Answer with Step-by-step explanation:
Let there be r rows and s seats in every row.
An audience of 450 people is seated in an auditorium and each seat is occupied.
i.e. rs=450
or s=450/r
With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats.
i.e. (s-3)(r+5)=450
s(r+5)-3(r+5)=450
rs+5s-3r-15=450
450+5s-3r-15=450
Subtracting both sides by 450,we get
5s-3r-15=0
i.e. 5s-3r=15
5(450/r)-3r=15
Dividing both sides by 3 and multiplying by r, we get
750-r²=5r
r²+5r-750=0
r² + 30r - 25r - 750 = 0
r(r + 30) - 25(r + 30) = 0
(r + 30)(r - 25) = 0
either r+30=0 or r-25=0
either r= -30 or r=25
r can't be negative
Hence, number of rows in auditorium are:
25
Enter the degree of the polynomial below.
7x7 + 10x4 + 4x3 - 5x11 - 10x6 - 6x7
A. 6
B. 7
C. 11
D. 10 ...?
Answer:
degree of the polynomial is 11.
C is the correct option.
Step-by-step explanation:
We have been given the polynomial
[tex]7x^7+10x^4+4x^3-5x^{11}-10x^6-6x^7[/tex]
Rewrite this polynomial in standard form i.e from descending exponents
[tex]-5x^{11}-6x^7+7x^7-10x^6+10x^4+4x^3[/tex]
On simplifying, we get
[tex]-5x^{11}+x^7-10x^6+10x^4+4x^3[/tex]
Now, we know that the degree of the polynomial is the highest exponent.
Here, the highest exponent is 11.
Therefore, the degree of the polynomial is 11.
C is the correct option.
Which of the following is the solution to the equation 5/6 x = -1/6 ?
is the simplified form of 2√3 - 2√3 rational?
The simplified form of 2√3 - 2√3 is 0, which is a rational number.
Explanation:In order to determine if the simplified form of 2√3 - 2√3 is rational, we first need to simplify the expression. Since we have the same terms being subtracted from each other, the expression will simplify to 0. Therefore, the simplified form is 0, and 0 is considered to be a rational number since it can be written as 0/1.
Would the placement of the parentheses affect the value of an expression when only multiplication is used? Explain.
Yes, the placement of parentheses can affect the value of an expression even when only multiplication is used. This is because parentheses can change the grouping of factors, which can in turn change the order of operations.
The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. When there are no parentheses, the order of operations is as follows:
Exponents
Multiplication and division (from left to right)
Addition and subtraction (from left to right)
However, when there are parentheses, the operations inside the parentheses are performed first. This means that the order of operations is not always followed strictly from left to right.
For example, consider the following expression:
3 * 2 * 4
According to the order of operations, this expression should be evaluated as follows:
3 * 2 = 6
6 * 4 = 24
However, if we add parentheses to the expression, we can change the value:
(3 * 2) * 4
In this case, the parentheses tell us to evaluate the expression inside the parentheses first. So, we have:
(3 * 2) = 6
6 * 4 = 24
Therefore, the value of the expression is different depending on the placement of the parentheses.
This is because the parentheses change the grouping of factors. In the first expression, the factors are grouped as (3)(2)(4). In the second expression, the factors are grouped as ((3)(2))(4). This change in grouping changes the order in which the operations are performed, which can in turn change the value of the expression.
If I have a grade of 74.98% and if I get an 80% on my test what will my grade go up to?
If the point (8,4) is on the graph of an even function ,what other point must also be on the graph ?
If the point (8,4) is on the graph of an even function, the point (-8,4) must also be on the graph.
Explanation:An even function is a function that satisfies the property f(x) = f(-x) for all values of x in the domain of the function. If the point (8,4) is on the graph of an even function, then the point (-8,4) must also be on the graph. This is because substituting x = -8 into the function would give the same y-value as when x = 8.
if f(x)=x^2+3x+5, what is f(3+h)
A.(x^2+3x+5)(3+h)
B.h^2+9h+23
C.(3+h)^2+8+h
D.h^2+h+23
Answer:
The value of the f (3 +h) is h² + 9h + 23 .
Option (B) is correct.
Step-by-step explanation:
As the function given in the question be
f(x)= x² + 3x + 5
Now
f(3 +h )= (3 +h )²+3(3 + h)+5
Now by using the formula
(a + b)² = a² + b² + 2ab
f(3 +h )= 3² + h² + 2 × 3 × h +3 × 3 + 3 ×h +5
f(3 +h )= 9 + h² + 6h + 9 + 3h +5
f(3 +h )= h² + 9 + 9 + 5 + 3h + 6h
f(3 +h )= h² + 9h + 23
Therefore the value of the f (3 +h) is h² + 9h + 23 .
Option (B) is correct.
How many solutions does this equation have?
Chris is calculating his deductions for his tax return. He is filing singly. He can claim $1,813 from property taxes, $1,513 from medical expenses, and $761 from state income tax. The standard deduction for a single filer is $5,700. How does the standard deduction compare to Chris’s deductions? a. Chris’s deductions are $1,437 better than the standard deduction. b. Chris’s deductions are $4,087 better than the standard deduction. c. The standard deduction is $1,613 better than Chris’s deductions. d. The standard deduction is $664 better than Chris’s deductions.
Answer:
(C)
Step-by-step explanation:
Chris's deductions for tax return = claim from property taxes +claim from medical expenses+claim form state income tax
= $1813+$1513+$761
= $4087
Standard deductions = $5700
Difference between standard deduction and Chris's deductions = 5700-408
= $1613
Hence standard deductions is better than Chris's deductions by $1613
Therefore, option (C) is correct.
mary has $500 in her savings account and she buy a pair of shoes every week for $125 write a function
What is the solution of the system?
Use the substitution method.
{y−2x=8
{16+4x=2y
The only solution is (24, 0)
The only solution is (1, 10)
There is no solution.
There are an infinite number of solutions.
What makes the statement true? 8^-2=?
Answer:
[tex]\frac{1}{64}[/tex] makes the statement true.
Step-by-step explanation:
Given expression,
[tex]8^{-2}[/tex]
By using the property of exponent, i.e. [tex]a^m=\frac{1}{a^{-m}}[/tex]
[tex]\implies 8^{-2}=\frac{1}{8^{2}}[/tex]
[tex]=\frac{1}{64}[/tex]
Hence, the true statement would be,
[tex]8^{-2}=\frac{1}{64}[/tex]
Let h(x)=2x+5h(x)=2x+5h, left parenthesis, x, right parenthesis, equals, 2, x, plus, 5 and g(x)=8-3xg(x)=8−3xg, left parenthesis, x, right parenthesis, equals, 8, minus, 3, x. What is the value of h(g(1.5))h(g(1.5))h, left parenthesis, g, left parenthesis, 1, point, 5, right parenthesis, right parenthesis?
The question is asking for the value of h(g(1.5)) using given functions h(x) and g(x). First, find g(1.5) by substituting 1.5 into g(x) to get 3.5. Then, substitute 3.5 into h(x) to get the final answer of 12.
Explanation:Firstly, identify the functions h(x) and g(x) given to you. h(x) =
2x+5
and g(x)=
8-3x
. The question requires you to find h(g(1.5)). This means that you need to plug g(1.5) into h(x).
Start by calculating g(1.5). In the function g(x), replace x with 1.5. g(1.5) = 8 - 3*1.5 = 3.5.
Now, substitute the value obtained, which is 3.5, into h(x). So, h(g(1.5)) turns into h(3.5) = 2*3.5 + 5 = 12. Therefore, the value of h(g(1.5)) is
12
.
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To calculate the composite function h(g(1.5)), first calculate the value of g(1.5) which is 3.5, then substitute this value into the function h(x) to get the answer, which is 12.
Explanation:The question is asking us to find the value of h(g(1.5)). This means we need to first find the value of g(1.5) and then substitute that value into the function h(x).
So, let's first determine g(1.5). We know that g(x)=8-3x. Substituting 1.5 in place of x in g(x), we get: g(1.5) = 8 - 3*(1.5) = 8 - 4.5 = 3.5.
Next, to find h(g(1.5)), we substitute the value of g(1.5) which is 3.5 into h(x) to get: h(3.5) = 2*(3.5) + 5 = 7 + 5 = 12. Thus, the value of h(g(1.5)) is 12.
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an airplane takes off with a full tank of 40,000 gallons of fuel and flies at an average speed of 550 miles per hour. after 8 hours in flight, there are 14,000 gallons of fuel left. it will take another 3.5 hours for the plane to reach its destination. how much fuel will be left in the tank when the plane lands? what is the total distance of the flight?
Fuel in aeroplane when tank was full = 40,000 gallons.
Fuel left after flying for 8 hours = 14,000 gallons
Fuel consumed in 8 hours flight =40,000-14,000= 26000 gallons.
Fuel consumed in 1 hour time = 26000÷8= 3250 gallons.
Fuel consumed in remaining 3.5 hours = 3250x3.5=11375 gallons.
Total fuel consumed = 26000+11375 =37375 gallons.
Fuel left after landing =40,000 -37375=2625 gallons.
The second part is asking us to find total distance of the flight.
Total time of flight= 8+3.5=11.5 hrs
Speed of aeroplane = 550 miles per hour.
Distance covered = speed x time
Distance (Total ) covered = 550x11.5=6325 miles.
There will be a circular patio with a diameter of 7 metres. greg is going to put a tiled edge around the patio. what is the circumference of the patio? m circumference of a circle = 2πr use π = 3.14
Answer: The circumference of the patio is 21.98 meters.
Step-by-step explanation: Given that there is a circular patio with a diameter of 7 meters. Greg is going to put a titled edge around the patio.
We are to find the circumference of the patio.
If 'r' units is the radius of a circle, then the circumference of the circle is given by
[tex]C=2\pi r.[/tex]
Since the diameter of the circular patio is 7 meters, so the radius 'r' will be given by
[tex]\textup{radius}=\dfrac{1}{2}\textup{ of the diameter}\\\\\Rightarrow r=\dfrac{1}{2}\times 7\\\\\Rightarrow r=3.5~\textup{meters.}[/tex]
Therefore, the circumference of the patio is given by
[tex]C=2\pi r=2\times 3.14\times 3.5=21.98~\textup{meters}.[/tex]
Thus, the circumference of the patio is 21.98 meters.
Celine has 2 coupons. One is for $5 off a purchase and the other is for 20% off a purchase. At what purchase price will the coupons have the same value?
To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, solve the equation x - $5 = 0.8x by isolating x.
Explanation:To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, we need to set up an equation and solve for the purchase price.
Let's assume the purchase price is x dollars. The $5 off coupon would give us a discount of $5, so the price after the discount would be x - $5. The 20% off coupon would give us a discount of 20% of x, so the price after the discount would be 0.8x.
We can set up the equation:
x - $5 = 0.8x
Now we can solve for x:
x - 0.8x = $5
0.2x = $5
x = $25
Therefore, the coupons will have the same value at a purchase price of $25.
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When rewriting y = 2x + 1 in function notation, what do you replace with f(x)?
Answer:
You replace y with f(x)
Step-by-step explanation:
- Function is a relation between two sets of numbers, with every element
in the first set has only one corresponding element in the second set
- The first set is called the domain of the function (input)
- The second set is called the range of the function (output)
- If the first set is set X and the second set is set of Y, then each value
of x has only one value of y and x is the input and y is the output
- Function notation is the way to write a function f(x) = y, where f(x)
represents the values of y
∵ y = 2x + 1
∵ f(x) = y
- Replace y by f(x)
∴ f(x) = 2x + 1
* You replace y with f(x)
Answer:
That is what I got off of USA Test Prep
Step-by-step explanation:
For function notation you are saying that you have a relation that is a function of another variable. To correctly rewrite using function notation you replace y with f(x).
What is 1,019.7 rounded to the nearest whole number?
What's 2015473 in expanded form
The expanded form of the number 2015473 is 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
What is an expanded form of the number?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so forth, results in the expanded form of the number.
The expanded form of the number is the one that is represented by the sum of each digit times its place value.
The given number is 2015473. The given number in the expanded form will be written as,
2015473 = 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
Therefore, the expanded form of the number 2015473 is 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.
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What is 3 5/8 as a decimal?
The required 3 5/8 as a decimal is 3.625, as of the given mixed fraction.
What is decimal value?Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,
Here,
To convert 3 5/8 to a decimal, we can first convert the mixed number to an improper fraction and then divide the numerator by the denominator using a long division or a calculator. Here are the steps,
3 5/8 = (3 x 8 + 5)/8 = 29/8
Dividing 29 by 8 using long division, we get:
3 5/8 = 3.625
Therefore, 3 5/8 as a decimal is 3.625.
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How many square feet of outdoor carpet will we need for this hole
Answer:
The actual answer is 36. If I am wrong i am sorry
Step-by-step explanation:
Answer:
36 square ft
Step-by-step explanation:
If v=5, what is the value of 3v 9?
Solve for x.
5x - 1 = 26
A)x=27/5
B)x=5
C)-5
Write a real- world problem that you can solve by writing an equation. the answer to the problem must be 6.
How do you write 9.76*10^-2 in standard form?
The number of fish (F) in a fish tank increases when the number of plants (P) increases. Write the correct equation for this scenario and solve for the number of fish when the number of plants is 3.
need answers............
There are 6 female goldfish for every 10 male goldfish in the aquarium. there are 216 female goldfish in the aquarium. how many male goldfish are in the aquarium?
If there are 6 female goldfish for every 10 male goldfish in the aquarium and if there are 216 female goldfish in the aquarium then there are 360 male goldfish in the aquarium.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let us use a proportion to represent the relationship between the number of female and male goldfish in the aquarium
6 female goldfish / 10 male goldfish = 216 female goldfish / x male goldfish
We know that there are 216 female goldfish in the aquarium, so we can substitute that value into the equation:
6 / 10 = 216 / x
Let us solve for x by cross-multiply:
6x = 10 × 216
6x = 2160
Divide both sides by 6
x = 360
Therefore, there are 360 male goldfish in the aquarium.
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Why do we use scientific notation, and what are the parts of an expression written in scientific notation?
You need to know how to use it propeller to also use it at all
If M is the midpoint of LN and LN=27.8 , find the length of MN.
A. 13.8
B. 13.9
C. 14.2
D. 14.5