If the angles 51 degrees, 88 degrees, and 41 degrees formed a tirangle what type of angle would it be
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD
Value of x for the similar triangles ΔABD ~ ΔCAD is equals to [tex]\frac{25}{4}[/tex].
What are similar triangles?" Similar triangles are defined as the triangles with same shape but different in their size, corresponding sides of similar triangles are always in proportion."
According to the question,
As per the diagram,
ΔABD and ΔCAD are similar triangles.
AB = 10 units
BD = x units
BC = 16 units
CD = BC - BD
= 16 - x
ΔABD is a right angle triangle.
Therefore,
Using Pythagoras theorem,
[tex]AD ^{2} = 10^{2} -x^{2}[/tex]
ΔABD corresponding ΔCAD as per the given diagram.
From the definition of similar triangles corresponding sides are in proportion.
[tex]\frac{AD}{CD} =\frac{BD}{AD}[/tex]
⇒[tex]AD^{2} =(BD )(CD)[/tex]
Substitute the value of AD, BD and CD we get,
[tex]10^{2} -x^{2} = (x) (16-x)[/tex]
⇒[tex]100 -x^{2} =16x-x^{2}[/tex]
⇒[tex]100 = 16x[/tex]
⇒[tex]x= \frac{100}{16}[/tex]
⇒[tex]x=\frac{25}{4}[/tex]
Hence, Option(F) is the correct answer.
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23 + 3 + 5 - 2 + 5 + 3 - 1 + 1 + 33 = ?
22 + 22 + 22 + 4 + 5 + 4 - 2 = ?
Given sin x = 0.9 , what is cos x ? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex]cos(x)=(+/-)0.44[/tex]
Step-by-step explanation:
we know that
[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]
In this problem we have
[tex]sin(x)=0.9[/tex]
substitute and solve for cos(x)
[tex]0.9^{2}+cos^{2}(x)=1[/tex]
[tex]cos^{2}(x)=1-0.9^{2}[/tex]
[tex]cos^{2}(x)=0.19[/tex]
[tex]cos(x)=(+/-)0.44[/tex]
Final answer:
The value of cos x is approximately ±0.44.
Explanation:
Given that sin x = 0.9, we need to find cos x. We can use the Pythagorean identity, which states that sin2(x) + cos2(x) = 1. Since we are given sin(x), we can rearrange the identity to solve for cos(x) as follows:
sin2(x) + cos2(x) = 1
cos2(x) = 1 - sin2(x)
cos2(x) = 1 - (0.9)2
cos2(x) = 1 - 0.81
cos2(x) = 0.19
Now, take the square root of both sides to find cos(x). Since the square root has both a positive and a negative value, and we do not have information about the angle's quadrant, we consider both possibilities.
cos(x) = ±0.43589
We can round the cosine value to the nearest hundredth. However, without knowing the quadrant, we cannot definitively determine the sign of cos(x). Assuming the angle is in the first quadrant where both sine and cosine are positive, cos(x) = +0.44.
Which high school math course, algebra or geometry, is more closely related to engineering? justify your answer?
Final answer:
Both algebra and geometry are integral to engineering, with algebra being more directly related to the numerical problem-solving aspects, and geometry being crucial for spatial understanding and design. A well-rounded engineering education incorporates both, to prepare students for advanced mathematical concepts and engineering science courses.
Explanation:
Both algebra and geometry are closely related to engineering, but they serve different purposes within the field. Algebra is fundamental for problem-solving and numerical analysis in engineering. It allows for the creation of mathematical models that can describe physical processes, and is often used alongside computer programs to solve complex real-life problems. Geometry, on the other hand, is essential for a thorough understanding of spatial relationships and structures, which are critical in fields such as mechanical, civil, and architectural engineering.
A trinket factory can produce 3,000 trinkets per day. The warehouse has a capacity of 50,000 trinkets. Currently, there are 8,000 trinkets in the warehouse. Assume that no trinkets are going to be shipped out of the warehouse for a while. 1) Write an equation for the number of trinkets in the warehouse after days. 2) How many days will it take to fill the warehouse?
The equation for number of trinkets after x days is 8,000 + 3000 * x = y and the number of days required to fill the warehouse is 14.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
The trinket factory can produce 3,000 trinkets per day
Total Capacity of warehouse is 50,000 trinkets
The trinkets in the warehouse is 8,000
The equation for the number of trinkets in the warehouse after x days is
Let y represents the total number of trinkets after x days
8,000 + 3000 * x = y
The days required to completely fill the warehouse is
8,000 + 3,000 * x = 50,000
3,000* x = 42,000
x = 14
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I need both answers now!
PLEASE HELP!!!!!!!!!!!!!!!!!
IS IT CORRECT?
BRAINLIEST AVAILABLE IF 2 PPL ANSWER
find the second, fourth, and eleventh terms of the sequence described by each explicit formula A(n)=2+(n-1)(-2.5)
Parallel lines Q and M are cut by transversal lines j and k.
1) What is the measure in degrees of ∠ 1?
2) What is the measure in degrees of ∠ 2?
3) What is the measure in degrees of ∠ 3?
4) What is the measure in degrees of ∠ 4?
5) What is the measure in degrees of ∠ 6?
Explain how you found∠" 6?".
A key difference between calculating the sample mean and the population mean is that:
a.we use and n instead of µ and n.
b.we divide the sum of the observations by n - 1 instead of n.
c.the sample observations are ranked and the middle value is selected as the population mean.
d.there are no differences.
Final answer:
The key difference between calculating the sample mean and the population mean is that when calculating the sample mean, we use x and n instead of µ and n. Additionally, we divide the sum of the observations by n - 1 instead of n. Correct Option -B
Explanation:
The key difference between calculating the sample mean and the population mean is that when calculating the sample mean, we use x and n instead of µ and n. Additionally, we divide the sum of the observations by n - 1 instead of n.
The reason for dividing by n - 1 in the sample mean calculation is that it provides a better estimate of the population variance. Dividing by n - 1 instead of n accounts for the fact that the sample mean is an estimate of the population mean based on a limited set of data.
MEDAAAL :D
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. How much money will be in the account after 4 years?,
A dealer dealt the following cards from a shuffled deck:
3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6
4 , 5 , K , 2 , 7 , 6 , A , J , J , A
What was the experimental probability of dealing a black card?
can someone help will give medal 8 cards are black and12 are red pleaaaasseee help do i divide 20 by 8 or 8 by 20,
Well we know that there are 20 cards as given by the equation. And there are 8 black cards.
8/20= .40 or 40% the answer for me is C. 40%
Answer: c is the answer is 40 hope u get it right goodluck
Step-by-step explanation:
Given 4c + 5 ≠ 0 and c is a real number, What is the multiplicative inverse of
4c + 5?
A. 0
B. 1
C. 1/
4c+5
D. 1/
4c +5
Answer:1/4c+5
Step-by-step explanation:
10) The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8 hour period. Worker B earns the same hourly rate as Worker A, but works for only 6 hours. What does Worker B earn?
A) $1008
B) $126
C) $1344
D) $160
$126 is correct. The hourly rate is $168/8 = $21, so the amount earned is (6)($21) = $126.
Time 6 years Interest rate 1.9% Principal- $850 What amount of simple interest will be earned? $16.15 O $96.90 $946.90 $9,690.00
A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the surface of the pool is equal to the area of the patio. what is the width of the patio?
The width of the patio is 4 feet.
Let's denote the width of the patio as "x" feet.
The length of the pool is given as 24 feet, and the width of the pool is given as 16 feet.
The area of the pool is the length multiplied by the width:
Area of the pool = Length * Width
Area of the pool = 24 ft * 16 ft
Area of the pool = 384 square feet
The area of the patio is also given to be equal to the area of the pool, so:
Area of the patio = 384 square feet
Now, the total dimensions of the pool and the patio together (including the patio's width on all sides) will be:
Total length = Length of the pool + 2 * Width of the patio
Total length = 24 ft + 2x
Total width = Width of the pool + 2 * Width of the patio
Total width = 16 ft + 2x
The area of the patio can also be expressed as the product of the total length and total width:
Area of the patio = Total length * Total width
Substitute the expressions for total length and total width:
384 square feet = (24 ft + 2x) * (16 ft + 2x)
Now, solve for "x" by expanding and rearranging the equation:
384 = 24 * 16 + 24 * 2x + 16 * 2x + 2x * 2x
384 = 384 + 48x + 32x + 4x²
Rearrange to get the equation in standard quadratic form:
4x² + 80x - 384 = 0
Now, we can solve this quadratic equation for "x" using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 4, b = 80, and c = -384.
x = (-(80) ± √(80² - 4 * 4 * (-384))) / 2 * 4
x = (-80 ± √(6400 + 6144)) / 8
x = (-80 ± √(12544)) / 8
x = (-80 ± 112) / 8
Now, we get two possible values for "x":
x = (-80 + 112) / 8
x = 32 / 8
x = 4
or, we have,
x = (-80 - 112) / 8
x = -192 / 8
x = -24
Since the width cannot be negative, we discard the negative value:
The width of the patio is 4 feet.
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complete question:
attached
The width of the patio is equal to half the sum of the length and width of the pool, given by (L + W) / 2.
Let's assume the rectangular swimming pool has length L and width W. The concrete patio surrounds the pool on all sides, and its width is denoted by P.
The area of the surface of the pool is given by the product of its length and width: A_pool = L * W.
Since the area of the pool surface is equal to the area of the patio, we have:
A_pool = A_patio
L * W = (L + 2P) * (W + 2P)
Expanding the right side of the equation:
L * W = L * W + 2PL + 2PW + 4P^2
Canceling out the L * W terms:
0 = 2PL + 2PW + 4P^2
Rearranging the equation:
2PL + 2PW + 4P^2 = 0
Dividing the entire equation by 2:
PL + PW + 2P^2 = 0
Factoring out the common factor of P:
P(L + W + 2P) = 0
Since the width of the patio cannot be zero, we can conclude that:
L + W + 2P = 0
Simplifying further:
2P = - (L + W)
P = - (L + W) / 2
Since the width of the patio cannot be negative, we disregard the negative sign:
P = (L + W) / 2
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Find the length of a line segment with endpoints of -9 and 7.
I don't understand how to do this.
A.-16
B.-2
C.16
D.26,
a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building
The slope of the line whose equation is x+2y=3 is
If f(x)= 1/3x and g(x)=3x, then what are g * f (x) and g*f(1/2)
1. 1/x, 2
2. 1/x, 1/2
3. x, 1/2
4. 1/9x, 1/18
WILL GIVE BRAINLIEST ! 12 POINTS !
Estimate the solution to the following system of equations by graphing.
-4x + 5y = 8
6x - y = 11
Options:
* ( 1 over 2 , 3 over 2 )
* ( - 4 over 3 , 8 over 3 )
* ( - 5 over 2 , - 7 over 2 )
* ( 5 over 2 , 7 over 2 )
USE DESMOS.COM AND CLICK START GRAPHING, IF YOU NEED A GRAPH !
Jill had an AGI of $25,000. She had $2800 in medical expenses, paid $6000 in rent, and had to buy a new uniform for work, which was not reimbursed by her employer. Which expense(s) can she itemize on her tax return?
A.Nonreimbursed work expenses, mortgage interest, and medical expenses
B.Mortgage interest and medical expenses
C.Medical expenses and nonreimbursed work expenses.
D.Mortgage interest only
Answer:
C.Medical expenses and nonreimbursed work expenses.
Step-by-step explanation:
just did it on apex
Answer:
C
Step-by-step explanation:
Medical expenses and nonreimbursed work expenses.
Some of the steps for completing the square to solve
x2 + 5x = 2 are shown.
x2 + 5x = 2
x2 + 5x + = 2 +
The value of y varies directly with x, and y = 12 when x = 16.
Find y when x = 6.
A. 8
B.12
C.2/9
D.9/2
Final answer:
Given that the value of y varies directly with x, and y = 12 when x = 16, we find that y when x = 6 is 9/2, corresponding to option D.
Explanation:
The question asks to find the value of y when x = 6, given that the value of y varies directly with x, and y = 12 when x = 16. This is a problem of direct variation, where the relationship between the variables can be represented by the equation y = kx, where k is the constant of variation.
To find k, we use the given values: y = 12 when x = 16. Substituting these into the equation gives 12 = k(16), leading to k = 12/16 or k = 3/4. Then, to find y when x = 6, we substitute x = 6 into the direct variation equation with our found k value: y = (3/4)(6), simplifying to y = 9/2.
Therefore, the value of y when x = 6 is 9/2, which matches option D.
To solve a problem, we often _________ the given information into algebraic expressions and equations.
Example: The phrase "4 more than twice a number" becomes '2n + 4'.,
Answer:
Translate or transform
Step-by-step explanation:
Took the test (USA test prep)
MATH!! please help me!!
Find the measure of angle x in the figure below
A.35°
B.47°
C.51°
D.62°
Find the derivative of f(x) = |x2 – 1| at the point (1, 0).
How many pairs of parallel line segments are shown?
1. 8
2. 24
3. 4
4. 18
Answer:
4. 18
Explanation:
Gradpoint