Mr. Chavez spent $199.99 for a new smart phone, 3

Solve the system by substitution. y = -4x 23 - 5y = 44

spin [16.1K]

<h3>Explanation</h3>

Given the system of equations.

$\begin{cases} y = - 4x \\ 23 - 5y = 44 \end{cases}$

Substitute y = -4x in the second equation.

$23 - 5( - 4x) = 44 \\ 23 + 20x = 44 \\ 20x = 44 - 23 \\ 20x = 21 \\ x = \frac{21}{20}$

Substitute the value of x in any given equations. I will substitute the value of x in the first equation.

$y = - 4x \Longrightarrow y = - 4( \frac{21}{20} ) \\ y = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \Longrightarrow y = - \frac{21}{5} \\ y = - \frac{21}{5}$

Answer Check by substituting both values in two equations.

First Equation

$y = - 4x \Longrightarrow - \frac{21}{5} = - 4( \frac{21}{20} ) \\ - \frac{21}{5} = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \\ - \frac{21}{5} = - \frac{21}{5} \: \: \: \checkmark$

Second Equation

$23 - 5y = 44 \\ 23 - 5( - \frac{21}{5} ) = 44 \\23 - \cancel{5}( - \frac{21}{ \cancel{5}} ) = 44 \\ 23 + 21 = 44 \\ 44 = 44 \: \: \: \: \checkmark$

Both equations are true for the value of x and value of y.

<h3>Answer</h3>

 $\begin{cases} x = \frac{21}{20} \\ y = - \frac{21}{5} \end{cases}$ 

Coordinate Point form

$( \frac{21}{20} , - \frac{21}{5} )$

5 0

2 years ago

Write the equation of the line through (-2,1) and parallel to y= -3x+1

DedPeter [7]

Use point slope equation y-y1=m(x-x1) Remember that a parallel line has the same slope.

y-1= -3(x-(-2))
y-1= -3(x+2)
y-1= -3x-6
y= -3x-5

Final answer: y=-3x-5

7 0

2 years ago

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Upper H 0: pequals0.6 versus U

kow [346]

Answer:

Step-by-step explanation:

From the given information:

The null and the alternative hypothesis can be well written as:

$H_o:P=0.6$

$H_1:P>0.6$

Given that:

n = 200

x = 135

Alpha ∝ = 0.05 level of significance

Then;

⇒ $n \times p\times (1-P)$

= 200 × 0.6 × (1 -0.6)

= 200 × 0.6 × 0.4

= 48 ≥ 10

The sample proportion $\hat P = \dfrac{x}{n}$

$= \dfrac{135}{200}$

= 0.675

The test statistics $Z = \dfrac{\hat P - P}{\sqrt{ \dfrac{P(1-P)}{n} }}$

$Z = \dfrac{0.675 - 0.6}{\sqrt{ \dfrac{0.6 \times 0.4}{200} }}$

$Z = \dfrac{0.075}{\sqrt{ \dfrac{0.24}{200} }}$

Z = 2.165

The P-value = P(Z > 2.165)

= 1 - P(Z < 2.165)

From the z tables

= 1 - 0.9848

= 0.0152

Reject the null hypothesis since P-Value is lesser than alpha. ( i.e. 0.0152 < 0.05).

Thus, there is enough evidence to conclude that the value of the population proportion is greater than 0.6

7 0

2 years ago

Find sin x/2, cos x/2, and tan x/2 from the given information.. cos x = −15/17, 180° < x < 270°. . sin x/2=. . cos x/2=. .

sukhopar [10]

So base on your question the possible answer to that kind of question and the solution are the following and i hope you will understand the formula and free to ask some questions if needed.

2cos2x2=1+cosx=1−1517=217,cos2x2=117 cosx2=−117−−√....(1) sinx2=117−−√,90<x2<135 sinx2>0,cosx2<0,tanx2<0 2sin2x2=1−cosx=1−−1517=3217,sinx2=417−−√.....(2) divide (2) by (1) and get the value of tan x/2

6 0

2 years ago

Read 2 more answers

What are the answer for your these questions?

ozzi

Answer:

a. 11

b. 9

Step-by-step explanation:

A:

2 x 4 = 8

8 + 3 = 11

B:

-2 x -2 = 4

4 + 5 = 9

Hope this helps! Let me know if it was right!

5 0

2 years ago