Question
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Answer:
[tex]Hypotenuse:37.56[/tex]
[tex]Other\ Legs: 26.56[/tex]
Step-by-step explanation:
Let the hypotenuse be y and the other legs be x.
So:
[tex]y = 11 + x[/tex]
Required
Determine the exact dimension of the triangle
Using Pythagoras theorem;
[tex]y^2 = x^2 + x^2[/tex]
[tex]y^2 = 2x^2[/tex]
This gives:
[tex](11+x)^2 = 2x^2[/tex]
Open bracket
[tex]121 + 22x + x^2= 2x^2[/tex]
Collect like terms
[tex]2x^2 - x^2 -22x - 121 = 0[/tex]
[tex]x^2 -22x - 121 = 0[/tex]
Using quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}[/tex]
[tex]x = \frac{-(-22)\±\sqrt{968}}{2*1}[/tex]
[tex]x = \frac{22\±31.11}{2}[/tex]
Split
[tex]x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\[/tex]
[tex]x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}[/tex]
x can not be negative.
So:
[tex]x = \frac{53.11}{2}[/tex]
[tex]x = 26.56[/tex]
Recall that:
[tex]y = 11 + x[/tex]
[tex]y = 11 + 26.56[/tex]
[tex]y = 37.56[/tex]
Hence, the dimensions are:
[tex]Hypotenuse:37.56[/tex]
[tex]Other\ Legs: 26.56[/tex]
Marco needs to buy some cat food if the next two or three bags of cat food cost 17.25 how much with Marco spend on two bags of cat food
Answer is in the file below
tinyurl.com/wpazsebu
Answer:
34.50
Step-by-step explanation:you multiply 17.25 times two because thats the amount of bags there is so that will give you 34.50
The bird population in a forest is about 2300 and is decreasing at a rate of 5% per year. Let t represent the number of years and P represent the population. Write an exponential decay model to represent this situation. (please fill in those blank spaces)
P = _____ (1 - ____ ) t
Answer: P=2300 (1- 0.05)^x
Step-by-step explanation:
Line d has a slope of 3/2. Line e has a slope of -2/3. Are line d and line e parallel or
perpendicular?
Answer:
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect
The cost of leveling a square park at Rs.15 per square meter is Rs.6000. Then the side of the square is ________. *
Answer:
20 m
Step-by-step explanation:
Given :
Leveling cost per square meter = 15
Total leveling cost = 6000
Number of square park leveled :
Tottal cost / unit cost
6000 / 15
= 400 m²
The length of one side of the square
Area of square = s²
where, s = side length
400 = s²
Sqrt(400) = s
s = 20 m
Length of one side = 20 m
Please help! 30 points!
Use the Law of Cosines to solve the problem.
A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.
Answer: [tex]64.2^{\circ}[/tex]
Step-by-step explanation:
According to the cosine rule
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
Here, [tex]a=83, b=111, c=165,\ C=180^{\circ}-\theta[/tex]
Putting values
[tex]\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}[/tex]
So, the ship turns by [tex]64.2^{\circ}[/tex] north of west
The ship turned an at angle of 64.2 degrees north of west
Represent the angle, the ship turned due north of west with theta.
From the figure, we have the following equation
[tex]\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}[/tex]
So, we have:
[tex]\cos(A) = \frac{83^2 + 111^2 - 165^2}{2 * 83 *111}[/tex]
Evaluate the expression on the right-hand side
[tex]\cos(A) = -0.4350[/tex]
Take the arc cos of both sides
[tex]A = \cos^{-1}(0.4350)[/tex]
[tex]A =115.8^o[/tex]
The value of theta is then calculated as:
[tex]\theta = 180 -A[/tex]
This gives
[tex]\theta = 180 -115.8^o[/tex]
[tex]\theta = 64.2^o[/tex]
Hence, the ship turned an at angle of 64.2 degrees north of west
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The table shows the running speeds of 10 randomly selected ostriches. Speed (mlles per hour) 35 40 37 33 36 34 32 36 41 36 Based on the data, select the most reasonable prediction about the speed of ostriches.
A. The typical ostrich runs at speeds greater than 40 miles per hour
B. The top speed of an ostrich is 40 miles per hour.
C. The typical ostrich runs at a speed of about 30 miles per hour
D. The typical ostrich runs at a speed of about 36 miles per hour.
Answer:
D;the tropical ostrich runs at a speed of about 36 miles per hour
Answer: It is D, The typical ostrich runs at a speed of about 36 miles per hour.
Step-by-step explanation:
I took the quiz on A p e x^^
Help ASAP pleaseee lol
I’ve attached my table of what I’ve done
Now do you guys understand the question?? I need help.
Answer:
6th period.
Step-by-step explanation:
factorise p-q-x(q-p)
Answer:
(1 + x)(p - q)
Step-by-step explanation:
Given
p - q - x(q - p) ← distribute parenthesis by - x
= p - q - qx + px ← rearrange terms in p and terms in q
= p + px - q - qx ( factor first/second terms and third/fourth terms )
= p(1 + x) - q(1 + x) ← factor out (1 + x) from each term
= (1 + x)(p - q)
Which of the following equations corresponds to the graph below
Answer:
d) y = -1/2 + 3
Step-by-step explanation:
Looking at the graph, we can use y = mx + b to find the equation. m is the slope and for slope, we go 1 unit down and 2 units to the right. b is the y variable and our b would be 3.
y = mx + b
y = -1/2x + 3
Hope this helps and stay safe, happy, and healthy, thank you :) !!
Jehle and Liam a bowl serving 0.5÷200 Jehle says the question will be Less than 0.5 Liam says the quotient would be more than 0.5 which student is correct
Answer:
Jehle is correct.
Step-by-step explanation:
Given - Jehle and Liam a both solving 0.5÷200.
Jehle says the quotient will be Less than 0.5.
Liam says the quotient would be more than 0.5
To find - Which student is correct ?
Proof -
Given expression is 0.5 ÷ 200
It is equivalent to
[tex]\frac{0.5}{200} = \frac{5}{2000} = \frac{1}{400}[/tex] = 0.0025 < 0.5
∴ we get
The expression is Less than 0.5
So, Jehle is correct.
besties besties please help im desparate
What in the flipping Jeapordy is this, but anyway:
1) Simran needs a 65% to score an 80 test average
2) The length is 13 centimeters
3) Jake purchased 4 gadgets
4) 100 candles would need to be sold
5) You bought 3 drinks
Answer:
Step-by-step explanation:
miss girl you need homework plugs sorry queen have a good day
Mr. Ramirez baked 24 cookies. 5 sixths of the cookies were oatmeal. How many oatmeal cookies did Mr. Ramirez bake?
Answer:
20 oatmeal cookies
Step-by-step explanation:
5/6 is the same as 20/24, thus 20.
Joe runs an M&M's factory and is reviewing the bagging machines. They drop M&M's into bags on a conveyor belt, with 39 M&M's going into each bag. Write an equation for the number of bags 'B' that can be filled from a supply of M&M's 'T'. Write your equation in the form of B=_____________.
The equation for the number of bags 'B' that can be filled from a supply of M&M's 'T' will be T / 39.
How to explain the equationThe formula to determine how many bags 'B' can be filled with M&M's from a stockpile of 'T', where each bag contains 39 candies, is:
B = T/39
This computation takes the sum of all M&M's in 'T' and divides it by the quantity of candies present in each sack (39), producing the amount of bags 'B' that can be filled.
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14 cm
12 cm
22 cm
Find the area of the trapezoid. and show Work
A. 108 cm
B. 432 cm
C. 60 cm
D. 216 cm
Answer:
D. 216 cm
Step-by-step explanation:
1. I assume 14 is a 22 is b and 12 is h
2. Trapezoid Area Formula
[tex]A = \frac{1}{2}(a+b)h[/tex]
3. Plug in numbers
[tex]A = \frac{1}{2}(14+22)12[/tex]
[tex]216 = \frac{1}{2}(14+22)12[/tex]
Lin and Kal's ages add up to 41 Lin is 5 years older than Kal. Use the equation from the to find their ages.
Determine which of the graphs represent the proportional relationships. Circle the appropriate response.
What is the value of x?
Answer:
I have no idea. But I just want to let you know to not put this many points, because people are going to take them without answering the question. And I don't know the answer because there are multiple x's.
Answer:
x = 8
Step-by-step explanation:
Remark
I agree with the other responder. You need only pay 20 points to get our attention. (20 will give us 10).
The length from the intersect point to the circle times the entire length of the secant is equal to any other secant divided up the same way.
Put simpler
Equation
(x + 2)(x + 2 + 2x- 8) = (x + 1)(x + 1 + 2x - 5)
Combine like terms
Solution
(x + 2)(3x - 6) = (x + 1)(3x - 4) Remove the brackets on both sides.
3x^2 + 6x - 6x - 12 = 3x^2 + 3x - 4x - 4 Combine the like terms
3x^2 - 12 = 3x^2 - x - 4 Subtract 3x^2 from both sides
- 12 = - x - 4 Add 4 to both sides
-12 +4 = - x
- 8 = - x Multiply both sides by -1
x = 8
Problem PLS HELP MY GRADES GOING DOWN
Answer:
$248
Step-by-step explanation:
given:
4 deposits
$62
solve:
4 × $62= $248
Answer:
$248
Step-by-step explanation:
You can answer it two ways:
1) add 62 + 62 + 62 + 62 = 248
2) multiply 4 * 62 = 248
Answer: $248
Geomotry 10th grade easy 25 points
Answer: 1=60°
Step-by-step explanation:
First, let's take our given angle of 30°
30° is in a right triangle, so the angles must be 90°, 60°, and 30°
Now the angle that is 45° makes angle 1 congruent to angle 60°
Meaning angle 1 is 60°
Answer:
m < 1 = 60
Step-by-step explanation:
Since the transversal is perpendicular to m,
it implies that the triangle formed by the perpendicular transversal, the slant transversal and the line m is a right angle triangle.
We use vertically opposite angles property to bring m<1 in to the right triangle.
We now use the sum of interior angles property to obtain,
m < 1 + 30 + 90 = 180
This implies that,
m < 1 + 120 + 180
We group like terms to obtain,
m < 1 = 180 - 120
This means that,
m < 1 = 60
We could have also used corresponding angles property, then
m < 1 + 30 = 90
m < 1 = 90 - 30
m < 1 = 60
Here are the score that Jenna has received on her seven quizzes 16 11 20 16 12 17 18 what is the lower quadrille
Answer:
12
Step-by-step explanation:
lower quartile is the median of 11, 12, and 16
HELP ASAP will give brainlist
please hurry if answer is correct i will give brainlyyyyest thx
In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches.
Answer:
i could only get part one done
Step-by-step explanation:
Perimeter is a measurement of the distance around a shape and area gives us an idea. Understanding how much space you have and learning how to fit shapes ... If the shape is a polygon, then you can add up all the lengths of the sides to find the perimeter. ... You can write “in2” for square inches and “ft2” for square feet
Hellohello, if you able to help me then please do. (:
What two numbers have a sum of 215 and a difference of 137
Answer:
see below
Step-by-step explanation:
let x = big number
let you = small number
x + y = 215-------> (1)
x - y = 137 ------>(2)
(1)
x = 215 - y ----->(1)
substitute 1 into 2
215 - y -y = 137
-2 y = 78
y = 39
substitute y = 39 into (1)
x = 215 - (39)
x = 176
thus the numbers are 176 & 39
hope this helps
please mark it brainliest
it took me quite long to do this
Given the definitions of f(c) and g(x) below, find the value of g(f(5)).
f(x) = 2x – 10
g(x) = x2 + 6x – 8
Answer:
gf(5) = -8
Step-by-step explanation:
gf(x) = g(x^-1) = x^2 + 6x - 8
f(x) = 2x - 10
gf(x) = 6(2x - 10) - 8
gf(x) = 12x - 60 - 8
gf(x) = 12x - 68
gf(5) = gf(x) = 12x - 68
gf(5) = 12(5) - 68
gf(5) = 60 - 68
gf(5) = -8
Two sides of a triangle have side lengths of 6 inches and 14 inches. Select all measurements that could be the length of the third side of this triangle
Answer:
14 on the bottom and 6 going up and down and then you complete the triangle make the other up and down side 6 so it makes a triangle not a sideway one
There are 11 possible values of side x, which are 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
The side lengths of the triangle,
a = 6 inches and b = 14 inches.
A triangle is formed when the length of third side is greater than difference of two sides and less than sum of two sides.
Let the third side is x,
So, the possible values of x could be,
14 - 6 < x < 14 + 6
8 < x < 20
The values of x can be 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
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Help will give b if correct
Answer:
0.28
Step-by-step explanation:
28 divided by 100=0.28
Answer:0.28m
Step-by-step explanation:
factorise fully :
4(x - y)^2 - 9(x + y)^2
Answer:
- ( 5x + y ) ( x + 5y )
or
-5x^2 - 5y^2 - 26xy
Answer:
Step-by-step explanation:
4(x^2-2xy+y^2)-9(x^2+2xy+y^2)
4x^2-8xy+4y^2-9x^2-18xy-9y^2
-5x^2-26xy-5y^2
-5x^2-xy-25xy-5y^2
-x(5x+y)-5y(5x+y)
(-x-5y)(5x+y) or you can also remove the negative one to get
-(x+5y)(5x+y)
I need help ASAP please
Answer:
It's actually B
Step-by-step explanation:
The measures of the sides are x , x , and x√2 . In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg. To see why this is so, note that by the Converse of the Pythagorean Theorem , these values make the triangle a right triangle.
So x = 4 in this example and the side measures would be 4, 4, and 4√2 which is B