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3 years ago

The second of two numbers is 8 less than twice the first. their sum is 19. Find the two numbers

1 answer:

3 0

The first number is 9 and the second number is 10. 10+9=10. 9*2=18 and 10 is 8 less than 18. All the requirements of the numbers are met.

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The Snack Shack is making a batch of trail mix. They use 9 1/3 pounds of granola, 9 1/3 pounds of mixed nuts, and 9 1/3 pounds o

m_a_m_a [10]

2 lb in each package

There are 3 types of nuts they all have 9 1/3 pounds in them. multiply 3 by 9 /13 to find out how many pounds of nuts there is. 3×9 1/3 That is 28 pounds. Now divide the 28 pounds of nuts into the 14 packages. 28 ÷ 14 There is 2 pounds of nuts in each package.

5 0

3 years ago

The quadrilateral ABCD has area of 58 in2 and diagonal AC = 14.5 in. Find the length of diagonal BD if AC ⊥ BD.

azamat

Answer:

(look in the the Step by step)

Step-by-step explanation:

When the diagonals of a quadrilateral are perpendicular, the area of that quadrilateral is half the product of their lengths.

.. A = (1/2)*d₁*d₂

Substituting the given information, this becomes

.. 58 in² = (1/2)*(14.5 in)*d₂

.. 2*58/14.5 in = d₂ = 8 in

The length of diagonal BD is 8 in.

4 0

2 years ago

What is the relationship between sin(90 degrees) and sin(-90 degrees)

Volgvan

Answer:

$sin(90\°)=-sin(-90\°)$

Step-by-step explanation:

we know that

$sin(90\°)=1$

$sin(-90\°)=-1$

therefore

$sin(90\°)=-sin(-90\°)$

4 0

3 years ago

NEED ASAP plz. I will also mark brainiest! Don't just take points, I will report you.

PilotLPTM [1.2K]

Part A:

You may choose the two lines connecting the origin and points A and B, and choose the portion of the space between them.

The line between the origin and A is

$y = 3x$

We want everything below this line (line included), so the first inequality is

$y \leq 3x$

The line between the origin and B is

$y = \dfrac{1}{3}x$

We want everything above this line (line included), so the second inequality is

$y \geq \dfrac{1}{3}x$

Create a system with these two inequalities and you'll have an area including only points A and B

Part B:

To verify the solutions, we can plug the coordinates of A and B in this system and check that we get something true: the coordinates of point A are (1,3), while the coordinates of point B are (3,1). The system becomes:

$A:\begin{cases}3 \leq 3\cdot 1\\3 \geq \frac{1}{3}\cdot 1\end{cases},\quad B:\begin{cases}1 \leq 3\cdot 3\\1 \geq \frac{1}{3}\cdot 3\end{cases}$

Which means

$A:\begin{cases}3 \leq 3\\3 \geq \frac{1}{3}\end{cases},\quad B:\begin{cases}1 \leq 9\\1 \geq 1\end{cases}$

And these are all true. So, the system is satisfied, which means that the points belong to the shaded area.

Part C

If you draw the line, you'll see that the only points that lay below the line are B and C. In fact, if we plug the coordinates we have

$B:\ 1$

And this are both true. You can check the coordinates of all other points, and see that they won't satisfy the inequality y<3x-6

3 0

3 years ago

Evaluate csc(-315°).

Maru [420]

Answer:

$\frac{2}{\sqrt{2} } = \sqrt{2}$

Step-by-step explanation:

Notice from the attached image that -315 degrees is the same as 45 degrees.

Recall as well that the csc function is defined as the reciprocal of the sine function: $csc(x)=\frac{1}{sin(x)}$

Then, you need to evaluate $\frac{1}{sin(45)} = 1/\frac{\sqrt{2} }{2} = \frac{2}{\sqrt{2} } =\sqrt{2}$

8 0

3 years ago