Tom has a large photo he wants to shrink to wallet size.it's width 20centimeters and it's length is 30 centimeters. if he wants the width to be 5 centimeters what should the length be

Look at the picture.

[tex]r=\sqrt{x^2+y^2}-\text{from the Pythagorean theorem}\\\\\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}[/tex]

We have the point

[tex](4,\ -8)\to x=4,\ y=-8[/tex]

Calculate r:

[tex]r=\sqrt{4^2+(-8)^2}=\sqrt{16+64}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]

Substitute:

[tex]\cos\theta=\dfrac{4}{4\sqrt5}=\dfrac{1}{\sqrt5}\to\boxed{C)}[/tex]

To change a cell color in a spreadsheet program, one should select the Fill drop-down menu, found in the Home tab, to choose and apply a new color to the cell.

When you want to change a cell color in a spreadsheet program such as Microsoft Excel, you should select the A) Fill drop-down menu. This is the option that allows you to change the background color of a cell. You can typically find the Fill drop-down menu in the Home tab of the ribbon at the top of your spreadsheet application. To change a cell's color, you simply click on the cell you want to format, then go to the Home tab, click the Fill drop-down menu, and choose the color you wish to apply.

Answer:

9

Step-by-step explanation:

45/5 = 9

Answer:

Length of the floor is about 11.75 feet.

Step-by-step explanation:

It is given that, it takes 12.5 tiles to cover the length of the floor.

The length of each square tile is 11.25 inches. So, if 12.5 tiles each of length 11.25 inches are joined, we will get to know the length of the floor.

So, the length of the floor is,

[tex]11.25 \times 12.5[/tex]

[tex]=140.625 \text {in}[/tex]

So the length of the floor is 140.625 inches or we can say roughly about 141 inches.

We can convert this length into feet.

1 feet = 12 inches, so the length of the floor in inches is,

[tex]\frac{141}{12} =11.75 \text {ft}[/tex]

So the length of the floor is 11.75 feet.

The total value of 2 Apple shares at $54.76 each is $109.52, resulting in a loss of $116.58.

To calculate the total value of your Apple stock now, we'll first determine the total value of your shares at their current price and then compare it to their original total value.

Current price per share: $54.76

Number of shares you own: 2

Total value of your shares now:

= Current price per share × Number of shares

= $54.76 × 2

= $109.52

Original total value of your shares: $226.10

Now, let's compare the current total value with the original total value:

Current total value: $109.52

Original total value: $226.10

As the current total value is less than the original total value, it indicates a loss.

To find out the loss incurred, we subtract the current total value from the original total value:

Loss = Original total value - Current total value

    = $226.10 - $109.52

    = $116.58

Therefore, the total value of your Apple stock now is $109.52, and you have incurred a loss of $116.58.

The total value of your 2 shares of Apple stock now is $109.52.

To determine the total value of your Apple stock now, we first need to calculate the total value of the stock when you first bought it and then compare it to the current value.

1. Initial Total Value: You initially bought 2 shares of Apple stock. Let's denote the initial price per share as P. The total value initially is the product of the number of shares and the initial price per share.

Initial total value = Number of shares * Initial price per share

Initial total value = 2 shares * Initial price per share = $226.10

2. Initial Price per Share: To find the initial price per share, we divide the initial total value by the number of shares.

Initial price per share = Initial total value / Number of shares

Initial price per share = $226.10 / 2 shares = $113.05 per share

3. Current Total Value: Now, we find the current total value of your 2 shares at the current price per share, which is $54.76.

Current total value = Number of shares * Current price per share

Current total value = 2 shares * $54.76 per share = $109.52

So, the total value of your 2 shares of Apple stock now is $109.52.

Answer:5250.00

Step-by-step explanation: percents are a multiplication so 35,000×15=5250.00

Answer:

$5,250

Step-by-step explanation:

The less must pay a minimum down payment that is equivalent to 15% the sales price of the new car.

Given that the price of the new car is $35,000, the product of 15% with this amount will equal the down payment.

As such, the down payment

= 15% * $35,000

= 0.15 * $35,000

= $5,250

The simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear expression is:

= 5x - 5x + 3x - 3x

After simplification:

= 0 + 3x - 3x

= 0

All terms are canceled out,

Thus, the simplification form of the expression 5x - 5x + 3x - 3x is 0 option (D) is correct.

Learn more about the linear equation here:

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Answer:

1350

Step-by-step explanation:

We can write a proportion to find the total amount in the school this year using the information given. A proportion is two equivalent ratios set equal to each other. If 10% has decreased, then 90% is now left.

[tex]\frac{10}{100}=\frac{y}{1500}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

10(1500)=100(y)

15000=100y

y=150

Y is the number of students who are now gone. We subtract 1500-150=1350

Real world examples of proportional and non-proportional relationships can be observed in the relationship between the distance a car travels and the fuel consumed (proportional), and in an employee's pay scale (non-proportional).

In the real world, one can identify numerous examples related to proportional and non-proportional relationships. For instance, consider the relationship between distance and fuel consumption in a car. Here, a car maintains a set distance per gallon ratio, which is a proportional relationship - if distance doubles, fuel consumed also doubles.

Contrasting this, the pay scale in many workplaces may illustrate a non-proportional relationship. For instance, if an employee works overtime, he/she may earn a higher rate, different from their regular hourly wage. In this case, a doubling of hours worked does not necessarily equate to a doubling of the total salary.

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Answer: 11 and 6

Step-by-step explanation:

I think this is it because she is 5 years younger and last year she was half of his age so he was 10 then you have to add another year to their age because that was last year, 5+1=6, 10+1=11. but im not completely sure so if you can wait for someone else or if you agree go ahead and answer it.

We'll call the ages n and s

Nancy is 5 yrs younger than her brother Stan

n = s - 5

Last year she was half as old as he was

n - 1 = (1/2) ( s - 1 )

We substitute for n

s - 5 - 1 = (1/2) (s - 1)

2s - 12 = s - 1

s = 11

n = s - 5 = 6

Answer: Nancy is 6, Stan is 11

Check:

Clearly they're five years apart.  Last year they were 5 and 10, half, good.

Answer:

25/24 pounds of total meat processed.

Step-by-step explanation:

We have been given pounds of bologna and 3/8 pounds of ham and 2/4 pound turkey

And we need to find the total number of pounds of meat processed.

The total number will be calculated by finding their sum of all the meats which is

1/6+3/8+2/4

Taking LCM of (6,8,4)=24 hence, we get:

1/6+3/8+2/4= 25/24

Answer:

B

Step-by-step explanation:

Answer: No, it is not sufficient to know that opposite sides of the garden plot are congruent and parallel to determine that the garden plot is rectangular.

Step-by-step explanation:

1. You have the following information given in the problem:

- Opposite sides of the garden plot are congruent.

- Opposite sides of the garden plot are parallel.

2. Therefore, keeping the information above on mind, you can conclude that the description is about a parallelogram, but to determine that it is rectangular, you need to know that the four interior angles measure 90° and the diagonals are congruent.

Final answer:

Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.

Explanation:

Phyllis Doran worked a total of two different shifts across Monday and Tuesday. On Monday, she worked for 7 1/2 hours. On Tuesday, she started at 8:00 a.m. and finished at 1:00 p.m., which is a 5-hour shift.

To find the total number of hours Phyllis worked, we add the hours from both days together.

Monday: 7.5 hours
Tuesday: 5 hours (since 1:00 p.m. is 5 hours after 8:00 a.m.)

Now, we sum these up:
Total hours worked = 7.5 hours + 5 hours = 12.5 hours.

So, Phyllis Doran worked a total of 12.5 hours between Monday and Tuesday at Symmes Medical Center.

For this case we must factor the following expression: [tex]6x ^ 2-9x-6[/tex]

We test the options:

Option A:

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

We apply distributive property for the first parenthesis:

[tex](6x + 3) (x-2) =[/tex]

We apply distributive property of the form:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

[tex]6x ^ 2-12x + 3x-6 =[/tex]

Different signs are added and the sign of the major is placed.

[tex]6x ^ 2-9x-6[/tex]

So, [tex]3 (2x + 1) (x-2) = 6x ^ 2-9x-6[/tex]

Answer:

Option A

Answer:

$1,093,026

Step-by-step explanation:

We have been given that real estate values in a town are increasing at a rate of 14% per year.  Mrs. Knoxville purchased a building for $590,000 in 2012.

We are told that real estate values are increasing at a rate of 14%, this means that values of real estates are increasing exponentially.

Since we know that an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r= growth rate in decimal form.

a= Initial value.

Let E(t) be value of real estates t years after 2012. Now let us substitute our given values in exponential function form.

Upon converting our increase rate to decimal form we will get,

[tex]14\text{ percent}=\frac{14}{100}=0.14[/tex]

[tex]E(t)=590,000*(1+0.14)^t[/tex]

[tex]E(t)=590,000*(1.14)^t[/tex]

Now let us substitute the value for building in 2020 by substituting t=8 as 2020-2012=8.

[tex]E(2020)=590,000*(1.14)^8[/tex]

[tex]E(2020)=590,000*2.8525864220672256[/tex]

[tex]E(2020)=1,683,025.989019663104\approx 1,683,026[/tex]

Now let us subtract 590,000 from 1683026 to find the amount that Mrs. Knoxville can get from selling the building.

1,683,026-590,000=1,093,026

Therefore, Mrs. Knoxville can get $1,093,026 from selling the building.

Answer:

9 balloons per student and 27 per group of 3 students.

Step-by-step explanation:

We have 6 groups of students with 3 students in each group. This means in group 1 there is 3. Groups 2 has 3. Group 3 has 3. Group 4 has 3. Group 5 has 3. Group 6 has 3.

So there are 3+3+3+3+3+3=18 total students.

The school carnival has 162 balloons, how much will each student have?

We will divide 162 balloons by the total number of 18.

162/18=9

9 balloons per student and 27 per group of 3 students.

Answer:

no

Step-by-step explanation:

SAS stands for side angle side. so in this question we know that one side is equal to another side, but we don't know wether or not there is another angle and another side that is congruent. so for that reason it is not congruent by SAS.

Since [tex]100=(\pm10)^2[/tex], the idea here is to find [tex]b[/tex] such that

[tex](x\pm10)^2=x^2+bx+100[/tex]

Expanding the left side completely, we find two possibilities:

[tex]x^2\pm20x+100[/tex]

so that [tex]b[/tex] can be either positive or negative 20.

The answer will be ±20

Let us consider a binomial (x ± a)

now squaring it we get      [tex]x^{2}[/tex] ± 2ax + [tex]a^{2}[/tex]

If we compare it to the question we get  [tex]a^{2} =[/tex] 100

                                                                 ⇒ a = ±10

According to the question we have to find the value of  2a

                            2a = 2×(±10) = ±20

Hence ±20 is the answer.

Learn more about binomial expansion:

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Answer:

Might not be congruent

Step-by-step explanation:

You don't have enough information

Answer with explanation:

It is given that,In ΔABC and Δ DEF

  ∠C =∠F⇒⇒[Given]

To prove that two triangles are similar, we can use following Similarity axiom which are

a.→ AA

b.→S AS

c.→SSS

→Ratio of sides of two triangles should be proportional while proving similarity of two triangles.

But, Here between two triangles , only one angle is congruent ∠C and ∠F.So, we can't conclude that these two triangles that is, ΔABC and Δ DEF are similar.

Option D:→ Not

11.73%

Step-by-step explanation:

Answer: 4,050, 12,150, 36,450

Step-by-step explanation: multiply each following number by 3

Answer:

4050; 12150; 36450

Step-by-step explanation:

[tex]a_5 = 50.3^4 \\\ a_5 = 4050 \\\ a_6 = 50.3^5 \\\ a_6 = 12150 \\\ a_7 = 50.3^6 \\\ a_7 = 36450[/tex]

I hope I helped you.

Answer:

it would be 20%

Step-by-step explanation:

out of 100% you would subtract the 23%, 30%, 15% and, 12% and you would get 20%

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

1. x ≤ 5 ≤ 8 then x + 5 > 8 → x > 8 - 5 → x > 3 therefore 3 < x ≤ 5.

2. 5 ≤ x ≤ 8 then 5 + x > 8 → x > 3 therefore 5 ≤ x ≤ 8

3. 5 ≤ 8 ≤ x then 5 + 8 > x → 13 > x → x < 13 therefore 8 ≤ x < 13.

Answer:

3 < x < 13

Step-by-step explanation:

Since, a triangle is possible when the sum of any two sides is greater than the third side,

Given,

The sides of the triangle are 5 inches and 8 inches,

If x shows the third side,

Then, by the above statement,

x < 5 + 8 ⇒ x < 13

5 < x + 8 ⇒ -3 < x

8 < x + 5 ⇒ 3 < x

Hence, the required inequality gives the range of possible values for x  is,

3 < x < 13

[tex]h(x+5)=3x+18\\\\h(x)=mx+b\to h(x+5)=m(x+5)+b=mx+5m+b\\\\\text{Therefore we have}\ m=3\ \text{and}\\\\5m+b=18\to5(3)+b=18\\\\15+b=18\qquad\text{subtract 15 from both sides}\\\\b=3\\\\Answer:\ \boxed{h(x)=3x+3}[/tex]

To find the function h(x) when given h(x+5)=3x+18, we substitute x with (x-5) in 3x+18 to make h(x) = 3x+3.

To find the function h(x), we need to replace (x+5) in the equation with x. The given equation is h(x+5)=3x+18.

We know that if we substitute x+5 with x in h(x+5), we must also substitute the x in 3x+18 with (x-5) to keep the equation and function consistent.

So, we replace x with (x-5) in 3x+18, and our new equation will be 3(x-5)+18.

This simplifies to 3x - 15 + 18, which further simplifies to 3x+3.

Consequently, the function h(x) = 3x+3.

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Answer:

13188

Step-by-step explanation:

Answer:

2.1 yards of blue material will she need.

Step-by-step explanation:

As per the given statement:  Sue buys material for a costume she buys 1.75 yards of red material.

As she bought 1.75 yards of the red material.

For blue material she bought 1.2 times as much as yard of the red material.

"times" represents multiply

Blue material she will need =  [tex]1.2 \times 1.75 = 2.1 yards[/tex]

therefore, 2.1 yards of blue material will she need.