Divide the following 42

Given three points of a quadratic function, find the equation that defines the function: (-2, 20)(0, -2)(1, -4)

Stels [109]

Answer:

$y=3x^2-5x-2$

Step-by-step explanation:

Let the quadratic function be

$y=ax^2+bx+c$

The given points must satisfy this function;

Substitute $(-2,20)$ .

$20=4a-2b+c..(1)$

Substitute (0,-2)

$c=-2...(2)$

Substitute (1,-4);

$-4=a+b+c...(3)$

Put equation (2) into equation (1)

$20=4a-2b+-2$

$4a-2b=22$

$2a-b=11...(4)$

Put equation (2) into equation (3)

$-4=a+b-2...(3)$

$a+b=-2...(5)$

Add equation (4) and (5)

$3a=9$

Divide both sides by 3

$a=3$

Put a=3 in equation 5.

$3+b=-2$

$b=-2-3$

$b=-5$

The quadratic function is;

$y=3x^2-5x-2$

6 0

3 years ago

Which of the following numbers can be expressed as decimals that terminate? 5 over 2, 4 over 5, 2 over 7, 4 over 3 5 over 2 and

algol13

Answer:

I hope this helps!!

Step-by-step explanation:

We have given that : numbers - 9 over 7, 5 over 3, 3 over 2, 6 over 4

To find : which are terminating decimal

Terminating decimals are those whose figures to the right of some place are zero or have an end.

Solution : we check one by one,

1) 9 over 7 = 9/7 = 1.285714285714285714.... -Non terminating

2) 5 over 3 = 5/3 = 1.666666666666666...... -Non terminating

3) 3 over 2 = 3/2 = 1.5 - Terminating

4) 6 over 4 = 6/4= 3/2 = 1.5 - Terminating

I'm sorry if this is wrong :(

3 0

3 years ago

A 12-tooth gear on a motor shaft drives a larger gear having 42 teeth. If the motor shaft rotates at 700 rpm, what is the spee

nata0808 [166]

Answer:

203 rpm

Step-by-step explanation:

The speed of the larger gear can be calculated using the following equation:

$v = \omega*R$

<u>Where</u>:

ω: is the angular velocity of the motor = 700 rpm

R: is the gear ratio

The gear ratio is the following:

$R = \frac{n_{(a)}}{n_{(b)}}$

<u>Where:</u>

n(a): is the number of teeth on the small gear = 12 teeth

n(b): is the number of teeth on the larger gear = 42 teeth

The gear ratio is:

$R = \frac{12}{42} = 0.29$

Now, the speed of the larger gear is:

$v = \omega*R = 700 rpm*0.29 = 203 rpm$

Therefore, the speed of the larger gear is 203 rpm.

I hope it helps you!

3 0

3 years ago

Consider a standard deck of 52 playing cards with 4 suits. If A is the event of drawing a 6 from the deck, and B is the event of

crimeas [40]

Answer: Intersection of A and B = 2

Step-by-step explanation:

Total cards = 52

Let A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck.

Total cards having 6 on them = 4

[There are 4 suits of two different colors red and black.]

Total black playing card =26

Intersection of A and B = Black cards having 6 = 2

hence, Intersection of A and B = 2

8 0

3 years ago

A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles

MA_775_DIABLO [31]

Answer:

$t=\frac{11.7-12}{\frac{0.2}{\sqrt{25}}}=-7.5$

Step-by-step explanation:

Information given

$\bar X=11.7$ represent the sample mean of amount of liquid

$s=0.2$ represent the standard deviation

$n=25$ sample size

$\mu_o =12$ represent the value that we want to check

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

System of hypothesis

We want to verify if the true mean for the amount of liquid is lower than 12 ounces, and the hypothesis are given by:

Null hypothesis: $\mu \geq 12$

Alternative hypothesis: $\mu < 12$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing we got:

$t=\frac{11.7-12}{\frac{0.2}{\sqrt{25}}}=-7.5$

4 0

4 years ago

Divide the following 42_2​

Divide the following 42_2