Answer:
Reflexive Property
A man walks 4km from point x due east of point Y. The bearing of a flag point x and y are due N80°W and N40°E respectively. Find the distance of the flag pole from point y
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
The triangle formed has angles A = 10°, B = 50°, C = 120°, c = 4 km, a = distance from point y.
Hence:
a / sinA = c / sinC
a / sin(10) = 4 / sin(120)
a = 0.8 km
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
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Please Help!!!!!
Write the equation of a parabola with focus (-1, 3) and directrix x = -5. Also include a sketch of the parabola. Show all your work.
Answer:
Equation of parabola is (x+1)²=20(y-3)
Step-by-step explanation:
And the graph above
(x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given, focus : (-1, 3)
directrix : x + 5 = 0 or x=-5
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
squaring both sides,
(x+1)²+(y-3)²=(x+5)²
(x+1)²=20(y-3)
Hence, (x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
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F(x)= (x-2)(x+4)(x+5)What is the sign of f on the interval -4
By evaluating the polynomial, we will see that the sign on the interval [-4, 2] is negative.
What is the sign of f on the interval [-4, 2]?Here we have the polynomial:
f(x) = (x - 2)*(x + 4)*(x + 5).
You can see that the roots of the polynomial are at:
x = 2
x = -4
x = -5.
Then, on the interval [-4, 2], the sign of the polynomial don't change. So to get the sign of f(x) on that interval we can just evaluate it in any value of x that belongs to the interval, for example, x = 0.
f(0) = (0 - 2)*(0 + 4)*(0 + 5) = -2*4*5 = -40
With this, we can conclude that the sign of f(x) on the given interval is negative.
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Answer:
always negative
Step-by-step explanation:
In the following situation, determine whether you are asked to determine the number of permutations or combinations. Then do the calculation.
How many ways are there to distribute 8 different books among 21 children if no child gets more than one book?
a.) Combination; Subscript 13 Baseline C Subscript 8 Baseline = 1287
b.) Combination; Subscript 21 Baseline C Subscript 8 Baseline = 203,490
c.) Permutation; Subscript 21 Baseline P Subscript 8 Baseline = 8,204,716,800
d.) Permutation; Subscript 13 Baseline P Subscript 8 Baseline = 51,891,840
Using the permutation formula, it is found that the number of ways to distribute the books is given by:
c. 8,204,716,800
The order is important, as the books are different, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 8 books are distributed among 21 children, hence the number of ways is given by:
[tex]P_{21,8} = \frac{21!}{13!} = 8,204,716,800[/tex]
Which means that option c is correct.
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At which point in the business cycle would the unemployment rate begin to increase? 1 2 3 4
Answer:
2 & 3
Step-by-step explanation:
2. High Interest Rates
High-interest rates make it more difficult for businesses to invest. For instance, a small store that is just starting is going to find it hard to make repayments at an interest rate of 20 or 30 percent. It also sucks out money from the economy and re-directs it to the banks. As the interest rates are so high, businesses and consumers reduce their demand for credit. In turn, there is a contraction in the money supply which can lead to deflation.
The effects of high interest rates can be dire if not managed correctly and subtly by central banks. If the interest rates are increased too fast, too high, and too rapidly, we will see the aforementioned effects such as lower business investment and deflation. Therefore, it can contribute to a transition towards an economic contraction in the business cycle.
3. Declining Real Incomes
Inflation can create a drain on consumer incomes as it decreases its value year on year. Therefore, if firms do not increase wages in line with inflation, the average worker will be able to afford less than before.
If real incomes decline, it means consumers have less income to spend on goods and services in the economy. In turn, a prolonged period of decline in real incomes can contribute to an economic contraction in the business cycle.
Answer
is 3 just did it on edge
Step-by-step explanation:
A 4-digit combination lock can be opened only if a correct combination of digits from 0-9 is chosen. Find the probability of guessing the correct combination if: none of the digits are repeated, any of the digits can be repeated, any of the digits can be repeated but the 3 and 8 are not in the combination.
The probabilities are as follows:-
if none of the digits is repeated 0.504If any of the digits can be repeated 1If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability will be calculated as follows:-
Total combinations are = 10⁴ = 10000
A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040
Probability = 5040 / 10000
Probaility = 0.504
B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000
Probabilityy = 10000 / 10000 = 1
C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401
Probability = 2401 / 10000 = 0.24
Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.
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Which rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C'?
The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
What is translation?When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).
The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).
From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.
Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)
Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
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The following clues will help us identify a shape:
The shape has no right angles.
The shape has no pairs of sides of equal length.
The shape is not a triangle.
it is a circle
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In the first picture can you please answer all of them in order I'm not sure if my answers are correct.
The number of cookies packs needed if the treasurer buys 1 package of brownies bites is 5 packs
EquationTotal attendance = 75 peopleCookies in each pack = 12Brownies in each pack = 15Number of cookies pack = cNumber of brownies pack = b15b + 12c = 75
If 1 package of brownies is bought
15b + 12c = 75
15(1) + 12c = 75
15 + 12c = 75
12c = 75 - 15
12c = 60
c = 60/12
c = 5 packs
It is a reasonable value in this contextIf 9 packages of brownies are bought
15b + 12c = 75
15(9) + 12c = 75
135 + 12c = 75
12c = 75 - 135
12c = -60
c = -60/12
c = -5 packs
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How many different committees
with 4 members can be formed
from a group of 8 people?
Answer:
70 is the right answer....
Answer:
70 ways
Step-by-step explanation:
8 C 4 = 8 ! / ( 4! * 4!) = 70 ways
Question 1 of 20
The volume of a rectangular box is 5x(x+3)(2x - 1).
Height: 2x-1
Length: x + 3
Width: 5x
Which statement is true?
A. The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
B. The volume is the sum of the length, x + 3, the width, 5x, and the
height, 2x - 1.
C. The volume is the product of the length, x + 3, and the width, 5x.
D. The volume does not depend on the height, 2x - 1.
Answer:
A. The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
Step-by-step explanation:
Volume is defined as the product of the Length, Width, and Height,
V = L*W*H
The Length x Width is the Area of the Base
L*W = Area Base)
Therefore:
The (L*W) in the equation V = L*W*H can be replaced with [Area of the Base]
[Area of the Base]
[Area of the Base] = (5x)*(x+3) [(or 5x^2 + 15x)]
Volume = [Area of the Base]*H
Volume = [(5x)*(x+3)]*(2x-1)
The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
That looks a lot like the answer in A: "The volume is the product of the area of the base, 5x(x + 3), and the height, 2x - 1."
what is is i^30?
A. -i
B. -1
c. 1
D.i
[tex]i^{30}=(i^2)^{15}=(-1)^{15}=-1[/tex]
sin 30°-cos 30°÷ sin 60°
Answer:
-1/2
Step-by-step explanation:
sin(30 degrees) = sin (pi/6) = 1/2
cos(30 degrees) = cos (pi/6) = [sqrt(3)]/2]
sin (60 degrees) = sin(pi/3) = [sqrt(3)]/2]
1/2 - [sqrt(3)/2] / [sqrt(3)/2] = -1/2
What is the completely factored form of this polynomial? 2x5 + 12x3 − 54x
Answer:
2x(x^2 - 3)(x^2 + 9)
Step-by-step explanation:
2x^5 + 12x^3 − 54x
2x(x^4 + 6x - 27)
Since -3 + 9 = 6 and -3 x 9 = -27:
2x(x^2 - 3)(x^2 + 9)
Answer:
[tex]2x(x^2-3)(x^2+9)[/tex]
Step-by-step explanation:
Given polynomial:
[tex]2x^5+12x^3-54x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies 2x(x^4+6x^2-27)[/tex]
To factor the trinomial [tex]x^4+6x^2-27[/tex]:
[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]
Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3
Rewrite the middle term as the sum of these two numbers:
[tex]\implies u^2+9u-3u-27[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+9)-3(u+9)[/tex]
Factor out the common term (u + 9):
[tex]\implies (u-3)(u+9)[/tex]
Substitute back [tex]u=x^2[/tex]:
[tex]\implies (x^2-3)(x^2+9)[/tex]
Therefore, the factored form of the given polynomial is:
[tex]\implies 2x(x^2-3)(x^2+9)[/tex]
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What should be added to (-10) to get (+10)
Answer:
20
Step-by-step explanation:
-10 + 20 = +10
Answer:
[tex]\fbox {20}[/tex]
Step-by-step explanation:
Let the required term be x
Then :
x + (-10) = 10x - 10 = 10x = 10 + 10x = 20whats 555 divided by 5
Answer:
111
Step-by-step explanation:
555÷5=111
and just to check, 5×111=555
Answer:
555 divided by 5 = 111
Step-by-step explanation:
This is common knowledge. The 5 in the hundreds place is divisible by 5 to get a quotient of 1. The 5 in the tens place is also divisible by 5 to get a quotient of 1 and the same is equally true for the 5 in the ones place.
Hence, the quotient of 555/5 = 111
Hope this helps! :D
Parent Functions
Question 4 of 10
On a piece of paper, graph:
{1 if -1 < x≤0
f(x) = {2 if 0 < x≤1
{3 if 1 < x≤2
Then determine which answer choice matches the graph you drew.
The graph of the parent function is given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given function is;
1, if -1<x≤0
f(x) = 2, if 0<x≤1
3, if 1<x≤2
Now, the graph of given function is given below.
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Answer:
The correct graph is in the image below
Step-by-step explanation:
need help with this question , pls help
Answer:
A = 80g B = 200g
Step-by-step explanation for A:
First, you would find what the serving size is divided by to get the number of people needed to feed 6/3 = 2. Then take that number (3) and divided it by the fish (240g) to get 240/3 = 80.
Step-by-step explanation for B:
You will first need to find how much butter goes into ONE pie by dividing 80 by 6 which is 1.33333333333333. Then do 1.333333333333333 times the number of people to feed (15) to get 200.
what choices are solutions to equation below x^-7x=-24/4
check all that apply
a. x=2
b. x=6
c. x=1
d. x=12
Express your answer as a decimal. 63÷12=
Answer:
5.25
Step-by-step explanation:
Answer:
5.25Step-by-step explanation:
type 63 : 12 in your calculator
see the example in the attachment.
lamy can paint 84 portraits in 6 weeks. at this rate , how many portraits can he paint in 2 weeks
Answer:
28 portraits
Step-by-step explanation:
Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.
In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is [tex]\frac{84 \text \: portraits}{6 \text \: weeks}[/tex] = 14 paintings per week.
Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.
Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.
Hope this helps!
What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
O-4
O-2
O2
O 5
Step-by-step explanation:
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What division problem does this area model represent?
Enter your answer in the boxes.
÷ 75 =
R
Rectangle with left side labeled 75. Vertical lines divide the rectangle into three parts. The left part has 40 above it and 3000 inside it. The middle part has 4 above it and 300 inside it. The right part has 53 inside it and nothing above it.
The division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
How to calculate the rectangle?
A rectangle is defined as a two-dimensional shape having four-sided and opposite sides equal and parallel.
From the information, it was stated that the rectangle with left side labelled 75 and the middle part has 4 above it and 300 inside it.
Therefore, the division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
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Use the law of cosines round to the nearest tenths
Answer:
x = 11.5
Step-by-step explanation:
Formula
a^2 = b^2 + c^2 - 2*b*c * cos(A) Substitute givens in formula
Givens
b = 31c = 26A = 21oa = x Let a = x to present the formula in it's most normal waySolution
a^2 = 31^2 + 26^2 - 2 * 31 * 26 * cos(21) Find -2*31*26*cos(21)
a^2 = 961 + 676 -1504.93 Combine
a^2 = 1637 -1504.93 Combine again
a^2 = 132.07 Take the √ on both sides
√a^2 = √132.07
a = 11.5 Rounded.
Answer
x = 11.5
What is the approximate area of the circle shown below?
60 cm C
A. 11,310 cm²
B. 94 cm²
C. 2827 cm²
D. 188 cm²
Determine the values for the pronumerals that make the following piece-wise functions continuous. (I really need help please).
Step-by-step explanation:
A function is continuous at x is
Limit as x approaches c= f(c).
Step 1: Find f(4).
4 is defined for 2x-1 so plug in. 4 for x.
[tex]2(4) - 1 = 7[/tex]
Note that what we just calculated was not only f(4) but also the left sided limit of f(x).
Step 2: Make sure the left sided and right sided limit are equal to 7.
[tex]a + 5x = 7[/tex]
Plug in 4 for x
[tex]a + 5(4) = 7[/tex]
[tex]a = - 13[/tex]
-Find the y-intercept of the line with the equation 2x+y=5.
A. -5
B.
-2
C. 1/2
D. 0
E. 5
Answer:
E. 5
Step-by-step explanation:
Let's rewrite the equation in the form of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
2x + y = 5
y = -2x+5
M, the slope, is -2
5, b, is the y-intercept
See attached graph.
pls tell the answer with explanation, i have finish this hw
Answer:
7 and 8
Step-by-step explanation:
49 - 1 = 48. (1)
48 - 3 = 45. (2)
45 - 5 = 40. (3)
40 - 7 = 33. (4)
33 - 9 = 24. (5)
24 - 11 = 13. (6)
13 - 13 = 0. (7) The answer is 7
64 - 1 = 63. (1)
63 - 3 = 60. (2)
60 - 5 = 55. (3)
55 - 7 = 48. (4)
48 - 9 = 39. (5)
39 - 11 = 28. (6)
28 - 13 = 15. (7)
15 - 15 = 0. (8) the answer is 8
Answer:
Step-by-step explanation:
Finding square root by repeated subtraction method:In this, the given number is subtracted by consecutive odd numbers (1,3,5,7,9.....) till we fer zero at the end. Count the number of steps performed and this number will be square root of the given number.
a) 49
49 -1 = 48 48 - 3 = 4545 - 5 = 4040 - 7 = 3333 - 9 = 2424 - 11 = 1313 - 13 = 0√49 = 7
b) 64
64 - 1 = 6363 - 3 = 6060 - 5 = 5555 - 7 = 4848 -9 = 3939 -11 = 2828 - 13 = 1515 - 15 = 0√64 = 8
the answer to this question
Answer:
positive 1!
Step-by-step explanation:
i got it right on the test trust me!
