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Zielflug [23.3K]
3 years ago
12

Use the graph to find the solution of the system of equations {y = x^2 + 6x + 8 {y = x + 4

Mathematics
1 answer:
Phantasy [73]3 years ago
8 0
Essentially when people ask you find the solution to system of equation, there asking at what x value do these to graphs intersect. The easiest way to do this is to get a graphing calculator, or desmos and type in the equation and find where they intersect. Heck, even the question says to solve it with a graph, but I'll demonstrate it algebraically.

One way you can do this is set the equation equal to each other. This is because you want to know at what x-value has the same y-value. So we get:

x^2 + 6x + 8 = x + 4

We can then combine like terms, or move everything to one side. So we get:

x^2 + 5x + 4 = 0.

Then we can use the quadratic formula to solve for x.

x=(-5 +/- sqrt(5^2 - 4(1)(4)))/(2(1)

This simplifies into:

(-5 +/- 3)/2

Finally we add and subtract:

(-5 + 3)/2 = x = -1
(-5 - 3)/2 = x = -4

And our solution is x = -1, x = -4
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2/5 of the children in a club are girls,if there are 24 boys,how many children are there altogether?how many more boys than girl
Masja [62]
2/5 are girls, therefore 3/5 are boys

3/5 = 24
1/5 = 24 ÷ 3 = 8
2/5 = 8 x 2 = 16

Altogether = 16 + 24 = 40 

24  - 1 6 = 8

There are 40 children altogether
There are 8 more boys than girls.


5 0
3 years ago
Read 2 more answers
(2) (x-7) (=3) (x+8)
Tasya [4]

Use the distributive property to get 2x - 14 = 3x + 24. Subtract 24 from both sides to get 2x - 38 = 3x. Subtract 2x from both sides to get -38 = x.

7 0
3 years ago
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Which is an equation of the line with slope –3 and passes through (2, –1)
Savatey [412]

using the formula:

y = mx +b

Using the given slope and coordinate points we get:

-1 = -3(2) + b

-1 = -6 + b

add 6 to each side

5 = b

y = -3x + 5

which is the same as:

3x + y = 5 ...answer choice a

7 0
3 years ago
Can 3.65909090909 be expressed as a fraction whose denominator is a power of 10? Explain.
GuDViN [60]
\bf 3.659\textit{ can also be written as }\cfrac{3659}{1000}\textit{ therefore }3.6590909\overline{09}\\\\
\textit{can be written as }\cfrac{3659.0909\overline{09}}{1000}

notice above, all we did, was isolate the "recurring part" to the right of the decimal point, so the repeating 09, ended up on the right of it.

now, let's say, "x" is a variable whose value is the recurring part, therefore then

\bf \cfrac{3659.0909\overline{09}}{1000}\qquad \boxed{x=0.0909\overline{09}} \qquad \cfrac{3659+0.0909\overline{09}}{1000}\implies \cfrac{3659+x}{1000}

now, the idea behind the recurring part is that, we then, once we have it all to the right of the dot, we multiply it by some power of 10, so that it moves it "once" to the left of it, well, the recurring part is 09, is two digits, so let's multiply it by 100 then, 

\bf \begin{array}{llllllll}
100x&=&09.0909\overline{09}\\
&&9+0.0909\overline{09}\\
&&9+x
\end{array}\quad \implies 100x=9+x\implies 99x=9
\\\\\\
x=\cfrac{9}{99}\implies \boxed{x=\cfrac{1}{11}}\\\\
-------------------------------\\\\
\cfrac{3659.0909\overline{09}}{1000}\qquad \boxed{x=0.0909\overline{09}} \quad \cfrac{3659+0.0909\overline{09}}{1000}\implies \cfrac{3659+x}{1000}
\\\\\\
\cfrac{3659+\frac{1}{11}}{1000}

and you can check that in your calculator.
8 0
3 years ago
Please help, Math is not for me
Bond [772]

Answer:

-25

Step-by-step explanation:

-5 * -5= -25

7 0
3 years ago
Read 2 more answers
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