Special right triangles

Answer:

The difference between the legs and the hypotenuse of a right triangle is that the hypotenuse will always be the longest side. Also, it will always be less than the two legs added together.

Step-by-step explanation:

Answer:

39.35 sec

Step-by-step explanation:

Given that:

The winning time is represented by the function:

T = 46.97 - 0.099x

Where x = year ; x = 0 corresponding to 1920

According to the formula, what was the winning time in 1997?

first find the value of x;

x = 1997 - 1920 = 77 years

Nowing plugging the value of x in the function :

T = 46.97 - 0.099(77)

T = 46.97 - 7.623

T = 39.347 seconds

T = 39.35 s

Answer:

g(x)=3x(superscript)2

Answer:

g(x) = 3x².

Step-by-step explanation:

In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).

Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.

So, g(x) = 3x².

Hope this helps!

Answer:

ray df or ray fd because both of these letters are consecutive in both of the angles.  

Step-by-step explanation:

Answer:

Answer is Ray FD

Step-by-step explanation:

Given the following angles, what ray is the common side of ∠CFD and ∠DFE?

A. Ray FC

B. Ray FE

C. Ray FD

Answer:

C) 1

Step-by-step explanation:

First half:

Invert and multiply

x²/y²*y³/x²=x²y³/y²x³=y/x

Second half:

Invert and multiply

1/y*x/1=x/y

Combine

y/x*x/y=xy/xy=1

Answer:

Amy types at a rate of 50 words per minute

Step-by-step explanation:

In this question, we are interested in calculating the rate at which April is typing.

From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.

Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words

Now, from here, we can see that 2,500 words were typed in 50 minutes.

The number of words per minute will be ;

Total number of words/Time taken = 2500 words/50 minutes

That will give a value of 50 words per minute

180 degree

Step-by-step explanation:

supplementary means anhke havinv sum of 180 degree

so sum to two supplemrntary angles is 180 drgree

Supplementary angles always add to 180.

One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".

In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.

Answer:

mean is adding up all the numbers.

range means the difference between the Lowest and highest value.

Step-by-step explanation:

when we add the answer is 240.6.

divide it to 12..do the final answer is 20.05

range is 25.4_16.3

9.1

Answer:

Mean: 20.05

Range: 9.1

Step-by-step explanation:

To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.

20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3

= 240.6

Now, divide by the quantity which is 12 since there's 12 numbers.

240.6 divided by 12 = 20.05.

The mean is 20.05.

To find the range in the problem, you must subtract the smallest value from the largest value.

In this case, 16.3 is the smallest value and 25.4 is the largest.

25.4 - 16.3 = 9.1

9.1 is the range.

Hope this helps you!

Answer:

A=48.81

Step-by-step explanation:

it is a right angle triangle find the hypotenuse c using Pythagorean theorem:

c²=a²+b²

c²=8²+7²

c=√64+49

c=10.63

sin A =opp/hyp

sin A=8/10.63

A=  48.81

another way :

tan A=opp/adj

tan A=8/7

A=48.81

Answer:

[tex]\huge\boxed{a = b-5}[/tex]

Step-by-step explanation:

Let the number be a

So, the given condition is:

a = b-5

Answer:

[tex]\Huge \boxed{a=b-5}[/tex]

Step-by-step explanation:

Let the number be [tex]a[/tex].

[tex]a[/tex] is equal to 5 less than [tex]b[/tex].

5 is subtracted from [tex]b[/tex].

Answer:

10

Step-by-step explanation:

-3 = 7 - x

Add x to both sides

x -3 = 7 - x +x

x - 3 = 7

Now, add 3 to both sides

x - 3 + 3 = 7 + 3

x = 10

Answer:

[tex]\boxed{10}[/tex]

Step-by-step explanation:

[tex]-3=7- \sf BLANK[/tex]

[tex]\sf Subtract \ 7 \ from \ sides.[/tex]

[tex]-3-7=-7+7- \sf BLANK[/tex]

[tex]-10=- \sf BLANK[/tex]

[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]

[tex]-10(-1)=(-1)- \sf BLANK[/tex]

[tex]10= \sf BLANK[/tex]

Answer:

Option C. P = 3/q

Step-by-step explanation:

To know the the correct answer to the question, do the following:

Let us assume a certain number for P say 2 and 3, and then, find the corresponding value for q in each case to see which will give a decreased value for q.

Option A

When P = 2, q =.?

P = 3q

2 = 3q

Divide both side by 3

q = 2/3

When P = 3, q =.?

P = 3q

3 = 3q

Divide both side 3

q = 3/3

q = 1

From the above illustration, we can see that as P increase, q also increase.

Option B

When P = 2, q =.?

P – 3 = q

2 – 3 = q

q = – 1

When P = 3, q =.?

P – 3 = q

3 – 3 = q

q = 0

From the above illustration, we can see that as P increase, q also increase.

Option C

When P = 2, q =.?

P = 3/q

2 = 3/q

Cross multiply

2 × q = 3

Divide both side by 2

q = 3/2

q = 1.5

When P = 3, q =.?

P = 3/q

3 = 3/q

Cross multiply

3 × q = 3

Divide both side by 3

q = 3/3

q = 1

From the above illustration, we can see that as P increase, q decreases.

Option D.

When P = 2, q =.?

1/p = 3/q

1/2 = 3/q

Cross multiply

1 × q = 2 × 3

q = 6

When P = 3, q =.?

1/p = 3/q

1/3 = 3/q

Cross multiply

1 × q = 3 × 3

q = 9

From the above illustration, we can see that as P increase, q also increase.

Now, haven done the above, only option C gives a decreased value for q as the value of P increases.

c  

this before

Step-by-step explanation:

Answer: You are correct, it is the second option.

Step-by-step explanation:

Volume of a cylinder formula is: pi*r^2*h. The diameter is 6 and the radius is half the diameter so we get r=3. The height is 10 inches, so h=10. pi(3)^2(10) is the volume of the vase.

Volume of a sphere (marbles) formula is: 4/3*pi*r^3

The marbles have a diameter of 3 so 3/2=1.5. r=1.5.

The volume of the marbles is 8(4/3*pi*1.5^3).

Then you subtract the volume of the marbles from the volume of the vase to find the volume of the water in the vase.

pi(3)^2(10) - 8(4/3pi(1.5)^3)

Hope this helps. :)

Answer:

You are absolutely correct, second option is the correct answer.

Step-by-step explanation:

Diameter of vase = 6 inches

Therefore, radius r = 3 inches

Diameter of marbles = 3 inches

Radius of marbles = 1. 5 inches

Height of water h = 10 inches

Volume of water in the vase = Volume of vase - 8 times the volume of one marble

[tex] = \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\

= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\[/tex]

Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = [tex]x[/tex]

Given that total number of tickets = 300

So, number of student tickets = 300 - [tex]x[/tex]

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $[tex]15x[/tex]

Total collection from student tickets =  [tex](300-x)\times 11 = 3300-11x[/tex]

Given that overall collection = $3630

[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632

Answer:

2y+6x=180

Step-by-step explanation:

Because we know that side lengths BD, DC, and AD are all congruent, we can conclude that triangles BDA and CDA are congruent because they have at least two congruent sides. Since these triangles are both 45-45-90 triangles, angle C is equal to 45 degrees, or 3x. 45/3 is 15, so x=15. Angle B is equal to 45 degrees, or y, so y=45.

From there, we plug these numbers into the equation with 2(45) + 6(15), or 90+90 = 180.

Answer:

That’s ez pz

Step-by-step explanation:

Answer:

The slope is -3 and the y intercept is -44

Step-by-step explanation:

6X+ 2Y= -88

The slope intercept form of a line is y= mx+b where m is the slope and b is the y intercept

Solve for y

6X-6x+ 2Y= -88-6x

2y = -6x-88

Divide by 2

y = -3x -44

The slope is -3 and the y intercept is -44

Answer:

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]

Answer:

box 1 and box2 are correct.

Answer:

2987.

Step-by-step explanation:

25(23) + 67(36) = 575 + 2412 = 2987.

Hi there! Hopefully this helps!

------------------------------------------------------------------------------------------------------------

Answer: 2987

First we need to rewrite the equation. Since x = 23 and y = 36 the equation should look like this for easier steps:

25(23) + 67(36) = ?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now since there numbers by other numbers in parentheses, we need to multiply them.

25 x 23 = 575.

67 x 36 = 2412.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now that the equation is in its final form, we write it like this for the answer:

575 + 2412 =

THIS IS THE COMPLETE QUESTION BELOW;

Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.

Last week: walked 18 miles in 6 hours

This week: d = 2.5h

Which statement must be true?

A.This week, she walked a greater distance.

B. Last week, she walked a greater distance

C. This week, she walked at a faster pace.

D. Last week, she walked at a faster pace

Answer

OPTION B is correct

B)Last week, she walked a greater distance

Step-by-step explanation:

We were told Rosemary walks each week for exercise.

From the question,

✓d represented the distance walked

✓h represent the number of hours spent walking.

A)Last week: she walked 18 miles in 6 hours

Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)

= 3 miles per hour

B)This week: d = 2.5h

This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.

So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.

Therefore, OPTION B is correct, (Last week, she walked a greater distance)

Answer:

It's b

Step-by-step explanation:

Answer:

i think 60 parts of blue paint are in the can.

Step-by-step explanation:

ratio should be equal in both cases

therefore,let blue part in second case be x(suppose)

5÷4=75÷x

by equating this we will be able to identify the value of x

and the value of x comes 60 which is the required answer....

hope this will help you..

i try my best to give correct answer..

if i am mistake, i am sorry for that...

Answer:

Manuel made his first mistake in step 2 leading to the continuous mistakes

Final answer=185

Step-by-step explanation:

Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.

2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)

Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)

Step 2: -40 - 75 + 100 +

200

Step 3: -115 + 300

Step 4: 185

Manuel made his first error in step 2 by combining two different terms into one as he has done

(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)

Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)

Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405

He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.

Answer:

We know that our triangle has one side along the line:

y = (1/4)*x

And other side along the line:

y = -(1/4)*x.

Now, we want to find the vertex.

And we know that the vertex is the point where the two sides conect, so the vertex must be a common point of both lines.

Then we have:

y = (1/4)*x = -(1/4)*x

x = -x

The only solution to that equation is x = 0.

now we evaluate our lines in x = 0 and get:

y = (1/4)*0 = 0

y = -(1/4)*0 = 0

Then the lines intersect in the point (0, 0)

Then the vertex must be in the point (0, 0)

Answer:

£22.40

Step-by-step explanation:

60% of 12 is 7.2 (you can also write it as 7.20) so you times that by 2 to get 14.4 (you can also write it as 14.40) and [tex]\frac{1}{3}[/tex] of 24 is 8, so you add that to the 14.4 and you get 22.4 (also writen as 22.4) hope this helps!

Answer:

Step-by-step explanation

Answer:

2 1/3 cupcakes

Step-by-step explanation:

A cupcake can make 3 four cups of flour

In 8 fourteen cups of flour, require (14 X 4)/(3 X 8) of cupcakes

  = 56/24 = 2 1/3 cupcakes

Answer:

y = 6x - 2

Step-by-step explanation:

slope-intercept form: y = mx + b

Note that:

m = slope = 6

b = y-intercept = -2

x = (x , y)

y = (x , y)

Plug in the corresponding numbers to the corresponding variables:

y = 6x + (-2)

y  = 6x - 2

y = 6x - 2 is your answer.

~

Answer:

y = 6x-2

Step-by-step explanation:

The slope intercept equation  form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 6x-2

Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.

[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.

The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.

To prove that, The square of the sum of two consecutive integers is odd.

The expression to prove is,

Let us assume that two consecutive integers are n and (n + 1).

Hence, the expression is written as,

[n + (n + 1)]² = (2n + 1)²

= (2n)² + 2 × 2n × 1 + 1²

= 4n² + 4n + 1

= 2 (2n² + 2n) + 1

= odd

Therefore, the number in the blanks are 2 and 2.

To learn more about the Number system visit:

https://brainly.com/question/17200227

#SPJ4

Answer:

-7/2

Step-by-step explanation:

cuz thats right