in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning
Answers
The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.
What is the similarity law?It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Triangle ABC ~ EDC
Angle ACD = Angle BCE = 90 degree (vertically opposite angle)
Angle ACB = Angle DCE = 90 degree (vertically opposite angle)
BE ║ AD
Angle EBC = Angle CDA = 40 degree (alternative angles)
Triangle ABC ~ Triangle EDC
Angle ABC = Angle CDE
Angle BAC = Angle DEC
∴ AB ║ DE
Triangle ACD ~ Triangle ECB
Angle EBC = Angle CDA and
Angle BEC = Angle CAD
∴ Triangle ACD ~ Triangle ECB
Angle A + Angle E = 180 degree
∠x + 50 + 50 + ∠x = 180
∠x = 40
Angle CAD = 40 degree
We know,
Angle A = Angle E = Angle B = Angle D = 90 degree
So ABCD is a square
AB = ED = 12
AD = AB = BE = ED = 12
Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.
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Related Questions
I need help with this
Answers
Step-by-step explanation:
please mark me as brainlest
Use triangles ABC and RST to answers the following questions. Is triangle ABC a right triangle? Explain your answer.
Answers
Answer:
[tex]\rightarrow \fbox {Yes} \leftarrow[/tex]
Step-by-step explanation:
ΔABC is a right triangle as it possesses a right angle (90°).
Triangle ABC is a right angled triangle since it holds Pythagoras theorem.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
For a right angled, triangle, there is a theorem called Pythagoras Theorem which relates the three sides of the triangle.
Pythagoras theorem states that,
Hypotenuse² = Base² + Altitude²
Here AC is the hypotenuse, BC is the base and AB is the altitude.
Base² + Altitude² = (BC)² + (AB)²
= 5² + 12²
= 25 + 144
= 169
= 13²
= AC²
= Hypotenuse²
Pythagoras theorem holds for the given triangle.
Hence the given triangle ABC is a right angled triangle.
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if(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers
Answers
Answer:
a = 4/3 and b = 0============================
Given expression:[tex]\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}[/tex]
Simplify it in steps:Step 1Bring both fractions into common denominator:
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]
Step 2Simplify:
[tex]\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =[/tex]
[tex]\dfrac{4\sqrt{14} }{7-4} =[/tex]
[tex]\dfrac{4}{3} \sqrt{14} }[/tex]
Step 3Compare the result with given expression to get:
a = 4/3 and b = 0Sofia is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Sofia's test score (out of 100) if she got 8 questions wrong? What would be her score if she got xx questions wrong?
Score with 8 questions wrong:
Score with xx questions wrong:
need answer quickly
Answers
Answer:
60 points
100 - 5x
Step-by-step explanation:
If she got 8 questions wrong she missed (8 * 5) points or 40 points. This means she only got 60 points
This can be further generalized by simply subtracting the amount of questions someone got wrong by 5 from the total available points of 100
100 - 5x
The members of a golf team contributed a total of $14.30 for a party to be held after their practice. Each member contributed the same amount of money in dimes only. How many members are in the team and how much money did everyone contribute? Give all possible answers. I NEED FULL ANSWER!!!!!!!!!!!!!!!!!!
Answers
Answer:
each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts
which is NOT an arithmetic sequence
-7,0,7,14
0,5,1,1.5
10,6,2,-2
2,4,8,16
Answers
Answer:
2,4,8,16
Step-by-step explanation:
2,4,8,16
difference is multiplied by 2
Which of the following problem types can always be solved using the law of
cosines or sines? Check all that apply.
A. SSS
B. ASA
C. SAA
D. SAS
E. SSA
F. AAA
Answers
Answer:
A, C, D, E, F
The graph shows the growth rate of a certain bacteria in a lab, where the number of bacteria depends on the number of hours since the start of the experiment.Based on the graph, what is the approximate number of bacteria after 16 hours? 6 bacteria 8 bacteria 60 bacteria 80 bacteria
Answers
The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.
What is a Function ?A function is a Mathematical statement which connects a dependent variable and an independent variable.
The graph shows the the growth rate of a certain bacteria in a lab
the number of bacteria is on the y axis and
the number of hours is on the x axis
The function is continuous ,
From the graph the approximate number of bacteria after 16 hours is
60 bacteria
Therefore Option C is the right answer.
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find the size of unknown angle
Answers
Answer:
x° = 75
(x + 30)° = 105°
Step-by-step explanation:
supplementary angle is two angles that sum is 180°
x° + (x + 30)° = 180°
2x + 30 = 180°
2x + 30 - 30 = 180 - 30
2x = 150
2x / 2 = 150 / 2
x° = 75
plug in 75,
75 + 30 = 105
check: 75 + 105 = 180
Answer: 75 degrees
Step-by-step explanation:
Do you see how both sides of the angle come together to form the straight line seen at the bottom? This means that these are supplementary angles.
Supplementary Angles: Both sides have to add up to a total of 180 degrees.
With this, form an equation: x+(x+30)= 180
Get rid of the parenthesis:
x+x+30= 180
Combine like terms.
2x+30= 180
2x= 180-30
2x= 150
x= 150÷2
x= 75
Checks:
x+x+30= 180
75+75+30= 180
You can also check using the equation in its simplified form: 2x+30= 180.
2x+30=180
2(75)+30=180
150+30=180
Hence x=75
Kindly solve this question 6 too !!
Answers
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]~~~~~x = \dfrac{1}{2 - \dfrac 1{2-\dfrac{1}{2-x}}}\\\\\\\implies x = \dfrac{1}{2 - \dfrac 1{\dfrac{4-2x-1}{2-x}}}\\\\\\\implies x= \dfrac{1}{2 - \dfrac{2-x}{3-2x}}\\\\\\\implies x = \dfrac{1}{\dfrac{6-4x-2+x}{3-2x}}\\\\\\\implies x = \dfrac{3-2x}{4-3x}\\\\\\\implies 4x -3x^2 = 3-2x\\\\\\\implies 3x^2 -4x +3-2x = 0\\\\\\\implies 3x^2 -6x +3 = 0\\\\\\\implies 3(x^2 -2x +1) =0\\\\\\\implies x^2 -2x +1 = 0\\\\\\\implies (x-1)^2 = 0\\\\\\\implies x -1 = 0\\\\\\\implies x = 1[/tex]
A 2-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent, total 100 percent. Column 2 has entries 40 dollars, 40 dollars, 40 dollars, 40 dollars, blank total.
Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show. After paying the agent, Daniel takes home $120. Use the diagram to answer the following questions.
Daniel’s agent made
.
Daniel and the agent made a total of
from the show.
Answers
Answer:
Amount in Blank total = $160
Amount of money Daniel’s agent made = $40
Amount of money Daniel and the agent made
from the show = $160
Step-by-step explanation:
this question is based on the calculation of percentages
so,
it is is given in the question that -
Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show.
After paying the agent, Daniel takes home = $120
so,
let 'x' is the total amount of money that Daniel earned form the show
it is also given that Daniel promised to give 25 % to his agent from what he earned from the show
so, percentage of money left to the Daniel is
100-25 = 75%
therefore according to the question,
75percent of the x = $120
75/100×(x) = 120
3/4×(x) = 120
3x = 120×4
3x = 480
x = $160
so the total amount of money Daniel earned from the show is $160
Now we know that Daniel’s agent made 25% of the total amount of money earned from the show
therefore
25percent of 160 = Daniel’s agent made
25/100 ×160 = Daniel’s agent made
$40 = Daniel’s agent made
so the amount of money earned by Daniel’s agent made is $40
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Answer: Daniel’s agent made
✔ $40
Daniel and the agent made a total of
✔ $160
from the show.
.
Step-by-step explanation:
x2) Triangle ABC is an isosceles triangle with BA = BC 72° D lies on AC ABD is an isosceles triangle with AB = AD Angle ABD = 72° 36 A D Show that triangle BCD is isosceles. You must give a reason for each stage of your working.
Answers
An isosceles triangle is one with two equal-length sides. The ΔBCD is an isosceles triangle.
What is an isosceles triangle?
An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
Given ΔABC is an isosceles triangle with side AB = AC. Therefore, as per the base angle theorem,
∠A = ∠C = 36°
Also, in ΔABC, the sum of the angles can be written as,
∠ABC + ∠BAC + ∠BCA = 180°
∠ABC + 36° + 36° = 180°
∠ABC = 108°
For ∠ABC we can write,
∠ABC = ∠ABD + ∠CBD
108° = 72° + ∠CBD
∠CBD = 36°
Now, in ΔBCD, the measure of ∠CBD and ∠DCB both equals to 36°. Therefore, we can write, that the ΔBCD is an isosceles triangle.
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5 14/15 on a number line rounded to the nearest whole number or half.
PLEASE HELP ME!!!!! I NEED HELP
Answers
Answer:
Step-by-step explanation:
Here we will show you step-by-step how to get the solution to: "What is 5/14 rounded to the nearest whole number?"
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
5 / 14 = 0.3
Then, we round to the nearest whole number using the following rules:
If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.
If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.
.4 is less than .5. Thus, we leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.
5/14 rounded to the nearest whole number is therefore:
0
If 4y = 3x - 1, then x = ?
Answers
Answer:
[tex]x = \frac{4y + 1}{3} [/tex]
The goal is to isolate the X value. So the first step would be to add 1 to both sides, making the equation 4y + 1 = 3x.
Then you divide both sides by 3, making the equation (4y + 1)/3 = x
If you have a Y value then you'd plug it in for Y and solve for x but since there isn't one provided you're done.
Pls help me solve this equation
Answers
Answer:
a
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, 4 ) into the partial equation
4 = 2 + c ⇒ c = 4 - 2 = 2
y = [tex]\frac{1}{3}[/tex] x + 2 ← equation of line
Which logarithmic equation is equivalent to this exponential equation?
Answers
Step-by-step explanation:
i think b is right answer
Answer:
see photo for detailed analysis
100 PTS!! PLEASE HELP! OVER DUE
Answers
Answer:
[tex]-\frac{1}{2} \vec {c}[/tex]
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].
If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:
[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]
Double checking that k works for the y-coordinates as well:
[tex]kc_y=d_y[/tex]
[tex](-\frac{1}{2}) (4)[/tex] ? [tex](-2)[/tex]
[tex]-2=-2 \text{ } \checkmark[/tex]
So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]
Answer:
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that , or equivalently, and .
If and , we just need to substitute known values and solve for k:
Double checking that k works for the y-coordinates as well:
?
So,
Write an equation for the n
term of each geometric
nth
sequence.
1, 4, 16, ...
Answers
a = 1 and r = 4/1 = 16/4 = 4
t(n) = 1 x 4^(n - 1)
What is the circumference of the circle shown below? (Round your answer to the nearest tenth.) A. 33.0 B. 66.0 C. 346.4 D. 206.2
Answers
Answer:
B. 66.0
Step-by-step explanation:
The formula for circumference is 2*π*r where r is the radius. MS and MR are both radii, so we can plug in 10.5 to the formula to get 2* π*10.5, which would be about 65.97, which rounds to 66.0. Hope this helps!
Does this graph represent a function? why or why not ?
Answers
Answer:
C- Yes, because it pases the vertical line test.
Step-by-step explanation:
It passes through one point exactly.
(basic algebra) please help me with question:
Answers
Find the sum.
-110 + (-102) + (-94) + ... + 66 + 74
Answers
Answer:
Step-by-step explanation:
a=-110
d=-102-(-110)=-102+110=8
let n be the number of terms.
74=-110+(n-1)×8
74=-110+8n-8
74+118=8n
192=8n
n=192/8=24
[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]
Which is equivalent to 80 1/4?
Answers
Answer:
B.[tex] \sqrt[4]{ {80}^{x} } [/tex]
Step-by-step explanation:
Hope it helps
What is the area of Vivian’s garage door?
Answers
The area of Vivian’s garage door is 62.5 square feet
Area of composite shape.The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;
Area = Area of rectangle + area of trapezoid
Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet
Hence the area of Vivian’s garage door is 62.5 square feet
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The ratio of players to soccer balls at practice sessions is 5:2. How many soccer balls are needed for 20 players?
Answers
Answer:
8 soccer balls
Step-by-step explanation:
Since the ratio of players to soccer balls is 5:2, we can conclude that:
Players = 5 peopleSoccer balls = 2 ballsThe question asks to find how many soccer balls are needed for 20 players.
Multiply both players and soccer balls by 4, this will get:
Players = 20 peopleSoccer balls = 8 ballsHenceforth, 8 soccer balls are needed for 20 players.
8. Complete the table below by drawing an example of each shape.
Answers
Answer:
Please see attachment.
The first one is a quadrilateral that is not a parallelogram.
The second one is a triangle with a right angle.
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Which function is increasing?
Answers
The only increasing function is the last option:
[tex]f(x) = 5^x[/tex]
Which function is increasing?
Here we only need to see that, is as x increases also do f(x). Then the function will be increasing.
The cases for exponential functions is actually more trivial than that.
If the base is between zero and 1, then the function is decreasing.If the base is larger than 1, then the function is increasing.In the given options there is only one function with a base larger than 1, which is the last option:
[tex]f(x) = 5^x[/tex]
That is the correct option.
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una cuerda al vibrar tiene una frecuencia fundamental de 200 Hz. Si su longitud se reduce en una cuarta parte, ¿cual será la nueva frecuencia fundamental? ¿se ha alterado la rapidez de la onda al acortar la cuerda? Suponga que la tensión es constante
Answers
I thank the answer is B
Step-by-step explanation:
10
Jack is reading a book. In ¾ of an hour, he finished 66 pages. If he keeps reading at the same rate, how many total pages will Jack read in one hour?
Answers
The velocity of a particle can be modeled by the function v(t)=1/10(3t-8)^3+2. Which graph accurately shows the velocity of the park or at any time, t?
Answers
The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.
How to draw a function Graph?Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.
Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.
The velocity of a particle is modeled by the function;
v(t) = ¹/₁₀(3t - 8)³ + 2
The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.
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