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2 years ago

Simplify: (4x - 6) - (5x + 1)

Mathematics

1 answer:

marissa [1.9K]2 years ago

3 0

Answer:

−x+−7

Step-by-step explanation:

Let's simplify step-by-step.

4x−6−(5x+1)

Distribute the Negative Sign:

=4x−6+−1(5x+1)

=4x+−6+−1(5x)+(−1)(1)

=4x+−6+−5x+−1

Combine Like Terms:

=4x+−6+−5x+−1

=(4x+−5x)+(−6+−1)

=−x+−7

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If gas costs $2.19 per gallon, how many whole gallons of gas could you buy with $17.00? (Make sure to answer with a whole number

ankoles [38]

Answer:

2.19*17.00

=37.23

=$37

Step-by-step explanation:

4 0

2 years ago

Solve for r in the diagram below.<br> (x + 12)<br> 100°

shusha [124]

Answer:

x = 34

Step-by-step explanation:

The sum of the three angles is 180 since they make a straight line

x+12 + 100 +x = 180

Combine like terms

2x+112=180

Subtract 112 from each side

2x+112-112= 180-112

2x = 68

Divide by 2

2x/2 =68/2

x = 34

7 0

2 years ago

Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Check

Kisachek [45]

<h3>1. The term $-2(x-2)^2$ is simplified by first squaring the expression (x – 2). </h3><h3>TRUE </h3><h3>2. The simplified product is a binomial. TRUE</h3><h3>3. After multiplying, the like terms are combined by adding and subtracting.</h3><h3>TRUE </h3><h3>4. The parentheses are eliminated through multiplication. TRUE</h3><h3>5. The final simplified product is $-28x^2 + 8x - 8$ FALSE</h3>

Step-by-step explanation:

Here, the given expression is :

$F(x) = 3x(x- 12x) + 3x^2-2(x-2)^2$

Now, let us first solve the given expression step wise:

$F(x) = 3x(x-12x) +3x^2 -2(x-2)^2\\= 3x(-11x) +3x^2 -2(x^2 +4 -4x)\\= -33x^2 + 3x^2 -2x^2 -8+8x\\= -32x^2 +8x - 8\\\implies F(x) = -32x^2 +8x - 8$

Now, here the given statements are:

1. The term $-2(x-2)^2$ is simplified by first squaring the expression (x – 2).

TRUE

2. The simplified product is a binomial. TRUE

3. After multiplying, the like terms are combined by adding and subtracting.

TRUE

4. The parentheses are eliminated through multiplication. TRUE

5. The final simplified product is $-28x^2 + 8x - 8$ FALSE

As the simplified expression is: $(-32x^2 +8x -8)$

7 0

3 years ago

G(x) = x to the power of 2 - 6 over 3x + 10 & g(4) = what over what

dalvyx [7]

Answer:

We have that:

$g(x) = \frac{x^2 - 6}{3*x + 10}$

And we want to find the value of g(4)

Then we are evaluating the function g(x) in x = 4, this means that we need to locate all the "x" in g(x), and replace them by 4.

If we do that, we get:

$g(4) = \frac{4^2 - 6}{3*4 + 10}$

Now we can just solve this to get:

$g(4) = \frac{4^2 - 6}{3*4 + 10} = \frac{16-6}{12-10} = \frac{10}{2} = 5$

8 0

3 years ago

The lengths of lumber a machine cuts are normally distributed with a mean of 106 inches and a standard deviation of 0.3 inch. (

Vinvika [58]

Answer:

a) $P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

b) $z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

Step-by-step explanation:

Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:

$X \sim N(106,0.3)$

Where $\mu=106$ and $\sigma=0.3$

Part a

We are interested on this probability

$P(X>106.11)$

And we can use the z score formula given by:

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

And using this formula we got:

$P(X>106.11)=P(\frac{X-\mu}{\sigma}\frac{106.11-106}{0.3})=P(z>0.37)$

And we can find this probability with the complement rule:

$P(z>0.37)=1-P(z$

Part b

For this case we select a sample of n =44 and the new z score formula is given by:

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

And if we find the z score we got:

$z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}= 2.431$

And if we use the z score we got:

$P(z>2.431) =1-P(z$

6 0

2 years ago

Simplify: (4x - 6) - (5x + 1)​

Simplify: (4x - 6) - (5x + 1)