MATHEMATICS HIGH SCHOOL

The lengths of the bases of the right trapezoid are 9 cm and 18 cm. The length of a longer leg is 15 cm. Find the area of the trapezoid.

Answers

Answer 1

Answer:

Firstly, we will draw figure

now, we will draw a altitude from B to DC that divides trapezium into rectangle and right triangle

because of opposite sides of rectangle ABMD are congruent

so,

DM=AB=9

CM=CD-DM

CM=18-9

CM=9

now, we can find BM by using Pythagoras theorem

$BM=√(BC^2-CM^2)$

now, we can plug values

we get

$BM=√(15^2-9^2)$

$BM=12$

now, we can find area of trapezium

$A=(1)/(2) (AB+CD)*(BM)$

now, we can plug values

and we get

$A=(1)/(2) (9+18)*(12)$

$A=162cm^2$

so, area of of the trapezoid is $162cm^2$ ..........Answer

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Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.

Answers

Answer:

$\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty$

General Formulas and Concepts:

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_(x \to c^+) f(x)$
Left-Side Limit: $\displaystyle \lim_(x \to c^-) f(x)$

Graphical Limits

Step-by-step explanation:

If we graph the function, we can see that as we approach 3 from the left, we go towards negative infinity.

∴ $\displaystyle \lim_( \to 3^-) (1)/(x - 3) = -\infty$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Do all of the digits in 8.88 have the same value? and explain why.

Answers

No, all of the digits in 8.88 does not have the same place value.

In the number 8.88, each digit occupies a specific position that determines its place value.

From left to right:

1. The first digit "8" is in the ones place. Its place value is 8.

2. The second digit "8" is in the tenths place. Its place value is 0.8 (or 8/10).

3. The third digit "8" is in the hundredths place. Its place value is 0.08 (or 8/100).

Since all the digits are located after the decimal point, they are decimal digits. Therefore, in the number 8.88, all digits have the different place value as decimals.

Learn more about place value here

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Answer:

Step-by-step explanation:

Mitochondria is the powerhouse of the cell

In the step by step simplification of expression below which property is not used? 3(1+x)
3(x+1)
3(x)+3(1)
3x +3

A) associative B) commutative C) distributive D) identity

Answers

D) identity............

$3(1+x)=3+3x\n 3(x+1)=3x+3\n 3(x)+3(1)=3x+3\n 3x +3\n\n Answer:D$

Half of a number is equal to 8 more than the number.

Answers

Set the number as x. So,
.5x=x+8
Put all of the x's on one side of the equation.
.5x=-8
Divide by .5 on each side,
x=-16
Hope this helps.

What is the value of the expression |x| + |y + z| when x = –6, y = –3, and z = –5?

Answers

x=-6, y=-3, z=-5

|x|+|y+z|=|-6|+|-3-5|=6+|-8|=6+8=14

Translate the following statement into a mathematical equation:Six, plus four times a number, is eighteen.

(6 + 4)n = 18
4n + 18 = 6
6 + 4n = 18
6 + 4 + n = 18