Determine if the lines are parallel, perpendicular, neither or coinsiding..
y=-3x+7
y = 3x - 7
A Perpendicular
B neither
C Parallel
D Coinciding

There are 30 different combinations of two members who can be selected to serve on the spring formal committee.

Permutation is the arrangement of elements in a specific order. In this scenario, the elements are the six members of the student council, and the order in which they are arranged is important.

To find the number of permutations, we use the formula nPk, where n is the number of elements and k is the number of elements we want to arrange.

In this case, n = 6 and k = 2,

so we have

=> 6P2 = 6!/(6-2)!

=> 6!/(4!) = 6 x 5/1 = 30.

So, there are 30 possible spring formal committees that can be formed from the six members of the student council.

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To find where p is increasing, we must decide where p' = 1.7p(1 − p/5600) is positive. Assuming that p > 0 always, then we need (1 − p/5600) > 0. Therefore, p' is positive whenever p < 5600.

In other words, the function p is increasing whenever the value of p is less than 5600. This is because the derivative p' is positive in this range, meaning that the function p is increasing. As soon as p reaches 5600, the derivative p' becomes negative, meaning that the function p is decreasing.

So, the answer is that p is increasing whenever p < 5600.

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Answer:

C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)

Step-by-step explanation:

The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)

Hope this helps

Answer:

closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. A rational expression is any polynomial divided by any polynomial except for zero.

Step-by-step explanation:

Answer:

x y

—————

1 3

2 6

3 9

4 12

5 15

Answer

put 1 on top and exo on bottom

Step-by-step explanation:

The table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

The answer is 85 degrees.

Step-by-step explanation:

This is because all four interior angles of the rectangle should add up to 360 degrees. So 360-85-95-95 equals 85.

I hope I helped you! :)

Let's assume that x represents the number of square feet in the garden, and y represents the number of carrots that can be grown at a time.

We are given that when the garden is 2 square feet, she can grow 8 carrots at a time. This suggests a linear relationship between x and y.

To find the equation, we can use the concept of proportionality. Since the number of carrots grown is directly proportional to the area of the garden, we can set up a proportion:

x/y = 2/8

Cross-multiplying, we have:

8x = 2y

Dividing both sides by 2, we get:

4x = y

So, the equation for the relationship between x and y is y = 4x.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.

To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.

The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.

The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.

The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.

The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.

Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.

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Answer:

360 × 3 ÷ 8 = 135

360 - 135 = 225

Circumference = 2 x radius x Pi

Circumference = 2 x 0.8 x pi

Circumference = 1.6pi or 5.024 yards

area = r^2 x pi

Area = 0.8^2 x pi

Area = 0.64pi or 2.0096 square yards

Given , radius of circle is 0.8 yards

We have to find circumference and area of the circle

Formula for finding area of circle :- πr²

Area :- 3.14×0.8² sq. yards

Area :- 2.0096 sq. yards

Formula for finding circumference of circle :- 2πr

Circumference :- 2×3.14×0.8 yards

Circumference :- 1.884 yards

create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.

then draw your trapezium in the given space using your scale

The sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.

In order for a partially ordered set (poset) to be a total order, every pair of elements must be comparable, i.e., for every pair of elements x, y in A, either x | y or y | x must be true.

Therefore, we should choose a set A that satisfies this condition.Let us consider each set in turn:(1, 4, 16, 64)This set contains powers of 4, which are not all divisible by each other.

For example, 16 | 64, but 16 does not divide 4.

Hence, this set is not a total order.{1.2,3, 4, 6, 12}In this set, 1 divides every other element, so it satisfies the condition for being a total order. Therefore, this set yields a poset that is a total order.

(1, 2, 3, 4, 6, 12, 18, 24)This set has the same elements as the previous set, plus some more. Hence, it also satisfies the condition for being a total order.

Therefore, this set yields a poset that is a total order.{1 , 2, 3, 6, 12}In this set, 1 divides every other element, 2 divides 6 and 12, and 3 divides 6 and 12.

Therefore, it satisfies the condition for being a total order.

Hence, this set yields a poset that is a total order.In conclusion, the sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.

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Answer:

1/2 Bh

Step-by-step explanation:

find the area of the base (B) by multiplying.5 xlengthxwidth. The take this answer, multiply by .5 and the height of the pyramid.

The volume of a  triangular pyramid is 1/2 × area of the base× height.

What is a triangular pyramid?

A pyramid with a triangular base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids have four vertices. Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of an object has defined as the space that is occupied by the object.

The volume of a triangular pyramid is 1/2 × B × h.

B =  area of the base of the triangular pyramid.

h = Height of  triangular pyramid

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Answer:

Four significant figures

Step-by-step explanation:

Rules of significant figure:

1. Zeros before any non-zero digit are considered to be NON-significant.

2. Any zeros between any non-zero digits are SIGNIFICANT

0.505

Here, there are three significant digits: 505

3. Any zeros that are to the right of the decimal point and a non-zero number are SIGNIFICANT.

4.0000

4. All non - zero digit are significant

Therefore,

0.002040 has four significant figures

2040

Answer:

The answer is  

20x + 17.5

Step-by-step explanation:

Multiply the 5 by the numbers inside the parenthesis.

5 x 4x

5 x 3.5

Answer:

8

Step-by-step explanation:

-3(6-r)= -18+3r because -*-=+

3r=24

r=8

The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.

To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h2 = s2 + t2

h2 = 31.32 + 13.32

h2 = 979.69 + 176.89

h2 = 1156.58

h = √1156.58

h ≈ 34.0

Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:

sin(θ) = s / h

sin(θ) = 31.3 / 34.0

sin(θ) ≈ 0.921

cos(θ) = t / h

cos(θ) = 13.3 / 34.0

cos(θ) ≈ 0.391

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Answer:

n + (n + 5) = 19

Step-by-step explanation:

n = boys

n + 5 = girls

19 = total

boys + girls = total

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Option 4 is the correct option. Keep the base the same and then subtract the exponents. The simplified value of the expression is 3 ^ -2. This can be obtained by using Quotient of Power Property.

Here in this question it is given that,

⇒ (3^-6)/(3^-4)

By using the Quotient of Power Property, we can find the simplified value of the expression.

Since the bases are equal we can subtract the exponents of the numbers.

Here the common base is 3 and -6 and -4 are the exponents of the numbers.

Now by subtracting the exponents we get,

⇒ (3^-6)/(3^-4)

= 3^ [-6 - (-4)]

= 3 ^ [-6 + 4]

= 3 ^ -2

Hence option 4 is the correct option. Keep the base the same and then subtract the exponents. The simplified value of the expression is 3 ^ -2.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Describe how to simplify the expression (3^-6)/(3^-4).

Option 1: Divide the bases and then add the exponents.

Option 2: Keep the base the same and then add the exponents.

Option 3: Multiply the bases and then subtract the exponents.

Option 4: Keep the base the same and then subtract the exponents.

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Answer:

(a)  D = 72.05 dB  (2 d.p.)

(b)  I = 2.51 W/m²  (2 d.p.)

Step-by-step explanation:

Given function:

\(\boxed{D(I)=10 \log_{10}(I)+120, \quad I\geq 0}\)

where:

Given:

Substitute the given value of I into the given function and solve for D:

\(\begin{aligned}\implies D(1.6 \times 10^{-5}) & =10 \log_{10}(1.6 \times 10^{-5})+120\\& = 10 \log_{10}(0.000016)+120\\& = 10 (-4.795880017)+120\\& = -47.95880017+120\\&=72.04119983\\&=72.04\; \sf dB\;(2\:d.p.)\end{aligned}\)

Given:

Substitute the given value of D into the given function and solve for I:

\(\begin{aligned}\implies 124 & =10 \log_{10}(I)+120\\4 & =10 \log_{10}(I)\\10 \log_{10}(I)&=4\\\log_{10}(I)&=0.4\\10^{\log_{10}(I)}&=10^{0.4\\I&=2.511886432\\I&=2.51\; \sf W/m^2\; (2\:d.p.)\end{aligned}\)

a. The equation representing the cost of buying and operating the Super Cool X1400 is: C = 800 + 60m. b. The equation representing the cost of buying and operating the Efficient Energy X2000 is: C = 1200 + 40m. c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase. d. Figuring your family will only use the air conditioner for four months each year, you would have to wait 5 years to start saving money overall.

a. The cost of buying the Super Cool X1400 is a one-time expense of $800. Additionally, the cost of operating it is $60 per month. Therefore, the equation representing the cost C as a function of months m is C = 800 + 60m.

b. The cost of buying the Efficient Energy X2000 is a one-time expense of $1200. The operating cost is $40 per month. Hence, the equation representing the cost C as a function of months m is C = 1200 + 40m.

c. To compensate for the additional cost of the original purchase (which is $400), we equate the two cost equations and solve for m:

800 + 60m = 1200 + 40m

20m = 400

m = 20

Therefore, your family would have to use the Efficient Energy model for 20 months (or 10 months more than the Super Cool X1400) to compensate for the additional cost.

d. Considering your family only uses the air conditioner for four months each year, we divide the total number of months (20) by four to find the number of years needed to start saving money overall:

20 months / 4 months/year = 5 years

Hence, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

a. The cost of buying and operating the Super Cool X1400 is represented by the equation C = 800 + 60m.

b. The cost of buying and operating the Efficient Energy X2000 is represented by the equation C = 1200 + 40m.

c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase.

d. Assuming your family uses the air conditioner for four months each year, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

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complete question- Your family plans to buy a new air conditioner. They can buy the Super Cool X1400 for $800, or they can buy the Efficient Energy X2000 for $1200. Both models will cool your home equally well, but the Efficient Energy model is less expensive to operate. The Super Cool X1400 will cost $60 per month to operate, while the Efficient Energy X2000 costs only $40 per month to operate. a. Write an equation to represent the cost of buying and operating the Super Cool X1400 where C= cost and m= months. b. Write an equation to represent the cost of buying and operating the Efficient Energy X2000. c. How many months would your family have to use the Efficient Energy model to compensate for the additional cost of the original purchase? d. Figuring your family will only use the air conditioner for four months each year, how many years ill you have to wait to start saving money overall?

Answer: Para convertir un decimal a una fracción, coloque el número decimal sobre su valor posicional. Por ejemplo, en 0.6, el seis está en el lugar de las décimas, entonces colocamos 6 sobre 10 para crear la fracción equivalente, 6/10. Si es necesario, simplifica la fracción.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total work hours: