MATHEMATICS COLLEGE

What is the solution of the following quadratic inequality? x2 – 4x – 21 ≤ 0

Answers

Answer 1

Answer:

Answer:

3, and -7

Step-by-step explanation:

First factor the trinomial

y=x2−4x−21

Find 2 numbers knowing sum (-4) and product (c = - 21). They are the numbers in the factor pair (3, -7).

y = (x + 3)(x - 7)

Solving the 2 binomials, we get:

x = -3 and x = 7

Answer 2

Answer:

We want to solve the given quadratic inequality.

The correct option is the second one, counting from the top.

So we need to solve:

x^2 - 4x - 21 ≤ 0

Because we have the graph, we can avoid all the algebra.

Notice that the equation must be equal to or smaller than zero, then we just need to find the values of x such that the graph intersects the x-axis or is below it.

By looking at the given graph, we can see that the given range goes from -3 to 7

Then the solution is:

-3 ≤ x ≤ 7

This would be represented with a number line going from -8 to 8, two closed circles (because we use the symbols ≤ ≥) at negative 3 and 7, and the region between the circles is shaded.

The correct option is the second one.

If you want to learn more, you can read:

brainly.com/question/11897796

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Estimate each product 7.1 x 2.1

Given h(x)= -5x+3,solve for x when h(x)=3

Answers

Answer: x = 0

Explanation

The idea is to replace h(x) with 3. Then we isolate x. Follow PEMDAS in reverse to get x by itself.

Here are the steps:

h(x) = -5x+3

3 = -5x+3

-5x+3 = 3

-5x = 3-3

-5x = 0

x = 0/(-5)

x = 0

As a check,

h(x) = -5x+3

h(0) = -5*0 + 3

h(0) = 0 + 3

h(0) = 3

Therefore, the input x = 0 in the domain leads to the output h(x) = 3 in the range. We have confirmed the answer x = 0

Another way to confirm the answer is to use a graphing tool like GeoGebra or Desmos.

Can someone please help me solve 4 & 5? I'll love you forever

Answers

Based on my little knowledge of statistics
4.
It's 8!/4!= 1680
(the exclamation point is basically the number of probabilities in the combination)
5.
(speculation) It's 10!-6!= 3,628,080
plus
8!-6!=39,600
equals
(3,628,080 + 39,600) / 6! = 5094
(the 6! is the amount of drink combinations you are limited to)
FYI- you can use the exclamation mark on your phone calculator, either swipe to side or press the ''extras'' button

I think #5 is actually 5096?
10x9x8x7=5040
8x7=56
5040+56=5096

A stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s

Answers

Answer:

23.7m

Step-by-step explanation:

Given parameters:

Time taken = 2.2s

Acceleration due to gravity = 10m/s

Unknown:

Depth of the well = ?

Solution:

To solve this problem, we simply apply one of the motion equations;

S = ut + $(1)/(2)$ gt²

where S = depth of the well

u = initial velocity

t = time taken

g = acceleration due to gravity

Input the parameters and solve for S;

Note initial velocity = 0;

S = $(1)/(2)$ x 9.8 x 2.2²

S = 23.7m

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p 1 be the proportion of customer complaints with the old dough and p 2 be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough g

Answers

Answer:

$z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)((1)/(385)+(1)/(340))}}=-2.469$

Now we can calculate the p value with this probability:

$p_v =P(Z<-2.469)= 0.0068$

Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.

Step-by-step explanation:

Information provided

$X_(1)=6$ represent the complaints with the old dough

$X_(2)=16$ represent the complaints with the new dough

$n_(1)=385$ sample 1 selected

$n_(2)=340$ sample 2 selected

$p_(1)=(6)/(385)=0.0156$ represent the proportion of complaints with the old dough

$p_(2)=(16)/(340)=0.0471$ represent the proportion of complaints with the new dough

$\hat p$ represent the pooled estimate of p

z would represent the statistic

$p_v$ represent the value

Hypothesis to test

We want to verify if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough, the system of hypothesis would be:

Null hypothesis: $p_(1) \geq p_(2)$

Alternative hypothesis: $p_(1) < p_(2)$

The statitsic is given by:

$z=\frac{p_(1)-p_(2)}{\sqrt{\hat p (1-\hat p)((1)/(n_(1))+(1)/(n_(2)))}}$ (1)

Where $\hat p=(X_(1)+X_(2))/(n_(1)+n_(2))=(6+16)/(385+340)=0.0303$

Replacing the info provided we got:

$z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)((1)/(385)+(1)/(340))}}=-2.469$

Now we can calculate the p value with this probability:

$p_v =P(Z<-2.469)= 0.0068$

You want to purchase a new car in 3 years and you anticipate the cost of the car to be $25,000. You are given an investment plan with a fixed APR of 5.3% if you make regular monthly deposits. How much should you deposit at the end of each month to reach your goal of $25,000 in 3 years?

a.$642.23

c.$648.62

b.$645.65

d.$649.13

Answers

Answer:

The answer is A: $642.23

Step-by-step explanation:

I just took the test lol

Lydia and Adam are buildng a display of soup cans at the market where they work. the display is in the form of a square pyramid, with a base of 81 cans. They will continue making smaller layers until there is one can at the top. Adam is going to the stockroom to get the can they will need. a. How many layers will be in the display?

b. How many canse will Lydia and Adam use total?