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2 years ago

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#8 Tessa has a plan for a set of stairs made of concrete, as shown. Each stair is 1 point the same width and height and is talle

r than the previous one by the same amount. What is the volume of concrete needed for the set of stairs?
Picture below:

1 answer:

Afina-wow [57]2 years ago

6 0

Answer: 2.43m^3

Step-by-step explanation:

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Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

kherson [118]

Answer: The correct line is

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

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3 years ago

87614.4 divided by 16

kifflom [539]

Answer:

5,475.9

Step-by-step explanation:

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2 years ago

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If you need more Spad

aksik [14]

Answer:

Just convert the number to the third digit and the answer will be b

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2 years ago

What is the solution to the equation 37x = 9x + 4?<br><br> -7<br><br> -1/7<br><br> 1/7<br><br> 7

aivan3 [116]

37x = 9x + 4

37x - 9x = 4

28x = 4

x = 7

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2 years ago

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The measure of angle M is_degrees.

jasenka [17]

Answer:

m=37

Step-by-step explanation:

The 2 angles are complementary, or add to 90 degrees. Wee know this because of the little square in the corner that indicates a right angle, which is equal to 90 degrees.

m+53=90

Solve for m by getting m by itself. To do this, subtract 53 from both sides to "reverse" the addition being done to m.

m+53-53=90-53

The 53s on the left cancel, and we are left with:

m=37

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3 years ago

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