The vertices of the polygon form a trapezoid, and the area of the polygon is 28 unit squares
How to determine the area of the polygon?The vertices are given as:
C = (3,3)
A = (8,-2)
S = (3,-4)
H = (0, -2)
The area of the polygon is calculated using:
[tex]A = \frac 12 \sum\limits^{n-1}_{k = 0}(x_ky_{k+1} - y_kx_{k+1})[/tex]
So, we have:
A = 1/2 * |(3 * -2 - 8 * 3 + 8 * -4 - 3 * -2 + 3 * -2 - 0 * -4 + 0 * 3 -3 * -2)|
Evaluate
A = 1/2 * |-56|
Remove the absolute bracket
A = 1/2 * 56
Evaluate the product
A= 28
Hence, the area of the polygon is 28 unit square
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Find the area of the sector of the circle.
A)40π
B)200π
C)60π
D)300π
Answer:
the answer is D) 300 π
Step-by-step explanation:
Formula for Area of sector is:
θ/360° * π * (r)^2
here,
θ= 30° and radius= 60 in
so, after we substitute, we get:
30/360* π* 60*60 after simplifying we get:
= 1/12* π* 5*60
=300π
Hope it helps.
Answer:
D
Step-by-step explanation:
area of sector=
[tex] \frac{theta}{360} \times \pi \: r {}^{2} \\ \\ \frac{30}{360} \times \pi \: (60) {}^{2} \\ \\ 300\pi[/tex]
360
A vending machine that takes only dimes and
quarters contains 30 coins, with a total value of
$4.20. How many of each coin are there?
Determine the length of the missing side.
Answer:
5
Step-by-step explanation:
pythagorean triple is 5-12-14 or use pythagorean theorem
b=[tex]\sqrt{ 13^{2} -12^{2} }=\\\sqrt{169-144} =\\\sqrt{25} =5[/tex]
Answer: 5
Step-by-step explanation: The square root of 13²- 12²
Sally's soccer team played 25
games this season and lost 9 of
those games. What percent of the
games did the team win?
Answer:
64%
Step-by-step explanation:
25 - 9 = 16, so 16 of the games were won by Sally's team.
16/25 = 64% of the games were won
The graph of a linear function is shown on the grid.
Which equation is best represented by this graph?
Answer:
C
Step-by-step explanation:
Because thats the answer
pls help with this maths question... feels like I'm missing something easy ;/
Answer:
10.34 cm.
Step-by-step explanation:
First we need to calculate the angle between the hour and minute hand
We see that there are 5 * 5-minute intervals between the 2 hands and the clock has 12 * 5-minute intervals, so:
This is 5/12 * 360 = 150 degrees,
So we apply the Cosine Rule to the triangle:
x^2 = 4.5^2 + 6.2^2 - 2*4.5*6.2cos150
= 107.014
x = √107.14 = 10.34.
Missing length is 10.3cm to 1.d.p
The clock is a circle divided into 12
360/12=30 degrees for each part
1) 7 to 8
2) 8 to 9
3) 9 to 10
4) 10 to 11
5) 11 to 12
5 parts
30 x 5 = 150 degrees
We've got an angle between 2 lengths - cosine rule comes to mind for me.
a = root 6.2^2 + 4.5^2 - 2x6.2 4.5 x cos 150
= 10.34476764
length is 10.3cm to 1.d.p
(the others are to 1.d.p too)
Hope this helps!
In 2010, Cameron invested $10,000 in an account that earns 8. 5% interest compounded monthly. How much money would Cameron have gained by 2025?
Answer:
Step-by-step explanation:
First, we need to calculate how many years will earn percent.
2010---->2025= 15 years elapsed. Now we have our time, we need to plug it in our compound interest formula=
Principal(rate+1)^time or A=P(1+R)^t
10,000(0.085+1)^15
=$33,997.43
To calculate how much Cam earned, you need to subtract from original amount.
=$33,997.43-10,000=
---->$23997.43
Please mark me brainiest :)
A notebook costs £1.60, a pen costs 37p, a pencil costs 21p and a sharpener costs 86p.
Remi buys 3 pencils, 2 pens, 3 sharpeners and some notebooks.
He pays with £8 and receives 85p change.
How many notebooks did he buy?
notebooks
Answer:
2
Step-by-step explanation:
£1 = 100p
3*21p+2*37p+3*86p+x*160p (x is the number of notebooks)
63p+74p+258p+x*160p = 395p+x*160p
He paid £8 so he paid 800p
800p-395p = 405p
405p-85p = 320p
320p:160p = 2
He bought 2 notebooks
Can you please help me really quick I need help with this
Check the picture below.
Tisha and her scout troop are heading to the Swing Time zipline park. They plan to purchase
the group package. With the package, the cost per person is $5 less than the normal cost for
an individual. There are 12 scouts in Tisha's troop. Her troop leader called ahead and found
that the total cost for the group will be $150. What is the normal cost for an individual?
Answer:
$17.5
Step-by-step explanation:
divide 150 by 12 to get 12.5. 12.5 is what they paid per-person with the discount. add 5 to get 17.5 and that is the on-discounted price
The normal cost for an individual is $17.50.
Let's denote the normal cost for an individual as "N."
According to the given information, with the group package, the cost per person is $5 less than the normal cost for an individual. So, the cost for each scout in Tisha's troop is "N - $5."
There are 12 scouts in Tisha's troop, so the total cost for the group is given as $150.
We can set up an equation based on the total cost:
Total Cost = Cost per Person × Number of People
$150 = (N - $5) × 12
Now, let's solve for the normal cost for an individual (N):
$150 = 12N - $60
12N = $150 + $60
12N = $210
N = $210 / 12
N = $17.50
So, the normal cost for an individual is $17.50.
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A sample of students is taken from the school's A honor roll. The school
estimates that there are 360 students on the A honor roll. Using this sample,
how many students on the A honor roll are 8th graders?
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
The tank of a car holds 10 gallons of gas.
How many liters does the tank hold? Round to the nearest tenth.
Answer:
37.9 liters
Step-by-step explanation:
Multiply the number of gallons by 3.785 to convert to liters
Multiplying by ten moves the decimal point over to the right
3.785 * 10 = 37.85
The tenths place is where the 8 is, and since 5 is [tex]\geq[/tex] (greater than or equal to) 5 that makes the 8 round up to a 9
resulting in...
10 gallons = 37.9 liters
hope this helps:)
Every day when Brandon arrives at work he must decide to either take the stairs or use the elevator to get to his office on the third floor. What type of decision is this
Answer:
would you rather, i think
Which of the following functions has a rate of change that stays the same?
A:y = 4x+10
B:y=-4x+10
C:y = 3^x
D:y = x² + 2
Answer:
C:y = 3^x
Step-by-step explanation:
The answer is C because the rate of change is always -6.
Whats 38240 divided by 4
Answer:
9560
Step-by-step explanation:
Use a calculator or do long division.
You can also divide by 2 twice.
38240/2 = 19120
19120/2 = 9560
Answer: 9560
Answer:
9560
Step-by-step explanation:
30000÷4=7500
8000÷4=2000
200÷4=50
40÷4=10
0÷4=0
7,500+2,000+50+10+0=9,500+60=9,560
P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. P The length of Q is 25% more than the length of P. The area of Q is 10% less than the area of P. Work out the ratio x : y x cm Give your answer in its simplest form. 40 cm Q y cm
From rectangle P and Q, the ratio of x to y is 25/18
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Area of P = 40 * x = 40x cm²
Area of Q = y * (1.25 * 40) = 50y cm²
Given that area of Q = 90% if P = 0.9(40x) = 36x cm²
50y cm² = 36x cm²
x/y = 50/36 = 25/18
From rectangle P and Q, the ratio of x to y is 25/18
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
c
Step-by-step explanation:
because 3 x 3 = 9
1 x 5 = 5
simplest form will be 1 4/5
Don't Send links, don't Write random things and get the points for free.
Answer:
2,714in^3
Step-by-step explanation:
V = pi*r^2*h
V = 3.14*6^2*24
V = 3.14*36*24
V = 2,714
The volume of the cylindrical fish tank is 2,714 inches cubed.
Answer:
Option A, [tex]2714\ in^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of the cylinder
[tex]V=\pi r^2h[/tex]
[tex]V=\pi *(12\ in/2)^2*24\ in[/tex]
[tex]V=\pi *(6\ in)^2*24\ in[/tex]
[tex]V=\pi * 36\ in^2 *24\ in[/tex]
[tex]V = \pi *864\ in^3[/tex]
[tex]V=2,714\ in^3[/tex]
Answer: Option A, [tex]2714\ in^3[/tex]
Bob has 30 coins, which are all dimes and quarters. If the total amount of money he has
is $4.80, how many of each coin does he have?
Answer:
that means he will have 25.2
please solve for x 3x + 22
Answer:
The x intercept is [tex](-\frac{22}{3} ,~0)[/tex]
The y intercept is [tex](0,~22)[/tex]
What lines are parallel?
A: y=3x-2 and y=1/3x-3
B: y=x and y=3
C: y=0 and y=3
Please explain the answer!!! Will give brainliest!!!
Answer:
C
Step-by-step explanation:
y=0 gives the straight horizontal line passing through (0,0)
y=3 also gives straight horizontal line passing through (0,3)
In order to find out which two lines are parallel, let's find the slope of each line first.
The slope of the line y=3x-2 is 3.
The slope of the line y=1/3x-3 is 1/3
The slope of the line y=x is 1
The slope of the line y=3 is 0
The slope of the line y=0 is 0
Now, if two lines have the same slope, they are parallel to each other.
So if a line's slope is 0, the line parallel to it has a slope of 0.
So the parallel lines here are ↓
y=0 and y=3
hope helpful ~
answer this super simple word problem for so many points
Answer:
60kph
Step-by-step explanation:
Distance = Rate X Time
640 = r x 4+ (r+5) x 7
640 = 4r + 7r + 35
640=11r + 35
640 - 35 = 11r
605 = 11r
r = 605 / 11
r= 55 kph
r=55 =5 =60 kph is the speed of the train
To see if the answer is right: 55 x 4 + 60 x 7 = 220 + 420 = 640 km
What's the range of f(x)=x+6 if x ∈(-4,-1)
Answer:
the range of is (2 , 5)Step-by-step explanation:
f(x)=x+6
f is an increasing function then the range of is
f(-4,-1) = (f(-4) , f(-1))
f(-4) = -4 + 6 = 2
f(-1) = -1 + 6 = 5
Therefore
the range of is f(-4,-1) = (2 , 5)
Brady dilates an oblique prism by a scale factor of 2/3. Determine the scale factors for perimeter, area, and Volume. (Answer as a fraction)
Using proportions, it is found that:
The scale factor for the perimeter is of [tex]\frac{2}{3}[/tex].The scale factor for the area is of [tex]\frac{4}{9}[/tex].The scale factor for the volume is of [tex]\frac{8}{27}[/tex].What is a proportion?A proportion is a fraction of a total amount.
For the perimeter, as it is given in units, the scale factor is the same, hence it is of [tex]\frac{2}{3}[/tex].
For the area, as it is given in units squared, the scale factor is squared, hence:
[tex]\left(\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]
For the volume, as it is given in cubic units, the scale factor is eleveted to the third power, hence:
[tex]\left(\frac{2}{3}\right)^3 = \frac{8}{27}[/tex]
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Draw a right trapezoid with bases of 8 and 10 cm
Answer:
Here is a picture of a right trapezoid with bases of 8 and 10 cm
27
5
to a mixed number
a
decimal.
Answer: 5.4 and 5⅖
Step-by-step explanation:
27/5 to a mixed number 5⅖
Decimal 5.4
Look at the image for the instructions! I need this asap! I will give points, 5 stars and brainliest ((:
(This is an essay)
Answer:
1. one is smaller by 5 cm and one is larger by 5 cm
2. well they are similar to each other, but one is dilated and isn't
I’m confused please help!
Answer:
See below
Step-by-step explanation:
c will be tha same as the labelled angle = 99 degrees
then c + b = a straight line = 180
99 + b = 180
b = 81 degrees
select the equivalent expression (3^3*6^6)^-3
Answer: Choice B and Choice D
Step-by-step explanation:
4^-2 * 7^-2= 16*49=784
Answer:
B & C
Step-by-step explanation:
[tex]4^-^2*7^-^2[/tex] is equal to [tex]\frac{1}{784}[/tex]
[tex]\frac{1}{28^2}[/tex] is also requal to [tex]\frac{1}{784}[/tex]
[tex]\frac{7^-^2}{4^2}[/tex] is also equal to [tex]\frac{1}{784}[/tex]
6. A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.
Answer:
46 feet
Step-by-step explanation:
it is a 8-15-17 Pythagorean Triple (or you can use the Pythagorean theorem)
P=8+8+15+15=46
The perimeter of the rectangle with a length of 15 feet and has a diagonal that measures 17 feet is: A. 46 feet.
What is the Perimeter of a Rectangle?To find the perimeter of the rectangle, we need to know the width of the rectangle. Let's call the width of the rectangle W.
In a rectangle, the diagonal, length, and width are related by the Pythagorean theorem:
Diagonal² = Length² + Width²
In this case, the diagonal (D) is 17 feet, and the length (L) is 15 feet. So we have:
17² = 15² + W²
289 = 225 + W²
Now, let's solve for W:
W² = 289 - 225
W² = 64
W = √64
W = 8 feet
Now that we know the width is 8 feet, we can calculate the perimeter (P) of the rectangle:
Perimeter = 2 * (Length + Width)
= 2 * (15 + 8)
= 2 * 23
Perimeter = 46 feet
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