Answers
We are given:
x (-4, 3)
y (2, -1.5)
z (4, -1)
A (3, 3)
And we are trying to find the hypotenuse of triangle YZA because that’s what the line from “point A to XZ” is.
The Pythagorean Theorem is a^2 + b^2 = c^2
We can use it to find the distance between any two points. If we imagine 2 more lines, one going straight down from the higher point, and the other one going horizontally from the lower point until it meets the vertical line. We have another triangle.
The length of the horizontal segment of a triangle is just the difference of. the x values. And the length of the vertical segment is just the difference of their y values.
So we have
(x2 - x1)^2 + (y2 - y1)^2 = c^2
Simplified:
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
Segment YZ =
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
sqrt((4 - 2)^2 + (-1 - -1.5)^2) = c
sqrt(4 + .25) = c
sqrt(4.25) = c
2.06155281281 = c
The length of YZ is 2.06155281281.
Now we need to know segment ZA.
Segment ZA =
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
sqrt((3 - 4)^2 + (3 - -1)^2) = c
sqrt(1 + 16) = c
sqrt(17) = c
4.12310562562 = c
The length of segment ZA is 4.12310562562.
Finally:
AZ^2 = YZ^2 + ZA^2
AZ^2 = (2.06155281281)^2 + (4.12310562562)^2
AZ^2 = 4.25 + 17
AZ^2 = 21.25
AZ = sqrt(21.25)
AZ = 4.60977222865
Related Questions
What is the graphical evidence of sequence
Answers
Answer:
11:02
If a sequence s which is the sequence D 1 up to DN is a degree sequence of some graph then the sequence s is called the graphical
A right triangle has a leg that is 2.70 m long and a hypotenuse that is 7.76 m long. What is the length of the other leg of the triangle in meters using the rules for significant digits?
Answers
Applying the Pythagorean Theorem and using the rules of significant digits, the length of the other leg of the right triangle is approximately 2.61 meters.
Recall:
Pythagorean Theorem is given as: [tex]a^2 + b^2 = c^2[/tex]a and b are the two other legs of a right-angled triangle, while c is the hypotenuse.Using the Pythagorean Theorem, we are going to find the length of the other leg of the triangle that has:
a = 2.70 m (a leg)c = 7.76 m (hypotenuse)Substitute and find the value of b (the other leg).[tex]2.27^2 + b^2 = 7.76^2\\\\b = \sqrt{7.76^2 - 2.27^2} \\\\b = 2.607[/tex]
Therefore, applying the Pythagorean Theorem and using the rules of significant digits, the length of the other leg of the right triangle is approximately 2.61 meters.
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(1/10x−2/3)−(4/5x−1/6)
Answers
Answer:
- 7x + 5/10
Step-by-step explanation:
I used a calculator, please let me know if im incorrect
Tell me whether (-1, 2) is a solution of 8x+y>-6
Answers
Answer: I believe not
Step-by-step explanation:
You plug in the x and y values and it equals -6 which is not greater than 6
:)
Jacob made lemonade for his birthday party. He made 4.5 gallons of
lemonade and wants to serve it in pint-sized glasses. How many
glasses will he need for the lemonade?
***Hint: 1 gallon = 8 pints
Not sure how to set this up using ratio
Answers
Answer:
36
Step-by-step explanation:
You see one gallon is 8 pints and using a unit converter we get 36
Hope that helps : )
the number that are being multiplied are called as.................
Answers
Answer:
Factors
Step-by-step explanation:
Factor*factor=product
Answer:
The numbers to be multiplied are generally called the "factors". The number to be multiplied is the "multiplicand", and the number by which it is multiplied is the "multiplier". ... The result of a multiplication is called a product.
Step-by-step explanation:
If Jamar can ride his bike 10 miles in 1 hour, how far can he ride his bike in 2 hours? How far did he go in 36 mins?
Answers
Answer:
Jamar can ride his bike 20 miles in 1 hour.
He went 6 miles in 36 minutes.
is -29 a whole number, integer, or rational number
Answers
Answer: its a integer...
Step-by-step explanation: it cant be a whole number its negitive and also doesn't look like a rational number those are mostly fractions decimals ect its prob a interger
What times what equals -7
Answers
Answer:
-7 x 1
hope that helped <3
-7 times one is equal to minus seven.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find what times what is -7.
Whenever we see a times in an expression its nothing but multiplication.
Multiplication is a method of finding the product of two or more numbers
We need to find the two numbers whose product will be equal to minus seven.
We know that there is only one possibility.
-7×1=-7
and 1×-7=-7
Hence ,-7 times one is equal to minus seven.
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The results of a national survey showed that on average, adults sleep 7.3 hours per night. Suppose that the standard deviation is 1.2 hours and that the number of hours of sleep follows a bell-shaped distribution. If needed, round your answers to two decimal digits. If your answer is negative use “minus sign”.
(a) Use the empirical rule to calculate the percentage of individuals who sleep between 4.9 and 9.7 hours per day.
Enter your answer as a percentage.
%
(b) What is the z-value for an adult who sleeps 8 hours per night?
(c) What is the z-value for an adult who sleeps 6 hours per night?
Answers
Using the Empirical Rule and z-scores, we have that:
a) 95% of individuals who sleep between 4.9 and 9.7 hours per day.
b) Z = 0.58.
c) Z = -1.08.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In item 2, both 4.9 and 9.7 are 2.4 hours from the mean, that is, 2 standard deviations, hence 95% of individuals who sleep between 4.9 and 9.7 hours per day.
What is the z-score formula?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
For this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 7.3, \sigma = 1.2[/tex]
The z-score for an adult who sleeps 8 hours per night is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (8 - 7.3)/1.2
Z = 0.58.
The z-score for an adult who sleeps 6 hours per night is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 7.3)/1.2
Z = -1.08.
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Note that a change can be an increase or a decrease.
For an increase, use a positive number.
For a decrease, use a negative number.
(b)Deon removed 72 fish from his pond over a period of 9 days. He removed the same number of fish each day. What was the change in the number of fish in the pond each day?
Answers
Answer:
72 fish = 9 days * x fish, x fish/day = 72 fish / 9 days = 8 fish/day
Step-by-step explanation:
Use the given information yo find the exact value of each of the following. A. Sin 2 theta . B. Cos 2 theta C. Tan 2 theta
Cot theta = 6, theta lies in quadrant III
Answers
Answer:
C
Step-by-step explanation:
Solve for x.
-3x + 50 = 101
Answers
-3x + 50 = 101
-50 -50 subtract 50 from both sides, 50's cancel out from the left.
___________ solve for 101 - 50.
-3x = 51
___ ___ divide -3 on both sides, -3's cancel out on the left.
-3 -3 solve for 51 ÷ -3.
x = -17, is the answer.
Hope this helps! Let me know if you have any other questions related to this problem. :)
Solve and graph "-14" < "-6x" - 2 ≤ 22
Answers
[tex]\\ \sf\longmapsto -14<-6x-2<22[/tex]
Add 2 on all sides[tex]\\ \sf\longmapsto -14+2<-6x-2+2<22+2[/tex]
[tex]\\ \sf\longmapsto -12<-6x<24[/tex]
divide all sides by 6[tex]\\ \sf\longmapsto -2<-x<4[/tex]
[tex]\\ \sf\longmapsto 2>x>-4[/tex]
if xr-st=r, which expression represents x
Answers
Answer:
To get an expression relating to x you need to have x alone on one side of your equation. ie x =
Try this:
rx - st = r
remove st from the rx side
rx = r + st
now divide by r
x = (r + st)/r
You now have your expression relating to x
MARKING AS BRAINLIEST
Answers
Answer:
113.1
Step-by-step explanation:
With this picture, I'm assuming that the diameter of the circle is 12m
If this is the case, the radius is equal to 12/2 = 6
Area = pi*r^2 = pi*36 = 113.1 (rounded to the nearest tenth)
Answer:
113.1 m²
Step-by-step explanation:
Diameter = 12m
Radius = Diameter/2 = 12/2 = 6
A=πr^2 = π·6^2 = 113.09734 m²
Rounded to the nearest tenth = 113.1 m²
Suppose a stock is selling on a stock exchange for 6 3/4 dollars per share. If the price increases 3/4 per share, what is the new price of the stock? Leave your answer as a proper fraction or mixed number.
Answers
Step-by-step explanation:
If the price increases 3/4 per share, the new price of the stock =
6¾ + ¾ =
27 /4 + ¾ =
30 /4 =
15/2 or 7½
The new price of the stock which increases 3/4 per share is $ 7 1/2.
Given data:
A stock is selling on a stock exchange for 6 3/4 dollars per share.
If the price of the stock increases by 3/4 dollars per share, you can add 3/4 to the current price of 6 3/4 dollars per share:
6 3/4 + 3/4
To add the whole numbers and fractions separately:
6 + 0 + 3/4 + 3/4
Adding the whole numbers and fractions:
6 + 1 1/2
A = 7 1/2
Hence, the price of the new stock is $ 7 1/2
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8/5 divided by -0.35
Answers
Answer:
-4.57142857143 rounded to -4.57 or -4.6
Step-by-step explanation:
calculator
Jacob went bowling over the weekend. On Saturday, he bowled at Bowlero, where he
rented shoes for $3.25 and paid $3.75 for each game. On Sunday, he bowled at the
Cowtown Bowling Center, where he rented shoes for $2.50 and paid $4.00 per game. If
he spent the same amount each day, how many games did he bowl? (Let the number of
games played = x.)
Answers
Answer:
x= 3
Step-by-step explanation:
Blowlero's cost of shoes + the cost of one game = $7.00. If we add the cost of a game two more times, we get $14.50
At Cowtown Bowling Center, we can do the same thing. The cost of shoes + the cost of a game= $6.50. If we add the cost of a game two more times, we get $14.50.
For Jacob to have spent the same amount each day, he would have had to played three games at both places.
Answer:
x = 3
Step-by-step explanation:
just took the test
what is the answer / product of 8x2
Answers
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*x^2-(8)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
23x2 - 8 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
8x2 - 8 = 8 • (x2 - 1)
Trying to factor as a Difference of Squares:
3.2 Factoring: x2 - 1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Equation at the end of step
3
:
8 • (x + 1) • (x - 1) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Equations which are never true:
4.2 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.3 Solve : x+1 = 0
Subtract 1 from both sides of the equation :
x = -1
Solving a Single Variable Equation:
4.4 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
Two solutions were found :
x = 1
x = -1
what is the GCF of 8 and 10
Answers
Answer:
2
Step-by-step explanation:
Calculate the prime factors of 8 and 10, than find the greatest common factor (greatest common divisor (GCD)) of the numbers by matching the biggest common factor of 8 and 10.
8 = 1, 2, 4, 8
10 = 1, 2, 5, 10
The Greatest Common Factor of both numbers is 2,...
Chow,...!
Help please ✨✨✨✨✨✨✨✨✨✨✨
Answers
Answer:
khuhkl
Step-by-step explanation:
bjknn.nl≥m;l
Answer:
midpoint of the segment is 7,7
4ab over 4a 8th power b2nd power
Answers
Answer:
Step-by-step explanation:
=1 over/ a to the 7th power b
fifty nine million four hundred seventy five thousand six hundred forty three in standard form
Answers
Answer:
59,475,643
Step-by-step explanation:
Which situation best represents the relationship between x and y presented in the graph? An elevator starts on floor 6 and ascends at a rate of 1 floor per second. Ally made 15 pancakes at a rate of 6 pancakes per minute. Andrew has $6 to spend at the arcade. He spends $1 per game he plays. 1 inch of rain falls every hour for 6 hours. Coordinate graph with horizontal axis numbered 0 to 10 and vertical axis numbered 0 to 15. A line runs through these points: begin ordered pair 0 comma 6 end ordered pair, begin ordered pair 1 comma 7 end ordered pair, begin ordered pair 2 comma 8 end ordered pair, begin ordered pair 5 comma 11 end ordered pair, begin ordered pair 6 comma 12 end ordered pair, begin ordered pair 7 comma 13 end ordered pair, begin ordered pair 8 comma 14 end ordered pair, and begin ordered pair 9 comma 15 end ordered pair.
Answers
Answer:
6 floors per 1 minute
2 and a half pancakes per minute
etc.
Step-by-step explanation:
Simplify to the ratios lowest form and the compare.
Express in the form of P/Q i) 0.675 (ii) 0.32
Answers
Express in the form of P/Q
i) 0.675
= 675/1000
(ii) 0.32
= 32/100
uoy clari od lobom sodo lo
8
ownload
Alex, Kiri, and Caleb played a computer game together. Alex scored
758 points more than Kiri. Kiri scored 912 points fewer than Caleb. Their
total score was 8,450 points. How many points did Caleb score?
758
758
+ *
-912
1670
7 13 Ls
suso
1670
6 7 8
Alex
gia
Kiri
Answers
Answer:
wiwheieneodjdhdjsoeke8ejso
What is the answer for this problem?
Answers
Answer:
The function has a maximum of 2 at [tex]x=1[/tex]
Step-by-step explanation:
The graph is a vertical parabola. The minimum, or min is when the parabola opens up, the vertex is at the lowest point on the graph. The maximum, or maxis when the parabola opens down, the vertex is the highest point on the graph.
Since it asks for "[tex]x[/tex]", we can tell that it is 1. If you look at the x-axis in the graph at where the point lies, you will find that [tex]x=1[/tex]
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Convert the percent to a decimal
2/5%
Answers
Answer:
0.4
Step-by-step explanation:
Step-by-step explanation
contruct an isosceles triangle PQR suxh that PQ=PR=10cm and QR=9cm.Measure and write down the size of QPR
Answers
Measurement = 10 + 10 + 9
= 29cm