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4 years ago

Factor the expression. 3x2 + 14x-5

Mathematics

1 answer:

Irina18 [472]4 years ago

8 0

Answer:

(3x-1)(x+5)

Step-by-step explanation:

Find two numbers that when they multiply, you get the third term,

which is -5 in this problem. And when they add up, you get the second term,

which is 14 in this problem.

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There are 173 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 46 fans?

Iteru [2.4K]

Answer:

4 buses

Step-by-step explanation:

There are 173 basketball fans

one bus can hold 46 fans

Hence the number of buses needed can be calculated as follows

= 173/46

= 3.76

= 4

Hence 4 buses are needed

3 0

3 years ago

Make and explain a prediction about the nature of the solution to the following system of equations, and then solve the system.

Dominik [7]

Answer:

(3,-4) and (-3,4)

Step-by-step explanation:

$x^2+y^2=25$

$4x+3y=0$

The first equation is a circle with radius of 5 units

The second equation is a line which has slope $\frac{4}{3}$

So, for 4 unit change in y there will be 3 unit chang in x.

The circle has its center at the origin and the line passes through the orgin.

The line will intersect the circle at two points giving us two solutions

From the second equation we get

$y=-\frac{4}{3}x$

Applying in the second equation

$x^2+\left(-\frac{4}{3}x\right)^2=25\\\Rightarrow x^2+\frac{16}{9}x^2=25\\\Rightarrow \frac{9x^2+16x^2}{9}=25\\\Rightarrow 25x^2=225\\\Rightarrow x^2=\frac{225}{25}\\\Rightarrow x^2=9\\\Rightarrow x=\pm 3$

When x = 3

$y=-\frac{4}{3}x\\\Rightarrow y=-\frac{4}{3}\times 3\\\Rightarrow y=-4$

When x = -3

$y=-\frac{4}{3}x\\\Rightarrow y=-\frac{4}{3}\times -3\\\Rightarrow y=4$

So, the points where the line and circle intersect are (3,-4) and (-3,4)

6 0

3 years ago

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bott

Andreyy89

Answer:

(15.8495,16.2505)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 16.05 ounces

Standard Deviation, σ = 0.2005 ounces

We are given that the distribution of amount poured into the bottles is a bell shaped distribution that is a normal distribution.

Empirical rule:

It states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ).

It shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Confidence interval:

$\mu \pm 2\frac{\sigma}{\sqrt{n}}$