Write each equation in logarithmic form. 5⁴=625

For the matrix:

[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]

The determinant is equal to 16.

Remember that for a general 2 by 2 matrix:

[tex]\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\\\end{array}\right][/tex]

The determinant is given by the simple formula:

D  = a₁*b₂ - b₁*a₂

This is the only thing we need to use in this problem, we will use this formula to find the determinant of the given 2 by 2 matrix.

In this case we have the matrix:

[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]

Then we can just use the given formula for the determinant, we will get

D = 4*2 - (-1)*8

We just need to solve that expression, we will get:

D = 8 - (-8) = 8 + 8 = 16

We can see that the determinant of the given matrix is equal to 16.

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The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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The step 2 should  be m∠p + m∠o  = 180 degrees(supplementary angles)

The external angle theorem  states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles(remote interior angles) .

Therefore,

Step 1

m∠m + m∠n + m∠o = 180°(sum of angles of a triangle)

It's very correct

Step 2

m∠p - m∠o = 90 degrees(Alternate angles)

This is incorrect.

It should be m∠p + m∠o  = 180 degrees(supplementary angles)

The angles  m∠p  and  m∠o are supplementary angles. This simply implies the angles add up to 180 degrees.

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (2x - y)⁴

By using binomial expansion theorem, we get

(2x - 3)⁷ = 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187

(2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.

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A composite function that represents the number of Mexican pesos equivalent to x Chinese yuan. h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15

x yuan to y dollars = f(x)

f(x) = 0.15 x

y dollars to x yuan

y= 0.15 x

x =  y / 0.15

y dollars to x pesos =g(y)

g(y) =14.07 y

x pesos to y dollars

x = 14.07 y

y = x / 14.07

Substituting the result of second into first,

pesos → dollars → yuan

Lets call this function, h(x) = converts x pesos into y yuan.

h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15

= 0.474 x

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Using addition, Total length of wire used by the electrician is 76 feet.

Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

We will use simple addition here,

Total length used by electrician is

(9 + 13 + 42 + 12) feet.

= 76 feet

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Answer:

A) No solution

B) No solution

Step-by-step explanation:

[tex]A)[/tex]  [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Which in this case leads to no solution because c cannot be less than 0 logically)

[tex]B)[/tex]  [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Whether you change the </> sign or not, c cannot be any less than 0 or it will lead to no solution.)

Answer:

All real numbers im pretty sure

Step-by-step explanation:

Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.

It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.

In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.

Therefore, it should be noted that 8.33 will be:

= 8 + 1/3

It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...

Therefore, the appropriate fraction for 8.33 will be 8 1/3.

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When the garden is recording the heights of its available trees. the display that can be used to represent the data by a Bar chart, because tree height is numerical. The correct option is A.

A bar chart or bar graph uses rectangular bars with heights or lengths proportional to the values they represent to show categorical data. A bar plot could be either vertical or horizontal. A vertical bar graph is sometimes known as a column chart.

A bar chart is used to show the distribution of data points or to compare metrics across different subgroups of your data. We may see how different groups compare to one another and which groupings are most common or prevalent using a bar graph.

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Answer:

Step-by-step explanation:

i think its A., bart chart

Answer:

Step-by-step explanation:

If a polygon does not have 5 sides, then it is not a pentagon.: TRUE

The third term of the expansion is 6a^2b^2

The binomial term is given as

(a - b)^4

The r-th term of the expansion is calculated using

r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)

So, we have

3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)

Evaluate the sum and the difference

3rd term = C(4, 2) * (a)^2 * (-b)^2

Evaluate the exponents

3rd term = C(4, 2) * a^2b^2

Evaluate the combination expression

3rd term = 6 * a^2b^2

Evaluate the product

3rd term = 6a^2b^2

Hence, the third term of the expansion is 6a^2b^2

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the range of the function in the graph is:

-4 ≤ y ≤ 2

For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.

Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.

If we look at the graph, we can see that the minimum value of y is:

y = -4

And we can see that the maximum value of y is:

y = 2

Then the range of the function in the graph is:

-4 ≤ y ≤ 2

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Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

The measure of all the angles are :

∠1 = 119°, ∠2 = 61°,  ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°

According to the question we have been given two parallel lines which is cut by a transversal line. There total 8 angles and given is the measure of

∠8 = 119°.

We need to find the measure of all other 7 angles.

Note that when two parallel lines are cut by a transversal then

i) corresponding angles are equal that is

                 ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8

ii) alternate interior angles are equal that is

                  ∠3 = ∠6, and ∠4 = ∠5

iii) alternate exterior angles are equal that is

                  ∠1 = ∠8, and ∠2 = ∠7

iv) Consecutive interior angle sum is 180°

           ∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.

So according to the rules given above the measure of all the angles are:

 ∠1 = 119°, ∠2 = 61°,  ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°

Hence measure of all the angles is given above

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Answer:

A linear function is of the form f(x)= mx+b

We will know 8 complete names after 2 days and 20 complete names after 8 days. Whether or not this function represents your learning rate will vary from person to person.

Here, we are given an exponential function: f(t)= c{1- e^(-kt)}

where

f(t) = number of tasks learned.

c = total number of tasks to be learned

k = rate of learning

t = time

Now, when we move to a new school, number of names we need to learn ⇒ c = 25

learning rate for new tasks = 20%

⇒ k = 0.2

and time = 2 days

⇒ t = 2

Substituting these values in the function we get-

f(2) = 25{1- [tex]e^{-0.2 * 2}[/tex]}

= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]

= 0.67

Thus, f(2) = 25( 1-0.67 )

f(2) = 25(0.33)

f(2) = 8.25

Thus, we will be able to learn 8 complete names in 2 days.

If t = 8f(8) = 25{1- [tex]e^{-0.2*8}[/tex]}

= 25{1- [tex]e^{-1.6}[/tex]}

= 25(1- 0.20)

= 25(0.80)

= 20

Thus, we will be able to learn 20 complete names in 8 days. Whether of not this function describes your own learning rate will vary from person to person. Some people are fast learners whereas others take their time. A fast learner will have a higher learning rate whereas a slow learner will have a lower learning rate as depicted by k. You can change the value of k to adjust the function as per your learning abilities.

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Your question was incomplete, check for full content below-

Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.

a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days?

b. After 8 days?

c. Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?

Answer: 1.3

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

9 is the hundredth and we round up with 8 so we’d round up 1 and we get 1.3

I don't know I really needed help on this one

A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.

If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.

Current Balanced Owned =$785

APR = 24.42%

Let’s suppose the billing cycle is 30 days, then

Finance charge = $15.76

The new balance you owe = $800.76.

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Based on the amount that Scott borrowed for the new TV and game system, and the interest paid, the simple interest rate is 15.7%

The simple interest rate can be found by the formula:

= Interest paid by Scott on the loan / Amount Scott borrowed x 100%

Solving for the simple interest rate gives:

= 155 / 985 x 100%

= 0.1573604060913705583756345177665 x 100%

= 0.157 x 100%

= 15.7%

This means that Scott paid 15.7% on the loan he borrowed.

In conclusion, Scott's simple interest rate is 15.7%.

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Answer:  f(x) = | x |

Step-by-step explanation:

when transforming and translating a function, you use the form a | x - h | + k  

a= vertical shrink/stretch factor

h = horizontal movement ( right or left)  

k = vertical movement ( up or down )

So a = 1/2  h = 0 and k =2

g(x) = 1/2 | x-0 | + 2

g(x) = 1/2 | x | + 2    [which means vert shrink of 1/2 and up 2 units ]

The probability that a string of 15 people passes through screening successfully before an individual is caught with a questionable object is 0.3040 and the expected number of people to pass through be- fore an individual is stopped 49

3% of people whose luggage is screened at an airport have questionable objects in their luggage i.e

P(x)=3/100=0.03

The probability of people whose luggage is screened at an airport and have no questionable object in their luggage is

〖P(x)〗^1=1-P(x)

〖P(x)〗^1=1-0.03

〖P(x)〗^1=0.97

Using Binomial probability which states that

P(x)=(nCx) (p)^x (q)^(n-x)

N= 16 total number in consideration

p= probability with no questionable luggage

q= probability with questionable luggage

P(15)=(16C15) (p)^15 (q)^(16-15)

P(15)=(16C15) (0.97)^15 (0.03)^(16-15)

16C15=16!/((16-15)!(15!))

15C15=15!/((1)!(15!))

16C15=20922789888000/((1)(1307674368000))

16C15=20922789888000/1307674368000

16C15=16

P(15)=(16) (0.97)^15 (0.03)^1

P(15)=(16)(0.63325)(0.03)

P(15)=0.3040

P(x) =(Required outcome)/(Total outcome)

0.3040 =15/(Total outcome)

Total outcome=15/0.3040

Total outcome=49.34

Total outcome=49

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l o o k    i t   u  p     o n    g a u t h m a t h      c o p y   u r    q e s t i o n   t h e r e

Step-by-step explanation: You're welcome

The coordinate of the point R' after translation will be (0, - 4).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

If ∆PQR is translated left 2 and down 6. Then the translation rule is given as,

(x', y') → (x - 2, y - 6)

From the graph, the coordinate of point R will be at (2, 2). Then the coordinate of the point R' after translation will be

(x', y') → (2 - 2, 2 - 6)

(x', y') → (0, - 4)

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The required solution of the given expression is -2/5 as a simplified form.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

The given expression is

2/5÷(−5/5)

According to given question we have

The expression is

2/5÷(−5/5)

=2/5÷(-1)

=2*(-1)/5

=-2/5

Therefore, the required solution of the given expression is -2/5 as a simplified form.

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The area of her garden where Riya is applying Mulch is 0.25m³.

To understand this answer, we will analyze the information in the question statement. So, we know that Riya is applying Mulch to her Garden. The application of Mulch is at the rate of 250 000 cm^3 for every m^2. Now to find the rate for every m^3, we will use the basic conversion formula for converting cm to m:
we know that,

100 cm = 1m

Now we can write this formula as follows,

1 cm = 1 / 100 m

1 cm = 0.01 m

We will use the same relation for the values given to us in the question:
250, 000 cm^3 = 250, 000 x 1 cm x 1cm x 1cm

1 cm^3 = 1 cm x 1cm x 1cm

250, 000 cm^3 = 250, 000 x 0.1 x 0.1 x 0.1

From, 1 cm = 0.01 m

250, 000 cm^3 = 250, 000 x 0.000001

250, 000  cm^3 = 0.25 m^3

Hence Riya is applying at 0.25 m^3 per m^2 (meter square).

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The output values of  x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.

Given the data in the question;

When x = -2. replace all the occurrence of x with -2 in the function and simplify to determine the output value.

r(x) = -x - 7

r(-2) = -(-2) - 7

r(-2) = 2 - 7

r(-2) = -5

When x = 0. replace all the occurrence of x with 0 in the function and simplify to determine the output value.

r(x) = -x - 7

r(0) = -(0) - 7

r(0) = 0 - 7

r(0) = -7

When x = 5. replace all the occurrence of x with 5 in the function and simplify to determine the output value.

r(x) = -x - 7

r(5) = -(5) - 7

r(5) = -5 - 7

r(5) = -12

Therefore the output values of  x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.

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The sum in scientific notation will give:

7.76*10⁶

Here we want to find the sum between the numbers (7.3*10⁶) and (4.6*10⁵).

To sum these numbers, we need to have the same exponent in the "10", then we can rewrite:

7.3*10⁶ = 73*10⁵

Now the sum will be:

73*10⁵ + 4.6*10⁵

Taking a common factor we get:

73*10⁵ + 4.6*10⁵ = (73 + 4.6)*10⁵ = 77.6*10⁵

Now we want to go back to scientific notation, so we need to move the decimal point one time to the left, we will get:

77.6*10⁵ = 7.76*10⁶

That is the outcome of the sum.

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