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3 years ago

Find the sum of the terms. The numerator of the simplified sum is

Mathematics

1 answer:

klio [65]3 years ago

8 0

Answer:

$4x+6$ is the numerator.

Step-by-step explanation:

The given term is:

$\dfrac{x}{x^{2}+3x+2 }+\dfrac{3}{x+1}$

First of all, let us have a look at the denominator of the 1st term:

$x^{2}+3x+2$

Factorizing by writing $3x$ as $2x+x$ and then taking 'x' and '1' common respectively:

$x^{2}+2x+x+2 \\\Rightarrow x(x+2)+1(x+2 )\\\Rightarrow (x+1)(x+2 )$

Now, solving the given expression by taking LCM:

$\dfrac{x}{(x+{2})(x+1)}+\dfrac{3}{x+1}\\\Rightarrow \dfrac{x+3(x+2)}{(x+{2})(x+1)}\\\Rightarrow \dfrac{x+3x+6}{(x+{2})(x+1)}\\\Rightarrow \dfrac{4x+6}{(x+{2})(x+1)}$

Any expression $\frac{p}{q}$ has $p$ as its numerator and $q$ as its denominator.

So, the numerator of simplified term is:

$4x+6$

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Pls Help

vodomira [7]

First solve the triangle:
75° + 75° + x = 180°
150° + x = 180°
x = 180° - 150°
Therefore x = 30°
Then, use the geometrical property of vertically opposite angles.
Therefore. x° = 30°

3 0

2 years ago

Read 2 more answers

Jennifer hit a golf ball from the ground and it followed the projectile ℎ(t)= −15t^2+100t, where t is the time in seconds, and ℎ

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

In order to find the max height the ball reached, we have to complete the square on that quadratic. That will also, conveniently so, give us the number of seconds it will take the ball to reach that max height, that answer to part b. Let's begin to complete the square. Normally, you would move the constant over to the other side of the equals sign, but there is no constant here. The next step is to get the leading coefficient to be a 1, and ours right now is a -15. So we have to factor it out. Here's where we start the process of completing the square.

$-15(t^2-\frac{20}{3}t)=0$ Next step is to take half the linear term, square it, and add it to both sides. Our linear term is 20/3. Half of 20/3 is 20/6, and 20/6 squared is 400/36.

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0+???$ Because this is an equation, what we add to the left side also has to be added to the right. BUT we didn't just add in 400/36, because we have that -15 out front as a multiplier that refuses to be ignored. What we actually added in was -15(400/36):

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0-\frac{500}{3}$

The reason we do this is to create a perfect square binomial on the left which will serve as the number of seconds, h, in the vertex (h, k), where h is the number of seconds it takes the ball to reach its max height, k. Simplifying both sides then gives us:

$-15(t-\frac{20}{6})^2=-\frac{500}{3}$ Finally, we will move the right side over by the left and set the quadratic back equal to h(t):

$h(t)=-15(t^2-\frac{20}{3})^2+\frac{500}{3}$ and from that you can determine that the vertex is $(\frac{20}{3},\frac{500}{3})$ .

The answer to a. is vound in the second number of our vertex: k, the max height. The max of the golf ball was 500/3 feet or 166 2/3 feet.

Part b is found in the first number of the vertex: h, the number of seconds it took the golf ball to reach that max height. The time it took was 3 1/3 seconds.

Part c. is to state the domain (the time) and the range (the height) of the ball.

Domain is

D: {x | 0 ≤ x ≤ 3 1/3} and

Range is

R: {y | 0 ≤ y ≤ 166 2/3}

8 0

3 years ago

Express the following fractions as the sum or difference of two fractions (x^2+y^2)/x^4

zlopas [31]

Answer:

$\frac{1}{x^2}$ + $\frac{y^2}{x^4}$

Step-by-step explanation:

$\frac{x^2 + y^2}{x^4}$ = $\frac{x^2}{x^4}$ + $\frac{y^2}{x^4}$ = $\frac{1}{x^2}$ + $\frac{y^2}{x^4}$

4 0

2 years ago

Help, please! 10 points to solve.

sineoko [7]

The answer is B, 7.6-(-1.7)=9.3

6 0

3 years ago

Please answer this correctly

bonufazy [111]

Answer:

The dependent variable is m

Step-by-step explanation:

A dependent variable is dependent on an independent variable. This variable is dependent on other variable that are measured . The dependent variable are expected to change as a result of the manipulation of the independent variables. Usually as the experiments changes the independent variable the dependent variable are observed and noted.

The independent variable is unaffected by the other variable you are measuring. The independent variable represent a quantity that is been manipulated in an experiment.

According to the question Jenny works as a server at Jefferson restaurant . The more table she is assigned to serve the more money she earns during a shift.

The independent variable is the number of table Jenny served because this is what she has control over.

The dependent variable is the amount of money Jenny earns because the amount of money she earns is dependent on the number of tables she served . Therefore the dependent variable is m

7 0

3 years ago