Given:
The volume of a prism with equilateral triangular cross-section is 270cm³.
Length of the prism = [tex]10\sqrt{3}[/tex] cm
To find:
The length of the side of the equilateral triangular cross-section.
Solution:
Formulae used:
Area of an equilateral triangle is
[tex]Area=\dfrac{\sqrt{3}}{4}a^2[/tex]
Where a is the side length of equilateral triangle.
Volume of prism is
[tex]V=Bh[/tex]
Where, B is base area and h is the height of the triangular prism.
Cross section of the prism is an equilateral triangular so the base area of the prism is [tex]\dfrac{\sqrt{3}}{4}a^2[/tex] sq. cm.
The volume of the prism is
[tex]V=\dfrac{\sqrt{3}}{4}a^2\times 10\sqrt{3}[/tex]
[tex]270=\dfrac{10(3)}{4}a^2[/tex]
[tex]270=\dfrac{30}{4}a^2[/tex]
[tex]270=7.5a^2[/tex]
Divide both sides by 7.5.
[tex]\dfrac{270}{7.5}=a^2[/tex]
[tex]36=a^2[/tex]
[tex]\pm \sqrt{36}=a[/tex]
[tex]6=a[/tex]
It takes only positive value because the side cannot be negative.
Therefore, the length of the side of the equilateral triangular cross-section is 6 cm.
Determine if the two triangles are congruent. If they are, state how you know. SAS , ASA, AAS, SSS or HL
Step-by-step explanation:
1. SAS
2. SSS
3. RHS
4. SAS
5. RHS
6. SAS
7. ASA
8. SAS
9. ASA
10. SSS
A city's population is currently 500,000. If the population doubles every 65 years, what will the population be 130 years from now?
Answer:
2,000,000
Step-by-step explanation:
Simple maths, really.
65 times 2 is 130, and the population is already 500,000 with no time passing. 65 years later, the population would be 1,000,000. 65 years after that, the population would double again, so the answer would be 2 million.
Hope this helped!
Last week, Leah worked 25 hours on weekdays and 11 hours on the weekend. Which ratio compares the number of hours Leah worked on weekdays to the total number of hours she worked? A.25 : 11 B. 11 : 25 C. 25 : 36 D. 36 : 25
Is this a function?
Answer:
yes its a function
Step-by-step explanation:
(if there are different kinds or functions
hoped this helped lmk if it did
i need the missing term
Answer:
-2x
Step-by-step explanation:
negative one times 2x is -2x
Answer:
-2x
Step-by-step explanation:
HOPE THIS HELPS YOU OUT! MAYBE JUST MAYBE CONSIDER ME BRAINLIEST I DONT EVEN HAVE 1 LOL
help meplease i give 5 star
Please help!!!!!
A special blend of coffee costs $15.00 for 8 pounds. To the nearest penny, how much will 10 pounds
cost?
Answer:
18.75
Step-by-step explanation:
Remark
For this question, you need to set up a proportion. The ratio on each side of the equal sign is dollars over pounds.
Proportion
15/8 = x / 10 Cross Multiply
Solution
8x = 15 * 10 Combine
8x = 150 Divide by 8
x = 150/8
x = 18.75
The radicand is the value inside of the radical.
O True
O False
Answer: TRUE
Step-by-step explanation:
Find the slope of the line that passes through the points (4, 3) and (2,7).
Answer:
Slope is -2
Step-by-step explanation:
he drawing shows the view of the top of a building. What is the value of x?
Answer:
65 degrees
Step-by-step explanation:
The angles in a triangle must add up to 180 so you subtract 90 and 25 from 180 and are left with 65
A fair dice has 6 sides numbered 1 to 6. After it is rolled, 5 of the numbers can be seen. What is the probability that one of these numbers is a 3
Answer:
[tex] \frac{5}{6} [/tex]
Step-by-step explanation:
Out of those 5 sides, we need to be able to see a 3 from a 6 sided dice.
The total will always be your demoninator and since we was looking at sides, we just need a side that has a 3.
Find a solution to this equation.
y = x + 2
Type an (x,y) ordered pair that is a solution to this
equation.
Answer:
x = -2
y = 2
(-2,2)
Step-by-step explanation:
First, we find the x-intercept. To do so we need to replace the y with 0 and then solve for x.
---> 0 = x + 2
-2 = x
Then, we need to find the y-intercept or the y-value. To do so we need to replace the x with 0.
---> y = 0 + 2
y = 2
Finally, we put our answer in an ordered pair.
---> (x,y)
(-2,2)
The ordered pair that is a solution to the equation is (-2, 2)
Given the equation y = x + 2
In order to get the ordered pair of the solution, we will find the x and y-intercept as shown:
x-intercept occurs at y = 0
If y = 0
0 = x + 2
x = 0-2
x = -2
y-intercept occurs at x = 0
If x = 0
y = 0 + 2
y = 2
Hence the ordered pair that is a solution to the equation is (-2, 2)
Learn more here; https://brainly.com/question/23907649
the coordinates of A and B are given
a= (4,3) b= (10,5)
1) calculate the gradient of the line AB
2) calculate the equation of the line passing through AB
Using the variable n for the term, describe the sequence.
Answer:
3 + 5n
Step-by-step explanation:
This is an arithmetic sequence.
First term = a = 8
Common difference = d =Second term - first term
= 13 - 8
= 5
Nth term = a + (n- 1)*d
= 8 + (n -1) * 5
= 8 + n*5 - 1 *5
= 8 + 5n - 5
= 8 - 5 + 5n
= 3 + 5n
Someone help and please make sure it’s right
Answer:
50 would be the correct response.
Step-by-step explanation:
The two interior angles are the sum of the exterior angle. 50 + 50 is 100, so 50 would be correct.
The average new car sells for 23,000 but loses value about 20% each year for the next 5 years
Answer:
I think It would be $18,400
Step-by-step explanation:
You would take 23,000 then divide it by 100 to get 230 then multiply that by 20 finally you would delete 23,000 by 4600 to get what do you know 18,400.
Antonio is starring in the high school play and has lots of family members and
friends who want to see him perform. He has purchased 17 tickets for the
play. Some of these are adult tickets and some are child tickets. The cost of an
adult ticket is $4 and the cost of a child ticket is $2. If the total cost of the 17
tickets was $60, find the number of each type of ticket purchased.
Answer:
4 Kids 13 Adults
Step-by-step explanation:
13 x 4 = 52 < Adults
4 x 2 = 8 <Kids
52
+ 8
----------
= $60
13 + 4 = 17 Tickets
HELP ME PLEASEE ASAP!!!! PLEASEE
Answer:
B is the correct option.
Hope it helps!!!
4-2x=10
just fing the answer :)))
Answer:
x = -3
Step-by-step explanation:
4 - 2x = 10
-2x = 6
x = -3
Which shows the expression below in simplified form?
(9.1 x 10-4)-(1.6 x 10-7)
A.9.084 x 10-5
В.9.084 x 10-4
C.9.0984 x 10-4
D.9.09984 x 10-4
Answer:
[tex]9.0984*10^{-4}[/tex] Answer C
Step-by-step explanation:
Help me ASAP!!!!!!!!!
Answer:
The answer is C
Step-by-step explanation:
C is the only option that represents the inequality 2x - 6 ≥ 6(x - 2) + 8.
William went to the supermarket with $15.00 in his pocket.
Supermarket
Choices
Item Price ($)
Bread $1.25
Soap $2.18
Steaks $7.25
Shampoo $5.62
Cheese $4.27
Which combination of items is not possible for William to purchase with $15.00?
steaks, bread, soap
steaks, bread, soap
steaks, cheese, soap
steaks, cheese, soap
soap, cheese, shampoo
soap, cheese, shampoo
steaks, shampoo, cheese
steaks, shampoo, cheese
Answer:
Steaks shampoo cheese
3/4 pounds make how many oz?
Answer:
12
Step-by-step explanation:
Find the missing dimension Use the scale 1:5
Model: 3ft
Actual: ?
Answer:
it will be 1 : 3
Step-by-step explanation:
What is the algebraic expression for the difference between seven times a number and three times that number?
Given
An algebraic expression is the difference between seven times a number and three times that number.
To find:
The algebraic expression.
Solution:
Let x be the unknown number.
Multiplication is used for times and subtraction is used for difference.
7 times of a number = 7x
3 times of that number = 3x
The difference between seven times a number and three times that number is
[tex]Difference = 7x-3x[/tex]
[tex]Difference =4x[/tex]
Therefore, the algebraic expression for the given statement is 7x-3x and its simplified form is 4x.
Answer:
I got you covered, friend!
the answer you want is 7x-3x
Step-by-step explanation:
7x-3x means the difference between seven times a number (x) and three times that number (also x)
have a great day
find the mean of the data set below 2,2,3,5,7,8
someone answer asap
Help me with this please
Answer: (17 , 5)
18 + 16 / 2 = 17
0 + 10 / 2 = 5
Answer:
Step-by-step explanation:
F = (18, 0 ) as ( x1 , y1)
G = (16 , 10) as (x2, y2 )
mid = (x1+x2) / 2 ,( y1 + y2) / 2
mid = (18+16)/2 , (0+10)/2
mid = 34/2 , 10 /2
mid =( 17, 5)
I don’t know the answer to this but what is f(x)=-0.5x+27? Can someone help me out please?
f(X)=-0.5x+27 is a linear function that has -0.5 as the slope nad 27 as the y intercept
Answer: f(x) = 26.5
-_-
The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only.)
Please Help!!!! Giving brainliest!!!
Answer:
54
Step-by-step explanation:
Both Triangles: 12
Square: 10.5
Back rectangle: 14
Front Rectangle: 17.5
And just add all of them together
Monica deposits $300 into a savings account that pays a simple interest rate of 4.2% paul deposits $400 into a savings account that pays a simple interest rate of 3.8% monica says that she will earn more interest in 1 year because her interest rate is higher is she correct?
Answer:
Paul earned $2.6 more interest than Monica.
Step-by-step explanation:
Giving the following information:
Monica:
Initial investment= $300
Interest rate= 4.2%
Paul:
Initial investment= $400
Interest rate= 3.8%
To calculate the income earned, we need to use the following formula:
I= P*r*t
P= principal
r= interest rate
t= time
Monica:
I= 300*0.042*1= $12.6
Paul:
I= 400*0.038*1= $15.2
Paul earned $2.6 more interest than Monica.