PLEASE HELP!!!! NEED NOW!!! 20 pts
Explain how the Quotient of Powers was used to simplify this expression.
2 to the 5th power, over 8 = 2 to the 2nd power
By finding the quotient of the bases to be one fourth, and cancelling common factors
By finding the quotient of the bases to be one fourth, and simplifying the expression
By simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents
By simplifying 8 to 2^3 to make both powers base two, and adding the exponents
Answers
If so like 8 it has the same base for [tex]2^{5}[/tex]
as they are both can be obtained by multiplying a certain number of 2s.
for example [tex] 8=2^{3}= 2*2*2 [/tex] which makes 8 can be obtained by multiplying three 2s.
in our example [tex] \frac{2^{5}}{8}=\frac{2^{5}}{2^{3}} = 2^{5} * 2^{-3} [/tex]
in this case, we can add the two powers as long as the basis are the same.
[tex] \frac{2^{5}}{8}=2^{5-3}=2^{2}=4[/tex]
I hope it make sense now ;)
Best Wishes
Related Questions
please help asap !! ill mark brainliest but be corrrecct
Answers
Answer:
k=4
Step-by-step explanation:
Given
A line x=7
The line has only y-intercept which means that it is a vertical line.
As the two points are
A(10,2) and B(k,2)
The y-intercepts of both the points are same i.e. y=2 which means that the line fomed by joining A and B is a horizontal line.
As x=7 is a vertical line and bisects the horizontal line, the mid-point of line AB will be the point where first line (x=7) bisects the second which is (7,2).
The x-coordinate of mid-point is 7 because the vertical line has 7 as x-intercept and y-intercept is two because the horizontal line has y-intercept 2.
So,
Mid-point=((10+k)/2 ,2)=(7,2)
Comparing the x-coordinate
(10+k)/2=7
10+k=7*2
10+k=14
k=14-10
k=4
helppppppppppppppppppppppppppppppppppppppppppppppppp
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The first thing we are going to do is decompose the numbers 16 and 54 into prime factors:
[tex]16=2^{4} [/tex] and [tex]54=(2)(3^{3} )[/tex]
Now we are going to separate each term into cubes:
[tex]2 ^{4} =(2)(2^{3} )[/tex]
[tex]x ^{6} =( x^{3} )( x^{3} )[/tex]
[tex]y^{5} =(y^{2})(y^{3} ) [/tex]
After that we can rewrite the expression:
[tex]2( \sqrt[3]{(2)(2^{3})x^{3}y }) +4( \sqrt[3]{(2)( 3^{3})( x^{3})( x^{3})(y^{2})(y^3}) } )[/tex]
Finally we can take out the cubes and simplify:
[tex]2(2)(x) \sqrt[3]{2y} +4(3)(x)(x)(y) \sqrt[3]{2 y^{2} } [/tex]
[tex]4x \sqrt[3]{2y} +12 x^{2} y \sqrt[3]{2 y^{2} } [/tex]
The first choice, [tex]4x \sqrt[3]{2y} +12 x^{2} y \sqrt[3]{2 y^{2} } [/tex], is the correct answer.
2[(16x³y)^(1/3)]+4[(54x³x³y³y²)^(1/3)]
2[(2³2x³y)^(1/3)]+4[(3³2x³x³y³y²)^(1/3)]
2[2x(2y)^(1/3)]+4[3x²y(2y)^(1/3)]
4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
the answer is the option A) 4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
The base and the height of sail b are x times greater than the base and the height of sail
a. how many times greater is the area of sail b? write your answer as a power.
Answers
Since your sail has a base and a height it can be a triangle, a square, a rectangle or a rhombus, but I believe most sails are either triangles or rectangle so let's explore those. That should be enough to see that the answer is the same for the shapes listed.
TRIANGLE
The area of a triangle is (1/2)(b)(h). This is the area of sail A. The area of sail B is (1/2)(bx)(hx) = [tex]( \frac{1}{2} bh) x^{2} [/tex]. That makes the area of B [tex] x^{2} [/tex] times greater.
RECTANGLE
The area of a rectangle is (b)(h). This is the area of sail A. The area of sail B is (bx)(hx) = [tex]bh x^{2} [/tex]That makes the area of B [tex] x^{2} [/tex] times greater.
When both the base and height of a shape are multiplied by x, the area increases by a factor of x^2. Therefore, the area of Sail B is x^2 times greater than that of Sail A.
Explanation:The area of a shape with a base and height is commonly found using the formula Area = 1/2 * Base * Height. If the base and the height of Sail B are x times greater than those of Sail A, then both the base and height of Sail B are multiplied by x, resulting in an area that is x^2 (x squared) times greater. This is because, in the formula, base and height are multiplied together, so if both are multiplied by x, the overall multiplication is by x*x, or x^2. Therefore, the area of Sail B is x^2 times greater than the area of Sail A.
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The width (l) of a sheet of plywood that is one half the length l
Answers
L=2+4W
W=L/2
f=3d
hope this is the right question????
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the numberof nickels, n, and the number of quarters, q, Yolanda used?
Answers
n + q = 28
If nickels are .05 and quarters are .25 and the total is $4 then it would be
.05n + .25q = 4
Answer:
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
And the pair [tex](n,q)=(15,13)[/tex] is the solution.
Step-by-step explanation:
We know that Yolanda paid for her movie ticket using 28 coins. She only paid with nickels and quarters.
We also know that the ticket cost $4.
We need to form a linear equation system that solves this problem.
We have the following variables :
n : number of nickels
q : number of quarters
We know that she used 28 coins ⇒ the number of nickels plus the number of quarters must be equal to 28.
We have our first equation :
[tex]n+q=28[/tex] (I)
For the second equation we need to use the ticket price information.
We know that the ticket cost $4 and she only paid with nickels and quarters.
Therefore we can write the following equation that relates the variable ''n'' and the variable ''q'' :
[tex]n(0.05)+q(0.25)=4[/tex] (II)
This equation represents that the number of nickels ''n'' per its value plus the number of quarters ''q'' per its value is equal to $4 that it is the value of the movie ticket.
With (I) and (II) we form the linear equation system :
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
This linear equation system can be used to find the value of ''n'' and ''q''.
For example, in equation (I)
[tex]n+q=28[/tex]
we can solve it in terms of ''n'' :
[tex]n=28-q[/tex] (III)
If we use (III) in (II) :
[tex](28-q)(0.05)+q(0.25)=4[/tex]
[tex]1.4-(0.05)q+(0.25)q=4[/tex]
[tex]q(0.2)=2.6[/tex]
[tex]q=\frac{2.6}{0.2}=13[/tex]
[tex]q=13[/tex]
Now replacing this value of q in (III) :
[tex]n=28-13=15[/tex]
[tex]n=15[/tex]
We find that Yoland used 15 nickels and 13 quarters to paid the movie ticket .
Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands.
Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.
There is a moment when the basketballs are at the same height.
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.
Answers
Answer:
Just took the K12 quiz, and like killdrone said in the comments, the correct answer is 9.8 m
Step-by-step explanation:
The height at which both basketballs are at the same height is approximately 16.3 meters.
Explanation:To find the moment when the basketballs are at the same height, we need to find the common height value for both functions.
Setting the functions equal to each other, we get: -4.9x^2 + 12x + 2.5 = -4.9x^2 + 14x
Simplifying the equation, we get 2x = 2.5, which means x = 1.25.
Substituting this value back into the original function for Eli, we get f(1.25) = -4.9(1.25)^2 + 12(1.25) + 2.5 = 16.325
Therefore, the height at which both basketballs are at the same height is approximately 16.3 meters.
**Giving away 20 points**. I need to know the arc length for EF and the area of sector EOF please:) (also plz show work thanks!!)
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now, EF = 18, wait a second! EF is the base of the triangle, and h = 10.725, wait a minute!! "h" is the height of the triangle.
so, what's the area of a triangle whose base is 18 and has a height of 10.725? yeap, we knew you'd know that one.
what's the length of the arcEF? well, we know the central angle of ∡FOE is 80°, well, arc's get their angle measurement from the central angle they're in, so if ∡FOE is 80°, so is arcEF then.
Which of the following pairs of numbers contains like fractions?
A. 6⁄7 and 1 5⁄7
B. 3⁄2 and 2⁄3
C. 3 1⁄2 and 4 4⁄4
D. 5⁄6 and 10⁄12
Answers
BECAUSE 5*2=10
6*2=12
Find the dimensions of a rectangle whose area is 221 cm2 and whose perimeter is 60 cm. (enter your answers as a comma-separated list.)
Answers
The dimensions of a rectangle with an area of 221 cm² and a perimeter of 60 cm are found by solving a system of equations derived from the definitions of area and perimeter. The dimensions are 13 cm by 17 cm, or equivalently, 17 cm by 13 cm.
Explanation:To find the dimensions of a rectangle with an area of 221 cm2 and a perimeter of 60 cm, we will let the length be x and the width be y. The area of a rectangle is found by multiplying the length and width, so we have the equation x * y = 221. The perimeter is twice the sum of the length and width, so we have 2x + 2y = 60, which simplifies to x + y = 30.
To solve these equations, divide the perimeter equation by 2 to find y = 30 - x. Substituting this into the area equation gives x(30 - x) = 221. Expanding this and bringing all terms to one side provides a quadratic equation: x2 - 30x + 221 = 0. Solving this quadratic equation by factoring or using the quadratic formula gives the dimensions of the rectangle.
The solutions to the quadratic equation are x = 13 and x = 17. Since x and y are interchangeable as length and width, the two sets of possible dimensions for the rectangle are 13 cm by 17 cm and 17 cm by 13 cm.
The dimensions of the rectangle are [tex]17\ cm , 13\ cm[/tex]
To find the dimensions [tex]\( l \)[/tex] (length) and [tex]\( w \)[/tex] (width) of the rectangle given its area and perimeter, we start with the following equations:
1. Area equation:
[tex]\[l \times w = 221\][/tex]
2. Perimeter equation:
[tex]\[ 2l + 2w = 60 \][/tex]
Step-by-Step Solution:
The dimensions of the rectangle are [tex]{{17, 13} \) cm.[/tex]
From the perimeter equation, divide everything by [tex]2[/tex] to simplify:
[tex]\[l + w = 30\][/tex]
Now we have a system of equations:
[tex]\[\begincases}l \times w = 221 \\l + w = 30\end{cases}\][/tex]
Let's solve this system using substitution or elimination:
From [tex]\( l + w = 30 \)[/tex], we can express [tex]\( w \)[/tex] in terms of [tex]\( l \)[/tex]
[tex]\[w = 30 - l\][/tex]
Substitute [tex]\( w = 30 - l \)[/tex] into the area equation:
[tex]\[l \times (30 - l) = 221\][/tex]
[tex]\[30l - l^2 = 221\][/tex]
Rearrange this equation to form a quadratic equation:
[tex]\[l^2 - 30l + 221 = 0\][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -30 \), and \( c = 221 \)[/tex]
[tex]\[l = \frac{-(-30) \pm \sqrt{(-30)^2 - 4 \times 1 \times 221}}{2 \times 1}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{900 - 884}}{2}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{16}}{2}\][/tex]
[tex]\[l = \frac{30 \pm 4}{2}\][/tex]
Calculate both possible values of [tex]\( l \)[/tex]
[tex]\[l = \frac{30 + 4}{2} = 17 \quad \text{or} \quad l = \frac{30 - 4}{2} = 13\][/tex]
Corresponding values of \( w \)
[tex]If\ \( l = 17 \), then \( w = 30 - 17 = 13 \)[/tex]
[tex]If\ \( l = 13 \), then \( w = 30 - 13 = 17 \)[/tex]
Therefore, the dimensions of the rectangle are [tex]\( 17 \) cm[/tex] by [tex]\( 13 \) cm.[/tex]
Verification:
[tex]Area: \( 17 \times 13 = 221 \) cm\(^2\)[/tex]
[tex]Perimeter: \( 2 \times (17 + 13) = 2 \times 30 = 60 \) cm[/tex]
Both conditions match the given area and perimeter, confirming that the dimensions are correct.
Dan has to carry 285 apples from a farm to the market. How many baskets will he need, given that each basket can hold 37 apples?
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divide number of apples by how many fit I a basket:
285 / 37 = 7.70
so he will need 8 baskets
) how many ways are there to divide a group of 10 kids into two groups of 5 to play soccer?
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C(5,10)= 10!/(5!*(10-5)!)=36
What is Y=x^2+6x+4 in vertex form?
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Find the lateral area and the total area of the prism.
27 sq. ft.
36 sq. ft.
54 sq. ft.
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1) the lateral area----------------> L=P*h
P=(3+3+3) h=6
L=(3+3+3)*6=54 in²
the answer part 1) is the lateral area is 54 in²
2) the total area=------------- > S=P*h+2B
2B=2*[3*3/2] P*h=54
S=2*[3*3/2]+54=63 in²
the answer part 2) is the total area is 63 in²
Answer:
54 sq. ft.
Step-by-step explanation:
LA=ph or in other words Lateral Area= base perimeter * height
The perimeter of the base is 9 because 3+3+3=9.
The height is 6. So 6 * 9 = 54
Suppose Karel wants to be the least expensive babysitter in the neighborhood. How much should she charge?
Suppose Karel wants to charge the same hourly rate as most of the other baby-sitters. How much should she charge?
Suppose Karel wants her hourly rate to be higher than the rate of half of other baby-sitters, but lower than the hourly rate of the rest of the babysitters. How much should she charge?
In addition to the babysitting rates charged by others, what might Karel consider when she sets her rates?
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B. She should charge $2.75 if she wants to charge what most other sitters are charged because this amount occurs more than any other(the mode).
C. She should also charge $2.75 if she wants to be in the middle (median).
D. When deciding on a rate, Karel should also consider if there are any rates that are a lot lower or a lot higher because there might be a reason (more kids, unusual hours, relatives, etc...).
To be the least expensive babysitter, Karel should charge less than $2.00. If she wants her hourly rate to be higher than half the babysitters but lower than the other half, she could charge slightly less than $2.75. Beyond these rates, Karel should consider factors like her own experience, the specific tasks she'll perform, and the hours she'll work.
Explanation:To determine how much Karel should charge for her babysitting services, we need to consider the other babysitting rates and find the midpoint. The other students charge the following amounts: Stephanie-$2.75, Jessica-$2.00, Michael-$3.00, Raoul -$2.50, Rolanda-$2.75, Harry -$2.25, Samuel-$2.25, Anita-$2.75.
To be the least expensive, Karel should charge less than the lowest rate, which is $2.00 charged by Jessica. So, Karel could charge $1.75, for example.
Now, suppose Karel wants to have an hourly rate higher than half the babysitters but lower than the other half. We need to organize the rates in ascending order, and then find the median value. If we do this, we find that the middle value (the median) is $2.75. Therefore, Karel could charge slightly less than this, for example, $2.70.
Lastly, Karel should also consider other factors when setting her rates. These might include her experience and skills as a babysitter, the average babysitting rates in her neighborhood or city, the specific tasks she'll be expected to perform, and the hours she'll be working.
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helpppppppppppppppppppppppppppppppppppppppppp
Answers
First choice is the correct one
Explanation:
The given is:
[(x+5) / (x+2)] - [(x+1) / x(x+2)]
First, we will need to have a common denominator and then we will solve the subtraction normally. To get a common denominator, we will have to multiply both numerator and denominator of first term by x.
Therefore:
[(x+5) / (x+2)] - [(x+1) / x(x+2)] = [x(x+5) / x(x+2)] - [(x+1) / x(x+2)]
= [x(x+5)-(x+1)] / [x(x+2)]
= (x^2 + 5x - x - 1) / [x(x+2)]
= [(x^2 + 4x - 1)] / [x(x+2)]
Hope this helps :)
Triangle HIJ has been reflected to create triangle H'I'J'. Segment HJ= H'J'= 4, segments IJ = I'J' = 7, and angles J and J' are both 32 degrees. Which postulate or theorem below would prove the two triangles are congruent?
A. SSS
B. SAS
C. ASA
D. HL
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you leave your house and walk for half an hour at a speed of 3 miles per hour. Then you run for 15 minuets at a speed of 7 miles per hour. You are now halfway to town. Write and solve an equation to find the distance from your house to town
Answers
Final answer:
To find the total distance to town, the distance walked (1.5 miles) and run (1.75 miles) were calculated, and it was found that the student is 3.25 miles away from home. This is halfway to town, so the total distance to town is 6.5 miles.
Explanation:
To solve the problem, we will calculate the distance traveled by walking and running and then use these to find the total distance to town.
Step 1: Calculate the distance walked
First, we convert the walking time into hours since the speed is given in miles per hour. Half an hour of walking at 3 miles per hour will cover:
Distance walked = Speed × Time = 3 mph × 0.5 hours = 1.5 miles
Step 2: Calculate the distance run
Since 15 minutes is a quarter of an hour, we can calculate the distance run at 7 miles per hour as:
Distance run = Speed × Time = 7 mph × 0.25 hours = 1.75 miles
Step 3: Determine the total half distance
Now, we combine the distances to find the halfway point to town:
Total half distance = Distance walked + Distance run = 1.5 miles + 1.75 miles = 3.25 miles
Step 4: Find the full distance to town
Since this is half the distance, the full distance to town is:
Full distance = Total half distance × 2 = 3.25 miles × 2 = 6.5 miles
Conclusion
Therefore, the total distance from the student's house to town is 6.5 miles.
Final answer:
The total distance from the house to town is found by doubling the sum of the distances walked and run, which were 1.5 miles and 1.75 miles, respectively. The full distance to town is 6.5 miles.
Explanation:
To solve for the distance from your house to town, we will use the information provided about your walking and running times and speeds. Since you walked for half an hour (0.5 hours) at a speed of 3 miles per hour and ran for 15 minutes (0.25 hours) at a speed of 7 miles per hour, and this brought you halfway to town, we can set up the following equation:
Distance walked = Speed walked × Time walked
= 3 mph × 0.5 hours
= 1.5 miles
Distance run = Speed run × Time run
= 7 mph × 0.25 hours
= 1.75 miles
The total distance you traveled to get halfway to town is the sum of the distance walked and the distance run:
Total distance halfway = Distance walked + Distance run
= 1.5 miles + 1.75 miles
= 3.25 miles
Since 3.25 miles is only halfway to town, the full distance to town is twice that amount:
Full distance to town = 2 × Total distance halfway
= 2 × 3.25 miles
= 6.5 miles
Therefore, the total distance from your house to town is 6.5 miles.
x+2/x+8 divided by 2x/3
Answers
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?
Answers
b1-------------> base △ABC
b2-------------> base △DEF
A1-----------> area △ABC
A2-----------> area △DEF
we know that
h1=20 in
h2=24 in
A1=b1*20/2-------------> A1=10b1
A2=b2*24/2 ------------> A2=12 b2
if △ABC∼△DEF
then
b1/20=b2/24------------> b1=b2*[20/24]-----> b1=b2*[5/6]
What is the ratio of the area of △ABC to the area of △DEF?
A1=10b1
A2=12b2
A1/A2=(10/12)*(b1/b2)-------> (10/12)*(b2*(5/6)/b2)-----> (10/12)*(5/6)=50/72
A1/A2=50/72--------> 25/36
the answer is (25/36)
Evaluate the function for
f(x) = x + 3 and g(x) = x2 − 2.
(f − g)(0)
(f − g)(0) =
Answers
To evaluate (f - g)(0), find f(0) and g(0) for the functions f(x) = x + 3 and g(x) = x^2 - 2, and then subtract the latter from the former. For f(0) we have 3, and for g(0) we have -2. Subtracting, we get (f - g)(0) = 5.
Explanation:To evaluate the expression (f - g)(0), it means we need to find the value of the function f at x = 0, subtract the value of the function g at x = 0, and combine them. Given the functions f(x) = x + 3 and g(x) = x^2 − 2, let's calculate their values at x = 0:
For f(x), we have f(0) = 0 + 3 = 3For g(x), we have g(0) = (0)^2 − 2 = 0 − 2 = −2Now, let's subtract g(0) from f(0):
(f - g)(0) = f(0) - g(0) = 3 - (-2) = 3 + 2 = 5
Therefore, the value of (f - g)(0) is 5.
Alvin financed $3,450 to buy a new car. If he made 36 payments of $138.50 each, how much interest did he pay on the loan? a. $153.60 b. $415.50 c. $1,536 d. $4,986
Answers
Multiply 138.50 by 36. (4,986)
Then, subtract 4,986 by 3,450.
What is the sum of the geometric series
Answers
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256
The amount of interest earned on a savings account varies directly with the amount of money saved. If $208 in interest is earned on $6,500 of savings, how much interest will be earned on $8,000 of savings over the same time period? $224 $240 $256 $272
Answers
.. interest = 208*(8000/6500) = 256
The 3rd selection is appropriate.
Given f(x)=3x^2+5 and g(x)=x−2 .
What is (fg)(x) ?
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PLEASE SOMEONE HELP ME ON THIS
Answers
What is the square root of -1
Answers
Given the inequality below: x + 2y ≥ 10
Answers
(x+2y)+(-10)≥10+(-10)
x+2y-10≥10-10
(x+2y-10)+(-x+10)≥-x+10
x+2y-10-x+10≥-x+10
2y≥-x+10
2y over 2 ≥ -x +10 over 2
y≥-1 over 2x + 10 over 2
y≥-1/2x+5
Kelly mixes the letters S E L E C T E and D thoroughly. Alex picks one letter. WHat is the probability that Alex will not select a consonant.
A. 3/8
B.3/5
C.5/8
D.1/2
Answers
There are 3 non-consonants (aka vowels) out of 8 letters total. That's why the answer is simply 3/8. It's the fraction of the number of things we want out of the number of things total.
How many points determine a unique line?
A.
1 point
B.
2 points
C.
any 3 points
D.
3 noncollinear points
I say 2 points!
Answers
Answer:
B. 2 points
Step-by-step explanation:
1 point is a dot in space, 2 can make a line
Find the exact volume of the cylinder.