Given: ∆ABC, AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
m∠ABC = 48°
Find: m∠PCD
Answers
Answer: The measure of angle PCD is 42 degree.
Explanation:
It is given that in ∆ABC,
AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
∠ABC = 48°
Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.
According to the angle sum property the the sum of interior angles of a triangle is 180.
[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]
[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]
[tex]\angle BAC=66^{\circ}[/tex]
The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.
[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]
Since PB=PC , so triangle BPC is an isosceles triangle.
[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]
From the figure it is noticed that,
[tex]\angle PCD+\angle PCB=\angle BCA[/tex]
[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]
[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]
[tex]\angle PCD=42^{\circ}[/tex]
Therefore, the measure of angle PCD is 42 degree.
Related Questions
order from greatest to least : 0.12 with bar over 2, 0.1225, 3/25, 7/125
Answers
that will be 0.122... , 0.1225, 0.12 and 0.056
so from greatest to least that is 0.1225 , 0.1222...., 0.12, 0.056
that is 0.1225 , 012(with bar over the 2) , 3/25 , 7/125
What units would you use to describe the volume of a box measured in inches?
Answers
cubic inches or inches³ would we use to describe the volume of a box measured in inches.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law
Volume is the measure of the 3-dimensional space occupied by matter, or enclosed by a surface, measured in cubic units.
As volume we measure by using three dimensions so the unit will be in cubics.
If we have to measure volume of box in inches then it will be cubic inches or inches³.
Hence cubic inches or inches³ units would we use to describe the volume of a box measured in inches.
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Cheryl wants to purchase a par value $500 bond from Agram Imports. Agram imports bonds have a market rate of 102.114 and offer 8.1% interest. If Cheryl’s broker charges a commission of 2.5% of the market value of each bond sold, what is the current yield on Cheryl’s bond?
A. 0.077
B. 0.078
C. 0.081
D. 0.040
Answers
Answer:
the answer is A. my friends
Suppose you flip a coint and roll a 10-sided die. what is the probability of flipping tails and rolling a 7?
Answers
The probability of rolling a 7 is 1/10
The two events are independent. Therefore the probability of flipping a tail and rolling a 7 is
(1/2)*(1/10) = 1/20
Answer: 1/20
nx-r=p
We need to solve for x.
Answers
Alex and Freddy collect stamps. The number of stamps in Alex’s collection is in ratio 3:5 to the number of stamps in Freddy’s collection. If Freddy gives Alex 10 stamps, the ratio will change to 7:9. How many stamps are in both collections together?
Answers
the new ratio is 7 to 9, so we have the equation: (3x+10)/(5x-10)=7/9
9(3x+10)=7(5x-10)
27x+90=35x-70
160=8x
x=20
So Alex has 3*20=60 stamps while Freddy has 5*20=100. Together they have 160
Answer:
160 stamps
Step-by-step explanation:
Suppose Alex has 3x stamps, Freddy has 5x stamps. After Freddy gives Alex 10 stamps, Alex has 3x+10 while Freddy has 5x-10
The new ratio is 7 to 9, so we have the equation: (3x+10)/(5x-10)=7/9
9(3x+10)=7(5x-10)
27x+90=35x-70
160=8x
x=20
So Alex has 3*20=60 stamps while Freddy has 5*20=100. Together they have
what is the perimeter of this triangle
Answers
Solve for x. 23=79(6x−36)+9 Enter your answer in the box.
Answers
The value of the equation 1429/237.
Let's solve for x in the given equation:
[tex]\[23 = 79(6x - 36) + 9\][/tex]
First, distribute the 79 on the right side:
[tex]\[23 = 474x - 2844 + 9\][/tex]
Combine like terms:
[tex]\[23 = 474x - 2835\][/tex]
Now, isolate the term with x by adding 2835 to both sides:
[tex]\[474x = 2858\][/tex]
Finally, divide both sides by 474 to solve for x:
[tex]\[x = \frac{2858}{474}\][/tex]
Now, you can simplify the fraction:
[tex]\[x = \frac{1429}{237}\][/tex]
So, the solution for x is [tex]\(x = \frac{1429}{237}\).[/tex]
Final answer:
To solve the equation, distribute the 79 on the right side, combine like terms, and then isolate and solve for x to get x = 6.05.
Explanation:
To solve the equation 23=79(6x−36)+9, we first expand the right side of the equation and then isolate the term with x on one side.
First, distribute the 79:
23 = 79(6x) - 79(36) + 9,
which simplifies to:
23 = 474x - 2844 + 9.
Combine like terms:
23 = 474x - 2835.
Now, add 2835 to both sides to isolate the term with x:
2868 = 474x.
Finally, divide both sides by 474 to solve for x:
x = 2868 / 474.
After performing the division, we find that x = 6.05.
A parchment fragment was discovered that had about 61% as much 14c radioactivity as does plant material on earth today. estimate the age of the parchment. (round your answer to the nearest hundred years.)
Answers
The estimated age of the parchment is approximately 4,086.17 years.
To estimate the age of the parchment, we can use the concept of carbon dating.
Carbon-14 (14C) is a radioactive isotope of carbon that is commonly used for dating archaeological artifacts.
The amount of 14C in an organism remains relatively constant while the organism is alive because it continuously takes in carbon from the atmosphere and food.
However, after the organism dies, it no longer takes in new carbon, and the 14C begins to decay at a known rate.
The half-life of carbon-14 is approximately 5,730 years. This means that after 5,730 years, half of the original amount of carbon-14 in a sample would have decayed.
Let's use the information provided: the parchment fragment had about 61% as much 14C radioactivity as does plant material on Earth today.
This means that the remaining 14C in the parchment is 61% of the original amount. The remaining 14C is the amount that has not yet decayed, and the rest has decayed over time.
Now, we can set up an equation:
[tex]0.61 = (1/2)^{(t/5730)[/tex]
Where:
t = time in years since the parchment was alive.
Now, we need to solve for 't.' Taking the logarithm of both sides to isolate 't':
[tex]\log(0.61) = (t/5730) \times \log(1/2)[/tex]
Now, solving for 't':
[tex]t = (5730 \times \log(0.61)) / \log(1/2)[/tex]
Using a calculator, we find:
t ≈ 4,086.17 years
So, the estimated age of the parchment is approximately 4,086.17 years.
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Using the concept of radiocarbon dating and the fact that the parchment has 61% as much 14C radioactivity as present plant material, the calculated estimate for the parchment's age is approximately 2,200 years, rounded to the nearest hundred years.
Explanation:To estimate the age of the parchment based on the information that it had about 61% as much 14C radioactivity as does plant material on Earth today, we use the concept of radiocarbon dating. The half-life of carbon-14 (14C) is 5,730 years, which means after every 5,730 years, the amount of 14C decreases by half. Given that the parchment retains 61% of its original 14C, we can formulate the decay equation to solve for the parchment's age.
The decay equation is given by: \(N_t = N_0(1/2)^{t/T}\), where \(N_t\) is the remaining amount of 14C, \(N_0\) is the original amount of 14C, \(t\) is time, and \(T\) is the half-life of 14C. In this case, \(N_t/N_0 = 0.61\), and we know \(T = 5730\) years.
By substituting the given values into the decay equation and solving for \(t\), we find that the parchment is approximately 2,200 years old, rounded to the nearest hundred years. This estimation assumes the natural 14C to 12C ratio in the atmosphere has been constant over the time period in question.
Which linear inequality is represented by the graph?
A) y > 2/3x - 2
B) y < 2/3x + 2
C) y > 2/3x + 1
D) y < 2/3x - 1
I NEED THE ANSWER ASAP ‼️
Answers
Answer:
y < [tex]\frac{2}{3}[/tex]x -1 .
Step-by-step explanation:
Given : Graph.
To find : Which linear inequality is represented by the graph.
Solution : We have given graph with shaded down .
We know that if the graph is shaded down then equation of inequality has less than sign.
On comparing with line slope form y = mx +b.
Where m = slope and b = y intercept ( where the graph line cut at y axis)
Then b = -1 and slope = [tex]\frac{2}{3}[/tex].
Then equation become
y < [tex]\frac{2}{3}[/tex]x -1 .
Therefore, y < [tex]\frac{2}{3}[/tex]x -1 .
A secant and a tangent meet at a 90 degree angle outside the circle. What must be the difference between the measures of the intercepted arcs?
45 degrees
90 degrees
180 degrees
270 degrees
Answers
Answer:
180
Step-by-step explanation:
hope this helps you
Answer:
180 90plus90
Step-by-step explanation:
Which statements are true? Choose all answers that are correct. A. All quadrilaterals can be classified as either parallelograms or trapezoids. B. All rhombuses are parallelograms. C. Some trapezoids are parallelograms. D. Some parallelograms are squares.
Answers
Answer:
A, B and C
Step-by-step explanation:
A function is created to represent amount of money spent on lunch if you spent five dollars a day. What restrictions would be made to the range?
A. The range would only include integers
B. The range would only include negative integers
C. the range would only include positive integers
D. the range would include allreal number
Answers
State the slope of the line shown below.
0
1
–2
undefined
Answers
Answer: 0
Step-by-step explanation:
From then given graph , it can be seen that the line is parallel to x axis passing through [tex]y=-2[/tex].
We know that if two lines are paralleled then they have equal slope.
We know that the slope of x-axis is 0.
[∵[tex]\text{Slope=}\dfrac{\text{Change in y coordinates}}{\text{Change in x coordinates}}=\dfrac{0}{\text{Chnage in x coordinates}}=0[/tex]]
Hence, the slope of the given line =0
-2log5 7x=2
the 5 is small please help me
Answers
log_5[1/(7x)^2] = log_5 2
log_5(1/49x^2) = log_5 2
log_5(1 - 49x^2) = log_5 2
1 - 49x^2 = 2
You finish.
Kelly wants to know the actual value of a house that she wants to buy. What should she do?
Answers
for plato the answer is, c. get a real-estate appraisal
posting this for future users!
A snail travels 3/8 feet in 1/2 hour. How many feet did the snail travel in one hour.
Answers
HELP ASAP ALGEBRA 2 QUESTION PLEASE!!!
Consider the function f(x)=1/3 x+4.
Find the inverse of f(x) and name it g(x) . Show and explain your work.
Use function composition to show that and are inverses of each other.
Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.
Answers
f(x) is the same as y
y=1/3 x +4
to find inverse, swap and x and y:
x=1/3 y + 4
x-4= 1/3 y
(x-4) x 3 = y
3x -12= y
the inverse(g(x)), is: 3x-12
b) if f(x) and g(x) are inverses of each other, than (f о g)(x) will end up with just "x"
(f о g)(x)=x
(f о g)(x)= f(g(x))
(f о g)(x)= f(3x-12)
(f о g)(x)= 1/3(3x-12)+4
(f о g)(x)= (3x-12)/3 +4
(f о g)(x)= x-4+4
(f о g)(x)= x
c)
You will find that the graphs are mirror images of each other
the graph for f(x) is an oblique line that passes through the points(-12,4)
the graph for g(x) is an oblique line that passes through the points(4,-12)
the graph of the equation y=2x+b passes through the point (b, -3). Find b. PLZ SHOW WORK!
Answers
Substitute in the y value for the y in the equation and do the same for the x.
-3=2b+b
-3=3b
-1=b
b is -1.
Hope this helps!
Your fortune is "Stop procrastinating - starting tomorrow."
What conclusions can be made about the series ∞ 6 cos(πn) n n = 1 and the integral test?
Answers
A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. a marble is chosen at random from the jar. after replacing it, a second marble is chosen. what is the probability of choosing a green and then a yellow marble
Answers
if √a/√b=x, which statement must be true? A. x^2=a/b B. √x=a/b C. |x|=a/b D. x=a/b
Answers
Answer:
x^2 = a/b
Step-by-step explanation:
[tex]\frac{\sqrt{a}}{\sqrt{b} } =x[/tex]
If we have square root at the top and bottom then we take single square root with fraction inside
[tex]\sqrt{\frac{a}{b}} =x[/tex]
To remove square root we take square on both sides because square and square root will get cancelled
[tex]\frac{a}{b}=x^2[/tex]
x^2 = a/b is true
The statement that must be true is:
[tex]x^2 = a/b[/tex]
How to find an equivalent expression?
To find an equivalent expression, we just need to rewrite the given expression.
Here we will use the fact that the square root is distributive with respect to the division, which means that we can rewrite:
[tex]\frac{\sqrt{a} }{\sqrt{b} } = x\\\\\sqrt{\frac{a}{b} } = x[/tex]
Now if we square both sides of that expression, we will get:
[tex]\sqrt{\frac{a}{b} }^2 = x^2\\\\\frac{a}{b} = x^2[/tex]
So we can see that the correct option is A.
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High School Mathematics 5+3 pts
Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.
Answers
Find the total amount after 2 years of an investment of $1500 in an account paying 4% interest, compounded quarterly.
A=P(1+r/n)nt ( '' nt '' are exponents )
Question 1 options:
$1622.40
$1624.29
$1560
$1620
Answers
A=P(1+r/n)^nt
A future value?
P present value 1500
R interest rate 0.04
N compounded quarterly 4
T time 2 years
A=1,500×(1+0.04÷4)^(4×2)
A=1,624.29
So the answer is B
Hope it helps!
Will give brainliest to person who answers first. Much appreciated
1. The physical components of computers that carry out the basic operations are:
A: software
B:hardware
C:firmware
D:vaporware
2. The piece of computer hardware that manipulates a machines memory in order to create images rapidly is the:
A:cpu
B:gpu
C:rom
D:ram
3. Pong is the first real video/ computer game
A: true
B: false
4. The magnavox odyssey was a commercial success
A:true
B: false
Answers
2. is B. Gpu
3. false I am almost certain there was a version of a pong styled game manipulating roughly the sane code first.
4.false it was not considered a commercial success
2:c
3:b
4:a
I think these are right i might be wrong
Is 14/25 bigger than 0.75
Answers
A candle is 7 in. tall after burning for 1 h. The same candle is in. tall after burning for 4 h. How tall will the candle be after burning for 6 h?
Answers
After burning 6 hours the candle will be 4 1/2 in. tall.
Evaluate the expression 15/3x-6, when x=4.
Answers
___________________________________________________
15/ (3x - 6) ;
Substitute "4" for "x" ; and solve:
___________________________________________________
Note: (3x -6) = 3(4) - 6 = 12 - 6 = 6 ;
Rewrite the expression:
15/6 = (15 ÷ 3) / (6 ÷ 3) = 5/2 ; or, write as: "2 ½ " ; or, write as: "2.5" .
___________________________________________________
The expression 15/3x-6 evaluates to -4.75 when x=4. The solution involves substitution followed by the order of operations: first multiplication, then division, and finally subtraction.
The student asked to evaluate the expression 15/3x-6 when x=4. To do this, we first substitute the value of x into the expression, which then becomes 15/(3*4)-6.
Now we simplify the expression step by step:
Multiply 3 by 4, which is 12.Divide 15 by 12, which gives 1.25.Subtract 6 from 1.25, which results in -4.75.So, when x equals 4, the value of the expression 15/3x-6 is -4.75.
If log3(4y−1)=log3(2y+7), what is the value of y?
Enter your answer as a number, rounded to one decimal place, if necessary, like this: 42.5
Answers
This leaves:
4y-1=2y+7 (solve for y)
4y-2y=7-1
2y=6
y=3
Hope this helped :)
Which is the endpoint of a ray?
point R
point S
point T
point U
Answers
Hope this helps
The endpoint of a ray in the diagram given is the point S.
A ray is often referred to as the sides of a angle.
An angle is produced when two different rays share or have a common endpoint which forms the vertex.
From the diagram given above ; an angle is formed at S.
S depicts a point where three different rays meet.
Rays SR, SU and ST
SINCE , the point where two or more rays meet leading to the formation of an angle is called an endpoint. Then , point S is an endpoint.
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