Answers
90p = 20p +50(p+600)
90p = 70p +30000 . . . . . . . eliminate parentheses
20p = 30000 . . . . . . . . . . . . subtract 70p
p = 1500 . . . . . . . . . . . . . . . . divide by 100
There were originally 1500 people in the fort.
Related Questions
Given: triangle ABC, AB = BC Perimeter of ΔABC = 50 Perimeter of ΔABD = 40 Find: BD
Answers
The measure of angle ABC and BDC is 80° and 90° respectively.
What is the triangle?In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.
We have to find the measure of angle ∠ABC and ∠BDC.
As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.
[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]
Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.
∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
To know more about triangles click the link given below.
https://brainly.com/question/12636178
#SPJ3
Find the length of JK and the measure of M
Answers
You have two different situations, but both of them are solved the same way.
Step One
Solve for the 2 equal sides.
21x - 9 = 3x + 27 Add 9 to both sides.
21x = 3x + 27 + 9
21x = 3x + 36 Subtract 3x from both sides.
21x - 3x = 36
18x = 36 Divide by 18
x = 36/18
x = 2
That's not quite the answer
Step Two
Find JK
JK = 21x - 9
JK = 21*2 - 9
JK = 42 - 9
JK = 33 <<<<<<< Answer
Step Three
Solve for y
5y + 11 = 12y - 10 Subtract 5y from both sides.
11 = 12y - 5y - 10
11 = 7y - 10 Add 10 to both sides.
11 + 10 = 7y
21 = 7y Divide by 7
21/7 = y
3 = y
Step Four
Solve for M
M = 12y - 10
M = 12*3 - 10
M = 36 - 10
M = 26 <<<<< Answer
M = 74
Hope this Helped!
;D
Brainliest??
Quadrilateral has angles 45 degrees, 150 degrees, 65 degrees, and N degrees
Answers
other angles=260
all interior angles of a quadrilateral add up to 360
Q # 8 please solve the question
Answers
Their sum is 20, so we can write
x + y = 20
Their difference is 14, so we can write:
x- y = 14
Adding the two equations, we get:
2x = 34
x = 17
Using the value of x, in first equation, we get:
17 + y = 20
so,
y = 3
Thus the two numbers are 17 and 3.
So, option a is the correct answer
x + y = 20
x-y = 14
Where,
x: real number
y: real number
Solving the system we have:
x = 17
y = 3
Therefore, the numbers are:
17 and 3
Answer:
17 and 3
option 1
From a group of 3 men and 4 women, a delegation of 2 is selected. let x be the random variable that represents the number of women selected. write the probability distribution and find the expected number of women in the delegation?
Answers
x values are 0, 1, 2, 3
The corresponding probabilities are:
P(x=0)= 3C2/7C2=3/21
P(X=1)=3C1*4C1/7C2=12/21
P(X=2)=3C2/7C2=3/21
P(X=3)=3C2/7C2=3/21
Hence the expected value will be:
E(x)=[0*3+1*12+2*3+3*3]/21
E(x)=27/21=1.29
Cards are dealt, one at a time, from a standard 52-card deck. a if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades?
Answers
Then third card being spades would be 11 / 50
Now there are 10 spades and 49 cards left.
So the probability for fourth card would be 10 / 49
Fifth card would be 9 / 48.
So the probability of next three cards being spades would be
[tex]\dfrac{11}{50}\cdot\dfrac{10}{49}\cdot\dfrac9{48}=\dfrac{33}{3920}\approx\boxed{0.00842}[/tex]
Hope this helps.
A theater received $8,917 in ticket sales for one performance of a play. Tickets for preferred seats cost $45 each and regular seats cost $34 each. All of the theaters 75?preffered seats were sold out that evening. How many tickets were sold?
Answers
P = Number of ticket for preferred seats costing $45 per seat
R = Number of regular seats costing $34 per seat.
Total revenue = P*45 + R*34 =8,917
45P + 34R = 8917
But, number of preferred seats is 75 or P=75 seats
Then,
45*75 +34R = 8917
3375 +34R = 8917
34R = 5542
R = 5542/34 = 163
Total number of seats = P+R = 75+163 = 238 seats. If each seat is sold for one ticket, then 238 tickets wee sold.
Question# 12, find the slope
Answers
(0,1) and (-4, -2)
Slope = m = (-2 - 1)/(-4 -0 ) = -3/-4 = 3/4
So the slope of given line is 3/4
Thus the correct answer is option B
m = (y2-y1) / (x2-x1)
We choose the ordered pairs:
(x1, y1) = (0, 1)
(x2, y2) = (4, 4)
Substituting values we have:
m = (4-1) / (4-0)
m = (3) / (4)
m = 3/4
Answer:
The slope for this case is given by:
m = 3/4
option 2
what is the value of x sin x + 11 degrees equals cos 2x + 22 degrees enter your answer in the Box
Answers
(x + 11) + (2x + 22) = 90
Simplifying,
3x + 33 = 90
Further simplification,
3x = 90 - 33 = 57
The value of x from the equation is 19.
Answer: x = 19
Answer:
it is 19
Step-by-step explanation:
I just took this test and got 100 :)
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?
Answers
x / y
Where,
x = numerator
y = denominator:
If the numerator of a fraction is increased by 3, the fraction becomes 3/4:
(x + 3) / y = 3/4
If the denominator is decreased by 7, the fraction becomes 1:
x / (y-7) = 1
Solving the system of equations we have:
x = 9
y = 16
The original fraction is:
9/16
Answer:
the original fraction is:
9/16
"If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is:
(x + 3) / y = 3/4
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.
Answers
ω = d/(t*r) = (14.13 ft)/((3 s)*(6 ft))
ω = 0.785 radians/second
There are 180/π degrees per radian, so the angular velocity can also be written as ...
ω = 45 degrees/second
given that an arithmetic sequence can be expressed as a linear function in the form f(x)=mx+b, write a linear function to describe the sequence {10,15,20,25,30,35...}
Answers
m = (y2-y1) / (x2-x1)
m = (15-10) / (2-1)
m = 5/1
m = 5
Then,
y-yo = m (x-xo)
where,
(xo, yo) = (1, 10)
Substituting:
y-10 = 5 (x-1)
y = 5x -5 + 10
y = 5x + 5
Answer:
a linear function to describe the sequence is:
y = 5x + 5
Answer:
a linear function to describe the sequence is:
y = 5x + 5
Step-by-step explanation: ik ur on usa te$t prep
Brad has 3 pairs of pants, 7 tee shirts, and 2 pairs of sneakers. How many different outfit combinations can he wear
Answers
Answer:
42
Step-by-step explanation:
Which answer shows a correct order to solve this story problem? Maurine had to pay $2.52 tax on her purchases. She bought 3 books for $12.99 each, 2 pens for $0.69 each, and a magazine for $2.99. How much did Maureen spend? A. Step 1: Add the price of a book and a pen. Step 2: Multiply by 3 and then by 2. Step 3: Add $2.99 to that result. Step 4: Add the tax to the total of the purchases. B. Step 1: Calculate the total price of the 2 pens. Step 2: Add $2.99 to that total. Step 3: Calculate the total price of the 3 books. Step 4: Add the tax to the price of the 3 books C. Step 1: Calculate the total price of the 3 books. Step 2: Calculate the total price of the 2 pens. Step 3: Add $2.99 to the total of the cost of the books and pens. Step 4: Add the tax to the total of the purchases. D. Step 1: Add $2.99 to the amount of the tax. Step 2: Calculate the total price of the 2 pens. Step 3: Calculate the total price of the 3 books. Step 4: Add the prices of the pens to the price of the books.
Answers
C. Step 1: find the price of the books; Step 2: find the price of the pens; Step 3: add the prices of the books, pens, and magazine; Step 4: add the tax.
_____
You can, of course, find and add the constituent prices in any order. Generally, you need to know that subtotal in order to figure the tax, which is then added to that subtotal. If you've ever done any shopping at a store where bills are added manually, or if you pay attention to any cash register receipt, you know this is the process.
David is making a mosaic using 63 glass tiles 105 ceramic tiles and 84 marble tiles he wants to put the same number of each type of tile and Rose what is the maximum number of times you can have in each row
Answers
David can put 21 of each kind of tile in a row.
_____
These numbers are 3*21, 4*21, and 5*21, respectively.
A snow storm left 1.25 feet of snow on the ground overnight. At noon today, the temperature will be above freezing and the snow will melt. If the melting snow is modeled by the equation y = -1 3 x + 1.25, how long will it take for the snow to melt away?
Answers
0 = -13x + 1.25
-1.25 = -13x
3.75 = x
then,
3.75 hours to 3 hours 45 minutes
An electrolyte solution has an average current density of 111 ampere per square decimeter \left( \dfrac{\text{A}}{\text{dm}^2}\right)( dm 2 A )left parenthesis, start fraction, A, divided by, d, m, start superscript, 2, end superscript, end fraction, right parenthesis. What is the current density of the solution in \dfrac{\text{A}}{\text{m}^2} m 2 A start fraction, A, divided by, m, start superscript, 2, end superscript, end fraction?
Answers
We have to find the average current density of the solution in ampere per square meter.
1 decimeter = [tex] \frac{1}{10} [/tex] meter
Squaring both sides we get
1 decimeter square = [tex] \frac{1}{100} [/tex] meter square
Current density = [tex]1 \frac{A}{dm^{2} } =1 \frac{A}{ \frac{1}{100} m^{2} } =100Am^{-2} [/tex]
Thus, the density of electrolyte solution is 100 ampere per square meter
Answer:
Answer is 100
Step-by-step explanation:
hey can you please help me posted picture of question
Answers
C. G(x)=(x-2)^3
The explanation is shown below:
1. You have the the red graph has the equation F(x)=x^3
2. If you shifted two units to the right, you must add -2 to the function x^3, as below:
G(x)=(x-2)^3
3. If you want to verify this is correct, you need to give values to the variable x and plot each point.
4. You will see that the correct answer is the option mentioned above.
What are the zeros of the function?
F (X) = x^3 - x^2 - 6x
A) -1, 0, and 3
B) -3, 0, and 1
C) -3, 0, and 2
D) -2, 0, and 3
Answers
if to re-write the function f(x)=x(x²-x-6), then to make up the equation x(x²-x-6)=0, it is possible to find the zeros requred:
x(x-3)(x+2)=0, x=0;x=-2;x=3.
answer: D -2;0;3
Regina's mom bought her some bracelets. There were a total of 85 bracelets in 5 packages.
Which of the following equations would describe n, the number of bracelets that were in one package?
A. n + 5 = 85
B. n ÷ 5 = 85
C. n - 5 = 85
D. n × 5 = 85
Answers
Find a unit vector that is perpendicular to the vector 5, −4
Answers
[tex]( \frac{4}{ \sqrt{41} } , \frac{5}{ \sqrt{41} } )[/tex]
find 1/9 as many as 3 divided by 5
Answers
Final answer:
To find 1/9 as many as 3/5, you multiply 3/5 by 1/9 to get 3/45, which simplifies to 1/15.
Explanation:
To solve the student's question, we need to find what is 1/9 as many as 3/5. This involves multiplying the fraction 3/5 by the fraction 1/9. Here is the step-by-step calculation:
Multiply the numerator of the first fraction (3) by the numerator of the second fraction (1) to get the numerator of the answer.Multiply the denominator of the first fraction (5) by the denominator of the second fraction (9) to get the denominator of the answer.Combine these to get the answer in fractional form.The calculation will look like this: (3/5) × (1/9) = 3/45 = 1/15.
Thus, 1/9 as many as 3/5 is 1/15.
Two graphs are shown below:
graph A shows scatter points 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 5graph A shows scatter points 1, 4 and 2, 4 and 3, 4 and 4, 4 and 5, 4
Which scatter plot shows a positive correlation between x and y?
Only graph A
Only graph B
Both graph A and graph B
Neither graph A nor graph B
Answers
The correct answer is graph A
Nan and sato are designing a coffee table would you sing 4 inches tile Nan uses 30 tiles and sato uses half as many many total tiles did they use
Answers
it is assumed that the tile is square
area of the square=b²
b is the length side of a square
b=4 in
area of the tile=4²----> 16 in²
Part 1) How many total tiles did they use?
Nao uses 30 tiles
and
Sato uses (1/2)*30=15
so
Nao and Sato uses----> 30+15----> 45 tiles
the answer Part 1) is
45 tiles
Part 2) If the area of the table is 36 inches by 26 inches, will they have enough tiles for the table?
find the area of the table
area of the table=36*26----> 936 in²
area of one tile=4*4----> 16 in²
if 1 tile------------------> 16 in²
x tiles-------------> 936 in²
x=936/16----> x=58.5 tiles
58.5 > 45
so
there are not enough tiles for the table
the answer part 2) is
there are not enough tiles for the table
Part 3) If not, how many more will they need?
tiles required=58.5-45------> 13.5-----> 14 tiles
the answer part 3) is
14 tiles
Nan and Sato together used 45 tiles for their coffee table design.
The student's question involves calculating the total number of tiles used by two individuals, Nan and Sato, who are designing a coffee table. Nan uses 30 tiles, and Sato uses half as many tiles as Nan does. To find out how many tiles Sato uses, we divide Nan's number of tiles by 2.
So, Sato uses 15 tiles because half of 30 is 15. To find out the total number of tiles used, we add Nan's tile count to Sato's tile count:
30 tiles (Nan) + 15 tiles (Sato) = 45 tiles in total.
Therefore, to determine the total number of tiles used, Nan's 30 tiles are added to Sato's 15 tiles (half of Nan's), resulting in a total of 45 tiles used for the coffee table design.
PLEASE HELP!
1. If you cut out all the nets carefully, fold along the inside lines and tape edges together to form 5 figures. Describe the figures formed. What shapes are they? Are any the same?
2. What does the fact that the figures fit together to make the prism tell you about their combined volume?
Answers
The first picture is A. The rest should be in order like this: A, B, E, D,C.
Yes I know I did a crummy job at taping but hey, I tried.
Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days.
Answers
Is that what you meant for the problem
or do u want to know how many yards he sprinted total for the 21 days
If it is,
he sprinted a total of 3390 yards
On Apex the correct one is 200 yards.
A display that shows how the values in a data set are distributed
Answers
Answer: Line Plot
Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.
Answer: histogram
Step-by-step explanation:
What is the ratio (fraction) of minivans to all vehicles on the forecourt?
A)1/120
B)1/20
C)1/6
D)1/4
Answers
20/120
1/6
I hope this helps
do u do keystone
? im just wondering i do
What is the distance d across the lake?
Answers
Answer-
The distance d across the lake is 90ft.
Solution-
In the picture,
ΔABC ≈ ΔCDE
Because,
∠ACB = ∠DCE (∵ vertical opposite angles)∠B = ∠D = 90°∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)So, from similarity properties
[tex]\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}[/tex]
[tex]\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}[/tex]
[tex]\Rightarrow d=\dfrac{120\times 15}{20}=90[/tex]
Find (tan A+B) if A and B are in quadrant 2 with tan A=(1/3) and sin B=(20/29)
Answers
The value of [tex]\( \tan(A + B) \)[/tex] in quadrant 2, where [tex]\( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], is [tex]\( \frac{11}{57} \)[/tex].
Explanation:To find [tex]\( \tan(A + B) \)[/tex], we can use the formula [tex]\( \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \)[/tex]. Given that \[tex]( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], we can determine [tex]\( \cos B \)[/tex] using the fact that [tex]\( \sin^2 B + \cos^2 B = 1 \)[/tex]. Therefore, [tex]\( \cos B = \sqrt{1 - \sin^2 B} = \frac{21}{29} \)[/tex].
Now, substitute the values into the formula for [tex]\( \tan(A + B) \)[/tex]:
[tex]\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \][/tex]
[tex]\[ = \frac{\frac{1}{3} + \frac{20}{29}}{1 - \frac{1}{3} \cdot \frac{20}{29}} \][/tex]
[tex]\[ = \frac{\frac{29 + 60}{87}}{\frac{87 - 20}{87}} \][/tex]
[tex]\[ = \frac{\frac{89}{87}}{\frac{67}{87}} \][/tex]
[tex]\[ = \frac{89}{67} \][/tex]
Therefore, [tex]\( \tan(A + B) = \frac{11}{57} \)[/tex] in quadrant 2.
To find (tan A+B) when A and B are in quadrant 2, find the components of A and B along the x- and y-axes using A = 34.0 m, θA = 63.0°. Calculate Ax = A cos θA and Ay = A sin θA. Then use the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B) to find the sum of the tangents.
Explanation:First, we find the components of A and B along the x- and y-axes. From the problem, we know that A = B = 34.0 m, and θB = 63.0°. We find the x-components by using Ax = A cos θ, which gives Ax = 34.0 cos 63.0° = -15.23 m.
Similarly, we find the y-components by using Ay = A sin θ, which gives Ay = 34.0 sin 63.0° = 29.88 m.
Now, we can find the sum of the tangents of A and B using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B). Substituting the given values, we have tan(A + B) = (1/3 + Ay/Ax) / (1 - (1/3)(Ay/Ax)).