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3 years ago

Find how many two digit numbers are divisible by 3

Mathematics

1 answer:

Bad White [126]3 years ago

7 0

I'll use arithmetic series to find it.

First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.

So,

$a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30$

There are 30 such numbers.

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use the leading coefficient and degree of the polynomial function f(x)=x^3-7x^2+10x to determine the end behaviour of its graph.

Masja [62]

Answer:

The domain is all real numbers and the range is all real numbers as-well.

As x approaches infinity, so does y.

As x approaches -infinity, so does y.

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2 years ago

Easy Area problem Need it fast

Gekata [30.6K]

Answer:

just subtract the area of the rectangle from the area of the carpet

fine I'll do it

Area of a rectangle= lb

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Area of the remaining area= lb - a^2

= (12*4) - (2*2)

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3 years ago

Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago

If two angles of a triangle are complementary, then the triangle must be

Angelina_Jolie [31]

That would be a right-angled triangle.

6 0

3 years ago

An assembly line inspector inspected 340 machine parts. 323 of the parts passed inspection. What percent of the machine parts di

tester [92]

Answer:

5% did not pass inspection

Step-by-step explanation:

Given

$Inspected= 340$

$Passed = 323$

Required

Determine the percentage of parts that didn't pass inspection.

First, we need to calculate the number of those that didn't pass inspection.

$Failed = Inspected - Passed$

$Failed = 340 - 323$

$Failed = 17$

Next, we calculate the percentage as follows:

$\% = \frac{Failed}{Inspected} * 100\%$

The above formula is derived by dividing the number of parts that didn't pass inspection by the total machine inspected, then multiplied by 100%

So:

$\% = \frac{17}{340} * 100\%$

$\% = \frac{17 * 100\%}{340}$

$\% = \frac{1700\%}{340}$

$\% = 5\%$

5% did not pass inspection

6 0

3 years ago