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3 years ago

Solve the following system using substitution: x + 12y =68, x = 8y -12

2 answers:

6 0

Plug 8y - 12 in for X of X + 12y =68. Solve for y by getting the variable of y on one side and the whole numbers on the other. Divide the number in front of y on both sides to find y.

dusya [7]3 years ago

3 0

The answer should be y=4

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Triangle ABC has vertices at A(-2,1), B(-2,-3), and C(1,-2). What is the area of the triangle? a 18 square units b 9 square unit

natka813 [3]

Answer:

Option C. 6 square units

Step-by-step explanation:

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

Let

a,b,c be the lengths of the sides of a triangle.

The area is given by:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

where

p is half the perimeter

p= $\frac{a+b+c}{2}$

we have

Triangle ABC has vertices at A(-2,1), B(-2,-3), and C(1,-2)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

$d=\sqrt{(-3-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(-4)^{2}+(0)^{2}}$

$dAB=4\ units$

step 2

Find the distance BC

$d=\sqrt{(-2+3)^{2}+(1+2)^{2}}$

$d=\sqrt{(1)^{2}+(3)^{2}}$

$dBC=\sqrt{10}\ units$

step 3

Find the distance AC

$d=\sqrt{(-2-1)^{2}+(1+2)^{2}}$

$d=\sqrt{(-3)^{2}+(3)^{2}}$

$dBC=\sqrt{18}\ units$

step 4

$a=AB=4\ units$

$b=BC=\sqrt{10}\ units$

$c=AC=\sqrt{18}\ units$

Find the half perimeter p

p= $\frac{4+\sqrt{10}+\sqrt{18}}{2}=5.70\ units$

Find the area

$A=\sqrt{5.7(5.7-4)(5.7-3.16)(5.7-4.24)}$

$A=\sqrt{5.7(1.7)(2.54)(1.46)}$

$A=\sqrt{35.93}$

$A=6\ units^{2}$

7 0

3 years ago

denny can deliver 6 papers every 15 minutes and brendan can deliver 5 papers in that same amount of time. how many papers can th

Evgesh-ka [11]

So for this problem you know that 15 is 1/4 of an hour so to get the amount of papers each individual could deliver by themselves in an hour you would multiply the amount they can deliver in 15 minutes by 4. Denny delivers 6 so multiplying that by 4 is 24. Next Brendan delivers 5 in 15 minutes so multiplying that by 4 you get 20. The final step is to add 20 and 24 to get the total amount of papers between the two of them that gets delivered in an hour. This will result in your answer of 44.

7 0

4 years ago

Read 2 more answers

What s the length of the arc for the half circle

Andrej [43]

Answer`Step-by-step explanation:

The length of an arc depends on the radius of a circle and the central angle Θ. We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:

Hope that help, at least a bit.

3 0

4 years ago

Lian is paid for SR 75 per hour. Using p for her pay and h for the hours of work, which function rule represents

Andru [333]

Answer:

The function p = 75h represents this situation.

Step-by-step explanation:

We know the equation of linear equation in the slope-intercept form is

$y = mx+b$

where

m = rate of change = slope

b = y-intercept

Let 'h' be the number of hours

Let 'p' be the pay

Given that Lian is paid SR 75 per hour.

so the rate of change of slope = m = 75

As there is no initial condition, so b = 0

y = mx+b

Now, mapping the information data into the slope-intercept form

p = y

m = 75

h = x

b = 0

Thus, the equation becomes

p = 75h

Therefore, the function p = 75h represents this situation.

VERIFICATION:

Given the equation

p = 75h

for h = 1

p = 75(1)

p = 75

Thus, Liam is paid SR 75 per hour.

4 0

3 years ago

Factor out each GCF

anyanavicka [17]

15cd(1+2cd) is correct

3 0

3 years ago