The hypotenuse is [tex]c = a\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
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what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select three options.
positive slope
negative slope
constant slope
increasing function
decreasing function
Answer: negative slope
constant slope
decreasing function
B-C-E
Step-by-step explanation:negative slope
constant slope
decreasing function
What is the multiplicity of f(x) = -2x3(x + 2)2?
Henry will need a total of 15 pints of paint. The 3 pints of yellow were multiplied by 3 to get 9 total, so 2 pints of red would be multiplied by 3 to get 6 total.
Which ideas did you include in your response? Check all that apply.
Henry will need 15 pints altogether.
The number of pints of yellow (3) is multiplied by 3 to get 9, so he would multiply 2 by 3 to get 6 pints of red.
Add: 6 + 9 = 15 pints.
Answer:
All answers are correct.
Step-by-step explanation:
Henry needs a total of 15 pints.
3 pints of yellow multiplied by 3 gives 9 pints of yellow, he needs 6 pints of red to get to 15, so he multiplies 2 pints of red by 3 to get 6 pints of red.
You add 9 + 6 to get the total of 15 pints he needs.
find the value of p and of q for which x-3 is a common factor of the expressions [tex]x^{2} + (p + q)x-q[/tex] and [tex]2x^2 + (p-1)x + (p+2q)[/tex]
WILL GIVE BRAINLIEST PLS ANSWER
Step-by-step explanation:
Use the Factor Theorem,
" if x-a is a factor of f(x), then f(a) =0,
So here, since x-3 is a factor then f(3)=0,
So first step, plug in 3 for x for the serperate equations.
[tex] {3}^{2} + ( p + q)3 - q = 0[/tex]
[tex]2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0[/tex]
Simplify both equations,
[tex]9 + 3p + 2q = 0[/tex]
[tex]15 + 4 p + 2q = 0[/tex]
Isolate the constants,
[tex]3p + 2q = - 9[/tex]
[tex]4p + 2q = - 15[/tex]
We have a system of equations so let eliminate a variable, by subtracting the two equations.
[tex] - p = 6[/tex]
[tex]p = - 6[/tex]
Plug p back in for any one of the equations to find q.
[tex]3( - 6) + 2q = - 9[/tex]
[tex] - 18 + 2q = - 9[/tex]
[tex]2q = 4.5[/tex]
So p is -6
q is 4.5
Natalie charges $1,490 per month to rent each of her three rental houses. natalie must pay $5,850 in maintenance costs per house per year. if all three houses are occupied, how much money will natalie earn over seven years? a. $334,250 b. $252,630 c. $84,210 d. $375,480
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
According to given information:Natalie charges $1490 in rent for each home.
Given that Natalie owns three homes, her monthly rent will be:
= $4470 (3 * 1490) dollars.
The annual income Natalie receives from her three homes is
=($12 * $4470)
= $53680.
Natalie spends $5850 a year on maintenance for each home.
The total amount Natalie spends annually to maintain her three homes is therefore:
=(3 * 5850) dollars, which comes to 17550 dollars.
Then Natalie's annual income would be
= [(53640 - 17550) dollars]
= 36090 dollars.
The total amount Natalie made over the course of seven years was
= ($7 * 36090)
=$252630
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
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Answer:B) $252630
Step-by-step explanation:edge
25 Points + BRANIEST. PLEASE HELP
Answer:
sorry I don't know please forgive because I can't copy the question
Translate the triangle by
(-2
-4)
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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Geometry: write formal proofs, ASAP!!!!!
Two lines are said to be parallel if and only if the value of the angle between them is [tex]180^{o}[/tex].
Thus the required proofs for each question are stated below:
6. A bisector is a line that divides a given line or angle into two equal parts.
Thus to prove that: AD ║BC
Given that: AC ⊥ BD, then:
BX ≅ DX (midpoint property of a line)
<ADX ≅ <DBX (alternate angle property)
<DAX ≅ <BCX (alternate angle property)
<AXD ≅ <BXC (vertical opposite angle property)
Also,
ΔAXD ≅ ΔBXC (congruent property of similar triangles)
Therefore, it can be deduced that;
AD ║BC
7. Given: CD ≅ CE
<B ≅ <D
proof: AB ║DE
<ABC ≅EDC
Thus,
CB ≅ CA (congruent property of similar triangle)
<BAC ≅ <EDC (alternate angle property)
ABC ≅ <DEC (alternate angle property)
Also,
CA ≅ CB (congruent side of similar triangles)
ΔABc ≅ ΔCDE (congruent property of similar triangles)
Thus,
AB ║DE (congruent property)
8. Prove: AB ║ DE
Given: <1 ≅ < 3
Then,
<1 ≅ <2 ≅ <3 ≅ [tex]90^{o}[/tex]
So that,
BC ≅ EF
also,
<1 + <2 = [tex]180^{o}[/tex] (supplementary angles)
Therefore it can be inferred that;
AB ║ DE (congruent property of parallel lines intersected by transversals)
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Elena reflects the word 'MOM' over the x-axis and finds that it makes a new word. What is the new word?
Which of the graphs below represents the equation 4x+y=7
Find the slope of the line.
Simplify completely.
1 2 3 4
-4 -3 -4 -1
-1
Slope = [?]
Hint: The slope of a line is the rise
run
The slope of a line is -2.
How to find the slope a line?The slope of a line can be described as follows:
The slope of a line is a measure of its steepness
Slope = rise / run
slope = y₂ - y₁ / x₂ - x₁
using (0, -4)(-1, -2)
x₁ = 0
x₂ = -1
y₁ = -4
y₂ = -2
Therefore,
slope = -2 - (-4) / -1 - 0
slope = -2 + 4 / -1
slope = 2 / -1
slope = -2
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Which of the following equations can be used to find the length of EF in the
triangle below?
OA. EF = 24 +12
OB. (EF)2 = 242 +12²
OC. EF = 24-12
D. (EF)2 = 242-12²
D
24
E
12 F
W
The equation which can be used to find the length of EF is option A which is EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].
Given the length of base of right angled triangle is 12 and the hypotenuse be 24.
We are to find the length of EF and tell which equation can be used to find the length of EF.
We know that pythagoras theorem applies in a right angled triangle.
Pythagoras theorem says that in a right angled triangle the square of the hypotenuse is equal to the sum of square of base and perpendicular.
[tex]H^{2} =B^{2} +P^{2}[/tex]
In this triangle we are only given base and hypotenuse and we have to find EF which is perpendicular.
[tex](DE)^{2} =(EF)^{2} +(DF)^{2}[/tex]
EF=[tex]\sqrt{DE^{2}-DF^{2} }[/tex]
=[tex]\sqrt{(24)^{2} -(12)^{2} }[/tex]--1
=[tex]\sqrt{576-144}[/tex]
=[tex]\sqrt{432}[/tex]
Hence the equation which can be used to find the length of Ef is option A which is EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].
Question is incomplete as it should include the figure also.
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If the store has only 12 red balloons and only 8 blue balloons but at least 29 of each other color of balloon, how many combinations of balloons can be chosen?
The number of combinations of balloons that can be chosen is 1716.
Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.
Number of red balloons = 12
Number of blue balloons = 8
First, we figure out how to choose from 13 red and 9 blue balloons.
There are 7 balloons left out of the 29 total (i.e. 29 - 13 - 9)
So, n = 7+7-1
n = 13
r = 7
Number of combinations of balloons = [tex]_{13} C_{7}[/tex]
= 13!/(13-7)!7!
= 13!/6!7!
= 1716
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Given the parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π. convert to a rectangular equation and sketch the curve
The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] which is an ellipse.
For given question,
We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.
We need to convert given parametric equations to a rectangular equation and sketch the curve.
Given parametric equations can be written as,
x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.
We know that the trigonometric identity,
sin²t + cos²t = 1
⇒ (x/2)² + (- y/3)² = 1
⇒ [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex]
This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.
The rectangular equation is [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex]
The graph of the rectangular equation [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] is as shown below.
Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] which is an ellipse.
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Which of the following inequalities is graphed on the coordinate plane? A. y>-2x+1 B. y>-2x+1 C. y<-2x+1 D. y<-2x+1
The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?
The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Step-by-step explanation:
What is the point slope form of a line with the slope -4 that contains the point (2,-8)
Answer:
y + 8 = -4(x - 2)
Step-by-step explanation:
Point-slope form of an equation is a fill-in-the-blank, shortcut way to write an equation of a line. This is the format:
y - Y = m(x - X)
You just fill in the slope for m and fill in the point for the X,Y.
Just leave the first y; it stays a y and the first x in the parenthesis stays as an x. You just have to be careful with your minus and negative signs.
Slope is given as -4 so fill that in for m.
and put (2,-8) in place of the X and Y.
y - Y = m(x - X)
y - -8 = -4(x - 2)
y + 8 = -4(x - 2)
Done! Hope this helps!
Select the order in which the operations should be performed
12-4/4
Divide 12 by 4, then subtract 4 from that number.
Divide 4 by 4, then subtract that number from 12.
Subtract 4 from 12, then divide that number by 4.
Subtract 4 from 12, then multiply that number by 4.
None of the above
Answer: Divide the 4/4 then subtract that from 12.
Step-by-step explanation:
Use PEMDAS. The Division comes first, then the subtraction.
PLEASE HELP ME PLEASE
WHICH EQUATION DOES THE GRAPH REPRESENT
Answer:
Step-by-step explanation:
B is the best answer
23. Which expression is NOT equivalent
to the expression 38 – 14?
A 2(19-7)
B 24
C (19-7)2
D 2(36-12)
Answer: [D] 2(36-12)
Step-by-step explanation:
First, we will simplify the given expression.
38 – 14 = 24
Now, we will see if the other expressions are equivalent or not.
[A] 2(19-7) = 24
[B] 24 = 24
[C] (19-7)2 = 24
[D] 2(36-12) = 48
The expression is NOT equivalent to the expression 38 – 14 is;
[D] 2(36-12)
Hi :)
Let's evaluate all these expressions
———————[tex]\boldsymbol{\boxed{38-14=24}}}[/tex]
So Now the question boils down to --
What expression is NOT equivalent to [tex]\boldsymbol{24?}[/tex]
Option (A).[tex]\boldsymbol{2(19-7)}[/tex]
[tex]\boldsymbol{2(12)}[/tex]
[tex]\boldsymbol{24}[/tex]
Option (A) is ruled out, because we're looking for expressions that are not equivalent to 24.
Option (B)Well 24 is always equal to 24!
Option (C)[tex]\boldsymbol{(19-7)2}[/tex]
[tex]\boldsymbol{(12)2}[/tex]
[tex]\boldsymbol{24}[/tex]
Option (D)[tex]\boldsymbol{2(36-12)}[/tex]
[tex]\boldsymbol{2(24)}[/tex]
[tex]\boldsymbol{48}[/tex]
[tex]\tt{Learn\;More;Work\;Harder}[/tex]
:)
If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas?
Answer:
4 : 25
Step-by-step explanation:
given 2 similar figures with linear ratio a : b , then
ratio of areas = a² : b²
here the linear ratio = 2 : 5 , then
area ratio = 2² : 5² = 4 : 25
Which measurements of triangle BAC are correct
The measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
Trigonometrical ratiosFrom the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct
The given triangle is a right angle triangle
Using SOH CAH TOA
sin C = 9/15
∴ The option sin C = 9/15 is correct
Also,
Using SOH CAH CAH
tan B = 12/9
∴ The option tan B = 9/12 is NOT correct
To determine the measure of angle B (m ∠B)
From tan B = 12/9
Then,
tan B = 1.33333
B = tan⁻¹(1.33333)
∴ B ≈ 53.13°
Thus, the option B ≈ 53.13° is correct
Hence, the measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
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please help!
Amara needs 90 kilograms of meat to feed her 4 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Amara need to feed 2 pet dragons each day?
45 kilograms of meat is required to feed 2 pet dragons each day.
Amara needs 45 kilograms of meat to feed 2 pet dragons each day.
What is unitary method ?Unitary method is a mathematical way of deriving a single unit then obtaining the required units by multiplying it with the single unit.
According to the given question Amara needs 90 kilograms of meat to feed her 4 pet dragons each day.
Also given that each pet dragon eats the same amount of meat.
∴ 1 pet dragon eat 90/4 kilograms of meat which is
= 22.5 kilograms of meat.
So, Amara need (22.5×2) = 45 kilograms of meat to feet 2 pet dragons.
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For the transformation t, what is t-1? t : (x, y) (x 4, y 3) t-1: (x, y) (x - 4, y - 3) (-4x, -3y) (x 3, y 2)
The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex]
The value of a exists -4 and value of b exists -3.
How to determine the value of [tex]$\mathrm{T}^{-1}$[/tex]?
The transformation T exists given as
[tex]$T:(x, y) \rightarrow(x+4, y+3)[/tex]
Let the transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x+a, y+b)$$[/tex]
If T and [tex]$T^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(x)\right)=x \\[/tex]
[tex]$&T(x+a)=x \\[/tex]
[tex]$&x+a+4=x \\[/tex]
[tex]$&a=-4[/tex]
The value of a exists -4.
If T and [tex]$\mathrm{T}^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(y)\right)=y \\[/tex]
[tex]$&T(y+b)=y \\[/tex]
[tex]$&y+b+3=y \\[/tex]
b = -3
The value of b exists -3.
The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex].
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Grade 11 Circle Geometry(Tagents)(Find g)
Answer:
g = 4
Step-by-step explanation:
if 2 tangent segments are drawn to a circle from the same external point then they are congruent , that is
RJ = RW and MJ = MB and KB = KW
given MR = 6 , then
MJ = 6 - g = MB
given KM = 5 , then
KB = 5 - MB = 5 - (6 - g) = g - 1 = KW
given KR = 7 , then
RW = 7 - KW = 7 - (g - 1) = 8 - g
Then
RJ = RW , that is
g = 8 - g ( add g to both sides )
2g = 8 ( divide both sides by 2 )
g = 4
Find the value of sin J rounded to the nearest hundredth, if necessary.
12
13
K
The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
What is the measure of the missing angle?The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K). The measure of the missing angle can be found by using the trigonometric function of cosine:
cos m ∠ J = KJ / JL
cos m ∠ J = 12 / 13
m ∠ J = 22.620°
The measure of the angle J within the triangle JKL is approximately 22.620°.
And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:
sin m ∠J = √(1 - cos² m ∠J)
sin m ∠J = √[1 - (12 / 13)²]
sin m ∠J = 5 / 13
The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
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The Chens bought their house for $240 000 twenty years ago. They just sold the house
for $520 000. What percent is the new value of the house of the price they paid 20
years ago?
The percent is the new value of the house of the price they paid 20 years ago is 216.67%.
PercentageOld price = $240 000New price = $520 000percent is the new value of the house = New price / Old price
= 520,000 / 240,000 × 100
= 2.16666666666666
= 216.666666666666%
Approximately,
percent is the new value of the house = 216.67%
Therefore, the percent is the new value of the house of the price they paid 20 years ago is 216.67%.
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Rohan was planning a party and needed to provide 35 lunches. the cost for each plate 5$ and each plate was 6$. how many of each could he buy and spend $198 total?
for 5 bucks a plate its 39 for 6 bucks its 33
Step-by-step explanation:
Find the horizontal asymptote of the function
A. none
B. x = 0
c.y=0
D.y = 1
Reset Selection
(x-1)(x-3)²(x+1)²
(x-2)(x+2)(x-1)(x+3)*
Horizontal asymptote y = 1.
What is meant by horizontal asymptote?A slant asymptote has a specific instance known as a horizontal asymptote. A "recipe" for locating a rational function's horizontal asymptote is as follows: Let deg D(x) and deg N(x) represent the degree of the denominator and the numerator, respectively. No horizontal asymptote exists.1) If the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is y = 0. 2) The horizontal asymptote is y = c, where c is the ratio of the leading terms or their coefficients if the degree of the numerator and denominator are equal.The denominator of the function, n(x), can be used to find vertical asymptotes by solving the equation n(x) = 0 (note that this only works if the numerator, t(x), is not zero for the same x value). Find the function's asymptotes. The graph exhibits a vertical asymptote at x = 1.Find the horizontal asymptote of the function:
Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.
Horizontal asymptote y = 1.
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Can you please help me with this question
When you have negative exponents, you flip it around. Let me give you two examples below.
[tex]x^{-5} = \frac{1}{x^{5} }[/tex]
[tex]10^{-2} = \frac{1}{10^{2} }[/tex]
Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]
Your final answer is 1/25.
Brainliest would make my day :)
The price of a new car is £27000 In a sale, the price is reduced by 30% Brodie buys the car in the sale. He pays a £8000 deposit and pays the rest over 50 monthly payments. Find the cost of each monthly payment.
Answer:
£218
Step-by-step explanation:
price of the car = £27000
reduce 30% = 30/100 x 27000 = £8100
£27000 - £8100 = £18900
£18900 - £8000 = £10900
installment per month = £10900/50 = £218