Make selections to complete the proof.
Given: ∠WXZ≅∠YXZ, ∠XZW≅∠XZY, WX⎯⎯⎯⎯⎯⎯≅YX⎯⎯⎯⎯⎯, WZ⎯⎯⎯⎯⎯⎯≅YZ⎯⎯⎯⎯⎯
Prove: ∆WXZ≅∆YXZ
The required angles are,
∠BAC = 73 degree
∠BCA = 17 degree
∠DCF = 17 degree
∠CDF = 80 degree
∠CFD = 95 degree
Since we can see that,
In triangle ABC
The angle B is right angled
Since we know that,
Sum of interior angles of triangle = 180 degree
Therefore, in triangle ABC
⇒ (9x -8 ) + (2x-1) + 90 = 180
⇒ 11x = 99
⇒ x = 9
Thus,
Angle BAC = 9x - 8
= 9x9 - 8
= 73 degree
Angle BCA = 2x - 1
= 2x9 - 1
= 17 degree
Now in triangle, CDF,
Angle C is alternate angle for both the triangles,
Therefore,
Interior angle C of triangle CDF = angle DCF = 17 degree
Angle CDF = 9y - 1
= 9x9 - 1
= 80 degree
Angle CFD = 11y + 4
= 11x9 - 4
= 95 degree
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
The equation of line, L is given by r=3i+3j-k+t 2i-j+3k Find an Cartesian equation for the plane pi which contains L and the origin.
The equation of the plane pi is: -6x-7y-9z=0.
To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.
Let us now take t=0, and find the point on the line L:
r = 3i + 3j - k + 0(2i - j + 3k)
= 3i + 3j - k
So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.
Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:
n = (2i - j + 3k) * (3i + 3j - k)
= -6i - 7j - 9k
Therefore, the equation of the plane pi is: -6x-7y-9z=0.
Learn more about Cross-product at:
https://brainly.com/question/30284978
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The coordinates of vertex D in the parallelogram are (-7, -10).
We have,
To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.
One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.
Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:
Find the vector representing one of the sides of the parallelogram.
We can use the vector AB.
Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)
= (6 - 8, -4 - 2)
= (-2, -6)
Add this vector to point C to find the coordinates of D.
Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)
= (-5 - 2, -4 - 6)
= (-7, -10)
Therefore,
The coordinates of vertex D are (-7, -10).
Learn more about parallelograms here:
https://brainly.com/question/1563728
#SPJ1
Write the equation of the ellipse graphed below.
Answer:
(x +4)²/25 +(y -3)²/16 = 1
Step-by-step explanation:
You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.
Ellipse equationThe standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...
(x -h)²/a² +(y -k)²/b² = 1
Using the given values, we find the equation to be ...
(x +4)²/25 +(y -3)²/16 = 1
__
Additional comment
The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.
Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.
<95141404393>
Which statement accurately describes the relationship between JKL and MNP?
The triangles are not similar
Given data ,
Let the first triangle be ΔJKL
Let the second triangle be ΔMNP
Now , the corresponding sides are
JK / JL ≠ NM / MP
where the corresponding sides of similar triangles are not in the same ratio
And , the common angle to both the triangles is ∠J = ∠M
So , ∠J = ∠M and JK / JL ≠ NM / MP
Hence , the triangles are not similar
To learn more about similar triangles click :
https://brainly.com/question/29378183
#SPJ1
I have been doing this for 4 hours and still can’t figure these out
The equation of the line is y = x/7 - 1/7
What is equation of a line?The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of a line can be expressed as;
y-y1 = m(x -x1)
where m is the slope
The slope = 1/7
x1 = 8 and y1 = 1
Therefore;
y -1 = 1/7( x -8)
7(y-1) = x-8
7y -7 = x-8
collecting like terms
7y = x - 8+7
7y = x -1
y = x/7 -1/7
The intercept is -1/7 and the slope is 1/7
learn more about equation of a line from
https://brainly.com/question/18831322
#SPJ1
What is the slope of this line?
A line passing through the points (negative 4, negative 3) & (0, 1).
© 2017 StrongMind. Created using GeoGebra.
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]
2. Convert the following into a single log statement from the many log statements to 1.
2 Log w+ log 7-3 log x-8 log y
NOTE: You must show this in at least two steps.
1st line should be to convert the 2 the 3 and the 8 only.
2nd line can be the final answer.
A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]
The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.
Use the logarithmic identity:
log[tex](a^n)[/tex] = n*log(a)
to convert the coefficients 2, 3, and 8:
log w + log 7 - 3log x - 8log y
= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]
Combine the terms on the right-hand side using the logarithmic identity:
log(a) + log(b) = log(ab)
log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]
= log([tex]7wy^{-8}/x^3[/tex])
Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]
For such more questions on log statements
https://brainly.com/question/31946400
#SPJ11
Find the area of a triangle whose base (b) is 5 feet and whose height (h) is 2 ft.
(a) 5ft.²
(b) 20ft.²
(c) 100ft.²
(d) 3.5ft.²
Answer:
(a) 5 ft^2
Step-by-step explanation:
The formula for area of a triangle is given by the formula,
A = 1/2bh, where
A is the area in square units,b is the base,and h is the height.Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:
A = 1/2(5)(2)
A = (5/2)(2)
A = 10/2
A = 5
Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2
make t the subject of the formula k=2(t+3)/t-3
t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.
The given equation is k=2(t+3)/t-3.
We need to isolate t on one side of the equation.
Let's start by cross-multiplying:
k(t - 3) = 2(t + 3)
Expanding the brackets:
kt - 3k = 2t + 6
Now, let's gather all the terms with t on one side and all the constant
terms on the other side:
kt - 2t = 6 + 3k
Factoring out t on the left side:
t(k - 2) = 6 + 3k
Finally, we can solve for t by dividing both sides of the equation by (k - 2):
t = (6 + 3k)/(k - 2)
Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
In a rectangle, the value of x is,
⇒ x = 5
We have to given that;
ABCD is a rectangle.
And, AC = 5x + 2
BD = x + 22
Since, We know that;
Diagonal of a rectangle are equal in length.
Hence, We get;
AC = BD
(5x + 2) = (x + 22)
5x - x = 22 - 2
4x = 20
x = 20/4
x = 5
Thus, the value of x is,
⇒ x = 5
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
PLEASE HELPPP!!!!!!!!!
If tanA= 40/9 and sin B = 45/53
and angles A and B are in
Quadrant I, find the value of tan (A-B).
The value of tan (A-B) is equal to 715/2052.
To find the value of tan(A - B), we can use the trigonometric identity:
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:
sin^2(B) + cos^2(B) = 1
cos(B) = sqrt(1 - sin^2(B))
cos(B) = sqrt(1 - (45/53)^2)
cos(B) = sqrt(1 - 2025/2809)
cos(B) = sqrt(784/2809)
cos(B) = 28/53
tan(B) = sin(B)/cos(B)
tan(B) = (45/53)/(28/53)
tan(B) = 45/28
Now we can substitute the values into the formula for tan(A - B):
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))
tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))
tan(A - B) = (715/252) / (2052/252)
tan(A - B) = 715/2052
Therefore, tan(A - B) is equal to 715/2052.
For more such questions on value,click on
https://brainly.com/question/843074
#SPJ8
i need some help on this please
Using the intersecting chord theorem, we can calculate the value of x as: 12
How to solve the Intersecting chord theorem?The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.
Applying the intersecting chord theorem to the two chords of the circle, we can say that:
3x = (9 * 4)
3x = 36
x = 36/3
x = 12
Read more about Intersecting Chord Theorem at: https://brainly.com/question/13950364
#SPJ1
Find the area of the shape
The area of the given figure with rectangle and triangle is 27.5 square centimeters.
The given figure has a rectangle and two triangles.
The area of the rectangle is length times width
Length = 5 cm
Width = 4 cm
Area of rectangle = 5×4
=20 square centimeters
Area of triangle =1/2 base ×height
=1/2×2.5×3
=3.75 square centimeters
As there are two triangles, 2(3.75)=7.5 square centimeters
Total area = 20+7.5
=27.5 square centimeters
Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.
To learn more on Area click:
https://brainly.com/question/20693059
#SPJ1
Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. (A reading above 140 is considered to be high blood pressure). Find the percentage of people with blood pressure below 133.
The percentage of people with blood pressure below 133 is 78.81%.
First, we need to calculate the Z-score for the value 133 using the formula:
Z = (X - μ) / σ
where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).
Z = (133 - 121) / 15
Z = 12 / 15
Z = 0.8
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.
Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.
Therefore, the percentage of people with blood pressure below 133 is 78.81%.
Learn more about z score here:
https://brainly.com/question/31871890
#SPJ1
The sector of a circle has an area of 7π/5 square inches and central angle with
measure 56°.
What is the radius of the circle, in inches?
Answer:
3
Step-by-step explanation:
Area = 7pi/5
56/360 × pi r² = 7pi/5
Pi is canceled on both sides.
r² = 7/5 ÷ 56/360 = 9
r = root 9 = 3
can u give me an answer
Answer: 0 , 5
Step-by-step explanation:
Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.
X is the driving and Y is the flight.
The X is at 0, and the Y is at 5.
the graph of a quadratic function has a y intercept at (0,3) and its vertex at (4,8 1/3) what are its x intercepts in order from least to greatest
can you also explain the steps?
The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).
Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]
Use the y-intercept to find the value of "a".
The y-intercept is (0,3), so when x=0, y=3.
Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].
Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.
To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]
To find the x-intercepts, set y = 0 and solve for x.
The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].
Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]
Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,
we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]
Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]
Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.
for such more question on quadratic function
https://brainly.com/question/17482667
#SPJ11
The grid shown below is in the shapr of a rectangle. What is the area innsquare units, of the shaded part of the rectangle? It have 48
Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains option D. 48 square units.
To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.
If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,
which is Area = length × width. The result will give us the area of the shaded part in square units.
The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option D
The Question was Incomplete, Find the full content below :
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
Know more about dimensions here
https://brainly.com/question/26740257
#SPJ11
There are 3 feet in a yard. How many centimeters are in a yard?
Solve each equation by completing the square. Round to the nearest
necessary.
2x² - 2x +7=5
-2x^2 + 10x =14
4x^2 + 6x = 12
All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
Given that;
Expressions are,
⇒ 2x² - 2x + 7 = 5
⇒ -2x² + 10x = 14
⇒ 4x² + 6x = 12
Now, We can completing the square each equation as;
⇒ 2x² - 2x + 7 = 5
⇒ x² - x + 7/2 = 5/2
⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2
⇒ (x - 1/2)² = 1 + 1/4
⇒ (x - 1/2)² = 5/4
⇒ -2x² + 10x = 14
⇒ - x² + 5x = 7
⇒ x² - 5x = - 7
⇒ x² - 5x + 25/4 - 25/4 = - 7
⇒ (x - 5/2)² = - 7 + 25/4
⇒ (x - 5/2)² = - 3/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ 4x² + 6x = 12
⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12
⇒ (2x + 3/2)² = 12 + 9/4
⇒ (2x + 3/2)² = 57/4
Thus, All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ1
Hello! Find Domain and range, thank you :-)
Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.
Solving a system of equations we can see that Gavin worked 7 hours tutoring.
How to find the number of gours that Gaving worked tutoring?Let's define the variables:
x = number of hours tutoring.
y = number of hours land scaping.
We know that he worked for 10 hours and earned $137, then we can write a system of equations:
x + y = 10
14x + 13y = 137
Isolating y on the first equation we get:
y = 10 - x
Replace that in the second one to get:
14x + 13*(10 - x) = 137
14x + 130 - 13x = 137
x = 137 - 130 = 7
He worked 7 hours tutoring.
Learn moer about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
task1 part b evaluate
The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
We have to given that,
Expression to solve,
⇒ ∫ (0 to 10) (x + 1) dx
Now, We can simplify as,
⇒ ∫ (0 to 10) (x + 1) dx
⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx
⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀
⇒ 1/2 (10² - 0) + (10 - 0)
⇒ 1/2 × 100 + 10
⇒ 50 + 10
⇒ 60
Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
Learn more about integral at:
brainly.com/question/27419605
#SPJ1
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Does the table show a probability distribution? Select all that apply.
Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The standard deviation of the random variable x is 1.1145
Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
The probability of a value of x is never neg.
The sum of the probabilities is always 1.
The sum of all values of P(X = x) equals 1, which is, considering n values
There are no negative values of P(X = x).
Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:
E(X)= ∑xP(X=x)
Standard deviation = √Variance(x)
Var(x) = E(x²) - [E(x)]²
X 0 1 2 3 4 5
p(x=x) 0.032 0.152 0.316 0.316 0.152 0.032
First we have to find E(x)
E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)
The mean E(x) = 2.5
To find variance, we use Var(x) = E(x²) - [E(x)]²
But we have to calculate E(x²) first, since we already have found E(x)
So,
E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)
therefore, E(x²) = 7.492
Now we have all the values we can find the variance:
Var(x) = E(x²) - [E(x)]²
=7.492 - [2.5]²
= 1.242
With variance now we can find the standard deviation;
S.D = √Var(x)
= √1.242
= 1.1145
Learn more about probability distribution here:
https://brainly.com/question/13609688
#SPJ1
Convert the polar representation of this complex number into its standard form. A 4-451 B. -43-4/ C. -8√5 +8/ D. 4-4√3 i
The complex number in standard form is written as:
Z = 1.99 + i*0.201, so the correct option is a
How to write the complex number in standard form?Remember that a complex number can be written in standard form as:
Z = a + b*i
And in polar form the notation is (R, θ):
[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]
Here we have the complex number:
Z = 2(cos(11pi/6) + i*sin(11pi/6))?
So here we just need to solve these expressions, we will get:
Z = 2*(0.995 + i*0.100)
Z = 1.99 + i*0.201
Learn more about complex numbers:
https://brainly.com/question/10662770
#SPJ1
Complete question:
"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "
Susie paid 2/5 of the price of her movie ticket. Her parents paid the remaining portion of the movie ticket price. What decimal is equivalent to the fraction of the price of the movie ticket Susie paid?
17 points!!
Thanks to the other user
To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):
2 ÷ 5 = 0.4
Therefore, the decimal equivalent to 2/5 is 0.4.
(Mines) Simple Equation2/5 which is know as 2 ÷ 5 is 0.4TipWhenever you see a fraction like 2/5 just divide and it will turn into decimal.
find the numerical value of the log expression
Answer:
Step-by-step explanation:
The numerical value of the given log expression is -73.
From definitions of logarithms, we know that :
[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]
[tex]log(a^n) = n*log(a)[/tex]
Therefore,
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]
substituting the given values
[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]
we get the value of the given expression
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]
Therefore the numerical value of the given log expression is -73.
To learn more about logarithms:
https://brainly.com/question/12049968
a triangle is shown below, find the m
The value of angle L is 61°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;
A+B = C
Similarly,
angle L and angle E are the interior angles and 113 is the exterior angle, therefore;
113 = L + 52
L = 113 -52
L = 61°
Therefore angle L is 61°
learn more about exterior angle theorem from
https://brainly.com/question/17307144
#SPJ1
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
13 in
10 in
5 in
12 in
Answer:
12
Step-by-step explanation:
206
5x10 12x13=206 it may be incorrect but i not sure if it is incorrect