All categories

2 years ago

Solve the equation -3(x - 1) + 7x = 27

Mathematics

2 answers:

Lady_Fox [76]2 years ago

6 0

The answer is X=6 !!!!!!

svlad2 [7]2 years ago

6 0

-3x + 3 + 7x = 27

3 + 4x = 27
-3. -3

4x = 24

divide each side by 4

x=6

You might be interested in

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such tha

BartSMP [9]

Answer:

The decision rule is

Reject the null hypothesis

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 5.6 \ pounds/inch^2$

The sample size is n = 160

The sample mean is $\= x = 5.7 \ pounds/ inch^2$

The variance is $\sigma ^2 = 0.25$

The level of significance is $\alpha = 0.01$

The null hypothesis is $H_o : \mu = 5.6$

The alternative hypothesis is $H_a : \mu > 5.6$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\sigma ^2 }$

=> $\sigma = \sqrt{0.25 }$

=> $\sigma = 0.5$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{5.7 - 5.6 }{ \frac{0.5 }{\sqrt{ 160 } } }$

=> $z = 2.53$

From the z table the area under the normal curve to the left corresponding to 2.53 is

$p-value = P(Z > 2.53 ) =0.0057$

From the value obtained we see that the $p-value < \alpha$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the believe that the valve performs above the specifications is true

5 0

2 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

Sabeena had 15 3/4m long ribbon. She cut into two pieces such that the length of one pieces is 9 1/2m. Find the length of other

DochEvi [55]

Answer:

6 1/4

Step-by-step explanation:

Total length of the ribbon= 15 3/4 m= 63/4 m

One piece= 9 1/2 m= 19/2 m

Other piece length =X

X= 63/4-19/2

=63/4-38/4

=25/4

=6 1/4

3 0

2 years ago

Read 2 more answers

The domain of a function f(x) is the set of all integers from 0 to 10, and the range of f(x) is the set of all in

e-lub [12.9K]

I think that the correct answer is f(-1)=-8 and f(0)=-5
I hope this helps :D

6 0

2 years ago

The square pyramid pictured below has a surface area of<br> 9 m<br> 6 m<br> 6 m

Genrish500 [490]

Hey,just to let you know that they is no picture as I can’t answer it.

5 0

2 years ago

Read 2 more answers