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3 years ago

6. Complete the two-column proof.

Mathematics

2 answers:

olya-2409 [2.1K]3 years ago

8 0

Answer:

Given: $\frac{x}{6} + 2 = 15$ ......[1]

To prove : x =78

Subtraction property states that you subtract the same number to both sides of an equation.

Subtract 2 from both sides of an equation [1];

$\frac{x}{6} + 2 - 2= 15 -2$

Simplify:

$\frac{x}{6} = 13$ ......[2]

Multiplication property states that you multiply the same number to both sides of an equation.

Multiply 6 to both sides of an equation [2];

$\frac{x}{6} \times 6 = 13 \times 6$

Simplify:

$x = 78$ proved!

Statement Reason

1. $\frac{x}{6} + 2 = 15$ Given

2. $\frac{x}{6} = 13$ Subtraction property of equality

3. $x = 78$ Multiplication property of equality

natima [27]3 years ago

3 0

<span>For the answer to the question in the given equation above, substitute 78 for X because a quantity can be substituted for it's equal.

78/6 + 2 = 15,
13 + 2 = 15,Therefore
15 = 15.I hope my answer and solution helped you in your problem. Have a nice day!</span>

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MissTica

Answer:

Scale factor = 7

Step-by-step explanation:

Dilation with scale factor to map HEFG to DABC will be,

Scale factor = $\frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}$

= $\frac{\text{Length of CD}}{\text{Length of GH}}$

Length of CD = Distance between two points C(0, -7) and D(-7, 0)

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

= $\sqrt{(-7-0)^2+(0+7)^2}$

= $\sqrt{98}$

= $7\sqrt{2}$

Length of GH = Distance between G(0, -1) and H(-1, 0)

= $\sqrt{(-1-0)^2+(0+1)^2}$

= $\sqrt{2}$

Scale factor = $\frac{7\sqrt{2} }{\sqrt{2} }$

= 7

6 0

2 years ago

Miguel has two same size rectangles divivded into the same number of equal parts. One rectangle has 3/4 of the parts shaded, and

ivanzaharov [21]

Bother rectangles could be divided into 8 parts.

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3 years ago

(5,9), (5-3)<br> what is the slope?

monitta

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

When you want to find out what the slope is, you have to remember what the formula is first....

$m=\frac{y}{x} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

so in this case -3 would be the $y_{2}$ because it's the y in the ordered pair and it's the second one. Then one of the 5's would be $x_{2}$ and 9 would be $y_{1}$ and then the other 5 would be $x_{1}$ .

now if we plug it in

$\frac{-3-9}{5-5} =\frac{-12}{0}$

now we can tell that we can't divide by zero so the slope would be unidentified and that's it.

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2 years ago

Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

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2 years ago

PLS HELP ME ASAP! The height and width of a rectangular prism are 26 yards and 24 yards respectively. Find the length of the

Allushta [10]

Answer:

The length is 30 cubic yards.

Step-by-step explanation:

To find volume you use equation V=LxWxH

Since we already know the height, width, and volume we can input them into the equation.

18,720=L x 24 x 26

As you can see, the length is still unknown.

To figure it out though, you can multiply the height and width of the prism,

24 x 26 = 624

And then divide the volume, 18,720 by it.

18,720/624 = 30

Thus, your length is 30 cubic yards.

8 0

3 years ago