The number of blueberry muffins that a baker makes each day is

2^x * 2 = 15
2^x= 15/2
2^x = 7,5
x = log 2 (7,5)

8 0

3 years ago

Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number o

Aleonysh [2.5K]

The statement which best describes the steps to graph the solution to the inequality in x and y is the third option from the scale, because :

x nickels = 5x cents

y dimes in turn - 10y cents.

Multiply them together and now we have 5x + 10y cents.

Total amount sloud be less than $20 or 2000 cents.

Read more on Brainly.com - brainly.com/question/1870318#readmore

8 0

3 years ago

Explain how finding 4 x 384 can help you find 4x5384. then find both products.

Harman [31]

Finding 4 x 384 helps you find 4 x 5384 because once you have the answer to 4 x 384, you can then just add the answer to 4 x 5000 to the answer of 4 x 384.
4 x 384 = 1,536
4 x 5000 = 20,000
20,000 + 1,536 = 21,536

6 0

3 years ago

Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?

bagirrra123 [75]

$\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\$

$\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}$

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus $\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]$

5 0

3 years ago

If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle isosceles?

Ne4ueva [31]

Answer:

True

Step-by-step explanation:

The perpendicular bisector of the opposite side to the vertex bisects the angle at the vertex into two equal parts and also bisects the triangle into two equal parts.

Let A be the angle at the vertex, then assume that the angle is an isosceles triangle with base angles B.

We need to show that A = 180 - 2B for an isoceles triangle

The perpendicular bisector bisects A into two so the new angle in the vertex one half of the bisected triangle is A/2.

Since this half triangle is a right-angled triangle, the third angle in it is 90.

So, A/2 + B + 90 = 180 (Sum of angles in a triangle)

subtracting 90 from both sides, we have

A/2 + B + 90 - 90 = 180 - 90

A/2 + B = 90

subtracting B from both sides, we have

A/2 + B = 90

A/2 = 90 - B

multiplying through by 2, we have

A = 2(90 - B)

A = 180 - 2B

Since A = 180 - 2B, then our triangle is an isosceles triangle.

7 0

3 years ago