an arena is 1/2 full. After 1,500 people leave the arena, it is 1/3 full. What is the seating capacity of the arena?
Answer:
9000
Step-by-step explanation:
(x/2)-(x/3) = 1500
(x/6)=1500
x= 9000
Sum of the maximum and minimum values of y=2cos^2 x + 3sin^2 x + 5
To begin with, we can simplify y using the Pythagorean identity:
y = 2 cos²(x) + 3 sin²(x) + 5
y = 2 (cos²(x) + sin²(x)) + sin²(x) + 5
y = 2 + sin²(x) + 5
y = sin²(x) + 7
Next, we can further rewrite this using the half angle identity for sine:
y = (1 - cos(2x))/2 + 7
y = 15/2 - 1/2 cos(2x)
Now, since cos(x) is bounded between -1 and 1, we have
max(y) = 15/2 - 1/2×(-1) = 15/2 + 1/2 = 8
and
min(y) = 15/2 - 1/2×1 = 15/2 - 1/2 = 7
Then the sum of the maximum and minimum is 8 + 7 = 15.
Which two numbers have a mean of 10 and a range of 4?
Answer:
Two numbers that have a mean of 10 and a range of 4 are the numbers 12 and 8.
Hope this helps!
Answer:
12 and 8 it is easy and i rlly hope it helps
3(p – 6) + 15 = 0
PLEASE SOLVE PLEASE HELP IT IS URGENT
[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]
[tex] \sf3(p - 6) + 15 = 0 \\\sf 3p - 18 + 15 = 0 \\\sf 3p - 3 = 0 \\ \sf3p = 3 \\ \sf \: p = \frac{3}{3} \\ \boxed{\bf p = 1}[/tex]
The value of p is 1.
_______
Hope it helps.
RainbowSalt2222
[tex]\\ \rm\longmapsto 3(p-6)+15=0[/tex]
[tex]\\ \rm\longmapsto 3p-18+15=0[/tex]
[tex]\\ \rm\longmapsto 3p-3=0[/tex]
[tex]\\ \rm\longmapsto 3p=3[/tex]
[tex]\\ \rm\longmapsto p=\dfrac{3}{3}[/tex]
[tex]\\ \rm\longmapsto p=1[/tex]
Plz answer it's important
Answer:
[tex]x_{M}[/tex] = - 1
Step-by-step explanation:
The coordinates of the midpoint are the average of the x and y coordinates of the endpoints , that is
[tex]x_{M}[/tex] = [tex]\frac{4-6}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
write each expression as a single power of 10
Answer:
10⁸
Step-by-step explanation:
[tex]( \frac{10 ^{5} }{ {10}^{3} } ) ^{4} \\ (10 ^{5 - 3} ) ^{4} \\ (10 ^{2} )^{4} \\ (10 ^{2 \times 4} ) \\ (10^{8} )[/tex]
I hope it helped U
stay safe stay happy
because the expression is raised to a power, you're going to multiply the power inside the expression with the power outside the expression. Thus:
[tex] \frac{10 ^{20} }{10^{12} } [/tex]
Since the powers are being divided, you can just subtract 20 by 12. Then you would get:
[tex]10^{8} [/tex]
Solve 6x + ( 14x - 5 ) + ( 17 - 3x ) , - ( 2 - x ) -3 ( 6 + 8x ) -12, ( 4x - 9 ) + 8 ( 2x + 3 ) -7x
Answer:
Step-by-step explanation:
6x + ( 14x - 5 ) + ( 17 - 3x )
= 17x + 12
- ( 2 - x ) -3 ( 6 + 8x ) -12,
= -23x - 32
( 4x - 9 ) + 8 ( 2x + 3 ) -7x
= 13x +15
The TGV is a high speed train in France. The speed of this train can be modeled by the equation d = 347.2t, where d is the train’s distance, in miles, and t is the time, in hours. The Shanghai-Hangzhou Train is a high speed train in China, and the table below summarizes how long it takes this train to travel different distances. Assume that both trains always operate at constant speeds. Which train is faster?
Answer:5435
Step-by-step explanation:
PLSS HELP! What is -2m-5m=9m-12? ALGEBRA I
Step-by-step explanation:
1. -2m-5m-9m=-12
2. -16m= -12
3. m= -12/ -16
4. m=3/4
i have written / sign as a sign of division .
An image point has coordinates B'(7,-4). Find the coordinates of its pre-image if the translation used was
(x + 4, y + 5).
B 3.1
B[3.-9)
B|11,-9)
B/11, 1)
Answer:
B
Step-by-step explanation:
To go from B' to B , perform the inverse operation
That is the translation rule is (x - 4, y - 5 ) , then
B'(7, - 4 ) → B (7 - 4, - 4 - 5 ) → B (3, - 9 ) → option B
p 2 + m; use m = 1, and p = 5
Answer:
26
Step-by-step explanation:
p²+m
=> 5²+1
=> 25 + 1
=> 26
Answer:
26
Step-by-step explanation:
Substitute the given values into the expression
p² + m
= 5² + 1
= 25 + 1
= 26
m∠ABC = (9x + 4)° and m∠DEF = (13x − 22)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?
Answer:
∠ABC measures 85° and ∠DEF measures 95°.
Step-by-step explanation:
We are given that ∠ABC and ∠DEF are supplementary. Then by definition:
[tex]\displaystyle m\angle ABC + m\angle DE F = 180^\circ[/tex]
Substitute:
[tex]\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180[/tex]
Solve for x. Combine like terms:
[tex]22x -18 = 180[/tex]
Add:
[tex]\displaystyle 22x = 198[/tex]
And divide. Hence:
[tex]\displaystyle x = 9[/tex]
To find the measure of ∠ABC, substitute and evaluate:
[tex]\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}[/tex]
In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.
For a school assignment Brody weighed two different blocks of wood the red block weighed 9/10 of a pound and the blue block weighed 3/5 of a pound what is the difference in the two weights?
Answer:
3/10
Step-by-step explanation:
Difference = Red - blue
red = 9/10
blue = 3/5 = 6/10 multiply top and bottom by 2
Difference = 9/10 - 6/10 = 3/10
Find the midpoint of the segment with the given endpoints.
(-10.8) and (2.2)
Answer:
(-4,5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2
(-10 +2)/2 = -8/2 = -4
To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2
(8 +2)/2 = 10/2 = 5
(-4,5)
Answer:
(-4 , 5)
Step-by-step explanation:
(x₁ , y₁) = (-10 , 8) & (x₂ , y₂) = (2 , 2)
[tex]Midpoint = (\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2})\\\\[/tex]
[tex]=(\dfrac{-10+2}{2},\dfrac{8+2}{2})\\\\=(\dfrac{-8}{2},\dfrac{10}{2})\\\\=(-4 , 5)[/tex]
Seven of the algebra classes at a school have 23 students each. The eighth class has 25
students. What is the total number of students?
Answer: 186 students
Step-by-step explanation:
7x23+25= 186
write each expression as a single power of 10
Answer:
[tex]{ \underline{ \sf{it \: is \: {10}^{9} }}}[/tex]
Step-by-step explanation:
[tex](10 {}^{4} ). \frac{ {10}^{12} }{ {10}^{7} } = ( {10}^{4} ). {10}^{(12 - 7)} \\ \\ = ( {10}^{4} ). {10}^{5} \\ = {10}^{(4 + 5)} \\ = {10}^{9} [/tex]
Answer:
[tex]10^{9}[/tex]
Step-by-step explanation:
I. [tex]10^{4} * 10^{12-7}[/tex]
= [tex]10^{4} * 10^{5}[/tex]
= [tex]10^{4 + 5}[/tex]
= [tex]10^{9}[/tex]
Pls help !!!
find the rate of change on [-1, 4]
Answer:
Step-by-step explanation:
help me with this plsssssssss ps that is a 2
Answer:
14...
plz mark me brailiest
If the length L of a rectangle is 3 less than twice the width W, which of the following gives the length of the
rectangle in terms of the of the width
Answer:
L = 2W - 3
Step-by-step explanation:
If the length L of a rectangle is 3 less than twice the width W, then
L = 2W - 3
The expression for the length L of a rectangle is L = 2W - 3.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The length L of a rectangle is 3 less than twice the width W can be expressed as:
L = 2W - 3
Therefore,
The length of the rectangle can be found by taking twice the width and subtracting 3 from the result.
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g(x) = f(x) +2
if f(x) is 2x
Answer:
You didn't put the question well but if I am right, the question is asking of g(x) if f(x) is 2x.
then g(x)=2x+2
A gas has a density of 0.824 g/L and occupies a volume of 3.00 liters. What is the mass in grams?
Density is mass per unit volume,
ρ = m/v
Solving for mass gives
m = ρv
so that a gas with density 0.824 g/L that occupies 3.00 L has a mass of
m = (0.824 g/L) (3.00 L) = 2.47 g
the round trip distance between City X and City Y is 647 miles. A national park is between City X and City Y, and is 27 miles from City X. Find the round trip distance between the national park and city Y. Justify your answer.
The round trip distance between the national park and city Y is 593 miles.
Given:
Round trip distance from City X and City Y = 647 milesDistance between City X and national park = 27 milesTo find :
The round trip distance between the national park and city Y
Solution:
According to the question, the round trip distance between City X and City Y is 647 miles.
Let the distance from City X to City Y = d
Let the distance from City Y to City X = d
[tex]d+d=647 miles\\2d=647 miles\\d=\frac{647miles}{2}=323.5 miles[/tex]
Distance from City X to City Y = 323.5 miles
Distance of City X from national park = 27 miles
From the figure, the distance of the national park from the City Y = d -27 miles:
[tex]= 323.5 miles - 27 miles = 296.5 miles[/tex]
The distance from national park to City Y = 296.5 miles
When we will be going on the round trip between the national park and city Y we will be first traveling 296.5 miles from the national park to the City Y and then 296.5 miles from City Y to the national park.
So, the round trip distance between the national park and city Y:
[tex]296.5 miles + 296.5 miles = 593 miles[/tex]
So the round trip distance between the national park and city Y is 593 miles.
Learn more about- Round trip Distance
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3(m+1)+1>7 what is m?
Rewrite using a single positive exponent 4^2/4^-7
Pamella late for school 10% of time. Richard late for 15% of the time.
a) What percentage are they both late?
b) What is the probability only one of them is late?
Answer:
a) 25%
10%+15% = 25%
b) doesn't have any idea
The cube of a whole number is 100 more
than the square of the same number,
What is the number?
Answer:
The number is 0 or 100
Step-by-step explanation:
Let the number be x.
ATQ, x^3=100x^2, x^2(x-100)=0, x=0, 100
FIND x :
x+(x+1)+(x+2)=(x+1)^2
A. 1
B. 0
C. 3
D. 2
Answer:
2
Step-by-step explanation:
Answer:
x = - 1, x = 2
Step-by-step explanation:
Given
x + (x + 1) + (x + 2) = (x + 1)² ← expand using FOIL , then
x + x + 1 + x + 2 = x² + 2x + 1 , that is
3x + 3 = x² + 2x + 1 ( subtract 3x + 3 from both sides )
0 = x² - x - 2 ← in standard form
0 = (x - 2)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 2 = 0 ⇒ x = 2
In
Select the correct
function
that represents
this data.
21012 x
Out
8
3
-2
-7
-12
[?]
A. f(x) = -5x - 2
B. f(x) = -5x + 7
C. f(x) = -5x + 2
The correct function that represents this data is option A. f(x) = -5x - 2.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are three functions in the option.
We have a set of points on the table.
We have to find which function is representing the table.
Input values are the x values and the output values are the y values.
From the table, the y value corresponding to the x value of 0 is -2.
Substitute in each of the function.
A. f(x) = -5x - 2
= 0 - 2
= -2
B. f(x) = -5x + 7
= 0 + 7
= 7
C. f(x) = -5x + 2
= 0 + 2
= 2
The function in A is the only function which got the value as -2 when x = 0.
Hence the function is represented in option A. f(x) = -5x - 2.
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Cho is making a rectangular garden, where the length is x feet and
the width is 4x – 1 feet. He wants to add garden stones around
the perimeter of the garden once he is done. If the garden is 4 feet
long, how many feet will Cho need to cover with garden stones?
Answer:16x-6
Step-by-step explanation:4(4x-1) distributed is 16x-6
If you are performing the following translation (x,y) --> (x + 3, y -4) Determine how that would change the original ordered pair (10, 9). Select the new ordered pair after the Translation. (answer choices below)
(7, 9)
(10, 4)
(3, 10)
(13, 5)
Answer:
(13, 5 )
Step-by-step explanation:
The translation
(x, y ) → (x + 3, y - 4)
Means add 3 to the x- coordinate and subtract 4 from the y- coordinate, so
(10, 9 ) → (10 + 3, 9 - 4 ) → (13, 5 )