Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.

Answer:

Name an event that is impossible:  Drawing the name "John" out of the bag

Name and event that is certain:  Drawing a name that starts with the letter "J"

Name an event that is as likely as not:  Drawing a girl's name or a boy's name

Name an event that is more likely than not:  Drawing a name that is longer than 4 letters.

Step-by-step explanation:

tiene que sacar la raiz nena

Answer:  π and √5

Step-by-step explanation:

π is irrational

√5 is irrational

0.3333 is rational (repeating decimal)

√-4 is imaginary (equal to 2i) so is not a Real Number

1/9 is rational (repeating decimal) equal to 0.11111

The distance between rest stops on the new map is approximately 4.262 miles.

To find the distance between the rest stops on the new map, we need to determine the distance between each rest stop on the original map and then convert it to the new scale. The original map has a scale of 2 inches = 39 miles, so the distance between each rest stop on the original map is (9 inches / 7 rest stops) * 39 miles. Simplifying this gives us 5.571 miles. To convert this distance to the new scale, we use the scale of 1 inch = 30 miles. So, the distance between each rest stop on the new map is (5.571 miles / 39 miles) * 30 miles, which equals approximately 4.262 miles.

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The rest stops on the new map are approximately 19.2857 miles apart.

To find the distance between the rest stops on the new map, we need to determine the distance between the rest stops on the original map and then convert it to the new scale.

In the original map, the length of the highway is 9 inches and there are 7 rest stops.

Therefore, the distance between each rest stop on the original map is 9 inches / 7 rest stops = 1.2857 inches.

To convert this distance to the new scale, we multiply it by the ratio of the scales: 1.2857 inches * (1 inch / 2 inches) * (30 miles / 1 inch) = 19.2857 miles.

So, the rest stops on the new map are approximately 19.2857 miles apart.

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To determine the image width for Delisa's tablet, the width on the computer is divided by the ratio of the diagonals of the devices. The calculated width on the tablet is 7.4cm (74.0mm) when rounded to the nearest tenth of a millimeter.

Delisa is tasked with ensuring that the website is proportional on both computers and mobile devices.

Given the diagonal of her computer monitor (21 inches) and tablet (9.7 inches), we know that the scale of the image on the tablet should be in the same ratio as the diagonals.

Since the image is 16 centimeters wide on the computer, we can calculate the width on the tablet using the ratio of the diagonals.

The ratio of the tablet size to the computer size is 9.7/21.

To find the width of the image on the tablet, we use the proportionality:
Width on computer / Width on tablet = Diagonal of computer / Diagonal of tablet

We can then solve for the unknown width on the tablet:
16cm / Width on tablet = 21 / 9.7

By cross-multiplying and solving the equation, we get:
Width on tablet = 16cm * (9.7 / 21)
Width on tablet = 7.390476 cm

Rounded to the nearest tenth of a millimeter, the width on the tablet will be approximately 7.4cm or 74.0mm.

Final answer:

The width of the image on the tablet is calculated using a proportion based on the diagonal screen sizes of the computer and tablet. After converting the image width from centimeters to inches, and using the ratio of the diagonals (9.7 inches to 21 inches), the width on the tablet is determined and then converted back to centimeters, rounded to the nearest tenth of a millimeter.

Explanation:

Delisa is designing a website and wants to ensure that an image displayed on different devices remains proportional. The diagonal of her computer monitor is 21 inches, and the diagonal of her tablet is 9.7 inches. When scaled down, the image width on the tablet should maintain the same proportion to the tablet's screen size as the image on the computer does to the computer's screen size.

To find the proportional width of the image on the tablet, we use the ratio of the diagonals of the two devices. The ratio is the diagonal of the tablet (9.7 inches) to the diagonal of the computer (21 inches), which simplifies to 9.7/21. Since we know the width of the image on the computer is 16 centimeters, we can set up a proportion:

(Width on tablet / 9.7 inches) = (16 cm / 21 inches)
To solve for the width on the tablet, we cross-multiply and divide:

Width on tablet = 16 cm × (9.7 inches / 21 inches)
Before solving, we need to convert 16 cm to inches, since the diagonal measurements are in inches. There are approximately 2.54 cm in an inch, so:

16 cm ÷ 2.54 cm/inch = 6.2992 inches
Now, we can calculate the width for the tablet:

Width on tablet = 6.2992 inches × (9.7 inches / 21 inches)
Performing the multiplication gives us the width on the tablet in inches. To convert back to centimeters, we multiply the result by 2.54 cm/inch. Finally, we round the answer to the nearest tenth of a millimeter.

My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.

Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.

Answer:

Last choice that shows points on +4 and -4 is the correct graph.

Step-by-step explanation:

We have been given equation [tex]|m|=4[/tex]. Now we need to find out which of the given number lines shows the corret solution set for [tex]|m|=4[/tex].

We know that [tex]|x|=a[/tex] can be broken into two parts as:

[tex]x=+a[/tex] and [tex]x=-a[/tex]

Same way we can break [tex]|m|=4[/tex] into two parts as:

[tex]m=+4[/tex] and [tex]m=-4[/tex]

Hence last choice that shows points on +4 and -4 is the correct graph.

Answer:

D is correct

Step-by-step explanation:

Answer:

Minimum area is : 1 * 35 = 35

Maximum area is : 19 * 17 = 323

Step-by-step explanation:

The parameter (P) of rectangle is calculated using:

P = 2(a+b)

We are given that,

P = 72

=> 2(a+b) = 72

=> a+b = 36

In rectangle, the lengths of both sides are different and a whole number (as mentioned in question), Therefore, the length of smaller side a can be varied from 1 to 17. Similarly, the length of larger side varies from 19 to 35.

The area can be easily calculated using a*b.

Minimum area is : 1 * 35 = 35

Maximum area is : 19 * 17 = 323

Answer:

23

46

99

1/3

1/2

7/8

Step-by-step explanation:

Let's find out by writing out each of the numbers.

17 = Seventeen (Seventeen stands alone)

20 = Twenty (Twenty stands alone)

23 = Twenty-three will be hyphenated

46 = Forty-six will be hyphenated

99 = Ninety-nine will be hyphenated

1/3 = one-third will be hyphenated

1/2 = one-half will be hyphenated

7/8 = seven-eights will be hyphenated

Now we ask ourselves why are they hyphenated?

We hyphenate because we need the two words to be glued together to show readers that the two or more elements of a sentence are link to each other.

Answer:

23

46

99

1/3

1/2

7/8

8/1 or 16/2 or 24/3 or 32/4 or 40/5

Answer:  16

Step-by-step explanation:

[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=\boxed{16}[/tex]

Answer:

c

Step-by-step explanation:

The price of a plane ticket has increased by 33% from $150 to $200, determined by computing the difference between the new and old prices, dividing by the original price, and converting to a percentage.

The question is asking by what percent the price of a plane ticket has increased from $150 to $200. To calculate the percentage increase, you subtract the original price from the new price and divide by the original price. Then multiply by 100 to convert it to a percentage. Using this method:

So, the price of the plane ticket has increased by 33%, which means the correct answer is C) 33%.

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Answer:

It should be $2.45.

Step-by-step explanation:

12.25 divided by 5 equals 2.45.

Answer:

Step-by-step explanation:

If breadth =x

length =x+2

Area =length *breadth

Area =x(x+2)=80

X^2+2x-80=0

X^2 +10x - 8x - 80=0

X(x+10)- 8(x+10)=0

(X-8)(x+10)=0

X=8 or x=-10

X=8(since breadth cannot be a negative value x cannot be negative)

Answer: [tex]y=-2x-3[/tex]

Step-by-step explanation:

The equation of the line in slope-intercept form, is:

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

Where m is the slope and b is the y-intercept.

By definition, parallel lines have the same slope.

Then:

- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]

- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:

[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]

Then, the equation for the line containing the side opposite the side containing the first two vertices is:

[tex]y=-2x-3[/tex]

-4/3 is the nth term

Answer:

5

Step-by-step explanation:

3(2n-7)=9

^        ^

6n-21=9

   +21  +21

 6n=30

  6     6

n=5      :)

Answer:

(-2 , -2)

Step-by-step explanation:

Solution of the system of equations is where the lines intersect

So they intersect at x = - 2 and y = -2

Answer (-2 , -2)

Answer:

Step-by-step explanation:

The solution of the system of equations is the point of the intersection of a lines.

Answer:

8.) x = 15

Step-by-step explanation:

8.) divide 40 by 2 = 20 to only find half the triangle..

20^2 + b^2 = 25^2

400 + b^2 = 625

-400            -400

√b^2 = √225

b = 15

Answer:

c

Step-by-step explanation:

Answer:

Asa has $13 and owes $39

Step-by-step explanation:

25 + 14 = 39$ (amount of money he owes)

25 - 12 = 13$ (amount of money he has)

Answer:

The final solution is all the values that make  

( x 4  +  5  x 2  −  36 ) ( 2  x 2  +  9 x  −  5 )  =  0  true.  x  =  − 2 ,  2  ,  3  i  ,  −  3  i  , 1  2 ,  −  5

Step-by-step explanation:

x 4  +  5  x 2  −  36  =  0  2  x 2  +  9 x  −  5  =  0

Answer:

1,2,2,5,3

Step-by-step explanation:

it's right you idiots

Answer:

Step-by-step explanation:

Look at the picture.

We have the rectangle 2πr × h and two circles.

Therefore the formula of a Surface Area is:

[tex]S.A.=2\pi rh+2\pi r^2[/tex]

We have r = 5m and h = 9m. Substitute:

[tex]S.A.=2\pi(5)(9)+2\pi(5^2)=90\pi+50\pi=140\pi\ m^2[/tex]

[tex]\pi\approx3.14\to S.A.\approx(140)(3.14)\approx440\ m^2[/tex]

Final answer:

To calculate the surface area of the cylinder, use the formula 2π(radius)(height) + 2π(radius)², with radius = 5m and height = 9m. The answer is approximately 440 square meters when rounded to the nearest square meter.

Explanation:

To find the approximate surface area of the cylinder, we can use the formula: Surface area = 2π(radius)(height) + 2π(radius)². Given a radius of 5 meters and a height of 9 meters, we can plug these values into our formula.

The area of the two circular bases is 2π(radius)² = 2π(5)² = 2π(25) = 50π square meters.

The area of the side (the rectangular part when the cylinder is unrolled) is 2π(radius)(height) = 2π(5)(9) = 90π square meters.

Adding both of these areas together gives us the total surface area:
50π + 90π = 140π square meters.

Using 3.14159 as an approximation for π, we get 140π = 140(3.14159) ≈ 439.8226 square meters, which can be rounded to the nearest square meter as 440 square meters.

Answer:

The sum of terms 12  the geometric sequence 1,3,9...   = 265720

Step-by-step explanation:

Formula:-

Sₙ = a₁(1 - rⁿ)/(1 - r)

Where Sₙ - sum of n terms in the GP

a - First term of GP

r - Common ratio

n - Number

It is given the  geometric sequence 1,3,9....

To find the sum of 12 terms

Here a = 1, r = 3 and n = 12

Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720

Answer:

The sum of the 12 terms = 265720

Step-by-step explanation:

* Lets study the geometric sequence rule

- If a1 = a , a2 = ar ,  a3 = ar² , a4 = ar³ , .........................

∴ an = a[(r)^(n-1)]

- Where a is the first term and r is the common ratio and

  n is the position of the term in the sequence

- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)

- Where n is the number of terms we want to add

* Lets check our terms in the sequence

- The terms are 1 , 3 , 9 , ..........

- To find the common ratio divide the 2nd term by 1st term

∵ the second term is 3 and the first term is 1

∴ 3/1 = 3

∴ The common ratio is 3

∵ n = 12 and a = 1

* Lets substitute the values of a , r , n in the rule of the sum to

  find the sum of the 12 terms

∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720

* The sum of the 12 terms = 265720

Answer:

The Field's length is 93ft

Step-by-step explanation:

P=2L+2w

360=2(w+6)+2w

360=2w+12+2w

360=4w+12

348=4w

348/4=w

87=w

L=w+6

L=87+6

L=93

The width of a rectangular field surrounded by 360 feet of fencing is 87 feet. The length of the field, which is 6 feet more than the width, is 93 feet.

We are dealing with a rectangular field here, and we know that the length of a rectangle is equal to the total fencing (perimeter), divided by two, minus the width. Now, the problem states that the length is 6 feet more than the width. Therefore, we can create the following equation: 2x + 2(x + 6) = 360, where x is the width.

After simplifying this equation, we find that 4x + 12 = 360. Subtract 12 from both sides to get 4x = 348, and then divide by 4 to find that x = 87 feet. Thus, the width of the field is 87 feet. Since the length is 6 feet more than the width, we add 6 to 87 to get a length of 93 feet.

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The answer is: There is no solution, it's not possible for Shawn to catch up with Jason since both are riding at the same constant speed, there is always be a distance of 1 mile between.

If it's possible to Shawn to catch up with Jason, the following equation will be true:

Let be the station our origin, so:

[tex]ShawnPosition=JasonPosition\\20mph.x-2miles=20mph.x-1mile\\-2=-1[/tex]

So, since the equation is not fulfilled, there is not solution, meaning that it's not possible to Shawn to catch up with Jason since both started riding from different points keeping the same constant speed, there will always be a distance of 1 mile between them if they keep the speed constant.

Also, Shawn could have caught up with Jason if he were started with a speed of 21mph instead the Jason speeds (20mph), let's prove that:

[tex]ShawnPosition=JasonPosition\\21mph.x-2miles=20mph.x-1mile\\\\21mph.x-20mph.x=2miles-1mile\\\\mph.x=1mile\\x=1h[/tex]

So, by substituting "x" into the equations, we have:

[tex]ShawnPosition=JasonPosition\\21mph.1h-2mile=20mph.1h-1mile\\21miles-2miles=20miles-1mile\\19miles=19miles[/tex]

So, Shawn could have caught up with Jason if he were started with a 21 mph speed  instead starting with the Jason speed (20 mph).

Have a nice day!

Answer:

A=3x^2+5x-6

B=-2x^2-6x+7

A-B=(3x^2+5x-6)-(-2x^2-6x+7)

remove parentheses

A-B=3x^2+5x-6+2x^2+6x-7

combine like terms

A-B=5x^2+11x-13

Replace x in each equation with 4:

f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21

g(x) = x^2-9 = 4^2 -9 = 16-9 =7

Now you have values for f(x) and g(x) now you can solve for f/g and f+g:

f/g = 21 / 7 = 3

f+g = 21 + 7 = 28

For this case, we have that by definition:

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

We have the following functions:

[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]

So:

[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]

On the other hand:

[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]

[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]

Answer:

[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]

Answer:

the first one i believe

Step-by-step explanation:

hope this helps

Answer:

3√4

Step-by-step explanation:

Final answer:

To find the diameter of Monica's shirt button with a radius of 1 centimeter, we multiply the radius by 2, resulting in a diameter of 2 centimeters.

Explanation:

The question asks to determine the diameter of a button given its radius. The radius of Monica's shirt button is 1 centimeter. In geometry, the diameter of a circle is defined as twice the radius. Therefore, to find the button's diameter, you simply multiply the radius by 2.

Formula: Diameter = 2 × Radius

Calculation: Diameter = 2 × 1 cm = 2 cm.

Thus, the diameter of Monica's shirt button is 2 centimeters

Answer:

Lets firts mention that the rule presented in the question does not apply for all real numbers

But, we can see that in some cases it might be true.

Let

a = 1

b = 0

√1 + √0  = 1 + 0 = 1

Likewise,

√(1 + 0)  =  √(1) = 1

And we see that the result is the same.