On Monday, Harry had 75\%75% as many toys as Teddy did. On Tuesday, after Harry acquired 3232 more toys and Teddy acquired 15\%15% more than he had on Monday, Harry had as many toys as Teddy did. How many toys did Harry have on Monday?

[tex]\dfrac{5+2\sqrt3}{7+4\sqrt3}=\dfrac{5+2\sqrt3}{7+4\sqrt3}\cdot\dfrac{7-4\sqrt3}{7-4\sqrt3}\\\\\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{(5+2\sqrt3)(7-4\sqrt3)}{7^2-(4\sqrt3)^2}\\\\\text{use distributive property}\\\\=\dfrac{(5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3)}{49-4^2(\sqrt3)^2}\\\\=\dfrac{35-20\sqrt3+14\sqrt3-8(3)}{49-16(3)}=\dfrac{35-6\sqrt3-24}{49-48}=\dfrac{11-6\sqrt3}{1}\\\\=11-6\sqrt3\\\\11-6\sqrt3=a+b\sqrt3\to\boxed{a=11\ and\ b=-6}[/tex]

[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{-20v^7x^7}{4v^5x^4}+\dfrac{12v^4x^7}{4v^5x^4}=-5v^{7-5}x^{7-4}+3v^{4-5}x^{7-4}\\\\=\boxed{3v^{-1}x^3-5v^2x^3}[/tex]

Used

[tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]

Other method:

[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{4v^4x^4(-5v^3x^3+3x^3)}{4v^4x^4(v)}=\dfrac{3x^3-5v^3x^3}{v}[/tex]

Answer: y=1/7am -1/7

Step-by-step explanation:

First: 3y+4y+z =am - z

Second: 7y=am - z

Third: y=1/7am -1/7z

Finally: y=1/7am -1/7

Answer:

$120.

Step-by-step explanation:

We have been given that Libby sold $60 worth of vegetables at the farmer's market.

Jess sold 3/4th of what Libby sold. Let us find 3/4 of 60.

[tex]\text{Jess sold}=60\times \frac{3}{4}[/tex]

[tex]\text{Jess sold}=15\times 3[/tex]

[tex]\text{Jess sold}=45[/tex]

Therefore, Jess sold $45 worth of vegetables.

We are told that Stephanie sold 1/3rd of what Jess sold. So let us 1/3rd of 45.

[tex]\text{Stephanie sold}=45\times \frac{1}{3}[/tex]

[tex]\text{Stephanie sold}=15[/tex]

Therefore Stephanie sold $15 worth of vegetables.

Now let us add amounts of money earned by Libby, Jess and Stephanie to get the total money earned by all.

[tex]\text{The total money earned by Libby, Jess and Stephanie}=60+45+15[/tex]

[tex]\text{The total money earned by Libby, Jess and Stephanie}=120[/tex]

Therefore, they all sell $120 worth of vegetables together.

Answer:

As per the statement: Libby sold $60 worth of vegetables at the farmer's market.

⇒ Libby sold vegetables at the farmers market = $60

Jess sold 3/4th of what Libby sold.

⇒ Jess sold = [tex]\frac{3}{4} \times 60 = \$45[/tex]

Also, Stephanie sold 1/3rd of what Jess sold.

⇒ Stephanie sold = [tex]\frac{1}{3} \times 45 = \$15[/tex]

To find how much did they all sell together.

Together they all sell together = Libby sold + Jess sold + Stephanie sold

                                                    =$60 + $45+$15 = $120

Therefore, they all sell together is, $120                                                                                

Answer:

The cost of the bench is 425 dollars.

Step-by-step explanation:

Let x represent the garden table.

Let y represent the bench.

x + y = 804

x = y - 46

Use the substitution method.

y - 46 + y = 804

2y - 46 = 804

Add 46 to both sides.

2y = 850

Divide both sides by 2.

y = 425

Answer:

The cost of the bench is 425 dollars.

Answer:

As shown, both terms are equal to 192. To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same. To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same.

Step-by-step explanation:

Answer:

The radius of the circle is 3 unit.

Step-by-step explanation:

Given : The diameter of a circle is 6 units.

To find : What is the radius of the circle?

Solution :

The radius of the circle is [tex]r=\frac{d}{2}[/tex]

Where, d is the diameter d=6 units

Substitute the value,

[tex]r=\frac{6}{2}[/tex]

[tex]r=3[/tex]

Therefore, the radius of the circle is 3 unit.

Answer: 59,000

Step-by-step explanation:

(2.5 * 10^4) + (3.4 * 10^4)

(2.5 * 10,000) + (3.4 * 10,000)

25,000 + 34,000

59,000

10 • 10 • 10 • 10 = 10,000

(2.5 • 10,000) + (3.4 • 10,000)

    25,000             34000

25,000 + 34,000 = 59,000

Answer: 2 pairs of angles

As the name "angle angle" suggests, we need 2 pairs of angles proven congruent in order to prove that two triangles are similar. Each "angle" refers to a pair of angles between the two triangles, which are corresponding angles. We could use the third pair, but it's extra unnecessary work. This theorem is often written as "AA similarity" or something along those lines.

One way to check for similar triangles is to compare the ratios of the sides. If the corresponding sides divide to the same value, then you have similar triangles. This method only works of course if you know the side lengths.

Answer:

$4.10

Step-by-step explanation:

Subtotal = (3 pairs of socks) x (price of socks):  

Subtotal = (3 x $1.29) = $3.87  

To get the overall total, you add tax, which is 6% of the subtotal:  

6% of the subtotal = 0.06 x subtotal = 0.06 x $3.87 = $0.23  

Subtotal + tax = $3.87 + $0.23 = $4.10

Answer:

3 1/13 hours

Step-by-step explanation:

Lets create a variable:

Samantha and Kylee together (NOT the answers) = [tex]T_{SK}[/tex]

Now lets create an equation:

[tex]1/T_{SK} = 1/T_{S} +1/T_{K}[/tex]

Let's look at the time Samantha and Kylee takes to decorate the cake by themselves:

Samantha: 5 hours

Kylee: 8 hours

Let's create an equation to find the answer now:

[tex]1/T_{SK} = 1/5 + 1/8[/tex]

Note that now that's its basically algebra, change the variable to [tex]x[/tex] like this:

[tex]1/x = 1/5 +1/8[/tex]

Now let's find the LCM (Lowest Common Multiple) of 5, 8, and [tex]x[/tex] which is 40[tex]x[/tex].

[tex]40 = 8x + 5x[/tex]

[tex]40 = 13x[/tex]

[tex]13x = 40[/tex]

[tex]x = 40/13[/tex]

[tex]x[/tex] = 3 1/13 hours

Please note that the step where it swapped 13[tex]x[/tex] and 40 is only my way, it is not necessary, it's just my own comfort.

The savings that Barret makes by joining the art museum instead of the science museum is $2.50 + $1.25m.

The one time fee charged by the art museum is $8.25 and the one charged by the science museum is $3.50. The saving here is:

= 10.75 - 8.25

= $2.50

The savings made per month is:

= Amount charged per month by science - Amount charged per month by art

= 3.50 - 2.25

= $1.25

In conclusion, the savings per month is $2.50 + $1.25 per month.

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Answer:

slope is easy it is rise over run

Step-by-step explanation:

rise/run

rise means up

run means move sideways

Answer:

Slope = rise/run

Step-by-step explanation:

Example: (6,3) (2, 2)

Add the x's and divide by two and then add the y's and divide by two.

6 + 2 = 8

8/2 = 4

3 + 2 = 5

5/2 = 2.5

So, the slope would be 4/2.5

Answer:

1/3

Step-by-step explanation:

To determine the common ration, we take the second term and divide it by the first term

9/27 = 1/3

We verify this by taking the third term and diving by the second term

3/9 = 1/3

The common ratio is 1/3

Answer:

1/3

Step-by-step explanation:

Divide a term by the previous term.

For example, divide 1 by 3 to get 1/3.

Answer: Hello there!

We know that Jada has 12 books checked out, and Han has one third less than that.

one-third of a number is equal to the number divided by 3, in this case, we have the number 12, so a third of 12 is: 12/3 = 4

then if Han has a third less than 12, Han has 12 - 4 = 8 books checked out.

Answer:

Step-by-step explanation:

First, we can transform y = cos(x) to y = 3*cos(x) by stretching the graph vertically by a factor of 3. At x = 0, the y value would now be 3 * 1 = 3 instead of 1 (the stretching would cause all new y-values to be 3 times their original values for any given x).  

Now transforming y = 3*cos(x) to y = 3*cos(10*x) will stretch the graph horizontally by a factor of 10 (for any given y value, the new x value corresponding to it is 10 times the original x value).

Finally, to transform y = 3*cos(10*x) to y = 3*cos(10(x-pi)), shift the graph to the right by pi.

Answer:

It's B or C

Step-by-step explanation:

Answer:

$156.35

Step-by-step explanation:

we know that

A group of friends went to lunch, and their bill was $132.50

In this problem

$132.50 represent the 100%

100%+18%=118%

so

using proportion

Find out the total amount that represent 118%

Let

x ----> the total amount of the bill

[tex]\frac{\$132.50}{100\%}=\frac{x}{118\%}\\\\x=132.50(118)/100\\\\x=\$156.35[/tex]

Answer:

Step-by-step explanation:

The answer is $156.35

Answer:

[tex] d > -9 [/tex]

Step-by-step explanation:

[tex] -\dfrac{1}{4}(d + 1) < 2 [/tex]

First, multiply both sides by -4. You must also change the inequality sign since you are multiplying both sides by a negative number.

[tex] -4 \times \left(-\dfrac{1}{4}\right)(d + 1) > 2 \times (-4) [/tex]

[tex] d + 1 > -8 [/tex]

Subtract 1 from both sides.

[tex] d + 1 - 1 > -8 - 1 [/tex]

[tex] d > -9 [/tex]

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

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following equation given in the problem above:

[tex]4x-2(3x-2)=3x[/tex]

2. Apply the Distributive property:

[tex]4x-6x+4=3x[/tex]

4. Now, you must add like terms:

[tex]4=3x-4x+6x\\4=5x[/tex]

5. Solve for [tex]x[/tex], then the result is:

[tex]x=\frac{4}{5}[/tex]

Answer:

The correct option is A.

Step-by-step explanation:

From the given table it is noticed that the line is passing through the points (-1,1), (1,2), (3,3), (5,4) and (7,5).

Slope of a line is calculated as

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose any two pair of coordinates from the given points.

Let the line is passing through (5,4) and (7,5).

[tex]m=\frac{5-4}{7-5}[/tex]

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

Therefore the slope of line is [tex]\frac{1}{2}[/tex] and option A is correct.

Answer:

The actual answer is C

Step-by-step explanation:

Answer:

20 years

Step-by-step explanation:

Simple interest is only interest on the original principal amount. Every year, you earn the same interest amount.

At 5% simple interest, you earn 5% of the principal each year.

In any year, you earn

5% of $500 = 5% * 500 = 0.05 * 500 = $25

Each year, you earn $25 in interest.

How many years will it take to earn a full $500 by earning $25 per year?

$500/$25 = 20

It takes 20 years to double the $500.

Answer:

Distance: 435.9 ft

Step-by-step explanation:

This is a right triangle shown in the picture.

To solve for [tex]x[/tex], we can use trigonometry.

The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is [tex]x[/tex] (what we are seeking to find).

The ratio that relates opposite and hypotenuse is sine.

We know that,

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

Thus we can write:

[tex]sin(35)=\frac{250}{x}[/tex]

Cross multiplying and solving for [tex]x[/tex] gives us:

[tex]sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9[/tex]

Second answer choice is right: 435.9 ft

so we have s(t), namely the positional equation for the particle.

now, let's recall that the derivative of s(t) will be v(t), namely the derivative of the positional equation will be the velocity, and the derivative of the velocity will be the acceleration.

s'(t) = v(t) and s''(t) = a'(t)  <--- acceleration

so we need the 2nd derivative of s(t) firstly, and then we can check for any critical values and find its extrema.

[tex]\bf s(t)=t^4-rt^3+6t^2-20\implies \stackrel{\textit{velocity}}{s'(t)=4t^3-12t^2+12t} \\\\\\ \stackrel{\textit{acceleration}}{s''(t)=12t^2-24t+12}\implies \stackrel{\textit{derivative of acceleration}}{s'''(t)=24t-24} \\\\[-0.35em] ~\dotfill\\\\ 0=24t-24\implies 24=24t\implies \cfrac{24}{24}=t\implies 1=t[/tex]

now, if we run a first-derivative test on that acceleration derivative, namely s'''(t), let's say we test s'''(0) and that gives us a negative value, and then test s'''(2) and that gives us a positive value, so the test goes like in the picture below, clearly, 1 = t is a minumum, and is between [0, 3].

s'''(0) = -24

s'''(3) =  48

so clearly the maximum happens at the s'''(3) endpoint, when t = 3.

Answer:

your answer is h=2.65 hours

Answer: $20.5

Step-by-step explanation:

Let x  denotes the amount for total bill.

We are given that ,  Sierra left $4.50 as a tip for a waiter.

This was 18% of the bill before the tip.

We can write 18% = 0.18. [To convert percent into decimal we divide it by 100.]

Then, the tip amount = 0.18 x Total bill

[tex]\Rightarrow\ 4.5=0.18x\\\\\Rightarrow\ x=\dfrac{4.5}{0.18}=25[/tex]

So, the total bill amount = $25

Hence, her total bill before the tip= Total bill amount - Tip amount

= $25- $4.50=$20.5

Thus ,her total bill before the tip= $20.5

To find Sierra's total bill before the tip, an equation can be created where the tip amount ($4.50) is 18% of the total bill. Solving the equation provides that Sierra's total bill before the tip was $25.

To solve this problem, you want to figure out the original bill amount before the tip was added. We know that the tip amount, $4.50, represents 18% of the original bill. Therefore, we can set up an equation to find the total bill before the tip was included.

The equation is as follows: 0.18x = $4.50, where 'x' stands for the total bill before the tip. By dividing both sides of the equation by 0.18, we can find 'x' which represents the initial bill.

So, x = $4.50 / 0.18 and calculating this gives us x = $25. Therefore, Sierra's total bill before the tip was $25.

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Answer:

x+y = 50

Step-by-step explanation:

We can find the slope of the line

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

   = (50-41)/(0-9)

   = 9/-9

   =-1

We can use the point slope form of the equation to make an equation for a line

y-y1 = m(x-x1)

y-50 = -1(x-0)

y-50 = -x

To get it in standard from, subtract y from each side

y-y-50 = -x-y

-50 = -x-y

Multiply each side by -1

50 = x+y

x+y = 50

The equation representing the relationship between the number of bus rides and the amount of bus money is  [tex]\( x + y = 50 \)[/tex]. The option (a) is correct.

The amount of bus money Shawn will have left is [tex]y[/tex].

Representing the relationship between the number of bus rides [tex]\( x \)[/tex] .

We can see that for every 9 rides, Shawn's remaining bus money decreases by $9.

This suggests that the cost of each ride is $1 (since $9 divided by 9 rides equals $1 per ride).

We know that Shawn starts with $50 and each ride costs $1.

So, after [tex]\( x \)[/tex] rides, Shawn will have spent  [tex]\( x \)[/tex] dollars.

So, the equation is :

[tex]\[ y = \text{Initial amount} - \text{Cost per ride} \times \text{Number of rides} \][/tex]

[tex]\[ y = 50 - 1 \times x \][/tex]

[tex]\[ y = 50 - x \][/tex]

This equation can be rearranged to standard form, which is [tex]\( Ax + By = C \)[/tex] , where [tex]\( A \), \( B \), and \( C[/tex]   are constants.

For our equation,[tex]\( A = -1 \), \( B = 1 \) , and \( C = 50 \)[/tex]  , so in standard form, it is :[tex]\[ -x + y = 50 \][/tex] .

We can multiply the entire equation by -1 to get :

[tex]\[ x - y = -50 \][/tex]

[tex]\[ x + y = 50 \][/tex]

This is the equation in standard form that represents the relationship between the number of bus rides, [tex]\( x \)[/tex], and the amount of bus money Shawn will have left, [tex]\( y \)[/tex].

Therefore, the correct answer is  [tex]\( x + y = 50 \)[/tex] .

The complete question is:

Shawn has a budget of $50 per month to spend on bus fare. He made a table showing the total amount of bus money he will have left after the given number of rides.

Which equation, in standard form, represents the relationship between the number of bus rides, x, and the amount of bus money Shawn will have left, y?

a) x+y = 50

b) 50x + 50y = 1

c) 50y = x

d) 50x = y

Answer:

(A) y= -1.026x^2 + 1016.402x - 162075

Step-by-step explanation:

Given is the data 'x' -Items produced. The equation that satisfies the given data can be found by simply substituting the values of x in the given equations. For example:

Substituting the value of x= 100 in the given equations,

A) y= -1.026(100)^2 + 1016.402(100)-162075= -70,500

Similarly you can check the values on the rest of the equations and if they satisfy the equation, then the given is the required equation.

Answer:

(A)

Step-by-step explanation:

WE are given the data which represents the company's profit based on number of items produced.

The equation which best represents the data can be found out by substituting the values of x in the given equations.

So,substituting x=100 in first equation, we have:

[tex]y=-1.026x^{2} +1016.402x-162075[/tex]

[tex]y=-1.026(100^{2})+1016.402(100)-162075[/tex]

[tex]y=-10260+101640.2-162075[/tex]

[tex]y=-70500[/tex]

which satisfies the equation. Hence, option A satisfies.

We can also substitute the different values of x in the equations to check whether it satisfies or not.

Answer:

93.5 in^2

Step-by-step explanation:

we know that

Jodi is cutting out pieces of paper that measure  inches by  inches

The area of each piece that jodi is cutting out is equal to the area of a rectangle

Answer:

Your range is (1,2,4,8)

A set of rules used to determine the proper order for performing operations in an expression that involves more than one operation is a(n) order of operations.

The number or amount of a group or part of something when compared to the whole is called proportion.

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

Something produced as a result of some input is called output.

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

Output of operations is the set of rules used to determine the proper order for performing operations in an expression that involves more than one operation

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