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2 years ago

Can someone help with the first question on he sheet thanks

Mathematics

1 answer:

Novay_Z [31]2 years ago

3 0

The first figure is a rectangle. Rectangles are known for having four right angles. Thus, one of the angles in this figure is 90 degrees.

The second figure is an equilateral triangle. Because all its sides have the same length, the angles are all the same. There is a principle stating that the sum of the 3 interior angles of a triangle is 180 degrees. Thus, the measure of one of these 3 angles is 180 degrees / 3 = 60 degrees.

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A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer

kogti [31]

Area is 6000 yd2

LW = 6000

field must be 40 yards longer than its width

L = W + 40

Replace L with W+40 in 1st equation to solve for Width

(W+40)(W) = 6000

W2 + 40W - 6000 = 0

This is a quadratic but is factorable

Factors of -6000 that add to 40 are (100)(-60)

(W+100)(W-60) = 0

W = -100 or W = 60

Since the width will not be negative discard -100

The width is 60 yards

Length is W+40 = 100 yards

4 0

2 years ago

Read 2 more answers

An apple orchard sold 155 apples in September in November it sold 17 times as many apples as it did in September how many apples

borishaifa [10]

9514 1404 393

Answer:

2635

Step-by-step explanation:

17 times the September number is ...

17×155 = 2635 . . . . apples sold in November

8 0

2 years ago

Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?

malfutka [58]

$\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}$

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

$\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}$ $\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}$ $\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}$ $\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}$

Hence, the correct options that apply are options A, D, E and F

7 0

2 months ago

5 + 8(3 + x) =<br> =<br> Simplify the expression

alisha [4.7K]

Answer:

29 + 8x

Step-by-step explanation:

5 + 8(3 + x) by PEDMAS parentheses first

= 5 + 3(8) + x(8)

= 5 + 24 + 8x

= 29 + 8x