Answer:
[tex]120^{0}[/tex]
Step-by-step explanation:
Given: pentagon (5 sided polygon), two interior angles = [tex]90^{0}[/tex] each, other three interior angles are congruent.
Sum of angles in a polygon = (n - 2) × [tex]180^{0}[/tex]
where n is the number of sides of the polygon.
For a pentagon, n = 5, so that;
Sum of angles in a pentagon = (5 - 2) × [tex]180^{0}[/tex]
= 3 × [tex]180^{0}[/tex]
= [tex]540^{0}[/tex]
Sum of angles in a pentagon is [tex]540^{0}[/tex].
Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;
[tex]540^{0}[/tex] - (2 × [tex]90^{0}[/tex]) = [tex]540^{0}[/tex] - [tex]180^{0}[/tex]
= [tex]360^{0}[/tex]
So that;
the measure of the interior angle = [tex]\frac{360^{0} }{3}[/tex]
= [tex]120^{0}[/tex]
The measure of one of its three congruent interior angles is [tex]120^{0}[/tex].
Prove that angle ABD is congruent to angle CBE
with solution!
ANSWER:
the conditions are the angle a is equal to angle c and ab = bc . Hence we need to prove that the triangles is congruent to the triangle cbe. ... angle A =angle C and AB=BC.
If =x/y=5/8
then x/5=
[tex]\dfrac{x}{y}=\dfrac{5}{8}\Big|\cdot\dfrac{y}{5}\\\\\dfrac{x}{5}=\dfrac{y}{8}[/tex]
Answer:
x/5 = y/8
Step-by-step explanation:
x 5
----- = -------
y 8
Using cross products
8x = 5y
Divide each side by 8
x = 5/8 y
Divide each side by 5
x/5 = y/8
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point) [tex]y=\frac{7}{x^{2} } +10[/tex]
Answer:
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Step-by-step explanation:
Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:
[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]
[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]
Thus,
[tex]f(x) = 7\cdot x + 10[/tex]
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Sally is now 10 years older than Suki. 5 years ago, the sum of their age was 40. How old are they now?
Answer:
Sally is 30 and Suki is 20
Step-by-step explanation:
x = Sally's age
y = Suki's age
x = 10 + y
(x - 5) + (y - 5) = 40
x = 30, y = 20
A bus travels from Station A to Station B, and a truck travels from Station B to Station A on the same road. The speed of the bus is 54 km/h, and the speed of the truck is 48 km/h. After they pass each other, they continue drive to the destinations. Once they reach the destination, they turn around to continue travel along the same road. When they meet again, the bus travels 216 km more than the truck. What is the distance between the two stations in kilometers?
Answer:
The distance between the two train stations is 1728 km
Step-by-step explanation:
The speed of the bus = 54 km/h
The speed of the truck = 48 km/h
When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck
Let the distance between the two train stations = x
Let the location where they first meet be y from station A we have;
The location where they meet again = y - 216 km
Therefore, we have;
Location where they
The time for the truck and the bus to meet again = t
Therefore, 54 × t - 48 × t = 216 km
6·t = 216 km
t = 36 hours
Therefore, the time for the bus to travel x + 216 km = 36 hours
54 × 36 = 1944 = x + 216
x = 1944 - 216 = 1728 km
The distance between the two train stations = 1728 km.
Initial Knowledge Check
Question 2
Suppose that $4000 is placed in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year
sc
(b) Find the amount in the account at the end of 2 years.
?
Answer:
Step-by-step explanation:
We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation
[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where
(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:
[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to
[tex]A(t)=4000(1.11)^t[/tex]
Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.
When t = 1:
A(t) = 4000(1.11) so
A(t) = 4440
When t = 2:
[tex]A(t)=4000(1.11)^2[/tex] which simplifies to
A(t) = 4000(1.2321) so
A(t) = 4928.40
I NEED HELP ASAP ITS FOR MY SCHOOL WORK AND I CANT FIGURE THIS OUT
Answer:
28.
megabyte- [tex]10^6[/tex]
terabyte- [tex]10^{12}[/tex]
gigabyte- [tex]10^9[/tex]
For [tex]10^6, 10^9, 10^{12},[/tex] and [tex]10^{15}[/tex], put the 1, and add the exponent # of 0s.
29.
The cube is 6×6×6 or 216 in. It would be 6³, because the 6 is multiplied 3 times.
30.
a. 10
b. 5120
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:
Question 28
megabyte: 10⁶
terabyte: 10¹²
gigabyte: 10⁹
Question 29
6³
Question 30
a. 20
b. 5,120
Thirteen people on a sports team show up for a game. a. How many ways are there to choose 10 players to play the game? b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?
Answer:
a)286 ways
b)1,037,836,800 ways
Step-by-step explanation:
a. How many ways are there to choose 10 players to play the game?
We have to take note of a key word here which is CHOOSE. For question a, order does not matter.
Hence, we use the combination formula. This is given as:
C(n, r) = nCr = n!/r! (n - r)!
n = 13, r = 10
13C10 = 13!/10! (13 - 10)!
= 13!/ 10! × (3!)
= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (3 × 2 × 1)
= 1716/6
= 286 ways.
b. How many ways are there to assign the 10 different positions by selecting players from the 13 who show up?
For question b as well, we take note of a key word which is ASSIGN. For question b, order is very important.
Therefore, the formula we use is the permutation formula.
P(n, r) = nPr = n!/(n - r)!
n = 13, r = 10
13P10 = 13!/ (13 - 10)!
= 13!/ 3!
= 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / (3 × 2 × 1)
= 1,037,836,800 ways
How to do this question plz answer my question plz
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!
17/7=3x + 2(5) / 3x - 2(5)
A group of 6 people planned to spend $10.00 each to
rent a boat for an outing. At the last minute, 1 person
could not go on the outing. The others then paid
equally for the boat. How much did each pay?
Answer:
the ansser is $12
Step-by-step explanation:
becases 10 *6 is equal to 60 so if 1 person can not pay then you divide 60 by the remaineing 5 to get 12
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. Each person have to pay 12 dollars.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. At the last minute, 1 person could not go on the outing.
10 x 6 = 60
So if 1 person can not pay then
We will divide 60 by the remaining 5
60/ 5 = 12
Therefore, Each person have to pay 12 dollars.
Learn more about unit price here:
https://brainly.com/question/945712
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kim places £500 in a bank account the pays 3% simple interest each year
how much interest will she earn each year?
how much will she have in her account after 1 year
Andrew is an avid archer. He launches an arrow that takes a parabolic path.
The equation of the height of the arrow with respect to time is
y = -4.9x2 + 48x, where y is the height of the arrow in meters above
Andrew's bow and x is the time in seconds since Andrew shot the arrow.
Find how long it takes the arrow to come back to a height even with his bow
height.
Answer:
9.7959 sec
Step-by-step explanation:
For the arrow to reach the same height as the bow again, - 4.9x^2+48x=0, 48=4.9x, x=48/4.9=9.7959
The time arrow take to come back to a height even with his bow height is 9.79 seconds.
We have an equation of the height of the arrow with respect to time -[tex]y = -4.9x^{2} +48x[/tex] where y is the height of the arrow in meters above Andrew's bow and x is the time in seconds since Andrew shot the arrow.
We have to find out - how long it takes the arrow to come back to a height even with his bow height.
The motion of arrow in the above situation is an example of which type of motion?It is an example of two - dimensional Projectile motion.
We have the function that depicts the variation of height of the arrow with respect to time given by -
[tex]y=-4.9x^{2} +48x[/tex]
To find the time taken by the arrow to come to a height even with his bow height, we should equate y = 0.
[tex]y=-4.9x^{2} +48x=0\\-4.9x(x-9.79)=0\\-4.9x=0\;\;\;and\;\;\;x-9.79=0\\x =0\;\;\;and\;\;\;x=9.79[/tex]
Time cannot be 0, hence the time arrow take to come back to a height even with his bow height is 9.79 seconds.
To solve more questions like these, visit the link below -
https://brainly.com/question/13630358
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Which of these functions could have the graph shown below?
O A. f(x) = e^30x
O B. f(x) = 30^30x
O C. f(x) = 30^x
O D. f(x) = 30e^x
The functions could have the graph shown below will be y = 30eˣ. Then the correct option is D.
What is an exponent?Let a be the initial value and x be the power of the exponent function and e be the increasing factor.
The exponent is given as
y = a(e)ˣ
From the graph, the value of the exponent function at x = 0, will be 30.
Then the function will be
30 = a(e)⁰
30 = a
Then the exponent function is given as,
y = 30eˣ
Thus, the functions could have the graph shown below will be y = 30eˣ.
Then the correct option is D.
More about the exponent link is given below.
https://brainly.com/question/5497425
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I'LL GIVE BRAINLIEST !!! FASTERR !
Answer:
Option A, 86°
Step-by-step explanation:
each diagonals of a rhombus divides the angles at half, so a+b+c+d = 360°/2 = 180°
now, a+b+c+d-94° = 180°-94° = 86°
Answer:
D 266°
Step-by-step explanation:
a+b+c+d-94°
90°+ 90°+ 90°+ 90° -94°
360°-94°
266°
solve for x 13x + 7 = 5x - 20
Answer:
13x + 7 = 5x - 20
Step-by-step explanation:
SOLVE for X
13x + 7 = 5x - 20
-------------------------
-5x -7
------------------------
8x=-27
x= -3.375 or -27/8
Answer:
x = -27/8
Step-by-step explanation:
combine the x terms. To do this, subtract 5x from both sides. We get:
8x + 7 = -20.
Next, subtract 7 from both sides, obtaining:
8x = -27, or x = -27/8
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer: 280 tons
Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons
Answer: 10 ships
Step-by-step explanation:
Is the quotient of a rational number and
an irrational number always irrational?
Explain.
HELP ASAP
Answer = No,It can be either rational or irrational.
________________________________
Prroof —
4 ÷ √8 = √2 { Which is an irrational number }
________________________________
Now, Here comes a twist,
We know that — 0 is a rational number.
And, 0 ÷ √56666 = 0 ________________________________
Note—
But, √56666 ÷ 0 = Error ( Lol )
________________________________
What is the simplified expression for 22 • 2?
24
O 20
021
O 22
0 23
2^1 would be the answer.
2^2 x 2^3 is 32
2^4 is 16
32/16 is 2
2^1 is 2 so the answer is 2^1
Answer:
2¹
Step-by-step explanation:
When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.
The equation of C is (x - 2)^2 + (y - 1)^2 = 25. Of the points P(0,5), Q(2,2) R(5,-2), and S(6,6), which point is located outside the circle?
Answer:
( 6,6) is outside
Step-by-step explanation:
(x - 2)^2 + (y - 1)^2 = 25
This is of the form
(x - h)^2 + (y - k)^2 = r^2
where ( h,k) is the center and r is the radius
(x - 2)^2 + (y - 1)^2 = 5^2
The center is at ( 2,1) and the radius is 5
P(0,5), Q(2,2) R(5,-2), and S(6,6)
Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)
( 6,6) is outside the circle
A square of side 40 cm and a rectangle of length 50 cm has the same perimeter. Which has greater area? Please write the answer with steps.
Answer:
[tex]\huge\boxed{The\ area\ of\ square\ is\ greater.}[/tex]
Step-by-step explanation:
Perimeter of Square:
P = 4(Length)
P = 4(40)
P = 160 cm
This means that the rectangle also has a perimeter of 160 cm
So, Finding the width of rectangle by Perimeter formula:
2L + 2W = Perimeter
2(50) + 2W = 160
100 + 2W = 160
Subtracting 100 to both sides
2W = 60
Dividing both sides by 2
W = 30
Now, Area of Square:
Area = Length * Length
Area = 40 * 40
Area = 1600 cm²
Area of Rectangle:
Area = Length * Width
Area = 50 * 30
Area = 1500 cm²
When we compare both of the area of the figure, we come to know that the area of square is greater.
If a ray bisects a right angle, then each newly formed angle measures 45 degrees.
A) Sometimes
B) Always
C) Never
Answer:
Always
Step-by-step explanation:
Bisects means to divide in half
90/2 = 45
So the angles are each 45 degrees
Fogoh!! Plz HELPi suck at math haha
Answer:
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
Step-by-step explanation:
f(x) = x^4 + 4
g(x) = x - 1
h(x) = sqrt(x)
g(h(x)) = sqrt(x) - 1
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
the length of rectangle is 6/5 of its breath and perimeter is 132 m find area of rectangle
Answer:
1,080 meters squared.
Step-by-step explanation:
Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.
The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.
2(x) + 2(6/5x) = 132
2x + 12/5x = 132
10/5x + 12/5x = 132
22/5x = 132
22x = 660
x = 30.
That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.
The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.
Hope this helps!
What is the unit rate 25 for $50.00
Answer:
1/2
Step-by-step explanation:
For every 1 item bought, $2.00 are spent.
Brainliest please!
Answer:
1/2
Step-by-step explanation:
Unit rate is the division of two things where the quantity of an object is divided over the units.
25 / 50 = 1/2
So, the unit rate is 1/2.
Hope this helped.
How did you solve 43? I need explanation I’ll give brainliest
Answer:
Its 6
Step-by-step explanation:
Answer:
C. 4
Step-by-step explanation:
There are a total of 24 marbles. If you take out 8 of them, that leaves you with 16 marbles left. After doing that, if the chances of withdrawing a white marble are now 1/4, then there would have to be 4.
4/16 = 1/4
Hikes a location 27 meters above sea level. Brain hikes to a location 21 meters below sea level. Write an integer yo represent each hiker location with respect to sea level
Answer:
The number describing its location of Melissa to the sea-level is= 27
The number which would be the position of Brian to the sea-level is = -21
Step-by-step explanation:
The number may be negative, positive, or zero.
Let the sea level be 0.
They realize that the location of Melissa is 27 meters and above the sea-level, per the relevant information given throughout the exercise.
It also may assume that it's numerical representing its position becomes greater than zero throughout terms of sea-level (this means that it is positive).
It would then be= 27
The place of Brian is 21 m away from the sea.
The integer of its location is less than zero (negative), as regards the amount of the sea.
It is, therefore= -21
The inequality 1 ≤ 2x − 5 is true for all values of x in which of the following sets?
1. 0, 1, and 2
2. 1, 2, and 3
3. 2, 3, and 4
4. 3, 4, and 5
Answer:
4. 3, 4, and 5
Step-by-step explanation:
1 ≤ 2x − 5
Add 5 to each side
1+5 ≤ 2x − 5+5
6 ≤ 2x
Divide by 2
6/2 ≤ 2x/2
3 ≤ x
x must be greater than or equal to 3
Factor 8(9) + 18
8(9+18)
9(8+2)
18(4+1)
18(1+4)
[tex]8(9)+18[/tex]
$=8\cdot9+2\cdot9$
$=(8+2)\cdot9$
Point M is on line segment LN. Given MN=2 and LM=4, determine the length LN.
Answer:
LN = 6
Step-by-step explanation:
Since M is on LN, then
LN = LM + MN = 4 + 2 = 6
Answer:
[tex]\huge \boxed{6}[/tex]
Step-by-step explanation:
Point M is on the line segment LN.
LM = 4
MN = 2
LN = LM + MN
LN = 4 + 2 = 6