Answer: -81a^2 + 27a + 10
Step-by-step explanation: We can do this question by using FOIL (first, outer, inner, last)
(-9a-2)(9a-5)
First, multiply the first two terms in the parentheses
-9a times 9a is -81a^2
Second, multiply the outer terms
-9a times -5 is 45a
Third, multiply the inner terms
-2 times 9a is -18a
And lastly, multiply the last terms
-2 times -5 is 10
After doing this we end up with -81a^2 + 45a - 18a + 10 = -81a^2 + 27a + 10
There are 1,000,000 nanometres in a milimetre
Molecules of water can be modelled as spheres with a diameter of 0.275 nanometres. What is the measurement in millimetres. Write your answer in standard form
On solving the provided question we can say that 1,000,000 nanometers = 1 millimeter; 1e-6 millimeter = nanometers
what is nanometers?A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.
1,000,000 nanometers = 1 millimeter
1e-6 millimeter = nanometers
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Question 3
{(-1, 1), (1, 1), (-2, 4), (2,4)}
Is the relation a function and why?
Ayes each input has exactly one output
Byes each output has been repeated
C no the inputs are not repeated
D no the inputs cannot have the same output
The given relation {(-1, 1), (1, 1), (-2, 4), (2, 4)} is a function because: A. yes each input has exactly one output.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two (2) or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
In this context, we can reasonably infer and logically deduce that given relation is a function because each input variable (domain) has exactly an output variable (range) as illustrated below;
x F(x)
-1 1
1 1
-2 2
2 4
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x.
(2x3 + x4 - 6x2 + 11x - 10) (x2 + 2 - x)
The division of the given polynomial would be (x^4) + 81.
What is the synthetic division?
Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.
To divide the polynomials using polynomial division, we will use the following steps:
Write the polynomials in descending order of exponents.
(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)
Create a grid with the dividend on the left and the divisor on the right.
2x^3 x^4 -6x^2 11x -10
x^2 2 -x
Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
Subtract the second row from the third row and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
0 -x^4 -2x^2 11x -10
Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
0 -x^4 -2x^2 11x -10
-x^2
So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).
Hence, the division of the given polynomial would be (x^4) + 81.
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Help with question please
Answer:
b.
Step-by-step explanation:
the result is created :
first result row first result element =
= first A row × first B column
first result row second result element =
= first A row × second B column
...
third result row second result element =
= third A row × second B column
third result row third result element =
= third A row × third B column
the multiplication of a row and a column is done by :
left row element × top column element +
middle row element × middle column element +
right row element × bottom column element
AB =
-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2
-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2
-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2
=
-2 16 11
7 46 -3
11 26 -9
so, b is correct.
Jamie downloaded 75.24 gigabytes of music onto her computer. The download took 3.8 hours. If the music downloaded at a constant rate, how many gigabytes of music were downloaded in one hour?
The gigabytes of music downloaded in one hour is 19.8 gb per hour
How many gigabytes of music were downloaded in one hour?From the question, we have the following parameters that can be used in our computation:
Size = 75.24 gigabytes
Time = 3.8 hours
The rate is then calculated as
Rate = Size/Time
Substitute the known values in the above equation, so, we have the following representation
Rate = 75.24/3.8
Evaluate
Rate = 19.8
Hence, the rate is 19.8 gb per hour
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PLEASE HELP I NEED WORK SHOWN DONT UNDERSTAND
3. A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel
Hills. The tower emits a signal that reaches receivers that are within 45 miles of its
location.
A) Write an equation in general form that describes the locations within the receiving
distance of the tower.
B) Determine if Squirrel Hills is within the receiving distance of the signal.
I
An equation in general form that describes the locations within the receiving distance of the tower is (x - 25)² + (y - 32)² = (45)².
And Squirrel Hills is within the receiving distance of the signal.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel Hills.
The tower emits a signal that reaches receivers that are within 45 miles of its location.
From the attached image,
(25, 32) is the location of the tower.
And (0, 0) is the location of Hill.
So, equation,
(x - 25)² + (y - 32)² = (45)²
To determine if Squirrel Hills is within the receiving distance of the signal:
That means,
when (x, y) = (0, 0),
(0 - 25)² + (0 - 32)² = (45)²
1649 < 2025
That means, the Squirrel Hills is within the receiving distance of the signal.
Therefore, the Squirrel Hills is within the receiving distance of the signal.
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Janelle bought a beach chair on sale at 60% of. The original price was 46.95. Find the the amount of discount in dollars
The amount of discount in dollars is 28.17
To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.
Discount = Original Price x (Discount Percentage/100)
Discount = 46.95 x (60/100) = 28.17
So, the amount of discount in dollars is 28.17
Please help me with this question.
The constants A and B for the differential equation are given as follows:
A = 0.B = -64.How to obtain the constants A and B?The solutions to the differential equation are given as follows:
y(t) = e^(8t).y(t) = e^(-8t).This means that the roots of the characteristic equation are given as follows:
r = -8 and r = 8.
Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:
(r + 8)(r - 8) = r² - 64.
Hence the differential equation is given as follows:
y'' - 64y = 0.
Hence the constants are given as follows:
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Ready
Linear Functions: Model from a Verbal Description-Instruction-Level H
Khloe spends the day in a state park. Then she hikes back to her car at a constant rate. After 1 h,
she is 8 miles (mi) from her car. After 3 h, she is 2 mi from her car.
Write an equation for Khloe's distance from her car in miles, y, as a function
of the time in hours, z.
y= x+ ?
The equation for Khloe's distance from her car in miles, y, as a function of the time in hours, x, is y = -3x + 11.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.
We have the two points of x and y.
After 1 hour, Khloe is 8 miles from her car.
When x = 1, y = 8
After 3 hours, Khloe is 2 miles from the car.
When x = 3, y = 2
Points of the linear function are (1, 8) and (3, 2)
Slope of the line = (2 - 8) / (3 - 1) = -6/2 = -3
Take a point (1, 8).
Equation of the linear function in point slope form can be written as,
y - 8 = -3(x - 1)
y - 8 = -3x + 3
y = -3x + 3 + 8
y = -3x + 11
Hence the linear function representing the situation is y = -3x + 11.
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A study done at a polling organization Randomly surveyed 1031 adults by phone. The poll found that 42% of the respondents said they spend less than three hours a day watching TV. Based on this finding calculate to 2 decimals places the ((% confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day.
Answer: To calculate the % confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day, we can use the following formula:
p +/- z*(sqrt(p(1-p)/n))
Where:
p = proportion of US adults who spend less than three hours watching TV on an average day (0.42)
z = standard normal score for a given level of confidence (e.g. for a 95% confidence level, z = 1.96)
n = sample size (1031)
Plugging in the given values, we get:
0.42 +/- 1.96*(sqrt(0.42*(1-0.42)/1031))
Simplifying, we get:
0.42 +/- 0.0156
So the 95% confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day is approximately (0.40,0.44)
So the answer is (0.40,0.44)
Step-by-step explanation:
PLS HELP ME PLSSS plsssss
Answer:
The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.
For the old bicycle with 12 inch diameter tires, the circumference is:
C = π * 12 = 12 * π inches
For the new bicycle with 16 inch diameter tires, the circumference is:
C = π * 16 = 16 * π inches
To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:
16π - 12π = 4π inches
So the difference in the circumference of the two tires is 4π inches.
It's around 12.56 inches.
If a 4 lb bag of sugar costs $2.99, what is the unit cost for a pound of sugar?
Answer: The unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.
Step-by-step explanation:
To find the unit cost for a pound of sugar, we need to divide the total cost of the 4 lb bag of sugar by the weight of the bag.
Unit cost = Total cost / Weight
Total cost = $2.99
Weight = 4 lbs
Unit cost = $2.99 / 4 lbs = $0.75 per pound
So, the unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.
It's worth noting that this calculation gives us the unit price of the sugar, which is the price per pound of sugar, and not the unit cost which is the total cost of production divided by the total number of units produced.
It's also worth noting that some sellers may use different units of measurement, and you should always check that you are comparing the same units when comparing prices.
Answer:
The unit cost for a pound of sugar would be $0.75.
To find the unit cost, divide the total cost by the number of pounds: $2.99 / 4 lbs = $0.75/lb.
Step-by-step explanation:
The debt-to-assets ratio formula is: Debt-to-assets ratio = total liabilities/total assets. If your total liabilities are $3,228 and your total assets are $5,091. What is your debt-to-assets ratio?
The debts to assets ratio is 0.63
How to calculate the debts to assets ratio ?The formula for calculating debts to assets ratio is
total liabilities/total assets
The total liabilities is $3,228
The total assets is $5,091
Therefore the debts to assets ratio is
3228/5091
= 0.63
Hence the debts to assets ratio is 0.63
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Make sure to show working
Hope it helps. If you have any query, feel free to ask.
if a1=7 and an= an-1
Answer: -2
Step-by-step explanation:
Given, aₙ = aₙ - ₁ - 3
so,
a₂ = a₁ - 3 = 7 - 3 = 4
a₃ = a₂ - 3 = 4 - 3 = 1
a₄ = 1 - 3 = -2
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The distance from Earth to the sun is about 1.47 X 10^11 meters. The distance from Earth to the moon is 3.71 X 10^8 meters. The distance from Earth to the sun is about how many times larger than the distance from the Earth to the moon? Round your answer to the nearest whole number!
The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.
Scientific notation.
This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.
In the given question, we have;
distance from Earth to the Sun = 1.47 X 10^11 meters
and
distance from Earth to moon = 3.71 X 10^8 meters
Thus,
to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;
n = distance from Earth to the Sun/ distance from the Earth to the moon
= 1.47 X 10^11/ 3.71 X 10^8
= 3.962 x 10^2
n = 396
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Is the quotient of two real numbers an integer?
Answer:
The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.
Step-by-step explanation:
please help me !!! thankss
Answer: (6,2) (0,-2) (-3,-4)
Step-by-step explanation:
If you find the other coordinate pair groups on the graph, there is at least one that doesn't land on the line on the graph.
In the top left, (-6,-5) is not on the graph. If it had been (-6,-6) then it would've been correct, but it isn't.
In the bottom left, (0,-3) isn't on the graph. Instead, (0,-2) is.
In the bottom right, (3,-4) isn't on the graph, but (-3,-4) is.
steps to solve 5x+2y=9 when x+y=-3
The simultaneous equation 5x + 2y = 9 and x + y = -3 is solved by elimination method as follows
How to solve the simultaneous equationThere are various methods of solving simultaneous equation however for this problem we solve with elimination method
The equation is 5x + 2y = 9 and x + y = -3
multiply x + y = -3 by 2
2x + 2y = -6
subtract 2x + 2y = - 6 from 5x + 2y = 9
5x + 2y = 9
2x + 2y = - 6
this will result to 3x = -15
solve for x by dividing by 3
x = -5
substitute x = -5 to x + y = -3
-5 + y = -3
y = -3 + 5
y = 2
hence x = -5 and y = 2
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Derive by means of the direct formulas the following functions
The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.
Define the method of direct formula.The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.
Explain the generic steps involved in direct formula method.The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.
To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:
y = (4x+9x^2)(3x-7x^4)
y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4
Using the distributive property, we can simplify the expression by combining like terms:
y = 12x^2 - 28x^5 + 27x^3 - 63x^6
y = (12x^2 + 27x^3) - (28x^5 + 63x^6)
So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6
The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.
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Find a counterexample to show that the statement is false. (Select all that apply.)
X >
none of these
X> 2
-1 < x < 0
0 < x < 1
XS-1
X> 1
X
If a1=3 and an=-2an find f 8
Answer:
a₄ = 25
Step-by-step explanation:
using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then
a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7
a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13
a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25
Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
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Last time it said 14 was wrong, is 14.1 correct?
Quadrilateral GHIJ is similar to quadrilateral KLMN find the measure of side MN
Answer: I believe 14.1 should be correct
Step-by-step explanation:
Given that we know one side length is 52 and the other is 21, we can use these values to create a scale.
52/21 = 2.4761, so we know that all sides will decrease by a scale of this value.
Given that, we can find the length of the MN. 35/2.4761 = 14.135
The question asks to round to the nearest tenth, so the answer should be 14.1. hope this helps!
(v-7)(v+5)(v-3)=0 solve the quadraticequation
A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3
Solving quadratic equations?The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given the quadratic expression below:
(v-7)(v+5)(v-3)=0
Required
The solution to the system of equation
Equate each expression to zero calculate the value of 'v' as shown:
v - 7 = 0
v = 0 + 7
v = 7
Also, v + 5 = 0
v = 0 - 5
v = -5
Similarly, v - 3 = 0
v = 0 + 3
v = 3
Hence the solution to the given equation is v = 7, -5 and 3
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If P(D) = 0.26 and P(R) = 0.38, what is P(D or R) if D and R are independent?
If D and R are independent, then P(D or R) = 0.8412
What are independent events?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)
P(D) = 0.26 and P( R) = 0.26 , if D and R are independent, then,
P(D or R) = P(D) + P(R) - P(DnR)
then P(DnR) = P(D) × P(R) = 0.26×0.38 = 0.0988
P(D or R) = 0.26+0.38-0.0988
= 0.8412
Therefore the probability of P(D or R) if D and R are independent is 0.8412
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Please help answer this !!!!
The area of the rectangle with a length of (x + 5) cm and width of (x + 2) cm is (x² + 7x + 10) cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. The area of a rectangle is the amount of space that it occupies. The area is calculated using:
Area = length * width
The rectangle shown has a length of (x + 5) cm and width of (x + 2) cm. Hence:
Area = length * width
Substituting:
Area = (x + 5)(x + 2)
Area = x² + 2x + 5x + 10
Area = (x² + 7x + 10) cm²
The area of the rectangle is (x² + 7x + 10) cm²
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1) Given f(x) = 3(1.04)^x
a) Is the function growth or decay?
b) Determine the growth/decay rate in %.
Answer:
a) The function is growth.
b) The growth rate in % is 4%. This can be determined by taking the natural logarithm of the coefficient (1.04) and multiplying it by 100.
ln(1.04)*100 = 3.98% ≈ 4%.
1.) How are the tangents of complementary angles related?
2.) How are the sine and cosine of complementary angles related?
3.) How are the two non-right angles in a right triangle related?
a.)They are equal.
b.)They are complementary.
c.)They are reciprocals.
(All these three questions have the same three answer choices.)
The relationship between the trigonometric ratios of the non-right angles in a triangle and the measures of the angles are;
1.) c.) They are reciprocals
2.) a.) They are equal
3. b.) They are complementary
What are non-right angles in a right triangle?The non-right angles in a right triangle are he two acute angles in the right triangle.
1) Complementary angles are angles that have a sum of 90°
Let A and B be two complementary angles, we get;
m∠A + m∠B = 90°
Let a and b represent the lengths of the opposite sides to the complementary angles ∠A and ∠B
Let side a represent the side opposite to the angle ∠A and let side b represent the side opposite to the angle ∠B, we get
tan(A) = a/b tan B = b/a
Therefore, tan(B) is the reciprocal of tan(A)
The correct option is c,) They are reciprocals
2) Let r represent the length of the hypotenuse of the right triangle, we get;
sin(A) = a/r
cos(A) = b/r
sin(B) = b/r
cos(B) = a/r
The values, sin(A) = cos(B), and sin(B) = cos(A), therefore;
The sine and cosine of complementary angles are equal, therefore, option a is correct3) The sum of angles in the right triangle is 180°, therefore;
m∠A + m∠B + 90° = 180°
m∠A + m∠B = 180° - 90° = 90°
m∠A + m∠B = 90°
The sum of the two non-right angles in a triangle is 90°, therefore, the two non-right angles re complementary.
The correct option is therefore; b.) They are complementary
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1. Amanda is attempting to launch a model rocket over the roof of her two-story house.
The path of the rocket, without consideration of the house, can be modeled by a
quadratic equation, where y represents the distance above the ground in yards
and x represents the horizontal distance in yards away from Amanda.
•The rocket will be launched from the ground 1 yard in front of Amanda.
•The rocket will reach a maximum height of 16 yards above the ground when the
rocket is 5 yards in front of Amanda as measured along the ground.
• The rocket would land on the ground 9 yards in front of Amanda.
Which equation represents the rocket's path?
A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec
How to determine when is lands?Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.
Ans as h = -5t2+30t+10
at t=0, H = 10, which is height of the building from the ground
at t= 2 sec
h= -5.4+30.2+10
= -20+60 +10 = 50 m
For max height dh/dt = 0
-10t+30 = 0
t=3 sec
Therefore, the Distance from ground = 10 + height after 3 sec
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