Answers
We need to know about congruency to solve the problem. Two pairs of congruent angles prove that the triangles are similar.
We can define similarity of two geometrical objects on a plane as possibility to transform one into another using dilation optionally combined with congruent transformations of parallel shift, rotation and symmetry. We need to use transformation to verify whether the triangles in the diagram are similar. The two triangles have a common angle D and angles ABD and ECD are equal. Thus we can say that we have two pairs of congruent angles in the two triangles, so the two triangles are similar.
Therefore the triangles are similar since they have two pair of congruent angles.
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Related Questions
10. A recipe for banana bread calls for 3 bananas for every 6 cups of
What is the ratio of bananas to sugar?
Answers
1:2
Explanation:
If we divide both terms in the ratio 3:6 by the number 3, it equals 1:2
Have an AWESOME day! :)
how can i get an elimination out of this equatio
Answers
The simultaneous equations are:
[tex]\begin{gathered} -2x+7y=-23 \\ 6x-7y=-1 \end{gathered}[/tex]Since, the unknown y has the same co-efficient across the two(2) equations, we can eliminate it directly.
Thus, we have:
[tex]\begin{gathered} -2x+7y=-23 \\ 6x-7y=-1 \\ ----------- \\ -2x+6x=-23-1 \\ 4x=-24 \\ x=\frac{-24}{4} \\ x=-6 \end{gathered}[/tex]To find y, substitute for x = -6 into any of the equations.
Thus, we have:
[tex]\begin{gathered} \text{from equation i)} \\ -2x+7y=-23 \\ -2(-6)+7y=-23 \\ 12+7y=-23 \\ 7y=-23-12 \\ 7y=-35 \\ y=-\frac{35}{7} \\ y=-5 \end{gathered}[/tex]Hence, the correct option is option A
Colton’s gym charges an initiation fee of $40 plus a monthly fee of $50 . Which of the following he equations below shows the cost c of joining the gym for m months ? A . C = 50 + 40mB . C = 40 + 50mC. C = 40 - 50 m
Answers
given that Colton gym charges initial fee of $40
there is an addiontional fee of $50
C is the cost of joining the gym
m is the number of months
so the equation that can show the cost of joining the gym in m month is:
$40 which is the initial feel been added to $50 the additional charge multiply by m the number of months.
therefore the equation is:
C = 40 + 50m
so the correct option is B
Find the lenghts of the sides of the rectangle ABCD shown on the coordinate plane. Suppose you double the length of each side. What would be the new coordinates of point C if the coordinate of point A stay the same
Answers
Looking at the diagram,
each small box represents one unit
The number of units from A to B is 4 units
The number of units from B to C is 3 units
Thus, the length of rectangle ABCD is 4 units and its width is 3 units.
The original coordinates are
A(0, 0)
B(0, 4)
C(3, 4)
D(3, 0)
If
Is the point (-2, 2) a solution for the equation y-4 = 3(x + 1)?
Answers
Remember that ordered pairs are written in the form:
[tex](x,y)[/tex]To find it (-2,2) is a solution for the given equation, substitute x=-2 and y=2:
[tex]\begin{gathered} y-4=3(x+1) \\ \Rightarrow2-4=3(-2+1) \\ \Rightarrow-2=3(-1) \\ \Rightarrow-2=-3 \end{gathered}[/tex]Since the expression -2=-3 is false, then the point (-2,2) is not a solution for the given equation.
describe the center and spread of the data using the more appropriate status either the mean median range interquartile range or standard division
Answers
helppppppppppppppppppppppppppppppp
Answers
Answer:
b=4
I believe this is correct.
Step-by-step explanation:
-(2)^3+7(2)^2-2(2)+12=
-8+28-16
-8+12
4
Lindsay is designing a dog pen. The original floor plan is represented by figure PQRS. Lindsay dilates the floor plan by a scale factor of 1/2 with a center of dilation at the origin to form figure P'Q'R'S'. The final figure is P"Q"R"S". What are the coordinates of P'Q'R'S'?
Answers
Since we have the original coordinates P(-6, 9), Q(3, 9), R(3, 3) & S(-6, 3) and the scale factor, we multiply each x-component and y-component of each point by 1/2 in order to get P'Q'R'S', that is:
P'(-3, 9/2)
Q'(3/2, 9/2)
R'(3/2, 3/2)
S'(-3, 3/2)
And those are our P'Q'R'S' coordinates after the scaling,
PLEASE GIVE ME THE ANSWER AND HOW YOU GOT IT IM BEGGING YOU I WILL GET KICKED OUT IF I DONT GET A GOOD SCORE ON THIS
Answers
By solving the given equations, the values of x are 7 and -7.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, |x| -7:
Now, solve for x as follows:
|x| -7Then,
x - 7 = 0 and -x - 7 = 0Which gives, x = 7 and x = -7Therefore, by solving the given equations, the values of x are 7 and -7.
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Answer:
see below
Step-by-step explanation:
All the given equation have mod function in them .We know that, if
[tex]\longrightarrow |x| = y \\[/tex]
then ,
[tex]\longrightarrow x =\pm y \\[/tex]
1) |k| = 8
[tex]\longrightarrow k =\pm 8 \\[/tex]
__________________________
2)|x| = 7
[tex]\longrightarrow x = \pm 7\\[/tex]
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3) |a+2| = 8
[tex]\longrightarrow a + 2 =\pm \\[/tex]
[tex]\longrightarrow a = 8-2 \ or \ -8-2\\[/tex]
[tex]\longrightarrow a = 6 , -10 \\[/tex]
__________________________
4) |8a|/10 = 2
[tex]\longrightarrow |8a| = 20 \\[/tex]
[tex]\longrightarrow 8a =\pm 20\\[/tex]
[tex]\longrightarrow a =\pm\dfrac{20}{8} \\[/tex]
[tex]\longrightarrow a = \pm\dfrac{5}{2} \\[/tex]
___________________________
5)|-m+9| = 13
[tex]\longrightarrow -m+9 =\pm 13\\[/tex]
[tex]\longrightarrow m -9 =\pm 13\\[/tex]
[tex]\longrightarrow m = 13-9\ or \ -13-9\\[/tex]
[tex]\longrightarrow m = 4 , -22\\[/tex]
____________________________
6)|7-5x|=27
[tex]\longrightarrow 7-5x =\pm 27 \\[/tex]
[tex]\longrightarrow 5x -7 =\pm 27\\[/tex]
[tex]\longrightarrow 5x = 27 +7 \ or \ -27+7 \\[/tex]
[tex]\longrightarrow 5x = 34 \ or -20 \\[/tex]
[tex]\longrightarrow x =\dfrac{34}{5}, -4\\[/tex]
_____________________________
7)|2x+7|/5=5
[tex]\longrightarrow |2x+7|=25\\[/tex]
[tex]\longrightarrow 2x +7 =\pm 25 \\[/tex]
[tex]\longrightarrow 2x = 25-7 \ or \ -25-7\\[/tex]
[tex]\longrightarrow 2x = 18 \ or \ -32\\[/tex]
[tex]\longrightarrow x = 9 , -16 \\[/tex]
And we are done!
Find y if the line through (1, y) and (8, 2) has a slope of 3.
Answers
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]
The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.
Answers
• Volume of pentagonal prism = area of base x height
Volume = 247 unis^3
height = 13 units
Replacing:
V = A x h
A = V / h
A = 247/13 = 19 units^2
2. Using Vièta's theorem, find the solutions to the equation. a) x^2 - 3x + 2 = 0 b) x^2 + 2x - 15 = 0.
Answers
Given:
[tex]\begin{gathered} x^2-3x+2=0 \\ x^2+2x-15=0 \end{gathered}[/tex]Required:
We need to find the solution by Vièta's theorem.
Explanation:
Compare 1st equation with
[tex]ax^2+bx+c=0[/tex]we get
[tex]\begin{gathered} a=1 \\ b=-3 \\ c=2 \end{gathered}[/tex]Vièta's theorem is
[tex]\begin{gathered} x_1+x_2=-\frac{b}{a} \\ x_1x_2=\frac{c}{a} \end{gathered}[/tex][tex]\begin{gathered} x_1+x_2=3 \\ x_1x_2=2 \end{gathered}[/tex]now solve this equation and we get
[tex]\begin{gathered} x_1=1 \\ x_2=2 \end{gathered}[/tex]because addition of 1 and 2 is 3 and multiplication is 2
Now for 2nd equation
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-15 \end{gathered}[/tex]apply Vièta's theorem
[tex]\begin{gathered} x_1+x_2=-2 \\ x_1x_2=-15 \end{gathered}[/tex]by this
[tex]\begin{gathered} x_1=3 \\ x_2=-5 \end{gathered}[/tex]because addition of 3 and -5 is -2 and multiplication is -15
What is the inverse of the given relation?y = 3x + 12I need to understand the step by step breakdown for how to solve this problem.
Answers
Given the function y, we want to find the inverse function y^-1.
Then, replace every x with a y and every y with an x. It yields,
[tex]x=3y+12[/tex]now, solve the equation for y. So, by subtracting 12 to both sides, we have
[tex]x-12=3y[/tex]or equivalently,
[tex]3y=x-12[/tex]and, by dividing both sides by 3, we obtain
[tex]y=\frac{x-12}{3}[/tex]Finally, replace y with y^-1. Then, the inverse function is given by:
[tex]y^{-1}=\frac{x-12}{3}[/tex]I need help on a part of very hard question cuz it isn't very very very very very very far oh yeah. hear it is 2+2
Answers
Given:
The objective is to find the solution of 2+2.
Since the required operation in the given question is addition.
So, the addition of 2 and 2 will be,
[tex]2+2=4[/tex]Hence, the answer is 4.
An exam has 2 papers each scored differently. one is out of 120 and another is out of 80. Maryam scores 65% on the first and 80% on the second. work Maryam's total percentage score for her exam.
Answers
Maryam's total percentage score on her exam is 71%.
What is the total percentage score?
Percentage is the ratio of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
The first step is to determine the score on each paper.
Score on the first test = 65% x 120
(65 / 100) x 120 = 78
Score on the second test = 80% x 80
0.80 x 80 = 64
Total percentage score = (sum of scores / total score) x 100
Sum of scores = 64 + 78 = 142
Total score = 120 + 80 = 200
(142 / 200) x 100 = 71%
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ABC is a right angle. What is the measusre of DBE?
Answers
According to the given diagram the sum of ABD, DBE and EBC must be 90. Use this information to find the measure of DBE:
[tex]\begin{gathered} 33+\measuredangle DBE+33=90 \\ \measuredangle DBE=90-33-33 \\ \measuredangle DBE=24 \end{gathered}[/tex]The measure of DBE is 24 degrees.
Can you please help me to answer the question #46
Answers
Part A
S(0) = 1116 - 4.04(0) (Replacing h=0)
S(0)= 1116 (Multiplying)
The answer is 1116 ft/s
Part B
S(10) = 1116 - 4.04(10) (Replacing h=10)
S(10) = 1116 - 40.4 (Multiplying)
S(10)= 1075.06
The answer is 1075.06 ft/s
Part C
S(30) = 1116 - 4.04(30) (Replacing h=30)
S(30) = 1116 - 121.1 (Multiplying)
S(30)= 994.9 (Subtracting)
The answer is 994.9 ft/s.
The product 8 and the square of a number decreased by 5 is 67. Find the number.
Answers
Answer:
3 or -3
Explanation:
Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:
8x² - 5 = 67
Now, we can solve the equation for x. Add 5 to both sides
8x² - 5 + 5 = 67 + 5
8x² = 72
Divide both sides by 8
8x²/8 = 72/8
x² = 9
Find the square root of both sides
x = √9
x = 3 or x = -3
Therefore, the number is 3 or -3
vuvvvvvvvyvhvhccvccv
Answers
There are two families who visit a park and pay the entrance fee. The distribution of each family and the total cost paid at the entrance by each are given:
Family 1:
[tex]\begin{gathered} NumberofAdults(A_1\text{ )= 2} \\ NumberofChildren(B_{1\text{ }})\text{ = 3} \\ TotalEntryCost(C_1)\text{= }20\text{ pounds} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} NumberofAdults(A_2\text{ ) = 1} \\ NumberofChildren(B_2\text{ )= 4} \\ TotalEntryCost(C_2\text{ )= 15 pounds} \end{gathered}[/tex]Now we will define the ticket rates for adults and children at this park:
[tex]\begin{gathered} \text{Adult Rate = x} \\ \text{Children Rate = y} \end{gathered}[/tex]Next step is to express the total entry cost born by each family. This is done by multiplying the rate of each age group with the respective distribution of age group comprising each family.
Family 1:
[tex]\begin{gathered} C_1\text{ = x}\cdot A_1\text{ + y}\cdot B_1 \\ 20\text{ = 2}x\text{ + 3}y\text{ }\ldots.\text{ Eq1} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} C_2\text{ = x}\cdot A_2\text{ + y}\cdot B_2 \\ 15\text{ = x + 4y }\ldots Eq\text{ 2} \end{gathered}[/tex]We have two equation with two unknowns representing the cost charged for adults ( x ) and cost charged for children ( y ) at the park entrance.
We will solve the equation simultaneously ( Eq1 and Eq2 ) by using the process of Elimination:
[tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -2\cdot(15\text{ = x + 4y) = -30 = -2x -8y} \end{gathered}[/tex][tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -30\text{ = -2x -8y} \\ ========== \\ -10\text{ = 0 -5y} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}[/tex]Plug the value of ( y ) in either of the two equations and solve for ( x ):
[tex]\begin{gathered} 15\text{ = x + 4(2)} \\ x\text{ = 15 - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7 }} \end{gathered}[/tex]Therefore, the rates charged for each age group are:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Adult ticket = x = 7 pounds}} \\ \text{\textcolor{#FF7968}{Child ticket = y = 2 pounds}} \end{gathered}[/tex]Answer:yes
Step-by-step explanation:
If the radius of a sphere increases from 3 feet to 9 feet, by how many cubic feet does the volume of the sphere increase? 967 ft3 A 1087 ft3 936 ft 0
Answers
The volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]The original sphere, with radius r=3, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(3)^3 \\ =36\pi \end{gathered}[/tex]The second sphere, with radius r=9, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(9)^3 \\ =972\pi \end{gathered}[/tex]To find how much the volume increased we substract the first volume to the second one:
[tex]972\pi-36\pi=936\pi[/tex]Therefore the v
The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where isthe number of adults and y is the number of children. Explain what the 2- and y-intercepts mean.
Answers
Explanation:
Given the equation that models the number of passengers who can sit in a car expressed as 3x + 2y = 120
x is the number of adults
y is the number of children
The x-intercept is the point where y is zero i.e. the number of adults when there is no number of children.
when y = 0
3x + 2(0) = 120
3x = 120
x = 120/3
x = 40
This means that there will be 40 adults if there are no children
The y-intercept is the point where x is zero i.e. the number of children when there is no number of adults.
when x = 0
3(0) + 2y = 120
2y = 120
y = 120/2
y = 60
This means that there will be 60children if there are no adults
A system of equations is shown below. Solve for x.
y = x² - 6x + 4
y = x + 1
Answers
The value of x in the given quadratic equations is either -2.7 or -11.3.
What are quadratic equations?A quadratic equation is a second-degree algebraic equation in x. ax² + bx + c = 0, where a and b are coefficients, x is the variable, and c is the constant term, is the quadratic equation in its simplest form.
Given first equation, y = x²- 6x + 4 second equation, y = x +1
Put the value of y in the first equation to get
x + 1 = x² - 6x + 4
Solving this equation
x² - 7x + 3 = 0
Using quadratic formula,
x = - b ± [tex]\frac{\sqrt{(b^{2}- 4ac)}}{2a}[/tex]
x = - 7 ± [tex]\frac{\sqrt{(-7)^{2}- 4(3)}}{2}[/tex]
x = - 7 ± 4.3
Therefore in the given quadratic equations, the value of x can be either -2.7 or -11.3
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Solve the following system of equations Detailed step by step
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]\begin{gathered} 2\text{ x + y = 2 ------equation 1} \\ 4\text{ x + 3y =- 2--- -equation 2} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
The graphical solution for the two systems of equations are as follows:
CONCLUSION:
The solutions to the systems of equations are:
[tex]x\text{ = 4 , y = -6}[/tex]
Identify the slope and y-intercept of the line y=−2x−1.
Answers
Given the equation of the line:
[tex]y=-2x-1[/tex]The given equation as the slope-intercept form: y = m * x + b
where m is the slope and b is the y-intercept
the y-intercept is the value of y when x = 0
By comparing the given equation with the slope-intercept form
So,
The slope = m = -2
The y-intercept = b = -1
the point of y-intercept = ( 0, -1 )
You are making a kite and need to figure out how much binding to buy. You need the binding for the perimeter of the kite. The binding comes
in packages of two yards. How many packages should you buy?
12 in.
15 in.
12 in.
20 in.
You should buy packages.
Answers
With the help of the Pythagorean theorem, we know that we should buy 3 packages.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.So, Pythagorean formula: c² = a² + b²
Each package contains 2 yards of binding.In the kite, there are right triangles, so use the Pythagorean theorem.(Refer to the image of the kite attached below)
△1:
a² + b² = c²15² + 12² = x₁²x₁ = √15² + 12²x₁ = 19.2 in△2:
x₂ = x₁ = 19.2 in
△3:
a² + b² = c²12² + 20² = x₃²x₃ = √12² + 20²x₁ = 23.3 in△4:
x₄ = x₃ = 23.3 inTotal: 19.2(2) + 15 + 2(12) + 20 + 2(23.3) = 144 in
Total (actual) > 144 inNow,
1 package = 2 yards = 6ft = 72 in2 yards × 3ft/1yrd × 12in/1ft = 72 in2 packages: 2(72) = 144 in3 packages: 3(72) > 144So, we should buy 3 packages.
Therefore, with the help of the Pythagorean theorem, we know that we should buy 3 packages.
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B 961 m Solve the triangle 40° 41 С b B= degrees minutes m (Round to the nearest whole number.) b = m (Round to the nearest whole number.)
Answers
To find the angle B we can use the propertie that sya that the sum of the internal angles of a triangle is equal to 180º so:
[tex]\measuredangle b+90º+40º,41^{\prime}=180[/tex]and we solve for angle b so:
[tex]\begin{gathered} \measuredangle b=180º-90º-40º,41^{\prime} \\ \measuredangle b=49º,19^{\prime} \end{gathered}[/tex]So B is equal to: 49 degrees and 19 minutes
So now to find a we can use the trigonometric identitie of sin so:
[tex]\begin{gathered} \sin (40.68)=\frac{a}{961} \\ a=961\cdot\sin (40.68) \\ a\approx626 \end{gathered}[/tex]and to find b we use the trigonometryc identitie of cos so:
[tex]\begin{gathered} \cos (40.68)=\frac{b}{961} \\ b=961\cdot\cos (40.68) \\ b\approx729 \end{gathered}[/tex]One Sunday night, the Celluloid Cinema sold $ 1,585.75 in tickets. If the theater sold a children's ticket for $ 7.7S and an adult ticket for $ 10.25, a) write an equation to represent this situation. b) If the theater sold 75 children's tickets, solve your equation to find the number of adult tickets.
Answers
Answer:
98 adult tickets
Explanation:
Part A
Let the number of children's ticket sold = c
Let the number of adult's ticket sold = a
Cost of a children's ticket = $7.75
Cost of an adult's ticket = $10.25
Total income from ticket sales = $1,585.75
An equation to represent this situation is:
[tex]7.75c+10.25a=1585.75[/tex]Part B
If the number of children's ticket sold, c = 75
Then:
[tex]\begin{gathered} 7.75c+10.25a=1585.75 \\ 7.75(75)+10.25a=1585.75 \\ 581.25+10.25a=1585.75 \\ 10.25a=1585.75-581.25 \\ 10.25a=1004.50 \\ \frac{10.25a}{10.25}=\frac{1004.50}{10.25} \\ a=98 \end{gathered}[/tex]The number of adult tickets sold by the cinema is 98.
Hello,Can you help me with the following word problem?A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?This might be using the nCr formula
Answers
Solution:
Given that a medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, this implies that
[tex]\begin{gathered} total\text{ number of options in the set = 13} \\ number\text{ of oprions to be chosen = 6} \end{gathered}[/tex]To evaluate the number of people that can be selected, we use the combination formula expressed as
In this case,
[tex]\begin{gathered} n=13 \\ r=6 \end{gathered}[/tex]Thus, the question involves combination.
Julie has a total of 16 chickens. If she has 4 times as many chickens as dogs, write and solve an equation to determine the number of dogs she has.
Answers
The equation that can be used to determine the number of dogs that Julie has =
4× (number of chicken) = 64
What is an equation?An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.
The number of chicken owned by Julie = 16 chickens
The number of dogs = X
But she has 4× (number of chicken) = X
That is 4 × 16 = X
X= 64
Therefore the number of dogs that Julie has = 64 dogs.
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|x|=-5 why is there no solution?
Answers
Absolute value is the distance a number is from zero.
Because distance cannot be negative, an absolute value can never be a negative.
Therefore,
|x| = -5 has no solutions