What value of X makes the equation true?<br><br> 12x-15=16-3x

The angle measures associated with which set of ordered pairs share the same reference angle? (Negative StartFraction StartRoot

Katarina [22]

Answer:

$(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

$(A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

5 0

2 years ago

Read 2 more answers

1. Which solid has one base that is a rectangle and four lateral surface that are triangles?

Ber [7]

1. Triangular prism
2. Sphere i think

7 0

2 years ago

(8p - 2) (6p+2) <br><br> help plz

qaws [65]

Answer:

$48p^2+2p-4$

Step-by-step explanation:

We can use the FOIL method to expand two multiplied binomials. It states that $(a+b)(c+d)=ac+bc+ac+bd$ . The FOIL method stands for First(first terms) outer(outer terms) inner(inner terms) last(last terms).

So, we can expand our binomials now!

$(8p-2)(6p+2)=(8p)(6p)-2(6p)+(8p)(2)-2(2)=48p^2-12p+14p-4=\boxed{48p^2+2p-4}$

8 0

2 years ago

Simplify the expression 2√ 20 − 3√ 7 − 2√ 5 + 4√ 63 .

earnstyle [38]

Answer:

The simplified form is,

$\boxed{\boxed{6\sqrt{5}+9\sqrt{7}}}$

Step-by-step explanation:

The given expression is,

$=2\sqrt{20}-3\sqrt{7}+2\sqrt{5}+4\sqrt{63}$

$=2\sqrt{4\times 5}-3\sqrt{7}+2\sqrt{5}+4\sqrt{9\times 7}$

$=2(\sqrt{4}\times \sqrt{5})-3\sqrt{7}+2\sqrt{5}+4(\sqrt{9}\times \sqrt{7})$

$=2(2\times \sqrt{5})-3\sqrt{7}+2\sqrt{5}+4(3\times \sqrt{7})$

$=4\sqrt{5}-3\sqrt{7}+2\sqrt{5}+12\sqrt{7}$

$=4\sqrt{5}+2\sqrt{5}+12\sqrt{7}-3\sqrt{7}$

$=6\sqrt{5}+9\sqrt{7}$

8 0

3 years ago

Read 2 more answers

He rain caused the river to ride a total of 6 2/3 inches. The river was rising at an average of 2/3 of an inch each hour. How ma

Kobotan [32]

To find out how many hours it rained, divide the total rise in the river by the amount it rose every hour.

$\sf 6\dfrac{2}{3}\div\dfrac{2}{3}$

First convert the mixed number into an improper fraction. We do this by multiplying the denominator to the whole number, adding it to the numerator, which becomes our new numerator, and we keep the denominator the same:

$\sf\dfrac{20}{3}\div\dfrac{2}{3}$

When dividing fractions we flip(the reciprocal) the one we're dividing by and multiply:

$\sf\dfrac{20}{3}\times\dfrac{3}{2}$

Multiply the numerators and denominators together:

$\sf\dfrac{60}{6}$

Simplify by dividing:

$\boxed{\sf 10}$

So it rained for 10 hours.

5 0

3 years ago

What value of X makes the equation true? 12x-15=16-3x