Triangle FYJ is congruent to triangle HYJ using the
Triangle Congruence Theorem. Therefore, segment
FJ is congruent to segment
Figure FJHW
JW 1 FH, FY≈ HY, JY WY
W
H
Answers
Triangle FYJ is congruent to triangle HYJ using the RHS congruency theorem.
FJ is congruent to segment HJ.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
We know right angle hypotenuse congruency, which states two right angle triangles are congruent if one of the legs and hypotenuse corresponding to the other right angle triangle is equal in measure.
Triangle FYJ is congruent to triangle HYJ as FY is congruent to HY and JH is congruent to JH.
So, Their hypotenuses are also equal in measure.
Hence, FJ is congruent to JH.
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Related Questions
DUE SOON! PLEASE HELP!
QUESTIONS ARE BELOW!
MANY THANKS!
Answers
An equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y= 1/4 ((x-3)²-6).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Translation rules:
When the shape is moved towards the left by k units, then replace x with x - k.
When the shape is moved up by k units, then replace y with y + k.
3) Given that, the equation of the parabola is y=(x-3)²-7
The equation is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter.
Here, 1/4 ((x-3)²-7-4+5)
y= 1/4 ((x-3)²-6)
4) The given equation is h=-4.9t²+180t+2
a) the maximum height of the rocket
Use the formula
x =-b/2a to find the maximum and minimum.
(18.36734693,1655.06122448)
b) the time required for the rocket to reach its maximum height
Find where the first derivative is equal to 0 to find the local maxima and minima.
(18.36734693, 1655.06122448) is a local maxima
c) the time required for the rocket to reach the ground
Solve the equation for t by finding a, b, and c of the quadratic then applying the quadratic formula.
t=900+3.16227766√(81098−49h)/49
t=900-3.16227766√(81098-49h)/49
Therefore, an equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y= 1/4 ((x-3)²-6).
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What is the product?
(4s+2)(5s²+10s+3)
20s²+20s+6
20s³ +40s²+12s
20s^3 +10s^2 +32s+6
20s³ +50s²+32s+6
Answers
Answer:
Answer
Step-by-step explanation:
20s³ +50s²+32s+6
0.
A woman on a billboard is 8
3
8
feet tall. If the
scale of the billboard is 1 foot = 8 inches,
what is her actual height?
Answers
Answer: The scale of the billboard is 1 foot = 8 inches, so to find the actual height of the woman, we need to multiply the height on the billboard by 8.
8 3/8 feet x 8 inches/foot = 66 inches (8 x 8) + (3 x 8) = 66
So the woman's actual height is 66 inches.
Step-by-step explanation:
Explain how you can check to see if your prime
factorization is correct.
Answers
Answer:
The simplest algorithm (a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.) to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, by prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, and 5/5 = 1. Since we received the remainder, it cannot be further factorized.
Step-by-step explanation:
pls tell me if wrong have a good day/night<3
There are two typical approaches to prime factorization. The Prime Factor Tree and the Upside-Down Division are the first and second, respectively.
How many ways can you find prime factorization?There are two typical approaches to prime factorization. The Prime Factor Tree and the Upside-Down Division are the first and second, respectively. I'll also demonstrate two approaches to prime-factorize 40 using this. Divide the supplied number by the smallest prime, 2, to begin.To factorize an equation is to write it as the product of its factors. An irreducible factor is one that cannot be further represented as the product of other factors, much like prime factors. Every algebraic term also has the number 1 as a factor, however this is only indicated when it is necessary.Factorization is the technique of representing an expression as the sum of two or more factors.First, imagine that the given number is the tree's root. Step 2: Draw a tree with the two elements as its branches. Step 3: Refactor the composite factors and make a branching list of the factor pairs. Method 4: Repeat the previous step until all of the composite factors' prime factors have been identified.To learn more about prime factorization refer to:
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4. The 92 million Americans of age 50 and over control 50% of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1,873 for individuals in the age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550. a. At 95% confidence, what is the margin of error? b. What is the 95% confidence interval for the population mean amount spent on restaurants and carryout food? c. What is your estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food? d. If the amount spent on restaurants and carryout food is skewed to the right, would you expect the median amount spent to be greater than or less than$1,873?
Answers
a) The margin of error for the 95% confidence interval is given as follows: $122.4.
b) The 95% confidence interval for the population mean amount spent on restaurants and carryout food is given as follows: ($1,750.6, $1,995.4).
c) The estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food is between $161,055,200,000 and $183,576,800,000.
d) As the distribution os skewed to the right, the median would be expected to be less than the mean.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The margin of error is then defined as follows:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 80 - 1 = 79 df, is t = 1.9905.
The parameters for this problem are given as follows:
[tex]\overline{x} = 1873, s = 550, n = 80[/tex]
Hence the margin of error is of:
[tex]M = 1.9905 \times \frac{550}{\sqrt{80}} = 122.40[/tex]
Considering the sample mean and the margin of error, the bounds of the confidence interval are given as follows:
Lower bound: 1873 - 122.40 = $1,750.6.Upper bound: 1873 + 122.40 = $1,995.4.Considering the bounds of the confidence interval and the population of 92 million, the bounds of the estimate of the total amount are given as follows:
Lower bound: 92,000,000 x 1,750.6 = 161,055,200,000.Upper bound: 92,000,000 x 1,995.4 = 183,576,800,000.The relation between mean, median and skewness is given as follows:
Mean greater than median: Positively(right) skewed.Mean less than the median: Negatively(left) skewed.More can be learned about the t-distribution at https://brainly.com/question/17073112
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Lynne bought a bag of grapefruit, 1 5/8 pounds of
apples, and 2 3/16 pounds of bananas. The total
weight of her purchases was 7 1/2pounds. How
much did the bag of grapefruit weigh?
Answers
Using the mathematical operations of addition and subtraction, the weight of the bag of grapefruit is 3¹¹/₁₆.
What are the mathematical operations?The basic mathematical operations we have studied so far include addition, subtraction, division, and multiplication.
In addition operation, two or more addends are added to obtain a result known as the sum or total.
Using subtraction operation, the minuend, subtrahend, and difference are the major parts, including the subtraction operator (-).
There are two ways of solving this problem, we can add the fractional weights of apples and bananas and subtract the sum from the total weight of fruits Lynne bought.
We can also subtract each fractional weight from the total weight of fruits to arrive at the fractional weight of the bag of grapefruit.
The total weight of Lynne's purchases = 7¹/₂ pounds
The weight of apples = 1⁵/₈ pounds
The weight of bananas = 2³/₁₆ pounds
The weight of grapefruit = x
= 7¹/₂ - 1⁵/₈ - 2³/₁₆
= 3¹¹/₁₆
Add fractional weights:
1⁵/₈ + 2³/₁₆ = 3¹³/₁₆
Subtract the sum of the fractional weights from the total weight:
7¹/₂ - 3¹³/₁₆ = 3¹¹/₁₆
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In interest rate 6% in 2500$ in year when go to investment at the end how many amount of 3 yrs and 5 months in simple interest ?
Answers
Answer: So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.
Step-by-step explanation:
To calculate the simple interest on an investment of $2500 at a 6% interest rate for 3 years and 5 months, you would use the formula:
Simple Interest = (Principal x Interest Rate x Time in Years)
In this case, the time in years would be 3.5 (3 years and 5 months)
Simple Interest = (2500 x 0.06 x 3.5) = $525
So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.
Please look at the picture and answer the question, thank you!
Answers
one fctor of the function f(x)= x^3 -9x^2 +20x -12 is (x-6) describe how to find the x-intercepts and the y-intercept
Answers
The x-intercepts and the y-intercept of the cubic function f(x) = x³ - 9·x² + 20·x - 12 for which (x - 6) is a factor are;
The x-intercepts are; (6, 0), (2, 0), and (1, 0)The y-intercepts of the function is the point (0, -12)What is a function?A function is a rule that uniquely maps each value from the set of input variables to exactly one value in the set of the output variables.
The specified cubic function is; f(x) = x³ - 9·x² + 20·x - 12
A factor of f(x) = x - 6
The x-intercepts are the points on the graph of the function, where the value of the function, f(x) = 0, which are found as follows;
At the x-intercept, f(x) = x³ - 9·x² + 20·x - 12 = 0
x³ - 9·x² + 20·x - 12
Dividing the cubic function by the factor (x - 6), we get;
x² - 3·x + 2
(x - 6) | x³ - 9·x² + 20·x - 12
[tex]{}[/tex] x³ - 6·x²
[tex]{}[/tex] -3·x²
[tex]{}[/tex] -3·x² + 18·x
[tex]{}[/tex] 2·x
[tex]{}[/tex] 2·x - 12
[tex]{}[/tex] 0
The other factor of the cubic function is; x² - 3·x + 2
x² - 3·x + 2 = (x -2)·(x - 1)
Therefore;
f(x) = x³ - 9·x² + 20·x - 12 = (x - 6)·(x - 2)·(x - 1)
From which at the x-intercepts, we get;
f(x) = (x - 6)·(x - 2)·(x - 1) = 0
x = 6, x = 2, and x = 1
The x-intercepts are the points (6, 0), (2, 0), and (1, 0)The y-intercept are the points the x-values is zero, therefore, at the y-intercepts, we get;
f(0) = 0³ - 9·0² + 20·0 - 12 = -12
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Write 8,400,000 m3 as a fraction of 0.012 km3. Give your answer in its simplest form.
Answers
8,400,000 m^3 / 10^9 = 0.0084 km^3
So, 8,400,000 m^3 is equal to 0.0084 km^3.
Next, divide 0.0084 km^3 by 0.012 km^3 to get the fraction:
0.0084 km^3 / 0.012 km^3 = 0.07.
The answer is 0.07 in its simplest form.
Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a) Find n(A).
n(A) =
(b) T/F: 20 A
True
False
Answers
Part (a)
Answer: 7Reason:
There are 7 items inside set A. The notation n(A) counts the number of elements in a set.
==========================================
Part (b)
It's not clear what your teacher is asking. It seems this part is incomplete. Please revise.
solve the equation
(x + 2)(x + 6) = 0
Answers
Answer:
The zeroes of the equation are -2 and -6.
Step-by-step explanation:
(x + 2)(x + 6) = 0
=> x = -2, -6
Hope it helps.
A boat can travel 370 miles in 185 gallons. How much gasoline it needs to travel 444 miles. [tex]370:185[/tex]
Answers
Answer: 222 gallons of gasoline to travel 444 miles.
Step-by-step explanation: To find how much gasoline the boat needs to travel 444 miles, we need to use the formula:
distance = rate x time
Where distance is the total distance to be traveled, rate is the distance per unit of fuel (370 miles/185 gallons) and time is the amount of fuel required to travel 444 miles.
So we can calculate the fuel required as:
Fuel = (distance) / (rate)
Fuel = (444 miles) / (370 miles/185 gallons) = 444/ (370/185) = 444/2 = 222 gallons.
So the boat needs 222 gallons of gasoline to travel 444 miles.
find the interval(s) of numbers that are at least a distance of 3 away from "-7"
Answers
Answer:
x ≥ - 4 and x ≤ - 10 - as inequality( - ∞, - 10] ∪ [ - 4, ∞) - as intervals-----------------------------
The numbers that are at least a distance of 3 away from -7 are the numbers 3 units or more away from -7 either side on the number line :
x ≥ - 7 + 3 = - 4or
x ≤ - 7 - 3 = - 10This is same as:
( - ∞, - 10] ∪ [ - 4, ∞)Please can someone help me on this question i will give out 30 points and brainly if you give me the right answer
Answers
Answer: A irregular
b. irregular
c neither
d. Regular
e. regular
Step-by-step explanation: Regular polygons have all sides equal in length but an irregular polygon does not have all sides equal.
Answer:
A: Irregular polygon
B: Irregular polygon
C: Neither
D: Regular polygon
E: Regular polygon
Step-by-step explanation:
To start off with, we can eliminate C for being a polygon (neither), because being a polygon states the shape must be closed with a finite number of line segments (a circle has an infinite amount of line segments).
A regular polygon states that it must have an equal distance on all sides. We can find this by looking at what shapes have a line (which represents that it has the same length) on all sides. The only polygons that fit this requirement are D and E.
From here we can see that the remaining polygons of A and B are in fact irregular polygons by process of elimination.
How can you write an equation to represent this problem for any number of guards?
A man entered an orchard through 7 gates and picked some apples. When he left, he gave the first guard half his apples and 1 apple more. To the second guard he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with 1 apple. How many apples did he gather in all?
Answers
Answer:
Step-by-step explanation:
This problem can be represented by the equation: x + (x/2 - 1) + (x/4 - 1) + (x/8 - 1) + ... + (x/128 - 1) + 1 = x, where x is the total number of apples gathered.
This equation represents the process described in the problem, where the man gives half of his remaining apples (x/2, x/4, x/8, etc.) to each guard, minus 1 apple each time, until he is left with 1 apple.
Find the missing length.
Answers
Answer:
125
Step-by-step explanation:
2^2+11^2=c^2
4+121=c^2
125=c^2
c=125 square root
To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is $271.95. Write and solve a linnear equation to find the total cost to order 12 tickets.
Answers
The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
What is linear equation?A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.
A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.
Given that cost for 5 tickets is $174.45
Let x be the cost of each ticket and y be the processing fee
5x + y = 174.45
And for the cost for 8 tickets is $271.95
8x + y = 271.95
Subtract the terms
8x + y = 271.95
- 5x + y = 174.45
3x + 0 = 97.5
If 3x = 97.5
Then,
x = 97.5/3
x = 32.5
Each ticket costs $32.5 then processing fees
5(32.5) + y = 174.45
y = 174.45 - 162.5
y = 11.95
8(32.5) + y = 271.95
y = 271.95 - 260
y = 11.95
Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
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HELP FAST
How to find the complex zeroes of [tex]x^2-6x+13[/tex]
Answers
Answer:
There are few possible ways to find the complex zeros
You can find the complex zeros by using quadratic formula
[tex]x^2-6x+13=0[/tex]
[tex]=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:13}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:4i}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-\left(-6\right)+4i}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4i}{2\cdot \:1}[/tex]
[tex]x=3+2i,\:x=3-2i[/tex]
What’s the answer Question 43
Answers
Answer:
90
Step-by-step explanation:
15 to first 20
so 120 = 6*20
so 6*15 =90
The sum of the page numbers on the facing pages of a book is 553. Find the smaller page number.
Answers
Answer: To solve this problem, we can use algebra. Let x be the smaller page number. Then, the larger page number is x + 1, since the pages are facing each other. We know that the sum of these two numbers is 553, so we can set up the equation:
x + (x+1) = 553
Next, we will solve for x by combining like terms:
2x + 1 = 553
Now we will subtract 1 from both sides of the equation:
2x = 552
Finally, we will divide both sides by 2:
x = 276
So the smaller page number is 276.
Step-by-step explanation:
Which angle is vertical to 1?
Answers
Answer:
Have a good day!:)
Step-by-step explanation:
When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Answer to this angle question
Answers
Check the picture below.
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
Answers
The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.
-2x/11 can be written as twice the number multiplied by the reciprocal of -11
√2x + 11 can be written as sum of square root of twice the number and 11
Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
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In the Olympic Games, Michael Phelps won eight gold medals in swimming. Following are some of the events he won, along with his margin of victory, in seconds
Answers
The median margin for victory will be 1.89.
What defines median?The median of the data is the value of the middle observation discovered after the data are organized in ascending order. The median is useful in situations where it is difficult to express anything while taking into account all of the data.
One of the easy to calculate statistical summary metrics is the median. Since it bases its value on the data that is in the middle of a sequence, the median is often referred to as the place average.
Given Data:-
1.89,2.32,0.08,4.74,0.30
Mean margin of victory= 1.866
Median margin of victory= 1.89
So the median margin for victory will be 1.89.
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Complete question -
A trader sold 1.6 lot EURUSD. How many units of Euros did he sell?
Answers
Answer:
let's see jssjsjnsjsjsjsjsjsjsjsjsjs
A factory that produces toy wheels finds that they must discard 3 out of 100 wheels because they are defective. How many wheels would they expect to discard everyday if the factory produces 1200 wheels per hour in each 8 hr day.
Answers
they expect to discard everyday 288.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, given that,
they must discard 3 out of 100 wheels because they are defective.
the factory produces 1200 wheels per hour in each 8 hr day.
total per day = 9600
so, they expect to discard everyday =9600 * 3%
=288
hence, they expect to discard everyday 288.
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20 POINTS PLEASE I NEED THIS RIGHT NOW!!!!!!!
A system of equations is given.
Equation 1: 5x − 2y = 10
Equation 2: 4x − 3y = 15
Explain how to eliminate x in the system of equations.
Answers
Hope it helps.
Please send your query through comment section.
Step-by-step explanation:
the funny thing with equations is we can transform them (as long as we do every operation in both sides), and we can even add them up or subtract from each other to get new equations that are maybe simpler to solve.
to eliminate x i would recommend to multiply the first equation by 4, and the second equation by 5 and then subtract equation 2 from equation 1 (comparable term by comparable term).
5x - 2y = 10
4x - 3y = 15
would then turn into
20x - 8y = 40
- 20x - 15y = 75
------------------------
0 7y = -35
y = -35/7 = -5
now we can pick any original equation to solve for x.
e.g.
5x - 2×-5 = 10
5x + 10 = 10
5x = 0
x = 0
Emilia is sending her three children to different week-long daytime summer camps. The cost of the summer camp is $468
for the youngest child, $231
for the middle child, and $350
for the oldest child. Estimate how much it will cost to send the three kids to summer camp by rounding each cost to the nearest hundred.
Answers
Answer:
$1,100
Step-by-step explanation:
The cost of the summer camp for the youngest child is around $500, when rounded to the nearest hundred.
The cost of the summer camp for the middle child is around $200.
The cost of the summer camp for the oldest is around $400.
500+200+400=1100
18712−9412 i dont know what the final product would be
Answers
18712-9412= 9,000
Answer:
Step-by-step explanation:
Solution:- this is question of subtraction , so 18712-9412=9300(Answer)
