Which of the following could be the first step in solving the equation below 4+2log_(3)x=17

The exponential equation with a base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

We start with:

[tex]f(x) = 6*(14)^x[/tex]

We want to rewrite this to:

[tex]f(x) = 6*(e^n)^x[/tex]

So we only need to find the value of n such that:

[tex]e^n = 14[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]

Then the exponential equation with base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

If you want to learn more about exponentials:

https://brainly.com/question/11464095

#SPJ1

Answer:

the next number is 47+ 16 =63

20% of the participants are girls and got a medal, and 33% of the girls got a medal.

First, we know that 40% of the participants were boys, so the other 60% were girls.

We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:

P = (0.4)*(0.5) = 0.2

So, 20% of the participants are boys and got a medal.

We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.

Then if the percentage of girls that got a medal is x (in decimal form), we must have that:

Q = (0.6)*(x) = 0.2

      x = 0.2/0.6 = 0.33

x = 0.33

This means that 33% of the girls got a medal.

If you want to learn more about percentages:

https://brainly.com/question/843074

#SPJ1

Answer: B=16 and m=6

Step-by-step explanation:

in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.

Answer:

sure how can I help you? please tell me

Differentiate using the Quotient Rule –

[tex]\qquad[/tex][tex]\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\[/tex]

According to the given question, we have –

Let's solve it!

[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2) \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5) - ( x^3+5x+2) 2x}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex] \pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\[/tex]

[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\[/tex]

[tex]\qquad[/tex][tex]\pink{\therefore \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}} = \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\[/tex]

Answer:

Aprism =  483.246 yd2

Step-by-step explanation:

The surface area is the sum of the 2 circles areas and the rectangle area.

Ac1 = PI*r2

Ac1 = (3.14)*(11.4/2)2

Ac1 = 102.0186 yd2

Ac1 = Ac2 then

Ac2 = 102.0186 yd2

Now the perimeter of the circle is one the sides of the rectangle:

Pc = 2PI*r

Pc = 2*3.14*(11.4/2)

Pc = 35.796 yd

Now the area of the rectangle is:

Ar = 7.8yd*35.796yd

Ar = 279.2088 yd2

Then, the surface area of prism is:

Answer:

(i) 8b-32

(ii) 7z^3+12z^2-20z

(iii) –q+p

(iv) a+ab

(v) 8x^2y+8xy^2-4x^2-7y^2

(vi) 4y^2-3y

Step-by-step explanation:

Answer:

3,36 in^2

Step-by-step explanation:

The geometric shape shown in image is called a trapezoid

to calculate the area of a trapezoid we use the following formula:

1/2*(a+b)*h (a and b are bases, h: height)

bases are 1.3 and 3.5 and height is 1.4

1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is

3,36 in^2

There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.

A perfect square is a number which can be written as the product of an integer with itself.

It is given that Mark divided a basket of apples evenly into small bags.

Let there be n no. of bags and therefore n number of apples in each bag

Then the total number of apples will be

n * n

n²

The value of total number of apples should be a perfect square,

In the option given only 25 is the perfect square

Therefore the equation can be made as

n² = 25

n = 5

There are 5 bags and each bag has 5 apples and total there are 25 apples.

To know more about Perfect Square

https://brainly.com/question/385286

#SPJ1

Answer:

Step-by-step explanation:

Comment

The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.

Givens

Arc 1 = 94

Arc2 = d

interior angle = 75

Formula

(d + 94)/2 = interior angle/1

Solution

(d + 94)/2 = interior angle/1               Cross Multiply

1*(d + 94) = 75 *2                           Combine

d + 94 = 150                                        Subtract 94 from both sides

d + 94 - 94 = 150 - 94                         Combine

d = 56

Answer: d = 56

Answer:

P=2l+2W

if l=12 and W=8

then,

P=2L+2W

=2.18+2.8

=36+16

=52

Answer:

this is pretty easy we just replace the x with -1 so

(-1)^2+(-1)9+10

-1*-1=1

-1*9=-9

1+-9=-8

-8+10=2

f(-1)=2

Hope This Helps!!!

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]

[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]

[tex]\qquad \tt \rightarrow \: - x + 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:6-x

Step-by-step explanation:

The solution is in the image

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

The domain of the function is t ≥ 0

The greatest concentration of the medication is 5mg/L

Given that:

C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is: t ≥ 0

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

Learn more about functions and graphs here:

https://brainly.com/question/18806107

#SPJ10

The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have:

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(5/12)x

The equations we have:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

From the equation first:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

The value of a and b are:

a = 12

b = 5

Vertices of the hyperbola = (0, b) and (0, -b)

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(b/a)x

Asymptotes: y = ±(5/12)x

Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

Learn more about the hyperbola here:

brainly.com/question/12919612

#SPJ1

Answer:

A

Step-by-step explanation:

The margin error of the confidence interval 0.87<p<0.93 is 0.03.

Given confidence interval 0.87<p<0.93.

We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random  sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.

Confidence interval is 0.87<p<0.93.

Width of the interval= 0.93-0.87

=0.06

=0.03

Hence the margin of error is equal to 0.03.

Learn more about confidence interval here  https://brainly.com/question/15712887

#SPJ10

Answer:

the answer is D

Step-by-step explanation:

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

The viewer represents the correct answers with x and the incorrect ones with y.

x+y = 20

for every correct answers 2 points;

and for every incorrect answers, -1 point

This can be written as

2x-y = 28

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

now

2x-y = 28

x+y = 20

On adding the equations

]3x = 48

x = 16

y = 4

This means that the contestant answered 16 questions correctly and 4 questions incorrectly

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

To know more about Equation

https://brainly.com/question/10413253

#SPJ1

A function assigns the values. The value a is 11.

A function assigns the value of each element of one set to the other specific element of another set.

The given logarithmic function can be solved as shown below.

[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]

Hence, the value a is 11.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

Answer:

Power of a quotient

Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%

The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.

On the basis of given data

The number given is 2,4,7

Size of the sample = 2 with replacement

The Total outcome with replacement will be given by

3² = 9

Possible outcome can be

2,2   2,4   2,7   4,4  4,2  4,7  7,7  7,2  7,4

The sample mean can be calculated as

(a+b)/2

(2+2)/2 = 2

similarly the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

To know more about Mean

https://brainly.com/question/521501

#SPJ1

Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

Hope I helped

Answer:

$331.02

Step-by-step explanation:

compound interest formula

A = P ( 1 + r/n)^nt

P = principal amount

r = rate decimal

n = number of times interest is compounded

t = time

A = 100 * (1 + .06/12)^(12*20)

A = 331.02

Answer:

78.7

Step-by-step explanation:

To find the mean, we can do the sum of all scores divided by the total amount of scores.

We see that there are 7 scores of 70, and 70*7=490.

We see that there are 5 scores of 75, and 75*5=375.

We see that there are 4 scores of 80, and 80*4=320.

We see that there is 1 score of 85, and 85*1=85.

We see that there are 6 scores of 90, and 90*6=540.

Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]