Jacob can swim the 400-meter distance in 6.4 minutes now.How many more meters per minutes will Jacob need to swim to reach is goal?Explain how you found your answer.

Answer:

-1/2 is correct

Step-by-step explanation:

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]. To evaluate the expression (g - f)(2), you need to first find the values of g(2) and f(2), and then subtract f(2) from g(2).

Given:

[tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \) \\ \( g(x) = \log_4(x) \)[/tex]

Let's start by calculating the values of f(2) and g(2): 1. [tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \)[/tex]

Substitute (x = 2):   [tex]\( f(2) = \frac{2 + 3}{2^2 + 2 \cdot 2 - 3} = \frac{5}{7} \)[/tex]

2. [tex]\( g(x) = \log_4(x) \)[/tex]  Substitute ( x = 2):  [tex]\( g(2) = \log_4(2) \)[/tex]

Now, evaluate the expression [tex]\( (g - f)(2) \):[/tex]

[tex]\( (g - f)(2) = g(2) - f(2) = \log_4(2) - \frac{5}{7} \)[/tex]

To determine which option matches this value, calculate [tex]\( \log_4(2)[/tex]) and subtract [tex]\( \frac{5}{7} \)[/tex] from it.

Approximately,[tex]\( \log_4(2) \)[/tex] is around 0.5.

So, [tex]\( (g - f)(2) \approx 0.5 - \frac{5}{7} \)[/tex]. To compare this result with the options provided, convert the fractions to a common denominator:

[tex]\( \frac{5}{7} = \frac{35}{49} \)[/tex]. So, [tex]\( (g - f)(2) \approx 0.5 - \frac{35}{49} \)[/tex].

Now, simplify the subtraction: [tex]\( 0.5 - \frac{35}{49} = \frac{24}{49} \)[/tex]

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]

To know more about expression:

https://brainly.com/question/34132400

#SPJ3

Answer:

25

Step-by-step explanation:

5 > x/5

5 × 5 > (x/5) × 5

25 > x

Answer:

Step-by-step explanation:

Use the order of operations to solve this problem.

[tex]\Longrightarrow: \sf{\sqrt{28-3(4)} }[/tex]

Remove parentheses.

→ (4)=4

Rewrite the problem down.

[tex]\Longrightarrow:\sf{\sqrt{28-3*4} }[/tex]

PEMDAS stands for:

→ 28-3*4

Multiply.

→ 3*4=12

→ 28-12

Subtract.

→ 28-12=16

[tex]\Longrightarrow:\sf{\sqrt{16} }[/tex]

[tex]\Longrightarrow\sf{\sqrt{16}=4^2 }[/tex]

Use the radical rule.

[tex]\Longrightarrow: \sf{4^2=\boxed{\sf{4}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

[tex]\±4[/tex]

Step-by-step explanation:

Given expression: [tex]\sqrt{28 - 3(4)}[/tex]

Here, we can see that the terms, 28 and 3(4) are inside the root. Since the two terms are inside the root, we can subtract them. Therefore:

Usually, [tex]\sqrt{16}[/tex] can also be written as [tex]\sqrt[2]{16}[/tex]. Therefore:

Therefore, the simplified expression is ±4.

Learn more about this topic: https://brainly.com/question/20971929

Step-by-step explanation:

here you want to isolate the y.

so what you do in the beginning is divide both sides by x-2.

then, you'll have y-3 = 0

so y = 3

this is a horizontal graph that crosses the y axis and y = 3.

Answer:

Step-by-step explanation:

12y = 2x + 12

y = 2/12x + 12/12

y = 1/6x + 1

The slope intercept form is y = (1/6)x + 1.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

12y - 2x = 12

The slope intercept form is y = mx + c.

So,

12y - 2x = 12

Add 2x on both sides.

12y = 12 + 2x

12y = 2x + 12

Divide both sides with 12.

y = (2/12)x + (12/12)

y = (1/6)x + 1

Thus,

The slope intercept form is y = (1/6)x + 1.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

well, at the beginning of the 6th year, you've been there for 5 whole years, so you've gotten 5 increases hmmm

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=16000(1 + 0.03)^{5}\implies A=16000(1.03)^5\implies A\approx 18548.39[/tex]

Answer:

no idea

is the answer

if you like my answer please like comment and mark me as brilliant

Answer:

Step-by-step explanation:

r (2 x + 8) - x - 4

(2 r - 1) x + 8 r - 4

Answer:

Below in bold.

Step-by-step explanation:

Supplementary angles add up to 180 dgrees, so we have the equation:

3x + 19 + 7x - 9 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17.

So m <ABC = 3(17) + 19 = 70 degrees

and m < DBC = 7(17) - 9 = 110 degrees.

Answer:

3x + 19+7x-9=180

10x+10=180

10x=180-10

10x=170

x =17

Nandyan na po

Step-by-step explanation:

Step-by-step explanation:

please make it a little bit clear

Answer:

1/6

Step-by-step explanation:

There are 6 possible numbers for the spinner to land on, and only 1 of those cases will be where the spinner lands on 6.

Therefore, the answer is 1/6

The mean amount of money Sadie saves each month is $10,724.29.

Mean is a measure of central tendency that is used to determine the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10150 + 102211 + 10424 + 10769 + 11155 + 11477) / 7 =  $10,724.29.

To learn more about mean, please check: https://brainly.com/question/25842202

Answer:

34 cm

Step-by-step explanation:

Keep in mind that the perimeter of a rectangle is the sum of the measures of its sides. This means that the sum of the longer sides and the shorter sides is the perimeter of the rectangle.

Let "L" represent the longer side (length) of the rectangle and "S" represent the shorter side (width) of the rectangle.

⇒ Perimeter of rectangle = L + S + L + S

⇒ Perimeter of rectangle = 2(L) + 2(S)

⇒ Perimeter of rectangle = 2(L + S)

Now, let's substitute the length and the width in the perimeter and simplify.

⇒ Perimeter of rectangle = 2(10 + 7)                                                [L = 10; S = 7]

⇒ Perimeter of rectangle = 2(17)

⇒ Perimeter of rectangle = 34 cm

Answer: 70 cm

Step-by-step explanation: 10 x 7 = 70

hope this helps

The work done by the machine is the product of force and distance

The amount of work done by the machine is 10 joules

The amount of work done is calculated using:

W = Fd

Where:

The distance moved to the living room is the same when you move the chair or a machine does is the same.

Also, if the force applied in moving the chair remains unchanged, the amount of work done would be the same.

Hence, the amount of work done by the machine is 10 joules

Read more about work done at:

https://brainly.com/question/18762601

Start at 3 and multiply by -4 each time.

The length of the other two sides is 10 and 35 respectively.

A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.

From the given information:

We are being told that the longest side is the triangle is equal to 40.

i.e.

[tex]\mathbf{\to\dfrac{8}{17}\times x = 40}[/tex]

[tex]\mathbf{x = 40 \div \dfrac{8}{17}}[/tex]

[tex]\mathbf{x = 40 \times \dfrac{17}{8}}[/tex]

x = 85

Now for the other two sides 2 and 7, their length is as follows.

[tex]\mathbf{\dfrac{2}{17}\times 85 = 10}[/tex]

[tex]\mathbf{\dfrac{7}{17}\times 85 = 35}[/tex]

Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.

Learn more about ratios here:

https://brainly.com/question/2328454

Answer:

Mean Absolute Deviation (MAD): 3

Step-by-step explanation:

Answer:

Yes;

Step-by-step explanation:

5/2 = 2 1/2

2 1/2 > 1

Yes, 5/2 is to the right of 1 on a number line.

Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

The answer to this question is D 2/4

Answer:

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

Step-by-step explanation:

The rule for graphs is:

[tex]y = mx + c[/tex]

Where [tex]m[/tex] is the gradient and [tex]c[/tex] is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So... [tex]c=4[/tex]

To work out our gradient of a straight line (which is what we have)

We use the formula:

[tex]m = \frac{\triangle y}{\triangle x}[/tex]

The triangle [tex]\triangle[/tex] just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

[tex]m = \frac{\triangle y}{\triangle x} = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{4}{6} = \frac{2}{3}[/tex]

Using our formula

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

Answer:

The answer is shown in the picture. you basically have to do integration by parts 2 times to get final answer.

Answer:

[tex]\sf \dfrac{1}{10}[/tex]

Step-by-step explanation:

From the table:

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(Sophomore)=\dfrac{10}{37}[/tex]

[tex]\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}[/tex]

[tex]\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}[/tex]

Answer:

1/10

Explanation:

Given Boy Sophomores: 1

Given Total Boy: 3 + 1 + 4 + 2 = 10

So

⇒  P(Boy|Sophomore)  

⇒  Boy Sophomore/Total Boy

⇒  1/10

Step-by-step explanation:

oh that is again something you can nicely envision :

the inner circle has a radius of 59 ft.

so, because of the 2 ft wide track the outer circle has a radius of 59+2 = 61 ft.

the circumference of a circle is

2×pi×r

the answer to the question is simply the difference bergen the 2 circumference values.

inner circle :

2×pi×59 = 118pi

outer circle :

2×pi×61 = 122pi

the difference is

122pi - 118pi = 4pi = 12.56637061... ft ≈ 12.6 ft

the wheel on the outer track travels about 12.6 ft farther than a wheel on the inner track in one full turn.

Answer:

10

Step-by-step explanation:

The least common denominator can be found by finding the LCM of the 2 denominators:

First let's list the multiples of the first denominator :

10,20,30,40,50

Now let's list the multiples of the second denominator :

5,10,15,20,25

As we can see the lowest number that appears in both lists is 10.

Therefore 10 is the least common denominator.