Answer:
12√2
Step-by-step explanation:
Use the Pythagorean Theorem here:
(12 cm)^2 + (12 cm)^2 = 288 cm^2.
The length of the hypotenuse is √288 = (√4)(√72) = 2(√36)(√2) = 12√2
Given that both legs of a 45, 45, and 90 degree triangle are 12cm, find out the length of the hypotenuse.
To solve for the hypotenuse, we will use the Pythagorean Theorem.
The formula to find the hypotenuse is:
a^2 + b^2 = c ^2
We already know that both legs are 12cm, so we can plug them in.
12^2 + 12^2 = c^2
Solve.
144 + 144 = c^2
Add.
288 = c^2
Find the square root of 288.
sqrt(288) = 16.97
Therefore, the square root of 288 is 16.97
If we round 16.97 to 17 and then square it, that would equal 289.
So, the best choice is to leave it as 16.97.
Thus, the length of the hypotenuse is 16.97 or 17 if you want to round it.
plz hurryA 3-column table with 6 rows. Column 1 is labeled Number Rolled with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Observed Frequency with entries 10, 12, 10, 10, 8, 10. Column 3 is labeled Relative frequency with entries StartFraction 1 over 6 EndFraction, A, StartFraction 1 over 6 EndFraction, StartFraction 1 over 6 EndFraction, B, StartFraction 1 over 6 EndFraction. A number cube is rolled 60 times. The results of those 60 trials are recorded in the table. Complete the table. A = B =
Answer:
The complete table is shown below.
Step-by-step explanation:
The data provided is:
Number Rolled Observed Frequency Relative frequency
1 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
2 12 [tex]\frac{12}{60}=\frac{1}{5}[/tex]
3 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
4 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
5 8 [tex]\frac{8}{60}=\frac{2}{15}[/tex]
6 10 [tex]\frac{10}{60}=\frac{1}{6}[/tex]
TOTAL 60 1
The complete table is shown above.
Answer:
A= 1/5
B.2/15
Step-by-step explanation:
trust me i got it right on edg
A ball is dropped from 16 feet above a hard surface. After each time it hits the surface, it rebounds to a
height that is 3/4 of its previous maximum height. What is the total vertical distance, to the nearest foot, the ball has traveled when it strikes the ground for the 10th time? Write out the first five terms of this sum to help visualize.
Answer:
a) Total distance travelled to the nearest foot = 105ft
b) First 5 terms = 12, 9, 6.75, 5.0625, 3.796875
Step-by-step explanation:
From the question above, we can see that this is a geometric series or progression
Formula for geometric progression:
Tn = arⁿ-¹
Where
a = first term
r = common ration
n = number of terms
From the question, we are told that the ball dropped from 16 feet
Hence First term(a) = 16
We are told that the ball rebounds to 3/4 of it's previous height anytime it hits the surface.
Hence, common ratio(r) = 3/4
a) We are told to find total distance to the nearest foot that the ball travelled when it strikes the ground for the 10th time
This means we are to find the sum of the first 10 terms.
Because the ball rises and falls, we would use the rises form
Where the first term = 12 and the number of times is 9 because it rises 9 times
The formula we would use to find this sum is based on if the common ratio is less than or greater than 1
Our common ratio = 3/4, hence it is less than 1.
When r< 1, sum of n terms =
Sn = a(1 - rⁿ)/ 1 - r
It is important to
Where a = 12
r = 3/4
n = 9
Sn = 12( 1 - (3/4)^9) / 1- 3/4
Sn = 104.79ft
Approximately = 105ft
b) First five terms
Using the formula
Tn = arⁿ-¹
Where
a = first term = 12
r = common ration
n = number of terms
First term, n = 1 = 12 × 3/4^(1-1)
= 12 × 3/4 ^(0)
= 12× 1
= 12
Second term, n = 2 = 12 × 3/4^(2-1)
= 12 × 3/4 ^(1)
= 36/4
= 9
Third term, n = 3 = 12 × 3/4^(3-1)
= 12 × (3/4)²
= 6.75
Fourth term, n = 4= 12 × 3/4^(4-1)
= 12 × (3/4)³
= 5.0625
Fifth term, n = 5 = 12 × 3/4^(5-1)
= 12 × (3/4)⁴
= 3.796875
Therefore, the first 5 terms = 12, 9, 6.75, 5.0625, 3.796875
The rebound of the ball from the height is an illustration of a geometric series
The total vertical distance at the 10th rebound is 60.352 feetThe first five terms of the sum are 16, 12, 9, 6.75 and 5.0625(a) The total vertical distance
The given parameters are:
[tex]\mathbf{a = 16}[/tex] -- the first term
[tex]\mathbf{r = \frac 34}[/tex] -- the common ratio
[tex]\mathbf{n = 10}[/tex] -- number of terms
The total vertical distance when it strikes for the 10th time is the sum of nth terms of the geometric series.
So, we have:
[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1- r}}[/tex]
Substitute values for (a), (r) and n
[tex]\mathbf{S_{10} = \frac{16(1 - 3/4^{10)}}{1- 3/4}}[/tex]
Simplify
[tex]\mathbf{S_{10} = \frac{16(0.943)}{0.25}}[/tex]
[tex]\mathbf{S_{10} = 60.352}[/tex]
Hence, the total vertical distance at the 10th rebound is 60.352 feet
(b) The first five terms of this sum
The nth term of a geometric series is:
[tex]\mathbf{T_n = ar^{n-1}}[/tex]
So, we have:
[tex]\mathbf{T_1 = 16}[/tex]
[tex]\mathbf{T_2 = 16 * 3/4 = 12}[/tex]
[tex]\mathbf{T_3 = 12 * 3/4 = 9}[/tex]
[tex]\mathbf{T_4 = 9 * 3/4 = 6.75}[/tex]
[tex]\mathbf{T_5 = 6.75 * 3/4 = 5.0625}[/tex]
Hence, the first five terms of the sum are 16, 12, 9, 6.75 and 5.0625
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HELP GUYS PLEASE ANSWER FAST
Answer:
5/4
Step-by-step explanation:
Slope is y1-y2/x1-x2 so if you plug in the coordinates you get 4-(-1)/4-0 which you would get 5/4
Find the value of x in the figure below:
a. 20
b. 60
c. 180
d. 40
Answer:
d. 40
Step-by-step explanation:
2x + x +( x + 20) have to all equal 180 degrees in a triangle.
2x + x + x + 20 = 180
2x + 2x + 20 = 180
4x + 20 = 180
4x = 180 - 20
x = (180-20) / 4
x = 160 / 4
x = 40
Answer:
D. 40Step-by-step explanation:
This is the answer that was right for me, I just did this question :) Hope this helps! :D
Yuson must complete 30 hours of community service. She does 2 hours each day. Which linear equation represents the hours Yuson has left after x days?
A.) y= -2x + 30
B.) y= 2x + 30
C.) y= -2x - 30
D.) y= 2x - 30
Answer:
A
Step-by-step explanation:
Because it's subtracting 2 hours every day, the slope is -2. Also because it's 30 hours, it's 30. Therefore: A.) y=-2x+30 is the answer.
Hopes this Helps!
What is the volume of a sphere with a radius of 9.9 ft, rounded to the nearest tenth of a cubic foot?
Answer:
the answer is attached to the picture
The volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of the sphere is 4/3πr³
Radius is 9.9 ft.
Volume =4/3×3.14×(9.9)³
=4/3×3.14×970.3
=12187/3
=4062.3
Hence, the volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.
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factorise x square - 7 x minus 42
Answer:
x =(7-√217)/2=-3.865
x =(7+√217)/2=10.865 mark brainliest please
Step-by-step explanation:
Factoring x2-7x-42
The first term is, x2 its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -42
Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -7 .
-42 + 1 = -41
-21 + 2 = -19
-14 + 3 = -11
-7 + 6 = -1
-6 + 7 = 1
-3 + 14 = 11
-2 + 21 = 19
-1 + 42 = 41
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 7x - 42 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-7x-42
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.5000
Plugging into the parabola formula 3.5000 for x we can calculate the y -coordinate :
y = 1.0 * 3.50 * 3.50 - 7.0 * 3.50 - 42.0
or y = -54.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-7x-42
Axis of Symmetry (dashed) {x}={ 3.50}
Vertex at {x,y} = { 3.50,-54.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-3.87, 0.00}
Root 2 at {x,y} = {10.87, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-7x-42 = 0 by Completing The Square .
Add 42 to both side of the equation :
x2-7x = 42
Now the clever bit: Take the coefficient of x , which is 7 , divide by two, giving 7/2 , and finally square it giving 49/4
Add 49/4 to both sides of the equation :
On the right hand side we have :
42 + 49/4 or, (42/1)+(49/4)
The common denominator of the two fractions is 4 Adding (168/4)+(49/4) gives 217/4
So adding to both sides we finally get :
x2-7x+(49/4) = 217/4
Adding 49/4 has completed the left hand side into a perfect square :
x2-7x+(49/4) =
(x-(7/2)) • (x-(7/2)) =
(x-(7/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-7x+(49/4) = 217/4 and
x2-7x+(49/4) = (x-(7/2))2
then, according to the law of transitivity,
(x-(7/2))2 = 217/4
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(7/2))2 is
(x-(7/2))2/2 =
(x-(7/2))1 =
x-(7/2)
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-(7/2) = √ 217/4
Add 7/2 to both sides to obtain:
x = 7/2 + √ 217/4
Since a square root has two values, one positive and the other negative
x2 - 7x - 42 = 0
has two solutions:
x = 7/2 + √ 217/4
or
x = 7/2 - √ 217/4
Note that √ 217/4 can be written as
√ 217 / √ 4 which is √ 217 / 2
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-7x-42 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -7
C = -42
Accordingly, B2 - 4AC =
49 - (-168) =
217
Applying the quadratic formula :
7 ± √ 217
x = —————
2
√ 217 , rounded to 4 decimal digits, is 14.7309
So now we are looking at:
x = ( 7 ± 14.731 ) / 2
Two real solutions:
x =(7+√217)/2=10.865
or:
x =(7-√217)/2=-3.865
Answer:
x^2 - 7x - 42
x^2 - x (21 - 14 ) - 42
x^2 - 21x + 14x -42
7x ( x - 3) + 14 ( x- 3)
(x -3) (7x + 14)
hope this helps you
a basket contains 20 green apples and 30 red apples if a piece of fruit is selected at random from the basket what is the probability that it will not be a red apple
Answer:
because
most people like green apples
Can someone please help me with this question
Answer:
u = -4w+9
Step-by-step explanation:
u - 5 = -4(w-1)
Distribute
u - 5 = -4w +4
Add 5 to each side
u -5+5 = -4w +4+5
u = -4w+9
When 18 is subtracted from six times a certain number, the result is − 42.
What is the number?
Answer:
18-6×10=-42
Step-by-step explanation:
all i did was put it in my calculator
Find 3 rational numbers between ¼ and ½
Answer:
5/16 and 3/8 are two
Step-by-step explanation:
idk a third
Helpppp meee pleaseee!!!! Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Use the drop-down menus to explain how to determine the volume of the paperweight.
Answer:
1. 1/2 * 5 * 5
2. 4
3. 7
4. 79
Step-by-step explanation:
IReady test
The volume of the paperweight will be 79.17 cubic inch
PrismA solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms is known as prism
What are steps to solve this problem?The steps are as follow:
Let volume of pyramid be [tex]V_{1}[/tex]Let volume of prism be [tex]V_{2}[/tex]Since the floor area is triangle∴ Area of floor = Area of triangle = ah/2
Where a=5 and h=5 from figure given
∴ Area of floor = (5*5)/2 = 12.5 sq.inch
Now, let us find the volume of pyramid and prism as follow:[tex]V_{1} = \frac{1}{3}sh \\V_{1} = \frac{1}{3}*7*\frac{1}{2}*5*5\\V_{1} = 29.17[/tex]
[tex]V_{2} = sh\\V_{2} = 4*\frac{1}{2}*5*5 \\V_{2} = 50[/tex]
Total Volume of paperweight will be [tex]V_{1}+V_{2}[/tex]∴ Total volume
[tex]=50+29.17\\=79.17[/tex]
Therefore the total volume of paperweight will be 79.17 cubic inch
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hey everyone! can u guys please help i really struggle in math and i just need some help
i will follow and mark u as brainleist even if u know a friend or google that could help me
thanks everyone and have a great corona time day
Answer:
d= 5.2
[][][]-[][][]
P = √5.2 ^3
P = √5.2 × 5.2 × 5.2
P = √140.608 (plug into calculator)
P = 11.857824421
P = 11.86
The orbital period of Jupiter is 11.86 Earth years.
Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon‐lime soda to make punch for a party. He allows 2 cups of punch for each guest. Will there be enough punch to serve all 14 guests? How much, if any, punch will be left?
Answer:
In total there are 30 cups and there are 2 left over
Step-by-step explanation:
The first thing is to clarify the equivalences, we have to:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
We will pass everything to cups,
1 gallon of orange juice = 16 cups
3 pints of pineapple juice = 6 cups
2 quarts of lemon ‐ lime soda = 8 cups
So in total they would be 16 + 6 + 8 = 30 cups
How to get 2 cups for 14 guests in total would be 28 cups, which means that if 2 cups are left and left over.
5+3 I’m just asking a dumb question so that u can get points so ya!
Answer:
8
Step-by-step explanation:
thank u god!
Answer:
5+3 = 8!!!! :D
Step-by-step explanation:
Five plus three, is going to equal to eight total.
What is the purpose of a regression line
Answer:
B. to show the general tendency of the points in a scatterplot
Step-by-step explanation:
MAKE AN EQUATION, solve it.
A man has $0.70 in dimes and nickels. He has 8 coins altogether. How many nickels does he have?
Answer:
Number of nickels: 2,
Number of dimes: 6
Step-by-step explanation:
Say d ⇒ number of dimes, n ⇒ number of nickels; from this we can formulate two equation knowing the cost per dime ⇒ $ 0.1, and the cost per nickel ⇒ $0.05
d + n = 8,
0.1 * d + 0.05 * n = 0.7 ⇒ Let us solve through substitution
d = 8 - n into 0.1 * d + 0.05 * n = 0.7,
0.1 * ( 8 - n ) + 0.05 * n = 0.7,
0.8 - 0.1 * n + 0.05 * n = 0.7,
0.8 - 0.1n + 0.05n = 0.7,
- 0.05n = - 0.1,
Number of nickels: 2 ⇒ Now let us substitute this value into the first equation as to solve for d, dimes
d = 8 - 2,
Number of dimes: 6
A stock has a price of $72.31. This is $6.28 less than the price of the stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday. An equation is =72.31. The price of the stock yesterday was $ .
Answer: The price of the stock yesterday was $78.59
Step-by-step explanation:
p - 6.28=72.31
+6.28 + 6.28
p= 78.59
Answer:
78.59$
Step-by-step explanation:
p-6.28=72.31
p=72.31+6.28
p=78.59$
What is the definition of exponential growth?
A. A condition in which a quantity decreases at a steady rate
B. A condition in which a quantity increases at a steady rate
C. A condition in which a quantity increases at a rate that is
proportional to the current value of the quantity
D. A condition in which a quantity decreases at a rate that is
proportional to the current value of the quantity
Answer:
C. A condition in which a quantity increases at a rate that is
proportional to the current value of the quantity
Step-by-step explanation:
Exponential growth is increasing, but not at a steady rate. On a graph, it has a curve instead of being a straight line.
PLEASE HELP!!! Due very soon!! - The graph below represents the height of a football pass, in feet, x seconds after it is thrown. Which of the following best describes the interpretation of f(2) ?
I think it is either b or c. Please tell me which is correct!!! Pls!!!
Answer:
The answer is D.
Step-by-step explanation:
By the time 4 seconds has passed, the line is at the bottom of the graph, which represents the time the ball has landed. I hope this helps.
Maren used the table shown to find a ratio which is equivalent to 2:6.
A multiplication table.
Which ratio is equivalent to 2:6?
8:18
8:24
10:36
10:42
Answer:
8:24
Step-by-step explanation:
dont ask me
I don’t know how to find this out
Answer:
C many solutions
Have a good day !There are 10 students in a class: 6 boys and 4 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Answer:
1/ 6
Step-by-step explanation:
Therefore, the required probability is 1/6.
Answer:
1/6
Step-by-step explanation:
Think of drawing 1 student at a time without replacement.
First drawing:
p(boy) = 6/10
Second drawing:
p(boy) = 5/9
Third drawing:
p(boy) = 4/8
p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6
Answer: 1/6
Evaluate l-a21, given a = 5, b=-3, and c= -2.
-10
10
-25
25
Answer:
10
Step-by-step explanation:
assuming those are meant to be absolute value brackets you have -5 x 2 which is -10 but because it is in the absolute value lines all answers become positive =10
A total of 511 tickets were sold for the school play. They were either adult tickets or student tickets. There were 61 more student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
255
Step-by-step explanation:
EXPLANATION We are looking for the number of adult tickets sold. number of adult tickets sold =x We are given that there were 61 more student tickets sold than adult tickets. number of student tickets sold =+x61 The total number of tickets sold was 511.
Is 8/6 equivalent to 16/12 as a ratio
Answer:
they are equivalent
Step-by-step explanation:
8/6
Divide the top and bottom by 2
4/3
16/12
Divide the top and bottom by 4
4/3
They are the same so they are equivalent
Find the volume of the given
shape.
2 points
5cm
3.5cm
6cm
Answer:
to find volume you multiply length x width x height
Step-by-step explanation:
5 x 3.5 x 6= 105
Answer:
5 x 3.5 x 6= 105
Step-by-step explanation:
PLZZZ give me brainliest
Use the Distributive Property to determine which of the following statements is equivalent to 5(6 – 1).
A. 6 - 1
B. 5 • 5
C. 30 - 5
D. 11 - 5
[tex]\text{You would use the distributive property to get your answer} \\\\\text{This means that you would distribute the 5 to the numbers inside the}\\\text{parenthesis}\\\\\text{When you distribute, you would multiply}\\\\\text{Distribute:}\\\\5(6-1)\\\\5(6)-5(1)\\\\30-5\\\\\text{You would see that this is equal to answer choice C, therefore making}\\\text{C your answer}\\\\\boxed{\text{C). 30 - 5}}[/tex]
what is the slope of the line passing through (13,-2) and (3,-2)
Answer:
Slope (m) =0
Slope (m) =
ΔY
ΔX
= 0
θ =
arctan( ΔY )
ΔX
= 0°
ΔX = 3 – 13 = -10
ΔY = -2 – -2 = 0
Distance (d) = √ΔX2 + ΔY2 = √100 = 10
3. An acute triangle with angles measuring 60 degrees,62°, and 58 degrees,
Possible or impossible
Answer:
Possible
Step-by-step explanation: