The standard form of the equation for the given p value and theta is equal to -x + y = 26√2.
Standard form of the equation is :
x cosθ + y sinθ = p
Here p = 26 and theta 'θ' = 3π /4
Substitute the value in the standard form we get,
x cos (3π/4 ) + y sin( 3π /4 ) = 26
⇒ x cos ( π - π/4 ) + y sin ( π - π/4 ) = 26
⇒ - x cosπ/4 + y sinπ/4 = 26
Substitute the value of cosπ/4 and sinπ/4 is equal to 1/√2 we get,
⇒ -x /√2 + y / √2 = 26
⇒ -x + y = 26√2
Therefore, the standard form of the equation is equal to -x + y = 26√2.
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Courtney’s Bookstore is having a clearance sale. All paperbacks are one price and all hard covers are another price. Abigail buys 5 paperback books and 2 hardcover books for $29. Rodney buys 2 paperback books and 1 hardcover books for 13 dollars. What is the price of each type of book? Use a system of equations to solve.
Answer: Total price: $28.67
Step-by-step explanation: From Courtney Summers, the author of Cracked Up To Be, comes a dark new tale of high school rivalry in which vicious rumors and nasty tricks are the currency that buys you popularity or seals your fate at the bottom of the food chain.
Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 5 units long. Point C is on the line x = −2. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C. (1 point)
5
6
7
8
Answer: The area of right triangle ABC can be found using the formula (1/2)bh, where b is the length of the base and h is the height. Since the base of the triangle is 5 units and the area is 12.5 square units, the height must be 2.5 units.
Knowing that point C is on the line x = -2, we can use the height of 2.5 units to find the y-coordinate of point C.
Starting from the line y = 2, moving 2.5 units down will give us a y-coordinate of y = 2 - 2.5 = -0.5.
So, a possible y-coordinate of point C is -0.5.
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
A = 1/2 (b)(h)
12.5 = 1/2 (5)(h)
Multiply both sides by 1/2 or 2 to cancel out the fraction
2 x 12.5 = 1/2 (5)(h) x 2
25 = 5h
Divide both sides by 5 to get h on its own
25/5 = 5h/5
h = 5
HOWEVER, 5 is not our answer because we started on y = 2.
So,
5 + 2 = 7
what does it mean if the first of a two step tuberculin skin test is negative and the second is positive? what does it mean if both tests are negative?
It reads the second test. o Negative - assume that the person is not infected. o If positive, take a prior TB infection into consideration. Any asymptomatic person whose chest X-ray shows no signs of an active illness will be forwarded to the health department.
What brings about TB infection?
The bacteria Mycobacterium tuberculosis is the one that causes tuberculosis (TB).
When someone who has active TB disease in their lungs coughs or sneezes and the TB bacteria-containing droplets are ejected, the disease is disseminated when the other person inhales them.
What transpires if you have TB?
Feelings of sickness or weakness, weight loss, a high temperature, and nocturnal sweats are some of the common signs of TB disease.
Coughing, chest pain, and the coughing up of blood are other signs of TB lung disease. Depending on the location affected, TB illness symptoms may manifest in various body parts.
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As part of their opening day celebration, Benny’s Bakery made 150 cupcakes. The cupcakes all looked identical on the outside, but 6 of them had caramel inside. Customers who bought a cupcake with a caramel inside won a free cake. The cupcakes were randomly arranged and customers were allowed to choose their own cupcakes. Zoe was the first customer in line and bought three cupcakes. What is the probability that exactly one of Zoe’s cupcakes had caramel inside?
The probability that exactly one of Zoe's cupcakes had caramel inside after the cupcakes were randomly arranged and customers were allowed to choose their own cupcakes is 1/3266.
The probability that exactly one of Zoe's cupcakes had caramel inside can be calculated as follows:
P(exactly one cupcake with caramel) = (number of ways to choose one cupcake with caramel) / (total number of combinations of three cupcakes)
There are 6 cupcakes with caramel, so there are 6 ways to choose one cupcake with caramel.
Out of 150 cupcakes, there are 150 choose 3 = 19,600 ways to choose three cupcakes.
So, the probability that exactly one of Zoe's cupcakes had caramel inside is:
P(exactly one cupcake with caramel) = 6 / 19,600 = 1/3,266
Therefore, the probability that exactly one of Zoe's cupcakes had caramel inside is 1/3,266.
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1 kg of wheat costs $10 how much does 260g cost
a 14 oz bottle of hair gel lasts Emily 21 weeks. how long will and 18 oz bottle last her?
Answer:
27 weeks
Step-by-step explanation:
first you would figure out how long one oz. of hair gel would last her. You would do this by dividing 21 by 14. 21/14 is 1.5. Next, if 1 oz. lasts 1.5 weeks, and there is a 18 oz bottle, then all you need to do is multiply 18 by 1.5. 18 times 1.5 is 27. Therefore, an 18 oz. bottle of hair gel would last Emily 27 weeks.
Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!
Answer:
Angle D
Step-by-step explanation:
The answer should be Angle D
Answer:
hey! the answer is angle D
Because in quadrilateral ECFD and WVUX
Step-by-step explanation:
ANGLE E = ANGLE W
ANGLE C = ANGLE V
ANGLE F = ANGLE U
AND,
ANGLE D = ANGLE X
which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?
The expression fails to compute the area of a triangle having base b and height h is (1.0 /2.0)*b*h.
Therefore the answer is A.
The correct expression to compute the area of a triangle having base b and height h is (1/2) * b * h, or equivalently, 0.5 * b * h.
Expression A is incorrect because it uses floating-point division, which may result in round-off errors or inaccuracies in the computation.
Expression B is the correct expression because it uses integer division and the division by 2 is clear.
Expression C is also correct because it uses floating-point division and the division by 2.0 is clear.
Therefore, both expressions B and C are correct, and expression D is a correct equivalent form of B and C.
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--The question is incomplete, answering to the question below--
"which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?
A. (1.0 /2.0)*b*h
B. (1 /2)*b*h
C. (b*h)/2.0
D. 0.5*b*h"
There were 84 runners to start a race in the first half of the race 1/3 of them dropped out in the second half of the race 2/7 of the remaining runners dropped out how many runners finish the race 
Answer:
40
Step-by-step explanation:
84 runners to start a race
in the first half of the race 1/3 of them dropped out = 84/3 = 28 dropped out
so 56 left
in the second half of the race 2/7 of the remaining runners dropped out
2/7 *56 =16 dropped out
so 56-16 = 40 left
how many runners finish
40
Nader plans to buy a used car. He can afford to pay $280 at the end of each month for three years. The best interest rate he can find is 9.8%/a, compounded monthly. For this interest rate, the most he could spend on a vehicle is $8702.85. Determine the amount he could spend on the purchase of a car if the interest rate is 9.8%/a, compounded annually.
Nader can spend on the purchase of a car if the interest rate is 9.8%/a, compounded annually, is $8715.82
Compound interest is the interest that is earned on the principal amount of a loan or investment, as well as the interest that is earned on the accumulated interest.
In this case, Nader wants to purchase a used car and can afford to pay $280 per month for three years. He has found the best interest rate he can get, 9.8%/a, compounded monthly. However, if the interest rate is compounded annually, the most he could spend on the vehicle will be different.
To calculate this, we need to use the formula for compound interest, which is
A = P(1 + r)ˣ,
where A is the total amount, P is the principal amount, r is the interest rate, and x is the time period.
When we apply the values on it, then we get,
=> A = $8702.85(1 + 9.8)³
=> A = $8715.82
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a scatter plot shows multiple select question. if an obvious association exists between two variables. pairs of observations (x1, y1) . . . (xn, yn) on an x-y graph. only nonlinear relationships. only linear relationships..
A linear relationship can be expressed by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
This equation can be used to calculate the relationship between two variables, x and y. For example, if we have two sets of data points (x1, y1)…(xn, yn) we can calculate the slope m and the y-intercept b as follows:
m = (sum of (x_i - x_mean)*(y_i - y_mean))/(sum of (x_i - x_mean)^2)
b = y_mean - m*x_mean
Where x_mean and y_mean are the sample means of the x and y variables respectively.
Once we have calculated m and b, we can use the equation y = mx + b to describe the linear relationship between x and y. We can also use this equation to predict the value of y for a given x value. For example, if m = 2 and b = 0, then the equation becomes y = 2x and we can predict that when x = 1, y = 2.
In contrast, a nonlinear relationship is one which cannot be described by the equation y = mx + b, as the relationship between x and y is not linear. Instead, a nonlinear relationship is one in which the relationship between x and y is described by a more complex equation, such as y = ax^2 + bx + c.
To summarise, a linear relationship between two variables can be described by the equation y = mx + b, where m is the slope and b is the y-intercept, while a nonlinear relationship is one which cannot be described by this equation and is instead described by a more complex equation.
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A ballon archway has been ordered for decorating the high school gym for a 1950 style prom. The archway will contain 275 balloon , each holding 1. 2 liters of helium. Each balloon has a mass of 2. 7 milligrams when empty , and all the string and fixing that hold the balloon together total another 45 grams , If the helium has a density of 0. 1785 grams per liter , what is the mass of the entire archway ?
Step 1: Calculate the total volume of helium needed for the archway.
The total volume of helium needed for the archway is 275 balloons x 1.2 liters/balloon = 330 liters.
Step 2: Calculate the mass of the helium needed for the archway.
The mass of the helium needed for the archway is 330 liters x 0.1785 grams/liter = 58.85 grams.
Step 3: Calculate the mass of the balloons and string.
The mass of the balloons and string is 275 balloons x 2.7 milligrams/balloon + 45 grams = 74.75 grams.
Step 4: Calculate the total mass of the archway.
The total mass of the archway is the sum of the mass of the helium and the mass of the balloons and string.
Therefore, the total mass of the archway is 58.85 grams + 74.75 grams = 133.6 grams.
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Unemployment rose from January to March a year from 2.5% to 2.9%. How big was the increase in percentage points and in percent?
Answer:
0.4% increase although I don't know what a percentage point is sorry.
Step-by-step explanation:
Answer:
The increase in percentage points was 0.4
The increase in percent was 16%
Step-by-step explanation:
To find the increase in percent, divide the increase in percentage points by the initial unemployment rate and multiply by 100: (0.4 / 2.5) * 100 = 16%.
how much commission would a salesperson earn for selling a $25.000. car? he receives an 18% commission
The commission earned by the salesperson for selling a $25,000 car with an 18% commission rate can be calculated by multiplying the price of the car by the commission rate:
Commission = 0.18 * $25,000
Commission = $4,500
Therefore, the salesperson would earn a commission of $4,500 for selling the car.
2. Recall the 7 bridge problem you studied in this lesson. As you
saw, there was no possible path which uses each bridge once
and only once. This is because there were more than two dots
which had three lines connected to them.
Can you add a single bridge so that there is a path which
uses each bridge once and only once? Give one example
and indicate what points you have to use for your starting
and stopping point.
There is no possible way that you can add a single bridge so that there is a path that uses each bridge once and only once.
Hence, the answer is no solution.
What is the seven bridge problem?The seven bridges problem was seven bridges linking the various land masses of the town of Königsberg which straddles the Pregel River and that contained two islands.
The challenge was coming up with a route through the city that would only cross each of those bridges once. blatantly inappropriate. Euler demonstrated that the issue cannot be solved.
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If each quadrilateral below is a square, solve for x.
X =
Answer:
x=11°
Step-by-step explanation:
We can see that the square is split into 4 triangles. We also have the midpoint T. Because Each angle of a square is 90 degrees and ∠PQR is divided in half, m∠PQT=45 degrees. By substitution, (4x+1)=45°
Solve:
(4x+1)=45°
4x=44°
x=11°
PLEASE MARK AS BRAINLIESTThe number of bees in a large garden is decreasing by 2.5% every year. If this year it has 8 million bees, how many millions of bees will be there in 6 years? Round to the nearest hundredth. million bees
Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
Ravi had a rope. He used 45 cm of the rope to tie a parcel
He then cut the remaining rope equally into 4 pieces. Each piece was 65 cm long. (A)
As per unitary method,
a) The length of the rope left after tying the parcel 260 cm
b) The initial length of the rope was 305cm.
The unitary method is a mathematical tool used to solve problems involving the partition of a whole into parts.
(a) To find the length of the rope left after tying the parcel, we subtract the length of the rope used to tie the parcel from the initial length of the rope. The length of the rope left is:
=> Initial length of the rope - Length of rope used to tie the parcel = Length of rope left
We are told that Ravi used 45cm of the rope to tie a parcel. Therefore, the length of rope left can be expressed as:
Initial length of the rope - 45 = Length of rope left
(b) To find the initial length of the rope, we add the length of the rope used to tie the parcel to the length of the rope left.
We know that the length of the rope left is divided into 4 pieces of 65cm each. Therefore, the total length of the rope left is
=> 4 x 65 = 260cm.
We can now use this information to find the initial length of the rope:
Length of rope left + Length of rope used to tie the parcel = Initial length of the rope
260 + 45 = 305cm
Complete Question:
Ravi had a rope. He used 45cm of the rope to tie a parcel. He then cut the remaining rope equally into 4 pieces. Each piece was 65cm long.
(a) Find the length of the rope left after tying the parcel.
(b) How long was the rope at first?
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3/4 - 1 1/4
Just need an step by step
Answer:
Step-by-step explanation: 3/4 + 11/4= (3 + 11)/4
= 14/4
= 7/2 or 3[tex]\frac{1}{2}[/tex]
Jen is a biologist studying endangered and at-risk species in Mongolia. When she first started
studying the snow leopard population, she estimated that there were 1,000 snow leopards in
Mongolia. After one year, Jen estimated that the population had decreased to 990. She
expects the snow leopard population to continue decreasing each year.
Write an exponential equation in the form y = a(b) that can model the estimated snow
leopard population in Mongolia, y, in x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
00
(0)
To the nearest whole number, how many snow leopards can Jen expect there to be in
Mongolia in 5 years?
snow leopards
O
3
31
D
2
The population of the leopard in 5 years is 951
How to determine the exponential functionFrom the question, we have the following parameters that can be used in our computation:
Initial population, a = 1000
After one year = 990
This means that the rate r is
r = 990/1000
r = 0.99
The function is represented as
y = ar^x
So, we have
y = 1000(0.99)^x
In 5 years, we have
y = 1000(0.99)^5
y = 951
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HELP DUE TOMORROW WILL GIVE U BRAINLIEST!! solve for the value of q
Answer:
Step-by-step explanation:
The straight line is an angle of 180. If given an angle of 57 and 90, subtract from 180.
180 - 90 - 57 = 8q + 1
33 = 8q + 1
8q = 32
q = 4
in 1991, the moose population in a park was measured to be 3270. by 1997, the population was measured again to be 4770. if the population continues to change linearly: a.) find a formula for the moose population, , in terms of , the years since 1990
Step 1: Calculate the rate of change in the moose population.
The rate of change in the moose population can be calculated by subtracting the 1991 population (3270) from the 1997 population (4770) and dividing the result by the number of years (7).
Therefore, the rate of change in the moose population is (4770 - 3270) / 7 = 700 moose/year.
Step 2: Find the formula for the moose population in terms of the years since 1990.
The formula for the moose population in terms of the years since 1990 is P(t) = 3270 + 700t, where t is the number of years since 1990.
A population may grow as a result of certain changes. Animal populations that consume certain plants may grow if there are more plants present than typical in a region. If the population of one species rises, the population of animals that consume that animal may also rise.
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Help me please not sure how to do this. it doesn't make sense to me.
Answer:
? = 5cm
Step-by-step explanation:
We know the right side is 14 cm; that is the combination of the 9 cm and the length of the ?
So, to find the ? we take
14 - 9 = 5cm
So, the ? equal 5cm
Mr.White is renting a van for one week and a few additional days d he does not have to pay a per mile fee evaluate the expression 260+70d to find how much he will pay for a 10-day rental
Answer:
For a 10-day rental, d = 10 - 7 = 3 days.
Step-by-step explanation:
So, the total amount Mr. White has to pay is 260 + 70d = 260 + 70 * 3 = 260 + 210 = 470 dollars.
equations 4 x minus 5 y = 5, 3 x + 10 y = 20, 4 x minus 5 y = negative 5, and 3 x + 10 y = negative 20 are shown on the graph below.
On a coordinate plane, there are 4 lines. Green line goes through (0, 1) and (2.5, 3). Orange line goes through (0, negative 1) and (2.5, 1). Blue line goes through (0, 2) and (3.5, 1). Pink line goes through (0, negative 2) and (3.5, negative 3).
Which system of equations has a solution of approximately (–2.7, –1.2)?
4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20
4 x minus 5 y = 5 and 3 x + 10 y = 20
4 x minus 5 y = 5 and 3 x + 10 y = negative 20
4 x minus 5 y = negative 5 and 3 x + 10 y = 20
The solution is Option A.
The system of equations is 4x - 5y = -5 and 3x + 10y = -20
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
4x - 5y = -5 be equation (1)
3x + 10y = -20 be equation (2)
Now , the solution to the equations is ( -2.7 , -1.2 )
Substituting the values of x and y in the equation , we get
4 ( -2.7 ) - 5 ( -1.2 ) = -5
-10.8 + 6 = -5
-4.8 ≈ 5
And ,
3 ( -2.7 ) + 10 ( -1.2 ) = -20
-8.1 + ( -12 ) = -20
-8.1 - 12 = -20
-20.1 ≈ 20
Hence , the equations are 4x - 5y = -5 and 3x + 10y = -20
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In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands was only 200, but the population triples every 25 years. Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles. The total area of the Nisos Isles is 24,900 square miles. c In how many years, approximately, from 1998 will the population of Nisos be as large as Queen Irene has proclaimed that the islands can support?
The population of Nisos be as large as Queen Irene has proclaimed that the islands can support is 16600.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles.
The total area of the Nisos Isles is 24,900 square miles.
Here, 24,900/1.5
= 16600
Therefore, the population of Nisos be as large as Queen Irene has proclaimed that the islands can support is 16600.
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At lake view middle school, there are 2 homeroom teachers assigned to every 48 students. Is the number of students at this school proportional to the number of teachers? Explain your reasoning
Answer:
Yes
Step-by-step explanation:
Since it literally says "there are 2 homeroom teachers assigned to every 48 students", this means that it is a ratio because 2 teachers: 48 students are proportional.
the maximum weight, w, that a stepladder can hold is 250 pounds. which inequality represents this situation?
w ≤ 250
This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, the weight, w, must be less than or equal to 250 pounds.
The weight, w, must be less than or equal to 250 pounds. This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, if the weight of the object being placed on the stepladder is greater than 250 pounds, it is not safe to use the stepladder. This inequality helps to ensure the safety of the person using the stepladder, as it limits the amount of weight that can be placed upon it. Furthermore, it also helps to protect the stepladder itself, as it prevents it from being overloaded with too much weight, which could cause it to break or malfunction. In conclusion, the inequality w ≤ 250 represents the maximum weight that a stepladder can safely hold.
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Test (Spring 2023)
Solve the equation. Check your solution.
2x-4-18x + 4
Answer:
bring -18x to 2x
2x-18x
then bring -4 to +4
2x-18x+4-4
Find the number that should be added to the expression to create a perfect square trinomial.
x^2-7x+?
Answer:
To find the
c
value
c
=
(
b
2
)
2
, divide the coefficient of
x
by
2
and square the result.
49
4
Add
49
4
to get the perfect square trinomial.
x
2
−
7
x
+
49
4