Use long division to the quotient is [tex]5 x^5+90 x^2-134 x+3[/tex]
What is quotient?
A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.A fraction's quotient is the whole number that results from simplifying the fraction. The quotient is the fraction's decimal form if the simplified fraction yields a non-whole number.
[tex]\begin{aligned}& \text { Simplify }\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-134 x+3 \\& \text { Steps } \\& \left(5 x^5+90 x^2-135 x\right)+(x+3)\end{aligned}[/tex]
[tex]Simplify $\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-135 x+x+3$[/tex]
[tex]=5 x^5+90 x^2-135 x+x+3[/tex]
[tex]Add similar elements: $-135 x+x=-134 x$[/tex]
[tex]=5 x^5+90 x^2-134 x+3[/tex]
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-2(2x-3)=-22 i dont get it
An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
By solving a linear equation, it can be calculated that-
The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet
What is a linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, the linear equation is
Let the time taken by the airplane to meet the same altitude be t minutes
An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.
So altitude of the first airplane after t minutes = 55800 - 3500t
At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.
Altitude of second airplane = 2700t
By the problem,
The linear equation is
55800 - 3500t = 2700t
2700t + 3500t = 55800
6200t = 55800
t = 9 minutes
Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet
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Write the linear equation in slope intercept form
The given linear equation (1/3)x+ y=2 in the slope-intercept form is
y=(-1/3)x+2.
Explain about slope-intercept form?Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).
Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.
Given linear equation is:
(1/3)x+ y=2
The following is the slope-intercept form of the given linear equation:
y=(-1/3)x+2
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the quadtratic expression -3x^2 +6x + 72 will equal zero when x equals
The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Here in the problem, we have to find the roots of the quadratic equation
- 3x² + 6x + 72 = 0.
3x² - 6x - 72 = 0.
x² - 2x - 24 = 0.
x² - 6x + 4x - 24 = 0.
x(x - 6) + 4(x - 6) = 0.
(x - 6)(x + 4) = 0.
x = 6 Or x = - 4 are the values of x when the expression will be zero.
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write a system of three linear equations with three variables each that has the unique solution . write your equations in standard form. use the variables , , and with non-zero coefficients.
the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
2x + 3y + 4z = 30
3x + 4y + 5z = 45
5x + 6y + 7z = 75
The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.
The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.
The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.
Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.
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a mistake was made in the steps shown to simplify the expression. which step includes the mistake?
The step in which there is a problem is the operation in step 4. option C
Where is the mistake?In this question, we are expected to solve the problem in a number of steps. We know that in mathematics, the solution to a given problem can only be worked out through a number of steps that can help us to be able to know what the correct solution of the problem ought to be.
In this case we have a simplification problem. It should be know that the acronym of BODMAS has to be called to mind here and that is;
BracketOfDivisionMultiplicationAdditionSubtractionMathematical operations would have to be carried out in this order else there would be a mistake in it. We can see that the addition in step 4 before division did not follow the principle of BODMAS thus that step is wrong.
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The wholesale price for a chair is $169. A certain furniture store marks up the wholesale price by 16%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.
Need Help!
The price of the chair in the furniture store is $94.
How to calculate the price of the chair in the furniture store?Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.
The price of the chair in the furniture store will be:
= $169 + (16% × $169)
= $169 + $27.04
= $196
The price is $194.
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two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price
Store B offers better $0.85 per-roll price than store A.
What is division?One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.
Given, two stores sell identical sandwich rolls in different size packages.
Store A sells a six-pack for $5.28.
To find the unit price,
we take division of 5.28 with number 6.
The unit price of sandwich roll for store A,
= 5.28 / 6
= $0.88
To find the unit price of sandwich roll for store B,
we take division of 3.40 with number 4.
= 3.40 / 4
= $0.85
And $0.85 < $0.88.
Therefore, Store B offers better per-roll price.
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Let f(x) be a 4th-degree polynomial function with zeroes 1,-1, and 3-i. If f(0)=20, write the equation in:
a) Factored form
b) Standard form
The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10
How to determine the polynomial expression?Factored form
The given parameters are
Degree = 4Zero = 1,-1, and 3-iThere are complex numbers in the above zeros
This means that, the other zero is
Zeros = 3 + i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))
This gives
P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)
Evaluate the products
P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]
So, we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
P(x) = (x - 1)(x + 1)[(x - 3)² + 1]
The standard form
In (a), we have
P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]
Expand
P(x) = (x² - 1) * (x² - 6x + 9 + 1)
So, we have
P(x) = (x² - 1) * (x² - 6x + 10)
Remove the brackets
P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10
Evaluate the like terms
P(x) = x⁴ - 6x³ + 9x² + 6x - 10
Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10
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Luis typically eats 4 1/4 ounces of fruit each day. Today he ate his usual amount. Write each answer as a fraction and as a decimal. Use bar notation is necessary.
Answer:
Fraction: 4 1/4 = 17/4
Decimal: 17/4 = 4.25
Step-by-step explanation:
mathematics-help-dilate-
The dilated figure is plotted and attached and the coordinates is written as
preimage image
A (-4, 3) A; (-8, 6)
B (3, 2) B' (6, 4)
C (-4, 0) C' (-8, 0)
How to find the coordinates of the dilationDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
A (-4, 3) → (-4 * 2, 3 * 2) → A' (-8, 6)
B (3, 2) → (3 * 2, 2 * 2) → B' (6, 4)
C (-4, 0) → (-4 * 2, 0 * 2) → C' (-8, 0)
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A random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the test statistic is?
Answer:
Step-by-step explanation:
Sorry if this is different, but based on what I read, here is the answer.
100 x 0.85 = 85
therefor it is 85%, which is significantly more than 80%
Which expression is equivalent to 10d+d-2d?
d+8
9d9d
1+8d1+8d
11d11d
pls help
Answer: 9d
Step-by-step explanation:
10d+d-2d = 9d
show that the picture and board aren't mathematically similar (diagram below)
Answer:
See below
Step-by-step explanation:
If the figures were similar the corresponding sides would be proportional.
[tex]\frac{10}{12}[/tex] = [tex]\frac{8}{10}[/tex] This statement would be true if the sides were proportional, but it is not true. Cross multiply.
10(10) ≠ (8)(12)
100≠96
Please help meee !!!??
its A
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Q9.
Rachel, Samina and Tom share £600 between them.
2
Rachel gets 2/5 of the £600
ima
Samina gets 1/4 of the money that is left over.
Tom gets the rest of the money.
Tom says,
"I would have got more money if we had shared the £600 equally between us."
Is Tom correct?
You must show how you get your answer.
No. Tom is not correct.
If the money were split equally everyone would've gotten £200.
But, if everyone went by the mentioned distribution, then,
Rachel would get = 2/5 x 600 = £280
Remainder money = 600 - 280 = £320
Samina would get = 1/4 x 320 = £80
Tom would get the remaining money = 600 - (280 + 80)
= 600 - 360
= £240
Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.
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a surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called a) lot-and-block. b) torrens. c) metes and bounds. d) rectangular survey.
The method which the surveyor followed was the method of metes and bounds.
The surveyor followed a property's legal description by starting at a point of beginning, then following the indicated directions between natural and artificial landmarks to arrive back at the point of beginning, using the method called metes and bounds.
Metes and bounds are the natural markers that define the limits or boundaries of a piece of property. Rivers, roads, stakes, and other natural or artificial markers are examples of metes and bounds landmarks.
A system or method of representing land, real property (as opposed to personal property), or real estate is known as metes and bounds. The technique has been used in England for centuries and is still used to define general boundaries there.
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The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to
clean 2 hamster cages.
Complete the table.
Minutes
15
Cages cleaned 2 4
Graph the data from the table.
Cages cleaned
20
18
16
14
12
10
8
30 55
•
90
8 10
The complete table will be;
Minutes 15 30
Cages cleaned 2 4
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Now,
Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.
Hence, By definition of proportion we get;
Let the time to clean 4 hamster cages = x
So, We get;
⇒ 15 / 2 = x / 4
⇒ 15×4 / 2 = x
⇒ 30 = x
⇒ x = 30
Thus, It take 30 minutes to clean the 4 hamster cages.
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20
Write "less" or "greater" in the blank.
972 is
than 792
Answer:greater
Step-by-step explanation:
Answer:
972 is greater than 792.
Jin went to the grocery store and bought bottles of soda and bottles of juice. Each
bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar.
Jin purchased a total of 16 bottles of juice and soda which collectively contain 300
grams of sugar. Graphically solve a system of equations in order to determine the
number of bottles of soda purchased, x, and the number of bottles of juice
purchased, y.
Answer: x = 6, y = 10; as a point, that would be (6, 10).
Step-by-step explanation:
To do it graphically, you would just graph the equations 25x + 15y = 300 and x + y = 16. Then, you would find the intersecting point.
To do this, you should convert to point-slope format.
15y = -25x + 300 and x + y = 16
1) y = -5/3x + 20 and 2) y = -x + 16
Now, for equation 1, you start at the y-intercept (0, 20) and for every increase of 1 on the x-axis, you decrease -5/3 on the y-axis. To graph this in the software, you click on the point (0, 20) and on another point on the line y = -5/3x + 20. (Any will do, but it should be an integer. (3, 15) works.)
Do the same for equation 2. Start at the y-intercept (0, 16) and decrease 1 for every increase of 1 on the x-axis.
Look for the point(s) where the lines intercept. It is (6, 10). If you have the time, you can verify this algebraically.
What is the total cost of the rental is Dana drives the car for 15 miles?
The total cost of the rental if Dana drives the car for 15 miles is $90.2
How to determine the total cost?From the question, we have the following parameters that can be used in our computation:
C = 73.25 + 1.13m
Where
m = number of miles
This means that
m = 15
SO, we have the following equation
C = 73.25 + 1.13 * 15
Evaluate
C = 90.2
Hence, the total cost is $90.2
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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m
(a) Calculate the simple interest collected by a bank if $1500 is loaned for 3 years at 8% per annum.
(b) What amount of money did the borrower actually pay the bank?
(c) What amount of money was paid monthly?
Answer:
Step-by-step explanation:
(a)Given:
Principal Amount=$1500
Time = 3 years
Rate of Interest = 8% per annum
Find:
Simple Interest=?
According to the formula of simple interest
Simple Interest=Principal x Time x Rate of Interest
i.e., SI=PRT
SI= 1500 X 3 X 8/100
SI= $360
Therefore, the simple interest for the principal amount of the loan $1500 in 3 years at a rate of 8% per annum will be $360.
(b) According to the formula:
Total Amount= Principal Amount + Simple Interest
i.e., Total Amount = $1500+$360
Total Amount = $1860
Therefore, the loan amount the borrower will pay the bank is $1860.
a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?
The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:
0.189 = 18.9%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of these parameters in the context of this problem are given as follows:
n = 3, p = 0.7.
Then the probability of exactly one success is calculated as follows:
P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.
Missing InformationThe proportion of voters that approve the mayor's work is of 70%.
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Erica takes out a loan to purchase a car. She borrows 12,000 at 12% annual percentage rate. Complete the statements. The graph is [Drop Down 1]. Erica's loan is a [Drop Down 2] loan. The equation which models this loan is [Drop Down 3]. If Erica pays off the loan in six years, she will have paid [Drop Down 4].
An increasing exponential function is modeled as follows:
A(t) = A(0)(1 + r)^t.
The parameters of the exponential function are given as follows:
A(0) is the initial value of the exponential function.r is the growth rate of the exponential function, as a decimal.She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:
A(0) = 12,000, r = 0.12.
Then the function that describes her loan is given as follows:
A(t) = 12000(1.12)^t.
After six years, the value of the loan is calculated as follows:
A(6) = 12000(1.12)^6 = $23,686.
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Given:NP=MP,NP PL prove NPL≈MPL
50 points please help asap
The domain is set of all real numbers and the range is y ≥ -4
How to determine the domain and the range of the function?From the question, we have the following parameters that can be used in our computation:
The equation is given as
g(x) = |x + 4|
The domain
The above equation is an absolute value equation
An absolute value equation can take any value as its input
This means that the domain is the set of all real numbers
When represented as an interval, we have
The domain is (-∝, ∝)
Also, we have
-∝ < x < ∝
Hence, the domain is the set of all real numbers
The range
Here, we have
g(x) = |x + 4|
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-4, 0)
Remove the x value
y = -4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
[-4, ∝)
Another representation is
y ≥ -4
So, the range is y ≥ -4
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PLEASE HELP WITH THIS PROBLEM
Answer:
y -2 = 2(x +7)y -2 = -1/2(x +7)Step-by-step explanation:
You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).
SlopeThe given equation is written in slope-intercept form:
y = mx + b
where m = 2, and b = -1.
The slope of the line is m, the x-coefficient. For the given line, the slope is 2.
A parallel line will have the same slope: 2.
A perpendicular line will have the opposite reciprocal slope: -1/2.
Point-slope equationWhen you have a point and slope, it is useful to use the point-slope form of the equation for a line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...
equation of parallel line: y -2 = 2(x +7)equation of perpendicular line: y -2 = -1/2(x +7)On a team,8 girls and 5 boys devoted a total of 87 points. The difference between the number of points scored by the 8 girls and the number of points scored by the 5 boys is 57. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and boy
Answer:
Girls: 7 points each
Boys: 11 points each
Step-by-step explanation:
Josiah began earning an allowance each day. At the end of 6 days he buys a video game that costs $150 and has $102 left over. How much money does he earn each day in allowance
Answer:
42
Step-by-step explanation:
150+102=252
252/6=42
Jaime y rocío están pintando una pared con cubos de pintura idénticos. Si Jaime ha gastado 2/5 de su pintura y rocío,3/5. ¿Quién ha gastado más? ¿Qué cubo de pintura estará más lleno?
Answer:
Step-by-step explanation:
Rocio ha gastado mas. El cubo de Jaime esta mas lleno.
Rocio gasto otro poco mas porque 3 esta mas grande que 2
