show that the triangles are similar by measuring the lengths of their sides and comparing the ratios of their corresponding sides
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ANSWER
EXPLANATION
The ratio between corresponding sides of similar triangles is constant - in other words, the ratio between each pair of corresponding sides gives the same value.
As shown in the questions, the ratios between corresponding sides are,
[tex]\begin{gathered} \frac{DE}{AB}=\frac{3}{2}=1.5 \\ \frac{DF}{AC}=\frac{1.5}{1}=1.5 \\ \frac{EF}{BC}=\frac{2.4}{1.6}=1.5 \end{gathered}[/tex]Since the three ratios between corresponding sides are the same, 1.5, the triangles are similar.
Related Questions
Graph y < -1 in a coordinate plane. And Label the Axis
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Answer:
Explanation:
Given the below inequality;
[tex]y<-1[/tex]To graph the above, we have to note that since we have the less than sign without an inequality sign, the line will be broken lines and we'll shade the downward part of the graph as shown below;
To support the high school, the local businesses will donate $2 for every ticketsold at the homecoming game. If 113 student, 158 home and 52 visitor ticketswere sold, how much did they donate?
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we know that
to find out the total amout donate, multiply the total tickets sold by $2
so
step 1
Find the total tickets sold
adds
113+
Determine the amount of an investment if $100 is invested at an interest rate of 5.5% compounded semi-annually for 6 years.
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We have an investment that is compounded semi-anually.
The equation for the future value of an compounded interest investment is:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]where:
FV is the future value.
PV is the present or initial value of the investment (PV=100).
r is the annual nominal interest rate (r=5.5%=0.055).
m is the number of capitalization subperiods in the year. In this case, as it is semiannually, m=12/6=2.
n is the number of yearly periods that the investment last (n=6 years).
Then, we can replace the variables with the values and calculate:
[tex]\begin{gathered} FV=100\cdot(1+\frac{0.055}{2})^{2\cdot6} \\ FV=100\cdot(1+0.0275)^{12} \\ FV=100\cdot1.0275^{12} \\ FV\approx100\cdot1.3848 \\ FV\approx138.48 \end{gathered}[/tex]Answer: the value of the investment after 6 years is $138.48.
Determine if the triangles are similar; if they are then what is the reason?
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From the given triangles,
[tex]\frac{OP}{PN}=\frac{RS}{SQ}[/tex][tex]\angle OPN=\angle RSQ=89^O[/tex]Thus the triangles are similar by SAS property.
The relation is SAS: two sides+included angle congruent.
*Express the end behavior of the followingFunction in limit notation.G(x)=-x(x^2 + 3) (x - 2)^3 (x + 5)^2
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we have the function
[tex]g(x)=-x(x^2+3)(x-2)^3(x+5)^2[/tex]In this problem, we have that
the leading coefficient is negative (-1)
The degree of the function is 8 (even)
therefore
the end behavior of the function is
f(x)→−∞, as x→−∞
f(x)→−∞, as x→+∞
What is the slope of a linear function that passes between (2, 7) and (5, 12)?
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The formula of slope,
→ (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (12 - 7)/(5 - 2)
→ [ m = 5/3 ]
Hence, thy slope is 5/3.
Combine Like Terms -8w + 16x + 20w – 40x
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Answer:
12w - 24x
Step-by-step explanation:
-8w + 16x + 20w - 40x
20w - 8w = 12w
-40x + 16x = 24x
Answer:
12w - 24xStep-by-step explanation:
Start by grouping terms that are alike. You can identify such terms by looking at the variables. Anything associated with x is considered a like term to another number associated with x.[tex]-8w+16x+20w-40x\\-8w+20w+16x-40x[/tex]
Add both like elements for each side.[tex]-8w+20w=12w\\12w+16x-40x\\16x-40x=-24x\\\bold{=12w-24x}[/tex]
Hope this helps!
Write a linear function rule for the data in the table.x01234y31–1–3–5A.f(x) = 2x + 3B.f(x) = –2x + 3C.f(x) = 2x – 6D.f(x) = –2x – 6
Answers
From the given table
Choose two-point for x and y from the table
So,
The point will be:
(0, 3) and (1, 1)
Now,
From the standard for of the linear function
[tex]y=mx+b[/tex]Then,
First, find the value of the slope (m) from the given point
So,
From the formula of the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1_{}-3_{}}{1_{}-0_{}} \\ m=-2 \end{gathered}[/tex]Now,
To find the value of b, put the value of m = -2, x = 0 and y = 3 into the standard form of the equation
[tex]\begin{gathered} y=mx+b \\ 3=-2(0)+b \\ 3=b \end{gathered}[/tex]Then,
Put the value of b into the standard form of the equation
[tex]\begin{gathered} y=mx+b \\ y=-2x+3 \end{gathered}[/tex]Hence, the correct option is B.
Write a two column proofGiven: q is parallel to r Prove: angle 1 is supplementary to angle 3
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Answer:
Proved.
Explanation:
Given: q is parallel to r
Statement: m∠1 = m∠2
Reason: Vertically Opposite Angles
Statement: m∠2+m∠3=180°
Reason: Same-side Interior Angles
Recall that m∠1 = m∠2
Statement: m∠1+m∠3=180°
Reason: Congruent Angles (m∠1 = m∠2)
Therefore, angle 1 is supplementary to angle 3.
Proved.
Solve for a.2(a+4)+6a=48 Enter your answer in the box.a =
Answers
Step 1
Given
[tex]2(a+4)+6a=48[/tex]Required : To find the value of a
Step 2
Expand the bracket
[tex]2a+8+6a=48[/tex]Step 3
Bring like terms together
[tex]\begin{gathered} 2a+6a=48-8 \\ \end{gathered}[/tex]Step 4
Find the value of a
[tex]\begin{gathered} 8a\text{ = 40} \\ \frac{8a}{8}=\frac{40}{8} \\ a=\text{ 5} \end{gathered}[/tex]Hence, a = 5
I need help with this, I need it step by step please.
Answers
In this problem we have a translation
the rule is
(x,y) ------> (x-6,y)
that means
the translation of the point is 6 units at left
so
we have
E(2,4) ------> E'(2-6,4)
E'(-4,4)
you must to subtract 6 units from the x coordinate
F(4,4) -----> F'(4-6,4)
F'(-2,4)
G(2,1) -----> G'(2-6,1)
G'(-4,1)
151617= 1819Write an equation in slope-intercept form for the line with slope 5 and y-intercept - 1.00=0:Х?
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The slope-intercept format of a line is given as y=mx+c where m is the slope and c is the intercept.
Since m=5 and c=-1
Therefore the equation of the line is y = 5x-1
Please help I was sick and missed out on class.Thank you
Answers
The slope of the line passing through given points is 5/7
We know that the slope is the ratio of the change in y-values to the change in x-values.
We use slope formula,
m = (y2 - y1)/(x2 - x1)
For pair of points (1, 3) and (8, 8),
m1 = (8 - 3)/(8 - 1)
m1 = 5/7
For pair of points (8, 8) and (15, 13),
m2 = (13 - 8)/(15 - 8)
m2 = 5/7
For pair of points (22,18) and (29, 23),
m3 = (23 - 18)/(29 - 22)
m3 = 5/7
For pair of points (15, 13) and (22, 18),
m4 = (18 - 13)/(22 - 15)
m4 = 5/7
Since the rate of change of output values to the input values is constant i.e., 5/7, the slope of the line is 5/7
Therefore, the slope of the line passing through given points is 5/7
Learn more about the slope here:
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(8.5-2x)(11-2x)(x) what is the approximate value of x that would allow you to construct an
open-top box with the largest volume possible from one piece of paper
Answers
The largest volume possible from one piece of paper for open-top box is 64.296 cubic unit.
What is meant by the term maxima?The maxima point on the curve will be the highest point within the given range, and the minima point will be the lowest point just on curve. Extrema is the product of maxima and minima.For the given question dimensions of open-top box;
The volume is given by the equation;
V = (8.5-2x)(11-2x)(x)
Simplifying the equation;
V = x(4x² - 39x + 93.5)
Differentiate the equation with respect to x using the product rule.
dV/dx = x(8x -39) + (4x² - 39x + 93.5)
dV/dx = 8x² - 39x + 4x² - 39x + 93.5
dV/dx = 12x² - 72x + 93.5
Put the Derivative equals zero to get the critical point.
12x² - 72x + 93.5 = 0.
Solve using quadratic formula to get the values.
x = 4.1 and x = 1.9
Put each value of x in the volume to get the maximum volume;
V(4.1) = 4.1(4(4.1)² - 39(4.1) + 93.5)
V(4.1) = 3.44 cubic unit.
V(1.9) = 1.9(4(1.9)² - 39(1.9) + 93.5)
V(1.9) = 64.296 cubic unit. (largest volume)
Thus, the largest/maximum volume possible from one piece of paper for open-top box is 64.296 cubic unit.
To know more about the maxima, here
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4312345L2-3445To find the rate of change of the function, Kevin did the following:
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Could you help walk me through this problem? I keep getting the problem wrong and I don't know why.
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to solve this we can get the equation in the form
F(x)=a(x-X1)(x-X2)
where X1 and X2 are the values of X where the line cross the axial X
in this case
X1= -1
X2= 2
so the function will be
F(x)=a*(x+1)*(x-2)
now we need to find the value of a
So for this we can replace with a random point of the curve, for example the point x= 0 y=-2
So if we replace
-2=a*(0+1)*(0-2)
-2=a*1*-2
-2=a*-2
-2/-2=a=1
So the answer is:
F(x)=1*(x+1)*(x-2)
The graph below shows the cost for going roller skating at 2 roller rinks . Bianca is going roller skating with a group of friends . Roller Rink A charges $3.00 per person and a $60 group fee . Roller Rink B charges $7.00 per person and an $8.00 group fee . When comparing costs ,which statement is true ? • Roller Rink B always cost less • Roller Rink A always cost less • Roller Rink B costs less if Bianca's group has fewer then 13 people• Roller Rink A costs less if Bianca's group has fewer then 13 people
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In this case we can see that the cost of each company is increasing but the slopes are diferent. also we can see that the cost of company B is is cheaper at the begining but after some peaple is more expensive so the correct statement will be:
Roller Rink B costs less if Bianca's group has fewer than 13 people
V8 to the nearest tenth is about ?
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Find the sum of the first 46 terms of the following series, to the nearestinteger.12, 15, 18, ...
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We can see that this is an arithmetic sequence. The first term is 12 and the common difference is 3.
Using the formula to calculate the sum of the first 46 terms, we have:
[tex]undefined[/tex]evaluate. Reduce your answer to lowest terms.2 1/5-10×(3/5)2
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8 1/3% Convert each percent to a fraction and a decimal.
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We must convert the percentage 8 1/3% to:
0. a fraction,
,1. a decimal.
First, we rewrite the number 8 1/3 in the following way:
[tex]8\text{ 1/3 }=8+\frac{1}{3}=8\cdot1+\frac{1}{3}=8\cdot\frac{3}{3}+\frac{1}{3}=\frac{8\cdot3+1}{3}=\frac{25}{3}\text{.}[/tex]Now, we have that:
[tex]8\text{ 1/3 \% }=\frac{25}{3}\text{ \%.}[/tex]1) Because 8 1/3 % is 8 1/3 per 100, we have that:
[tex]8\frac{1}{3}％=\frac{8\frac{1}{3}}{100}=\frac{\frac{25}{3}}{100}=\frac{25}{3\cdot100}=\frac{25}{3\cdot4\cdot25}=\frac{1}{12}\text{.}[/tex]2) Using a calculator, we have:
[tex]8\frac{1}{3}％=\frac{1}{12}\cong0.083.[/tex]Answer
• 8 1/3% as a ,fraction, is ,1/12,,
,• 8 1/3% as a ,decimal, is ,0.083,.
At the Avonlea Country Club, 54% of the members play bridge and swim, and 89% of the members play bridge. If a member is selected at random, what is the probability that the members swims, given that the member plays bridge?
Answers
ANSWER
[tex]P(S|B)=0.61[/tex]EXPLANATION
We are given that 54% of the members at the club play bridge and swim, and 89% of the members play bridge.
[tex]\begin{gathered} P(\text{BnS)}=0.54 \\ P(B)=0.89 \end{gathered}[/tex]To find the probability that the member swims given that he/she plays bridge, we have to apply conditional probability.
The probability that the member swims given that he/she plays bridge is gotten by dividing the probability that the member plays bridge and swims by the probability that the member plays bridge:
[tex]\begin{gathered} P(S|B)=\frac{P(B\cap S)}{P(B)} \\ \Rightarrow P(S|B)=\frac{0.54}{0.89} \\ P(S|B)=0.61 \end{gathered}[/tex]That is the answer.
I just need the answer
Answers
The Solution.
The line of symmetry occurs at x= -2
And the maximum value of the given function is 8, and it occurs at x = -2
For the polynomial below, -3 and 1 are zeros. Express f (x) as a product of linear factors.
Answers
Explanation
Since -3 and 1 are zeros of the functions, it implies that
[tex](x+3)\text{ }and\text{ }(x-1)[/tex]are factors of the equation.
Therefore we can find the remaining factors below
[tex](x+3)(x-1)=x^2+2x-3[/tex]By long division
[tex]remaining\text{ expression =}\frac{x^4+6x^3+7x^2-8x-6}{x^2+2x-3}=x^2+4x+2[/tex]By quadratic formula
[tex]\begin{gathered} x_{1,2}=\frac{-4\pm\sqrt{4^2-4\times1\times2}}{2\times1} \\ x_1=\frac{-4+2\sqrt{2}}{2},x_2=\frac{-4-2\sqrt{2}}{2} \\ x=-2+\sqrt{2},x=-2-\sqrt{2} \\ therefore \\ (x+2-\sqrt{2})(x+2+\sqrt{2}) \end{gathered}[/tex]The linear factor are
Answer:
[tex]f(x)=(x+3)(x-1)(x+2-\sqrt{2})(x+2+\sqrt{2})[/tex]
for every dollar of revenue the government takes in, it pays 5 cents in interest on its debtwhat is the ratio of debt interest to total revenue a. 1:4b. 1:5c. 1:10d. 1:20
Answers
Answer;
D. 1:20
Explanation
According to the question, we are given the following
Total revenue = 1 dollars
Debt interest = 5cents
Ratio of debt interest to total revenue = 5cents : 1 dollar
Since 1 dollar = 100cents
ratio of debt interest to total revenue = 5cents : 100cents
ratio of debt interest to total revenue = 5/100 = 1/20
Hence the ratio of debt interest to total revenue is 1:20
Find the slope of a line a. parallel and b. perpendicular to the line y = - 3x + 8.a. Parallel:b. Perpendicular:
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The slope of a line parallel to the given line is -3
The slope of the line perpendicular to the given line is 1/3
Explanation:
Given:
y = -3x + 8
To find:
a) slope of a line parallel to the given line
b) slope of a line perpendicular to the given line
a) For two lines to be parallel, their slopes will be the same
From the given equation, we will get the value of the slope
[tex]\begin{gathered} linear\text{ equation: y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \\ \\ comparing\text{ y = mx + b with y = -3x + 8}: \\ mx\text{ = -3x} \\ m\text{ = -3} \end{gathered}[/tex]The slope of a line parallel to the given line is -3
b) For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the other line
The slope from the line given is -3
reciprocal of the slope = 1/-3 = -1/3
negative reciprocal = -(-1/3) = 1/3
The slope of the line perpendicular to the given line is 1/3
Find FG.FL x + 113x + 1EН.FG=
Answers
Answer:
FG = 16
Explanation:
The triangles EFG and EHG are congruent because they share the side EG and they have the same interior angles.
If they are congruent the lengths of the corresponding sides are equal, so we can write the following equation:
FG = GH
Then, subtitute FG = x + 11 and GH = 3x + 1 to get:
x + 11 = 3x + 1
So, solving for x, we get:
x + 11 = 3x + 1
x + 11 - 1 = 3x + 1 - 1
x + 10 = 3x
x + 10 - x = 3x - x
10 = 2x
10/2 = 2x/2
5 = x
Then, replacing x by 5, we get that FG is equal to:
FG = x + 11
FG = 5 + 11
FG = 16
So, the answer is FG = 16
The volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h. Find the equation of the joint variation if v =285, r=4, and h = 17.
Answers
Answer:
V = 1.05r²h
Explanation:
The expression ''the volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h'' can be represented as:
[tex]V=k\cdot r^2\cdot h[/tex]Where the k is a constant.
So, replacing V = 285, r = 4, and h = 17, we get:
[tex]285=k\cdot4^2\cdot17[/tex]Solving for k, we get:
[tex]\begin{gathered} 285=k\cdot16\cdot17 \\ 285=k\cdot272 \\ \frac{285}{272}=\frac{k\cdot272}{272} \\ 1.05=k \end{gathered}[/tex]So, the equation of the joint variation is:
[tex]V=1.05r^2h[/tex]21 The number of students in each of 2 exercise classes was the same. The box and whiskerplots below represent the average amount of time the students in each class spent exercisingdaily outside class.First class九术也Second class A+153012010545 6075 90Time Spent Exercising(minutes)Based on the information in the box and whisker plots, which statement about the time spentexercising outside class appears to be true?A The median amount of time the first class spent exercising was greater than the medianamount of time the second class spent exercising.B The range for the second class was less than the range for the first class.C The interquartile range for the first class was less than the interquartile range for thesecond class.D The minimum amount of time the second class spent exercising was greater than theminimum amount of time the first class spent exercising.
Answers
We are given a box and whiskers plot and we are asked the following questions:
A. The median amount of time the first class spent exercising was greater than the median amount of time the second class spent exercising.
The median of the first class is 60 and the median of the second class is 75, therefore, the median of the second class is greater than the median of the first class.
B. The range for the second class was less than the range for the first class.
The range of the first class is:
[tex]r_1=90-30=60[/tex]The range of the second class is:
[tex]r_2=105-30=75[/tex]Therefore, the rage of the second class is greater than the range of the first class.
C. The interquartile range for the first class was less than the interquartile range for the
second class.
The Interquartile range of the first class is:
[tex]IQ_1=75-45=30[/tex]The interquartile range of the second class is:
[tex]IQ_2=90-45=45[/tex]Therefore, the interquartile range of the first class is less than the interquartile range of the second class.
D The minimum amount of time the second class spent exercising was greater than the minimum amount of time the first class spent exercising.
The minimum time for the first class is 30 and the minimum time for the second class is 30, therefore, the minimum times are equal.
reduce the radical of 200