Pythagorean Theorem Quiz.
1.) Find the unknown side length. Simplify answers that are radicals.
4
3
2.) Find the unknown side length. Simplify answers that are radicals.
16
12
Answers
Answer:
1.) 5 2.) 10.58
Step-by-step explanation:
For each one, you use the equation a^2 + b^2 = c^2 where c is the "hypotenuse"-- the side of the triangle opposite (facing) the right angle which is shown with a small box. The variables a and b do not matter, as long as they are the "legs", the other 2 sides.
So it is 4^2 + 3^2 = c^2 which simplifies to 16+9=25=c^2 and square root both sides and you get c=5
and 12^2 + b^2 = 16^2 which simplifies to 144+ b^2 = 256 and subtract 144 from both sides and you get b^2 = 112 and square root both sides and it is approximately 10.6 :)
Related Questions
if two fair coins are tossed simultaneously, what are the chances of both coming up 'heads'?
Answers
Answer:
i think 1/4
Step-by-step explanation:
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
We name the coins coin 1 and coin 2 for the sake of simplicity.
There are four possible situations:
coin 1 head, coin 2 head
coin 1 head, coin 2 tails
coin 1 tails, coin 2 head
coin 1 tails, coin 2 tails
Only case 1 results in both 'heads'. So the probability is 1/4.
A large tank is partially filled with 100 gallons of fluid in which 40 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 30 minutes. (Round your answer to two decimal places.
Answers
Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]
[tex]R_{in} =3 \ lb/min[/tex]
At a slower of 4 gal/min, the solution gets pumped out;
So,
[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]
[tex]R_{out} = \dfrac{2A}{50+t }[/tex]
The differential of the equation is:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]
For the linear differential equation, the integrating factor is determined as:
[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]
[tex]= (50+t)^2[/tex]
Multiplying [tex](50+t)^2[/tex] with the above integration factor;
[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]
[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]
[tex](50+t)^2 A = (50 +t)^3 + c[/tex]
[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]
[tex]A(30) = 76.09 \ pounds[/tex]
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
........................
Answers
Answer:
Step-by-step explanation:
Figure (1)
x° = 107° [Vertically opposite angles]
Since, vertical angles are equal in measure.
Figure (2)
x + 71° = 90° [Given, complementary angles]
x = 90° - 71°
x = 19°
Figure (3)
x + 21° = 180° [Given as supplementary angles]
x = 180° - 21°
x = 159°
Figure (4)
x = 129° [Vertical angles]
Figure (5)
x° = 90° [Given]
z° + 34° = 90°
z° = 90° - 34°
z° = 56°
Since, x° + y° + z° = 180° [Linear angles]
90° + y° + 56° = 180°
y° + 146° = 180°
y° = 180° - 146°
y° = 34°
Given the coordinates, determine whether PQR & XYZ are congruent
P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)
PQ=
XY=
QR=
YZ=
PR=
XZ=
Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.
Answers
Answer:
The triangles are congruent
Step-by-step explanation:
Given
[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]
Required
Determine if PQR = XYZ
To do this, we make use of distance formula.
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For PQ:
[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]
So:
[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]
[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]
[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]
[tex]PQ = \sqrt{64+121}[/tex]
[tex]PQ = \sqrt{185}[/tex]
For XY:
[tex](x_1,y_1) = (-2,-1)[/tex]
[tex](x_2,y_2) = (9,7)[/tex]
So:
[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]
[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]
[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]
[tex]XY = \sqrt{121+64}[/tex]
[tex]XY = \sqrt{185}[/tex]
For QR:
[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]
So:
[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]
[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]
[tex]QR = \sqrt{(3)^2 + 25}[/tex]
[tex]QR = \sqrt{9 + 25}[/tex]
[tex]QR = \sqrt{34}[/tex]
For YZ:
[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]
So:
[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]
[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]
[tex]YZ = \sqrt{36+25}[/tex]
[tex]YZ = \sqrt{61}[/tex]
For PR:
[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]
So:
[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]
[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]
[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]
[tex]PR = \sqrt{25+36}[/tex]
[tex]PR = \sqrt{61}[/tex]
For XZ:
[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]
So:
[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]
[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]
[tex]XZ = \sqrt{5^2+3^2}[/tex]
[tex]XZ = \sqrt{34}[/tex]
From the calculations above:
[tex]PQ = XY = \sqrt{185[/tex]
[tex]QR = XZ = \sqrt{34[/tex]
[tex]PR = YZ = \sqrt{61[/tex]
Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)
50 POINTS PLEASE HELP!!!!!!!!!!!!!
On average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes. Which absolute value equation can be used to calculate Carter's maximum and minimum time to get ready? Let x represent the maximum and minimum time.
|x−15|=25
|x+15|=25
|x+25|=15
|x−25|=15
Answers
Answer:
i thinking a or d
Step-by-step explanation:
The absolute value equation is |x+15|=25. Therefore, option B is the correct answer.
What is a absolute value equation?To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.
Given that, on average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.
Let x represent the maximum and minimum time.
So, the absolute value equation is |x+15|=25
Therefore, option B is the correct answer.
To learn more about a absolute value equation visit:
https://brainly.com/question/2166748.
#SPJ2
Question 1 (3 points)
(6.03)
Which expression shows a sum of three terms? (3 points)
O a
x3
3 + x + 3
Ob
ос
3x
Od
3(x + 3)
Answers
Answer:
more context please:)
Step-by-step explanation:
Answer:
3 + x + 3
Step-by-step explanation:
Hope it helps!
A manager of a clothing store always orders 2 small T-shirts and 3 large T-shirts for
every 4 medium T-shirts. The manager plans to order 24 medium T-shirts. How
many small T-shirts and large T-shirts should the manager order? Show your work.
Answers
Answer:
12 small, 18 large
Step-by-step explanation:
x - small
y - large
z- medium
4z=2x=3y then she orders 24
24/4=6 times more than usually, so we should *6 for every x and z
24z=6*2x=6*3y
12 - x - small tshirt
18 - y - large
6.) Which is the best description of the equation
below?
2x-2y=6
Answers
A Cause I'm big brain and we learned that
what is 4 1/2-3 5/6 from page 393 GO Math book
Answers
Answer:
The answer is 1/6
Step-by-step explanation:
This is the answer because it is.
This is the answer because
can some one please help me please
Answers
Answer:
x = 65.4
Step-by-step explanation:
I solved this question already. My explanation is here: https://brainly.com/question/20456072
Hope this helped! <3
please help if u can! :)))
Answers
Help me please thanks
Answers
Answer:
y=x+4
Step-by-step explanation:
Slope intercept is y= mx+b
The slope is rise/run or change in y/change in x. Here the slope is 1 since when y goes up1, x goes to the right 1 (1/1=1).
The y intercept is 4 since it hits the y axis at 4.
so it would be y= 1x+4 which is y=x+4
10p - 3p-2/4+5 when p = 10
*I'm in 5th grade pls help*
Answers
Answer:
10(10)-3(10)-2/4+5=149/2 (decimal 74.5)
How do I do this?
My son school just gave him this and he doesn’t know how to do it and I don’t know.
Answers
Answer:
I would just search online what are corresponding angles and then base it off of angles like angle number 4 is corresponding because corresponding angles are just angles with the same size and same line
The corporate team building ecent will cost $6 if it has 3 attendees. if there are 8 attendees how much will the corporate team building event cost?
Answers
Answer:
The team building event will cost $24 for 4 attendees.
Step-by-step explanation:
Given,
Cost charged corporate team building = $6 for every attendee
Number of attendees = 4
We will multiply the amount of one ticket with number of attendees in order to find the total cost.
Cost charged for 4 attendees = 6*4
Cost charged for 4 attendees = $24
3 digit number
when it is divided by 9 the remainder is 3
Answers
Answer:
Mabey 102 try that.
Step-by-step explanation:
Hope this helps!
John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for different hours? (1 point)
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,10 and 2,20 and 3,30.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 50 and 2,50 and 3,50.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 5 and 2,10 and 3,15.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,20 and 2,40 and 3,60.
Answers
Answer:
Graph A <==
Step-by-step explanation:
$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr
so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.
So ur x axis will be the hours and your y axis will be the total cost.
so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6
the y axis (the vertical axis)...since it is the total cost, will be labeled
0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)
help asap no trolls pls!!
Answers
Answer:
U
Step-by-step explanation:
Answer:
V
Step-by-step explanation:
Sum of angles in a triangle = 180°
66c + 40c +74c = 180°
106c + 74c =180
180c = 180
c=1
Side v is the largest
Select all of the equations where x = 3 is a solution.
A.7x - 2 = 19
B.5x = 15
C.5x + 6 = 21
D.2x=5
E.3x = 33
F.3x = 1
Answers
Answer:
x=3 in equation ;5x=15 and in equation C.
What’s 2*4 equal to in a Meath knowledge
Answers
Answer: 8
Step-by-step explanation:
I think the answer is 8
Need done ASAP 25 points!!!!!!!!
Answers
Answer:
Step-by-step explanation:
A
2y-x=8 and y-2x=-5. Solve the system of equations
Answers
Answer:
y = 7 x = 9
Step-by-step explanation:
2y-x=8
2(2y-x=8)
4y-2x=16
-(y-2x= -5)
3y +0x= 21
3y=21
y=7
2(7)-x=8
14-x=8
9=x
Which expression is equivalent to 4x4x4x4x4
Answers
Answer:
Step-by-step explanation:
4x4x4x4x4=4^5=1024
How can you rewrite -8 -− 10 as an addition problem?
A:-8- -10
B -8+10
C-8+18
D-8+ -18
Answers
Answer:
B. -8+10
Step-by-step explanation: keep the -8 change - sign to +sign then change -10 to 10 .
Hope it helps :)
please help I am stuck... Liner equations & graphs!!!
Answers
Answer:
T is correct (the fourth answer)
Step-by-step explanation:
Step-by-step explanation:
I believe it's graph T..
I WILL BRAINLIEST PLS HELP ME I NEED HELP PLS ,
If 2 cm = 5 ft, what is the area of the playground?
Answers
Answer:
Step-by-step explanation:
Ok so
2 cm is 5 feet and there are 24
2 = 5
4 = 10
6 = 15
8 = 20
10 = 25
11 = 30
So for this one there are about . 10 feet at the top and 8 feet for the other
Answer:
The scale of the drawing is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale drawing
x-----> the area of the playground in the scale drawing
y----> the area of the actual playground
we have
substitute
simplify
or
Divide by 4 both numerator and denominator
PLEASE HELP ME IN SUPER CONFUSED!
Represent the following sentence as an algebraic expression, where "a
number" is the letter x. You do not need to simplify.
Twice the difference of a number and 3.
Answers
Answer:
x-3*2
Step-by-step explanation:
ASAP HELP!! sorry the photo is bad it’s the lighting but please help
Answers
Answer:
3
Step-by-step explanation:
Find the value of each.
4 boxes of pasta at $1.25 each
Answers
Answer:
The total of all the boxes would be $5.00.
ons: Practice
Question 5 of 5
Type the correct answer in the box. Use numerals instead
What value of x makes this equation true?
X/6 - 7 = -4
Answers
Answer:
[tex]x = 18[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{6} - 7 = -4[/tex]
Required
Solve for x
[tex]\frac{x}{6} - 7 = -4[/tex]
Add 7 to both sides
[tex]\frac{x}{6} - 7+7 = -4+7[/tex]
[tex]\frac{x}{6} = -4+7[/tex]
[tex]\frac{x}{6} = 3[/tex]
Multiply through by 6
[tex]6 * \frac{x}{6} = 3 * 6[/tex]
[tex]x = 3 * 6[/tex]
[tex]x = 18[/tex]