What is the area of ΔABC A. 64 B. 128 C. 32 D. 42.6

What is the solution to the system of equations?

Maslowich

Answer:

B) (10, -20)

Step-by-step explanation:

Plug in the values to y = -5x + 30 to see if they match:

we already know that x = 10 so are equation will always be:

y = -5(10) + 30 = -50 + 30 = -20

our new equation is y = -20

so your answer is B) (10, -20)

because the X-value has to be 10 and Y-value is equal to -20

4 0

4 years ago

The Paddock family drove 360 miles on a full tank of gasoline. How many miles per gallon were they able to get if their gas tank

timofeeve [1]

Answer:the number of miles per gallon that they were able to get is 18

Step-by-step explanation:

The Paddock family drove 360 miles on a full tank of gasoline.

if their gas tank holds 20 gallons of gas, it means that the number of miles per gallon that they were able to get would be total number of miles driven divided by the car's tank capacity. It becomes

360/20 = 18 miles per gallon

6 0

3 years ago

A box with a square base and an open top is to be constructed using 7500 sq. in. of cardboard. Find the dimensions of the box th

umka2103 [35]

Answer:

Step-by-step explanation:

Let the length of one side of the square base be x

Let the height of the box by y

Volume of the box V = x²y

Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy

S = x² + 4xy

Given

S = 7500sq in.

Substitute into the formula for calculating the total surface area

7500 = x² + 4xy

Make y the subject of the formula;

7500 - x² = 4xy

y = (7500-x²)/4x

Since V = x²y

V = x² (7500-x²)/4x

V = x(7500-x²)/4

V = 1/4(7500x-x³)

For us to maximize the volume, then dV/dx = 0

dV/dx = 1/4(7500-3x²)

1/4(7500-3x²) = 0

(7500-3x²) = 0

7500 = 3x²

x² = 7500/3

x² = 2500

x = √2500

x = 50in

Since y = (7500-x²)/4x

y = 7500-2500/4(50)

y = 5000/200

y = 25in

Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.

The Volume of the box V = 50²*25

V = 2500*25

V= 62,500in³

Hence the maximum volume is 62,500in³

3 0

3 years ago

WILL MARK AS BRAINLIEST FOR THESE QUESTIONS.

laiz [17]

1.

Let the sandwich be represented by = x

Let the drink be represented by = y

As given, Joe charges $10.00 for two sandwiches and one drink, so equation becomes 2x+y=10 ....(i)

He charges $6.50 for one sandwich and one drink, so equation becomes x+y=6.50 ....(ii)

Subtracting (ii) from (i) we get

x=3.50

And as x+y=6.50

y=6.50-3.50=3.00

Hence, cost of a sandwich is $3.50 and a drink is $3.00

2.

the question is incomplete. coordinates are missing

3.

Let x represent the number of performances

cost = 8000+300x

revenue = 700x

To break even, the cost must be equal to the revenue.

$8000+300x=700x$

$400x=8000$

so x=20

Hence, 20 performances are needed to break even.

4.

Let us take x for 20% material, y for 50% material

$\frac{20x+50y}{200}=30$

$20x+50y=6000$ ......... (1)

Accounting for volumes to use, x+y=200 or x=200-y ................ (2)

Putting the value of x in (1)

$20(200-y)+50y=6000$

$4000-20y+50y=6000$

$4000+30y=6000$

$30y=2000$

y=66.67

x=200-y = 200-66.67 =133.33

Hence, 133.33 ml of 20% acetic acid and 66.67% of 50% acetic acid is needed.

3 0

4 years ago

Pls Help sue tmr pls pls pls

MAXImum [283]

Step-by-step explanation:

3.

the net of a cylinder looks like a rectangle with two circles attached at opposite ends. we also define a base radius for the cylinder as the radius of the base, and the height of the cylinder as the distance between the bases.

in other words, imagine you cut open a soda can (and leave the top and bottom just a little bit attached - don't cut them off completely).

the mantle turns into a rectangle. and the base and top are two circles. the length of the rectangle is the circumference of one of the circles (2×pi×r), and the width of the rectangle is the height of the original can.

4.

remember what you did when calculating the size of the area of a square ? or a rectangle ?

in each case it is in principle length×width.

and we expressed an area not in units of e.g. cm but in cm², because we simply said how many little squares of 1 unit side length fit into the area.

now, for the volume, we apply the same principle and simply add a third dimension.

we express a volume not in cm² squares but in cm³ cubes, saying how many such little cubes fit inside.

a cube with 5 cm side length has therefore a volume of

5×5×5 = 5³ = 125 cm³ (= 125 little cubes of 1cm side length).

5.

this is simply a box, a 3-dimensional rectangle.

similar to 4. fit the volume we just multiply now so 3 dimensions :

6×7×9 = 378 cm³ (= 378 little cubes of 1cm side length).

5 0

2 years ago

What is the area of ΔABCA. 64B. 128C. 32D. 42.6​

What is the area of ΔABCA. 64B. 128C. 32D. 42.6