MATHEMATICS HIGH SCHOOL

Systems of equations word problem."Flying with the wind a plane went 183 km/h. Flying into the same wind the plane only went 141 km/hr. Find the speed of the plane in still air and the speed of the wind.

Answers

Answer 1
Answer: Well, the plane has speed p and the wind has speed w.
p+w=183, p-w=141. Add them up to get 2p=324 or p=162. The wind has speed 183-162=21 km/h, while the plane has the speed in still air 162 km/h.

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Factor this polynomial expression. x3 - 64 A. (x + 4)(x2 + 4x + 16) B. (x - 4)(x2 + 4x + 4) C. (x + 4)(x2 + 4x + 4) D. (x - 4)(x2 + 4x + 16)
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William cut two similar triangular slices of cheese with the dimensions shown below. Explain/ show work please

Answers

The ratio of side lengths is approximately 1.4.
We need to first figure out which sides correspond to which.

13/9.29 = 1.39935 which is close to 1.4, so the sides 13 cm and 9.29 cm are corresponding sides.

8/5.71 = 1.401 which is close to 1.4, so the sides 8 cm and 5.71 cm are corresponding sides.

That leaves the 7 cm side corresponding to the unknown side.

7 cm/1.4 = 5 cm

Answer: D. 5 cm

8The first term of an arithmetic sequence is 5. The third term of the sequence is 13.
Which of the following expressions represents the nth term of the sequence?
A 4n +1
B) 4n + 5
5n+1
D) 5n + 5

Answers

If the first term of an arithmetic sequence is 5 and the third term of the sequence is 13 then the nth term is A) 4n +1.

What are arithmetic and geometric sequence?

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference(d).

aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, The first term of an arithmetic sequence is 5.

The third term of the sequence is 13.

As we can conclude that for 2 terms the common difference is increased by 8.

∴ Common difference (d) = 8/2 = 4.

Now, we know the nth term of an arithmetic sequence is,

aₙ = a₁ + (n - 1).d.

aₙ = 5 + (n - 1)×4.

aₙ = 5 + 4n - 4.

aₙ = 4n + 1.

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Answer:A 4n+1

Step-by-step explanation: found the answer key

Click through and select the graph that represents the function shown in the table.

Answers

It the graph that represents the function given in the table is the graph [3].

What is the point slope form of the equation of a line?

The point slope form of a line is given by -

y - y₁ = m(x - x₁)

Given is a line that passes through the points (-2, 5), (0, 3), (1, 2) and (4, -1).

The general equation of the straight line is -

y = mx + c

where -

m is the slope of line

c is the y - intercept

Now -

We can calculate the slope as follows -

m = (2 - 3)/(1 - 0) = -1/1 = -1

Now, at [x] = 0, [y] = 3

Which is the y - intercept.

The equation of the line will be -

y = - x + 3

We will plot the graph and match it with the given ones.

It can be seen that graph 3 is the correct choice.

Therefore, it the graph that represents the function given in the table is the graph [3]. It is plotted and attached with the answer for reference.

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The graph that represents the table is the one in the image at the end.

Which graph represents the line in the table?

Here we want to identify the line that represents the given table.

The first thing we can notice is the pair (0, 3). This means that the y-intercept of this line is y = 3.

Also, the next pair is (1, 2)

So, for each increase in x of one unit, we have a decrease of one unit in y, which means that the line goes downwards.

So the correct graph is the one posted below.

What is the equation in slope-intercept form of the line that passes through the points ( -4, 47) and ( 2 , -16)?A) y= -
21
2
x +
979
21

B) y= -
2
21
x +
979
21

C) y= -
21
2
x + 5

D) y= -
2
21
x +5

Answers

Answer:c

Step-by-step explanation:

Simplify.

n 6 · n 5 ÷ n 4 · n 3 ÷ n 2 · n

Answers

Answer: n^(9)

Step-by-step explanation:

Given expression: n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n

The law of exponents are given by :_

a^m\cdot a^n=a^(m+n)\n\na^m/ a^n=a^(m-n)

Using PEDMAS, first we solve division, we get

n^6\cdot n^(5-4)\cdot n^(3-2)\cdot n\n\n=n^6\cdot n\cdot n\cdot n

Now, using product law of exponent we get

n^(6+1+1+1)\n\n=n^(9)

Answer:

The given expression  n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n is n^9            

Step-by-step explanation:

Given : Expression  n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n

We have to write the simplified form for the given expression  n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n

Consider the given expression  n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n

Rewrite it in simpler form, we have,

n^6\cdot(n^5)/(n^4)\cdot (n^3)/(n^2)\cdot n

Apply exponent rule, \:a^b\cdot \:a^c=a^(b+c), we have,

n^6n=\:n^(6+1)

=(n^5)/(n^4)\cdot (n^3)/(n^2)n^(7)

Apply exponent rule, (x^a)/(x^b)=x^(a-b)

(n^5)/(n^4)=n^(5-4)

(n^3)/(n^2)=n^(3-2)

Expression becomes,

=n^7nn

Again apply exponent rule, we have,

\:a^b\cdot \:a^c=a^(b+c)

=n^(1+1+7)=n^9

Thus, The given expression n^6\cdot n^5/ n^4\cdot n^3/ n^2\cdot n is n^9

After a party there were 2 2/3 pepperoni pizzas and 1 5/6 cheese pizza left. How much pizza was there left?

Answers

Answer: 4  (1)/(2)  pizzas

Step-by-step explanation:

    We can add the leftover pizzas together to find the total pizza leftover.

         2 + 1 = 3

         \displaystyle (2)/(3) +(5)/(6) = (4)/(6) +(5)/(6)=(9)/(6) =(3)/(2) =1\;(1)/(2)

         3 + 1 (1)/(2) = 4  (1)/(2)

Answer:

Step-by-step explanation:

I would convert 2 2/3 into something with a denominator of /6 to make it easy

2 4/6 = 16/6

16/6 + 5/6 = 21/6

(simplify)

7/2

or

3.5 pizzas
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