Answer:
The length = The width = The height ≈ 5.8 cm
Step-by-step explanation:
The volume of a rectangular pyramid, V = l × w × h
The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200
∴ l × h + w × h + l × w = 200/2 = 100
We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;
At maximum volume, l = w = h
∴ l × h + w × h + l × w = 3·l² = 100
l² = 100/3
l = 10/√3
Therefore, the volume, v = l³ = (10/√3)³
The length = The width = The height = 10/√3 cm ≈ 5.8 cm
Slope of (5a, b) and (2a, 2b)
Answer:
8a+4b
Step-by-step explanation:
A student correctly evaluated an expression with P = -2 and a = 3 and got 3 as the result. Which of the following expressions could she have been evaluating
Answer:
B
Step-by-step explanation:
A student correctly evaluated an expression where p = -2 and q = 3 and acquired 3 as the result.
And we want to determine which expression could the student have been evaluating.
Thus, we simply need to check each expression by letting p = -2 and q = 3 and see which one equals 3.
Checking the first one:
[tex]\displaystyle \begin{aligned} 3p^2 +2pq - 6q +2 &= 3(-2)^2+2(-2)(3)-6(3) + 2\\ &= (12)+(-12) +(-18) + 2 \\ &=-16\end{aligned}[/tex]
The result is not 3. Hence, A is not correct.
The second expression:
[tex]\displaystyle \begin{aligned} p^3 + 2p^2q-p^2+2pq+q &= (-2)^3+2(-2)^2(3)-(-2)^2+2(-2)(3)+(3)\\ &= (-8)+(24)-(4)+(-12)+(3) \\ &= 3\stackrel{\checkmark}{=}3\end{aligned}[/tex]
Therefore, we can conclude that our answer is B.
We can check the other two regardless.
The third expression:
[tex]\begin{aligned} p^2+q-4q^2 &= (-2)^2 + (3) - 4(3)^2 \\ &= (4) + (3) -(36) \\ &= -29\end{aligned}[/tex]
And the fourth:
[tex]\displaystyle \begin{aligned} p^2+3q^2-q^2+p &= (-2)^2+3(3)^2-(3)^2+(-2) \\ &= (4) + (27) - (9) + (-2) \\ &= 20\end{aligned}[/tex]
Thus, neither the third expression nor the fourth is also correct.
In conclusion, our answer is B.
Simplify. Write your answer in exponent form.
Answer:
8x^3/2
Step-by-step explanation:
(4x)^3/2 = ( 4^3/2 ) ( x^3/2 ) =8x^3/2
Help me find x- geometry
Answer:
We know that,
The sum of the two opposite angles of a circular quadrilateral is 180 degrees.
So,
[tex] \sf {47}^{ \circ} + 7x + {21}^{ \circ} = {180}^{ \circ} \\ = > 7x = {180}^{\circ} - {47}^{\circ} - {21}^{\circ} \\ = > 7x = 112 \\ = > x = \frac{112}{7} \\ = > x = {16}^{\circ} \\ [/tex]
The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚
Using the above theorem
47 + 7x + 21 = 180
7x + 68 = 180
7x = 180 - 68
7x = 112
x = 112/7
x = 16
Therefore value of x is 16°
Answered by Gauthmath must click thanks and mark brainliest
What is the function rule that represents the sentence y is 7 less than the product of 6 and x?
Answer:
y = 6x-7
Step-by-step explanation:
product of 6 and x
6x
7 less than the product of 6 and x
6x-7
y = 6x-7
A sinusoidal graph has an amplitude of 9 and a midline of y = –2. Determine
the range of the graph.
Answer:
[tex]( - 11.7)[/tex]
Range 18
Step-by-step explanation:
Twice the amplitude.
Help me pls asappp with Pythagorean theorem
2). 2, x, 14 are in Arithmetic progression, then the value of x is :
A. 28
B. 16
C. 7
D. 8
A small bird can flap its wings 120 times in 30 s. What is the rate of change of wing flaps?
Answer:
4 Flaps per second
Step-by-step explanation:
M = 120/30
Answer:
4 times per second
Step-by-step explanation:
120 ÷ 30 = 4
30 ÷ 30 = 1
4 flaps per 1 second
so basically 4
Which graph represents a function?
1, 2, 3, or 4
Answer:
The given graph is a function.
Step-by-step explanation:
There is only one given graph, and that graph is a function. In order to determine which graph is a function, conduct the vertical line test. Can a vertical line pass through the represented data set without crossing two y-values? (i.e. A 'sideways parabola' is not a function).
please help me answer this math question, it is really important
Answer:
3 three point baskets
9 two point baskets
4 one point baskets
Step-by-step explanation:
Since you cannot have a 1/3 or 2/3 of a three point basket, finding multiples of threes for the initial two point baskets is the easiest way to start.
Triangle ABC is reflected across the line y = x. What are the coordinates of the vertex B' of the resulting triangle A'B'C?
Answer:
B' (2, - 5 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
B (- 5, 2 ) → B' (2, - 5 )
indio, california is located at an elevation that is below sea level. which is a possible elevation for indio, california?pls help besties!!
Answer:
Let me look some things up.
Step-by-step explanation:
Then I will get back to you
en el coliseo de una ciudad, se jugo la final de un campeonato de voley . En total , 1200 personas asistieron al coliseo . esta cantidad de personas representa a los 3/4 de su capacidad. ¿Cual es la capacidad que tiene este coliseo?
a)900
b)1200
c)1600
d)4800
c. 1600
1200 : 3 * 4
= 400 * 4
= 1600
The capacity of this coliseum is 1600
The correct option is (C)
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Given:
Total people attended the Coliseum= 1200
let he capacity be x
3/4*x= 1200
x= 1200*4/3
x= 1600
Learn more about fraction here:
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Your question is incomplete/other language, probably the traslated question/missing part is:
In a city coliseum, the final of a volleyball championship was played. In total, 1,200 people attended the Coliseum. this number of people represents 3/4 of its capacity. What is the capacity of this coliseum?
How would I find cos(180º) without a calculator?
Answer:
Step-by-step explanation:
The cos of an angle is the adjacent / hypotenuse.
In this case the adjacent and hypotenuse are the same length so the answer is 1 in some form.
You are going left when you talk about 180 degrees. So the adjacent = - 1
The answer you want is -1 / 1
Cos(180) = - 1
what type of variation is this relationship
=========================================================
Explanation:
We don't have a direct variation because the initial cost isn't $0
The equation for this situation is y = 25x+375, where x is the number of yearbooks purchased and y is the total cost.
Notice how this line doesn't go through the origin. All direct variation graphs are straight lines through the origin.
So that's why we have partial variation instead.
The initial cost is simply the set up cost, aka the cost when x = 0. That initial cost is $375. The initial cost is located at the y intercept.
From that initial cost, we then add on multiples of $25 depending on how many yearbooks are purchased.
-----------------
In short, because the initial cost is $375, which is some nonzero value, this means we don't have direct variation. Instead, we have partial variation.
What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minus 9 x EndFraction minus StartFraction x + 1 Over x squared minus 9 EndFraction StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction
Answer:
A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction
Step-by-step explanation:
Given:
(2x + 5) / (x² - 3x) - (3x + 5) / (x³ - 9x) - (x + 1) / x² - 9
Factor the denominators
(2x + 5) / x(x - 3) - (3x + 5) / x(x - 3)(x + 3) - (x + 1) / (x - 3)(x + 3)
Lowest common multiple of the 3 fractions is x(x - 3)(x + 3)
= (2x+5)(x+3) - (3x + 5) - (x + 1)x / x(x - 3)(x + 3)
= (2x²+6x+5x+15) - (3x + 5) - (x² + x) / x(x - 3)(x + 3)
= 2x² + 11x + 15 - 3x - 5 - x² - x / x(x - 3)(x + 3)
= x² + 7x + 10 / x(x - 3)(x + 3)
Solve the numerator.
Solve the quadratic expression by finding two numbers whose product is 10 and sum is 7
The numbers are 5 and 2
= x² + 5x + 2x + 10 / x(x - 3)(x + 3)
= x(x + 5) + 2(x + 5) / x(x - 3)(x + 3)
= (x + 5)(x + 2) / x(x - 3)(x + 3)
A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction
Recall,
x(x - 3)(x + 3) is a factor of x³ - 8x
A. StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction
(x + 5)(x + 2) / x³ - 9x
B. StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction
(x + 5)(x + 4) / x³ - 9x
C. StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction
2x + 11 / x³ - 12x - 9
D. StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction
3(x + 2) / x² - 3x
Enter a recursive rule for the geometric sequence?
4, -16, 64, -256,...
a^1 = __; a^n = __
Plzz help!
Answer:
Step-by-step explanation:
a^1=-2
a^n=a×a^n-1
Tell answer
find in exponenial form
a) 27³x9²x3 options
1) 3³
2) 3 to power 14
answer in detail
Answer:
[tex]{ \tt{ {27}^{3} \times {9}^{2} \times 3 }} \\ = { \tt{ {3}^{3} \times {3}^{2} \times {3}^{1} }} \\ = { \tt{ {3}^{(3 + 2 + 1)} }} \\ { \tt{ = {3}^{6} }}[/tex]
100 points please help... i think the answer is 288 pie squared but not sure
What is the surface area of a dome (a half sphere) with a radius of 12 meters?
576 pie meters squared
48 pie meters squared
288 pie meters squared
96 pie meters squared
9514 1404 393
Answer:
(c) 288π m²
Step-by-step explanation:
The area of a sphere is found using the formula ...
A = 4πr²
Then the area of a half-sphere with radius 12 m will be ...
A = (1/2)(4π)(12 m)² = 288π m²
The step function g(x) is defined as shown.
-3, X < 0
g(x) = 2 0 < x < 4
5, 4 < x < 10
What is the range of g(x)?
0 -3 = g(x) 5
Os g(x) = 10
O {-3, 2, 5)
{0, 4, 10}
The 3rd option is correct.
The range refers to the y-values so the multiple choice answer is restricted to the 1st and 3rd options. The range of the step function is not continuous, it is only the discrete values {-3, 2, 5}.
Pepe and Leo deposit money into their savings accounts at the end of each
month. The table shows the account balances.
If their patterns of saving continue, and neither earns interest nor withdraws
any of the money, how will the balances compare after a very long time?
Pepe's balance will be greater as it is increasing exponentially while Leo's is increasing linearly
(see graph, where red is Pepe and blue is Leo)
Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]
where a is a constant and a>1
We have:
Pepe and Leo deposit money into their savings accounts at the end of each month.
From the table, we can plot a graph on a coordinate plane.
As we can see in the graph:
Because Pepe's balance is growing exponentially and Leo's is growing linearly, it will be bigger.
Thus, Pepe's balance will be greater because Pepe's balance is growing exponentially option (A) is correct.
Learn more about the exponential function here:
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4. Which expression is a simplified form of -5(8x)?
a. 40x
b. -40%
C. 3x
d. -40x?
Answer:
Option d
Step-by-step explanation:
-5(8x)
= -5×8×x
= -40x
Answered by GAUTHMATH
A car is purchased for $21,500. After each year, the resale value decreases by 25%. What will the resale value be after 5 years?
Answer:
$5,102.05
Step-by-step explanation:
Present value of the car = $21,500
Present percentage value = 100% = 1
Percentage of Depreciation per year = 25% = 0.25
Years of depreciation = 5 years
The value of the car after 5 years = Present value of the car (Present percentage value - Percentage of Depreciation per year)^Years of depreciation
= 21,500(1 - 0.25)^5
= 21,500(0.75)^5
= 21,500(0.2373046875)
= 5,102.05078125
Approximately,
The value of the car after 5 years = $5,102.05
"A parabola has the equation y=3x^2+ 6x- 12 . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
enjoy it
it best answer for you
you hold a sale for $5 sandwiches at your restaurant.you end up selling 359 sandwiches to 245 customers
A. how much money do you have in sandwich sales?
B. how many sandwiches per customer did you sell ?
Answer:
A. $1795
B. 7
Step-by-step explanation:
Given the following data;
Cost price, Cp = $5
Number of sandwiches sold, Ns = 359 sandwiches.
Number of customers, Nc = 245 customers.
a. To find how much money you have in sandwich sales;
Total amount of money = Cp * Ns
Total amount of money = 5 * 359
Total amount of money, T = $1795
B. To find how many sandwiches per customer did you sell;
Sandwiches per customer = T/Nc
Sandwiches per customer = (1795/245
= 7.33 ≈ 7
PLEASE HELP!
Part C
What if the first six-sided die is replaced by an eight-sided die. How can you change the table to show the sample space for rolling an eight-sided die and then a six-sided die? Explain.
Answer:
If the first die is changed from a six-sided to an eight-sided die, add two rows to the bottom of the table and number them 7 and 8.
Step-by-step explanation:
Answer:
If the second die is changed from a six-sided to an eight-sided die, add two columns to the right of the table and number them 7 and 8.
Step-by-step explanation:
Which Venn Diagram is NOT correct?
Pls help me with this question ASAP
Answer:
8
Step-by-step explanation:
(3+5)^2/8=(8)^2/8=64/8=8
Answer: 8
Step-by-step explanation:
(3+5)^2/8=
(8)^2/8=
64/8=
8
Please help! Thank you.
Answer:
B
Step-by-step explanation:
x((7/2)-(7/3))=y+x
x(7/6)=y+x
7x=6y+6x, x=6y. y/x=1/6
