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Marta_Voda [28]
2 years ago
10

16x-15-9x=13 how do I solve for x

Mathematics
1 answer:
dangina [55]2 years ago
7 0
Add two like terms: 16x+(-9x)=7x
Add 15 to both sides: 7x=28
Divide 7 on both sides: x=4
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Greg has an 18% chance of being elected both positions.



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Consider the function f(x) = 4x² - x + 3. What is f(1)?
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.. Which of the following are the coordinates of the vertices of the following square with sides of length a?
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Option A: O(0,0), S(0,a), T(a,a), W(a,0)

Option D: O(0,0), S(a,0), T(a,a), W(0,a)

Step-by-step explanation:

Option A: O(0,0), S(0,a), T(a,a), W(a,0)

To find the sides of a square, let us use the distance formula,

d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

Now, we shall find the length of the square,

\begin{array}{l}{\text { Length } O S=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } S T=\sqrt{(a-0)^{2}+(a-a)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } T W=\sqrt{(a-a)^{2}+(0-a)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } O W=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a}\end{array}

Thus, the square with vertices O(0,0), S(0,a), T(a,a), W(a,0) has sides of length a.

Option B: O(0,0), S(0,a), T(2a,2a), W(a,0)

Now, we shall find the length of the square,

\begin{aligned}&\text { Length } O S=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\\&\text {Length } S T=\sqrt{(2 a-0)^{2}+(2 a-a)^{2}}=\sqrt{5 a^{2}}=a \sqrt{5}\\&\text {Length } T W=\sqrt{(a-2 a)^{2}+(0-2 a)^{2}}=\sqrt{2 a^{2}}=a \sqrt{2}\\&\text {Length } O W=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a\end{aligned}

This is not a square because the lengths are not equal.

Option C: O(0,0), S(0,2a), T(2a,2a), W(2a,0)

Now, we shall find the length of the square,

\begin{array}{l}{\text { Length OS }=\sqrt{(0-0)^{2}+(2 a-0)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } S T=\sqrt{(2 a-0)^{2}+(2 a-2 a)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } T W=\sqrt{(2 a-2 a)^{2}+(0-2 a)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } O W=\sqrt{(2 a-0)^{2}+(0-0)^{2}}=\sqrt{4 a^{2}}=2 a}\end{array}

Thus, the square with vertices O(0,0), S(0,2a), T(2a,2a), W(2a,0) has sides of length 2a.

Option D: O(0,0), S(a,0), T(a,a), W(0,a)

Now, we shall find the length of the square,

\begin{aligned}&\text { Length OS }=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } S T=\sqrt{(a-a)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } T W=\sqrt{(0-a)^{2}+(a-a)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } O W=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\end{aligned}

Thus, the square with vertices O(0,0), S(a,0), T(a,a), W(0,a) has sides of length a.

Thus, the correct answers are option a and option d.

8 0
2 years ago
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