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The equivalent expression of (10⁻² . 4⁵)⁻² is 10⁴ / 4¹⁰

We have to find the expression that is equivalent to the expression below:

(10⁻² . 4⁵)⁻².

Therefore, using the law of indices,

[tex](x^{a} )^{b} = x^{ab}[/tex]

Hence, let's find the equivalent expression by applying the laws of indices.

(10⁻² . 4⁵)⁻² = 10⁴ . 4⁻¹⁰

Also, applying the law of indices,

[tex]x^{-b} = \frac{1}{x^{b} }[/tex]

Therefore,

10⁴ . 4⁻¹⁰ = 10⁴ / 4¹⁰

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Answer:

  26.0 cm

Step-by-step explanation:

Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.

The law of sines tells you the relation between sides and opposite angles is ...

  a/sin(A) = b/sin(B) = c/sin(C)

This lets us write two proportions that can be solved for the measure of CD.

In triangle ABD:

  BD/sin(A) = AB/sin(D)

  BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm

In triangle BCD:

  CD/sin(B) = BD/sin(C)

  CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm

The length of CD is about 26.0 cm.

Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

Answer: 0.17

Step-by-step explanation:

Plug the equation into a calculator (17 divided by 100).

You can also think of the problem like this; move both decimal places to the left twice since, in 100, there are two 0's.

17 -> 0.17

100 -> 1

This can also work with 17 and 1000, but you would have to move the decimal place three times.

17 -> 0.017

1000 -> 1

Equation of the line with slope -1/2 passing through the point (-1,-4) is x + 2y = -9

Given,

the slope of the line = -1/2

the line passes through the point (-1,-4)

=> s = -1 and t = -4

The following equation can be used to find the line's equation:

( y - t ) = slope ( x - s )

We get by substituting the values in the equation

=> y + 4 = - 1/2 * ( x + 1 )

=> x + 2y = -1 - 8

=> x + 2y = -9

Therefore, by using the formula for equation of line, we get the equation of the line with slope -1/2 passing through the point (-1,-4) as x + 2y = -9

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Answer:

17

Step-by-step explanation:

We can substitute x = -4 and y = 1 since the point lies on the line.

[tex]5(-4)-3(1)=B \\ \\ B=17[/tex]

Answer:

2^2×3×5

Step-by-step explanation:

hope this works :)

By doing some changes of units, we can see that we will need 22.61 gallons of paint to cover 800 square meters.

We know that with one liter of interior paint we can cover 100 square feet.

Remember the relation between square feet and square meeters:

1ft^2 = 0.092 m^2

Then with one liter we can cover:

100ft^2 = 100*0.092 m^2 = 9.2 m^2

So the number of liters of paint that we need to cover the 800 m^2 is given by the quotient:

L = 800m^2/9.2m^2 = 86.96

We need 86.96 liters of paint, and the relation between liters and gallons is:

1 L = 0.26 gal

Then we need:

86.96 L = 86.96*(0.26 gal) = 22.61 gal

We will need 22.61 gallons of paint to cover 800 square meters.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.

i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.

And as we can see in the given tables,

1.) 12.23 is the value of x for both 5.4 and 6.4

2.) 0.31 is the value of x for both 55 and 59

4.) 20 is the value of x for both 245 and 255

So, the only table representing y as a function of x is table 3.

Answer:

table 3 is correct i took the test

Step-by-step explanation:

Answer:

===========================

y is greater by 100 times

Answer:

y = -34x - 270

Step-by-step explanation:

m = -34, y = 2, x = -8

y = mx + b

2 = -34(-8) + b

b = 2 - 272

b = -270

y = -34x - 270

Answer:

A and D

Step-by-step explanation:

[tex]\sf \boxed{\text{\bf Volume of rectangular box = length * width * height}}[/tex]

A) Volume of the given box = 6 * 3 * 5

                                             = 90 cubic meters.

D) Volume of the given box = 3 * 2 * 15

                                             = 90 cubic meters

Answer:

4 and 5

Step-by-step explanation:

We need 2 positive numbers that are right beside each other, like 1 and 2. When the problem is translates into number format we get:

y^2+4x=41

x = 1st # and y = 2nd #

so if we do 4 (x) and 5 (y)

5^2+4(4)=41

the statement is true.

Answer: x = 4

Step-by-step explanation:

   Given:

3x - 1 = 11

   Add 1 to both sides of the equation:

3x = 12

   Divide both sides of the equation by 3:

x = 4

Answer:

Step-by-step explanation:

400

30

1

400 FOR HUNDREDS

Answer:

5/3 + 15/4 are the fractions

The water that a bobcat drink in 1 day will be 3x.

Let the amount of water be represented by x.

From the information, it was stated that each day a bobcat drinks about 3 times as much water as a canada goose drinks.

Let the water that the Canada goose drank be represented as x

Therefore, the water that a bobcat drink in 1 day will be 3x.

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Answer:

True

Step-by-step explanation:

Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".

Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)

and maybe the question has more chance to be false because if a statement is false at least in one case it is false.

Answer:

[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]

Translation:

Option C.

Since the values on both sides of the expression are different, hence the equation has no solution.

Linear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b

Given the expression 4x+3x-x=-5+6x

Collect the like terms

4x+3x-x = -5+6x

4x+3x-x-6x = -5

7x - 7x = -5

Simplify

-0x = -5

0x = 5

x = 5/0

Since the values on both sides of the expression are different, hence the equation has no solution.

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The value of x is -5

Algebraic expressions are expressions that comprised of;

They are also made of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc

Given the equation;

4x + 3x = -5 + 6x

Let's solve for x

We have;

collect like terms

4x + 3x - 6x = -5

Add or subtract like terms

7x - 6x = - 5

x = -5

Thus, the value of x is -5

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The shape of the distribution of the given data set is : Bell shaped

What is Frequency distribution ?

Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart.

Data: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1

Classes = 5

Class  Frequency

1-3      →3

4-6     →4

7-9     →9

10-12  →2

13-15   →2

The shape of the distribution is peak at the center and down at both the ends,

Therefore, we can say that the shape of the distribution is bell shaped.

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8 x 10^16/4 x 10^11

do exponents first

8 x 10,000,000,000,000,000/4 x 100,000,000,000

than multiply

80,000,000,000,000,000/4 x 100,000,000,000

than divide

20,000,000,000,000,000x 100,000,000,000

2,000,000,000,000,000,000,000,000,000

Answer:-26

Step-by-step explanation:

Answer:-14-12=-26

Step-by-step explanation: PEMDAS. You do the first parentheses which is 7-21, which will get you -14. Then you do the second parentheses, 4+8. That will get you 12. Then since there’s no multiplication/division, you go to addition/subtraction and since there’s a subtraction symbol in between the parentheses, that’s what you do. -14-12 which will get you -26.

Hope this helps!

Btw PEMDAS stands for (for those people who don’t know or don’t remember)

Parentheses

Exponents

Multiplication*

Division*

Addition’

Subtraction’

*do both together, whichever one comes first when reading it

’do both together, whichever one comes first when reading it

I think you are supposed to add the the numbers in that row and if it's more that 18 and less that 37 that's the answer. exapmle:

2,8,3,9,5

Add those together and get 27. 27 is less than 37 and more that 18 so it would be one of the answers.

I could be wrong but I'm pretty sure that is what you do

Answer:

40

Step-by-step explanation:

=125x32

=4,000÷100

=40