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3 years ago

Which graph represents the solution set of y=x^2+4x+3and y=2x+6?

Mathematics

2 answers:

rewona [7]3 years ago

3 0

Answer:

(1,8) and (-3,0)

Step-by-step explanation:

We simply graph the two functions in the same graph. The solution set to the system is given by the points where the two functions intersect. For this case, the two functions intersect at;

(1,8) and (-3,0)

The solution set is thus; (1,8) and (-3,0)

Check the attachment below;

ehidna [41]3 years ago

3 0

Answer:

(1,8) and (-3,0) is the solution.

Step-by-step explanation:

We have given the system of equations:

y=x^2+4x+3 and y=2x+6

We have to find the graph which represent the solution set of given system.

The solution set in the graph is the point of intersection of the lines.

So, in this graph the intersection points are (1,8) and (-3,0).

Which is the solution set if the given equations.

We attached the graph.

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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find

Blababa [14]

$After\ adding\ equations\ and\ simplifying:\\\\One\ solution:\\\\x=number\\ example: x=2\\\\ infinitely\ many\ solutions:\\\\ Left\ side=\ Right\ side\\ example:\\ 2=2\\\\ No\ solutions:\\\\2 \neq 5$ $\left \{ {{x+3y=9} \atop {3x-y=7}\ \ |*3} \right.\\\\ \left \{ {{x+3y=9} \atop {9x-3y=21}} \right.\\+--------\\\\Addition\ method:\\\\10x=30\ \ |:10 \\\\x=3\\\\x+3y=9\\\\3y =9-x=9-3=6\\\\y=2\\\\ \left \{ {{y=2} \atop {x=3}} \right.$

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3 years ago

What is least to greatest 2/8 2/1 3/4 5/6 7/6

yKpoI14uk [10]

Answer:

2/8, 3/4, 5/6, 7/6, 2/1

Step-by-step explanation:

To convert the fractions into ascending order (least to greatest):

1. Determine the LCM (Least common multiple) of the denominators.

2. Then, using the LCM, multiply such number to the denominators such that the product is equivalent to the LCM of the denominators.

Note: The number we multiply to the denominator must also be multiplied to the numerator.

3. Finally, create the set, in ascending order.

<h3>Determine the LCM of the denominators:</h3>

Given fraction set;

$\dfrac{2}{8} ; \ \dfrac{2}{1}; \ \dfrac{3}{4}; \ \dfrac{5}{6};\ \dfrac{7}{6}$

Therefore, the denominators of the fraction set are;

$\implies \text{Denominators: 8, 1, 4, 6, 6}$

Determining the LCM using Division method;

$\ \ \underline{................}\\2\underline{| 8, 1, 4, 6, 6}\\ 2\underline{|4, 1, 2, 3, 3} \\ 2\underline{|2,1,1,3,3} \\3 \underline{|1, 1,1,1,1}$

LCM of denominators: 2 × 2 × 2 × 3 = 24

<h3>Multiplying the denominators:</h3>

LCM of denominators: 24

<u>Multiply such number such that the denominators are equivalent to 24.</u>

$\implies \dfrac{2}{8} ; \ \dfrac{2}{1}; \ \dfrac{3}{4}; \ \dfrac{5}{6};\ \dfrac{7}{6}$

$\implies \dfrac{2 \times 3}{8 \times 3} ; \ \dfrac{2 \times 24}{1 \times 24} ; \ \dfrac{3 \times 6}{4 \times 6} ; \ \dfrac{5 \times 4}{6 \times 4} ; \ \dfrac{7 \times 4}{6 \times 4}$

$\implies \dfrac{6}{24} ; \ \dfrac{48}{24} ; \ \dfrac{18}{24} ; \ \dfrac{20}{24}; \ \dfrac{28}{24}$

<h3>Creating the set, in ascending order;</h3>

<u>Simply compare the fractions and put them in "smallest to biggest" order.</u>

$\implies \dfrac{6}{24} ; \ \dfrac{48}{24} ; \ \dfrac{18}{24} ; \ \dfrac{20}{24}; \ \dfrac{28}{24}$

$\implies \dfrac{6}{24} < \dfrac{18}{24} < \dfrac{20}{24} < \dfrac{28}{24} < \dfrac{48}{24}$

$\implies \dfrac{6}{24} \ \ \huge{\text{(}\dfrac{2}{8} } \text{)}; \ \dfrac{18}{24} \ \huge{\text{(}\dfrac{3}{4}\huge{\text{)} ; \ \dfrac{20}{24} \ \huge{\text{(}\dfrac{5}{6} \huge{\text{)} ; \ \dfrac{28}{24} \ \huge{\text{(} \dfrac{7}{6} \huge{\text{)}; \ \dfrac{48}{24} \ \huge{\text{(} \dfrac{2}{1} \huge{\text{)}$

Therefore, the set, in ascending order, is 2/8, 3/4, 5/6, 7/6, 2/1

Learn more about this topic: <u>brainly.com/question/27432239</u>

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2 years ago

40 points!!<br> What's the equation for this ellipse?

Ostrovityanka [42]

Answer:

(x +5)²/4 +(y +8)²/36 = 1

Step-by-step explanation:

The equation of an ellipse with center (h, k) and semi-axes "a" and "b" (where "a" is in the x-direction and "b" is in the y-direction) can be written as ...

((x -h)/a)² +((y -k)/b)² = 1

Here, the center is at (h, k) = (-5, -8), and the semi-minor axis is a=2, while the semi-major axis is b=6.

The equation can be written as ...

((x +5)/2)² +((y +8)/6)² = 1

More conventionally, it is written ...

(x +5)²/4 +(y +8)²/36 = 1

3 0

2 years ago

Read 2 more answers

How do you multiply fractions with cross canceling<br />

AVprozaik [17]

3 9
_ * _
15 6

Compare diagonally to see if they the 2 numbers simplify.

Ex:

3 and 6 Simplify to 1 and 2 because they are both multiples of 3.

9 and 15 Simplify to 3 and 5 because they are both multiples of 3 as well.

Now our fractions are

1 3
_ * _
5 2

Now multiply across to get your final fraction/answer

3
_
10

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3 years ago

Find the gradient of the line segment between the points (-3,2) and (-2,5).

IrinaVladis [17]

-3
Solution,
Let the points be A and B
A(-3,2)------->( X1,y1)
B(-2,5)------>( x2,y2)

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2 years ago