A chessboard is made of 64 small squares. Suppose a single square on a chessboard has an area of 9 square centimeters. How long is one side of the entire board?
PLEASE HELPPP​

Answer:

Steps below.

Step-by-step explanation:

Unit Conversion is definitely needed in this question. Therefote, we will do some conversions first.

[tex]1m = 1000 mm \\ 1 {m}^{2} = {(1000)}^{2} {mm}^{2} \\ 1 {m}^{2} = 1000000 {mm}^{2} [/tex]

Now we can use the above converted unit to solve for the question.

[tex]32 {m}^{2} = 32 \times 1000000 \\ = 32000000 {mm}^{2} [/tex]

The height of the street light is approx. 3.5m.

Angle of depression is defined as the angle formed between the horizontal line and the line of sight when the observer looks down .

In the given question  

let h be the height of the street light

let d be the distance from the base of building to the street light .

form the figure given below.

In ΔADE

[tex]tan(57.8)=\frac{AD}{DE}[/tex]

Substituting the value of AD and DE from the figure

[tex]tan (57.8)=\frac{35}{d} \\ \\ d=\frac{35}{tan(57.8)} \\ \\ d=\frac{35}{1.5879}[/tex]....substituting the value of tan (57.8)

d=22.04 m      ...(i)

In ΔABC

[tex]tan(55)=\frac{AB}{BC}[/tex]

Substituting the value of AB and BC from the figure

since AD=AB+BD

35=AB+h

AB=35-h

[tex]tan (55)=\frac{35-h}{d}[/tex]

Substituting the value of d from (i)

[tex]tan (55)=\frac{35-h}{22.04}\\ \\ 35-h=tan(55)*22.04\\ \\ 35-h=1.428*22.04[/tex]( substituting the value of tan(55)  )

[tex]35-h=31.47[/tex]

[tex]h=35-31.47\\h=3.53\\[/tex]

h≅3.5

Therefore , the height of the streetlight is approx. 3.5m  .

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Step-by-step explanation:

To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.

Reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{-4}{1}=-4[/tex]

Now plug the slope into point-slope form with the known x and y values:

[tex]x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}[/tex]

Answer:

x = 8 and x = 2 are both valid solutions.

There are no extraneous answers.

Step-by-step explanation:

Given absolute value function:

[tex]|2(x-5)|+11=17[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies |2(x-5)|+11=17[/tex]

[tex]\implies |2(x-5)|+11-11=17-11[/tex]

[tex]\implies |2(x-5)|=6[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations.

Equation 1 (positive)

[tex]\implies 2(x-5)=6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{6}{2}[/tex]

[tex]\implies x-5=3[/tex]

[tex]\implies x-5+5=3+5[/tex]

[tex]\implies x=8[/tex]

Equation 2 (negative)

[tex]\implies 2(x-5)=-6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{-6}{2}[/tex]

[tex]\implies x-5=-3[/tex]

[tex]\implies x-5+5=-3+5[/tex]

[tex]\implies x=2[/tex]

Therefore, the solutions are x = 8 and x = 2.

Check if the solutions are valid by substituting them into the original equation:

[tex]\begin{aligned}x=8 \implies |2(8-5)|+11 & =17\\|2(3)|+11 & =17\\|6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies |2(2-5)|+11 & =17\\|2(-3)|+11 & =17\\|-6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

Therefore, both solutions are valid and there are no extraneous answers.

Note:  An extraneous solution is a solution that is produced by solving the problem, but is not a valid solution to the problem.

Answer:

- 3b + 21

Step-by-step explanation:

- 3(b - 7) ← multiply each term in the parenthesis by - 3

= - 3b + 21

answer:

-30

explanation:

-5/2=-2.5

-2.5*12=-30

Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store

Given data

price before tax and discount = $34

price after discount = $30.60

solving for discount

$34  -  $30.60 =  $3.4

percent discount

= 3.4 / 34 * 100 / 1

= 0.1 * 100

= 10%

Therefore we can say that Ian got a discount of 3.4 and percent discount is 10% after buying the items he wants in the local grocery store

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Answer:

The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).

Step-by-step explanation:

The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).

Answer:

The measure of angle 3 is 30 (C).

Step-by-step explanation:

m<1, m<2, and m<3 have a sum of 180        Linear Pair Postulate

So 2x + 3x - 20 + x - 4 = 180

6x - 24 = 180

6x = 204

x = 34

Then you substitute and get 34 - 4 for angle 3 which = 4

Hope this helps!

204

You get 204 because first you divided 85 and 5 which equals 17.

Then you multiply 12 and 17 which equals 204.

I hope that this helps! :)

Answer:

204 miles

Step-by-step explanation:

So first we have to divide 85 by 5 which we get 17 then we multiply 17 by 12 which is 204. I hope this help but sorry I'm not that good at explaining thing

Answer:

109.

Step-by-step explanation:

62+41+(2)+(4)       we can remove the brackets:

= 62 + 41 + 2 + 4

= 109.

Answer: i feel like all of them but dont go by my word

Step-by-step explanation:

Answer: “The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.”

      - https://www.mathplanet.com

Step-by-step explanation:

Answer:

[tex] \dfrac{x^{5}}{y^{8}} [/tex]

Step-by-step explanation:

[tex] \dfrac{y^{-8}}{x^{-5}} = [/tex]

[tex] = \dfrac{x^{5}}{y^{8}} [/tex]

The expression is simplified to give y⁻⁸x⁵

First, it is important to note that index forms are described as mathematical forms that are used to represent numbers of variables that are too large or that are too small in more convenient forms.

These index forms are also known as scientific notations or standard forms

From the information given, we have that;

y to the negative eighth power over x to the negative fifth power

This is represented as;

y⁻⁸/x⁻⁵

Since the forms are not of the same bases, we cannot add the exponents

y⁻⁸x⁵

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The guarantee period of the electronic components by Accrotime manufactures is 38 months.

mean = μ = 24 months

standard deviation = σ = 5 months

2 years = 24 months

a) P(x < 24)

= P[(x - μ ) / σ < (24 - 28) / 5]

= P[(x - μ ) / σ < -0.8

= P(z < -0.8 )

Using z table,

= 0.212

Percentage = 21.2%

b) Use standard normal table,

Refund percentage = 12%

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 0.174 ) = 0.94  

z = 0.174

Using z-score formula,

x = z ×σ  + μ

x = 1.74 × 5 + 28

x = 36.7

The guarantee period = 38 month

Thus, the guarantee period of the electronic components by Accrotime manufactures is 38 months.

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The inequality represented by the given number line is; -4 ≥ x ≥ 5

From the given number line we can find the inequality. Some of the rules are that;

For a shaded circle pointing to the left means less than or equal to (≤)

For a shaded circle pointing to the right means greater than or equal to (≥).

For an unshaded circle pointing to the left means less than (<)

For a shaded circle pointing to the right means greater than (>)

Thus, applying the above to the inequality line gives;

-4 ≥ x ≥ 5

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Answer:

[tex]x\leq 25[/tex]

Step-by-step explanation:

Since x can equal anything 25 and lower, here are some of the possibilities x can be.

x = 25, 24, 23, 22, 21, 20, etc.

X could also be a decimal and doesn't have to be an integer.

x = 24.7, -20.4, 24 5/7

So to put these numbers in one equation, we can use the [tex]\leq[/tex] symbol.

Therefore, [tex]x\leq 25[/tex].

Hope this helped! Have a great day!

Answer:  4 players can play and still have 8 cards each.

39÷8=4.875

Answer:

4 people

Step-by-step explanation:

39 cards / 8 cards = 4.87500

each person must have 8 cards, so only 4 people can play

There is 0.329 probability or chance that the software really has a virus.

The calculation will be based on Bayes' theorem which relates the probability and statistics, as is mentioned in the given question. The values provided are True positive = 97%, False positive = 2% and Prevalence = 1%.

Probability = (True positive × user) ÷ (True positive × user) + (false positive × non user)

Keep the values in formula to find the probability

Probability = (0.97 × 0.01) ÷ (0.97 × 0.01) + (0.02 × 0.99)

Probability = 0.0097 ÷ (0.0097 + 0.0198)

Probability = 0.0097 ÷ 0.0295

Probability = 0.329

Thus, there is 0.329 chance that the software really has a virus.

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Answer:

3n+5

Step-by-step explanation:

you don’t know the official age, all you know is that his age is 3 times whatever number

Answer:

64

Step-by-step explanation:

Angles DBF and EBF form a linear pair, so:

[tex]5x+6+3x-2=180 \\ \\ 8x+4=180 \\ \\ 8x=176 \\ \\ x=22 \\ \\ \implies m\angle DBF=116^{\circ}[/tex]

Similarly, because angles DBF and DBC form a linear pair, the answer is 64°.

In geometry "rule of detachment," states that if P leads to Q and P is true, then Q must also be true

The area of mathematics known as geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. The terms "geometry" and "metron" are derived from Ancient Greek words that mean "measuring" and "Earth," respectively.

The most widely applied deductive reasoning premise is the Law of Detachment. This law states that the conclusion is valid whenever a conditional statement and its hypothesis are true. The conclusion can therefore be "separated" from the conditional.

According to the geometry's "rule of detachment," if P leads to Q and P is true, then Q must also be true. Despite the fact that it is stated in a different format, this is still a conditional statement.

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Answer:

A) "If q, then p."

B) "If not p, then (not) q."

C) "If (not) q, then not p."

Answer:

1. 12

2. 36

Step-by-step explanation:

3 * 2 / 3

multiply & divide by 2

= 3 * 2 * 2 / ( 3 * 2)

= 12 / 6

12 (twelve) sixths

Study

Answer:

36 tenths

Explanation:

Well the first part to working this out is understanding that there are 10 tenths in a whole. So 3 wholes is 30 tenths.

The second part is 3 over 5 or 3/5. To write this in tenths you have to effectively double it (if you double the denominator you must double the numerator) What ever you do to the top you must do to the bottom and vice versa. So that 3 over five becomes six over ten. Add them together now you can add these fractions because they are over the same denominator (their bottom number is the same)

30 tenths plus 6 tenths equals 36 tenths.

The solutions of the expression are;

a. - 5 - 2 = -7

b. 6 - (-5) = 11

What is Addition?

A process of combining two or more numbers are called Addition.

The given expression are;

a. -5 - 2

b. 6 - (-5)

Now, Solve the expression as;

-5 - 2 = - 7

And, 6 - (-5) = 6 + 5 = 11

So, The solutions of the expression are;

- 5 - 2 = -7

6 - (-5) = 11

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Answer:

6

Step-by-step explanation:

Terms are what is separated by addition and subtraction.

The measure of the missing angle is 112°.

When you need to find some interior angle of polygons, you can apply the  formula for the sum of interior angle. This formula relate the number of sides of the polygon with the sum of interior angle. The formula is presented below.

S = (n – 2 )*180º, where:

S= sum of interior angles

n= number of sides of the given polygon

The given figure shows:

Applying the formula, S = (n – 2 )*180º, you find:

S=(5-2) * 180

S=3*180

S=540°

Now  that you know the sum of the interior angles for the given polygon, thus:

x+105+118+75+130=540

x+428=540

x=540-428

x=112°

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