Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100

The logarithmic expression given as logₙ(1/63) has its value to be -4.143

From the question, the given parameters are

logₙ(7) = 1.946

logₙ(9) = 2.197

logₙ(16) = 2.773

The logarithmic expression to calculate is given as

logₙ(1/63)

Express 1/63 as 1/7 * 1/9

So, we have the following representation

logₙ(1/63) = logₙ(1/7 * 1/9)

Apply the product of logarithm

This gives

logₙ(1/63) = logₙ(1/7) + logₙ(1/9)

Apply the exponent of logarithm

This gives

logₙ(1/63) = -logₙ(7) - logₙ(9)

Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)

logₙ(1/63) = -1.946 - 2.197

Evaluate

logₙ(1/63) = -4.143

Hence, the value of the logarithmic expression is -4.143

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Answer:

14-3x=25

Step-by-step explanation:

-3x=25+14

-3x=39

-3 -3

x = -13

Answer:

4x(2x−1)

Step-by-step explanation:

[tex] {8x}^{2} - 4x[/tex]

Factor out 4.

[tex]4( {2x}^{2} - x)[/tex]

Consider

[tex] {2x}^{2} - x[/tex]

Factor out x.

x(2x−1)

Rewrite the complete factored expression.

=4x(2x−1)

The total amount of interest and the final debt owed under the US Rule is $191.09.

Given that,

Comet Lee took out a $16,000 loan with a 90-day, 6% note. Comet settled the note for $2,000 after 20 days. Comet settled the note for $4,000 on day 50.

We have to find what is the total amount of interest and the final debt owed under the US Rule.

First,

To calculate $2000 per 20 days.

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $1600

r is 6%

t is 20 days is 20/360

So,

i= 1600×0.06×20/360

i= $53.33

Apply partial payment to interest due,

$2000-$53.33= $1946.67

Next,

Subtract remainder of payment from principal is adjusted balance

Adjusted balance =$16000-$1946.67

Adjusted balance =$14053.33

Now, Second,

To calculate $4000 per 50 days.

We know that,

i=p×r×t

So, p is $14053.33

r is 6%

t is 50 days is 30/360

So,

i= 14053.33×0.06×30/360

i= $70.27

Apply partial payment to interest due,

$4000-$70.27= $3929.73

Next,

Subtract remainder of payment from principal is adjusted balance

Adjusted balance =$14053.33-$3929.73

Adjusted balance =$10123.6

Now, for 40 days

i= 10123.6×0.06×40/360

i= $67.49

So, balance is 10123.6+67.49= $10191.09

When max make two makes partial payments,

The total interest is $53.33+$70.27+$67.49= $191.09

Therefore, the total amount of interest and the final debt owed under the US Rule is $191.09.

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The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given function,

f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x

f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)

=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)

f'(x)=0

((1/x)-4x)=0

1-4x²=0

4x²=1

x=±1/4

Given that, f(x) is decreasing function then,

f'(x)<0

((1/x)-4x)<0

(1-4x²)/x<0

1-4x²<0

1<4x²

1/4<4x²

x²>1/4

x>1/2

x∈(1/2,∞)

Hence, f(x) is decreasing on the interval x∈(1/2,∞)

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Answer:

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

Since both points have same x-coordinate, the distance between them is the difference of y-coordinates:

Correct choice is D

Answer:

32 units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Define the two given points:

Substitute the two points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]

[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]

[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]

[tex]\implies d=\sqrt{32^2}[/tex]

[tex]\implies d=32[/tex]

Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:  

[tex]\implies 8 - (-24) = 8+23=32[/tex]

Answer: The answer is A

Step-by-step explanation:

-5/8 is literally equal to -0.625 meaning this asnwer is equal not less

-0.5 is Greater than -0.625 because -0.6 is much larger

-8/5 is -1.6 which is Less than -0.625

The decimal form of the number is :

9804.0

What is the decimal number?

Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.

If the question is,

4x1+8 x 100 + 9 × 1000, then simplify it first

4x1+8 x 100 + 9 × 1000=4+800+9000=9804

So, the decimal form is :

9804.0

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Answer:

14 and 15

Step-by-step explanation:

[tex]196<201<225 \\ \\ \sqrt{196}<\sqrt{201}<\sqrt{225} \\ \\ 14<\sqrt{201}<15[/tex]

The value to make the inequality true is n > 3

Inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

We need to solve this problem and determine what value will solve this problem.

2(n + 2) < 5(n - 1)

2n + 4 < 5n - 5

Collect like terms

4 + 5 < 5n - 2n

9 < 3n

3n > 9

n > 3

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Answer:

the answer Is D 19/18

1/9 +2/3=1/9+ 6/9 =7/9

7/9 +5/18= 14/18 + 5/18 = 19/18

The values of the variables x and y are 2 and -7.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is y = -2x + 5. We are given two sets of ordered pairs. The ordered pairs are (6, y) and (x, 1). These points satisfy the given equation. We need to find the values of the variables x and y. We will substitute the coordinates into the equation.

y = -2x + 5

First, we will put (6, y).

y = -2(6) + 5 = -12 + 5 = -7

Now, we will put (x, 1).

1 = -2x + 5

2x = 4

x = 2

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Answer:

4(m+10)

Step-by-step explanation:

sum is adding

Hopes this helps please mark brainliest

The measure of the angle 'x' will be 41°. Then the correct option is c.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The measure of the angles will be 76° and 63°.

By the property Supplementary angle, the equation is given as,

76° + x + 63° = 180°

Simplify the equation, then we have

x + 139° = 180°

x = 180° - 139°

x = 41°

The measure of the angle 'x' will be 41°. Then the correct option is c.

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Answer:  The correct answer is 17 bags of fertilizer to cover the lawn

Step-by-step explanation:

1 bag of fertilizer covers 3000 SF of lawn

How many bags are needed for an area of 290 feet x 170 feet

Calculate the Square Feet:

290 x 170 = 49,300 SF

Divide space (SF) by bag coverage (SF):

49,300 / 3,000 = 16.43 bags of fertilizer

Round up answer to 17 bags of fertilizer

Answer:

x = 2

Step-by-step explanation:

For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.

Hope this helps!

Answer:

It's an example of the distributive property

For the given functions f(x) = 3x and g(x) = 1/x then domain of

(gof)(x) =1/3x is all the real numbers excluding zero.

As given in the question,

Given functions are as follow:

f(x) = 3x

g(x) = 1/x

Now ,

(gof)(x)

= g(f(x))

Substitute f(x) = 3x in the above function we have,

=g(3x)

Replace the value of x by 3x in the given function g(x) we get,

= 1/ 3x

For x = 0 (gof)(x) =1/3x is undefined.

Domain include all the real numbers except zero.

Therefore, for the given functions f(x) = 3x and g(x) = 1/x then domain of (gof)(x) =1/3x is all the real numbers excluding zero.

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Answer:

x is 70°

hopefully this will help u

Answer:

LCM = 42

Step-by-step explanation:

There are many ways to do this.

Listing Multiples:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 14:

14, 28, 42, 56, 70

Multiples of 21:

21, 42, 63, 84

Therefore,

LCM(14, 21) = 42

Prime Factorization:

List all prime factors for each number.

Prime Factorization of 14 is:

2 x 7  =>  21 x 71

Prime Factorization of 21 is:

3 x 7  =>  31 x 71

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 3, 7

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 7 = 42

In exponential form:

LCM = 21 x 31 x 71 = 42

LCM = 42

Therefore,

LCM(14, 21) = 42

Cake / Ladder:

Divide your numbers by prime numbers as long as both numbers are evenly divisible by that prime.

Cake / Ladder

7 14 21

2       3

When there are no more primes that evenly divide into both numbers you are done.

The LCM is the product of the numbers in the L shape, left column and bottom row.

LCM = 7 x 2 x 3

LCM = 42

Therefore,

LCM(14, 21) = 42

Division Method:

Write your numbers in the top row.

Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.

Division Table

2 14 21

3 7 21

7 7 7

1       1

Bring down any numbers that are not evenly divisible by the prime number.

When the last row of results is all 1's you are done.

Find the product of the prime numbers in the first column to get the LCM:

LCM = 2 x 3 x 7

LCM = 42

Therefore,

LCM(14, 21) = 42

GCF Method:

LCM(14,21) = (14 × 21) / GCF(14,21)

= (14 × 21) / 7

= 294 / 7

= 42

Therefore,

LCM(14, 21) = 42

Venn Diagram:

Inside circle 14: 2

In between circles: 7

Inside circle 21: 3

Then, use prime factorization.

Find the set of prime factors for each number.

Prime Factorization Set for 14 is:

2, 7

Prime Factorization Set for 21 is:

3, 7

Identify the intersections of prime numbers and put them into the Venn Diagram where their circles intersect. Remove the numbers from the original sets.

14 ∩ 21

7

With the remaining prime numbers in each set, if any, put them into their respective circles, not in intersections.

14

2

21

3

Find the union of the sets in the Venn Diagram. This is the superset of all of the prime numbers in the diagram.

14 ∪ 21

The new superset list is

2, 3, 7

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 7 = 42

LCM = 42

Therefore,

LCM(14, 21) = 42

The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:

a) President and vice from different grades: 79,800.

b) At least one from each: 141,960.

It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, there are two possible cases for the parameters, as follows:

Hence the number of ways is:

N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.

For item b, the total number of outcomes is obtained as follows:

N = 22 x 21 x 20 x 19 = 175,560.

The number of outcomes with only grade 11 students is:

N = 7 x 6 x 5 x 4 = 840.

The number of outcomes with only grade 12 students is:

N = 15 x 14 x 13 x 12 = 32760.

Hence the number of students with at least one of each is:

N = 175,560 - (840 + 32,760) = 141,960.

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Answer:

An arithmetic sequence occurs when the difference between each term and the next is constant. Therefore, only addition or subtraction is possible. Also, the amount (4, in this case) must remain the same when added to each successive term.

Answer:

can you pls clear your questions?

Answer: a.) 397.5 b.) 1.3333

Step-by-step explanation:

1 cent = £0.75

530 x 0.75 = 397.5

530 / 397.5 = 1.3333

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12)  (2, 3) over the x - axis becomes, (2, -3).

13)  (7, -2) over the y - axis becomes, (-7, -2).

14) (4, 5) 90° about the origin becomes, (-5, 4).

15) (-3, -2) 270° about the origin becomes, (-2, 3).

16) (17, -23) over the line y = x becomes, (-23, 17).

What is transformation of points?

The reflection is the type of alteration that takes place when each point in the shape is reflected over a line. The picture is on the opposite side of the line from the pre-image when the points are reflected across a line, but it is still at the same distance from the line as the pre-image. The reflection of each point (p, q) onto an image point (q, p).

12) Reflect (2, 3) over the x axis:

Since, the x-coordinate of a point that is reflected across the x-axis stays constant, but the y-coordinate is assumed to be the additive inverse.

The x-axis' reflection of point (x, y) is (x, -y).

So, (2, 3) becomes, (2, -3).

13) Reflect (7, -2) over the y axis:

Since, the y-coordinate of a point that is reflected across the y-axis stays constant, but the x-coordinate is assumed to be the additive inverse.

So, (7, -2) becomes, (-7, -2).

14) Rotate (4, 5) 90° about the origin:

(x, y) → (-y, x) is the formula for a 90° rotation about the origin.

So, (4, 5) becomes, (-5, 4).

15) Rotate (-3, -2) 270° about the origin:

(x, y) → (y, -x) is the formula for a 270° rotation of the origin.

So, (-3, -2) becomes, (-2, 3).

16) Reflect (17, -23) over the line y=x.

The angle at which the point (x, y) is reflected across the line y = x is (y, x).

So, (17, -23) becomes, (-23, 17).

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The total number of tongue depressors and Band-Aids are 56 and 128 respectively.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that, a medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total,

Let the number of wrapped tongue depressors be w and that of Band-Aids be b,

Therefore,

w+b= 184

0.04w+0.08b = 12.48

w+2b = 312

On solving the equation, by elimination method, we get,

b = 128

Therefore, w+128 = 184

w = 56

Hence, the total number of tongue depressors and Band-Aids are 56 and 128 respectively.

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The equation of line parallel to 2x +3y = 9 and passing through the point (6,4) is 3y + 2x = 24

Gradient or slope is the ratio of the change in y to the change in x between two points in a line.

Gradient tells how steep a line is. A perfectly vertical or horizontal line has no slope.

2x + 3y = 9

making y the subject,

3y = 9 - 2x

y = 9/3 -2x/3

Comparing the above equation, with equation of a straight line, y = mx + c

m, which is slope = -2/3

The new line will also have a slope of -2/3 because they are parallel.

Equation for new line,

y-[tex]y_{1}[/tex] / x - [tex]x_{1}[/tex] = slope

The new point is (6,4)

y - 4 / x -6 = -2/3

By cross multiplying

3(y-4) = -2(x - 6)

3y - 12 = -2x + 12

3y + 2x = 24

In conclusion, the equation o the new line is 3y + 2x = 24

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