Plot and connect the points A(-5,2),B(-2,-2),C(2,3),D(6,3), E(6,-5),F(-5,-5), and find the length of

Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none

Marysya12 [62]

Answer: The required solution of the given system is

(x, y) = (3, 1) and (4, 0).

Step-by-step explanation: We are given to solve the following system of equations :

$x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (i), we have

$x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii), we get

$y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.$

When, x = 3, then from (iii), we get

$y=4-3=1.$

And, when x = 4, then from (iii), we get

$y=4-4=0.$

Thus, the required solution of the given system is

(x, y) = (3, 1) and (4, 0).

8 0

3 years ago

What is the measure of ZABD?

pshichka [43]

39° because a right angle adds up to 90°

7 0

3 years ago

Read 2 more answers

Solve the word problem.

Mazyrski [523]

I would say a because you would divide distance by time giving you the rate 48mi/hr

3 0

3 years ago

Heeeeeeeeeeeeeeeeelp!!!

Verizon [17]

3.

A.-4

B.-12

C.-6

D.1

E.-7

F. 18

8 0

3 years ago

In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase

weqwewe [10]

Answer:

There is enough evidence to support the claim that the average number of sheets recycled per bin was more than 59.3 sheets.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 59.3

Sample mean, $\bar{x}$ = 62.4

Sample size, n = 79

Alpha, α = 0.05

Sample standard deviation, s = 9.86

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 59.3\text{ sheets}\\H_A: \mu > 59.3\text{ sheets}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{62.4 - 59.3}{\frac{9.86}{\sqrt{79}} } = 2.7945$

Degree of freedom = n - 1 = 78

Now, $t_{critical} \text{ at 0.05 level of significance, 78 degree of freedom } = 1.6646$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

Thus, there is enough evidence to support the claim that the average number of sheets recycled per bin was more than 59.3 sheets.

3 0

3 years ago

Plot and connect the points A(-5,2),B(-2,-2),C(2,3),D(6,3), E(6,-5),F(-5,-5), and find the length of —