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3 years ago

What are the solutions to the system of equations graphed below? Select all that apply.

Mathematics

2 answers:

postnew [5]3 years ago

7 0

Answer is A and B. Solutions are where the two graphs cross, so you just need to find those coordinates, which are (-5,-13) and (2,-6).

Fudgin [204]3 years ago

4 0

Answer:

The solution points are:

(2, -6)

(-5, -13)

Therefore, option (A) and option (B) is true.

Step-by-step explanation:

We know that the solution to the system of equations on the graph is the point of intersection of the equations. In other words, the point or points, where both the graphs of the equations meet or intersect.

POINT OF INTERSECTION (2, -6)

From the given diagram, it is clear that there are two points of intersections which are:

at point x = 2, the graphs of both equations meet, and the corresponding y-value is y = -6.

Thus, (2, -6) is the point of intersection.

POINT OF INTERSECTION (-5, -13)

Now, also check at point x = -5, the graphs of both equations again meet, and the corresponding y-value is y = -13.

Thus, (-5, -13) is the point of intersection.

Therefore, the solution points are:

(2, -6)

(-5, -13)

Therefore, option (A) and option (B) is true.

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12. Determine the slope of the line having the equation 2x + y = 12

Virty [35]

Answer:

b. -2

Step-by-step explanation:

Note the slope-intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

First, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides of the equation:

2x (-2x) + y = (-2x) + 12

y = -2x + 12

Remember, m is the variable for the term that stands for the slope (directly next to the x variable). In this case, your answer will be -2

b. -2 is your answer.

4 0

2 years ago

Read 2 more answers

Susan wants to make pumpkin bread and coffee cakes for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry.

aev [14]

15 eggs and 16 cups flour 
Pumpkin bread (x) : 2 eggs & 3 cups of flour 
Coffee cake (y) : 3 eggs & 4 cups of flour 
2x + 3y ≤ 15 { number of eggs used} 
3x + 4y ≤ 16 { number of cups of flour used } 
Objective function 
P = 5x + 4y

6 0

3 years ago

Civil an airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. the airport

vekshin1

Answer:

The shortest possible length for the service road is 2.88 miles.

Step-by-step explanation:

According to the below diagram, $A, B$ and $C$ are the positions of airport, shopping center and factory respectively.

Given that, $AB= 3.6 miles, BC= 4.8 miles$ and $AC= 6.0 miles$

In right triangle $ABC$

$tan(\angle ACB)=\frac{AB}{BC} \\ \\ tan(\angle ACB)= \frac{3.6}{4.8}=0.75\\ \\ \angle ACB= tan^-^1(0.75)=36.8698.... degree$

The shortest possible length for the service road from the shopping center to the highway that connects the airport and factory is $BD$ .

That means, $\triangle BCD$ is also a right triangle in which $\angle BDC=90\°$ , Hypotenuse $(BC)= 4.8$ miles and $BD$ is the opposite side in respect of $\angle DCB$ or $\angle ACB$ .

Now in right triangle $BCD$

$Sin(\angle ACB)=\frac{BD}{BC}\\ \\ Sin(36.8698...)=\frac{BD}{4.8}\\ \\ BD=4.8*Sin(36.8698...)=2.88$

So, the shortest possible length for the service road is 2.88 miles.

4 0

3 years ago

Find the hypotenuse of right angle triangle whose sides are 6.03 units and 7.96 units also find

xxMikexx [17]

The hypotenuse is is 9.98 units

<h3>What is Pythagoras theorem?</h3>

The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Given:

Sides are 6.03 units and 7.96 units

Using Pythagoras theorem,

H²=P²+B²

H²= 7.96²+6.03²

= 63.3616+36.3609

= 99.7225

H=9.98 units.

Hence, the hypotenuse is 9.98 units.

Learn more about Pythagoras theorem here:

brainly.com/question/343682

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