What is the area of the trapezoid?

Answer:

8. Number of student tickets = 460

Number of teacher tickets = 100

9. Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Step-by-step explanation:

8.

Let number of students' tickets = [tex]x[/tex]

Let number of teachers' tickets = [tex]y[/tex]

Total number of tickets = 480

[tex]x+y=480[/tex] ...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

[tex]x +5y = 560[/tex] ...... (2)

Subtracting (1) from (2):

[tex]4y = 80\\\Rightarrow y = 20[/tex]

By equation (1):

[tex]x = 460[/tex]

Number of student tickets = 460

Number of teacher tickets = 100

9.

Let the speed of airplane in still air = [tex]u[/tex] km/hr

Let the speed of air = [tex]v[/tex] km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind = [tex]u+v[/tex] km/h

Time taken against the wind = 8 hours.

Speed with the wind = [tex]u-v[/tex] km/h

Using the formula:

Distance = Speed [tex]\times[/tex] Time

[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]

[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]

By equation (1):

[tex]v = 48.5\ km/hr[/tex]

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Answer:

BC= 3

Step-by-step explanation:

Suppose a line BD is 10 and it has a point C somewhere on the  line. It is given that BC is  3times and CD is 7 times  or algebraically  if we take x as a variable then according to the given information

BC+ CD= BD

3x+ 7x= 10

10x= 10

x= 10/10

x= 1

3x would give 3 (1)= 3

Hence the Line BC = 3

and the line CD= 7

Answer:

15 meters

Step-by-step explanation:

Because angle BFD and angle DFC are supplementary (they form a 180 degree angle, as you can see from the fact that they both form a straight line) and angle BFD is 90 degrees, angle DFC must also be 90 degrees. Since it is 90 degrees, you can use the Pythagorean theorem to solve for DF as a part of triangle DFC=> 8^2(x^2)=17^2.

=>64(x^2)=289

subtract 64 from both sides=> x^2=225

take the square root of both sides=> x=15

Since triangles BED and BFD are equal by way of angle-side-angle, we know that all of their corresponding sides and angles are equal, and therefore, DF=DE, so DE=15 meters

Answer:

Mindy bought 7 pounds of candy.

Step-by-step explanation:

In order to solve this question we need to understand that based on the question itself there is 4 people (Mindy and the three friends) that each have [tex]1\frac{3}{4}[/tex] pound of candy. Now if you image in that way you see that in order to understand how much pounds of candy Mindy bought you will have to multiply [tex]1\frac{3}{4}[/tex] by 4 (because there is 4 people who got [tex]1\frac{3}{4}[/tex]  pounds of candy each).

So now we can find the answer by doing the following.....

[tex](1\frac{3}{4} )(4) = ( \frac{7}{4})(\frac{4}{1}) = \frac{(7)(4)}{(4)(1)} = \frac{28}{4} = 7[/tex]

Answer:

23 is the answer

Step-by-step explanation:

i holed this helped

Answer : -12

a = 4x

plug in the numbers for a and x

3 - 4(-5)

3-15

-12

Hope this helps!!!

Answer:

(10, -2)

Step-by-step explanation:

x = 10 (its given in the problem)

then plug in 10 for x in the second equation and solve for y

3(10) + 5y = 20

30 + 5y = 20

5y = -10

y = -2

so the solution is (10, -2)

Answer:

The length of the missing side is

[tex]4 \sqrt{5} \\ if \: you \: want \: it \: not \: simplified \: it \: would \: be \: \\ \sqrt{80} [/tex]

Step-by-step explanation:

You could do Pythagorean theorem which is:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {8}^{2} + {4}^{2} = {c}^{2} \\{64} + {16} = {c}^{2} \\ \sqrt{80} = {c}^{2} \\ 4\sqrt{5} = c[/tex]

Answer:

9,500

Step-by-step explanation:

Answer:

The strategy is to find the x and y intercept of the given equation

Step-by-step explanation:

4x+3y≥12

In order to determine where the boundary line, we need to first get the x and y-intercept of the inequality expression given;

x-intercept occurs at where y = 0

when y  = 0

4x + 3(0)≥12

4x ≥12

x ≥12/4

x≥ 3

Also y intercept occurs at where x = 0

4x+3y≥12

4(0)+ 3y ≥12

3y≥12

y≥12/3

y≥4

Hence the intercept of the line is at (3, 4). A thick line will pass through this point and the upper part of the graph will be shaded. The strategy is to find the x and y intercept of the given equation

Step-by-step explanation:

Triangles ABX and DCX are similar.

Since they are similar, AX/DX = AB/DC.

Hence AX/2.8 = 8/4 and AX = 5.6.

Answer:

53.3

Step-by-step explanation:

Answer:

D

x is less than or equal to -3

Step-by-step explanation:

I hope I was fast enough ^^

Answer:

Step-by-step explanation:

No problem

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

Putting all the values of y=9, 6, 0, and -3 to complete the table

FOR y=9

putting y=9

switch sides

subtract 3 from both sides

Hence,

when y=9, x=4

FOR y=6

putting y=6

switch sides

subtract 3 from both sides

Hence,

when y=6, x=2

FOR y=0

putting y=0

switch sides

subtract 3 from both sides

Hence,

when y=0, x=-2

FOR y=-3

putting y=-3

switch sides

subtract 3 from both sides

Hence,

when y=-3, x=-4

Hence, the table becomes:

x                     y

9                    4

6                    2

0                    -2

-3                   -4

2.4 millimetres into meter is 0.0024.

Answer:

0.0024 meters

Step-by-step explanation:

Using conversion.

Hope this helps!

xoxo,

cafeology

Answer:

1

Step-by-step explanation:

Subtract

Since they have the same denominator you can subtraact normally

so 2 2/3- 1 2/3

That would be 1

Answer:

About 15 minutes

Step-by-step explanation:

It takes her 6 minutes to read 20 pgs. If she reads 20 more pages (which will be 40 now) she will have been reading for 12 minutes. This leaves you with 7 pages left, about 3 or 4 minutes.

Answer:  3 necklaces and bracelet sets can be made from the  28 1/3 inches of wire.

Step-by-step explanation:

step 1

LET  I set of necklace and bracelet be represented as ( A bracelet and a necklace)

 if Tominka uses 6 1/9 inches of wire to make a necklace and 3 1/3 of wire to make a bracelet  for a set

Then Total Length of wire that can be used for a set = 6 1/9 inches+ 3 1/3 inches = 9 (1+ 3)/9

= 9 4/9 inches.

Step 2

IF  a set (One necklace and bracelet) can use = 9 4/9 inches

and Total wire used = 28 1/3inches

Then Number of  necklaces and bracelet sets that can be made  from the 28 1/3 inches wire = 28 1/3inches /9 4/9 inches

=85/3 / 85/ 9  = 85/3  x 9/ 85  = ( 85 cancels 85 )

9/3 = 3

 3 necklaces and bracelet sets can be made from the  28 1/3 inches of wire.

Answer:

y= 3/4x + 6.4

Step-by-step explanation:

If your teacher asks why it's so specific tell them you used desmos <3

Answer: [tex]61.9miles/hr[/tex]

Step-by-step explanation:

given data:

distance travelled by the car =  195 miles

time taken = 3 hours and 15mins

solution

average speed of the car

[tex]= \frac{195miles}{3hrs15mins} \\\\= 61.9miles/hr[/tex]

Answer:

The average speed is [tex]v=60 miles/h[/tex]

Step-by-step explanation:

The equation of the average speed os given by:

[tex]v=\frac{\Delta x}{\Delta t}[/tex] (1)

here:

Δx is just 195 miles

Δt is the time traveled. 3.25 h ( 3 h + 15 min or 0.25 h)  

So we just need to put this into the equation (1)

[tex]v=\frac{195}{3.25}[/tex]

Therefore, the average speed is [tex]v=60 miles/h[/tex]

I hope it helps you!

Answer:

(199+0.32)minus 350

Step-by-step explanation:

199 is the cost plus fee per mile 0.32 subtract 350 to see if he can afford it

Answer:

$9.35

Step-by-step explanation:

14.86+25.88+5.76=46.5

55.85-46.5=9.35

Answer:

The rounded number would be nine

Step-by-step explanation:

It would be nine because you convert 55.85 to 56 then convert 14.86 to 15 convert 25.88 to 26 and convert 5.76 to 6 then subtract all of that to get nine hope it helps

Answer: 1600

Step-by-step explanation:

If there is a total amount of 19200 pieces within 12 puzzle boxes, then we'll have to divide 19200 by 12.

19200 ÷ 12 = 1600.

In conclusion, 1600 pieces are in each puzzle box.

Hope this helps!

Answer:

1,600 pieces per puzzle

Step-by-step explanation:

19,200/12= 1,600

you divide because you have the total amount of puzzle pieces and you have the amount of puzzles so

Answer:I’m pretty sure it’s b (20.8)

Step-by-step explanation:

Answer:

−8+32

Step-by-step explanation:

...................

Answer:

Step-by-step explanation:

Table representing the function 'f' is,

x     -3      2       3        7    

y     -2      8      10       18

In this table for every input value of x, there is a different output value.

So the function is one to one function.

Therefore, inverse of the given function will have the table as,

x       -2      8      10       18

y       -3      2       3        7    

Answer:

Part 1:    7/3 degrees/hour

Part 2:    28/3 degrees

Step-by-step explanation:

Part 1:

3 1/2 degrees per 1 1/2 hours =

= (3 1/2)/(1 1/2)

= (7/2) / (3/2)

= 7/2 * 2/3

= 7/3 degrees/hour

The rate is 7/3 degree per hour

Part 2:

In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.

4 hours * 7/3 degree/hour = 28/3 degrees

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Principal= $450

Number of periods= 8 years

Interest rate= 6%

We will determine the interest earned and future value using simple interest and compound interest:

Simple interest:

I= P*r*t

I= 450*0.06*8= $216

Total Future Value= I + P

Total Future Value= 216 + 450= $666

Compound interest:

I= [P*(1+r)^t] - P

I= [450*(1.06^8)] - 450= $267.23

Total Future Value= P*(1+r)^t

Total Future Value= 450*1.06^8

Total Future Value= $717.23

Answer:

Step-by-step explanation:

6