The expression x²- 4x - 21 represents the area of the basketball court in square meters.
What is Area ?The area can be defined as the space occupied by a flat shape or the surface of an object.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
It is given that the area of a rectangle is (x − 7)(x + 3)
when It has a length of (x − 7) meters and a width of (x + 3) meters.
The simplified expression of the area is equal to
(x-7)(x-3)
This can also be written as
x *(x+3) - 7*(x+3)
x²+3x-7x-21
x²- 4x - 21
Therefore x²- 4x - 21 represents the area of the basketball court in square meters .
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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
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.
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
Choose the best verbal statement for the following inequality: m > 13
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:
What is 1,019.7 rounded to the nearest whole number?
If I have a grade of 74.98% and if I get an 80% on my test what will my grade go up to?
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).
The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
Answer:
The correct equation is 3n + 3 = 303
Correct value of n is 100
Step-by-step explanation:
The sum of three consecutive integers is 303.
Consecutive integer is next number of previous one.
Let n be smallest integer.
Next two integer: n+1, n+2
Sum of n, n+1 and n+2 is 303
Therefore,
n + n + 1 + n + 2 = 303
3n + 3 = 303
3n = 300
n = 100
Hence, The correct equation is 3n + 3 = 303
need answers............
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.
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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How do you write 9.76*10^-2 in standard form?
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
The expression representing the total number of letters that Julia wrote after 'y' months is '14y', as she writes 14 letters each month.
Explanation:This is a mathematics problem related to writing algebraic expressions. In this case, Julia has written 14 letters each month for 'y' months. Hence, the expression to determine the total number of letters Julia has written is '14y'. Let's break this down:
Julia writes 14 letters each month. This is a constant, represented by the number 14. The time period over which she continues this action is variable, represented by 'y'. So, for every month 'y', she writes 14 letters. We multiply 14 (letters per month) by 'y' (number of months) to get the total number of letters, hence the expression 14y.Learn more about Algebraic Expression here:
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The expression to show how many total letters Julia wrote is 14y.
Explanation:To find the total number of letters Julia wrote, we need to multiply the number of letters she wrote each month (14) by the number of months she wrote letters (y). So, the expression to show how many total letters she wrote is 14y.
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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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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.
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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If Y is between X and Z, then X, Y, and Z are collinear?
A) Always true
B) Sometimes true
C) Never true ...?
Yes, its always true that if Y is between X and Z, then X, Y and Z are collinear.
Here,
Given that;
Y is between X and Z.
We have to find X, Y and Z are collinear.
What is Collinear points?
Two or more points are Collinear points if they are lie in one straight line.
Now,
Y is between X and Z.
Clearly, XZ is a line and Y is lie in between X and Z.
So, X, Y and Z are Collinear points.
Therefore, its always true that if Y is between X and Z, then X, Y and Z are Collinear.
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If v=5, what is the value of 3v 9?
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.
Write a real- world problem that you can solve by writing an equation. the answer to the problem must be 6.
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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From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year. What will the population be in 2040? Round to the nearest whole number. Enter your answer in the box.
actually i just took the test and it said the answer was 9384
mary has $500 in her savings account and she buy a pair of shoes every week for $125 write a function
Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
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.
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.
What are the different mathematical relationships in data?
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.