We have been given that a right triangle with integer sides has area equal to 30. We are asked to find the length of hypotenuse of right triangle.
We know that area of triangle is half the product of its base length and height.
Since our given triangle is a right triangle, so its base and height will be legs of right triangle.
[tex]\frac{1}{2}\cdot\text{Base}\times \text{Height}=\text{Area}[/tex]
[tex]\frac{1}{2}\cdot\text{Base}\times \text{Height}=30[/tex]
[tex]\frac{1}{2}\cdot 2\cdot\text{Base}\times \text{Height}=30\cdot 2[/tex]
[tex]\text{Base}\times \text{Height}=60[/tex]
This means that product of two bases is 60.
Now we need to find two multiples of 60 such that they are make a right triangle.
Multiples of 60:
1, 60
2, 30
3, 20
4, 15
5, 12
6, 10
We know that (5, 12 and 13) is a Pythagoras triplet.
[tex]5^2+12^2=13^2[/tex]
[tex]25+144=169[/tex]
[tex]169=169[/tex]
Therefore, the hypotenuse of right triangle is 13 units.
Answer quick please.
Answer:
V = (1/2) mile per (5/10) hour, multiply both mile and hour by 2, => V = 1 mile per 1 hour (1 mile/hour)
Hope this helps!
:)
Answer:
1
Step-by-step explanation:
In reference to patterns there is a process of getting from one term to another or to finding a certain term in the pattern. first two words ru
There is no question asked, and the statement is incomplete, but this describes Series and Sequence. They are usually arithmetic or geometric progressions. A set of numbers are written to follow a particular pattern, when the pattern is clear, one can find any number of the sequence or series.
For example, consider the sequence below (Arithmetic Progression)
2, 4, 6, 8, ...
This sequence has a particular pattern.
The first term of the sequence is
a = 2
The common difference d, which is the difference between any two consecutive terms is
d = 2
The nth term, which is the formula that defines every single term of the sequence is given as
Tn = a + (n - 1)d
Check
T1 = a = 2
T2 = 2 + 2 = 4
T3 = 2 + 2(2) = 6
T4 = 2 + 2(3) = 8
T20 = 2 + 2(19) = 40
And so on.
Geometric progression
2, 4, 8, 16, 32, etc
First term, a = 2
Common ratio r, is the division of a particular number by the number preceding it.
r = 4/2 = 8/4 = 16/8 = 32/16 = 2
The nth term is given as
Sn = ar^(n-1)
S1 = a = 2
S2 = 2×2 = 4
S3 = 2×2^(2) = 8
S4 = 2×2^(3) = 16
S5 = 2×2^(4) = 32
S20 = 2×2^(19) = 1048576
And so on.
Answer:it’s rule
Step-by-step explanation:
I got it right on usatestprep
Graph the solutions of the linear equation
y=-2x + 1. Then explain how the graph is
different from the graph in the example,
Answer:
c
Step-by-step explanation:
Given: A = 1 −1 −2 3 B = 1 5 8 −8 C = 1 2 3 4 Solve: AX + B = C X =
Answer:
-5 3, -5 6
Step-by-step explanation:
just did it
Answer:
1st row: [-5 3] 2nd row: [-5 6]
Step-by-step explanation:
Edge 2020
Enter the value of the exponential expression 5^0
Answer:
1
Step-by-step explanation:
whenever something is to the power of 0, it equals 1
Ben needs to mix 1.5 cups of lemonade concentrate with 4 cups or water to make lemonade. He has 6 cups of concentrate. How much water does he need?
Answer:
24
Step-by-step explanation:
To get your answer, you need to multiply 1.5 and 6.
1.5 x 6 = 9
Then you multiply 4 and 6.
4 x 6 = 24
Which is your final answer.
I hope this helps you! Good Luck!(a(1) = -2
[a(n) = a(n − 1) – 5
Find the 4th term in the sequence.
The 4th term in the sequence is -17.
To find the 4th term in the sequence defined by the recursive formula [tex]\(a(n) = a(n-1) - 5\)[/tex] with the initial condition [tex]\(a(1) = -2\)[/tex], you can use the recursive formula to compute each term. Let's find the first few terms:
1. [tex]\(a(1) = -2\)[/tex] (given)
2. [tex]\(a(2) = a(1) - 5 = -2 - 5 = -7\)[/tex] (using the recursive formula)
3. [tex]\(a(3) = a(2) - 5 = -7 - 5 = -12\)[/tex] (using the recursive formula)
4. [tex]\(a(4) = a(3) - 5 = -12 - 5 = -17\)[/tex] (using the recursive formula)
The recursive formula tells us how to calculate each term in the sequence based on the previous term. Starting with \(a(1)\), we use the formula to find [tex]\(a(2)\)[/tex], then use [tex]\(a(2)\) to find \(a(3)\)[/tex], and so on.
So, the 4th term [tex](\(a(4)\))[/tex] is found by taking the previous term [tex](\(a(3)\))[/tex], which is -12, and subtracting 5.
Complete the question:
a(1) = -2;
a(n) = a(n − 1) – 5
Find the 4th term in the sequence.
Final answer:
The 4th term in the sequence defined by a(1) = -2 and a(n) = a(n − 1) − 5 is -17, which is found by successively subtracting 5 from the previous term.
Explanation:
To find the 4th term in a sequence where a(1) = -2 and a(n) = a(n − 1) − 5, we will use the recurrence relation to determine each subsequent term:
First term (a(1)) is given as -2.The second term (a(2)) equals a(1) - 5 = -2 - 5 = -7.The third term (a(3)) equals a(2) - 5 = -7 - 5 = -12.The fourth term (a(4)) equals a(3) - 5 = -12 - 5 = -17.Therefore, the 4th term in the sequence is -17.
How should the decimal point in 948.921 change to get the correct answer to 948.921 ÷ 10 to the power of 4?
move it 4 places to the left
move it 4 places to the right
move it 5 places to the left
move it 5 places to the right
Answer:
move it 4 places to the left
Step-by-step explanation:
10 to 4th power is basically 10000 so 948.921 divided by 10000 so its obvious it will not move to the right, making the number bigger.
A bag contains 8 red marbles, 7 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
The exact probability that both marbles drawn will be red is 4/25.
Given that:
Number of red marbles in the bag, R = 8
Number of blue marbles in the bag, B = 7
Number of green marbles in the bag, G = 5
The total number of marbles in the bag is:
T = 8 + 7 + 5
= 20
The probability of drawing a colored marble is the number of marbles of that color by the total number of marbles.
So, P(R) = 8/20, P(B) = 7/20 and P(G) = 5/20
If two marbles are drawn out of the bag, the probability that both marbles are red is:
P = P(R) P(R)
= (8/20)(8/20)
= (2/5)(2/5)
= 4/25
Hence, the probability s 4/25.
Learn more about Probability here :
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Final answer:
The exact probability of drawing two red marbles from the bag without replacement is the product of the individual probabilities, calculated as (2/5) × (7/19).
Explanation:
To find the probability that both marbles drawn from a bag will be red, given the bag contains 8 red marbles, 7 blue marbles, and 5 green marbles, we need to calculate the probability of drawing one red marble and then another red marble without replacement.
The total number of marbles in the bag is 8 red + 7 blue + 5 green = 20 marbles. The probability of drawing the first red marble is 8/20, which simplifies to 2/5. After drawing one red marble, there are now 7 red marbles left and the total drops to 19 marbles. The probability of drawing a second red marble is now 7/19.
To find the probability of both events happening, we multiply the probabilities of each event: (2/5) × (7/19). Therefore, the exact probability of drawing two red marbles in succession without replacement is (2/5) × (7/19).
Write the word sentence as an equation. Then solve.
The difference between a number p
and 6 is −14.
Answer:
p - 6 = -14
p = -8
If someone confuses the order, p might be 20, But here I am going to choose p= -8
Step-by-step explanation:
The difference between a number p
and 6 is −14.
The difference between a number p and 6 = -14
I replace "is" with an equal sign
p - 6 = -14
so
p = 6 - 14
p = -8
it can be confused as 6 - p = -14, p = 20
Answer:
The difference between a number p
and 6 is −14.
The difference between a number p and 6 = -14
I replace "is" with an equal sign
p - 6 = -14
so
p = 6 - 14
p = -8
it can be confused as 6 - p = -14, p = 20
Step-by-step explanation:
Solve 14x + 1 = 36.
Round to the nearest ten-thousandth.
Answer:
x≈ 3.2056
Step-by-step explanation:
Set both sides by log. Then, solve for x.
1. 14^(x + 1) = 36
(x + 1)log(14) = log(36)
x + 1 = log(36)/log(14) . . . Divide both sides by log(14)
x = log(36)/log(14) - 1 . . . . Subtract both sides by 1.
x ≈ 0.3579 . . . . . . . . . . . .Use calculator to simplify the expression.
Note that the second problem is similar to the first.
2. 12^(y - 2) = 20
(y - 2)log(12) = log(20)
y - 2 = log(20)/log(12)
y = log(20)/log(12) + 2
y ≈ 3.2056
Answer:
X=2.5
Step-by-step explanation:
14x +1 =36
14x + 1 =36
- 1 = 36
14x = 35
14x / 2 = 35 / 2
x = 2.5
The test scores for a math class are shown below.
83, 85, 82, 93, 83, 84, 95, 87, 86, 94
What is the standard deviation of the data set? Round your answer to the nearest tenth.
A. 4.8
B. 4.6
C. 4.7
D. 4.3
Answer:
c. 4.7
Step-by-step explanation:
first, you find the mean of data set:
83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94 = 872/10 = 87.2
then, you take each number and subtract the mean and square it:
(87.2 - 83)² = (4.2)² = 17.64
(87.2 - 85)² = (2.2)² = 4.84
(87.2 - 82)² = (5.2)² = 27.04
(93 - 87.2)² = (5.8)² = 33.64
(87.2 - 83)² = (4.2)² = 17.64
(87.2 - 84)² = (3.2)² = 10.24
(95 - 87.2)² = (7.8)² = 60.84
(87.2 - 87)² = (0.2)² = 0.04
(87.2 - 86)² = (1.2)² = 1.44
(94 - 87.2)² = (6.8)² = 46.24
now, find the mean of the squared numbers:
17.64 + 4.84 + 27.04 + 33.64 + 17.64 + 10.24 + 60.84 + 0.04 + 1.44 + 46.24 = 219.6/10 = 21.96
then, take the square root of the number you just got:
√21.96 = 4.68
and last but not least, round to the nearest tenth: 4.7
Answer:
5.5 is the answer, I just took the test
p v q is true for a total of how many cars?
Answer:D. 80
Step-by-step explanation:
all you do is add 40, 14 and 26 from the graph
Evalute the expression. 80 + (8x4) divided by 2
Answer:
If you meant [80 + (8*4) ]/2, then [80 + (8*4) ]/2=56
or if you meant 80 + [ 8*4 / 2], then 80 + [ 8*4 / 2] = 96
Step-by-step explanation:
Evalute the expression. 80 + (8x4) divided by 2
so do you mean
the whole expression 80 + (8x4) is over 2 ?
If so then:
evaluate 8x4 = 8 * 4 = 32.
so we have 80 + (8x4) is over 2 = (80 + 32)/2 = 112/2 = 56
If you meant 80 + [ 8*4 / 2]
then 80 + [ 8*4 / 2] = 80 + 8*2 = 80 + 16 = 96
After a 35% discount, a book costs 11.21, what is the normal undiscounted price of the book?
Answer:
$17.25
Step-by-step explanation:
First, we know that $11.21 is 65% of the original price, so divide 11.21 by 65 to find 1% of the original price
Then just multply your result of .17246 by 100 to get 17.246, which rounded to 17.25
The normal undiscounted price of the book is $17.24.
Explanation:To find the normal undiscounted price of the book, we need to calculate the original price before the discount. Let's assume the original price of the book is 'x'. After a 35% discount, the book costs $11.21. We can set up the equation:
x - 0.35x = 11.21
Simplifying the equation, we get:
0.65x = 11.21
Dividing both sides by 0.65, we find:
x = 11.21 / 0.65
Using a calculator, we get:
x ≈ $17.24
Therefore, the normal undiscounted price of the book is $17.24.
Learn more about calculating undiscounted price here:https://brainly.com/question/16322266
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Determine the volume of the oblique cylinder. Use 3.14 for
π. Round your answer to the nearest tenth. Show all of your work.
Answer:
602.88 in ^ 3
Step-by-step explanation:
To calculate the volume of a cylinder, is the multiplication of the base area by the height the formula is as follows:
Vc = pi * (r ^ 2) * h
we have the necessary data, the radius equals 4 inches and the height equals 12 inches, replacing:
Vc = 3.14 * (4 ^ 2) * 12
Vc = 602.88 in ^ 3
that is, the volume of the oblique cylinder is 602.88 cubic inches
Answer:
The volume is 602.9in³
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder
To find the volume of the oblique cylinder we use the formula for the volume of a cylinder
V= πr²h
Given data
Radius r = 4in
Height h= 12in
Substituting our given data we have V= πr²h
V=3.14*(4)²*12
V= 3.14*16*12
V= 602.88in³
To the nearest tenth
V= 602.9in³
Red box weighs 50 pounds, blue box weighs 60 pounds, and yellow box weighs 115 pounds. What is the average weight in pounds?
Answer: 75
Step-by-step explanation:
Add the three factors and divide by three.
John was given a math equation. He completed it in 5 seconds. Is his answer correct? If it is, show how he got the answer. Show your work. See picture down below.
Answer:
He is definitely correct.
Step-by-step explanation:
1 + 1 = 2 is a very easy equation and is the simplest equation to do.
what is f^7 . f^1 please help
Answer:
is f^8
Step-by-step explanation:
For each statement determine if it is True or False for the graph of 6x – 3y = 21.
The x-intercept is 3 1/2.
A).Yes B).No
The y-intercept is -7.
А). Yes B). No
The slope is 3.
A). Yes B). No
1. Yes, the x-intercept is 3 1/2
2. Yes, the y-intercept is -7
3. No, the slope is 2
Explanation:6x -3y = 21
-3y = -6x + 21
y = 2x - 7
find the 104 term of the sequence -2,1,4,7,...
Answer:
307.
Step-by-step explanation:
Arithmetic sequence with first term a1 = -2 and common difference d = 1 - -2 = 3
an = a1 + d( n - 1), so
a104 = -2 + 3(104 - 1)
= -2 + 309
= 307.
What percent is equivalent to the fraction 10/25 (ten twenty-fifths)? *
20 points
A
10%
B
40%
C
25%
D
5%
How much is x? Round it to the nearest tenth.
Answer:
The answer is 7.3
Step-by-step explanation:
when a trend line is drawn on a scatter plot, there are four points above the trend line. about how many points should be below the trend line?
a. 0
b. 2
c. 4
d. 8
Answer:4
Step-by-step explanation:
A cylinder with height 9 inches and radius 6 inches. What is the exact volume of the cylinder? Cylinder V=Bh V = 54 pi inches cubed V = 108 pi inches cubed V = 324 pi inches cubed V = 486 pi inches cubed
Answer:
V=324 pi inches cubed
Step-by-step explanation:
The formula for the volume of a cylinder is πr²h
π(6)²(9)
π(324)
Answer:
c : 324 pi in cubed. on edge 2020
Step-by-step explanation:
HIGH POINT QUESTION
A shape is rotated 180 degrees about the origin and then its image is reflected in the Y-axis. Describe fully the single transformation that would have the same result as the two transformations described above.
Answer:
Reflection in the x-axis
Step-by-step explanation:
If the point (x, y) of the shape is rotated 180° about the origin, it will be transformed into the point (-x, -y).
If the point (-x, -y) is reflected in the Y-axis, it will be transformed into the point (x, -y). This transformation is equivalent to the reflection of (x, y) in the x-axis.
clarissa has 3 pints of ice tea that she divides into 1/2-pint servings. how Many 1/2 -pints servings does she have?
Answer:
6
Step-by-step explanation:
1 pint of tea will produce 2 half pints
So since there are 3 pints of tea it will produce 6 half pints of tea
Jimmy's fishing boat is sailing near the shoreline when a lighthouse on the top of a 250-foot cliff is lit up. If Jimmy's sight line is 400 feet away from the lighthouse, what is the angle of depression from the lighthouse to the fishing
Answer:
32.0054
Step-by-step explanation:
i think
The angle of depression is approximately 32.01 degrees.
To find the angle of depression, we can use the concept of trigonometry. Specifically, we use the tangent function, which relates the height of the lighthouse to the distance from the lighthouse to Jimmy's boat.
Steps to solve:
Let θ be the angle of depression.The height of the lighthouse (opposite side) is 250 feet.The distance from the lighthouse to the boat (adjacent side) is 400 feet.Use the tangent function: tan(θ) = opposite / adjacent.Substitute the values: tan(θ) = 250 / 400.Simplify the fraction: tan(θ) = 0.625.Find the angle by taking the arctangent: θ = [tex]tan^{-1}[/tex](0.625).The result is approximately: θ ≈ 32.01 degrees.Therefore, the angle of depression from the lighthouse to the fishing boat is about 32.01 degrees.
A school paid $31.25 for each calculator. If the school spent $500 on calculators, how many did the school buy?
Answer:
A school paid $31.25 for each calculator.
If the school spent $500 on calculators, the number of purchased calculators:
N = 500/31.25 = 16
Hope this helps!
:)
Answer:
Divide 500 by 31.25$ which equals to 16
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
Video Rental Fines
A graph titled Video Rental Fitness has videos rented on the x-axis, and fines (dollars) on the y-axis. Points are scattered all over the graph.
a.
negative; as the number of videos rented increases, the amount of fine increases.
b.
negative; as the number of videos rented increases, the amount of fine decreases.
c.
no correlation
d.
positive; as the number of videos rented increases, the amount of fine decreases.
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
Answer:
cccccccc
Step-by-step explanation: