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valentina_108 [34]
3 years ago
7

1. Alexander’s grandparents get him a puppy for his thirteenth birthday, and he names the puppy Boomer. When Boomer is 1 month o

ld, he weighs 4 pounds. When he is 2 months old, he weighs 7 pounds. In this relationship, x represents Boomer’s age (in months), and y represent her weight (in pounds). 1a.) Graph the two points for this relationship and the line passing through them on the coordinate plane. (2 points).

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
3 0

See attached graph.

Step-by-step explanation:

Form a table for the information given as shown;

Boomer's age (in months)           Boomer's weight (in pounds)

1                                                             4

2                                                             7

Putting this information as pairs of coordinates will be;

(1,4)  and (2,7)

Plotting the points on a graph tool will give the attached graph.

Finding the equation of the line passing through the points;

m=slope of the line=rise/run

rise=Δy=7-4 = 3

run =Δx =2-1 =1

m=3/1 =3

Δy/Δx =3

y-4/x-1 =3

y-4=3(x-1)

y-4 =3x-3

y=3x-3+4

y=3x+1

Learn More

Linear graphs :brainly.com/question/11954757

Keywords : relationship,graph, line, coordinate plane

#LearnwithBrainly

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The sum of two numbers is 84. The square of the first number is 6 more than the second number.
DerKrebs [107]

The system of equations to find the value of x, the first number, and y, the second number are;

<em>y = -x + 84</em>

<em>y = x² + 6</em>

<h3>System of equation</h3>

The system of equation are equations that contains more than two equation and unknown.

Let the two unknown numbers x and y

If the sum of two numbers is 84, hence;

x +y = 84

y = -x + 84

If the square of the first number is 6 more than the second number, hence;

x² = y + 6

Substitute equation 2 into 2 to have:

x² = y + 6

x² = (-x+84) + 6

x² = -x+84 + 6

x² +x+84 + 6  = 0

x² +x + 90 = 0

Hence the system of equations to find the value of x, the first number, and y, the second number are;

<em>y = -x + 84</em>

<em>y = x² + 6</em>

Learn more on system of equation here; brainly.com/question/12861087

#SPJ1

4 0
2 years ago
a line segment of length 84cm has been divided into two parts in the ratio 4:3 find the length of each part​
Tanzania [10]

Answer:

48 and 36

Step-by-step explanation:

Let the two numbers be 4x and 3x

or4x+3x=84

or, 7x=84

or, x=84÷7

or, x=12

now,

4x=12×4

=48

3x=3×12

=36

5 0
3 years ago
50 POINTS! :D
Alexxandr [17]

Answer:

The speed of the first car is 60 mph

Step-by-step explanation:

speed = distance/time

Solve the above equation for distance to get

distance = speed * time

or simply

d = st

Now we use this formula for distance to write an equation for each car.

Let s = speed of second car

Then since the speed of the first car is 10 mph faster, the first car's speed is s + 10.

The time the two cars traveled is equal but unknown, so let the time = t.

First car: speed = s + 10; time = t; distance = 120 miles

d = st

120 = (s + 10)t    

(s + 10)t = 120      Equation 1

Second car: speed = s; time = t; 100 miles

d = st

100 = st

st = 100       Equation 2

Equations 1 and 2 form a system of 2 equations in 2 unknowns.

(s + 10)t = 120

st = 100

Distribute t in the first equation.

st + 10t = 120

From the second equation we know st = 100, so substitute 100 for st.

100 + 10t = 120

10t = 120

t = 2

The time traveled was 2 hours.

Equation 2:

st = 100

Substitute t with 2.

s * 2 = 100

s = 50

The speed of the second car was 50 mph.

The speed of the first car is s + 10.

s + 10 = 50 + 10 = 60

Answer: The speed of the first car is 60 mph

8 0
3 years ago
PLEASE HELP
poizon [28]
Part A
The given line passes through (-2,2) and it is parallel to the line

4x - 3y - 7 = 0


We need to determine the slope of this line by writing it in slope -intercept form.


3y = 4x - 7


y =  \frac{4}{3} x -  \frac{7}{3}
The slope of this line is
\frac{4}{3}


The line parallel to this line also has slope

m =  \frac{4}{3}


The equation is

y =  \frac{4}{3} x + c


We substitute (-2,2)

2 =  \frac{4}{3}( - 2)  + c


c = 2 + \frac{8}{3}  =  \frac{14}{3}


The required equation is


y =  \frac{4}{3} x + \frac{14}{3}


PART B


The given line is


4x - 3y - 7 = 0




The slope of this line is
\frac{4}{3}


The slope of the line perpendicular to it is

m = -  \frac{3}{4}

The equation of the line is

y =  -  \frac{ 3}{4} x + c




We substitute the point, (-2,2)



2=  -  \frac{ 3}{4} ( - 2) + c


2=  \frac{ 3}{2}  + c



c = 2 -  \frac{3}{2}  =  \frac{1}{2}


The equation of the perpendicular line is


y=  -  \frac{ 3}{4} x +  \frac{1}{2}
6 0
3 years ago
Find the mean of the data given.
Wittaler [7]

Answer:

The mean number of children is 3.

Step-by-step explanation:

8 0
3 years ago
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