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mariarad [96]
3 years ago
7

Find the sum. 5 2a a? + 2a + 1 + a2 + 4a + 3

Mathematics
2 answers:
Vinvika [58]3 years ago
7 0

Answer:

=  \frac{2 {a}^{2}  + 11a + 5}{  {(a + 1)}^{2}(a + 3)} \\

Step-by-step explanation:

\frac{2a}{ {a}^{2}  + 2a + 1} +  \frac{5}{ {a}^{2} + 4a + 3 } \\  \frac{2a}{(a + 1)(a + 1)}    +  \frac{5}{(a + 1)(a + 3)}  \\   \frac{2a}{ {(a + 1)}^{2} }  +  \frac{5}{(a + 1)(a + 3)}  \\  \frac{2a(a + 3) + 5(a + 1)}{ {(a + 1)}^{2}(a + 3) }  \\  \frac{2 {a}^{2} + 6a + 5a + 5 }{ {(a + 1)}^{2}(a + 3)} \\  =  \frac{2 {a}^{2}  + 11a + 5}{  {(a + 1)}^{2}(a + 3)}

Salsk061 [2.6K]3 years ago
5 0

\frac{2a}{a^2+2a+1}+\frac{5}{a^2+4a+3}

Factor the denominators.

\frac{2a}{\left(a+1\right)^2}+\frac{5}{\left(a+1\right)\left(a+3\right)}

Adjust fractions based on LCM.

\frac{2a\left(a+3\right)}{\left(a+1\right)^2\left(a+3\right)}+\frac{5\left(a+1\right)}{\left(a+1\right)^2\left(a+3\right)}

Denominators are same, so add the fractions.

\frac{2a\left(a+3\right)+5\left(a+1\right)}{\left(a+1\right)^2\left(a+3\right)}

Expand the numerator.

\frac{2a^2+11a+5}{\left(a+1\right)^2\left(a+3\right)}

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The sets of numbers 7, 24, 25 and 9, 40, 41 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain
salantis [7]

Answer:

25^2=625

24^2= 576

7^2= 49

as 625 = 576+49 so 7,24,25 form a Pythagorean triplet

similarly

9,40,41 also is a Pythagorean triplet

8 0
3 years ago
Find the equation of the parabola whose vertex is the origin and whose directrix is x = -4
lapo4ka [179]

Try this option:

1) if V(0;0) and x= -4, then common view of the required equiation is:

(y-k)²=4p(x-h), where focus is in (h-p;k), the vertex is in (h;k), the directrix is x=h+p, p<0 and y=k is simmetry axis;

2) if the V(0;0), then h=k=0 and the required equiation is:

y²=4px;

3) if the directrix equation is x=h+p, where h=0, then p= -4 (according to the condition the directrix equation is x= -4), then the required equation is:

y²= -16x

answer: y²= -16x

6 0
3 years ago
Which of the following equations has a slope of -2 and passes through the point (2,3)?
ryzh [129]

Option C (Same as Option D)

<h2>Explanation:</h2>

Option C and D are the same, so I'll assume you made a mistake when writing this question. However, let's figure out which of the following equations has a slope of -2 and passes through the point (2,3):

A. y = -2x + 6

B. y - 3 = -2(x + 2)

C. y = -2x + 7

<em />

<em>All these equations have a slope of -2.</em>

FROM OPTION A:

Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+6 \\ \\ 3=-4+6 \\ \\ 3=2 \ False!

Since 3\neq 2 then the line doesn't pass through the point (2, 3)

FROM OPTION B:

Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3-3=-2((2)+2) \\ \\ 0=-2(4) \\ \\ 0=-8 \ False!

Since 0\neq -8 then the line doesn't pass through the point (2, 3)

FROM OPTION C:

Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+7 \\ \\ 3=-4+7 \\ \\ 3=3 \ True!

Since 3\neq 3 then the line passes through the point (2, 3)

<em>Finally, the equation that has a slope of -2 and passes through the point (2,3) is Option C (Same as Option D)</em>

<em></em>

<h2>Learn more:</h2>

x and y intercepts of a line: brainly.com/question/13770925#

#LearnWithBrainly

5 0
3 years ago
Solve the following equation for x.<br><br> 28.8 = 1.8x
Alisiya [41]

Answer:

x=16

Step-by-step explanation:

28.8 / 1.8 is 16.

7 0
3 years ago
Given the system of equations, what is the solution?
pychu [463]
Answer is C. By solving x-y=-5 to x=-5+y and converting 2x + y = -1 into 2x + x + 5 = -1 the answer becomes -2 =x. By plugging that into 2 (-2) + y = -1, the answer is y=3. So your answer is C
3 0
3 years ago
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