42
X
40
Find the unknown side length, x. Write your answer in simplest radical form.
A. 241
B. 4 29
C. 48
D. 58
Answers
The unknown side length of the right triangle is 58 units.
What is pythagoras theorem for a right triangle?
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Mathematically, Hypotenuse² = Base² + Perpendicular²
Given, the length of the perpendicular of the right triangle = 42 units
Also, the length of the base of the right triangle = 40 units
Let the length of the hypotenuse of the right triangle = 'x' units
Following the statement of the pythagoras theorem as established in literature, we have: Hypotenuse² = Base² + Perpendicular²
Substituting the values from the question given, we get:
x² = 42² + 40² = 3364 ⇒ x = √3364 ⇒ x = √58² ⇒ x = 58
Therefore, the unknown side length of the right triangle is 58 units.
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Related Questions
find the distance between the parallel lines. if necessary, round your answer to the nearest tenth. coordinate plane shows two lines. line y equals negative 3 x plus 1 and line y equals negative 3 x plus 4.
Answers
By taking the difference between the y-intercepts, we conclude that the distance between the lines is 3 units.
How to find the distance between the parallel lines?A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two linear equations are parallel if and only if both lines have the same slope and different y-intercepts.
And the distance is given by the difference between the y-intercepts.
Here the lines are:
y = -3*x + 1
y = -3*x + 4
The difference between the y-intercepts gives:
4 - 1 = 3
That is the distance between the lines.
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BRAINLIEST!! Find the arc length on a circle of radius 10 cm intercepted by a central angle of 6 rad
Answers
The length of the arc intercepted by a central angle of
6 radians is 60.34 cm.
What is an Arc?
An arc is any smooth curve joining two points.
Given is an circle of radius 10 cm intercepted by a central angle of
6 radians.
We can calculate the length of the arc using the formula -
L[arc] = (Ф/360°) x 2πr
Ф = 6 radians = 343.78 degrees
L[arc] = (343.78/360) x 2π x 10
L[arc] = 0.96 x 2π x 10
L[arc] = 60.34 cm
Therefore, the length of the arc intercepted by a central angle of
6 radians is 60.34 cm.
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Find the slope that passes through the points
(3, 5) and (7, 17)
Answers
Answer:
y=3x-4
Step-by-step explanation:
I need help asap!!!!
Answers
Answer: -1 and 5
Step-by-step explanation:
6+5m<1 how do I do this this is to hard
Answers
Answer: m < -1
Step-by-step explanation:
Step 1: 6 + 5m < 1. Step 2: 5m/5 < -5/5 m = -1
-6. -6
Answer: m < −1
Step-by-step explanation:
1. Rearange: 5m+6<1
2. 5 + 6−6 < 1−6
3. 5m < -5
4. 5m/5 < -5/5
5. Cancel terms that are in both the numerator and denominator then divide the numbers.
6. answer: m < -1
Bella is learning to type. She typed a letter to her teacher but misspelled 8 words. If she misspelled 25% of the words she typed, how many words did she type in her letter.
Answers
Bella is learning to type. She typed a letter to her teacher but misspelled 8 words. If she misspelled 25% of the words she typed, how many words did she type in her letter?
_________________________________________
She misspelled 8 words = 25% of the words she typed
25%= (8 / total words)* 100
0.25 = 8 / total words
total words = 8/0.25
total words = 32
__________________________-
The total words she typed in her letter were 32
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24500 kilograms. Other shipments weighing 13100 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 40-kilogram crates that can be loaded into the shipping container.
HURRY !
Answers
We can load less than or equal to 285 number of 40 kg crates in the shipping container.
The inequality is like 13100 + 40x ≤ 24500
Given,
The weight of crates transported by a shipping container = 40 kg
The greatest weight that can be loaded into the container = 24500 kg
The weight of already loaded shipments in the container = 13100 kg
We have to find and solve an inequality that determines the number of 40 kg crates that can be loaded into the shipping container:
Lets take x as the number of 40 kg crates.
Therefore, weight of container = 40x
The weight should be less than or equal to the maximum weight that can be loaded into the container:
That is,
13100 + 40x ≤ 24500
Now, solve the inequality:
40x ≤ 24500 - 13100
40x ≤ 11400
x ≤ 11400/40
x ≤ 285
So,
We can load less than or equal to 285 number of 40 kg crates in the shipping container.
The inequality is like 13100 + 40x ≤ 24500
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Solve for all values of y in simplest form.
10 = |y/9|
Answers
Answer: y = -90, 90
Step-by-step explanation:
To solve this, we will isolate the variable.
Given:
10 = |[tex]\frac{y}{9}[/tex]|
Absolute value:
10 = [tex]\frac{y}{9}[/tex] & -10 = [tex]\frac{y}{9}[/tex]
Multiply both sides of both equations by 9:
90 = y & -90 = y
Answer:
y = -90, 90
Which following conditions are necessary to use the binomial distribution
Answers
The conditions necessary for binomial distribution is option C that is I and III only "There is a series of N trials." and "The outcomes are mutually exclusive."
What is binomial distribution?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.
What are the conditions of binomial distribution?If the following circumstances hold true, the binomial distribution describes the behavior of a count variable X: 1: There will always be n observations. 2: Every observation stands alone. Three: Each observation corresponds to one of two results ("success" or "failure").
Option C, which consists solely of I and III, meets the requirements for the binomial distribution. "The results are mutually exclusive" and "There is a series of N trials."
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In a company's first year in operation, it made an annual profit of $111, 000. The
profit of the company increased at a constant 24% per year each year. How much
total profit would the company make over the course of its first 24 years of operation,
to the nearest whole number?
Answers
The total profit made by the company over the course of its first 24 years of operation is $10,016,640
Given,
The annual profit made by a company in first year = $111,000
The increase in profit per year = 24% = $26640
We have to find the total profit made by the company over the course of its first 24 years of operation
Lets take this as an arithmetic progression.
First term, a = 111,000
Common difference, d = 26640
nth term = 24
Sum of nth term,
Sₙ = n/2 [2a + (n - 1) d]
S₂₄ = 24/2 [2 × 111,000 + (24 -1) 26640]
S₂₄ = 12 [222,000 + 23 × 26640]
S₂₄ = 12 [222,000 + 612,720]
S₂₄ = 12 × 834,720
S₂₄ = 10,016,640
That is,
The total profit made by the company over the course of its first 24 years of operation is $10,016,640
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help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answers
-2 - 5
-7
f(0)
0 - 5
-5
f(5)
5 - 5
0
can someone help pls????
detail for me as well
Answers
Step-by-step explanation:
the easy straight forward method is to simply sum up the 5 terms.
you know that this symbol just means "sum", right ?
and that the index variable is "running" from 1 to 5.
so, you have to sum up
3×1 + 3×2 + 3×3 + 3×4 + 3×5 = 3 + 6 + 9 + 12 + 15 = 45
now, if you want it done via a summary formula to add the first n terms of an arithmetic sequence, like in this case
a1 = 3
an = an-1 + 3 = a1×n = 3n
then
the sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ).
it simply means : first plus last term added up n/2 times.
why ?
because a1 + an = a2 + an-1 = a3 + an-2 = ...
we get n/2 times such part sums.
so, in our case, n = 5, and we get
(3 + 3×5)×5/2 = (3 + 15)×5/2 = 18×5/2 = 9×5 = 45
Answer:
∑ (i = 1 to 5) (3·i)
= 3·∑ (i = 1 to 5) (i)
= 3·(1 + 2 + 3 + 4 + 5)
= 3·15
= 45
please help me
ling earns $11.95 per hour. how much is she paid for working:
8 hours?___ 15 hours?___ 38 hours?___
Answers
it's so easy just use a calculator:
8h: $95.60
15h: $179.25
38h: $454.1
kusa rode his bike for 10 miles /hour for 0.75 hours chaman rode his bike for 12 mile/hour for 0.6 hours
need please asap will give brainlyies
who rode farthur and how far did trhat person ride?
A. kusa he rode 10 miles
B. kusa he rode 7.5 miles
C. charman he rode 6 miles
D. charman he rode 7.2 miles
Answers
Answer:
B
Step-by-step explanation:
Kusa=10x0.75=7.5
Chaman=12x0.6=7.2
7.5>7.2
so kusa rode further than chaman.
Answer:
b
Step-by-step explanation:
-5y - 35
C cncbfbfbdbdjxdbxjdjdvdbfbfbfbfnfnfnfb
Answers
Answer:
5(y - 7)
Step-by-step explanation:
common factor
5-y-35
5(y - 7)
An angle measures 82° less than the measure of its complementary angle. What is the measure of each angle?
Answers
Answer: 4 and 82 i think
M- (-7)<5
-helpppp please
Answers
Answer: M + 7
Step-by-step explanation:
Well, it doesn’t show the variable’s number correct?
So, since we don’t have the number, we are going to multiply -1 by -7, getting 7 from this. Now, change it to addition. You should have m + 7.
I hope this helps!
Shanika is thinking of a rational number, but tells you its opposite. What is true about the number she is thinking of?
a- it is located at zero on the number line
b-it is to the right of zero on the number line
c- it is twice as far from zero as the number she tells you
d-it is the same distance from zero as the number she tells you
Answers
Answer:
d. It is the same distance from zero as the number she tells you.
Step-by-step explanation:
Case 1: Let Shanika thought a positive rational
number
Let the number that Shanika thought be c.
Then, the distance of it from zero = lc - Ol = c.
But, the number she told = -c
The distance of -c from zero = 10--(-c)| = c
Case 2: Let Shanika thought a negative rational number
Let the number that Shanika thought be -c (c>0).
Then, the distance of it from zero = 10--(-c)| = c.
But, the number she told = c
The distance of -c from zero = Ic-01 = c
In both cases, the number she thought is the same distance from zero as the number she tells us.
the non-engineer wants 600 pounds of total initial thrust from the 20 rockets. what is the probability that his/her scheme will produce the minimum required thrust?
Answers
The exit mass flow rate times the exit velocity less the free stream mass flow rate times the free stream velocity equals the force (thrust).
If we take into account the factors mentioned above, we will see that if the aircraft can fly at full thrust in cruise, this fits nicely with a static sea level thrust force equivalent to one third of its weight force. The thrust required to sustain flight is approximately 1/18 of the aircraft weight. It takes classroom teaching, ground training, and flying training from a certified instructor to obtain a high-altitude endorsement. we will learn about the warning signs and symptoms of altitude sickness, when to use supplemental oxygen, how long you can use that oxygen safely, and more during ground school.
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Hong has 16 one-dollar bills. he wants to give each of his 6 children the same number of bills. how many bills can he give each child? how many bills will hong have remaining?
Answers
Hong has 16 one-dollar bills. he wants to give each of his 6 children the same number of bills. Then Hong will give 12 bills to his 6 children and 4 bills Hong have remained
Hong has 16 one-dollar bills.
he wants to give each of his 6 children the same number of bills.
how many bills can he give each child?
how many bills will Hong have remaining?
since Hong has 16 one dollar bills and he wants 6 children the same number of bills
then he give 6 children two bills to each
then the total number of bills he give to 6 children is 12
and he has 16 bills and 12 bills give to his children
the remaining bills left = 16 bills - 12 bills = 4 bills
Hence , Hong will give 12 bills to his 6 children and 4 bills Hong have remained
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A Ferris wheel is designed in such a way that the height (h), in feet, of the
seat above the ground at any time, t, is modeled by the function h(t) = 49cos
(π/15+T) + 50. What is the maximum height of the wheel?
Answers
Mikey is conducting a science experiment about the rate at which different materials will burn. In his hypothesis, he states that a pencil and a lemon will burn at the same rate because they are both yellow. Which logical fallacy has Mikey used? False analogy Hasty generalization Red herring Slippery slope
Answers
The logical fallacy which Mikey has used is referred to as: A. False analogy.
What is a fallacy?A fallacy can be defined as a mistaken or false belief (assumption) that are based on illogical arguments or reasoning.
The types of fallacy.In Science, there are different types of fallacy and these include the following:
Red herringAppeal to authoritySlippery slopeHasty generalization.Ad HominemAppeal to Popularity (Ad populum)Fallacy of exclusionFalse analogyAdditionally, a false analogy simply refers to a type of informal fallacy which states that since quantity A and quantity B both share the same quality X (color yellow), then, they must also share quality Y in common (burning rate).
In this context, we can reasonably infer and logically deduce that Mikey's hypothesis is a false analogy.
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Answer: hey sis! the answer is a
Step-by-step explanation: A.) false analogy
(btw this language arts not math)
Please help I will give brainliest
Answers
Answer:
y=1/2x+2
Step-by-step explanation:
y=mx+b
m = slope = rise/run
b = y-intercept
Look at the graph, and find the slope.
m= slope = rise/run = 1/2
b = y-intercept = 2
Therefore, the correct answer is option y=1/2x+2
what unit would you use to measure the length of Supermarket
Answers
The length of the building should be measured in meters, as that is the most appropriate unit.
What are units?A unit of measurement is a specific magnitude of a quantity that has been established and adopted by law or convention and is used as a benchmark for measuring other quantities of the same kind. A multiple of the unit of measurement can be used to express any other quantity of that type. A length, for instance, is a physical quantity.The most suitable unit to measure the length of the building will be measuring the length of the building in meters.
Therefore, the length of the building should be measured in meters, as that is the most appropriate unit.
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round to 1 significant figure
Answers
Round to 1 significant figure
What is Rounding?
To estimate a certain number in a context, rounding is a process. Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures.
How to round a figure
It rounds to the most important figure in the number. To round to a significant figure: look at the first non-zero digit if rounding to one significant figure. look at the digit after the first non-zero digit if rounding to two significant figures.
To understand this term lets take and example:
24982 correct to 1 significant figure
If we round up, then the answer is
30,000
but if we were to round down, the answer would be
20,000;
If we want to determine which one is correct, we have to look at the second digit of the original number, which is
4
Since the second digit is less than 5
we can round down, so the answer would have to be
20,000
Hence, 24982 round to 1 significant figure is 20,000
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I need help with 1-4 please and thanks
Answers
Estimate intercepts of the graph of the functions
1. [tex]y=\frac{1}{3} x+1[/tex]
=>At x axis
x = 0
y= 0+ 1
y = 1
=>At y axis
y= 0
1/3x = -1
x= -3
The x intercepts:( -3, 0)
The y intercepts : (0,1)
2. [tex]y= x^{2} -3x-4[/tex]
=> At x axis
x=0
y= - 4
=> At y axis
y= 0
[tex]x^{2} -3x-4= 0[/tex]
(x-4)(x+1) = 0
x= 4,-1
The x intercepts: (4,0) ( -1, 0)
The y intercepts : (0,-4)
3. y= -2 |x-5|
=> At x axis
x=0
y= -2(5)
y= -10
=> At y axis
y= 0
-2|x-5|=0
Divide both sides by -2
|x - 5|= 0
x- 5 = 0
x = 5
The x intercepts: (5,0)
The y intercepts : (0,-10)
4. [tex]y= -4x^{3} -13x^{2} -10x[/tex]
=> At x axis
x= 0
y = 0
=>At y axis
y=0
[tex]0=-4x^{3} -13x^{2} -10x \\\\4x^{3} +13x^{2} +10x =0[/tex]
By factorization ,
x( 4x+5 )( x+2)= 0
x= 0, -2, -5/4
The x intercepts: (0,0) (-2,0) ,(-5/4,0)
The y intercepts: (0,0)
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Solve for m.
D=(m− 3)
m=
(Simplify your answer. Use integers or fractions for any
numbers in the expression.)
Answers
m = D +3
What is algebra?The basics of algebra include numbers, variables, constants, equations, linear and equations. It also includes the basic arithmetic operations : addition, subtraction, multiplication, and division within the algebraic expressions. Algebra is the study of mathematical symbols and the rules for using these symbols in formulas .
The three most used laws are the Commutative, Associative, and Distributive Laws. The main rule of algebra is balancing. The equation has equals sign and both the sides should be equal.
Given, D = (m -3)
we can write,
m = D+3
if D is assumed to be 2 (integer) then,
m = 2+3= 5 (integer)
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A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n=16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student’s reaction time is measured. The scores for the sample averaged 220 milliseconds with a standard deviation of 20. Assuming that reaction time for students in the regular population averages 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Use a two-tailed single-sample (one-group) t-test with alpha = .05.
What are the null and alternative hypotheses?
Answers
The null hypothesis is that the reaction time for students in the regular population averages 200 milliseconds.
The alternate hypothesis is that the reaction time for students in not the regular population averages 200 milliseconds.
What is null hypothesis?In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.
With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims:
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12 | 13
1
3/4
5/6
7/8
li
2
Angles 1 & 5 are an example of:
1₂
13
Answers
Answer:
corresponding angles
Step-by-step explanation:
1 and 5 are corresponding angles
they are in the same place
that is why they are corresponding
Levi’s chooses three different numbers the sun of the three numbers is 24 one of the number is a square number the other two numbers are factors of 20 find the three numbers chosen by Levi’s write the number in ascending order
Answers
The three numbers that are chosen by Levi are 5, 9 and 10.
How to calculate the value?It should be noted that the factors of 20 are 1, 2, 4, 5, 10 and 20.
Possible sum of factors of 20 are: 3, 5, 6, 7, 9, 11, 12, 14, 15, 21, 22, and 24.
Difference between 24 and a possible sum of factors of 24 are:
(21, 19, 18, 17, 15, 13, 12, 10, 9, 3, 2 , 0.)
The square numbers less than 24 are ( 1, 4, 9, 16).
Therefore the square number is 9.
And sum of the factors of 20 is 24 -9 = 15.
Therefore, the factors of 20 are = 5 and 10
Thus the given numbers are 5, 9 and 10.
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