Answers
remember Pythagorean theorem
if we have a right triangle with legs a and b and hytponuse c then
[tex]a^2+b^2=c^2[/tex]
we are given a right triangle with legs x and y and hypotohuse 10
so therfor
[tex]x^2+y^2=10^2[/tex]
[tex]x^2+y^2=100
solve for x
minus y² from both sides
[tex]x^2=100-y^2[/tex]
sqare root both sides
[tex]x=\sqrt{100-y^2}[/tex]
the answer is the 4th option
An equation represents the value of x is x=√100-y².Therefore, option D is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given triangle ABC, AB=x units, BC=y units and AC=10 units
By using Pythagoras's theorem, we get
10²=x²+y²
x²=100-y²
x=√100-y²
Therefore, option D is the correct answer.
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Related Questions
How do I write 6 x 3/20 as a fraction in simplest form?
Answers
To simplify 6 x 3/20, we first perform the multiplication to get 18/20. Then, we divide both the numerator and denominator by their greatest common divisor, which is 2, resulting in 9/10.
Explanation:Firstly, in the given expression, 6 x 3/20, the order of operations (BIDMAS/BODMAS) requires us to perform multiplication and division from left to right. So, we multiply 6 and 3 to get 18. This gives us a new expression, 18/20. Then, we simplify this fraction by finding the highest number that both the numerator (18) and denominator (20) can be divided by, which is 2. So we divide both by 2, getting us 9/10. So, 6 x 3/20 simplifies to 9/10 in its simplest form.
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What is the solution to –4|–2x + 6| = –24?
A.) x = 0
B.) x = 0 or x = –6
C.) x = 0 or x = 6
D.) no solution
Answers
-4║-2x+6║=-24
-4/-4║-2x+6║=-24/-4 division property
║-2x+6║=6 simplified
Positive Negative
-2x+6=6 -2x+6=-6
-2x+6-6=6-6 -2x+6-6=-6-6 subtraction property
-2x=0 -2x=-12 simplified
-2/-2x=0/-2 -2/-2x=-12/-2 division property
x=0 x=6
C.) x = 0 or x = 6
The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x 2 + 7x + 12. Factor the trinomial to find the length and width of the rectangle.
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Since it is given that the formula for area is length times width and the area is already given, we are going to find out the value of the width and the length by factoring. The first thing we are going to do is to find first the factors of 12. The factor that can be used for this are 4 and 3. Then, continue with the solution.
So the correct answer for this would be the last option. l = x + 4; w = x + 3.
Please mark me Brainliest and hope this helps :)
Simplifly by using the distributive property 4r+3(r-2)
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Let's focus on the 3(r-2)
In order to distribute this, we multiply 3 to r AND -2 each
After using the distributive property, we get the following
3(r - 2) = 3r - 6
Now, let's go back to the whole equation
4r + 3(r - 2)
= 4r + 3r - 6
Combine like terms
7r - 6
That's your answer.
Have an awesome day! :)
A color printer prints 27 pages in 9 minutes. how many pages does it print per minute?
Answers
The printer is printing 3 pages per minute
32x-28y=-36. and y=-7/8x-1 parallell or perpendicular
Answers
Provide conditions under which the mean function is linear but has a negative coefficient
Answers
To convert degrees Fahrenheit (F) into degrees Celsius (C) use the formula 2003-05-04-00-00_files/i0150000.jpg. Rewrite the equation to convert degrees Celsius to degrees Fahrenheit.
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To convert Celsius to Fahrenheit, use the formula [°F] = [°C] x 9/5 + 32. For example, a 16°C temperature would convert to approximately 60.8°F.
The formula you are looking for to convert degrees Celsius to degrees Fahrenheit is [°F] = [°C] x 9/5 + 32. To perform the conversion, you multiply the temperature in degrees Celsius by 9/5 (or 1.8) and then add 32 to the result. This will give you the temperature in degrees Fahrenheit.
For example, if you wanted to convert 16°C to Fahrenheit (perhaps for planning a trip to Spain), you would do the following calculation: [°F] = 16 x 9/5 + 32 = 28.8 + 32 = 60.8°F. Thus, a weather forecast predicting 16°C is approximately equivalent to 60.8°F.
Choose the correct ordered pair !!
Answers
x+y=3
y=9
To solve the equation you would substitute 9 in for y (in the first equation) and get
x+9=3
You would then subtract 9 from both sides of the equation to get
x=-6
B is the only choice where -6 is first in the ordered pair, but just to make sure, you could substitute -6 back in to the equation to get
-6+y=3
Add 6 to both sides to get y=9, and you know that the correct ordered pair is
(-6,9)
x + 9 = 3
Next, you would have to do is isolate the x. To do this, you would subtract both sides by 9.
x + 9 = 3
x = -6
So, this is what we know.
y = 9
x = -6
Now, all you would have to do is change them into coordinates. (x,y)
(-6,9)
Your answer would be B. (-6,9).
I hope this helps!
According to the data reported by the new york state department of health regarding west nile virus for the years 2000-2004, the least squares line equation for the number of reported dead birds (x) versus the number of human west nile virus cases (y) is y = −10.2638 + 0.0491x. if the number of dead birds reported in a year is 748, how many human cases of west nile virus can be expected? (round your answer to the nearest whole number.)
Answers
Final answer:
Using the least squares line equation y = −10.2638 + 0.0491x and substituting 748 for x, the number of reported dead birds, we find the expected number of human West Nile virus cases to be approximately 26 when rounded to the nearest whole number.
Explanation:
The question asks to predict the number of human West Nile virus cases based on the number of reported dead birds using a least squares line equation provided. Given the equation y = −10.2638 + 0.0491x and the value x = 748, which represents the number of dead birds, we can substitute x into the equation to calculate y, the expected number of human cases.
The calculation is as follows:
y = −10.2638 + 0.0491 × 748
y = −10.2638 + 36.7268
y = 26.463
After performing the calculation, we round the result to the nearest whole number:
Expected number of human cases = 26
Help please don't get it!!!!!!!!!!!!!!
Answers
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Work Shown:
Replace every x with -4 and then simplify the right side
f(x) = 9(3)^x
f(-4) = 9(3)^(-4)
f(-4) = 9*(1/(3^4)) See note below
f(-4) = 9*(1/(3*3*3*3))
f(-4) = 9*(1/81)
f(-4) = 9/81
f(-4) = 9/(9*9)
f(-4) = 1/9
Note: I used the rule x^(-n) = 1/(x^n) which allows us to convert from negative exponents to positive ones.
Factor completely. a 2 + 28a + 27 (a + 1)(a + 27) (a + 3)(a + 9) (a - 1)(a - 27)
Answers
Answer:
(a+1)(a+27)
Step-by-step explanation:
Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial [tex]Ax^2+Bx+C[/tex] multiply A*C then find two numbers which multiply to this number and add to B. When you find those numbers, write them as [tex](x-/+ number)(x-/+number)[/tex].
[tex]a^2+28a+27[/tex]
A=1, C=27
A*C=27 and add to B=28 which 1 and 27 satisfy
The factors are (a+1)(a+27)
a model rocket launches into the sky. An observer on the ground measures the angle of elevation to the rocket at its peak height to be 67 degrees. How high did the rocket get if the observer was 100' away from the launchpad?
Answers
The angle is 67 deg.
The adjacent leg is the 100 ft side of the triangle along the ground.
The opposite leg is the unknown height, h.
tan x = opp/adj
tan 67 = h/100
h = 100 * tan 67
h = 100 * 2.36
h = 236
Answer: 236 ft
Liam's bookstore sold 40 notebooks and 20 newspapers for a total of $130. A day later, the bookstore sold 8 notebooks and 4 newspapers at the same prices, for a total of $28. How much does a notebook and a newspaper cost at Liam's bookstore?
Answers
40x + 20y = 130
and 8x + 4y = 28
With this, if we divide the left hand side by the left hand side of the equation number 2, we have 5. However, 130 divided 28 is not 5 but 4.64. Hence, the system does not have any solution.
Let us say that:
X = price of each notebook
Y = price of each newspaper
So from the problem statement we can create the following equations:
40 X + 20 Y = 130 --> eqtn 1
8 X + 4 Y = 28 --> eqtn 2
Divide both equations by the lowest coefficient to simplify:
Divide eqtn 1 by 20 => 2 X + Y = 6.5
Divide eqtn 2 by 4=> 2 X + Y = 7
So we can see that although both equations has equal left side, the right side do not match. Hence this problem is impossible to solve.
-> The given information describes an impossible situation.
N equation of a line through (0, 2) which is perpendicular to the line y=3x+3y=3x+3 has slope
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I could and will make assumptions regarding what you meant. (Feel free to correct me if need be.)
Find the equation of a line through (0,2) which is perpendicular to the line y=3x+3. To find the slope of this perpendicular line, take the negative reciprocal of 3 (the slope of the given line). It is -1/3.
Using the point-slope form of the equation of a straight line:
y = (-1/3)x + 2 (answer)
round 0.947 to the nearest 10
Answers
Hope that helps
What is the answer to 45,469.23 rounded to the nearest thousand?
Answers
When rounding numbers to the nearest thousand, you look at the hundreds place digit. If it's 5 or higher, you round up, and if it's 4 or lower, you don't. Therefore, 45,469.23 rounds down to 45,000.
Explanation:When rounding numbers to the nearest thousand in mathematics, you must first look at the hundreds digit of the number. In the case of 45,469.23, the hundreds digit is 4. If this digit is 5 or higher, you round up; if it's 4 or lower, you don't round up. Therefore, since the digit in question is 4, which is less than 5, you don't need to increase the thousands digit. As a result, when you round 45,469.23 to the nearest thousand, you get 45,000.
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How to find the y-intercept from two points?
Answers
To find the y-intercept from two points, first calculate the slope using the formula m = (Y₂ - Y₁) / (X₂ - X₁). Then, substitute the slope and one coordinate into the equation y = mx + b and solve for b, which is the y-intercept. The y-intercept reveals the value of y when x = 0.
Explanation:The subject at hand pertains to the field of Mathematics, specifically, how to determine the y-intercept from two points on a line. The objective is to find the point at which the line intercepts the y-axis, denoted generally in equations as b in the form of y = mx + b, where m signifies the slope.
Here's a step-by-step process to find the y-intercept:
First, calculate the slope (m) from your two points using the formula: m = (Y₂ - Y₁) / (X₂ - X₁). Y₂ and Y₁ represent the y-values from your two points, and X₂ and X₁ represent their respective x-values.Substitute the slope (m) and one of your points into the equation y = mx + b. Solve for b which is your y-intercept.The y-intercept represents the value of y when x = 0. In context, it shows where the line crosses the y-axis.
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Find three consecutive integers whose sum is -21. 2. find three consecutive odd integers whose sum is 144. 3. the sum of three consecutive even integers is 48. what are the numbers?
Answers
-21÷3=-7 which is the exact center so
-6, -7, -8
Equation
x + (x+1) + (x+2) = -21
3x + 3 = -21
3x=-24
x=-8
x+1=-7
x+2=-6
2. Consecutive Odd Integers
X, X+2, X+4
X + (X+2) + (X+4) = 144
3X+6=144
3X=144-6=138
X = 138/3 = 46 .....There are no 3 odd Integers that can equal an even integer
3. 3 consecutive even number x, x+2, x+4
X + (X+2) + (X+4) = 48
3X+6=48
3X=48-6=42
X=42/3=14
14, 16, 18
Final answer:
Explanation of determining between which two consecutive integers a square root lies.To find out between which two consecutive integers numbers like √18, √29, √5, and √79 lie, we use the squares of integers to estimate their positions without a calculator, illustrating these numbers lie between integers whose squares are immediately below and above the given number.
Explanation:
To determine between which two consecutive integers a given square root lies without a calculator:
For<6: √18 is between 4 and 5 because 4< √18<5.
For<5: √29 is between 5 and 6 because 5< √29<6.
For=5: √5 is between 2 and 3 because 2< √5<3.
For>7: √79 is between 8 and 9 because 8< √79<9.
The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
3. Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
Answers
Jason has 34 blueberry scones and 85 blackberry scones. He wants to make as many identical bags of scones as possible. Each bag should have an equal number of blueberry scones and an equal number of blackberry scones. What is the greatest number of bags Jason call fill? Explain how you know.
Answers
i believe it would be 17.
hope it helps :)
Answer:
Each Bag can fit 2 Blueberry Scones and 5 Blackberry Scones
Step-by-step explanation:
Given:
34 Blueberry scones
85 Blackberry scones
34 Blueberry so 34 divided by the Bag 17 (34 ÷ 17 = 2)
85 Blackberry scones so 85 divided by the Bag 17 ( 84 ÷ 17 = 5)
Therefore Jason can put 2 Blueberry scones and 5 Blackberry scones in each Bag
Multiply. (6x−7)(5x+8)
Answers
Using the distributive property:
= 6x(5x+8) -7(5x+8)
= 30x^2 +48x -35x -56
= 30x^2+13x-56
The multiplication of the polynomial (6x − 7) and (5x + 8) will be 30x² + 13x − 56.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The polynomial is given below.
(6x − 7) and (5x + 8)
Multiply the polynomials, then we have
⇒ (6x − 7) · (5x + 8)
⇒ 6x · (5x + 8) − 7 · (5x + 8)
⇒ 30x² + 48x − 35x − 56
⇒ 30x² + 13x − 56
The multiplication of the polynomial (6x − 7) and (5x + 8) will be 30x² + 13x − 56.
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Jane, andre and maria pick apples. andre picks three times as many lbs as maria. jane picks two times as many as andre. the total weight of the apples is 840 lbs. how many lbs of apples does andre pick?
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Andre picked 252 apples.
1. The expression x3+3x2+x-5 represents the total length across the front of the mansion. Find the length of side I. Show all work. X will stay a variable and your answer will be a polynomial.
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[tex]x^4-2x^3+x-10+a-x^3+5x^2+2=x^3+3x^2+x-5 \\ \\ \Rightarrow a=x^3+3x^2+x-5-x^4+2x^3-x+10+x^3-5x^2-2 \\ \\ =\bold{-x^4+4x^3-2x^2+3}[/tex]
Solve the inequality 2x + 8 < 5x - 4
A) X > 4
B) X > 1
C) X < 1
D) X < 4
Answers
2x + - 5x < -8 - 4
-3x < -12
x > 4
answer
A) X > 4
What value is added to both sides of the equation x^2 − 8x = −10 in order to solve by completing the square?
−8
16
−4
4
Answers
we need to get (x-a)^2 with x^2-8x to figure it out
using (x-4)^2=x^2-8x+16 we see to add 16
x^2-8x=-10
x^2-8x+16=6
(x-4)^2=6
x-4=sqrt6
x=4+sqrt6 to solve for x
Triangles are congruent is they have the same ?
Answers
Not really sure how to do this one (ignore writing above)
Answers
Clearview Window Cleaners washes 20 office windows in 168 minutes. How many hours is that?
Answers
describe the end behavior of the function. f(x)=x^3+11x^2+35x+30
Answers
First, the leading term is positive, so we won't have to negate anything.
The leading term has a power that is odd.
Since the exponent is odd, this means that the function goes to positive infinity as x goes to positive infinity.
This also means that the function goes to negative infinity as x goes to negative infinity.
Those are the end behaviors.
Have an awesome day! :)