Answers
Since segment AD bisects angle BAC, the value of x is equal to 14.6.
What is an angle bisector?In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.
By applying the angle bisector theorem to this triangle (ΔABC), we have:
AB/BD = AC/DC
19/x = 17/(20 - x)
17x = 19(20 - x)
17x = 380 - 19x
19x + 17x = 380
26x = 380
x = 380/26
x = 14.6.
In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.
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Related Questions
The points represented by the table lie on a line . Find the slope of the line x-1,1,3,5. Y 10, 5, 0,-5 m=
Answers
Answer: The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
We can choose any two points from the table to find the slope. Let's use the points (1, 10) and (5, -5):
m = (-5 - 10) / (5 - 1) = -15 / 4 = -3.75
So, the slope of the line represented by the table (x = 1, 3, 5, y = 10, 5, 0, -5) is -3.75.
Step-by-step explanation:
Where can the bisectors of the angles of an obtuse triangle intersect?
Answers
Answer: Hello! I'm JK!.....
B. I Only. (inside the triangle)
Step-by-step explanation:
I really hope this helps you. XoXoGoldenMaknae <3
Kaj observes a marble travel along a horizontal path at a constant rate. The marble travels 1/20 of the length of the path in 2 1/2 seconds. At that rate, how many seconds does it take the object to travel the full length?
Answers
It takes 50 seconds to travel the full length at the constant rate R.
How many seconds does it take the object to travel the full length?Remember the relation between speed, distance and time:
distance = speed*time
Here we know that at a rate R (or speed S, these are equivalent) it moves (1/20) of the total distance D in (2 + 1/2) seconds, then we can write:
R*(2 + 1/2) = (1/20)*D
Now we only need to isolate D on the right side, to do so we need to multiply both sides by 20.
20*R*(2 + 1/2) = D
The time is:
20*(2 + 1/2) seconds
40 + 10 seconds
50 seconds
It takes 50 seconds to travel the full length,
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What is the cost and area of the mat
Answers
1. The area of the mat is 1 in² and the cost is $0.05
2. The area of the mat is 4 in² and the cost is $0.2
What is area ?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
The area of a square = l²
1. the area = 1×1 = 1 in²
since $0.05 is the cost per in²
therefore the cost of the mat is $0.05
2. the area = 2× 2 = 4 in²
therefore the cost = 4 × 0.05
= $0.2
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if u and v are in r n , how are u t v and v t u related? how are uv t and vu t related?
Answers
They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.
If u and v are vectors in R^n, then:
u^T v and v^T u are related as transposes of each other. Specifically, if
u = [u_1, u_2, ..., u_n]^T
and v = [v_1, v_2, ..., v_n]^T
then:
u^T v = v^T u
= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n
So, u^T v and v^T u are scalar values that represent the dot product of u and v.
uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T
then:
uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;
u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;
...;
u_n * v_1, u_n * v_2, ..., u_n * v_n]
vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;
v_1 * u_2, v_2 * u_2, ..., v_n * u_2;
...;
v_1 * u_n, v_2 * u_n, ..., v_n * u_n]
So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.
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Given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of z), the absolute value of y, and the square root of (xy to the power of z). Ex: if the input is: 3. 6 4. 5 2. 0 the output is: 12. 96 1. 841304610218211e11 4. 5 16. 2.
Answers
The absolute value of y, and the square root of (xy to the power of z) is [tex]xy^{z}[/tex]
Floats are a type of number representation that allows us to store very large or very small numbers with a high degree of precision. In computer programming, it is often used to represent real numbers, such as decimals.
In this problem, we are given three float numbers x, y, and z and asked to perform various mathematical operations with them.
Let's start with the first operation: x to the power of z. This means that we want to find x raised to the power of z. This can be written mathematically as xᵃ.
The next operation is x to the power of (y to the power of z). This means that we want to find x raised to the power of y raised to the power of z. This can be written mathematically as x(yᵃ).
The third operation is the absolute value of y. The absolute value of a number is its magnitude, or distance from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. Mathematically, it can be written as |y|.
Finally, we have to find the square root of (xy to the power of a). The square root of a number is the value that, when multiplied by itself, gives the original number.
The square root of 25 is 5 because 5 * 5 = 25. This can be written mathematically as
=> √(xyᵃ).
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For what interval is f(x)=2x+10 positive?
Answers
Answer:
[tex]x>-5[/tex]
Step-by-step explanation:
[tex]2x+10>0 \implies 2x>-10 \implies x>-5[/tex]
There's a 30% chance of it raining each day in Narnia. On how many days would you expect it to rain during your visit there that lasts 110 days?
Answers
Answer:
Step-by-step explanation:
Since there is a 30% chance of rain on any given day, there is a 70% chance that it will not rain on a given day.
To calculate the expected number of days it will rain during your visit, we can use the formula:
Expected number of rainy days = total number of days * probability of rain
Expected number of rainy days = 110 days * 0.3 = 33 days
Therefore, we can expect it to rain on approximately 33 days during a 110-day visit to Narnia.
I need to find the table for a parabola and the equation is
y=-2x^2+8x
Answers
The table for the parabola is
x y
-2 24
0 0
2 8
4 0
6 -24
How to create the table for the parabolaTo create a table for a parabola with equation y = -2x^2 + 8x, we can simply plug in values of x and solve for y.
with x-values from -2 to 6,:
For x = -2, y = -2(-2)^2 + 8(-2) = -24
For x = 0, y = -2(0)^2 + 8(0) = 0
For x = 2, y = -2(2)^2 + 8(2) = 8
For x = 4, y = -2(4)^2 + 8(4) = 0
For x = 6, y = -2(6)^2 + 8(6) = -24
To plot the parabola on a graph, we can plot the points from the table and draw a smooth curve through them. The graph of y = -2x^2 + 8x looks like a downward-facing parabola with its vertex at the point (2, 8).
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True or False? All of these figures are similar
Answers
Answer:
True
Step-by-step explanation:
They Are all Equal and The Same By the Degrees and Angles and Numbers
What is the y=mx+b formula for these points: (67,67), (65,65), (63,63), (69,69), (57,57), (65,65), (68,66), (48,48), (72,72)?
Answers
The y = mx + b formula for these points is y = 2x - 67.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (67, 65).Points on y-axis = (67, 65).At point (67, 67), a linear equation of this line can be calculated in slope-intercept form (y = mx + b) as follows:
y - 67 = (65 - 67)/(65 - 67)(x - 67)
y - 67 = 2(x - 67)
y = 2x - 134 + 67
y = 2x - 67
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WORTH 100 POINTS!!!
OPEN RESPONSE A city parking garage charges $4 to park for up to two hours. After that, an additional charge of $2.50 per hour applies. Write an equation in point-slope form that models the total cost y for parking x hours, where x > 2
Answers
Answer: y = 4 + 2.50(x > 2)
Step-by-step explanation: y is the outcome, the fixed cost is 4, and the variable cost is 2.50 × (x > 2).
This table shows a linear function.
x y
-1 7
0 5
1 3
2 1
3 -1
Based on the information given, how can you verify that the function is linear? Select all that apply. choices shown in image
Answers
Step-by-step explanation:
the 3rd, 5th and 6th answers are correct.
Answer:
3, 5, 6
Step-by-step explanation:
For every change in x of 1, there is a change in y of -2.
For an equation to be linear, equal changes in x must produce equal changes in y.
Since that is true here, it is a linear equation.
Point (0, 5) gives you the y-intercept, b = 5.
From (0, 5) to (1, 3), you can calculate the slope:
slope = m = (3 - 5)/(1 - 0) = -2
The equation is y = -2x + 5
The true statements are: 3, 5, 6
Andrea backyard is 400 square feet.her rectangular swimming pool is 10 feet long and 6 feet wide what is the area Andrea's backyard not including the swimming
pool
Answers
The area of Andrea’s backyard, not including the swimming pool, is 340 feet²
What is area of Rectangle?The Area of rectangle is the product of its length to its width.
i.e., Area of rectangle = length x width.
Given:
A rectangular swimming pool has 10 feet long and 6 feet wide.
The area of a rectangle is:
A= L x W
A = 10 x 6
A = 60 ft²
Now, the area of the Andrea’s backyard (A2) is 400 ft²,
So, area of backyard not including the swimming pool
Area = Area of backyard - area of pool
A =400 ft²-60 ft²
A =340 ft²
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What is the sum of the 10th square number
and the 9th square number?
Answers
The sum of the 10th square number and the 9th square number is, 181
What is the squaring of numbers ?A number is multiplied by itself when it is squared. For instance, when you square the number 3, you get the result 9 (3 x 3). Superscript "2" is the symbol for squaring a number. For instance, 32 = 9 can be used to represent the square of 3.
Numerous crucial mathematical properties and applications of squaring a number can be found in number theory, algebra, and geometry. Squaring, for instance, can be used to solve quadratic equations or to determine the area of a square, the distance between two points, or both. A number's ability to form a perfect square can also be determined by squaring it.
The 10th square number is 10² = 100
and the 9th square number is 9² = 81.
So, the sum of the 10th square number and the 9th square number is:
= 100 + 81
= 181
Therefore, the sum of the 10th square number and the 9th square number is 181.
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The scores from a 20 point algebra quiz are shown.
7, 9, 10, 12, 13, 15, 17, 18, 19, 20
The percentile of a test score can be defined as the percent of test scores less than or equal to that test score
Use this definition to find the percentile of the test score 12
The test score 12 is at the ___th percentile
Answers
The test score of 12 is at the 40th percentile.
What is a percentile?
A Percentile divides a data set into the 100 equal parts. A percentile is a measurement that tells us what percent of the total frequency of a data set was at or below that measure.
From the question,
The test score of 12 is less than or equal to 7, 9, 10, 12, so 4 out of the 10 scores are less than or equal to 12.
So, the percentile of the test score 12 can be calculated as:
Percentile = (number of scores less than or equal to 12) / (total number of scores) x 100
percentile = (4) / (10) x 100
percentile = 40
Hence, the test score of 12 is at the 40th percentile.
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A boat leaves the dock and travels 10 miles due south, then 24 miles due west. How far is the boat from the dock? Boat 24 mi OA. 676 mi OB. 14 mi OC. 34 mi O D. 26 mi Dock 10 mi
Answers
The distance from the boat to the dock will be 26 miles. Then the correct option is D.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A boat leaves the dock and travels 10 miles due south, then 24 miles due west.
Then the distance from the boat to the dock is given as,
d² = 10² + 24²
d² = 100 + 576
d² = 676
d = 26 miles
The distance from the boat to the dock will be 26 miles. Then the correct option is D.
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What are the basic means of differentiation?
Answers
In mathematics, differentiation refers to the process of finding the derivative of a function. The basic means of differentiation include:
Limit definition: The derivative of a function is defined as the limit of the difference quotient as the interval over which the quotient is taken approaches zero.
Power rule: The derivative of a function of the form f(x) = xⁿ is given by f'(x) = nx⁽ⁿ⁻¹⁾
Product rule: The derivative of a product of two functions u(x) and v(x) is given by (u × v)'(x) = u'(x) × v(x) + u(x) × v'(x).
Quotient rule: The derivative of a quotient of two functions u(x) and v(x) is given by (u/v)'(x) = [u'(x) × v(x) - u(x) × v'(x)] / v(x)².
Chain rule: The derivative of a composition of functions f(g(x)) is given by f'(g(x)) × g'(x).
These basic means of differentiation are essential tools for analyzing and modeling functions in calculus and related fields.
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An employee put $7,000.00 in a retirement account that offers 5% interest compounded annually. The employee makes no additional
deposits or withdrawals. Which amount is closest to the interest the employees will have earned at the end of 4 years?
A
x B $7,350.00
1x C
$1,400.00
D
$1,508 54
$8,508.54
Answers
Answer:
$1508.54
Step-by-step explanation:
A = p(1 + [tex]\frac{r}{n}[/tex])^nt
A = 7000(1+ .05)^4
A = 7000(1.05)^4
A = 8508.54 This is the total amount (principle and interest
Subtract out the principle
8508.54 - 7000 = 1508.54
35 cm
What is the volume of the solid shown above?
1 cm
3 cm
Answers
The volume of the solid shown can be found to be 105 cm ³ .
How to find the volume ?The volume of the solid can be found by the formula :
= Length x Width x Height
This is because this is a rectangular prism and their volumes require multiplying the sides of the rectangle in the above manner .
The volume of the solid is therefore:
= 35 x 1 x 3
= 35 x 3
= 105 cm ³
In conclusion, the volume of the solid would be 105 cm ³ .
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What is equation of a semicircle?
Answers
The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
What is the equation of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The equation of the semicircle upper side of the x-axis will be given as,
(x - h)² + (y - k)² = r²
x - h = √[r² - (y - k)²]
x = √[r² - (y - k)²] + h
The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
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A store bought shirts for $5.75 each. If they want
to make 65% profit on selling them what should
the selling price be?
Answers
The selling price of a shirt should be $8.97.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Given that, a store bought shirts for $5.75 each and profit percent = 65%.
We know that, Selling price = (100+Profit%)/100 ×CP
Here, Selling price =(100+65)/100 ×5.75
= 1.56×5.75
= $8.97
Therefore, the selling price of a shirt should be $8.97.
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what is the definition of opposite rays in geometry
Answers
Answer:
Opposite rays point in opposite directions and therefore make a 180-degree angle with each other.
Step-by-step explanation:
what is the image of (7,3)?
use the translation: T<3,-5>
HELP ASAP
Answers
The image of (7, 3) after a translation of T(3, - 5) would be at (10, - 2).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A point has a coordinate of (7, 3).
We know, Translation shifts coordinate into the x-y coordinate.
Therefore, The image of (7, 3) after a translation of (3, - 5) would be,
(7 + 3, 3 - 5) which is now at (10, - 2).
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What is the area of a square with side lengths of 3/5
Answers
Answer: 0.36
Step-by-step explanation:
A=L*W
Since all sides of a square is the same you just do 3/5(3/5) which is 0.36 or 9/25
Can someone help me out with this? I haven't had any time to catch up on math work lately... It would be greatly appreciated.
Answers
Answer:8
Step-by-step explanation:
-8a+32b in distributive property
Answers
-8a + 32b using the distributive property as 8(-a + 4b).
What is Expression?An expression is combination of variables, numbers and operators.
To express -8a + 32b using the distributive property, we need to factor out the greatest common factor that the terms share.
The greatest common factor of -8a and 32b is 8.
-8a + 32b
= 8(-a + 4b)
Using the distributive property, we can check that this expression is equivalent to the original:
8(-a + 4b) = 8(-a) + 8(4b) = -8a + 32b
Therefore, we can express -8a + 32b using the distributive property as 8(-a + 4b).
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6. Find the area and perimeter of the following figure.
3 5/6
4 4/3
3
Answers
The area is 5.627 square units and the perimeter is 12.167 units of the given figure.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
perimeter of the given figure = 3 5/6 + 4 4/3 + 3
perimeter of the given figure = 12 1/6 = 73/6 = 12.167 units
Area of triangle = √[s(s – a)(s – b)(s – c)],
where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of the three sides of the triangle.
According to the given question, we have
a = 3 5/6
b = 4 4/3
c = 3
s = (3 5/6 + 4 4/3 + 3)/2 = 12.167/2 = 6.083
Substitute the values in the area formula, and we get
Area of triangle = √[6.083(6.083 – 3 5/6)(6.083 – 4 4/3)(6.083 – 3)]
Area of triangle = 5.627 square units
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The question seems incomplete, the missing figure has been attached below.
1) There are three consecutive positive integers, such that the largest
is 44 less than twice the smallest. What is the value of the smallest
of these three consecutive integers?
Answers
The three consecutive integers are 46, 47, 48.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
Let the three consecutive integers be represented as x,x+1,x+2
As per the requirement, largest integer is 44 less than twice the smallest.
=> x+ 2 = 2x -44
=> 2x -x = 2+44
=> x= 46
So the three integers are 46, 47, 48
Verification:
Largest integer = 48
Smallest integer = 46
2 * smallest integer - 44
= 2* 46 - 44
= 48
Largest integer is also 48.
So the required condition in the question is satisfied by these three integers.
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What is 4x + 11 < -21 on a number line
Answers
Answer: x <- -8
x is less than negative eight.
Step-by-step explanation:
First, subtract 11 from both sides. Then divide both sides by 11. The arrow should be open and pointing to the left.
Answer:
x <- -8
Step-by-step explanation: