In each part (a)-(d) below, some additional assumptions about the
picture are given. In each problem, determine whether the given
assumptions are enough to prove that the two triangles are similar; and
if so, what the correct correspondence of vertices is. If the two triangles
must be similar, prove this result by describing a sequence of similarity
transformations that maps one triangle to the other. If not, explain why
not.
a. The lengths AX and XD satisfy the equation 2AX = 3XD.
AX
b. The lengths AX, BX, CX, and DX satisfy the equation A
c. Lines AB and CD are parallel.
d. Angle XAB is congruent to angle XCD.
=
DX
CX
Answers
In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.
How to explain the triangle?a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.
b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.
c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.
d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.
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Related Questions
need help with this question
Answers
Answer:
[tex]f(x) = a(x^2+4)(x-3)^2[/tex]
Step-by-step explanation:
So I'm assuming it means that one of the zeros is at x=3 with a multiplicity of 2 and it has an imaginary solution of 4i. Anyways, imaginary solutions come in conjugate pairs meaning if you have a complex solution of [tex]a-bi[/tex] there is another complex solution which is the conjugate of that which is [tex]a+bi[/tex] but since the imaginary solution is 4i, the complex number is just [tex]0+4i[/tex] so the conjugate is [tex]0-4i[/tex] or [tex]-4i[/tex]. So since you have x=3 as a zero that can be represented as [tex](x-3)^2[/tex] since 3 would make it 0 and it has a multiplicity of 2. As for the other factors, you won't just have ([tex](x-4i)(x+4i)[/tex], you'll have a factor that is set up in a way that the solutions are: [tex]x=\pm\sqrt{-4}[/tex]. That means it'll be a quadratic. So it'll be in the form [tex]x^2+b[/tex]. Since you're moving b to the other side and it's negative. that means it has to be positive and since the value is 4, you'll have the factor [tex](x^2+4)[/tex] which when set equal to zero has the solutions sqrt(-4). So this gives you the equation
[tex]f(x) = a(x^2+4)(x-3)^2[/tex]
Find the equation of a line whose slope is 1/2 and intersects negative y-axis at a distance of 7 units from the origin.
Answers
Answer:
Step-by-step explanation:
[tex]y=\frac{1}{2} x-7[/tex]
Answer:
y = 1/2x - 7
Step-by-step explanation:
The slope equation is: y = mx + b
m being the slope
b being the y-intercept
The problem says that the slope is 1/2, and says that it intersects negative y-axis, therefore the y-intercept is negative, so -7
what is the inverse of this function? f(x)=-1/2 square root of x+3, x > -3
Answers
The inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
How to determine the inverse function?The function is given as:
[tex]f(x) = -\frac 12\sqrt{x + 3}[/tex]
Rewrite as;
[tex]y = -\frac 12\sqrt{x + 3}[/tex]
Swap the positions of x and y
[tex]x = -\frac 12\sqrt{y + 3}[/tex]
Multiply through by -2
[tex]-2x = \sqrt{y + 3}[/tex]
Square both sides
4x^2 = y + 3
Subtract 3 from both sides
y = 4x^2 - 3
Express as an inverse function
[tex]f^{-1}(x) = 4x^2- 3[/tex]
Hence, the inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
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what is the vertex form of y=2x^2+8x+1
Answers
Answer:
So, the vertex form of your function is [tex]y(x)=2*(x+2)^2-7[/tex].
The vertex is at [tex](-2|-7)[/tex]
Step-by-step explanation:
Given function:
[tex]y(x)=2*x^2+8x+1[/tex]
Steps:
[tex]y(x)=2*x^2+8x+1\\[/tex]
[tex]y(x)=2(x^2+4x+\frac{1}{2} )[/tex] (Factor out)
[tex]y(x)=2(x^2+4x+2^2-2^2+\frac{1}{2} )[/tex] (Complete the square)
[tex]y(x)=2((x+2)^2-2^2+\frac{1}{2} )[/tex] (Use the binomial formula)
[tex]y(x)=2((x+2)^2-\frac{7}{2} )[/tex] (Simplify)
[tex]y(x)=2*(x+2)^2-7[/tex] (Expand)
-b/2a to get x of vertex (x , y)
-8/4 = -2
So far we have (-2, y)
plug -2 into equation:
y = 2(-2)^2 - 16 + 1
y = -7
(-2, -7)
so 2(x+2)^2 - 7
What is the product of the following equation??
Answers
Answer:
B
Step-by-step explanation:
1.(5x^3)(xy^4 -2x^3y)
2.5x^4y^4 -10x^6y
Classify the following triangle as acute, obtuse, or right.
Answers
Answer:
cool
Step-by-step explanation:
pooop
The two-way table represents data from a survey asking students whether they plan to attend college, travel, or both after high school.
A 4-column table with 3 rows. The first column has no label with entries travel, not travel, total. The second column is labeled college with entries 43, 24, 67. The third column is labeled not college with entries 10, 5, 15. The fourth column is labeled total with entries 53, 29, 82.
Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent.
18%
22%
35%
82%
Answers
Using it's concept, it is found that the marginal relative frequency for students who plan to attend college is of 82%.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are a total of 82 students, 67 of which plan to attend college, hence the relative frequency is:
f = 67/82 = 0.82 = 82%.
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Answer:
82%
Step-by-step explanation:
The answer above is correct.
Classify the polynomial by its degree and number of terms
n³ - 12n² + 6m² n²
Answers
Answer: It’s a trinomial
Step-by-step explanation: It has three terms, so it’s classified as a trinomial. (Tri=three)
what is the area of triangle ABC if the height is 4 yards and the base is 15 yards
Answers
Answer:
30 square yards
Step-by-step explanation:
You can calculate the area of a triangle by using the formula: [tex]A = \frac{1}{2}bh[/tex], where b=base, and h=height, and since you have both values you can easily calculate the area by plugging the values in
Plug Values Into Equation:
[tex]A = \frac{1}{2}(15)(4)[/tex]
Multiply 15 and 4
[tex]A=\frac{1}{2}(60)[/tex]
Multiply by 1/2 (or technically divide by 2)
[tex]A = 30[/tex]
Answer:
The answer is 30yd²
Step-by-step explanation:
A=hb b/2
=4·15/2
=30yd²
Write a two-column proof.
Given: 7y = 8x – 14; y = 6
Prove: x = 7
Answers
1) [tex]7y=8x-14, y=6[/tex] [given]
2) [tex]7(6)=8x-14[/tex] [substitution]
3) [tex]56=8x[/tex] [addition property of equality]
4) [tex]7=x[/tex] [division property of equality]
5) [tex]x=7[/tex] [symmetric property of equality]
A two columns proof is given in the attached image below as per the concept of solving equations.
A two columns proof is given below:
Statement | Reasons
y = 6 | Given
7y = 8x - 14 | Given
7(6) = 8x - 14 | Substitution (Substitute y with 6 in statement 2)
42 = 8x - 14 | Simplification
42 + 14 = 8x | Addition Property of Equality (Add 14 to both sides)
56 = 8x | Simplification
56/8 = x | Division Property of Equality (Divide both sides by 8)
7 = x | Simplification (Simplify the fraction 56/8)
x = 7 | Symmetric Property of Equality (Rearrange statement 9)
In this two-column proof, we start with the given information that y is equal to 6 (statement 1).
Then, we substitute the value of y into the equation 7y = 8x - 14 (statement 2) to get 42 = 8x - 14 (statement 3).
We simplify the equation to isolate 8x and find that 56 = 8x (statement 6). Dividing both sides of this equation by 8 (statement 7) gives us x = 7 (statement 8).
Finally, we use the symmetric property of equality to rearrange the equation and conclude that x is indeed equal to 7 (statement 9).
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8. A school cafeteria
purchased 256
hotdogs, 332 apples,
and 154 cookies. How
many items did they
purchase in all?
Answers
the school purchased 742 items in total.
Just add 256+332+154
which equals...742. :)
Answer:
742 items
Step-by-step explanation:
Add up all the items that the cafeteria purchased. 256+332+154=742!
Which graph corresponds to the following inequality? -2x-3xy<6
Answers
you need to start from the beginning add 2 and 3
Step-by-step explanation:
The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.
Answers
Answer:
I think that's the answer
Data are collected about the amount of time, in minutes, each band member spends practicing. How does a single outlier change the lower and upper quartiles of the collected data?
A single outlier does not affect the values of the quartiles.
A single outlier causes the values of the quartiles to move slightly away from the outlier.
A single outlier doubles the values of the quartiles.
A single outlier causes the values of the quartiles to move slightly toward the outlier.
Answers
A single outlier does not affect the values of the quartiles.
What is the effect of the outlier on the value of the quartiles?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier does not affect the values of the upper and lower quartiles. This is an advantage of the upper and lower quartiles over range.
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(2x-1)²+8√2xy=4
4y-√8xy-1=1
Answers
(x² + 2√xy) = 5/4
2y - √2xy = 0
How to factorize the expressionFrom the first equation
(2x-1)²+8√2xy=4
Expand the bracket
(2x-1) (2x+ 1) + 8√2xy = 4
4x² + 2x -2x - 1 + 8√2xy = 4
4x² - 1 + 8√2xy = 4
Collect like terms
4x² + 8√2xy = 4 + 1
4x² + 8√2xy = 5
Find the common factor
4(x² + 2√xy) = 5
(x² + 2√xy) = [tex]\frac{5}{4}[/tex]
For equation 2, we have
4y-√8xy-1=1
4y - [tex]\sqrt{4 *2 xy }[/tex] = 1 -1
4y - [tex]2\sqrt{2xy}[/tex] = 0
Find the common factor
[tex]2(2y - 2\sqrt{2xy} ) = 0[/tex]
[tex]2y - 2\sqrt{2xy} = 0[/tex] × 2
[tex]2y - \sqrt{2xy} = 0[/tex]
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With the aid of an illustration from a well labelled diagram, explain a cross over experimental design using a scenario with three treatment
Answers
A crossover design is a reiterated assessments design in which each experimental unit (patient) receives various treatments at different time periods, i.e., the patients switch from one therapy to another during the trial.
What is the advantage of a crossover design?The crossover design has the benefit of each subject acting as his or her own control, and it requires a lesser number of patients than parallel-group trials.
There are various drawbacks. For example, crossover designs often last longer than parallel-group research.
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what is the range of y=x+3^2
All real numbers
{3^2}
{1, 3, 9}
All real numbers except 9.
Answers
Answer:
All real numbers
Step-by-step explanation:
See attached graph.
You’re involved in the design of a new facility. It is important for people to move between work stations quickly. Based on the figure below, how many feet would a person need to walk to get from Work Station 1 to Work Station 3?
Answers
Answer:
13 feet
Step-by-step explanation:
A^2 + B^2 = C^2
A=5 ^2 = 25
B=12 ^2 = 144
144 +25 = 169
C=13
Use factoring by grouping to completely factor the following.
4x^3−3x^2−36x+27=
Answers
Answer: 3 answers
Step-by-step explanation:
what is the degree of the polynomial below?
x⁵+1-3x⁴+3x⁹-2x
Answers
The degree of the polynomial, x⁵+1-3x⁴+3x⁹-2x, is: 9.
What is the Degree of a Polynomial?
The degree of a polynomial is determined by the monomial with the highest degree.
Given the polynomial, x⁵+1-3x⁴+3x⁹-2x, the monomial with the highest degree is 3x⁹.
Therefore, the degree of the polynomial given is: 9.
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
49^2m-m : Not equivalent
7^2m-2m : Not equivalent
7^2m-m : Not equivalent
This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.
For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.
Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.
Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.
But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!
Hope this helped!
Sin (5x-25) = COS (3x)
X=?
Answers
Answer:
x=23
Step-by-step explanation:
put it in desmos and was right
15) Complete.
Purchase Price: $450
Finance Charge: $82,50
Down Payment: $150
Number of Payments: 18
Monthly Payment:
O a.) $22.15
Ob.) $20.45
Oc.) $21.25
Od.) $22.25
Answers
The monthly payment for this purchase with a price of $450, a finance charge of $82.50, a down payment of $150, and 18 monthly payments is c.) $21.25.
What is the monthly payment?The monthly payment is the periodic payment made to settle a mortgage loan.
When the total mortgage payment is determined, the monthly payment can be calculated as the dividend of the total mortgage payment and the number of monthly payments.
Data and Calculaitons:Purchase Price: $450
Finance Charge: $82,50
Down Payment: $150
Number of Payments: 18
Total mortgage payment = $382.50 ($450 + 82.50 - 150)
Monthly payment = $21.25 ($382.50/18)
Thus, the monthly payment for this purchase with a price of $450, a finance charge of $82.50, a down payment of $150, and 18 monthly payments is c.) $21.25.
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Solve
f(x)= 2x -13
g(x) = x^2 - 6x + 3
Answers
Answer:
just hey effect me II rieirjttjhg shewtha
If arc mAD = 103°, and arc mBC = 115°, what is m∠BEC?
Answers
Applying the angles of intersecting chords theorem, m∠BEC = 109°.
What is the Angles of Intersecting Chords Theorem?According to the angles of intersecting chords theorem, the measure of angle BEC equals half the sum of the measures of arcs AD and BC.
arc mAD = 103°
arc mBC = 115°
Therefore, we would have:
m∠BEC = 1/2(103 + 115)
m∠BEC = 109°
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What is the range of the function graphed below?
Answers
Answer:
[tex]\boxed{-\infty < y\leq 2}[/tex]
Step-by-step explanation:
See the appendix.
The set of values is the interval [tex]y\in (-\infty , 2 >[/tex] .
[tex]y\in (-\infty , 2 > ~~\Leftrightarrow ~~\boxed{-\infty < y\leq 2}[/tex]
Enter the correct answer in the box.
The function (x)=7*+1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function g?
Substitute a numerical value for k into the function equation.
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P
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sin cos tan sin costan ö
csc sec cot log
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Answers
The equation of function g is f(x) = 7^3x + 1
How to determine the function g(x)?The function f(x) is given as:
f(x) = 7^x + 1
The rule of horizontal compression by a factor of 3 is represented as
g(x) = f(kx)
Where k = 3
So, we have:
f(x) = 7^3x + 1
Hence, the equation of function g is f(x) = 7^3x + 1
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There are red and blue files in a box. The ratio of red to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box? There are red and blue files in a box . The ratio of red to blue tiles is 3 : 5 . There are 12 more blue tiles than red tiles in the box . How many red tiles are in the box ?
Answers
The number of red tiles in the box given the chance ratio of red to blue tiles is 18
RatioNumber of red tiles = xNumber of blue tiles = 12 + xTotal tiles = x + 12 + x= 12 + 2x
Ratio of red = 3Ratio of blue = 5Total ratio = 3 + 5 = 8Number of red tiles = 3 / 8 × 12+2x
x = 3(12 + 2x) / 8
x = (36 + 6x) / 8
8x = 36 + 6x
8x - 6x = 36
2x = 36
x = 36/2
x = 18 tiles
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Answer: 28
Step-by-step explanation:
−5 = s−9. what is s?
Answers
Answer:
S= 4
Step-by-step explanation:
add 9 to -5
= 4
s=4
The Nutty Professor sells cashews for $7.40 per pound and Brazil nuts for $4.80 per pound. How much of each type should be used to make a 28 pound mixture that sells for $6.19 per pound?
Answers
Answer:
cos4B =1-8sin^2(B)+8sin^4(B)
Step-by-step explanation:
cos4B =1-8sin^2(B)+8sin^4(B)