The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?
Answer:
m+g[tex]\leq[/tex]40
12m + 14g[tex]\geq[/tex]250
Step-by-step explanation:
Jordan is paid $12 per hour for mowing lawns and $14 per hour for planting gardens.
Let m represents the number of hours mowing lawns and g represents the number of hours planting gardens.
He can work a maximum of 40 hours per week, and would like to earn at least $250 this week.
Then, the system of the inequality becomes
m+g[tex]\leq[/tex]40
12m + 14g[tex]\geq[/tex]250
-16x-32y=52 solve for y
Answer: I think 7/2?
Step-by-step explanation:
How do you convert log to the base e to log to the base 10?
To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)log10(2)=log(x)log(2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.
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210 students were asked whether they want to go to a water park or a roller skating rink for a class party.
I
• 50 students are girls who want to go to the water park.
• 45 students are girls who want to go skating.
60 students are boys who want to go to the water park.
Water park Skating Total
Boys
60
55
115
Girls
50
45
95
Total
110
100
210
Answer:
60.3
Step-by-step explanation:
hope this helps
Please answer all with explanation
Answer:
1:Exponents are not involved..try this 34% 1/2 + ==% 98) ::*37 21 /) ( ^ 11 56/77
2:make a little close parenthesis and make a little = and % x2 RX then multiply it 9 by 9
3:477/^54*(7632)**% 87÷32×(76*09×23) 2/8=97
4:9a/(92 28 ^^_× (32
Step-by-step explanation:
HOPE IT HELPS!!
Find and state the inverse of the function, and also state whether the inverse is a function.
((3,5), (2,8), (1.5), (0.3))
The inverse of the function is {(5, 3), (8, 2), (5, 1), (3, 0)} and it is not a function
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
((3,5), (2,8), (1.5), (0.3))
The above ordered pairs can be represented a
(x, y)
This means that the inverse function is
(y, x)
So, we have the following expression
(y, x) = {(5, 3), (8, 2), (5, 1), (3, 0)}
Also, the inverse is not a function
This is so because the x value 5 has different y values 3 and 1
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A square table 4 feet on each side has two drop leaves, each a semicircle 4 feet in diameter.
a. Find the area of the table with and without the drop leaves
b. Find the perimeter of the table with and without the drop leaves
Answer:
hurry
Step-by-step explanation:
Ron killed 8 times as many spiders as Harry,H (Write an expression to represent the following situations)
Answer:
Ron killed 8 times as many spiders as Harry: R = 8 * H
Step-by-step explanation:
This expression represents the situation in which Ron killed 8 times as many spiders as Harry.
F= 5 9 (K−273)+32space, F, equals, start fraction, 9, divided by, 5, end fraction, left parenthesis, K, minus, 273, right parenthesis, plus, 32 In order to convert a temperature in Kelvin, KKK, into a temperature in degrees Fahrenheit, FFF, the equation above can be used. Which of the following equations correctly expresses the temperature in Kelvin in terms of the temperature in degrees Fahrenheit?
The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
The given expression:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
Conversion from Kelvin (K) to degrees Fahrenheit (F)To find the formula for K
The formula for K is obtained by making K the subject of the formula as shown below:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
subtract 32 from LHS.
[tex]F-32 = \frac{9}{5} (K-273)[/tex]
multiply 5 with LHS
[tex]5(F-32) = 9(K-273)[/tex]
Take numerator 9 to LHS
[tex]\frac{5}{9}(F-32) = K-273[/tex]
take -273 from RHS to LHS
[tex]\frac{5}{9}(F-32) + 273 = K[/tex]
Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
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solve (x-3)^2=49. select the values of x
Answer:
x1=-4 x2=10
Step-by-step explanation:
step 1: x-3 = +/- 7 <--- take the square roots of both sides of the equation and use both positive and negative roots
step 2: x-3 = -7
x-3=7
step 3: x-3=-7--> x=-4
x-3=7--> x=10
step 4:x1=-4, x2=10 is the answer
hello i need urgent help with this assignment.
Answer:
AD = 1 3/4y + 5/8x - 3
Step-by-step explanation:
AD = 1/4x + 2y + 3 - 1/4y + 3/8x - 6
combine like terms:
AD = 1 3/4y + 5/8x - 3
HELP DUE IN 15 MINS!
Determine if the figure is a parallelogram. Justify your answer by picking the property that verifies it is a parallelogram or the one the property that it fails to meet the criteria for.
1. Is the figure a parallelogram? Yes or No??
2. Why?? A. Both sets of opposite sides are parallel, B . Both Diagonals Bisect Each Other, C. Both sets of opposite sides are congruent, D. Both Pairs of opposite angles are congruent, E . One set of Opposite Sides are parallel and congruent.
Answer:
Yes and E
Step-by-step explanation:
How do you graph 3 4 on a number line?
By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.
A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.
For drawing 3/4 on a number line, we will follow the following steps:
We will first draw a line and mark 0 and 1 on it.
In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.
As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.
Hence. by marking there we can locate 3/4 on the number line.
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The correct question should be like:
How do you plot 3/4 on number line
Find the volume and round to the nearest hundredths place when necessary.
Answer:
This is a prism since both sides are the same triangle,
Lets find the area of the triangle first then multiply it by the width which is 16.
20.5(base or height) x 13.3(height or base) = 272.65
272.65 divided by 2 ( x 1/2) = 136.325 is your area, now we multiply by the width.
136.325 x 16 = 2,181.2 mm3 is your volume.
Whenever coming across these types of volumes we must first find a shape and find its area then multiply it by the figure's height.
Formula area of a triangle:
B(base) x H(height) x 1/2(basically just dividing by 2)
What does Scrooge see out of the window when Marely leaves?
(A Christmas Carol) (it was an English question)
Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.
What is the ghost?Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.
Here, we have,
Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.
Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.
Therefore, option B is the correct option.
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Cual es mayor 0.08 o 0.2
Answer:
0.2
Step-by-step explanation:
Answer:
0.2 es mayor.
Step-by-step explanation:
0.2>0.08
What is ideal or real solution?
Answer:
An Ideal solution follows the Raoult's law strictly
A Real solution shows deviation from the Raoult's law.
Step-by-step explanation:
So we can say the the Volume of a Sphere is equal to 2 times the volume of a cone, or the Volume of a Sphere
Answer:
The Volume of a Sphere is equal to 2 times the volume of a cone.
Step-by-step explanation:
The volume of a sphere: 4/3 π r^3
The volume of a cone: 1/3 π r^2 h
r is the radius
h is the height
In this case, the height can be replaced by the 2r or the diameter, since it would correspond exactly to the height of the sphere of radius r.
So then,
sphere and cone
4/3 π r^3 1/3 π r^2 h
1/3 π r^2 * 2r
2/3 π r^3
Ratio sphere : cone
4/3: 2/3
2:1
Therefore the volume of the sphere is twice that of the cone or equal to twice the volume of the cone
hamza decides to increase the prices of all his item in his shop by 10 percent
workout the price of an item normally priced at 210 pounds
workout the new price of an item normally priced at 48 pounds
Answer:
231 and 52.8
Step-by-step explanation:
Given that
Hamza decided the price of the item would be increased by 10 percent
We need to find out the price that normally at 210 pounds and the price that normally at 48 pounds
So,
The price that normally at 210 pounds is
= 210 + 210 × 10%
= 210 + 21
= 231
And, the price that normally at 48
= 48 + 48 × 10%
= 48 + 4.8
= 52.8
Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5
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[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]
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[tex] \underline{ \large \rm Solution} : [/tex]
[tex]\rm Given : [/tex]
Two equations are -
y - x = -1 (i)x + y = -5 (ii)[tex] \rm Procedure : [/tex]
Considering the equations as (i) and (ii) respectively
From equation (i) -
y = x - 1put this value of y in equation (ii) -
x + y = -5x + x - 1 = -52x = -5 + 12x = -4 x = -2Next thing to do would be to put value of x we got in equation (i) to get y
y - x = -1y - (-2) = -1 y + 3 = -1 y = -1 - 3 y = -4Values asked are :
[tex] \rightarrow \rm y = - 4[/tex]
[tex] \rightarrow \rm x= - 2[/tex]
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[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]
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8/9 to what power equals 64/81
2nd
Step-by-step explanation:
8/9 to the second power equals to 64/81. Hope this helps!
Answer:
Hi
x = exponent
64 = 8·8 = 8^2
81 = 9·9 = 9^2
64/81 = 8^2/9^2 = (8/9)^2
(8/9)^2 = (8/9)^x
x = 2
Step-by-step explanation:
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a diagram shows a cube cut in half along one of its diagonal planes
each edge of the original cube has a length xcm
the diagonal y has a length 20cm
The length is 11.5 cm.
What is Pythagoras theorem?The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
Given: diagonal = 20 cm
In ABC,
AC² = BC² + AB²
AC²= x² + x²
AC²= 2x²
AC= √2 x
IN ACF,
AF² = AC² +CF²
20²= 2x² + x²
400= 3x²
400/3= x²
x= 11.5
hence, length is 11.5 cm.
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The cost of Katie’s meal at a restaurant is $15.00. She is charged 7.0% tax and leaves a tip of x dollars. Katie spent a total of $20.05 on the meal, tax, and tip.
Answer:
$5.05
Step-by-step explanation:
What are the three types of dilation?
Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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The circumference is 79.5
Need help with finding the diameter and radius
Answer:
Step-by-step explanation:
[tex]C=\pi D[/tex]
[tex]79.5=\pi D\\[/tex]
divide by [tex]\pi[/tex]
D = 25.30
radius = [tex]\frac{d}{2}[/tex]
[tex]\frac{25.30}{2} =12.65[/tex]
Answer:
r approx 12.7
d approx 25
Step-by-step explanation:
Find the Highest Common Factor (HCF) of 36 and 48
Answer: 12
Step-by-step explanation:
The mode of the raw data given as: 4, 7, 4, 3, 2, 7, 7, 6, 4, 7, 8
Answer:
7, since it is the number that pops up the most in the set of data given here
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
simplify the expression below. (-5 × -4)÷(-3+5)
Answer:
-10
Step-by-step explanation:
Answer: =10
Step-by-step explanation: Hope this help :D
(-5)(-4)/-3+5
=20/-3+5
=20/2
=10
What is the Average Rate of Change of the graph below from -5 < t < 8
Answer:47
Step-by-step explanation
Need help ASAP! Due very soon please help
Answer:
Lemme get you numba first
Answer:
y = -3/4x + 36
Step-by-step explanation:
You move down three spaces and over 4 spaces on the graph
36 is the y intercept of the line