is half of the circle, and a diameter is a whole circle. 2 radius are equal to one diameter. So divide the diameter by 2 to get the radius.
40/2 = 20
The radius of the circle is 20 inches.
Find the vertex of the parabola y=2x^2+8x-9
Answers
Answer:
The vertex is (-2,-17).
Step-by-step explanation:
We have given y=2x²+8x-9
To find the x-coordinates we use:
xv= -b/2a
where a=2 and b=8
Now put the values in the formula:
xv= -(8)/2(2)
xv=-8/4
xv= -2
Now to find the y coordinates, we will simply substitute the value in the given equation:
y=2x²+8x-9
y=2(-2)²+8(-2)-9
y=2(4)-16-9
y=8-16-9
y=-8-9
y= -17
Therefore the vertex is(-2, -17)....
What is the order of rotational symmetry for the figure
Answers
Answer:
B. 3
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.
Hence,
the correct answer is B. 3 ..
A Large school wants to put a clock in each of its 224 classrooms
The clocks are sold in packs of 14.
How many packs of clocks should the school buy?
Answers
Answer:
16 packs
Step-by-step explanation:
u just have to divide 224 by 14 to get 16
the school wants to get 224 clocks, they clocks come in packs of 14, so each pack has 14 clocks, how many packs are needed?
well, how many times does 14 go into 224? 224 ÷ 14, and you know what that is.
Bob's age is 4 times greater than Susanne age. Dakota is three years younger than Susanne. the sum of bobs , Susanne's , and Dakota's ages is 93. what is Susanne's age
Answers
Answer:
Susanne is 16 years old.
Step-by-step explanation:
You're gonna need three equations.
Key: B = Bob, D = Dakota, s = Susanne
B = 4s
D = s - 3
B + D + s = 93
Now plug in B and D into the third equation:
4s + (s - 3) + s = 93
Now solve it:
4s + s - 3 + s = 93
6s - 3 = 93
+3 +3
6s = 96
6s/6 = 96/6
s = 16
Bob's age is 4 times greater than Susanne's age, and Dakota is 3 years younger than Susanne.
The sum of their ages is 93. Susanne's age is 16.5.
Explanation:Let's assign variables to represent the ages of the individuals involved:
Bob's age: BSusanne's age: SDakota's age: DWe are given that Bob's age is 4 times greater than Susanne's age, so we can write the equation B = 4S.
We are also told that Dakota is three years younger than Susanne, so we can write the equation D = S - 3.
The sum of their ages is given as 93, so we can write the equation B + S + D = 93.
Substituting the first equation into the second equation, we get D = 4S - 3.
Substituting the values from the second and third equations into the fourth equation, we have (4S - 3) + S + (S - 3) = 93.
Simplifying this equation, we get 6S - 6 = 93. Adding 6 to both sides, we have 6S = 99. Dividing both sides by 6, we find that S = 16.5.
Therefore, Susanne's age is 16.5.
A 15-foot board rests against a wall. The angle that the board makes with the
ground is 60°. How far is the base of the board away from the wall?
Select the correct trig ratio and distance from wall.
Answers
Answer:
Step-by-step explanation:
Let the base of the board is x feet away from the wall .
And the hypotenuse, which is represented by the length of the board be 15 foot .
So here we have adjacent represented by the base and the hypotenuse .
And cosine function relates adjacent and hypotenuse , which is cos 60=15/x
And the value of cos 60 is half .
Performing cross multiplication
1/2=15/x
Dividing both sides by 2
x=7.5ft
Answer:
7.5 feet.
Step-by-step explanation:
The boardgame resting against the wall is creating a triangle rectangle and as it is forming a 60º angle with the ground that would be solve with the cosine of 60, which is the value of the division of the hypotenuse by the adjacent side, which would be the distance from the base of the board game to the wall:
Cos60= .5
cos60=adjacent side/hypotenuse
.5= adjacent side/15
adjacent side= 15x.5
Adjacent side=7.5 feet
what is the length of CD, given that figure ABCD is a rectangle
Answers
Answer:
where is rectangle???
Answer:
10
Step-by-step explanation:
The length of AB is 10 and the length of BC is 13. CD is parallel to AB so its 10.
What is the following quotient
Answers
Answer:
√(3)/2
Step-by-step explanation:
To find the quotient, rationalize the denominator by multiplying both the numerator and denominator by √(6)
3√(8)*√(6) = 3√(48)
4√(6)*√(6) 24
Next, simplify the top radical
12√(3) = √(3)/2, This is the answer, it cannot be simplified any further.
24
For this case we must find the quotient of the following expression:
[tex]\frac {3 \sqrt {8}} {4 \sqrt {6}} =[/tex]
We combine [tex]\sqrt {6}[/tex] and [tex]\sqrt {8}[/tex] into a single radical:
[tex]\frac {3 \sqrt {\frac {8} {6}}} {4} =\\\frac {3 \sqrt {\frac {4} {3}}} {4} =\\\frac {3 \frac {\sqrt {4}} {\sqrt {3}}} {4} =\\\frac {3 \frac {2} {\sqrt {3}} * \frac {\sqrt {3}} {\sqrt {3}}} {4} =[/tex]
[tex]\frac {3 * \frac {2 \sqrt {3}} {3}} {4} =\\\frac {\frac {6 \sqrt {3}} {3}} {4} =\\\frac {6 \sqrt {3}} {12} =\\\frac {\sqrt {3}} {2}[/tex]
Answer:
[tex]\frac {\sqrt {3}} {2}[/tex]
Which power raised to a power expression are equivalent to 8 to the power of 12? Check all that apply
Answers
Answer:
[tex]\tt{(8^{-3})}^{-4}; \ \ \ {(8^{1})}^{12}; \ \ \ {(8^{6})}^{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\tt {(a^m)}^n=a^{m\cdot n}}\\\\\\ \tt{(8^{-3})}^{-4}=8^{-3\cdot(-4)}=8^{12}\\\\{(8^{1})}^{12}=8^{1\cdot12}=8^{12}\\\\{(8^{6})}^{2}=8^{6\cdot2}=8^{12}\\\\[/tex]
Answer:A,D,F
Step-by-step explanation:
Find the height of the given pyramid.
Answers
Answer:
7m
Step-by-step explanation:
The volume of a pyramid is given by the following formula: 1/3bh. Where 'b' represents the area of the base and 'h' the height of the pyramid.
The area of the base is: b = (3m)(4m) = 12m^2
Now, we know that the volume is 28m^3, then:
28m^3 = (1/3)(12m^2)(h)
Solving for 'h':
h = 7m
The radius of a cylinder construction pipe is 1.5ft . If the pipe is 13ft long what is it’s volume? Use value 3.14 for pi
Answers
Answer:
V =91.845 ft^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi (1.5)^2 *13
Letting pi = 3.14
V = 3.14 (1.5)^2 * 13
V =91.845 ft^3
Answer:
V=91.89
Step-by-step explanation:
Given:
radius, r= 1.5 ft
height, h=13 ft
volume of cylinder= pi *r^2 *h
V=3.14 *(1.5)^2 *13
V=91.89 ft^3 !
How do you divide something like this?
Answers
Answer:
So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]
Step-by-step explanation:
Since we are dividing by a linear factor, I'm going to use synthetic division.
Since the linear factor that we are dividing by is (x-5), I'm going to put 5 on the outside:
5 | 1 -12 8
| 5 -35
|--------------------------
1 -7 -27
So the quotient x-7 while the remainder is -27.
So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]
You could do long division if you prefer:
x-7
------------------------
(x-5) | x^2-12x+8
- (x^2-5x)
--------------------------
-7x+8
-(-7x+35)
---------------------
-27
You still get the same thing that the quotient is x-7 and the remainder is -27.
Jane and Jill want their mom to ride the rollercoaster with them, but she thinks it will be too fast. She asks the girls to find out how fast the rollercoaster will be travelling. They find out that the speed of the rollercoaster, in miles per hour, is modeled by the function g(x) = x4 - 4x2 + 7x - 8, where x is time measured in
seconds. How fast is the rollercoaster travelling at 2 seconds?
6 miles per hour
22 miles per hour
26 miles per hour
54 miles per hour
Answers
Answer:
Given that the function is a model of miles per hour with x being representative of time in seconds, you simply have to plug 2 into the equation for each x.
Therefore,
g(x) = x^4 - 4x^2 + 7x - 8
becomes
g(x) = 16 - 16 + 14 - 8 = 6 miles per hour.
So, 6 mph is your answer!!
At rate of 6 miles per hour the rollercoaster travelling at 2 seconds.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(x) = [tex]x^4[/tex] - 4x² + 7x - 8
where x is time measured in seconds.
Now, the speed of roller-coaster for t= 2 seconds
g(2) = [tex]x^4[/tex] - 4x² + 7x - 8
g(2) = [tex]2^4[/tex] - 4(2)² + 7(2) - 8
g(2)= 16 - 16 + 14 - 8
g(2) = 6 miles per hour.
Hence, the speed 6 miles per hour.
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Factor completely
abb + abc
Idek how to factor letters
Answers
Answer:
ab( b+c)
Step-by-step explanation:
abb +abc
There is an a and b in each term
What remains goes inside the parentheses
ab( b+c)
Answer:
ab(b+c)
Step-by-step explanation:
Take out each variable like you would any other number
abb+abc
ab(b+c), This is the answer, with the distributive property, you can convert it back to its original form.
ab*b+ab*c=ab^2+abc
Divide (10m^8+4m^6+10m^5) / 2m^2
Answers
Answer:
5m^6 + 2m^4 + 5m^3
hope this works!!!!
To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², simplify each term by subtracting 2 from the exponents. The result is 5m⁶ + 2m⁴ + 5m³. The correct answer is D).
To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², follow these steps
Write the given expression: (10m⁸ + 4m⁶ + 10m⁵) / 2m².
Divide each term in the numerator by 2m² separately:
(10m⁸ / 2m²) + (4m⁶ / 2m²) + (10m⁵ / 2m²).
Simplify each term:
5m⁶ + 2m⁴ + 5m³.
The final result is 5m⁶ + 2m⁴ + 5m³.
The correct option is D).
In this division, we use the rule of exponents: when dividing terms with the same base, subtract the exponents.
The division by 2m² reduces the power of 'm' in each term by 2. So, 10m⁸ becomes 10m⁶, 4m⁶ becomes 2m⁴, and 10m⁵ becomes 5m³. The constants 10 and 4 remain unchanged. The simplified expression is the final result.
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