Salt water has a density of 1030 kg/m3. A piece of wood with

Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long.

kykrilka [37]

We can represent the base as z and the height as 2z+6. We are going to use the formula A=1/2*b*h and solve for z
180=1/2*z*(2z+6)
360=2z^2+6z
0=2z^2+6z-360
0=2(z^2+3z-180)
0=(z+15)(z-12)
So z=-15 and 12 but it must be positive so then the base is equal to 12

When we plug this into 2z+6 we get 30 for the height
2(12)+6=30

Hope this helps

4 0

3 years ago

(d) A car travels at an average speed of 80 km/h. How far does it travel in: (1) 2 hours? (11) 12 minutes?

zepelin [54]

Answer is (1) 160 km in 2 hours and
(2) 16 miles in 12 minutes.

Step by step.
80 km / 1 hour = x km /2 hours
Cross multiply =
x = 160

The second one requires a little more math. Because we are looking at how far in minutes, we change the rate of 80km in 1 hour to 80 km in 60 minutes.
80 km / 60 = x / 12
Cross multiply
12x = 960
Solve for x by dividing both sides by 12
X = 16

I did the math on a print screen to explain the cross multiply.

3 0

1 year ago

To make a sports drink for the football team, Jaylen filled 9/10 of a large cooler with water. Then, he filled the remaining spa

avanturin [10]

He made 3.75 gallons. There was 1/10 remaining, meaning each tenth was 6 cups. The entire thing is 10 tenths so you do 6(10) to get 60 cups. After converting to gallons by doing 60÷26, you get 3.75.

7 0

3 years ago

Read 2 more answers

Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. Which of the

kotykmax [81]

Answer:

Runner 1 has the fastest pace

Step-by-step explanation:

The first one we need to find the slope

m = (y2-y1)/(x2-x1) = (40-0)/(4-0) =40/4 = 10 minutes per mile

The second is 8.5 minutes per mile

The third we need to find the slope

m = (y2-y1)/(x2-x1) = (90-72)/(10-8) =18/2 = 9 minutes per mile

6 0

3 years ago

Read 2 more answers

A restaurant sells about 330 sandwiches each day at a price of $6 each $.25 decrease in price. 15 more sandwiches are sold per d

zmey [24]

Answer:

restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

Step-by-step explanation:

to calculate current revenue= $6 x 330 = $1980

suppose x as the number of times the price to be dropped by $0.25

then find new price.. i.e

new price= $(6-0.25x)

and, new sell=330 +15x sandwiches

therefore, the new revenue would be= (6-0.25x)(330 +15x)

in order to maximize the current revenue, simplify the above equation and make it complete square using x

(6-0.25x)(330 +15x)

=1980-82.5x +90x -3.75 $x^{2}$

=1980 + 7.5x -3.75 $x^{2}$

=1980-3.75 (-2x+ $x^{2}$ ) ----> taking out common

now, to make a complete square lets add and subtract 1 inside the parentheses

=1980-3.75(-1+1-2x+ $x^{2}$ )

=1980 +3.75 -3.75( $x^{2}$ -2x +1)

=1983.75 -3.75 $(x-1)^{2}$ ---->(1)

as $(x-1)^{2}$ is positive always, minimize the other term in order to maximize the total revenue.

so the minimum possible value of $(x-1)^{2}$ = 0

therefore, x=1

putting x in eq(1) the revenure becomes,

$(1983.75-0)=> $1983.75

therefore, restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

3 0

3 years ago