Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
Answers
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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Related Questions
PLEASE HURRY I WANT TO FIISH MY TEST PLEASE ASAP!!!
Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.
Answers
The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 32. This will be illustrated thus:
1/4(32 - 4) ≤ 1/8 (32 - 16)
= 1/4(28) ≤ 1/8(16)
= 7 ≤ 2
In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.
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1. Given segment AB with A(-3, 2) and B (5, -4). If point P lies on segment AB such that the ratio of
AP to PB is 2:6. Find the coordinates of p
Answers
The coordinates of P is ( -1 , 0.5) .
What is section formula ?
We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.
Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio of m:n then,
=> (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]
Here A[tex](x_1,y_1)[/tex] =( -3,2) and B[tex](x_2,y_2)[/tex] = (5,-4) and m:n = 2:6
Then,
=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]
=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]
=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]
=> (x,y) = (-1,0.5)
Hence the coordinates of P is (-1 , 0.5) .
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find zeros f(x)=x^4-6x^3-21x^2=150x-100 given k=5
Answers
The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100 are 0.6511 and 8.262 respectively
Zeros of a PolynomialZeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.
The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.
To find the zeros of this polynomial function, we have to write the function appropriately.
x⁴ - 6x³ - 21x² = 150x - 100
x⁴ - 6x³ - 21x² - 150x - 100 = 0
The roots of this function is 0.6511 and 8.262 respectively
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Does anyone know the answer to this problem?
Answers
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
Answers
The amount that Katy would have saved in her savings account in 2 years is $16, 000
How to find the amount saved?Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time
Principal = $100, 000
Interest rate = 8%
Time = 2 years
The amount that Katy would have saved is:
= Principal x Interest Rate x Time
= 100, 000 x 8% x 2
= $16, 000
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HELPPP FOR BRAINLEST????
Answers
Answer:
[tex]2,8,14,20[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:
[tex]a_n=6n-4[/tex]
Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].
Juan is playing a game in which he can win $100 with probability 0.2, $300 with probability 0.3, and $500 with probability 0.5. What is the expected value of Juan's winnings?
Answers
Juan's winnings has an expected value of $360
How to determine the expected value of Juan's winnings?The given parameters in the question are:
$100 with probability 0.2,
$300 with probability 0.3,
$500 with probability 0.5.
The expected value is then calculated as
E(x) = Sum of (amount * probability)
Substitute the known values in the above equation, so, we have the following representation
E(x) = 100 * 0.2 + 300 * 0.3 + 500 * 0.5
Evaluate
E(x) = 360
Hence, the expected value is $360
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FIRST ANSWER GETS FIVE STARS AND BRAINLIEST!
Pine Street, Rector Street, and Taylor Street intersect to form a triangular-shaped park as shown.
(picture below)
What is the correct order of the lengths of the streets from longest to shortest?
Answers
Answer:
Rector, Pine, Taylor
Step-by-step explanation:
The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!
(x-2x³-29x² - 43x+8)÷(x-7)
Answers
Answer:
-2x^2 - 43x - 343 - 2393/x-7
i need some help on these, can anybody help me?
Answers
All the ángles inside have to equal 180 º
Can you help me solve this problem?
Answers
The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:
0.1131 = 11.31%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion and the sample size are given as follows:
p = 0.73, n = 80.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.73[/tex].[tex]s = \sqrt{\frac{0.73(0.27)}{80}} = 0.0496[/tex]The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (0.67 - 0.73)/0.0496
Z = -1.21
Z = -1.21 has a p-value of 0.1131.
Hence the probability is:
0.1131 = 11.31%.
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A plant manufactures parts whose links are normally distributed with a mean of 16.3 cm and a standard deviation of 2.5 cm if one part is randomly selected find the probability that the part is between 10.8 and 12.8 cm
Answers
The probability that the part is between 10.8 and 12.8 cm is 0.0669.
What is a normal distribution?
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.
Here, we have
Mean = 16.3cm
Standard deviation = 2.5cm
We have to find the probability that the part is between 10.8 and 12.8 cm
Now,
we know that z = (x−μ)/σ
putting values in the normal distribution formula, we get
P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)
= P ( -2.2 < z < -1.4)
P( 10.8 < x < 12.8) = 0.0669, by normal distribution table
Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.
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The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?
Answers
A total of 12 5/8 pages is not meant for advertisement
How to determine the number of pages that are not for adverts?From the question, we have the following parameters
First section = 16 pages
Pages for advertisement = 3 and 3/8 pages
Rewrite the above parameters as
First section = 16 pages
Pages for advertisement = 3 3/8 pages
The number of pages that are not for adverts is then calculated as
Pages not for adverts = First section - Pages for advertisement
Substitute the known values in the above equation
So, we have the following equation
Pages not for adverts = 16 - 3 3/8
Evaluate the difference
Pages not for adverts = 12 5/8
Hence, the number of pages that are not for adverts is 12 5/8 pages
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A plant manufactures part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeters.
Question:
If one part is randomly selected, find the probability that the part is between 10.8 and 12.8 centimeters.
Answers
The probability that the plant manufactures a part between 10.8 and 12.8 centimeters 13%
How to find the probability that the part is between 10.8 and 12.8 centimetersThe probability is solved z scores, this measures the amount of standard deviation sample X is from mean. the formula is below
z = (X - μ) / σ
Definition of variables
mean, μ = 16.3 centimeters
standard deviation, σ = 2.5 centimeters
X = 10.8 and 12.8 centimeters
z score, z
substituting into the formula
for X = 12.8 centimeters
= (X - μ) / σ
= (12.8 - 16.3) / 2.5
= -1.4
the p value for z of -1.4 = 0.161513
for X = 10.8 centimeters
= (X - μ) / σ
= (10.8 - 16.3) / 2.5
= -2.2
the p value for z of -2.2 = 0.027807
the probability is calculated as below
0.161513 - 0.027807= 0.133706
= 0.13
=13%
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Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answers
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
pls i will give top rating
Answers
A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.
The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
How to find the value of x?Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.
From the given information, we get
x - y = 6 ...............(1)
"if five times the smaller number is two times the larger number"
from the above information, we get
5y = 4x + 2
5) To simplify the value of y:
y = (4x +2) / 5 ...............(2)
Substitute y = (4x +2) / 5 in (1), then we get
x - (4x + 2) / 5 = 6
5x / 5 - (4x + 2) / 5 = 6
simplifying the above equation, we get
(5x - 4x - 2) / 5 = 6
x - 2 = 5 x 6
x -2 = 30
x = 32
Substitute the value of x in (2)
y = 4(32) + 2 / 5
simplifying the above equation, we get
y = 130 / 5
y = 26
From (1), we get
x - y = 6
substitute the value of x and y in the above equation,
32 - 26 = 6
6 = 6
6) T is the 10s digit
X is the one's digit
The two digit number is 10T + X
It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits
10T + X = 7(T+X)
By using distributive law
10T + X = 7T + 7X
10T + X - 7T - 7X = 0
simplifying the above equation, we get
3T - 6X = 0
3(T - 2X) = 0
T - 2X = 0
T = 2X
The tens digit is 3 more than the one's digits, so
T = X + 3
Then we have
T = 2X = X + 3
Subtracting X from both sides,
T - 3 = X + 3 - 3
X = 3
The Tens digit is 6.
The number is 63.
The sum of the digits is 9.
9 × 7 = 63.
Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
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Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?
Answers
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
Given,
The share bought by Kyle of company XYZ = $50,000
The share price = $100
The share price after an year = $110
We have to find the gain amount by Kyle when Kyle sells all his shares.
Here,
We can apply Unitary method;
100 ⇒ 110
50000 ⇒ x
Compute;
100x = 110 x 50000
x = (110 x 50000) / 100
x = 110 x 500
x = $55000
Now,
Kyle gains,
55000 - 50000 = $5000
That is,
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
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hole me out on this thanks
Answers
Answer: [tex]5^{2} + 4[/tex]
Step-by-step explanation:
[tex]2 + 3^3[/tex] =?
2 + 27 = 29
10 * 2 - 9 = 20 - 9 = 11
[tex]5^2 + 4[/tex] = 25 + 4 = 29
[tex]5^3\\[/tex] = 5 * 5*5 = 125
3+ 4 * 3 = 3 + 12 = 15
Assessment Practice
5. A science teacher has $225 to spend on lab equipment.
He buys 4 posters with a guide to classifying rocks, for
$19 each. Student rock collections cost $9 each. How
many rock collections can he buy? Explain how you solve.
Use one or more equations and bar diagrams in your
explanation. Tell what your variables represent. 4.AR.1.1.4.AR.2.2
Answers
Answer:
Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve
Let
x -----> number of rock collections that he can buy
so
the algebraic expression that represents this situation is
Solve the inequality for x
subtract 76 both sides
Divide both sides by 9
therefore
The maximum number of rock collections that he can buy is 16
Step-by-step explanation:
The equation is 9x+76=225 and the number of rock collections he can buy is 17.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a science teacher has $225 to spend on lab equipment.
Let the number of rocks collected be x.
He buys 4 posters with a guide to classifying rocks, for $19 each.
That is 19×4=76
Student rock collections cost $9 each.
Now, 9×x=9x
So, the equation is 9x+76=225
Subtract 76 on both the sides of equation, we get
9x=149
Divide 9 on both the sides of equation, we get
x=16.5
x≈17
Therefore, the number of rock collections he can buy is 17.
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f(x)=(-3x^2-1)/3x^3 does f have an inverse function?
Answers
Answer: Yes, Probably
There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?
Answers
Answer:
1/5
Step-by-step explanation:
equation: 3/5-2/5=x
we can multiply the whole equation by 5 so that we can easily subtract the numbers
3-2=1
now we divide it by 5 so that we get our number in a fraction
after we divide we get 1/5
Which algebraic expression represents the amsplit the cost of a $20.00 gift?
A. f + 20
B. 20f
C. 20 ÷ f
D. f ÷ 20
Answers
Answer:
The answer is C: 20 ÷ f
Step-by-step explanation:
3.) Johannes sold an order of 3 Strawberry pies
for $12.50 each. She paid her assistant
$1.10 for each Strawberrye pie sold. How much
money did Johannesearn from the pies sold?
Answers
Answer:
$34.20
Step-by-step explanation:
Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.
We know that there were 3 pies sold so you must solve the equation below
11.40*3
The answer is $34.20
The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.
If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction
Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15
Answers
When a person from this group is selected at random, the probability that this person has type AB blood is 3/40
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:
= Number of AB blood type / Total number of people
= 15 / 200
= 3/40
The probability is 3/40.
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work out the size of angle x 24
Answers
Answer:
78°
Step-by-step explanation:
You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.
Base angleThe two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...
24° +2x = 180°
12° +x = 90° . . . . . . divide by 2
x = 78° . . . . . . . subtract 12°
The measure of angle x is 78°.
The formula for finding the surface area of a cube is 6s2, where s is the length of each side of the square. Evaluate for s=10 to find the number of square centimeters (cm2) for the surface area of a cube with a side length of 10 cm. i need helpp
Answers
The surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
Given:
The formula for finding the surface area of a cube is 6s2.
side length s = 10 cm.
Surface area of a cube = 6[tex]s^{2}[/tex] = 6*s*s
= 6 * 10 * 10
= 60 * 10
= 600 [tex]cm^{2}[/tex].
Therefore the surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
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Please refer to picture
Answers
Using the corresponding angle theorem, the value of x is 15 and y is 12.
In the given question we have to find the value of x and y.
From the graph we can see that
From the corresponding angle theorem
4x+2=62
Subtract 2 on both side, we get
4x=60
Divide by 4 on both side, we get
x=15
So the value of x is 15.
Similarly from the corresponding angle theorem
12y=144
Divide by 12 on both side, we get
y=12
So the value of y is 12.
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Given the inequality 4x ≤ 28, determine the value of x.
Answers
Step-by-step explanation:
Given the inequality 4x ≤ 28, determine the value of x.
4x ≤ 28
divide both sides by 4:
4x/4 ≤ 28/4
x ≤ 7
set builder notation: (-∞, 7]
answer:
The value of x is 7.
Step-by-step explanation:
4x ≤ 28 | divide both sides by 4
4x / 4 = x and 28 / 4 = 7
therefore, x ≤ 7
Marvin is helping his teachers plan a field trip. There are 136 people going on the field trip and each school bus holds 51 people. What is the minimum number of school buses they will need to reserve for the trip?
Answers
Answer: 3 busses
Step-by-step explanation:
A 6-foot-tall woman walks at 8ft/s toward a streetlight that is 30 ft above the ground. At what rate is the tip of her shadow moving? I got nothing on this bit the picture, and don't know where to start. does anyone know how to solve this one?
Answers
The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s
What are similar triangles?Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle
Height of the woman = 6 ft.
The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman
Height of the street light = 30 ft.
Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;
[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;
[tex]y = \dfrac{x}{4}[/tex]
The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;
[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]
[tex]\dfrac{dx}{dt} = 8[/tex]
Therefore, dx = 8·dt
x(t) = 8·t
Writing the function for the l in terms of time t gives;
[tex]l = \dfrac{5\cdot x}{4}[/tex]
[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]
The speed at which the tip of the shadow is moving,
[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]
The speed of the shadow dl/dx = 10 ft./s
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