Answer:
The rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3)
Step-by-step explanation:
The given polar coordinates is (7, 2·π/3)
Where, the 7 represent the distance, r, from the point of reference and 2·π/3, the angle, θ, from the reference point.
Polar coordinates are represented in rectangular form by the equivalence transformation equation given as follows;
The x-coordinate = Radius, r × cos(θ), which gives
We note that 2·π/3 radians = 2 × 180/3 = 120°
x = 7 × cos(2·π/3) = 7 × cos(120°) = 7 × (-0.5) = -3.5
x = -3.5
The y-coordinate = Radius, r × sin(θ), which gives
x = 7 × sin(2·π/3) = 7 × sin(120°) = 7 × (√3)/2 = 3.5·√3
y = 3.5·√3
Therefore, the rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3).
Evaluate f (x) = 2 x torx =-5.
Answer:
-10.
Step-by-step explanation:
f(x) = 2x, x = -5.
f(-5) = 2(-5)
= 2 * (-1) * 5
= 10 * (-1)
= -10.
Hope this helps!
A group of architects wish to recreate a modern pyramid like the ones built in
ancient Egypt. This huge monument is designed to have 199 stone bricks in the 5th
layer and 1 stone brick in the 27th and top layer. How many stones will they need to
build the entire pyramid?
Answer:
1,128,330 stones
Step-by-step explanation:
If you multiply how many total layers there are in the pyramid (210) by how many stones there are in each layer (199) before and after the 27th and top layer, you get 41790 stones. Then multiply the top 27 layers by the 41790 stones in those layers then you will get the total amount of stones which comes to 1,128,330 stones needed to build the entire pyramid.
8 m minus 6 less or equal than 10
Hi there! :)
Answer:
[tex]\huge\boxed{m\leq 2}[/tex]
Equation:
8m - 6 ≤ 10
Add 6 to both sides:
8m ≤ 16
Divide both sides by 8:
8m/8 ≤ 16/8
m ≤ 2
Answer:
8m - 6≤ 10
m≤2
Step-by-step explanation:
8m - 6≤ 10
Add 6 to each side
8m - 6+6≤ 10+6
8m ≤ 16
Divide each side by 8
8m/8 ≤16/8
m≤2
can someone explain mean and median to me?
Answer:
Mean is obtained by adding of all of the term values by the number of terms in a given set of data. Mean is also called "average".
Median on the other hand is the arrangement of numerical data in chronological order from least to greatest and finding the middle number from that arranged set of data.
Which equation represents a population of 300 animals that decreases at an annual rate of 23%? A. p=300(1.23)t B. p=300(1.77)t C. p=300(0.77)t D. p=300(0.23)t
For a given initial quantity A, a decrease of x% can be written as:
A - A*(x%/100%) = A*(1 - x%/100%)
With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:
P(t) = 300*(0.77)^t
Now let's see how we found that.
In this case, we know that:
The initial number of animals is 300.
They decrease at an anual rate of 23%.
This means that after the first year, the population will be:
P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)
After another year, the population decreases again, so we get:
P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2
Here we already can see the pattern, the population in the year t, we will get:
P(t) = 300*(0.77)^t
Then we can see that the correct option is C.
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Move ABC so it lies on top of , DEF, GHI and JKL. How many units do you have to move ABC from its original location to coincide with each of the other triangles? Specify how ABC moves up, down, left, or right.
Answer: triangleDEF - 3 units down
triangleGHI - 5 units left
triangleJKL - 4 units left and 5 units down
Step-by-step explanation:
When six basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order)=
Answer as a fraction = 1/720
Answer in decimal form (approximate) = 0.001388
Answer in percent form (approximate) = 0.1388%
========================================================
Explanation:
Let A = 1 to indicate the number of ways to get the names to line up in alphabetical order.
There are B = 6*5*4*3*2*1 = 720 different ways to arrange the six people. Notice how I started at 6 and counted my way down to 1, multiplying all along the way. This can be shortened to factorial notation to say 6! = 720. Or you could use the nPr permutation formula to get the same result (use n = 6 and r = 6).
Once you have the values of A and B, we form the fraction A/B = 1/720 which is the probability of getting the names in alphabetical order.
If you need the answer in decimal form, then use your calculator to find
1/720 = 0.001388
which converts over to 0.1388%
B is the midpoint of AC. What is the value of x if AC = 52 and AB = 3x - 4
Answer:
x = 10
Step-by-step explanation:
Since B is the midpoint of AC then AB = BC = 3x - 4 and
AB + BC = AC , thus
3x - 4 + 3x - 4 = 52, that is
6x - 8 = 52 ( add 8 to both sides )
6x = 60 ( divide both sides by 6 )
x = 10
calculate 6/√2 and express it in form of a√b
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \frac{6}{ \sqrt{2} } = \frac{6}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]
We can't have a fraction that has a number under square root as it's denominator. So we will have to rationalize it, which means we will multiply the numerator and also the denominator by the number that is under the square root.
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\sf 3\sqrt{2}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6}{\sqrt{2} }[/tex]
[tex]\sf Multiply \ both \ numerator \ and \ denominator \ by \ \sqrt{2}[/tex]
[tex]\displaystyle \frac{6 \times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }[/tex]
[tex]\displaystyle \frac{6\sqrt{2} }{2 }[/tex]
[tex]\sf Simplify[/tex]
[tex]3\sqrt{2}[/tex]
solving polynomial(2x+8)(-3y-8)
Answer:
-6xy - 16x -24y -64
Step-by-step explanation:
(2x+8)(-3y-8) =
To find the answer,
First multiply, the first number on both sides,
2x * -3y = -6xy
Then the first number on the left side and the second number on the right side,
2x * -8 = -16x
Then the second number on the left side and the first number on the right side,
8 * -3y = -24y
Then the second number on the left side and the second number on the right side,
8 * -8 = -64
Now add all the answers,
-6xy -16x -24y -64
Answer:
-6xy-16x-24y-64
Step-by-step explanation:
(2x+8)(-3y-8)
Foil
First 2x*-3y = -6xy
outer -8*2x = -16x
inner -3y *8 = -24y
last -8*8 = -64
Add them together
-6xy-16x-24y-64
What is the difference between a coefficient and variable (such as 3x) and a constant (5)? Why can these two types of terms not be combined?
Answer:
see below (I hope this makes sense!)
Step-by-step explanation:
Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.
The diagram shows 2 straight line , PQ and QR
Find the equation of QR
Help me to explain :)
Answer:
Step-by-step explanation:
We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:
3h + 4(3) = 6 and
3h + 12 = 6 and
3h = -6 so
h = -2
The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:
[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]
So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:
y - 8 = 1(x - 3) and
y - 8 = x - 3 and
y - x = 5 or
-x + y = 5. If your teacher does not want you to lead with a negative:
x - y = -5 would be your equation in standard form.
How would you write 7 is subtracted from the cube of a number
Answer:
n³ - 7
Step-by-step explanation:
n³ - 7
The required expression for the 7 subtracted from the cube of a number is x³- 7.
Given that,
A string of statements is given,
Here, we have to transform the statement, 7 is subtracted from the cube of a number into a mathematical inscription.
Arithmetic, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is an expression?A mathmetical expression is formulated structure of a statement using variables.
Let the number be x,
Now 7 subtracted from the cube of number x
= x³ - 7
Thus, the required expression for the 7 subtracted from the cube of a number is x³- 7.
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Find the area of the following rectilinear figure.
Answer:
Area : 14+10+40=64 square unit
Step-by-step explanation:
the area of the top rectangle with sides 2 and 7
A=2*7=14 square unit
the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5
Area=5*2=10 square unit
the bottom rectangle : sides 10 and 4
Area=10*4=40
add the areas : 14+10+40=64 square unit
Find the distance between the two points (-4,4) and (1,0)
Answer:
The answer is
[tex] \sqrt{41} \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
( x1 , y1) and ( x2 , y2) are the points
So the distance between (-4,4) and (1,0) is
[tex] \sqrt{( { - 4 - 1})^{2} + ( {4 - 0})^{2} } [/tex][tex] = \sqrt{ ({ - 5})^{2} + {4}^{2} } [/tex][tex] = \sqrt{25 + 16} [/tex]We have the final answer as
[tex] \sqrt{41} \: \: \: units[/tex]Hope this helps you
What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to
help find the height. Show your work.
Answer:
21.7 cm²
Step-by-step explanation:
Given:
Right ∆BCD,
<D = 60°
adjacent length = 5 cm
Required:
Area of ∆BCD
SOLUTION:
Step 1: find the height (opposite side length) of ∆BCD
[tex] tan(D) = \frac{opp}{adj} [/tex]
[tex] tan(60) = \frac{h}{5} [/tex]
Multiply both sides by 5
[tex] tan(60)*5 = \frac{h}{5}*5 [/tex]
[tex] tan(60)*5 = 8.7 cm [/tex] (approximated)
Step 2: find the area of ∆BCD
Area = ½*base*height
Area = ½*5*8.7 = 21.7 cm² (nearest tenth)
1) Which is a prime number?
19
15
18
22
Answer: 19
Definition:
Prime: Prime numbers are numbers that can only be multiplied ONE time.
Example: 19×1=19
Composite: Composite numbers are numbers that can be multiplied MORE THAN ONE time.
Number 15: 15×1=15, 15×2=30, 15×3=45
Number 18: 18×1=18, 18×2=36, 18×3=54
Number 22: 22×1=22, 22×2=44, 22×3=66
Answer: The answer is 19.
Step-by-step explanation:
Patrick deposited $6,875 into a savings account 17 years ago. The account has an interest rate of 4.9% and the balance is currently $15,734.11. How often does the interest compound
Answer:
Quaterly
Step-by-step explanation:
5. Eight adults and six children travel in a cable car.
Estimate the total mass of the people in the cable car.
Answer: 1880 pounds
Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs
Mrs. Galindo decided to make Kool-Aid to serve along with the pizza at the Future Farmers of America party. The directions said to mix a half of a scoop of powdered drink mix with two gallons of water to make each pitcher of Kook-Aid. One of Mrs. Galindo's students said she will mix 4 scoops with 2 gallons of water to make 4 pitchers. Which choice best explains whether the student is correct and why. Question 1 options: The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is correct because 4 pitchers = 4 scoops times 2 gallons The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons The direction's constant of proportionality is 0.25 k = 0.5/4 There is a quarter of a gallon of water per one scoop The student is correct because 4 pitchers = 4 scoops times 2 gallons The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons
Answer:
The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons
Step-by-step explanation:
Direction :
1/2 of a scoop + 2 gallons = 1 pitcher
Mrs. Galindo's students:
4 pitcher = 4 scoops + 2 gallons of water
Correct mixture for 4 pitchers:
1/2 scoop + 2 gallons of water =1 pitcher
For 4 pichers, multiply both sides by 4
1/2(4) scoops + 2(4) gallons of water =4 pitchers
4/2 scoops + 8 gallons of water =4 pitchers
2 scoops + 8 gallons of water =4 pitchers
The direction's constant of proportionality is 4. k = 2/0.5 There are 4 gallons of water per one scoop. The student is incorrect because 4 pitchers does not equal 4 scoops times 2 gallons
...................................................
Answer:
11.21157846 =x
Step-by-step explanation:
We know log b (a) = c can be written as b^c =a
log 3 (x) = 2.2
3^2.2 = x
11.21157846 =x
Answer:
[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]
Step-by-step explanation:
[tex]\large \sf log_3 (x)=2.2[/tex]
Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:
[tex]\large \sf log_b(y)=x[/tex]
[tex]\large{\sf y=b^x}[/tex]
Apply the relationship.
[tex]\large \sf log_3 (x)=2.2[/tex]
[tex]\large \sf x=3^{2.2}[/tex]
[tex]\large \sf x=11.21157845...[/tex]
[tex]\large \sf x \approx 11.21[/tex]
the difference between y and 3/8 is 3/4. workout the possible values of y
Answer:
y-3/8 =3/4y=3/4-3/8y=3/8plz help ASAP!!!!!!!!!!!!!
Answer:
3rd option is correct
Step-by-step explanation:
If the table represents a function, that means that it is proportional. But the value increases and decreases, showing no proportional relationship.
So, the answer could be 1st or 3rd as they tell that the table doesn't represent a function.
1st answer says the table doesn't represent a function because the 2 (y-values) are similar;
Their x-values are different so, this answer is wrong.
3rd answer says that the table doesn't represent a function x-value increases, while y-value increases and decreases;
The statement is correct because it this table doesn't represent a proportional relationship as its y-values are increasing and decreasing while its x-values are only increasing.
So, the 3rd option is correct.
A blue print for a house has a scale of 1:10. A wall in the blueprint is 8in. What is the length of the actual wall?
6.67. inches
80 feet
969 feet
6.67 feet
Answer:
80 feet
Step-by-step explanation:
1 inch represents 10 feet
Then 8 inches represent = 8 × 10
= 80 feet
when would you write an x in an equation?)
Answer:
[tex]\Large \boxed{\mathrm{When \ a \ number \ is \ not \ known}}[/tex]
Step-by-step explanation:
For example, a sum of a number and 6 is 12.
The number is unknown.
Let the number be x.
x + 6 = 12We can solve for x (unknown number). Subtract 6 from both sides of the equation.
x = 6Question 2(Multiple Choice Worth 1 points) (06.03 MC) Choose the correct simplification of the expression (5xy5)2(y3)4 A.25x2y22 B.10x2y22 C.25x3y14 D.10x3y14
Question 3(Multiple Choice Worth 1 points) (06.05 MC) Aurora is selling tickets to a carnival. The function f(x) = 0.5x represents the amount of money Aurora earns per ticket, where x is the number of tickets she sells. The function g(x) = 8x represents the number of tickets Aurora sells per hour, where x is the number of hours she works. Find f(g(x)), and explain what it represents.
Answer:
Question 2;
A. 25·x²·y²²
Question 3;
f(g(x)) = 4·x, represents the amount Aurora earns per hour
Step-by-step explanation:
Question 2;
(5·x·y⁵)²(y³)⁴ = (25×x²×y¹⁰)×y¹²
(25×x²×y¹⁰)×y¹² = 25×x²×y¹⁰⁺¹² = 25×x²×y²²
Therefore, the correct option is A. 25·x²·y²²
Question 3;
The given functions are;
The function f(x) = 0.5·x is the earnings of Aurora per ticket sold
The function g(x) = 8·x is the number of tickets Aurora sells per hour
Therefore, we have;
f(g(x)) = 0.5 × g(x) = 0.5 × 8·x = 4·x
The value of the function of a function f(g(x)) = 4·x, represents the amount Aurora earns per hour.
jessica weighs x+34 pounds and Ronda weighs 12 pounds less. If Jessica gains 5 pounds and Ronda loses 2 pounds, what is the sum of their new heights.
Answer:
2x+59.
Step-by-step explanation:
Let J represent Jessica's weight and R represent Ronda's weight.
Jessica weighs x+34 pounds. Thus:
[tex]J=x+34[/tex]
Ronda weighs 12 pounds less than Jessica. In other words:
[tex]R=J-12=(x+34)-12\\R=x+22[/tex]
The sum of their weights, therefore, is:
[tex]J+R\\=(x+34)+(x+22)=2x+56[/tex]
Now, if Jessica gains 5 pounds and Ronda loses 2 pounds, the net gain of the total weight would be 3 pounds. Thus, we only need to add 3 to the original total to find the sum of their new weights:
[tex]2x+56+3=2x+59[/tex]
The sum of the new [weights] is represented by 2x+59.
Andrea is comparing the prices charged by two different taxi firms.
Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey, and there is a linear relationship between the price and the length of the journey.
Firm B charges a pickup fee of £3 and then £2.40 for each mile travelled.
Find the length of the journey for which both firms would charge the same amount.
Answer: 17.5 miles
Step-by-step explanation:
P=price, L=length
Firm A:
P=2L+10
Firm B:
P=2.40L+3
2.40L+3=2L+10
L=17.5
The fare would be the same for 17.5 miles for both firms.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have, 20=5x+k. . . (1)
30=10x+k. . . .(2)
solving these two equations we get x=2 and k = 10
Now let the length of the journey that both firm charge the same is equal to L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get
2L+10=2.40L+3
0.40L=7
L=17.5
Hence, The fare would be the same for 17.5 miles for both firms.
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find the Perimeter Of a circle whose radius is 14cm
Answer:
88 cm
Step-by-step explanation:
Perimeter = 2πr
=2(14)(22/7)
= 88 cm
Answer:
87.97cm
Step-by-step explanation:
This question is asking to solve for the circumference.
The formula for the circumference of a circle is: [tex]\pi*diameter[/tex]
To work this out you would first need to multiply the radius of 14 by 2, this gives you 28cm. This is because the radius is half of the diameter.
The final step is to multiply pi by the diameter of 28, this gives you 87.97cm (87.9645943). This is because the formula for the circumference of a circle is [tex]\pi * diameter[/tex].
1) Multiply 14 by 2.
[tex]14*2=28[/tex]
2) Multiply pi by the diameter.
[tex]\pi*28^2=87.97 cm[/tex]
Howard earns $46 for every 2 hours of work. What is the constant of proportionality in the scenario?
Answer:
23
Step-by-step explanation:
Take the amount of money and divide by the hour
46/2 = 23
23 dollars for every hour
The constant of proportionality is 23
