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4 years ago

Select the number property that will justify the step in the following expression.

Mathematics

2 answers:

Airida [17]4 years ago

7 0

Two of the numbers were switched in a multiplication equation, so the answer would be commutative- multiplication.

LekaFEV [45]4 years ago

4 0

<h2>Answer:</h2>

The number property that justifies the step in the following expression is:

Commutative-Multiplication

<h2>Step-by-step explanation:</h2>

We are given a steps to solve the problem as follows:

4 • 13 • 25 =

4 • 25 • 13 =

100 • 13 = 1,300

We know that the commutative property under multiplication states that:

If a and b are two real numbers then:

$a\cdot b=b\cdot a$

i.e. the multiplication of two real numbers are always equal no matter in which order they are applied.

Here in the second step the order 13 and 25 are changed.

and then they are operated.

<em> Hence, the property is:</em>

<em> Commutative-Multiplication.</em>

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A rectangular prism is packed with cubes that measure 1/4 inch on each side

AveGali [126]

This doesn't have enough information to solve the problem, like what the length or width, or how many cubes are in the length, or something. Not enough information leads to nobody being able to solve it

5 0

3 years ago

The parking space shown at the right has an area of 209 ft2. A custom

jeyben [28]

Given:

The parking space shown at the right has an area of 209 ft².

A custom truck has rectangular dimensions of 13.5 ft by 8.5 ft.

To find:

Whether the truck fit in the parking space or not?

Solution:

If the area of the truck is more than the area of the parking space, then the truck cannot fit in the parking space otherwise it will fit in the parking space.

The area of a rectangle is:

$Area=length\times width$

Area of the rectangular truck is:

$Area=13.5\times 8.5$

$Area=114.75$

The area of the truck is 114.75 ft² which is less than the area of the parking space, 209 ft².

Therefore, the truck can fit in the parking space because the area of the truck is less than the area of the parking space.

3 0

3 years ago

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$