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2 years ago

Calculate the length of AC to one decimal place in the trapezium below.

Mathematics

1 answer:

a_sh-v [17]2 years ago

7 0

Answer:

First we will split trapezium on two geometric figure.

One is rectangle and the second is right triangle.

When we subtract 11-4=7cm we get one cathetus of the right triangle a=7cm also we know hypotenuse which is c=16cm.

We will use Pythagorean theorem to find the second cathetus b

b=√16∧2-7∧2= √256-49= √207 ≈ 14.39cm =DC =>

AC =√(DC)∧2+(AD)∧2= √14.39∧2+11∧2= √207+121= √328= 18.1cm

AC=18.1cm

Good luck!!

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troy's truck has a 30 gallon gas tank and gets an average of 21 miles per gallon.write an equation to represent the amount of ga

GuDViN [60]

Let

x---------> represent the number of miles Troy's has driven

y--------> represent the amount of gas in Troy's truck

we know that

the equation that represents the amount of gas, y, in troy' s truck after driving a certain number of miles, x is

$y-y1=m*(x-x1)$

where

m is the slope---------> $\frac{gallon}{miles}$

in this problem the slope is equal to $-\frac{1}{21} \frac{gallons}{miles}$

it's negative because the tank is going to be consumed

assuming he starts with a full tank

$for\ x=0\ y=30\ gal$

substitute in the formula above

$y-y1=m*(x-x1)\\\\ y-30=-\frac{1}{21}*(x-0)\\\\ y=-\frac{x}{21}+30$

therefore

the answer is

the equation $y=-\frac{x}{21}+30$

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2 years ago

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Tyler needs to complete the table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup

olga_2 [115]

Answer:

1 cup = 48 teaspoons

C = 48t

Step-by-step explanation:

Given:

1 tablespoon = 3 teaspoons

1 cup = 16 tablespoon

Write an equation that represents the number of teaspoons, t, contained in a cup, C.

Since

1 tablespoon = 3 teaspoons

And

1 cup = 16 tablespoon

Then

1 cup = 3 teaspoons × 16

1 cup = 48 teaspoons

Let

cup = C

Teaspoons = t

Therefore,

C = 48t

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2 years ago

Two students from a group of eight boys and 12 girls are sent to represent the school in a parade. If the students are chosen at

kari74 [83]

Answer:

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- Probability of event not happened = 1 - P(A)

- P(A and B) = P(A) . P(B)

* Lets solve the problem

- There is a group of students

- There are 8 boys and 12 girls in the group

∴ There are 8 + 12 = 20 students in the group

- The students are sent to represent the school in a parade

- Two students are chosen at random

∴ P(S) = 20

- The students that chosen are not both girls

∴ The probability of not girls = 1 - P(girls)

∵ The were 20 students in the group

∵ The number of girls in the group was 12

∴ The probability of chosen a first girl = 12/20

∵ One girl was chosen, then the number of girls for the second

choice is less by 1 and the total also less by 1

∴ The were 19 students in the group

∵ The number of girls in the group was 11

∴ The probability of chosen a second girl = 11/19

- The probability of both girls is P(1st girle) . P(2nd girl)

∴ The probability of both girls = (12/20) × (11/19) = 33/95

- To find the probability of both not girls is 1 - P(both girls)

∴ P(not both girls) = 1 - (33/95) = 62/95

* The probability that the students chosen are not both girls is 62/95

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2 years ago

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Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 r

olga2289 [7]

Answer:

c)No, P is the distance from A to B, and Q is the distance from B to A.

Step-by-step explanation:

Point P partitions the directed segment from A to B into a 1:3 ratio.

Ratio is 1:3

So AP is 1 and PB is 3

Q partitions the directed segment from B to A into a 1:3 ratio.

Ratio is 1:3

So BQ is 1 and QA is 3.

That is AQ= 3 and BQ= 1

The ratio of Q and P varies

AP =1 and AQ=3

So P and Q are not at the same point.

Because P is the distance from A to B and Q is the distance from B to A

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A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

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Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

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$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

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2 years ago

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