In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs
Answers
Answer:
[tex] \frac{11\sqrt{2}}{2}[/tex]
Step-by-step explanation:
In a 45-45-90 triangle, the length if the hypotenuse is 11
WE use the common ratio of 45-45-90 degree triangle
common ration is x: x: x sqrt(2)
x sqrt(2) is the length of the hypotenuse
[tex]x\sqrt{2} = 11[/tex]
Divide by sqrt(2) on both sides
[tex]x= \frac{11}{\sqrt{2}}[/tex]
To rationalize the denominator, multiply by sqrt(2) at the top and bottom
sqrt(2) * sqrt(2) = 2
[tex]x= \frac{11\sqrt{2}}{2}[/tex]
Related Questions
What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors?
Answers
Difference of squares is simply written in the form of (a² - b²) and to find its roots, you simply simplify the previous expression to be (a+b)(a-b) where a and b are the roots
i.e. (a² - b²) = (a+b)(a-b)
2- As per square trinomials:
Let's assume that the square trinomial is written in the form of (ax² + bx +c) where a,b and c are constants.
Now the basic formula to get the two roots of this expression is given as shown in the below picture.
This formula is valid for almost all expressions, nevertheless, there is a special case (perfect square) in which we do not have to use to use this formula.
Perfect Square:
Let's assume that we have an expression written in the form of (ax² + cx +b) where a,b and c are constants. If you find that the value of a is the square of a first binomial, b is the square of a second binomial and c is the twice the value of multiplying a and b (i.e. c=2ab), then this expression is said to be a perfect square and can simply be simplified as (a+b)²
Note: If the expression of the perfect square was (ax² - cx +b), then the simplification would be (a-b)²
Final answer:
Square trinomials and difference of squares binomials can be rewritten into separate factors using methods such as completing the square, the difference of squares method, and factoring by grouping.
Explanation:
Completing the square method: Rewrite square trinomials by completing the square to factor them into separate factors. For example, [tex]x^2 + 6x + 9[/tex] can be written as (x + 3)(x + 3).
Difference of squares method: Rewrite binomials with a difference of squares by factoring them into separate factors. For instance, [tex]x^2 - 4[/tex] can be expressed as (x + 2)(x - 2).
Factoring by grouping: For more complex trinomials, you can use the method of factoring by grouping to rewrite them as separate factors.
The graph below shows four straight lines, P, Q, R, and S: graph of line P going through ordered pairs negative 2, negative 5 and 0, 3. Graph of line Q going through ordered pairs negative 1, negative 2 and 1, 6. Graph of line R going through ordered pairs negative 1, negative 4 and 1, 4. Graph of line S going through ordered pairs 0, negative 3 and 2, 5 Which line is represented by the function f(x) = 4x - 3?
Answers
f(x) = 4x - 3 = y
y = 4x - 3
for graph of line S we have the coordinates (0, -3) and (2, 5)
(0, -3)
-3 = 4(0) - 3
-3 = -3
(2,5)
5 = 4(2) - 3
5 = 8 - 3
5 = 5
So the answer is the graph of line S.
You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.
f(x) = 4x - 3 = y
y = 4x - 3
for graph of line S we have the coordinates (0, -3) and (2, 5)
(0, -3)
-3 = 4(0) - 3
-3 = -3
(2,5)
5 = 4(2) - 3
5 = 8 - 3
5 = 5
So the answer is the graph of line S.
How is the multiplication property for inequalities different from the multiplication property of equality?
Answers
If one multiplies or divides by a negative number, the inequality gets reversed:
x>3 ---> -x < -3!
What is the radius of a circle with an area of 32.1 sq ft
Answers
[tex] \pi * r^{2} = 32.1 [/tex]
[tex] r^{2} = \frac{32.1}{ \pi } [/tex]
[tex]r = \sqrt{ \frac{32.1}{ \pi } } [/tex] = 3.2 ft
Formula: [tex]A = \pi r^2[/tex]
Rearrange the formula.
[tex]A = \pi r^2 \\ \\ \frac{A}{\pi} = r^2 \\ \\ \sqrt{\frac{A}{\pi}} = r[/tex]
We let [tex]\pi[/tex] equal to 3.14.
Plug in the values.
[tex]\sqrt{\frac{32.1}{3.14}} = r \\ \\ \sqrt{10.22} = r [/tex]
3.19 ≈ r
So, the radius is approximately equal to 3.19 feet.
Which three lengths could be the lengths of the sides of a triangle? 9 cm, 22 cm, 11 cm10 cm, 15 cm, 24 cm12 cm, 5 cm, 17 cm21 cm, 7 cm, 6 cm
Answers
Answer: 10, 15, 24 is your answer
Step-by-step explanation:
If the volume for 3-D pyramid A is 300 cm3 and the volume for 3-D pyramid B is 900 cm3, how many times bigger is the volume of pyramid B than pyramid A?
Answers
Answer:
Volume of pyramid B is three times bigger than the volume of pyramid A
Step-by-step explanation:
We are given that:
The volume for 3-D pyramid A is 300 cm³ .
and the volume for 3-D pyramid B is 900 cm³.
We have to tell how many times bigger is volume of pyramid B than volume of pyramid A.
volume of 3-D pyramid B= 900 cm³
= 3×300 cm³
= 3×volume of 3-D pyramid A
Hence, Volume of pyramid B is three times bigger than the volume of pyramid A
Answer:
Step-by-step explanation: 3%
Determine the exact value of
sin(−135)°.
Identify the reference angle, Theta
Theta=?
Answers
To find the exact value, use the special triangles. sin(45°)=√2÷2 (rationalized form of 1÷√2, which you can get from the triangle: it has two sides of value 1, and by the Pythagoras theorem we get √2 as the hypotenuse; SOHCAHTOA gives us 1÷√2 for the sine value).The exact value of sin(-135°) would be -(√2÷2). (-135° is equivalent to 225°. sin(225°) does give the same answer as the negative of sin(45°)).
We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.
How to determine the reference angle?
We know that for any angle θ we have that:
sin(θ) = sin(θ + n*360°)
Where n is an integer value.
To find the reference angle of a given angle θ, we just need to find a value of n such that:
0 ≤ θ + n*360° ≤ 360°
So we can write our angle in the normal range.
in this case, our angle is -135°
Then we can write:
0 ≤ -135° + n*360° ≤ 360°
Is immediate to notice that we must take n = 1
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ 225° ≤ 360°
Now we know that θ = 225°.
Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.
We will get:
225° - 180° = 45°
So the reference angle is 45°.
Finally, to get the exact value we use:
sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707
If you want to learn more about trigonometry, you can read:
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PLEASEEE help shape equation puzzle
Answers
circle = 2
" shot-glass " = 0
check..
circle * shot-glass = shot-glass
2 * 0 = 0
circle * circle = triangle
2 * 2 = 4
triangle + shot-glass = triangle
4 + 0 = 4
circle + circle = triangle
2 + 2 = 4
yep...it checks out
Find the number of possible positive real zeros of 2x^4+14x^3-35x^2
Answers
The polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² has one possible positive real zero according to Descartes' Rule of Signs. We observe one change of sign in the coefficients. Thus, there is a maximum of one positive real root.
Determining the Number of Possible Positive Real Zeros:
To determine the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x², we can use Descartes' Rule of Signs. This rule helps us to count the number of sign changes in the polynomial and thus infer the number of positive real roots.
First, let's observe the original polynomial:
[tex]2x^{4}[/tex] + 14x³ - 35x²
We examine the coefficients: 2, 14, and -35. By running our eye across these coefficients:
From 2 to 14: No sign change (positive to positive).From 14 to -35: One sign change (positive to negative).The polynomial has one sign change. According to Descartes' Rule of Signs, there is a maximum of one positive real root.
Therefore, the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² is one.
George and Carmen went on a bicycle trip. They took a bus to their starting point, and then biked the rest. They traveled 275 kilometers in total, and they biked 55 kilometers more than they were bussed. Let x = kilometers traveled by bike and y = kilometers traveled by bus. Find how many kilometers they traveled by bike.
Answers
x = y + 55
(y + 55) + y = 275
2y + 55 = 275
2y = 275 - 55
2y = 220
y = 220/2
y = 110 ..... bus
x = y + 55
x = 110 + 55
x = 165 <=== bike
find the surface area of each figure to the nearest tenth. show your work, please!
Answers
A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:
A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]
where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:
l = w = 16 in
h = 15 in
Substituting:
A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]
A = 256 + 272 + 272
A = 800 in^2
B. We are given a cone, the formula for surface area is:
A = πr (r + h^2 + r^2)
where h is the height = 8 in and r is the radius = 3 in
Substituting:
A = π * 3 (3 + sqrt (8^2 + 3^2))
A = 34.63π in^2 = 108.80 in^2
Short fill in-
If two angles are adjacent and supplementary, then they are examples of the _____ Postulate.
Answers
Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.
Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2
Answers
8x5 + 25x3 + 48x2
Answer:
option C is correct
[tex]8x^5+24x^3+48x^2[/tex]
Step-by-step explanation:
As per the statement:
The length(l), width(w) and height(h) of the rectangular prism are:
l = 4x
w = 2x
[tex]h = x^3+3x+6[/tex]
We have to find volume.
Use the formula:
[tex]V = lwh[/tex]
Substitute the given values we have;
[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]
⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]
Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]V = 8x^5+24x^3+48x^2[/tex]
Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]
The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is 77 ft2 . find the dimensions of the rectangle.
Answers
let : y the length and : x the width
y = 2x +3.....(1)
xy = 77 .....(2)
by (1) subsct : y i n (2)
x(2x+3) = 77
2x²+3x -77 = 0
the descrimnent : b²-4ac ... a =2 b= 3 c = -77
3²-4(2)(-77) = 625 = 25²
x1 = (-3-25)/4 negatif refused
x2 = (-3+25)/4 =22/4 = 11/2
x= 5.5
y = 2(5.5) +3 =14
What is 10095 m/a to miles/s
Answers
[tex]\frac{10095 m}{1 s} \times \frac{1 mi}{1609m}=6.27\frac{mi}{s}[/tex]
One person can do a certain job in fifteen minutes, and another person can do the same job in thirty minutes. How many minutes will it take them to do the job together?
Answers
1/15 and 1/30
The amount of work that they can do together is:
t/15+t/30
And we want to solve for when they can complete the job together:
t/15+t/30=1 making a common denominator
(t/15)(2/2)+t/30=1
(2t+t)/30=1 multiply both sides by 30
2t+t=30 combine like terms on left side
3t=30 divide both sides by 3
t=10
So it will take them 10 minutes to complete the job when working together.
‘B’ can do the same job = 1/30 Job/minutes
Both ‘A’ & ‘B’ can do the Job = 1/15+1/30
=(2+1)/30
=3/30=1/10 job/minutes
Both A & B can do the Job in 10 minute
Which of the following is the definition of term? A. an ordered set of numbers B. an element in a sequence C. a sequence in which terms are given by multiplying the previous term by a common ratio D. a sequence in which terms are not given by multiplying the previous term by a common ratio
Answers
Element in a sequence
In PQR, point S lies on QR. If PS is perpendicular to QR, which term describes PS?A. Perpendicular bisector
B. Angle bisector
C. Median
D. Altitude
Answers
Hope it helps.
How would you graph a point at -5?
A: Put a point 5 units to the right of zero.
B: Put a point at zero.
C: Put a point 5 units to the left of zero.
Answers
means put a point 5 units to the left of 0
C is answer
Answer:
C: Put a point 5 units to the left of zero.
Step-by-step explanation:
Which of the following quadrilaterals have diagonals that are perpendicular to each other? Check all that apply.
A. Rectangle
B. Square
C. Parallelogram
D. Rhombus
Answers
Answer:
B. Square
D. Rhombus
Step-by-step explanation:
If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.
Since, for sides, AB , CD,AD and CB are congruent
For diagonals, AC = BD
As E is the bisecting point for diagonals,
AE = EC and ED = EB
Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent
ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent
Now the angles
∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,
So, we know that sum of interior angles of any quadrilateral is 360°
So each angle is 360/4 = 90°
This calculation is valid for square as well.
Answer:
B and D
Step-by-step explanation:
cya
The radius of a circle is 6 feet. What is the area of the circle?
A. 6π
B. 12π
C. 18π
D. 36π
Answers
-------------------------------------------------
The radius is given to be r = 6. Plug this into the area of a circle formula shown below
A = pi*r^2
A = pi*6^2
A = pi*36
A = 36*pi
A = 36pi
What is the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously? ≈ $5006.50 ≈ $6125.25 ≈ $4062.65 ≈ $3955.64
Answers
A=p e^rt
A future value?
P present value 1250
E constant
R interest rate 0.096
T time 12 years
A=1,250×e^(0.096×12)
A=3,955.64
The total amount for the investment is approximately $4062.65.
Explanation:To calculate the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously, we can use the formula A = P * e^(rt), where A is the total amount, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is the number of years. Plugging in the values, we have A = 1250 * e^(0.096 * 12). Using a calculator, we find that A is approximately $4062.65.
What value completes the square for the expression?
x2 - 18x
A. 9
B. -9
C. 81
D. -81
Answers
To complete the square for the expression x^2 - 18x, add 81 to become a perfect square trinomial in the form (x - 9)^2.
Explanation:To complete the square for the expression x^2 - 18x, we need to add a constant term to the expression in such a way that it can be factored as a perfect square trinomial. First, we take half of the coefficient of the linear term and square it:
Half of -18 is -9, and when we square it we get 81. Therefore, adding 81 to the expression gives us x^2 - 18x + 81. This can be factored as (x - 9)^2. So the value that completes the square is 81.
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A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon. It's an octagon with on side 4/3x - 1/3 and another side x+7
Answers
To find the perimeter of the regular octagon, set the expressions for the sides equal to each other to find the value of x, substitute this value into either of the expressions for the sides to find the side length, and finally multiply the side length by 8.
Explanation:In mathematics, a regular polygon is a polygon that is equilateral and equiangular. In this case, you have an octagon, which means it has 8 equal sides. If one side is defined as 4/3x - 1/3 and another side is defined as x+7, since it's a regular octagon, all sides must be equal. Therefore, to find the perimeter of the octagon, you need to set the two expressions for the sides equal to each other to find the value of x, and then substitute the value of x into either of the expressions for the sides. Multiply this side length by 8 to get the perimeter.
Here are the steps:
Set the expressions for the sides equal to each other: 4/3x - 1/3 = x + 7Solve for x.Substitute the value of x into either of the side expressions to find the side length.Multiply the side length by 8 to get the perimeter.Learn more about Perimeter of a Regular Polygon here:https://brainly.com/question/19034638
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In a regular polygon, all sides and angles are equal. Given a regular octagon with two sides expressed as 4/3x - 1/3 and x+7, the expressions should be equal since all sides are equal in a regular polygon. Having found x, you can multiply by 8 to find the perimeter of the octagon.
Explanation:Thus, If a polygon is regular, this means all of its sides have the same length. If we're given that one side of the regular octagon is 4/3x - 1/3 and another side is x+7, these two expressions should be equal to each other since it's a regular polygon. This gives us an equation:
4/3x - 1/3 = x + 7
Solving for 'x' will give us the length of one side of the regular polygon. Once you have the length of each side, you can find the perimeter of the regular octagon by multiplying this length by 8 (since an octagon has 8 sides).
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Which line is parallel to 4x + 2y = 0?
A. y=2x+3
B. -1/2×+3
C. y=-2x+3
D. y=1/2x+3
Answers
Convert the standard form equation to slope-intercept form as it will be easier to see the slope.
Solve for y.
4x + 2y = 0
2y = -4x <-- Subtract 4x from each side
y = -2x <-- Divide both sides by 2
In the slope-intercept form y = -2x, a y-intercept of 0 is implied
Now find a slope-intercept form equation that has the same slope as y = -2x
So, the answer is C y = -2x + 3.
2y = -4x
y = -2x so the slope of this line is -2
parallel lines have same slope
So its C.
4x + 5 - 2x + 1 = 2x - 5
Answers
(4x-2x)+(5+1)=2x-5
2x+6=2x-5
2x=2x-11
2x-2x=-11
0=-11 no solution
PLZ HELP! WILL MARK THE BRAINIEST!!!!!!!
The system Mx+Ny=P has the solution (1,3), where Rx+Sy=T
M,N,P,R,S and T are non zero real numbers. Which of the following system would not have (1,3) as a solution.
Answers
Answer: C.
[tex]Mx+Ny=P\\(2M-R)x+(2N-S)y=P-2[/tex]
Step-by-step explanation:
Given: The system [tex]Mx+Ny=P\\ Rx+Sy=T[/tex] has the solution (1,3), where M,N,P,R,S and T are non zero real numbers.
A.
[tex]Mx+Ny=P\\ 7Rx+7Sy=7T[/tex]
Divide 7 on both sides on the second equation , we will get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
B.
[tex](M+R)x+(N+S)y=P+T.......(1)\\\\ 7Rx+7Sy=7T................(2)[/tex]
Subtract equation (2) from equation (1), we get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
C.
[tex]Mx+Ny=P...........(1)\\\\(2M-R)x+(2N-S)y=P-2T............(2)[/tex]
We can rewrite the equation (2) as
[tex]2Mx-Rx+2Ny-Sy=P-2T............(3)[/tex]
Multiply 2 on both sides of equation (1), we get
[tex]2Mx+2Ny=2P.........(4)[/tex]
Subtract equation (3) from (4), we get
[tex]Rx+Sy=P+2T[/tex]
But [tex]Rx+Sy=T[/tex]
Thus, this system does not have solution as (1,3).
D.
[tex]\frac{M}{2}+\frac{N}{2}=\frac{P}{2}\\\\Rx+Sy=T[/tex]
Multiply 2 on both sides on the first equation , we will get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 7? 20 POINTS
Answers
3^y = 7, is equivalent to y = log_3(7)
We need to find which graph goes like log_3(x). For x =3, log_3(3) = 1, for x = 9, lo_3(9)=2, so .....
The first one!
Answer with explanation:
The exponential function is
[tex]3^y=7\\\\ \text{taking log on both sides}\\\\y\log3=\log7\\\\y=\frac{\log7}{\log3}\\\\y=\log_{3}7\\\\y=\frac{0.8450}{0.477}\\\\y=1.77[/tex]
It is equation of a line, parallel to X axis.
Drawn the graph of the function , which cuts the y axis at ,(1.77,0).
None of the curve matches with the given Options.
Write an equation of the line that passes through (-5,-1) and is parallel to the line y=4x-6
Answers
Martha can complete 15 activities a day at summer camp. She can choose between crafts or sport
Answers
Variable 1: X= number of craft activities
Variable 2: Y= number of sports activities
Equation: X + Y=15