The graph shows the amount of money that Janice saves each week from her summer job. Which equation best represents the graph?

The inverse proportionality expression is y =40/x

If the variable y is inversely proportional to x, this is expressed as;

y = k/x

where

k is the constant of proportionality

If y = 5 and x = 8. then;

5 = k/8

k = 5 * 8

k = 40

Determine the inverse proportionality

Recall that y = k/x

y = 40/x

Hence the inverse proportionality expression is y =40/x

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It looks like the equation is

[tex]\dfrac{du}{dt} = 2t + \dfrac12 \sec^2(t) u[/tex]

with initial value [tex]u(0) = \frac\pi2[/tex].

Rearrange the equation to

[tex]\dfrac{du}{dt} - \dfrac12 \sec^2(t) u = 2t[/tex]

Multiply both sides by the integrating factor

[tex]\displaystyle \mu = \exp\left( \int -\frac12 \sec^2(t)\,dt\right) = \exp\left(-\frac12\tan(t)\right)[/tex]

and solve for [tex]u[/tex].

[tex]\implies e^{-\frac12 \tan(t)} \dfrac{du}{dt} - \dfrac12 \sec^2(t) e^{-\frac12 \tan(t)} u = 2t e^{-\frac12 \tan(t)}[/tex]

[tex]\implies \dfrac{d}{dt}\left[e^{-\frac12 \tan(t)} u\right] = 2t e^{-\frac12 \tan(t)}[/tex]

By the fundamental theorem of calculus, integrating both sides yields

[tex]e^{-\frac12\tan(t)} u = e^{-\frac12\tan(t)} u \bigg|_{t=0} + \displaystyle \int_{\xi=0}^{\xi=t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies e^{-\frac12\tan(t)} u = 1\times\dfrac\pi2 + \displaystyle \int_{0}^{t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies \boxed{\displaystyle u = \frac\pi2 e^{\frac12\tan(t)} + 2e^{\frac12\tan(t)} \int_0^t \xi e^{-\frac12 \tan(\xi)} \, d\xi}[/tex]

Answer:

x = -7 and x = 4.

Step-by-step explanation:

f(x) = x^2 + 3x - 28

= (x + 7)(x - 4).

The reciprocal of f(x) can be written as

1 / (x + 7)(x - 4).

When the denominator is zero we have vertical asymptotes

so they are x = -7 and x = 4.

Answer:

1/2

Step-by-step explanation:

There is a couple ways of thinking about this.  Probably the fastest way is the rule, but the rule is not intuitive.  The rule is when you divide fraction, you keep the first fraction the same and then multiple and flip the second fraction.

2/8 x 18/9 = 36/72  To reduce the fraction, could keep dividing the top and the bottom by the same number until it is no longer possible, I could use: 2, 4 3, 9, 18, or 36.  If I used 36, I would only have to divide once.  36/16 is 1 and 72/36 is 2 so my answer would be 1/2.

I could have divided the top and bottom by 2 and got 18/36 and then divide by 2 again and get 9/18 and then by 9 and get 1/2.  As you can, see there are a lot of option.  

The second method is in the picture that I sent you, it is a little more work, but it makes sense.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{2}{8}\div\frac{9}{18} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Simplify \ \frac{2}{8} \ to \ \frac{1}{4}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\div\frac{18}{9} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: a\div \frac{b}{c}=a\times \frac{c}{b}a \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\times\frac{18}{9} }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: \frac{a}{b} \times \frac{c}d{}=\frac{ac}{bd}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1\times18}{4\times9} \ \to \ \ Multiply }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ \frac{18}{36}= }}\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{2} }} \end{gathered}$}} \end{gathered}$}[/tex]

Answer:

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

y = 3x² - 12x + 7 =

     3(x² - 4x) + 7 =                                  Factor out 3

     3(x² - 4x + 4) - 3*4 + 7 =                   Complete the square

     3(x - 2)² - 5                                       Simplify

Answer:

  y = 3(x -2)² -5

Step-by-step explanation:

It looks like you want to write the standard-form quadratic ...

  y = 3x² -12x +7

in vertex form.

The process is similar to that of "completing the square."

Factor out the leading coefficient

Do this for the variable terms only.

  y = 3(x² -4x) +7

Identify the x-term coefficient

The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.

  x coefficient: -4

  binomial constant: -4/2 = -2

  square of this: (-2)² = 4

Add this inside parentheses

To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.

  y = 3(x² -4x +4) +7 -3(4)

Simplify to vertex form

Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.

  y = 3(x -2)² -5

Answer:

2.25 ft

Step-by-step explanation:

Volume = length x height x width

54= 8 x 3 x ?

Combine: 54= 24 x ?

Find ?: 54/24=2.25

Recheck: 24 x 2.25 = 54

Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.

Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;

Reversing Carol's age gives;

The multiples of 3 that have the form X1 have 7 as the rightmost number.

Given that 1B is a teenager, we have;

When;

The reverse of Carol's age is therefore;

Therefore, from the given description, Bob's age 1B = 17 years

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The missing height is 65.

Mean is 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

Missing height = (mean x total number of students) - sum of existing heights

Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423

Missing height = (8 x 61) - 423 = 64

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The computation shows that the average monthly amount is 61.64.

The amount that's left will be:

= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075

= 3314.85 + 1853.3 - 3600 - 1075

= 493.15

The average monthly amount will be:

= 493.15/8

= $61.64

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The functions that have the properties are (d) I and II only

The function property is given as:

[tex]a(x) = a^{-1}(x)[/tex]

The above implies that the inverse function and the original function are equal.

From the list of options, we have:

(a) y = x

Make x the subject

x = y --- the same as the  original function

(b) y = 1/x

Make x the subject

x = 1/y --- the same as the  original function

Hence, the functions that have the properties are (d) I and II only

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El número decimal que no es un decimal periódico es dado por:

B. [tex]\frac{11}{400}[/tex].

Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.

La conversión de las fracciones para decimales són:

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Answer:

138

Step-by-step explanation:

There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.

23 * 6 = 138

Answer:

y =sin(x)

Step-by-step explanation:

small brain

Answer:

B: k pi for any integer k

Step-by-step explanation:

I took the test

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.

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You did not provide directions. What do you want us to do with your 8th degree polynomial?

The value of x is  2/9

Given equation x +2/3 = 8/9

We need to find the value of x

Simplifying the equation is

x+2/3 = 8/9

x = 8/9 -2/3

Taking L.C.M of the denominators 3 and 9

The L.C.M is 9

So we will multiply the numerator and denominator with 1 in 8/9

And we will multiply the numerator and denominator with 3 in 2/3

Hence the new equation formed = 8/9-6/9

Solving this equation we get

8-6 / 9

= 2 / 9

Hence the value of x is 2/9

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Part A

The two factors are 5 and 4x+6.

Part B

The first factor, 5, has 1 term.

The second factor, 4x+6, has 2 terms.

Part C

The coefficient of the variable term is 4.

Answer:

1/2

1/3

Step-by-step explanation:

x=1/2

x=-1/3

Answer:

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

Step-by-step explanation:

[tex]6x^{2} -x-1=0[/tex]

Factoring the equation:

[tex](3x+1)(2x-1)=0[/tex]

Extract the roots:

First factor

[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]

Second factor

[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]

Hope this helps

The distance that you run around the track in gym class is considered continuous data.

The variable is given as:

Distance

The distance travelled can take any value between 0 and the length of the track.

Take for instance;

The distance travelled can be 1km and it can also be 1.67 km

This means that the distance is continuous

Hence, the statement that completes the blank is (c) continuous

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Using it's concept, the domain of the function shown in the graph is:

B. [tex]-6 \leq x \leq 6[/tex].

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.

From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:

B. [tex]-6 \leq x \leq 6[/tex].

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Answer:

7. a) slope = 5

7. b) slope = 1/2

8. slope = 1

Step-by-step explanation:

slope = rise/run

rise is the vertical change, run is the horizontal change

7. a)

Pick any two points on your line. (0,0) and (1,5) are easy to work with.

The vertical change between the two points is 5

The horizontal change between those points is 1

so slope = 5/1 = 5

7. b)

Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.

slope = 4/2 = 1/2

8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...

m = slope = (y2-y1) / (x2-x1)

= (8 - 4) / (5 - 1)

= 4/4

= 1

I hope that helped!

Answer:

23/75

Step-by-step explanation:

8/15 + x = 21/25

x = 21/25 - 8/15

now we need to bring both fractions to the same denominator (bottom part), so that we can do the subtraction.

what is the least common multiple (LCM) of 25 and 15 ? that will be the common denominator.

I usually use the prime factor factorization of the involved numbers.

15 : 3, 5 (15 = 3×5, there are no smaller prime factors)

25 : 5, 5 (25 = 5×5, there are no smaller prime factors)

the LCM is the combination of the longest chains of each prime factor :

3×5×5 = 75

so, we bring both fractions to 75 denominators.

how many 1/75th are 1/25 ? as 25×3 = 75, we have 3/3 × 1/25 = 3/75 (= 1/25).

so,

21/25 = 21×3/75 = 63/75

how many 1/75th are 1/15 ? as 15×5 = 75, we have 5/5 × 1/15 = 5/75 (= 1/15).

so,

8/15 = 8×5/75 = 40/75

remember, we have to multiply the numerator and the denominator by the same value to keep the original value of the fraction unchanged.

and now our equation looks like

x = 63/75 - 40/75 = 23/75

The length of the road that connects the service station with Cray is 46.2 mi.

We need to apply the principle of similar triangles to obtain the length of the road that will connect the service station with Cray as shown in the image attached.

Hence;

The distance between Alba and Blare = 130 mi

The distance between Alba and Cray = 120 mi

Road connecting the service station with Cray =x

And;

120/130 = x/50

x =  46.2 mi

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The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.

Given :

Expression - 8 + (n - 4)

To simplify the given expression following steps can be used:

Step 1 - Rewrite the given expression.

= (n - 4) + 8

Step 2 - Now, remove the parenthesis in the given expression.

= n - 4 + 8

Step 3 - Now, write 8 as the addition of 4 and 4.

= n - 4 + 4 + 4

Step 4 - Subtract 4 by 4.

= n + 4

Therefore, the correct answer is (12+n).

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The length and width of the computer monitor is 23.36 inches

and 13.14 inches.

According to the given statement

we have given that  

The length of diagonal of rectangular monitor = 27 inches

The length to width ratio is 16:9

So , Let the Length of monitor = 16x

and The Width of monitor  = 9x

And we have to find the length and width of the computer monitor.

So, For this purpose,

From Pythagoras theorem

(Diagonal)² = Length² + width²

Put the values in it and then

27² = (16x)² + (9x)²

729 = 256x² + 81x²

After solving we get

337x² = 729

So, x² = 2.16

∴  x =  = 1.46 inches

So, The length = 16x = 23.36 inches

And The width = 9x = 13.14 inches.

Hence, The length and width of the computer monitor is 23.36 inches

and 13.14 inches.

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The probability that the next toss will be heads is 1/8.

The likelihood of an event occurring is described by probability. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.

Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the probability of an event happening can range from 0 to 1.

Probability of getting two tails and next heads in three tosses is,

=1/2*1/2*1/2

=1/8

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Using the laws of indices , 4⁵ ÷ 4² can rewritten as 4³.

Given the expression; 4⁵ ÷ 4²

To perform the division operation, we use one of the laws of indices;

[tex]n^a/n^b = n^{a-b}[/tex]

Given that;

Now, we apply the laws of indices ;

4⁵ ÷ 4² = 4⁵⁻² = 4³

Therefore, using the laws of indices, 4⁵ ÷ 4² can rewritten as 4³.

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Answer:

[tex]\sf 1\dfrac{2}{5} \ cm[/tex]

Step-by-step explanation:

    If two sides of the triangle are equal, then the triangle is called isosceles triangle.

Let the two equal sides = x cm

Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm

[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]

      [tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]

             [tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]

[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]

Answer:

y = 7x - 2

Step-by-step explanation:

first we need the slope of the line.

the slope is expressed a the ratio (y coordinate change / x coordinate change) when we go from one point on the line to another.

so, let's say we go from (0, -2) to (1, 5), we see

x changes by +1 (from 0 to 1).

y changes by +7 (from -2 to 5)

so the slope is +7/+1 = 7

the slope-intercept form is in general

y = ax + b

a being the slope, b being the y-intercept (the y-value for x = 0).

the point (0, -2) gives us therefore the y-intercept directly : -2.

by using the already established slope and the point (0, -2) for the y-intercept the equation of our line is

y = 7x - 2