MATHEMATICS HIGH SCHOOL

Find the sum of 13/20 and 0.72
Give your answer as a decimal.

Answers

Answer 1

Answer:

The sum of 13/20 and 0.72 when expressed in decimal form gives us the answer as; 1.37.

How to convert fraction to decimal?

We want to find the sum of ¹³/₂₀ and 0.72

This is expressed as;

¹³/₂₀ + 0.72

Now, we want to express the fraction as a decimal. Thus, let us convert to decimal as; ¹³/₂₀ = 0.65

Thus, we now have the decimal expression;

0.65 + 0.72 = 1.37

Thus, we can conclude that the sum of 13/20 and 0.72 when expressed in decimal form gives us 1.37.

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Answer 2

Answer:

The sum of 13 / 20 and 0.72 when expressed in decimal form gives us the answer as; 1.37.

To find the sum of 13 / 20 and 0.72, we can first convert 13/20 to a decimal by dividing 13 by 20.

This is expressed as;

13 / 20 + 0.72

Now, we want to express the fraction as a decimal. Thus, let us convert to decimal as; 13 / 20 = 0.65

Thus, we now have the decimal expression;

0.65 + 0.72 = 1.37

Thus, we can conclude that the sum of 13 / 20 and 0.72 when expressed in decimalform gives us 1.37.

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What is the exact volume of the cone 4 in and 7 in

Answers

Answer: V=205.25 cubic inches.

Step-by-step explanation:

For the given cone height = 4 in and radius= 7 in .Volume of any cone can be calculated by the formula :

V= $(1)/(3) \pi r^(2) h$

Substituting the values of r and h we have:

V= $(1)/(3) \pi 7^(2) .4$

Solving for V we have:

V=205.25 cubic inches.

V = (1/3) *pi* (7)^2 * 4

V = ( 196 pi ) / 3

True or false? all right triangles are isosceles.***WILL AWARD BRAINLIEST ANSWER***

Thanks in advance! :)

Answers

The answer is false.

I think the answer is false

if sin (α+β) = 1, sin (α-β) = 1/2 then tan (α+2β) tan(2α+β) = a. 1 b.-1 c.0 d. none

Answers

$\alpha;\ \beta\in(0^o;\ 90^o)\n\nsin(\alpha+\beta)=1\to sin(\alpha+\beta)=sin90^o\to\alpha+\beta=90^o\n\nsin(\alpha-\beta)=(1)/(2)\to sin(\alpha-\beta)=sin30^o\to\alpha-\beta=30^o\n\n +\left\{\begin{array}{ccc}\alpha+\beta=90^o\n\alpha-\beta=30^o\end{array}\right\n---------\n.\ \ \ \ \ \ \ 2\alpha=120^o\ \ \ /:2\n.\ \ \ \ \ \ \ \ \ \alpha=60^o\n\n60^o+\beta=90^o\ \ \ /-60^o\n\beta=90^o-60^o\n\beta=30^o$

$tan(\alpha+2\beta)\cdot tan(2\alpha+\beta)\n\n=tan(60^o+2\cdot30^o)\cdot tan(2\cdot60^o+30^o)\n\n=tan120^o\cdot tan150^o=tan(180^o-60^o)\cdot tan(180^o-30^o)\n\n=-tan60^0\cdot(-tan30^o)=-\sqrt3\cdot(-(\sqrt3)/(3))=(3)/(3)=1\n\n\nAnswer:A$

Let $A = (5,12)$, $B = (0,0)$, and $C = (14,0)$. For a point $P$ in the plane, the minimum value of $PA^2 + PB^2 + PC^2$ can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

Answers

Answer:

Step-by-step explanation:

do it

To find the minimum value of the sum of the squares of distances, we can use calculus. The minimum value can be expressed as $233/9$.

To find the minimum value of $PA^2 + PB^2 + PC^2$, we need to find the point $P$ that minimizes the sum of the squares of the distances from $P$ to $A$, $B$, and $C$. Let's denote the coordinates of $P$ as $(x, y)$. Using the distance formula, we can find the expressions for the squares of the distances:

$PA^2 = (x - 5)^2 + (y - 12)^2$
$PB^2 = x^2 + y^2$
$PC^2 = (x - 14)^2 + y^2$

The sum of these expressions is $PA^2 + PB^2 + PC^2$:

$PA^2 + PB^2 + PC^2 = (x - 5)^2 + (y - 12)^2 + x^2 + y^2 + (x - 14)^2 + y^2$

Simplifying the expression:

$PA^2 + PB^2 + PC^2 = 3x^2 + 3y^2 - 38x - 24y + 365$

To find the minimum value, we can use calculus. Taking the partial derivatives of this expression with respect to $x$ and $y$ and setting them to zero, we can find the critical points. The coordinates of the point $P$ that minimizes the sum of the squares of the distances are $(x, y) = (13/3, 8/3)$. Plugging these values into the expression, we get:

$PA^2 + PB^2 + PC^2 = (13/3)^2 + (8/3)^2 = 233/9$

Therefore, the minimum value can be expressed as $233/9$, and $m + n = 233 + 9 = 242$.

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