Answer:
d = 4.5 cm
A = 1/4 (p x d²)
= 1/4 (3.14 x d x d)
= 1/4 (3.14 x 4.5 cm x 4.5 cm)
= 15.9 cm2
The area of the plate nearest square centimeters is 12cm².
What is a scalene triangle ?A scalene triangle has three different sides and corresponding to that three different interior angles.
According to the given question we have triangle with sides 4.5cm,6cm and 7.5cm.
We know for a scalene triangle given 3 sides.
area(A) = [tex]\sqrt{s(s-a)(s-b)(s-c)[/tex].
Where S is semi perimeter and a,b,c are the three sides.
= (a+b+c)/2.
= (4.5+6+7.5)/2 cm.
= 18/2 cm.
= 9 cm.
∴ The area of the triangle is
= [tex]\sqrt{9(9-4.5)(9-6)(9-7.5)[/tex]cm².
= [tex]\sqrt{9(4.5)(3)(1.5)}[/tex] cm².
= [tex]\sqrt{182.5}[/tex] cm² this is in between 13 square and 14 square approx 13.5 cm².
Now it has three small circles of radius of 4 mm or 0.4 cm.
We know area of a circle is πr² and area of 3 circles having same radius is 3(πr²) cm².
= 3{π(0.4)²}
= 3{3.14(0.16)} cm².
= 3(0.5024) cm².
= 1.5072 cm².
Now to obtain the area of the scalene triangle with those three holes of 0.4 cm we have subtract the area of the three circles from the triangle which is
= (13.5 - 1.5) cm².
= 12 cm².
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7[tex]\sqrt -9[/tex]
Answer:
= 21i
Step-by-step explanation:
√-9 = 3i
= 7 . 3i
Multiply the numbers: 7 . 3 = 21
= 21i
Hope this helps!
Kristin is saving up money to go on a trip around the world next year. In order to make enough to pay for her trip, Kristin has to work at least 260 days this year.
Which of the following inequalities represents Kristin's possible number of workdays, d
Answer:
A.
D needs to be equal or more to 260
Answer:
The correct option is A
Step-by-step explanation:
simplify into one fraction 8x/x-8 - 2/x-8
Answer:
- 2+8x/x
Step-by-step explanation:
See image below:)
FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free
Answer:
(8x-2) / (x-8)
Step-by-step explanation:
8x/x-8 - 2/x-8
Since the denominator is the same, we can add the numerators
(8x-2) / (x-8)
20 men can do a piece of work in 24 days. After working for few days, 3 men are added and the work was finished 3 days earlier. After how many days if 4 men are added?
Answer: 17 and a half
Step-by-step explanation:
M D W
20 24 480
20 21 420
24 17 and a half 420
= 17 and a half
In a class, three-fifths of 25 students are girls. What is the number of girls in the class?
Answer:
15
Step-by-step explanation:
3/5*25
Answer:
15 girls
Step-by-step explanation:
(3/5) x 25 = 15
Sima drinks 2.5 litres of water each day.
A full glass holds 125 mililitres of water.
How many full glasses of water does Sima drink each day?
Answer:
20 glasses a day
Step-by-step explanation:
2.5litres equals 2500millilitres
2500÷125=20
Karl set out to Alaska on his truck. The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is graphed.
What distance did Karl travel by the time he had 200 liters of fuel?
_____ kilometers
Answer:
500 kilometers
Step-by-step explanation:
The fuel (y) Karl has in his car is a function of the distance (x) Karl travelled. The amount of fuel (y) is dependent on the distance (x) Karl travelled.
On the y-axis, we have amount of fuel.
On the x-axis, we have distance travelled.
At the time Karl travelled when he had 200 liters of fuel (y) remaining in his car, he had travelled a distance (x) of 500 kilometers.
We know this by looking at the graph given. When x (distance) = 500, y (fuel) = 200.
AABC has been translated 5 units to the right, as shown in the diagram. What
is the length of AB?
A. 10
B. 6
C. 31
D. 15
I got a 90% on my quiz. Thanks to everyone who helped me!
Also this is a really is question but I'm to lazy to do it. Can someone give me the answer to this? (Question in the picture)
Answer: The answer is A
Step-by-step explanation:
In the picture, model A shows 3 groups and in the 3 groups are 4 lines !
I'm bad explaining but I hope this helps .
Given that 4x – 5y = 12 Find y when x = -3 Give your answer as an improper fraction in its simplest form.
Step-by-step explanation:
4(-3)-5y=12
-12-5y=12
-5y=12+12
-y= 24/5
y= -24/5
y= -4⅕
hope it helps
In the expansion of (1/ax +2ax^2)^5 the coefficient of x is five. Find the value of the constant a.
Answer:
80x⁴
Step-by-step explanation:
[tex](\frac{1}{ax} + 2ax^2)^5 = 5C_0(\frac{1}{ax})^5(2ax^2)^0 + 5C_1(\frac{1}{ax})^4(2ax^2)^1 + 5C_2(\frac{1}{ax})^3 (2ax^2)^2[/tex]
[tex]+ 5C_3 (\frac{1}{ax})^2(2ax^2)^3 + 5C_4(\frac{1}{ax})^1(2ax^2)^4 + 5C_5(\frac{1}{ax})^0(2ax^2)^5[/tex]
[tex]5C_0(\frac{1}{ax})^5(2ax^2)^0 =1 \times (\frac{1}{ax})^5 \times 1 = \frac{1}{a^5x^5}\\\\5C_1(\frac{1}{ax})^4(2ax^2)^1 = 5 \times (\frac{1}{ax})^4 \times (2ax^2)^1 = 10 ax^2 \times \frac{1}{a^4x^4} = \frac{10}{a^3x^2}\\\\5C_2 (\frac{1}{ax})^3 (2ax^2)^2= 10 \times (\frac{1}{ax})^3 \times (2ax^2)^2 = 10 \times \frac{1}{a^3x^3} \times 4a^2x^4 = \frac{40x}{a}\\\\5C_3 (\frac{1}{ax})^2 (2ax^2)^3 = 10 \times (\frac{1}{ax})^2 \times (2ax^2)^3 = 10 \times \frac{1}{a^2x^2} \times 8a^3 x^6 = 80ax^4\\\\[/tex]
[tex]5C_4(\frac{1}{ax})^1(2ax^2)^4 = 5 \times \frac{1}{ax} \times 16a^4x^8 = 80a^3x^7\\\\5C_5(\frac{1}{ax})^0(2ax^2)^5 = 1 \times 1 \times 32a^5x^{10}[/tex]
The fourth term of the expansion has the constant a,
the coefficient of a is 80x⁴
in the right triangle AB, mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Given:
In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].
To find:
The length of the hypotenuse.
Solution:
It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin A=\dfrac{a}{c}[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]
By cross multiplication, we get
[tex]1\times c=4\times 2[/tex]
[tex]c=8[/tex]
Therefore, the length of the hypotenuse is 8 units.
The answer and how to find the answer
Answer:
x = 1.9
Step-by-step explanation:
Thanks to a theorem we can use this proportion
10.47 : 4.44 = 4.44 = x
x = (4.44^2)/10.47 = 1,882865 = 1.9
A distribution of values is normal with a mean of 232.4 and a standard deviation of 92.2. Find the probability that a randomly selected value is between 66.4 and 241.6. P(66.4 < X < 241.6)
Answer:
P(66.4 < X < 241.6) = 0.5039 = 50.39%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A distribution of values is normal with a mean of 232.4 and a standard deviation of 92.2.
This means that [tex]\mu = 232.4, \sigma = 92.2[/tex]
Find the probability that a randomly selected value is between 66.4 and 241.6.
This is the p-value of Z when X = 241.6 subtracted by the p-value of Z when X = 66.4.
X = 241.6
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{241.6 - 232.4}{92.2}[/tex]
[tex]Z = 0.1[/tex]
[tex]Z = 0.1[/tex] has a p-value of 0.5398
X = 66.4
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.4 - 232.4}{92.2}[/tex]
[tex]Z = -1.8[/tex]
[tex]Z = -1.8[/tex] has a p-value of 0.0359
0.5398 - 0.0359 = 0.5039
P(66.4 < X < 241.6) = 0.5039 = 50.39%.
Write an equation of a line that passes through (3,2) and (-5,6).
please help show steps thx
Answer:
1) P = 282m, A = 141m^2
2) P = 82.4in, A = 40in^2
3) P = 62.7m, A = 73.1m^2
Step-by-step explanation:
1) top:L=12m, W=3m, mid: l= 12m, w= 12-7 = 5m, bot: l=15m, w=3m
Perimeter= 2(lw)
P = 2(12x3) + 2(12x5) + 2(15x3)
P = 2(36) + 2(60) + 2(45)
P = 72 + 120 + 90
P = 282m
Area= lw
A = (12x3) + (12x5) + (15x3)
A = 36 + 60 + 45
A = 141m^2
2) Rectangle:l=7in, w=5in, Right Triangle:a=5-3=2in, b=12-7=5in
Perimeter= 2(lw) + (a+b+sqrt(a^2+b^2))
P = 2(7x5) + (2+5+sqrt(2^2+5^2))
P = 70 + 12.39
P = 82.4in
Area= lw + ((ab)/2)
A = (7x5) + ((2x5)/2)
A = 35 + 5
A = 40in^2
3) Semi-Circle: d=8m, r=8/2=4m, Right Triangle: a=8m, b=12m
Perimeter= pid + (a+b+sqrt(a^2+b^2))
P = 9pi + (8+12+sqrt(8^2+12^2))
P = 28.27 + 34.42
P = 62.7m
Area= (1/2)pir^2 + ((ab)/2)
A = (1/2)pir^2 + ((ab)/2)
A = (1/2)pi(4)^2 + ((8x12)/2)
A = 25.13 + 48
A = 73.1m^2
The telephone company charges $25 for a service call, and $15 for every 15 minutes the service representative works on repairs. Write an equation you could use to find the total cost of a repair visit.
Answer:
C=$25+$15m
Step-by-step explanation:
C is Cost
m is 15 minutes
The price for a visit would be $25 + $15 times the amount of time they work on repairs.
The equation you could use to find the total cost of a repair visit is C=$25+$15m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The telephone company charges $25 for a service call, and $15 for every 15 minutes the service representative works on repairs.
Let C is Cost and m be 15 minutes
From the data given in the question:
C = 25 + 15m
Thus, the equation you could use to find the total cost of a repair visit is C=$25+$15m.
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The bike you have been saving for is discounted 25%. You have $500 saved to purchase it. The original, non-discounted price of the bike is $575. There is a 5.60% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
Q22. Solve the equation x – 25 = 25 and state which axiom do you use here.
Answer:
x=50
Step-by-step explanation:
The solution to the equation x – 25 = 25 is x = 50. The axiom used to solve the equation is the addition property of equality.
To solve the equation x - 25 = 25, we want to isolate the variable x to find its value.
Adding 25 to both sides of the equation, we get:
x - 25 + 25 = 25 + 25
Simplifying, we have:
x = 50
Therefore, the solution to the equation is x = 50.
In this case, the axiom used to solve the equation is the addition property of equality. According to this axiom, if two expressions are equal, adding the same value to both sides of the equation preserves the equality.
In the given equation, we add 25 to both sides of the equation to maintain equality and obtain the solution x = 50. The addition property of equality allows us to perform this operation and determine the value of x.
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3
5
6) through: (-3, -3), perp. to y=-**-4
5
A) y = 2x + B) y=--x+ 2
*
3
C) y=-x+2 D) y=-x+ 2
5
3
Step-by-step explanation:
answer in the image above
What is the perimeter of a triangle with the side lengths 4 cm, 6 cm, and (3y-2) cm?
Answer:
Step-by-step explanation:
P = 4 + 6 + (3y - 2) Remove the brackets
P = 10 + 3y - 2 Combine
P = 8 + 3y
Note 3y must be less than 8. That's because 2 sides of any triangle must be larger than the 3rd side or else you don't have a triangle.
Is the answer to this question 13.5
Answer:
i think its 13
Step-by-step explanation:
you are supposed to measure the lowest point of the liquid.
What is the length of side a? Round to the nearest tenth of an inch. Enter your answer in the box.
9514 1404 393
Answer:
14.4
Step-by-step explanation:
The Pythagorean theorem tells you ...
7² +a² = 16²
a² = 256 -49
a = √207
a ≈ 14.4
Question 20
A transformer has 500 turns in its primary coil and 200 in the secondary coil.
a) If an AC voltage of 220 V and frequency 50 Hz is established in the primary coil, find the voltage
and the frequency induced in the secondary coil. (2)
9514 1404 393
Answer:
88 V50 HzStep-by-step explanation:
The secondary voltage is proportional to the primary voltage. The constant of proportionality is the ratio of secondary turns to primary turns.
The secondary voltage is ...
(200/500)(220 V) = 88 V
__
A transformer does not change the frequency.* The voltage in the secondary coil is still 50 Hz.
_____
* Most transformers are designed to operate as linear devices. It is possible to design a transformer (with special core material) that operates non-linearly, and/or that is "tuned" to a frequency other than the one exciting the primary. That is, the secondary voltage may be some harmonic of the primary voltage. This would be a relatively unusual application of a transformer, beyond the apparent scope of the question here.
You need to save $1,300 to go overseas in two years. You deposit $800 in a savings account today. The account earns 10% interest. You will make an additional deposit in one year. How much must you deposit in one year in order to have enough to go on the trip?
Answer:
The additional deposit to be made in one year should be $ 301.81.
Step-by-step explanation:
Given that I need to save $ 1,300 to go overseas in two years, and I deposit $ 800 in a savings account today, that earns 10% interest, and I will make an additional deposit in one year, to determine how much must I deposit in one year in order to have enough to go on the trip, the following calculation must be performed:
800 x 1.1 = 880
(880 + X) x 1.1 = 1300
1300 / 1.1 = 1,181.81
1,181.81 - 880 = X
301.81 = X
Therefore, the additional deposit to be made in one year should be $ 301.81.
. year or once a year Your reading material illustrates a typical example of what happens if you pay just the minimum monthly payment every month on a credit card balance. In this example, approximately how long will it take to pay off the original debt completely? a. b. 2 years 5 years 12 years The debt will never be completely repaid. C. d.
What is the value of the expression 2x^2 + 3xy - 4y^2 when x = 2 and y = -4?
Answer:
-80
Step-by-step explanation:
2x^2 + 3xy - 4y^2
x = 2 | y = - 4
2(2)^2 + 3(2)(-4) - 4(-4)^2
2 * 4 + 3(2)(-4) - 4 * 16
8 - 24 - 64
-80
( 0 , -1 ) , ( 1,3)
Which equation is satisfied by BOTH of these pairs of numbers ( x , y ) ?
A. x + y = -1
B. 2x + y = 5
C. 3x - y = 0
D. 4x - y = 1
Answer:
D 4x-y=1
Step-by-step explanation:
4x-y=1. (x=0 ,y= -1)
4(0)-(-1)= 1
0+1= 1
4x-y=1 (x=1 y=3)
4(1)-3=1
4-3=1
6+t=1 pls help.............
6+T=1
Try T=-5
6+(-5) = 1
Correct, So...
T=-5
At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is
Answer:
The appropriate answer is "$12".
Step-by-step explanation:
As per the question,
Price per ticket,
= [tex]4+k[/tex]
Number of people,
= [tex]1800-90k[/tex]
Now,
The revenue (R) will be:
= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]
By putting the values, we get
= [tex](4+k) (1800-9k)[/tex]
= [tex]-90k^2+1440k+7200[/tex]
or,
⇒ [tex]R'=1440-180k=0[/tex]
⇒ [tex]180k=1440[/tex]
⇒ [tex]k=\frac{1440}{180}[/tex]
[tex]=8[/tex]
hence,
The ticket price will be:
= [tex]4+k[/tex]
= [tex]4+8[/tex]
= [tex]12[/tex] ($)