My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.
Answers
By knowing that S is bisected by the line shown, we will conclude that PD = 8
So here we know that PC = 8, we also can see that:
PCS is a right trianglePDS is a right triangle.Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.
Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.
And notice that both of these triangles share one side, then:
Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.
This implies that the triangles are congruent, thus, the measures of the corresponding sides must be the same.
Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.
So you are correct.
If you want to learn more about congruent triangles, you can read:
https://brainly.com/question/12077512
Related Questions
Find the exact value of tan π/12.
Answers
[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]
so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]
[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]
I need help on this 1 problem on math
Answers
Answer:
x = 21
Step-by-step explanation:
2x+78 = 5x+15,
because corresponding angles will allow (2x+78) to move diagonally from 5x+15.
from built geometry knowledge,
angles diagonal from one another equal,
because (example) the angle above it would be 180-(2x+78),
then 5x+15 = 180 - [180-(2x+78)], which would ultimately be 5x+15 = 2x+78.
so, 2x+78 = 5x+15
78-15 = 5x-2x
63 = 3x
21 = x
What is the common ratio of the sequence?
-2, 6, -18, 54,...
A.-3
B.-2
C.3
D.8
Answers
Netan surveyed 460 teenagers to find out their favorite type of movie. He found that 45% of the teenagers surveyed like comedies.
Part A: How many teenagers surveyed like comedies? Show your work. (4 points)
Part B: In another survey, Hannah found that 50% of the total number of teenagers surveyed like thrillers. If 40 teenagers like thrillers, what is the total number of teenagers that Hannah surveyed? Show your work. (4 points)
Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)
Question 3 options:
Answers
Answer with step-by-step explanation:
A: 207
We know that percentage is out of 100, so we can divide 460 by 100 to find 1%, which is 4.6. We also know 45% percent of teenagers like comedies, so we multiply 4.6 by 45, or 207. 207 teenagers like comedies.
B. 80 teenagers
We know that 50% of teens Hannah surveyed like thrillers. We also know that 40 teenagers like thrillers. Using multiplication, we can multiply 40 by 2, since 50% is half, we need to multiply by 2 to get the total number of teenagers. Hannah surveyed 80 teenagers.
C. Jamie went to the candy store and spent his entire allowance of $20 on candy. His friends gave him $5 more dollars, so he bought candy with that too. He spent 125% of his allowance on candy.
The number of teenagers who like comedy is 207, and The total number of teenagers Hannah surveyed is 100.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
Netan surveyed 460 teenagers, He found that 45% of the teenagers surveyed like comedies,
(a) Calculate the number of teenagers who like comedy as shown below,
The number of teenagers who like comedy = 45 × 460 / 100
The number of teenagers who like comedy = 207
(b) Calculate the total number of teenagers as shown below,
The total number of teenagers × 50% = 40
The total number of teenagers = 40 × 100 / 40
The total number of teenagers = 100
To know more about percentages:
brainly.com/question/20818421
#SPJ2
y
is directly proportional to
x
2
.
If
y
=
8
when
x
=
2
find
y
when
x
=
3
Answers
Answer:
y = 18 when x = 3
Step-by-step explanation:
y is directly proportional to x^2, meaning:
[tex]y=ax^2[/tex]
where a is the proportion between them. We're given the values for both x and y, so plug those in and solve for a:
[tex]8=a(2)^2\\8=a4\\2=a\\a=2[/tex]
Now you can use a to solve for y when x is 3:
[tex]y=ax^2\\y=(2)(3)^2\\y=2(9)\\y=18[/tex]
The length of a photograph is 6 inches less than little twice the width. The photograph is mounted in a frame that is 3 inches wide on all sides. If the area of the framed picture is 270 square inches, find the dimensions of the unframed photograph.
Answers
Answer:
syuare root 270 to get 16.4 then subtract 6 to get 10.4
Jenny bought 5 pounds of carrots for $2.50. What is the unit rate for
Jenny's purchase? Identify the true statement that corresponds to this
situation.
A. 2 pounds of carrots per $1
B. $5 per pound
Answers
Answer:
A. 2 pounds of carrots per $1
Step-by-step explanation:
[tex]\frac{5 pounds }{2.5 dollars}=\frac{2pounds }{1 dollars}[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Two tanks hold a total of 61 gallons of a toxic solvent. One tank holds 4 gallons more than twice the amount in the other. How many gallons does each tank hold?
Answers
Answer:
tank 1 : 19 gallons
tank 2 : 42 gallons
Step-by-step explanation:
tank 1 : x
tank 2 : 2x+4 ( 4 more than twice the other )
x + ( 2x + 4 ) = 61
3x + 4 = 61 [ add x + 2x = 3x ]
3x = 57 [ subtract 4 on both sides ]
x = 19 [divide 3 on both sides ]
tank 1 : 19 gallons
tank 2 : 42 gallons
Camden has a loyalty card good for a 17% discount at his local hardware store. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?
Answers
Answer:
0.83Step-by-step explanation:
Let the price is x.
With 17% discount it becomes:
x - 17% of x =x - 0.17x = 0.83xThe number we need is 0.83
Solution,
Assume That The Price is x
When Will Put It in Equation,
[tex] \frak{ \bigstar}{ \rm{ {We \: Will \: Get,}}}[/tex]
[tex]{ \longmapsto{ \sf{x-17 \% \: of x =}}}[/tex][tex]{ \longmapsto { \sf{x-0.17x}}}[/tex]0.83Hence, Required Price is “0.83”
What is the sum of 6/7 and 1/2?
Answers
Answer: [tex]\frac{19}{14}[/tex] in improper form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.
Step-by-step explanation: [tex]\frac{6}{7}[/tex] + [tex]\frac{1}{2}[/tex] = ? First you have to find the LCM (Least Common Multiple) of 7 and 2; also known as the LCD (Least Common Denominator). The LCM of 7 and 2 is 14 so you have to multiply both of the fractions by the number that equals 14, remember to multiply it for the numerator too. [tex]\frac{6}{7}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{12}{14}[/tex] Then [tex]\frac{1}{2}[/tex] x [tex]\frac{7}{7}[/tex] = [tex]\frac{7}{14}[/tex] Now you add [tex]\frac{12}{14}[/tex] and [tex]\frac{7}{14}[/tex] together. You leave the denominator as 14 because you found the LCD of 7 and 2 already, so you add 12 and 7 together which gives you 19. The answer would be [tex]\frac{19}{14}[/tex] in improper fraction form and [tex]1\frac{5}{14}[/tex] in mixed fraction form.
The sum of the fraction 6/7 and 1/2 is 19/14
How to add fractionsGiven:
sum of 6/7 and 1/2
Sum means addition(+)
= 6/7 + 1/2
The least common denominator is 7 × 2 = 14
= 6/7 + 1/2
= (12+7) / 14
= 19/14
Therefore, the sum of 6/7 and 1/2 is 19/14
Learn more about fraction:
https://brainly.com/question/11562149
Solve the system of two linear equations below graphically y= -x + 1 y= -1/3+ 3
Answers
Answer:
Step-by-step explanation:
Help pls, will give brainliest
Simplify 2^3 x 2^18
Answers
Answer:
it is 2^21
Step-by-step explanation:
Answer:
2^21
Step-by-step explanation:
add 3 and 18 together
dont change 2
What is the volume of the irregular figure?
Answers
Answer:
the answer u r looking for is 144
Step-by-step explanation:
if u know who this is i will follow u
hint: its from avatar tla
only the first person that answers!!!
What number group includes only the counting number and 0
Answers
Answer:
Integers
The set of numbers including all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero)
(6y^3) - 42y= -4y^3
please helpp
Answers
Answer:
i have no clue
Step-by-step explanation:
i said this bc apparently i have to help someone to get help and i just wanna finish this math homework lol
plssssssssss help me Graph y= –73x+2.
Answers
Refer to the attachment for the graph.
[tex]\mathbb{MIREU} [/tex]
Help, im incredibly confused
Answers
[tex]f[/tex](x) = 0.20x + 35 : 29.5
PLEASE HELPPPP QUICKLY LOOK AT THE ATTACHED PHOTO FOR TE QUESTION!!!
Answers
Answer:
[tex]\sqrt 10y[/tex]
Step-by-step explanation:
10*[tex]\sqrt{y}[/tex] is [tex]\sqrt 10y[/tex]
[tex]\sqrt{100y}[/tex]
Step-by-step explanation:
Recall that
[tex]10 = \sqrt{100}[/tex]
So we can write our original expression as
[tex]10\sqrt{y} = \sqrt{100}\sqrt{y}[/tex]
[tex]\;\;\;\;\;\;\;\;\;=\sqrt{100y}[/tex]
We figure 25 people will attend if it rains and 70 people will attend if it does not rain. The weather forecast indicates that there is a 20% chance of rain that day. What is the expected number of people who will attend the party?
Answers
Answer:
34
Step-by-step explanation:
20% of 70 + 80% of 25 = 14 + 20 = 34.
Answer:
61
Step-by-step explanation:
Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).
The expected number of people with a 20% chance of rain would be 61.
(hope it helps)
Explain this picture
Answers
Answer:
It's A bar graph but I got to see the question to be for sure but its a bar graph and it helps you measure rates of things from numbers , months , years etc .
Step-by-step explanation:
Solve for x. 3x+11=9x-14
Answers
Answer:
x=25/6
Step-by-step explanation:
3x+11=9x-14
11=6x-14
25=6x
x=25/6
Answer:
[tex]x=\cfrac{25}{6}[/tex]
or
[tex]x=4.16[/tex]
Step-by-step explanation:
[tex]3x+11=9x-14[/tex]
[tex]3x+11-11=9x-14-11[/tex]
[tex]3x=9x-25[/tex]
[tex]3x-9x=9x-25-9x[/tex]
[tex]-6x=-25[/tex]
[tex]\cfrac{-6x}{-6}=\cfrac{-25}{-6}[/tex]
[tex]x=\cfrac{25}{6}[/tex]
Have a good day!
Patrick gets an allowance of $30 per week. If he babysits his brother, his parents give him an additional $5 per hour for every hour he babysits. Which equation can Patrick use to find y, the amount of money he will have after a week in which x hours of babysitting is done?
y = 30 + 5x
y = 35x
y = 30x + 5
y = 30x
Answers
Find the perimeter of a semicircle with a radius of 9 in.
Please explain and be accurate.
Answers
Answer:
9π + 18
Step-by-step explanation:
The circumference of a circle is pi times diameter, so 9 x 2 = 18 inches, which is the diameter. That will be the flat side of the semicircle. Then the circumference of the whole circle will be 18π. To find the curved side of the semi-circle, divide this by 2, so you get 9π. Therefore the answer is 9π + 18. The rough answer to 3 decimal places is 46.274
identify a potential sustainable agriculture practice to reduce the impact of the large-scale intensive agriculture on
Answers
Answer:
Focus on planting trees and and getting healthier soil, improve energy efficiency and not use so much pesticides using natural ways to plant things.
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIESTTTT
Answers
Answer:
about 5.1 units
Step-by-step explanation:
to find the length between two points you can use the pythaogorean theorem
5^2 + 1^2 = c^2
25 + 1 = c^2
26 = c^2
c is about 5.09901
rounding to the nearest tenth we get 5.1
Mrs. Traynor's class is taking a field trip to the zoo. The trip will cost $26 for each student. There are 22 students in her class. Use compatible numbers to estimate the total cost of the field trip.
Answers
Answer:
$572
Step-by-step explanation:
Since she has to pay $26 for her 22 students, you need to multiply to find the answer$26 * 22 = 572Therefore, she has to pay $572Given that
P
=
x
+
y
.
Find
P
when:
x
=
3
and
y
=
−
11
Answers
Answer:
P=14
Step-by-step explanation:
Since P depends on two variables x and y as the sum of the two, then;
P = 3+ 11
P = 14
On a number line, where would
7/10 be located? Choose all answers that make
a true statement.
Answers
Answer:
Step-by-step explanation:
a person pays a loan of Rs. 3900 in monthly installments each in installment being less than the former by Rs. 20 ,the amount of first is Rs.400 in how many installment will entire amount be paid ? give reason
Answers
Answer:
15 installments
Step-by-step explanation:
3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex] 400 - 20*(n - 1)
What is 14ab+10a written in factored form?
Answers
Answer:
2a(7b+5)
Step-by-step explanation:
yeah-ya....... right?
2a(7b+5)