I don't understand this question​

The equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.

Given that

10^4 = 10000 - - - - - -( 1 )

We have [tex]a^{y}[/tex] = x - - - - - ( 2 )

Comparing ( 1 ) and ( 2 ) we get

a = 10, y = 4, x = 10000

The logarithmic form is written as logₐ (x) = y .It is rearrangement of the exponential form [tex]a^{y}[/tex] = x.

By logarithmic definition

y = logₐ (x)

so we got 4 = log₁₀ (10000)

Therefore, the equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.

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Answer:

Greater number = 58

Step-by-step explanation:

The equation is,

→ (x + 19) + x = 97

Now the value of x will be,

→ (x + 19) + x = 97

→ 2x = 97 - 19

→ x = 78/2

→ [ x = 39 ]

Then the greater number is,

→ x + 19

→ 39 + 19 = 58

Hence, the answer is 58.

Answer:

58

Step-by-step explanation:

first number=x

second number= x+19

x+x+19= 97

thus, the two numbers are 39 and

The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.

The slope of a line is y=mx+c, where m is the slope.

The given line is y = 1/4x -3.

slope m1=1/4.

slope of second line=-(1/m)

=-(1/1/4)

=-4

point slope intercept form is y-y1=m(x-x1)

Equation of the perpendicular line passing through point (0,6) is

y-6=-4(x)

y=-4x+6

Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.

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If a string has 20 light bulbs and these lights are all wired in series, so that if one light bulb fails, the whole string fails and the probability that any one light fails is 0.2 and each of the individual lights are independent of each other, then the probability that the string will not fail is 0.0115.

Probability in mathematics deals with the likelihood of an event to take place.

The probability that the string will not fail refers to when all 20 bulbs will not fail. As given in the conditions, each of the individual lights are independent of the other. Therefore;

the probability that any one of the lights will not fail is:

1 - probability that any one light fails = 1 - 0.2 = 0.8

And we need all 20 to be complete. The unity of events is a product of probabilities. Therefore the probability that the string will not fail is:

P = 0.8^20

P = 0.0115

Hence 0.0115 is the probability that the string will not fail.

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Answer:

Step-by-step explanation:

Martha spent 1/6 of her pocket money on magazines.

The quotient of 1 ÷ 17 is a rational number.

In this question, Amy inputs 1÷17 in her calculator.

The calculator displays 0.0588235294

We need to check whether the quotient is a rational or an irrational number.

The quotient of 1 ÷ 17 is a rational number.

1 ÷ 17 can be written as 1/17, which is a rational number.

The quotient of 1 ÷ 17 is a decimal: the quotient a rational or an irrational number.

Therefore, the quotient of 1 ÷ 17 is a rational number.

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The correct option regarding the bank amount as a function of time is:

This is an exponential function because there is a common ratio in the balance between the weeks.

For this problem, the differences are given as follows:

The ratios are given as follows:

Due to the same ratios, an exponential function should be used, and the correct option is given by:

This is an exponential function because there is a common ratio in the balance between the weeks.

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Answer:c

Step-by-step explanation:

Step-by-step explanation:

start by collecting like terms

4x² - 6x -9

use quadratic equation, a=4, b= 6 and 9 = c.

x = 5,78 or x = -4,28

Answer:

65-72

Step-by-step explanation:

points of discontinuity for each rational function. y=x+5 / x²+9 x+20 is x = -4

Given,

y=x+5 / x²+9 x+20

It can be expressed in the form of -

⇒ y = (x+5) / (x+5) (x+4)

⇒ y = 1 / (x+4)

The function will be undefined if the denominator will be 0

⇒ x+4 = 0

⇒ x = -4

So, we can conclude that the given function will be having points of discontinuity as x = -4

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Answer:

2 3/4

Step-by-step explanation:

the Smallest is 1/2

the biggest is 1 1/2

the most common is 3/4

Adding them all up will give you 2 3/4 or 11/4

Answer:

2[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

the smallest button is [tex]\frac{1}{2}[/tex]

the most common button is [tex]\frac{3}{4}[/tex]

the largest button is 1 [tex]\frac{1}{2}[/tex]

add these buttons together

[tex]\frac{1}{2} + \frac{3}{4} + 1 \frac{1}{2} =[/tex]

find the LCD of the denominators

factors of 2: 2, 4, 6, 8, 10

factors of 4: 4, 8, 12, 16, 20

find the factor that is the same in the two rows

factors of 2: 2, 4, 6, 8, 10

factors of 4: 4, 8, 12, 16, 20

2*2 = 4

[tex]\frac{1}{2}[/tex]· 2 = [tex]\frac{2}{4}[/tex]

[tex]\frac{2}{4} + \frac{3}{4} + 1 \frac{2}{4} =[/tex]

1[tex]\frac{7}{4}[/tex]

[tex]\frac{7}{4} = 1 \frac{3}{4}[/tex] + 1

2[tex]\frac{3}{4}[/tex]

The difference is 5ab + 7a + 13

An arithmetic operation is specified by combining operands with one arithmetic operator. Arithmetic operations can also be specified by the ADD, SUBTRACT, DIVIDE, and MULTIPLY

given:

(9ab+7a-7) (4ab-5)

So, the difference is

(9ab+7a-7) - (4ab-5)

=9ab + 7a - 7 -4ab + 20

=9ab - 4ab +7a -7 +20

=5ab + 7a + 13

Hence, the difference is 5ab + 7a + 13.

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The square root value of 7 is 2.645.

Irrational number

All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.

Any square root number that cannot be represented as a fraction [tex]\frac{P}{Q}[/tex] for any integer p and q is said to be irrational.

A real number that cannot be expressed as a straight forward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to [tex]\frac{P}{Q}[/tex] if N is irrational.

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After 1.842 hours the price of Stock A and Stock B will be the same using a set of linear equations.

A grouping of one or more linear equations containing the same variables is known as a system of linear equations.

For Stock A :

The initial price = $15.03

The rate of increase = $0.05

For Stock B :

The rate of decrease = $15.53

The rate of decrease per hour = $0.13

Then the price of stock A at noon will be:

$ 15.03 + $ (0.05 × 3) = $ 15.03 + $ 0.15 = $15.18

The period of time during which the stock price will remain constant:

15.18 + 0.05t = 15.53 - 0.14t

Simplifying the terms we get,

0.05t + 0.14t = 15.53 - 15.18

0.19t = 0.35

t = (0.35 ÷ 0.19) hours

t = 1.842 hours

Therefore, the stocks will be of equal price after 1.842 hours.

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Answer:

? = sin θ

Step-by-step explanation:

csc θ =1/?

csc θ =1/sin θ

Answer: 50,000 pennies

Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000

The distance that Nathan can ride his bike is 2 miles.

The rate is the total distance per time. Rate is determined by dividing the total distance travelled by the total time travelled.

Rate = total distance / total time.

Distance = rate x time

The rate is in miles per hour while the time given is in minutes. Thus, minutes has to be changed to hour. To do this, divide 24 minutes by 60.

60 minutes = 1 hour

24/ 60 = 2/5

Distance = 2/5 x 5= 2 miles

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Answer:

If it is a division problem, then it is 11.

If it is a multiplication problem then it is 1100.

But it looks like division, so probably 11.

Answer:

011

Step-by-step explanation:

         0 1 1

--------------------------------

1 /

          0 1 1 0

 − 0    

   1 1  

 − 1 0  

     1 0

   − 1 0

       0

well, we know the rate is compounding at 800% per minute.

the elapsed time will be 12 seconds, and since a minute has 60 seconds, that'd be 12/60 minutes.

the compounding period is 3 seconds, and since a minute has 60 seconds, that means is compounds 60/3 times, or namely 20 times.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 800\%\to \frac{800}{100}\dotfill &8\\ n= \begin{array}{llll} \textit{times it compounds per minute}\\ \textit{twenty times} \end{array}\dotfill &20\\ t=minutes\to \frac{12}{60}\dotfill &\frac{1}{5} \end{cases}[/tex]

[tex]A=20000\left(1+\frac{8}{20}\right)^{20\cdot \frac{1}{5}} \implies A =20000(1.4)^4\implies A=76832[/tex]

Answer:10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

8 + (9- 1) ÷ 4

Use PEMDAS to determine order of operations in a mathematical expression

The order of operations is

P = parentheses
E = exponent

M = multiplication

D == division

A = addition

S = subtraction

Note that multiplication and division have the same priority and we go from left to right that case. Because it does not affect the answer.

So 12 ÷ 4 x 6 = 12 x 6 ÷ 4
Same for addition and subtraction - same priority

Using PEMDAS

(9 - 1) is executed first giving 8

The expression becomes 8 + 8 ÷ 4

Next division is performed so 8 ÷ 4 is executed giving 2 as the answer

Finally 8 + 2 is executed giving 10

Answer:

The way you described this question was a bit confusing- but here is what I can provide based off of what you said.

Step-by-step explanation:

7x+5/x

Please provide a picture next time

Answer:

Step-by-step explanation:

180-degree rotation

I explained previously, but I will explain again.

A 180-degree rotation is just a switch of signs on the numbers

Explanation:

Answer:

hundred

million

hundredth

5800

2

460000

0.07

Step-by-step explanation:

At an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.

The exponential constant, denoted by the symbol e, is an essential mathematical constant. Its value is approximately equal to 2.718. This value occurs very frequently in mathematics when it is used to model physical and economic phenomena.

Here, we are given an exponential function- p = 101.3[tex]e^{-0.001h}[/tex]

where p = atmospheric pressure in pascals

h = altitude in meters.

If the altitude is 500m

h = 500

Then,

p = 101.3 [tex]e^{-0.001 * 500}[/tex]p

=  101.3 [tex]e^{-0.5}[/tex]p

=  101.3/ [tex]e^{-0.5}[/tex]p

= 101.3/ 1.648p

= 61.46

Thus, at an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.

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The equation of the parabola in discuss such that the parabola has a vertex at (2, 3) and passes through (0, 2) is; y = (-1/4) (x - 2)² + 3.

It follows from the task content that the equation of the parabola whose vertex is at (2, 3) and passes through (0, 2) is to be determined.

Since, the vertex form equation of a parabola is;

y = a (x-h)² + k

where the vertex is; (h, k) which is (2, 3) in this scenario.

Therefore, we have;

y = a (x - 2)² + 3

Ultimately, to find the value of a; substitute; x = 0 and y = 2 from the point (0,2) into the equation;

2 = a (0-2)² +3

-1 = 4a

a = -1/4.

Ultimately, the equation of the parabola as required in the task content is;

y = (-1/4) (x - 2)² + 3

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The fraction -1 2/5 is modeled on the number line by: graph A.

A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

In this scenario, we can reasonably infer and logically deduce that the fraction -1 2/5 is modeled on the number line by graph A because each interval increases by 2/5 or 0.4.

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Answer:

1) R = 1 S = 3 T = 1

2) R = 1 S = 3 T = 1

3) R = 1 S = 3 T = 1

Step-by-step explanation:

Surprisingly each of the situations end up with 1, 3, 1. I double checked with a calculator and they all end up being true. Hope this helps. Have a great night. :)

Answer:

x = -2

Step-by-step explanation:

The equation is,

→ 17 + x = 15

Now the value of x will be,

→ 17 + x = 15

→ x = 15 - 17

→ [ x = -2 ]

Hence, the value of x is -2.

Step-by-step explanation:

17+x=15

17+x-17=15-17

x=-2