Answer:
b = √c²-a²
Step-by-step explanation:
b² = c² - a²
b = √c²-a²
The Pythagorean theorem, denoted as a² + b² = c², can be rearranged as b = √(c² - a²) to solve for one of the sides of a right triangle. Once the lengths for a and c are known, they can be substituted into the formula to find the length of b.
Explanation:The Pythagorean theorem, a key geometric principle, can be used to solve for one of the sides in a right triangle given the lengths of the other two. Usually, it's denoted as a² + b² = c², where a and b are the lengths of the triangle's legs, and c is the length of the hypotenuse. In the question, you want to solve for b.
First, let's isolate b in the formula. Rewrite the formula as b² = c² - a². To find the length of b, take the square root of both sides, resulting in b = √(c² - a²).
Now, once you have the values for a and c, you can substitute them into the formula to find b. This application of the Pythagorean theorem can be very useful in various situations where you have a right triangle, and you know the lengths of two of its sides but need to find the length of the third side.
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Which function is the inverse of (x) = -5x-42
Answer:
f-1(x) = (-1/5)x - 42/5
Step-by-step explanation:
f(x) = -5x - 42
Switch the x and y
x = -5y - 42
solve for y
-5y = x + 42
y = (-1/5)x - 42/5
A rectangular pyramid was sliced parallel to its base. What is the shape of the cross section
Answer:
Trapezoid is the shape of the cross section of a rectangular pyramid.
Step-by-step explanation:
We are given a rectangular pyramid was sliced such that it becomes parallel to its base. We are to determine the shape of the cross section.
Slicing the pyramid with rectangular pyramid will form a trapezoid as a cross section which will be parallel to the base of the pyramid.
Refer to the figure below for better understanding.
it takes 91 kiloliters of water to fill the hendersons swimming pool. how much is this in liters
Answer:
91,000 Liters
Step-by-step explanation:
1 Kiloliters = 1,000 liters
91 times 1,000 = 91,000
To convert 91 kiloliters to liters, multiply 91 by 1,000, which equals 91,000 liters. Therefore, 91 kiloliters of water is equal to 91,000 liters.
To convert kiloliters to liters, you need to know the conversion factor. 1 kiloliter (kL) is equivalent to 1,000 liters (L). Therefore, to convert 91 kiloliters to liters, you simply multiply 91 by 1,000.
The calculation would be as follows:
91 kL × 1,000 L/kL = 91,000 L
So, 91 kiloliters of water is the same as 91,000 liters of water.
Footware manufacturing is projected to decrease output by 8.4% from 2006 to 2016. If footware manufacturing had 1.8 billion dollars of output in 2006, approximately how much output is expected in 2016?
Answer:
The output expected in 2016 is 1.6488 x 10 ^9 or 1.6488 billion
Step-by-step explanation:
The output is decreased by 8.4% from 2006 to 2016.
Amount of output in 2006 = 1.8 billion dollars
Decrease in output = 8.4%
We need to find the 8.4% of 1.8 billion dollars and then subtract the result from 1 billion dollars.
We know 1.8 billion = 1,800,000,000 or 1.8 x 10^9
8.4% of 1.8 billion = 8.4/100 * (1.8 x 10^9)
= 151200000
So, Output expected in 2016 = 1.8 x 10^9 - 151200000
= 1648800000 or 1.6488 x 10 ^9
So, the output expected in 2016 is 1.6488 x 10 ^9 or 1.6488 billion.
Answer:
It would be D
Step-by-step explanation:
$1.65 billion
Fran solved the equation 42 = x + 23. Although her final answer was correct, she could have found it in a simpler way. Which sentence best explains why?
The easier way to solve the equation 42 = x + 23 is by subtracting 23 from both sides of the equation. This will result in the value of x being 19. The process of isolating the variable on one side of the equation is important for finding the value of the variable.
Explanation:In this mathematical equation, 42 = x + 23, to find the value of x, we need to isolate x on one side of the equation. The operation involved is subtraction. We subtract 23 from both sides of the equation. This process is important to maintain the equality of the equation. By doing this operation, both sides of the equation still balance. After subtracting 23 from both sides, we get x = 42 - 23, resulting in x = 19.
In order to find the value of x, Fran needs to isolate it on one side of the equation. To do this, she can subtract 23 from both sides of the equation, resulting in 42 - 23 = x. Simplifying further, she finds that x = 19.
Alternatively, Fran could have recognized that 42 - 23 equals 19 and immediately concluded that x = 19, saving her the need to do the subtraction step.
Therefore, the sentence that best explains why Fran could have found the answer in a simpler way is that she could have recognized the subtraction step as an immediate result and skipped it.
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the art museum charges $13 for each adult admission and $8 for each child the total bill for the 182 people from a achool trip was $1606 how many adults and children went to the museum?
Answer:
152 kids and 30 adults
Step-by-step explanation:
To solve this, we must create a system of equations
Suppose:
x = the number of adults
y = the number of children
We know that a total of 182 people attended the trip.
So:
x + y = 182
This equation represents the number of people attending the trip.
To find out the cost, look at the problem.
It costs 13$ for one adult and 8$ for a child.
So:
13x + 8y = 1606
This equation represents the total cost to attend the museum. Now, we must solve.
[There are two ways to solve a system of equations, substitution and adding/subtracting. I will use adding and subtracting. The steps to solving the system of equations is in the photos below]
The final answer is 152 kids and 30 adults
I hope this helps!!! :)
An electronics store had a 20% off sale,if a stereo originally cost $125,how much did the stereo cost during the sale
100 dollars because yeah
Can someone please help me with this question please.
Step-by-step explanation:
[tex](a)\\h-\text{number of hours}\\\\8\dfrac{1}{5}\cdot h=32\dfrac{4}{5}\\(b)\\\text{convert the mixed numbers to the improper fractions}\\\\\dfrac{8\cdot5+1}{5}h=\dfrac{32\cdot5+4}{5}\\\\\dfrac{41}{5}h=\dfrac{164}{5}\qquad\text{multiply both sides by 5}\\\\41h=164\qquad\text{divide both sides by 41}\\\\h=4[/tex]
[tex]\text{Answer:\ 4\ hours}[/tex]
Which of the following statements is logically equivalent to, "If it is a holiday, then there is no school"?
Answer: If there is school, then it is not a holiday.
Step-by-step explanation:
Very easy just do
Contrapositive= negation and reverse
618 runners registered for the marathon. Of these runners 0.8% completed the race in under 2 hr 15 min. a) how many runners completed the race in this time?
EXPLAIN HOW TO SOLVE THIS
Answer:
Exact = 4.944 Rounded = about 5 Reality = 4 since there can’t be 99.4% of an human.
Step-by-step explanation:
0.8/100 = x/618
618(0.8) = 100x
494.4 = 100x
/100. /100
x = 4.944
The number of runners that completed the race in under 2 hr 15 min will be 5 approximately.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
618 runners registered for the marathon. Of these runners, 0.8% completed the race in under 2 hr 15 min.
Let "N" be the number of runners who completed the race. Then the equation is given as,
0.8% = (N / 618) x 100
0.008 = N / 618
N = 0.008 x 618
N = 4.944
N ≈ 5
The number of runners that completed the race in under 2 hr 15 min will be 5 approximately.
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Find the measure of each interior angle of a regular convex dodecagon. Show equations and all work that leads to your answer.
The exterior angles to any convex polygon sum to 360 degrees in measure, so that for a regular dodecagon (12-gon) each exterior angle has measure
[tex]\dfrac{360^\circ}{12}=30^\circ[/tex]
Exterior angles are complementary to interior angles, which means each interior angle has measure
[tex]180^\circ-30^\circ=\boxed{150^\circ}[/tex]
What is the approximate probability that a person is in the 45-54 age group given that they liked the movie?
A.1
B.0.52
C.0.35
D.0.18
Answer:
d.
Step-by-step explanation:
12+5+9+3+13+8=50=total
divide the total by the amount of 45-54s that liked the movie
9/50=0.18
find the value of x
5x+15+6x-10=180
Combine the common factors.
11x + 5 = 180
Subtract 5 from both sides.
11x = 175
Divide 11 from both sides to isolate the x.
x = 15.90909091
Answer:
x = 175/11
Step-by-step explanation:
Step 1: Combine like terms
11x + 5 = 180
Step 2: Subtract 5 from both sides.
11x = 175
Step 3: Divide 11 from both sides
x = 175/11
Can someone help me with this
Answer:
if you simplify and solve you will get y=3
Answer:
x=3
Can you mark me as brainliest???
Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
Answer:
Infinitely many solution
Step-by-step explanation:
The given equations are:
y = 3x + 2
3y = 9x + 6
We graph the two equations as shown in the attachment.
We can see that the second equation is lying on top of the first one.
This means that, they have infinitely many solutions.
Answer:
The provided system of equations have infinitely many solutions.
Step-by-step explanation:
Consider the provided system of equations:
y = 3x + 2 and 3y = 9x + 6
Now use the graphing technology in order to draw the graph of the equations.
The graph of the provided system of equations is shown in figure 1:
As it can be observed that the second equation is lying on top of the first one.
Therefore, they have infinitely many solutions.
How do you get the answer for 3n+5 I’m trying to get my grade up from a C so how do you find this answer?
I think it’s six because 3n=6-5 3 n=6-5 then subtract 5 5 from 6 6
if michelle rollerblades around a circular track with a radius of 40 meters, how far does she skate
Check the picture below.
Step-by-step explanation:
Circumference: 2πr
or 2×22/7×40
= 44/7×40
=251.4 m (approx.)
If sin is 3/4 and tan is -3/4, then cos is ?
Answer:
[tex]cos=1[/tex]
Step-by-step explanation:
Use the acronym SOH-CAH-TOA
sin = [tex]\frac{3}{4}[/tex]
So opposite is 3 and hypotenuse is 4.
tan = [tex]\frac{-3}{4}[/tex]
So opposite is -3 and adjacent is 4.
cos = adjacent/hypotenuse
cos = [tex]\frac{4}{4}=1[/tex]
What is the value of X?
These angles are vertical angles meaning that they are equal to each other. Here is the equation for this problem:
x + 40 = 3x
Combine like terms
(x-x) + 40 = 3x - x
40 = 2x
Isolate x
40/2 = 2x/2
x = 20
Hope this helped!
find the first five terms of a1=1/3 and d=1/2
Answer:
1/3, 5/6, 4/3, 11/6, 7/3.
Step-by-step explanation:
This is an arithmetic sequence where you add 1/2 to each term to get the next one.
a1 = 1/3 so a2 = 1/3 + 1/2 = 5/6, and a3 = 5/6 + 1/2 = 4/3.
The first 5 terms are:
1/3, 5/6, 4/3, 11/6, 7/3.
Write a verbal expression for 2n + 7
Answer:
Two times a number plus seven
Step-by-step explanation:
For this case we must give a verbal description for the following expression:
[tex]2n + 7[/tex]
Let "n" be the variable that represents an unknown number. Now we have that the expression is described as:
Twice a number plus seven.
Answer:
Twice a number plus seven.
Match the vocabulary word to its correct definition.
1. absolute value
2. continuous function
3. step function
4. piecewise-defined function
function whose graph consists of horizontal line segments
function defined on different intervals by different domain rules
function whose graph has no breaks
function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
Answer:
1. Absolute value: function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
2. Continuous function: function whose graph has no breaks
3. Step function: function whose graph consists of horizontal line segments
4. Piecewise-defined function: function defined on different intervals by different domain rules
Step-by-step explanation:
Answer:
Step-by-step explanation:Absolute value: function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
2. Continuous function: function whose graph has no breaks
3. Step function: function whose graph consists of horizontal line segments
4. Piecewise-defined function: function defined on different intervals by different domain rules
What is the longest side of the triangle shown?
Side DE
Side OD
Side OE
Side DE is the longest side of the triangle.
Answer:
Side DE
Step-by-step explanation:
Hello, the answer to your question is side DE.
According to one of the inequality theorems, it says that if two angles in a triangle are not equal, the side opposite to the largest angle is the longest side. Therefore, the side opposite 110* is side DE.
Hope this helps.
Find x and h in this trinomial right angle
Answer:
Step-by-step explanation:
Set up the Pythagorean Equation for the two triangles
x^2 + h^2 = 4^2 = 16
(x + 6)^2 + h^2 = 8^2 = 64
x^2 + h^2 = 16 Subtract. That will get rid of h^2
(x + 6)^2 - x^2 = 64 - 16 Expand the brackets. combine the right.
x^2 + 12x+36 - x^2 = 48 Combine
12x + 36 = 48 Subtract 36 from both sides
12x +36 -36 = 48-36 Combine
12x = 12 Divide by 12
12x/12 = 12/12
x = 1
==================
x^2 + h^2 = 4^2
1^2 + h^2 = 16
h^2 = 15
h = sqrt(15)
Which fraction is equivalent to
4/9?
14/19
2/3
6/11
8/18
Answer:
8/18
Step-by-step explanation:
[tex]\frac{4*2}{9*2} =\frac{8}{18}[/tex]
Answer:
8/18
Step-by-step explanation:
Teach me how to yeet
Answer:
d
Step-by-step explanation:
I'm thinking the last one
While 'yeet' is not an academically defined term, it typically refers to the act of throwing something with force. Drawing from a story on LibreTexts, one can learn the technique for effectively throwing objects such as a horseshoe, which involves grip, stance, focus on the target, and a smooth release.
To throw a horseshoe effectively, similar to learning how to "yeet," one must:
Hold the horseshoe in a comfortable but firm grip with your thumb along one of the sides of the horseshoe.
Stand at the designated throwing line and focus on the stake you're aiming at.
Swing your arm forward smoothly and release the horseshoe when your hand is about waist-high, keeping your eyes on the target for accuracy.
I know the answer but I need to understand HOW to get it. Bailey will roll a number cube and flip a coin for a probability experiment. The faces of the cube are labeled 1-6. The coin can land on heads or tails.If Bailey rolls the number cube once and flips the coin once which list contains only the outcomes in which the number cube lands on a number greater than 4.
The right answer was a list with says:
5, Heads
5, Tails
6, Heads
6, Tails
Answer:
Total output= H5, H6,T5, T6
Step-by-step explanation:
Bailey will roll a number cube and flip a coin for a probability experiment.
The faces of the cube are labeled 1-6= 6 possible outcomes
The coin can land on heads or tails= 2 possible outcomes
If Bailey rolls the number cube once= 1 output
and flips the coin once = 1 output
Total output will be combined outcome of cube and coin:
possible outcome of cube= 1, 2, 3 , 4 , 5, 6
possible outcome of coin= H, T
(H for heads and T for tails)
Total output =possible combined outcome of cube and coin= H1, H2, H3 , H4 , H5, H6, T1, T2, T3 , T4 , T5, T6
Now
the outcomes in which the number cube lands on a number greater than :
reduces the total required output by removing the combination when the number cube lands on a number less than or equals to 4
therefore removing H1, H2, H3 , H4 and T1, T2, T3 , T4 from the total outcome will result in following list:
Total output= H5, H6,T5, T6 i.e.
5, Heads
5, Tails
6, Heads
6, Tails !
Which expression is equivalent to 8a + 20? (5 points)
Select one:
a. 4(2a + 20)
b. 4(2a + 5)
c. 4(4a + 16)
d. 4(4a + 5)
It is B that is correct because:
4(2a + 5) = 8a + 20
Answer:
The answer is B. Hope it Helps
Step-by-step explanation:
y is two times the value of x
The equation is y=
Y=2x should be correct
Y is two times the value of X, which can be represented as Y = 2X.
This indicates a directly proportional relationship between Y and X, where Y increases as X increases.
470.47 in expanded form
Four hundred seventy and forty seven hundredth
Final answer:
The number 470.47 in expanded form is expressed as the sum of each digit's value according to its place value, which is 400 + 70 + 0 + 0.4 + 0.07.
Explanation:
You've asked to write the number 470.47 in expanded form. Writing a number in expanded form is a way of expressing the number as the sum of the values of each digit according to its place value. Here is how you convert 470.47 into expanded form:
400 (4 in the hundreds place is worth 400)
70 (7 in the tens place is worth 70)
0 (0 in the ones place doesn't add any value)
0.4 (The digit 4, after the decimal, represents 4 tenths or 0.4)
0.07 (The digit 7, in the hundredths place, represents 7 hundredths or 0.07)
Therefore, 470.47 in expanded form is: 400 + 70 + 0 + 0.4 + 0.07.