Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4% of the total interest paid was $475 how much did he invest in each

For solving a question like this where you have to find a function for a particular value, just put the given number in place of the unknown variable i.e. x in this case. Lets solve this function now.

We are to solve for f(9), so we will put 9 in place of x:

f(x) = 72+4x

f(9) = 72 + 4(9)

f(9) = 72 + 36

f(9)= 108

so, your function for the value 9 is 108.

Let us assume numbers are x and y.

Difference of the squares of x and y = 1100.

We can setup an equation:

x^2 - y^2 = 1100.

We can apply difference of the squares formula: a^2-b^2 = (a-b)(a+b).

Therefore,

x^2 - y^2 = 1100 would become (x-y)(x+y)=1100.

Let us find all factors of 1100 square of those differences is 1100.

Let us take factors of 1100 as 110 and 10.

Sum should be 110 and difference should be 10.

So, we could setup two eqautions as

x+y=110

x-y=10

Adding equations, we get

2x = 120.

Dividing both sides by 2, we get

x=60.

Plugging x=60 in x+y=110, we get

60+y=110.

y=50.

Therefore, 60 and 50 pair of square numbers gives a difference of 1100.

Answer:     The correct answer is: (Line segment E F)

Step-by-step explanation:  Took the assignment.

The segment CF is a reflection of segment AB over the line x = 1.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

The vertices of segment:

A(-4, 3) and B(-1, 1).

The reflection rule over the line x = 1:

(x, y) → {1-(x - 1), y)}

A(-4, 3) → A'(6, 3)

and B(-1, 1) → B'(3, 1)

Therefore, the segment is CF.

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Answer: Neither

The function is not even because it doesn't have y axis symmetry. In other words, reflecting it over the vertical y axis means it doesn't line up with itself. The left half is different from the right half.

The function isn't odd either. Why not? Because rotating it 180 degrees around the origin has the function curve looking completely different. A point like (3,6) will rotate to (-3,-6) which is not on the orange curve. This is just one counter-example as to why the function is not odd.

In mathematics, a function is classified as Odd or Even based on its symmetry. An Even function has symmetry about the y-axis while an Odd function has rotational symmetry. A function could also be neither even nor odd if it doesn't meet these criteria.

In mathematical terms, a function can be classified as Even if it meets the criteria of y(x) = y(-x), meaning it has symmetry about the y-axis. A function is classified as Odd if it meets the criteria of y(x) = -y(-x), meaning it is the mirror image of itself about the origin, or it has rotational symmetry.

Let's take some examples: even function is the square function x², and an odd function is the cubic function x³. The combination results could vary: an even function times an even function results in an even function, an odd function times an odd function results in an even function, whereas an odd function times an even function results in an odd function.

However, it's important to note that a function could also be Neither even nor odd. This happens if the function does not meet any of the above-mentioned criteria for even or odd functions.

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To find the cost of admission to the fair, subtract the cost of the ride tickets from the total spent. The linear equation for cost of ride tickets and admission is y = 2.50x + 18. The coefficient represents the cost per ride ticket, while the constant term represents the cost of admission.

(A) To find the cost of admission to the fair, we need to subtract the cost of the ride tickets from the total amount spent. Since Henry bought 15 ride tickets for $2.50 each, the cost of the ride tickets would be 15 * $2.50 = $<<15*2.5=37.5>>37.50. So, the cost of admission to the fair would be the difference between the total amount spent and the cost of the ride tickets: $55.50 - $37.50 = $<<55.50-37.50=18>>18.

(B) The linear equation to determine the cost of ride tickets and fair admission can be expressed as y = 2.50x + 18, where y represents the total cost and x represents the number of ride tickets.

(C) The coefficient on x, which is 2.50, represents the cost per ride ticket. The constant term of 18 represents the cost of fair admission.

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3x+4y=12

subtract 3x

4y=12-3x

divide by 4

y=3x/4+3

The equation solved for y is y = (-3/4)x -3.

Two or more expressions with an equal sign are defined as an equation.

The given equation is 3x + 4y = 12.

3x + 4y = 12

4y = -3x - 12

y = (-3/4)x -3

Hence, the equation solved for y is y = (-3/4)x -3.

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Replace X with a couple different numbers, solve the equation for the y value:

IF X = 2, then y would be 1/2(2) +2 = 1+2 = 3

so the first point would be on (2,3)

X = 4, y = 1/2(4) + 2 = 2+2 = 4

The second point would be on (4,4)

Plot those two points and then draw a line thought both points.

The graph of the function [tex]f(x) = \frac{1}{2}x + 2[/tex] is plotted below

The given equation is :

[tex]f(x) = \frac{1}{2}x + 2[/tex]

This can be written in the form:

f(x) =  mx  +  c

Above is the slope-intercept form of the equation of a line with:

slope represented as m

y-intercept represented as c

Comparing [tex]f(x) = \frac{1}{2}x + 2[/tex] with f(x) =  mx  +  c

m   =  1/2,   c  =  2

Plot the graph when m = 1/2 and c = 2

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The equation of ellipse:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

The formula of c (the distance to the foci)

[tex]c^2=a^2-b^2\qquad|\text{add}\ b^2\ \text{to the both sides}\\\\c^2+b^2=a^2[/tex]

The value of {c} for an ellipse can be written as -

c = √(a² - b²).

An ellipse has two focal points. The points on the ellipse are such that the the sum of the distance of the points from each foci remains the same.

Given is to find the equations to be used to find the value of {c} (the distance to the foci) for an ellipse.

We can write the expression for {c} in terms of the length of the semi - major and semi - minor axis of an ellipse as -

c = √(a² - b²)

or we can write -

c² = a² - b²

So, we can conclude that the value of {c} for an ellipse as -

c = √(a² - b²)

Therefore, the value of {c} for an ellipse can be written as -

c = √(a² - b²).

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It's b

Hope I'm right

If minivans and cars were sold at a 3:5 ratio each day and there were 12 minivans sold yesterday they would have sold 20 cars.

You can find this by dividing 12(the number of minivans sold) by 3(the ratio of vans v.s. cars), which equals 4. To find the amount of cars sold, use the same method, only multiply with by the ration of cars. 5*4 = 20

Answer:

A. He captured Fort Duquesne.

Step-by-step explanation:

General Edward Braddock was fatally injured in the battle field and died of wounds. He insisted upon using open field tactics which turned out to be very fatal leading to the death of 1000 soldiers. He did ignore the early warnings of his aides regarding his strategy.

A British force led by General Edward Braddock, moving to take Fort Duquesne, was defeated by a force of French and Canadian troops under Captain Daniel Liénard de Beaujeu with its American Indian allies.

Consequently, he failed to capture Fort Duquesne. So statement A is not true.

2.35  * 10 raised to 6

If he used the rule (x + 4, y + 7) then pre-image (4, 5) would result in image (4 + 4, 5 + 7) = (8, 12).  

He should have used the rule (x - 4, y - 7)

Answer:

Step-by-step explanation:

(2005, 12,000)        (2005, 12,000)

   x1          y1                x2           y2

m= (12,250-1200) /  (2010-2005) = 250/5 = 50/1 = or 50

The nth term of the arithmetic sequence 7, 10, 13, 16, ... is described by the equation an = 3n + 4, which is option (a).

To find the nth term of the arithmetic sequence 7, 10, 13, 16, ..., we need to recognize that this sequence has a common difference of 3, because each term increases by 3 from the previous term. The general formula for an arithmetic sequence is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference.

In this sequence, a1 is 7 and d is 3. Plugging these values into the general formula, we get:

an = 7 + (n - 1)*3

an = 7 + 3n - 3

an = 3n + 4

Therefore, the correct equation that describes the nth term of this arithmetic sequence is option (a): an = 3n + 4.

The equation in undefined when the denominator is equal to 0.

The denominator is (x+5) (x+11)

Solve for the x's to make the equations equal 0:

x+5 = 0

Subtract 5 from each side:

x =-5

x+11 = 0

Subtract 11 from each side:

X = -11

There are two answers -5 and -11.

For this question, you need to multiply 1,840 by 182.

1,840/182 = 334,880.

:)

Final answer:

To find the original price of a lamp that costs £65 after a 30% increase, divide £65 by 1.3 to obtain the original price, which is £50.

Explanation:

To calculate the original price of the lamp before the 30% price increase, we must consider the final price of £65 as being 130% of the original price since the increase is an addition to the original 100%. To find the original price (100%), we divide the final price by 130% (which is 1.3 in decimal form) and then multiply by 100% (which is represented as 1 in decimal form).

Here's the method in steps:

Let's do the calculation:

£65 ÷ 1.3 = £50

Therefore, the original price of the lamp was £50.

We know how wide the billboard will be. Therefore, to know how much the original image should be enlarged, you must divide the final width of the billboard between the current width of the invoice.

We know both data, then we perform the operation:

48 feet /6.14 inches = 7.81 feet / inches

Therefore the correct answer is option D. 1″ = 7.81′

For the bill to cover the billboard, the bill must be expanded by a factor of 7.81 feet long per inch long that has the original image.

The function would be 1+(1/2)h=d

This is because 1 more means addition and then 1/2 of the cost of a hamburger.

b: hamburger/ h: hotdog

B/2+1=h

Answer:

The correct option will be:  D. (6, 2)

Step-by-step explanation:

Point [tex]S[/tex] divides the line segment [tex]YB[/tex] in a ratio of [tex]4:1[/tex]

Given that, [tex]Y(-10, 6)[/tex] and [tex]B(10, 1)[/tex]

If a point [tex](x,y)[/tex] divides a line segment with endpoints as [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] in a ratio of [tex]m:n[/tex] , then...........

[tex](x, y)= (\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})[/tex]

Here,  [tex](x_{1}, y_{1})=(-10,6)[/tex] and [tex](x_{2}, y_{2})=(10,1)[/tex]

Also,  [tex]m:n=4:1[/tex]

Now plugging the values, we will get........

[tex]x=\frac{4(10)+1(-10)}{4+1}= \frac{40-10}{5}= \frac{30}{5}=6 \\ \\ \\ y=\frac{4(1)+1(6)}{4+1}= \frac{4+6}{5}= \frac{10}{5}=2[/tex]

So, the coordinates for point S will be:  (6, 2)

Answer:

a(t) = 700t-400

Step-by-step explanation:

Given that when Nour drove altitude increased at a constant rate. Let us consider sea level as 0 and starting time as 0 we have

At the start t =0 and a = -400 m

When t=2   a = 1000 m.

Rate of change of a wrt time = change in a/Change in time

= {1000-(-400)}/(2-0) = 700

i.e. slope = 700

a = 700 t +C

To find C:

When t =0, a =-400

Hence C =-400

Equation is a(t) = 700t-400

The subject of this question is Mathematics. The equation a(t) = 700t - 400 represents Nour's altitude relative to sea level as a function of time.

The subject of this question is Mathematics.

Nour's altitude can be represented as a linear function of time. Let's denote Nour's altitude relative to sea level a(t) as a function of time t. We know that initially, her altitude was 400 meters below sea level, and 2 hours later, her altitude was 1000 meters above sea level.

To find the equation of the line, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The slope is determined by the rate of change of altitude per unit of time.

Since her altitude increased at a constant rate, we can find the slope by taking the difference in altitude and dividing it by the difference in time:

The slope of the line representing Nour's altitude is therefore 1400/2 = 700 meters per hour. The equation of the line can be written as: a(t) = 700t - 400, where t is the time in hours.

In conclusion, the subject of this question is Mathematics and it is suitable for High School students. The equation a(t) = 700t - 400 represents Nour's altitude relative to sea level as a function of time.

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Hugo polled 100 randomly selected people to see if they had exercised that week and found that 85% said they had. Lily asked 400 randomly selected people the same question and found that 85% of them also responded that they had exercised that week. If Hugo and Lily use a 99% confidence level, then the true statement will be

Hugo's margin of error will be exactly 2 times as large as Lily's margin of error.

Answer:

The true statement is : Hugo’s margin of error will be exactly 2 times as large as Lily’s margin of error.

Step-by-step explanation:

[tex]\text{Margin of error : }\frac{\sigma \cdot z^*}{\sqrt n}.........,z^*=2.58\text{ for 99 percent level of confidence}[/tex]

And value of sigma is same as the response in both the cases is 85%

Hugo's margin of error : n = 100

[tex]\text{Margin of error of Hugo : }\frac{\sigma \cdot z^*}{\sqrt {100}}\\\\=0.258\times \sigma[/tex]

Lilly's margin of error : n = 400

[tex]\text{Margin of error of Lily : }\frac{\sigma \cdot z^*}{\sqrt {400}}\\\\=0.129\times \sigma\\\\=\frac{1}{2}\times 0.258\times \sigma\\\\=\frac{1}{2}\times\text{ Hugo's margin of error}[/tex]

Hence, the correct statement is : Hugo’s margin of error will be exactly 2 times as large as Lily’s margin of error.

E. n = 3

N. x = -6

A. x = 4

H. t = 10

E. v = -5

I. x = -8

T. y = 2

A. m = -16

Y. k = 7

S. x = -1

T. d = -12

F. u = 29

C. y = 1

E. 20n - 28 =10n+2

10n= 30

n=3

N. 9x+27 =4x-3

5x = -30

x= -6

A.   24-16x =x-11x

     24 = 6x

x= 4

H .  3t + 16t-48= 2+14t

5t =50

t= 10

E.  2v+18= 16 -4v -28

6v  = -30

v=-5

I.  4x-9 +3x=8x-1

x=8

T.  24+12y =10y+40

2y =16

y=8

Answer:

She will checked each account on Tuesday at 2 pm.

Step-by-step explanation:

Consider the provided information.

Julie has 2 email accounts she checks one of them every two hours the other she checks every 24 hours.

In order to solve this first find the LCM of both numbers.

2 = 2×1

24 = 2×2×2×3

The LCM of 2 and 24 is 24.

Thus, she will check each account at the same time after 24 hours.

It is given that she checked each account on Monday at 2pm.

That means after 24 hours of Monday 2 pm she will again check each account at the same time.

Hence, she will checked each account on Tuesday at 2 pm.

Answer:

1) m∠A=60°

2) [tex]BK=3\sqrt{3}[/tex]

3) The area of ABCD is 62.35

Step-by-step explanation:

1) - You can calculate the angle m∠A as following:

[tex]cos^{-1}(\alpha })=\frac{adjacent}{hypotenuse}\\adjacent=3\\hypotenuse=6\\[/tex]

- Substitute values and solve for the angle. Let's call the angle m∠A "[tex]\alpha[/tex]"

[tex]cos^{-1}(\alpha )=\frac{3}{6}\\ \alpha =60[/tex]

2) Apply the Pythagorean Theorem to find BK:

[tex]BK=\sqrt{6^{2}-3^{2}}=3\sqrt{3}[/tex]

3) - If you analize the figure, you can see that the triangle ABD and the triangle BCD are the same triangle, both are equal, therefore both have the same area.

- Then, you can calculate the area of ABD and multiply it by 2 to calculate the area of ABCD. The area of a triangle is:

[tex]Area=\frac{(base)(height)}{2}[/tex]

- The area ABD will be the sum of the area of the triangle ABK and the area of the triangle KBD.

- First, you must calculate the angle m∠D using the triangle ABD, which is a right triangle. The sum of the interior angles of a triangle is 180°. You know the angles m∠A (60°) and m∠B (90°), therefore:

[tex]60+90+D=180\\D=30[/tex]

m∠D=30°

- Now, you can calculate KD:

[tex]tan(30)=\frac{3\sqrt{3}}{KD}\\KD=9[/tex]

- The area of ABCD is:

[tex]A_{ABCD}=2(A_{ABK}+A_{KBD} )[/tex]

[tex]A_{ABCD}=2(\frac{(3)(3\sqrt{3})}{2}+\frac{(9)3\sqrt{3}}{2})\\A_{ABCD}=62.35[/tex]

Answer:

Option D

Step-by-step explanation:

See the letters in the word deadline.

We have d and e repeated twice , and a,l,i,n once.

There are in total 8 letters

These 8 letters can be arranged in 8x7x6...1 = 8! ways

But since there are repititions of letters, we have 2! x 2! times repeated letters.

Hence we have to divide by 2!x2!

No of ways = [tex]\frac{8!}{2!*2!}[/tex]

Option D is right