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Answer:

Step-by-step explanation:

Guiding Statement

You must find x before you can find y. If an altitude is dropped from the right angle to the hypotenuse, then the value of the altitude = the two parts of hypotenuse multiplied together = the altitude squared.

Formula

Perhaps, instead of all that language, it is easier just to show you this in terms of what you have been given.

Solution

x^2 = 72                        Factor 72 into prime factors.

x^2 = 8 * 9

x^2 = 2 * 2 * 2 * 3 * 3    Take the square root of both sides.

√x^2 = √(2 * 2 * 2 * 3 * 3)  

Rule

For every pair of equal prime factors, take 1 factor outside the root sign and throw the other one away.

√x^2 = √(2 * 2 * 2 * 3 * 3)

x = √(2 * 2 * 2 * 3 * 3)                 Apply the rule

x = 2 * 3 √2

x = 6√2

Now with y

a = 6√2

b = 12

c = y Use the Pythagorean Theorum

c^2 = a^2 + b^2

c^2 = (6√2)^2 + 12^2

c^2 = 36*2 + 144

c^2 = 72 + 144

c^2 = 216

c = 6 √6

answer

x = 6√2

y = 6√6

Answer:

1.65°

2.115°

3.132°

4.48°

5.67

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Answer:

5.291 x 10⁶

Step-by-step explanation:

Why is 5,291,000 written as 5.291 x 106 in scientific notation?

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10b

Follow the steps below to see how 5,291,000 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 5,291,000

New Number: 5.291000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 5 . 2 9 1 0 0 0

Decimal Count: 1 2 3 4 5 6

There are 6 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 5.291 (Please notice any zeroes on the end have been removed)

b = 6

Now the whole thing:

5.291 x 10⁶

Step 4

Check your work:

10⁶ = 1,000,000 x 5.291 = 5,291,000

Using an arithmetic sequence, it is found that the clock chimes 132 times in a 24-h period.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms is given by:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

In this problem, as the day is divided in two 12-hours period, the total will be twice the sum of the 12 elements of the following sequence:

{0, 1, 2, 3, ..., 11}

In which [tex]a_1 = 0, a_11 = 11, n = 12[/tex].

Then:

[tex]T = 2\frac{12(0 + 11)}{2} = 12 \times 11 = 132[/tex]

The clock chimes 132 times in a 24-h period.

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

Answer:

  2.37×10^-11 milliliters

Step-by-step explanation:

The exponential model for decay is ...

  y = a·b^x

where 'a' is the initial value, 'b' is the decay factor, and x is the number of intervals over which the decay is taking place.

__

Here, you're given an initial value of a=500 mL.

The decay factor is 1 more than the decay rate, so is ...

  b = 1 -12% = 0.88

We are asked for the remaining amount after 240 intervals (breaths), so that will be ...

  y = 500·0.88^x

  y = 500·0.88^240 ≈ 2.37×10^-11 . . . . milliliters

__

Additional comment

That's about 640 million molecules of air--not very much. After 400 breaths, there is about 1 molecule of the original air remaining.

Answer: 10 feet

The ratios:

1 inch : 2 feet

5 inch : x feet

Finding x:

1 * 5 = 5

2 * 5 = 10

             The real robot would be 10 feet tall.

Answer:

10 inches

Step-by-step explanation:

because 1 in= 2 ft
we can multiply 5 by 2 which is 10

your answer is 10 ft tall.

Answer:

Step-by-step explanation:

Use a slope formula.

Slope formula:

[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }[/tex]

y2=2

y1=6

x2=13

x1=1

Rewrite the problem.

[tex]\sf{\dfrac{2-6}{13-1}=\dfrac{-8}{12}=\dfrac{-8\div4}{12\div4}=\dfrac{-2}{3}=\boxed{\sf{-\dfrac{2}{3}}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

The question is not showing what we are supposed to find.

b+3b+10

Answer:

C:0.09

Step-by-step explanation:

probability of winning nothing = 0.72 = [tex]\frac{72}{100}[/tex]

probability of winning a small stuffed animal = 0.19 = [tex]\frac{19}{100}[/tex]

probability of winning nothing + probability of winning a stuffed animal

= [tex]\frac{72}{100}[/tex] + [tex]\frac{19}{100}[/tex] = [tex]\frac{91}{100}[/tex]

probability of winning an inflatable crayon = 1 -  [tex]\frac{91}{100}[/tex]

                                                                      = [tex]\frac{100}{100}[/tex] -  [tex]\frac{91}{100}[/tex]

                                                                      = [tex]\frac{9}{100}[/tex]

                                                                      = 0.09

Answer:

x = 7

Step-by-step explanation:

the given angles are vertically opposite and are congruent , then

4x - 5 = x + 16 ( subtract x from both sides )

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:

x=238 plus 0

Step-by-step explanation:

think

Answer:

-6, -5, -1

Step-by-step explanation:

Based on the question, (x+6) is a factor of f(x).

With this, you can do the long division method of dividing f(x) with (x+6) {Refer to the image}.

You'll get x²+6x+5 as a result.

Factorise it and you'll get

x²+6x+5 = (x+1)(x+5)

Then let (x+1)(x+5) = 0, x = -1, -5

Zero's of f(x) are -6, -5 -1

[tex]\text{Given that,}\\\\f(x) = x^3 +12x^2 +41x +30~~ \text{and} ~~ f(-6)=0\\\\\text{Since f(x)=0 when x = -6,}~ ~x-6 ~\text{is a factor of f(x).}\\\\x^3+12x^2+41x+30 = 0\\\\\implies x^3+6x^2+6x^2+36x+5x+30=0\\\\\implies x^2(x+6) +6x (x+6) +5(x+6)=0\\\\\implies (x+6)(x^2+6x+5)=0\\\\\implies (x+6)(x^2+5x+x+5)=0\\\\\implies (x+6)\textbf{[}x(x+5)+(x+5)\textbf{]}=0\\\\\implies (x+6)(x+1)(x+5)=0\\\\\text{Hence the roots are,}~ x = -6,~ x=-1~ \text{and}~ x = -5[/tex]

Answer:

426

Step-by-step explanation:

To determine how to round up or down, we look at the place after the one we want to round to. In this case, we look at the tenths place.

If the tenths place is [tex]\geq 5[/tex] then you round up, and if it is [tex]\leq 4[/tex] you round down.

We see that the number is five and we round up to 426

Answer:

78.5 units²

Step-by-step explanation:

First, we need to plot the center point of the circle. (Shown in image). Once we plotted the center point, we need to count how many units is the radius away from the boundary.

Note: I have marked each unit by a "red point". Simply, count the number of "red points" to determine the radius.

We can substitute the radius in the "area of circle" formula to determine the area. Keep in mind that pie is represented as 3.14.

Now, let's evaluate the area by simplifying the expression. Keep in mind that pie is represented as 3.14.

Answer:

Option D

Step-by-step explanation:

Given equation:

This equation can be solved by:

Subtracting 2 both sides of the equation (according to step 1):

Dividing -4 to both sides of the equation (according to step 2):

Therefore, Option D is correct.

Learn more about this topic: https://brainly.com/question/27460957

Answer:

d) 4

Step-by-step explanation:

Solving for the value of x,

→ -4x + 2 = -14

→ -4x = -14 - 2

→ -4x = -16

→ x = -16/-4

→ [ x = 4 ] {option d}

Verification of the value of x,

→ -4x + 2 = -14

→ -4(4) + 2 = -14

→ -16 + 2 = -14

→ -14 = -14

→ [ LHS = RHS ]

Hence, the value of x is 4.

Answer:

Step-by-step explanation:

Make the x-values same and solve for m

Let's see

x must be equal on both sides as it's not a function

Answer:

7

Step-by-step explanation:

As it is a RIGHT triangle, the formula is a^2+b^2=c^2.

We are given one leg and the hypotenuse. That means 4^2x2+b^2=81.

To find 4 root 2 square, you square them individually then multiply.

4^2=16 times 2 (root 2 squared is 2).

Simplified, that gives 16x2=32,

81-32=49.

The last leg is seven.

Length= 14inches and breadth= 10inches

We know, Perimeter of rectangle= 2(Length+Breadth)

[tex]2(14 + 10) \\ = 2 \times 24 \\ = 48 \: \text{inches}[/tex]

We know, Area of rectangle= Length × Breadth

[tex]14 \times 10 \\ = 140 \: \text{in} ^{2}[/tex]

Answer:

heya! ^^

here , we've been given a right angled triangle along with the measure of two of its sides.

and , we've to find the measure of its third side.

so , we'll be using Pythagoras Theorem to find the measure of the third side.

but first , let's take a look at what Pythagoras Theorem is-

Pythagoras theorem states that the square of the hypotenuse of the triangle is equal to the sum of squares of the remaining two sides.

according to the figure ,

side AB = hypotenuse = 60 cm

side AC = perpendicular = 48 cm

side BC = base = a

now by using Pythagoras Theorem ,

[tex]H {}^{2} = P {}^{2} + B {}^{2} \\ \\ (60) {}^{2} = (48) {}^{2} + a {}^{2} \\ \\ 3600 = 2304 + a {}^{2} \\ \\ a {}^{2} = 1296 \\ \\ a = \sqrt{1296} \\ \\ a = 36[/tex]

therefore ,

option ( 4 ) 36 is correct.

hope helpful :D

Answer:

[tex] \\ [/tex]

Step-by-step explanation:

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]

Here,

[tex] \\ [/tex]

So, substituting the values in the formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} + (48 {)}^{2} = ( 60{)}^{2} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} = ( 60{)}^{2} - (48 {)}^{2}}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =3600 - 2304}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =1296}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad a = \sqrt{1296}}}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\frak {\qquad a = 36 }}} \\ \\[/tex]

Therefore,

Answer:

61 degrees

Step-by-step explanation:

The THREE angles in the diagram sum to 180 degrees ( straight line = flat wall)

3x+1     +   58   +   4x-19     = 180

solve for x = 20     then A = 3x+1 = 61 degrees

Answer:

₹9900

Explanation:

Total sold : (41 + 59) = 100 watermelons

Amount earned : 100 * 99 = ₹9900

#Thursday

Money earned=41(99)

#Friday

Money earned

Total:-

5841+4059=$9900

The null hypothesis in this situation is "There are no differences in the mean completion times among the temperatures compared".

This is a hypothesis that states the independent variable or factor being studied has not effect on the dependent variable.

This implies the temperature has no effect on the completion times of the paper-folding test.

It is the effect of temperature because this is the factor being manipulated on purpose.

This refers to the factor being studied, in this case, these are the spatial reasoning abilities, which are tested through a specific test.

Learn more about null hypothesis in: https://brainly.com/question/16261813

Answer:

600 cm squared :)

Step-by-step explanation:

Surface area of cube: 6 x s^2

Now lets solve!!

6 x 10^2

6 x 100

600

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Answer:

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·3 = 18.85(*)

In terms of diameter:

Circumference = π·d = 3.14·6 = 18.84(*)

In terms of area:

Circumference C = √4·π·A = √4·π·28.27 =18.85

Step-by-step explanation:

radius= 3in.

the circumference of the circle.

formula C=2πr

=2·π·3

≈18.84956in

nearest hundredth= 18.85in