x + 2y = -4
2x + 3y = 1 ​

Answer:

[tex]\approx 4.39 \cdot 3^x[/tex]

Step-by-step explanation:

Recall a property:

[tex](c\cdot f(x))'=c\cdot f(x)'[/tex], where [tex]c[/tex] is a constant.

Apply the property to the task:

[tex](4\cdot 3^{x})'=4\cdot (3^x)'[/tex]

Recall a property of the derivative of an exponential function:

[tex](a^x)'=a^x \cdot \ln{a}[/tex]

Apply the property to the task:

[tex]4\cdot 3^x \cdot \ln 3[/tex]

Since [tex]\ln 3\approx 1.0986[/tex], it follows:

   [tex]4\cdot 3^x \cdot \ln 3 \approx 4\cdot 1.0986 \cdot \ln3[/tex]

Multiply the numbers.

The answer is about [tex]4.39\cdot 3^x[/tex].

Answer:

$37.42 / kg

Step-by-step explanation:

Divide 16.99 by 454 to get the unit cost per gram. This equals 0.037422907…

Take this number and multiply it by 1000, while rounding it to the nearest hundredth after.

This equals about $37.42 / kg.

The values of K that will make 23K10 to be divisible by 2, 3 and 5 are; 0, 3, 6 and 9

We want to find the number K in 23K10 that will make it divisible by 2, 3 and 5.

Now, for the number to be divisible by 2, 3 and 5, then it means it must be divisible by the LCM which is; 2 * 3 * 5 = 30

Now, the divisibility rule for 30 is that it must be divisible by 3 and 10.

If 23K10 is divisible by 3, sum of digits will be multiple of 3.

Thus;

2 + 3 + K + 1 + 0 = K + 6 must be equal to 0, 3, 6, 9, 12, 15, 18....

Thus, K could either be 0, 3, 6 or 9

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Answer:

isn't this already fully simplified?

Step-by-step explanation:

Answer:

89.25%

Step-by-step explanation:

65 is the lowest so it only counts for 20% of the grade

65*0.2=16.25

80*0.25=20

92*0.25=23

There is 30% left and 100% is the highest score

100*0.3=30

16.25+20+23+30=89.25

Answer:

86%

Step-by-step explanation:

From the information give:

Exam 1

Exam result = 65%

Overall grade weighting = 20%

⇒ Credit = 65% of 20% = 0.65 × 0.2 = 0.13 = 13%

Exam 2

Exam result = 80%

Overall grade weighting = 25%

⇒ Credit = 80% of 25% = 0.8 × 0.25 = 0.2 = 20%

Exam 3

Exam result = 92%

Overall grade weighting = 25%

⇒ Credit = 92% of 25% = 0.92 × 0.25 = 0.23 = 23%

Final Exam

The highest grade Brian can earn = 100%

Overall grade weighting = 100% - 20% - 25% - 25% = 30%

⇒ Credit = 100% of 30% = 1 × 30% = 30%

Highest potential class grade

Sum of each exam credit:

⇒ 13% + 20% + 23% + 30% = 86%

Therefore, the highest grade possible that Brian can earn in the class is 86%.

The value of x is ±0.7071 and x is an irrational number

The equation is given as:

[tex]4x^2 = 2[/tex]

Divide by 4

[tex]x^2 = 0.5[/tex]

Take the square roots

[tex]x = \pm 0.7071[/tex]

Hence, the value of x is ±0.7071

The equation is given as:

[tex]4^x = 5[/tex]

Take the logarithm of both sides

[tex]x\log(4) = \log(5)[/tex]

Divide both sides by log(4)

x = 1.16096....

The above number is a non-terminating decimal.

Non-terminating decimals cannot be represented as fractions of two integers

Hence, x is an irrational number

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Answer:

12

Step-by-step explanation:

Givens

Harpreet        = x + 3

Sukhpreet     = x

Komalpreet   = 2*(x + 3)

Average Age = 15

Equation

[(x + 3) + x + 2*(x + 3) ] / 3 = 15                  Multiply both sides by 3

Solution

3 [(x + 3) + x + 2*(x + 3) ] / 3 = 15 * 3         Combine

 [(x + 3) + x + 2*(x + 3) ]       =   45             Remove the brackets

x + 3 + x + 2x + 6                 =   45             Combine like terms

4x + 9 = 45                                                 Subtract 9 from both sides

4x + 9 - 9 = 45 - 9                                       Combine

4x = 36                                                         Divide by 4

4x/4 = 36/4

x = 9

Answer

Harpreet is  x+ 3 = 9 + 3 = 12

The linear equation that respects the given conditions is:

[tex]y = \frac{3}{2}x + [/tex]

A linear function is modeled by:

y = mx + b

In which:

When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.

[tex]2x + 3y = 4[/tex]

[tex]3y = -2x + 4[/tex]

[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]

Then:

[tex]-\frac{2}{3}m = -1[/tex]

[tex]m = \frac{3}{2}[/tex]

Hence:

[tex]y = \frac{3}{2}x + b[/tex]

It passes through (−2, 15), that is, when x = -2, y = 15, hence:

[tex]y = \frac{3}{2}x + b[/tex]

[tex]15 = \frac{3}{2}(-2) + b[/tex]

15 = -3 + b

b = 18.

So the equation is:

[tex]y = \frac{3}{2}x + [/tex]

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Answer:

1 child - 60 another child - 50

Step-by-step explanation:

we start from the end. they had a equal number.

child A lost half therefore we give them another half having 2 units as shown in the diagram. child B had 1 unit plus 20 because he lost 20 which total adds up to 110. from there you have

3 units + 20 = 110

3 units = 90

1 unit = 30

since A has 2 units,

30 × 2 = 60

child A has 60.

since B has 1 unit plus 20

30 + 20 = 50

Answer:

the range of each function for the given domain are the step of 3+2x are equal the -8,4

Answer:

Remainder is 13

Step-by-step explanation:

You can apply the remainder theorem here. You just equate the divisor to 0, then substitute the x-value in the expression.

[tex]x^3 + 4x^2 - 2x + 1 \\[/tex]       then, [tex]x+2=0\\x=-2[/tex]

substitute:

[tex]-2^3 + 4(-2)^2-2(-2) + 1 =13[/tex]

Therefore, the remainder is 13

Answer:

[tex]f(x)=x^2[/tex]

Step-by-step explanation:

The quadratic parent function, has no transformations, and has the vertex at (0, 0). Which is the function: [tex]f(x)=x^2[/tex]. Any other quadratic function, has some form of transformation, whether it be a reflection, translation, compression/stretch, etc...

Based on the data set given in the frequency table, the number of values that are less than or equal to 6 is 18.

The value that will be less than or equal to 6 are those that are valued at 6 or below.

The sum of these values are:

= 2 + 3 + 6 + 4 + 3

= 18

In conclusion, 18 values are less than or equal to 6.

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Using the hypergeometric distribution, it is found that there is a 0.1539 = 15.39% probability that all the four students like pizza.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given as follows:

N = 15, n = 4, k = 10.

The probability that all the four students like pizza is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,15,4,10) = \frac{C_{10,4}C_{5,0}}{C_{15,4}} = 0.1539[/tex]

0.1539 = 15.39% probability that all the four students like pizza.

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The domain (input values) of the cosine function is all negative and positive angle measures.

Let the function be f(x) = cos(x)

The domain of cos(x) is -∞ < x < ∞

The range is -1 ≤ f(x) ≤ 1

Hence, domain of cos(x) is all (+) and (-) angle measures.

Same goes with sine function as well

For function f(x) = sin(x)

The domain is -∞ < x < ∞ and range -1 ≤ f(x) ≤ 1

However for f(x) = tan(x) the same is not applicable.

Answer:

A.  all negative and positive angle measures.

Step-by-step explanation:

The domain of a function is the set of input values (x-values).

The cosine function is a continuous function, and therefore has no restrictions throughout its domain.

Therefore, its domain is all real numbers.

Set notation:  { x | x ∈ R }

Interval notation: (-∞, ∞)

The perimeter of the park is 3x^2 + 37x - 4

The side lengths of the triangular park are:

10x + 3x^2 - 8, 12x and 15x + 4

Add these sides to determine the perimeter

P = 10x + 3x^2 - 8 + 12x + 15x + 4

Collect the like terms

P = 3x^2 + 10x + 12x + 15x - 8 + 4

Evaluate the sum

P = 3x^2 + 37x - 4

Hence, the perimeter of the park is 3x^2 + 37x - 4

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[tex]\huge\boxed{\textsf{a.)}\ 10}[/tex]

Substitute [tex]\frac{1}{2}[/tex] for [tex]x[/tex].

[tex]f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}[/tex]

Use [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex].

[tex]\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}[/tex]

Answer:

Step-by-step explanation:

Question

64^m

--------

4^2m

Solution

(64)^m = (4^3)^m = 4^3m

4^3m/4^2m = 4^(3m - 2m) = 4^m

Answer

2^2m = (2^2)^m = 4^m                     Equivalent

16^0.5m = (16^0.4) ^m = 4^m          Equivalent

4^m                                                    Equivalent

All three of these are equivalent. The catch is in splitting the powers apart.  In this top one (2^2m) you move the brackets so that the right bracket is after the two which gives (2^2)^m =  4m

You do the same thing with (16^0.5)^m.  16^0.5 = 4 So the answer is 4^m

The last one is 4^m which is the answer you got from the division.

Given expression: [tex]64^{m} /{4^{2m} }[/tex]

We can rewrite the expression (in the numerator and the denominator) as the product of multiple fours. Then, we can apply the exponent rule to simplify the expression to its simplest form. The simplest form will be the required simplified expression (solution to the provided expression).

We can apply the following exponent rule to simplify the expression:

[tex]\boxed{\text{Exponent rule:} \ 4^{m} /4^{n} = 4^{m - n}}[/tex]

The exponent rule states that the "base" must be the same when subtracting exponents. If we divide a term with same bases, we can reduce work time by subtracting the exponent to simplify the expression.

Now, let us look at all the options to verify which term matches our simplified term, and which expressions do not match our simplified term.

Given term: [tex]2^{2m} \\[/tex]

Can be re-written as:

Simplifying the expression inside the long brackets:

Therefore, the first option is equivalent to our simplified term.

Given term: [tex]16^{0.5m}[/tex]

Can be re-written as:

Exponent Rule: (xᵃ)ᵇ = xᵃᵇ

Therefore, the second option is equivalent to our simplified term.

Given term: [tex]4^{m}[/tex]

This term already matches our simplified term.

Therefore, the third option is equivalent to our simplified term.

We can conclude that all the options provided are equivalent to the given expression. We proved it by applying exponent rules and formulas.

Answer:

59°

Step-by-step explanation:

ABC and ADF are congruent (that is the meaning of that symbol).

that means all their associated angles and side lengths are the same.

it is relatively clear to see that

A corresponds to A.

D corresponds to B.

F corresponds to C.

therefore, the angle D = angle B = 59°.

FYI - it also means that AD = AB = 16. but this information was actually irrelevant for this question.

Answer:

m=26, n=111

Step-by-step explanation:

Let 0,0234234... be x

Then 100x = 23,4234234...

100x-x=23,4234234...-0.0234234...

99x=23,4

999x=234

111x=26

x=26/111

m=26, n=111

the answer to this equation is 4

Answer:

Geometric mean is most commonly represented as:

[tex]\sqrt{abc}[/tex]

Geometric mean formula is represented by [tex]\sqrt[n]{\sf x_1 \cdot x_2 \cdot x_3 \cdot ... x_n}[/tex] where n resembles term position and x₁, x₂, x₃ are numbers and they continue.

The formula for geometric mean of three numbers [n = 3]:

Solution: [tex]\sqrt[3]{\sf x_1 \cdot x_2 \cdot x_3 }[/tex]

Example's:

Geometric mean of 5 numbers [n = 5] : [tex]\sqrt[5]{\sf x_1 \cdot x_2 \cdot x_3 \cdot x_4 \cdot x_5 }[/tex]

Geometric mean of 2 numbers [n = 2] : [tex]\sqrt[2]{\sf x_1 \cdot x_2 }[/tex]

The equation perpendicular to the line passing through the points (-4,7) and (1,3) is[tex]y=\frac{5}{4}x-2[/tex]

The slope of the given line is calculated as:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-7}{1-(-4)} \\\\m=\frac{-4}{5}[/tex]

The equation perpendicular to the given line will be of the form

[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]

Substitute [tex]x_1=-4, y_1=7, and m=\frac{-4}{5}[/tex]

[tex]y-7=\frac{5}{4}(x+4)\\\\ y=\frac{5}{4}x+5-7\\\\ y=\frac{5}{4}x-2[/tex]

Therefore, the equation perpendicular to the line passing through the points (-4,7) and (1,3) is [tex]y=\frac{5}{4}x-2[/tex]

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Answer:  [tex]y = -\frac{5}{4} x - 2[/tex]

Step-by-step explanation:

Answer:

x=40

Step-by-step explanation:

total sum of angle in a triangle =180

180-100=80

x+x =2x

x= 80/2

x=40

The probability that the randomly chosen marble will be red is 1/6 or 0.1667.

The probability of an event is the possibility, chance, or likelihood for an event to take place or occur.

From the given information:
Let us find the probability that if marble is drawn at random from the jar, the given marble will be red:

The total number of marble = 10 + 2 = 12 marbles.

The probability that the randomly chosen marble will be red is:

P(red) = 2/12

P(red) = 1/6

P(red) = 0.1667

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The true annual interest rate to the nearest tenth is 16.7%.

The interest amount for this scenario can be determined by computing the total mortgage payment and subtracting the mortgage amount from the earlier figure.

Since payment was made for 20 months, the interest rate can be annualized using 24 months as below.

Price of article = $315.50

Down payment = $31.55

Mortgage amount = $283.95

Monthly payment amount = $16.50

Duration of payments = 20 months

Total payment (mortgage and interest) = $330 (20 x $16.50)

Interest = $46.05 ($330 - $283.95)

Annualized interest rate = 16.7% ($46.05/$330 x 24/20)

Thus, the true annual interest rate to the nearest tenth is 16.7%.

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