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3 years ago

Are the expressions -0.5(3x + 5) and -1.5x + 2.5 equivalent? Explain why or why not

Mathematics

2 answers:

Gelneren [198K]3 years ago

7 0

Answer:

Step-by-step explanation:

-0.5(3x + 5) and -1.5x + 2.5

-0.5(3x + 5)...distribute the -0.5 thru the parenthesis

-1.5x - 2.5

no, these are not equivalent.... one is -1.5x + 2.5 and the other is -1.5x - 2.5....not the same

Anna71 [15]3 years ago

3 0

Answer:

Both expressions are not equal

Step-by-step explanation:

First expression is

-0.5(3x + 5)

By multiplying

-1.5x - 2.5

2nd expression is

-1.5x + 2.5

Only Sign is different with 2.5 in both cases

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4

Dmitry [639]

Answer:

$\boxed{\sf Standard-form :x + 4y -17=0 }\\$

$\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

$\longrightarrow x + 4y = 7\\$

Firstly convert it into slope intercept form of the line which is y = mx + x , as ;

$\longrightarrow 4y = -x + 7 \\$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\$

On comparing it to y = mx + c , we have ,

$\longrightarrow m =\dfrac{-1}{4}\\$

$\longrightarrow c =\dfrac{7}{4}\\$

Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}\\$

Now we may use point slope form of the line as ,

$\longrightarrow y - y_1 = m(x-x_1) \\$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\$

$\longrightarrow 4(y -5 ) =-1(x +3) \\$

$\longrightarrow 4y -20 = - x -3 \\$

$\longrightarrow x + 4y -20+3=0\\$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\$

6 0

2 years ago

If cos(x) = Three-fourths and tan(x) < 0, what is cos(2x)?

makvit [3.9K]

Step-by-step explanation:

The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

How to determine the value of sin(2x)

The cosine ratio is given as:

\cos(x) = -\frac 14cos(x)=−

Calculate sine(x) using the following identity equation

\sin^2(x) + \cos^2(x) = 1sin

(x)+cos

(x)=1

So we have:

\sin^2(x) + (1/4)^2 = 1sin

(x)+(1/4)

\sin^2(x) + 1/16= 1sin

(x)+1/16=1

Subtract 1/16 from both sides

\sin^2(x) = 15/16sin

(x)=15/16

Take the square root of both sides

\sin(x) = \pm \sqrt{15/16

Given that

tan(x) < 0

It means that:

sin(x) < 0

So, we have:

\sin(x) = -\sqrt{15/16

Simplify

\sin(x) = \sqrt{15}/4sin(x)=

sin(2x) is then calculated as:

\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)

So, we have:

\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗

∗

This gives

\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

6 0

2 years ago

Read 2 more answers

un aliaj de platina are titlu de 0,800 si contine 1968 g de platina pura. Aflati masa aliajului. E urgent!!!!!!!!!!!!!!!!!!!1

MrRissso [65]

așa că nu sunt sigur ce vrei să spui ce este întrebarea?

7 0

3 years ago

A community college has 150 word processors. The probability that any one of them will require repair on a given day is 0.025. T

Volgvan

Answer:

Binomial Distribution

Step-by-step explanation:

In this case there are only two possible outcomes that is either the processor requires repair or does not require.

In such cases binomial distribution is beneficial to use.

Binomial Distribution is simply the probability of failure or success in an experiment that is repeated multiple times.

for binomial to be used following three conditions are to be used:

1. Fixed number of trails

2. Each trial or observation is independent

3. probability of success is exactly same

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3 years ago

For Carolina's birthday, her mom took her and 4 friends to a water park. Carolina's mom paid $40 for 5 student tickets. What was

Law Incorporation [45]

Answer:

The price for one student ticket is $8

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3 years ago