3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.
what is polynomial?Algebraic expressions called polynomials include constants and indeterminates.
Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers.
Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
According to our question-
-3x3 + 2x2 + 11x - 20 + (10/(-x-7)) = 3x4 + 19x3 - 25x2 - 57x + 150
In order to perform synthetic division, we must first remove the minus sign from the divisor and write out
-7 | -3 -19 25 57 -150
| 21 -14 -77 140
-3 2 11 -20 -10
obtain that
3x4 + 19x3 - 25x2 - 57x + 150 / (-x-7) is equivalent to 3x4 - 19x3 - 25x2 - 57x + 150 / (x+7) is equivalent to 3x3 + 2x2 + 11x - 20 + (10/(-x-7)).
Hence, 3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.
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Triangle KJL is similar to triangle HGI what is the length of HG
Answer:
3.75mm
Step-by-step explanation:
4.5/3=1.5
1.5(2.5)=3.75
the ratios are the same
There is a dramatic change in desert temperatures from day to night because:
A: of the lack of nitrogen in the soil.
B: of the lack of water.
C: sand is such a poor insulator.
D: of the lack of vegetation
There is a dramatic change in desert temperatures from day to night because B. of the lack of water.
Why is there a change in temperature?It should be noted that because the air in the desert is so dry, heat escapes quickly at night, the temperature can vary dramatically from day to night. The temperature during the day averages 38°C, while at night it can drop to -4°C in some deserts. The temperature varies greatly depending on where you are in the desert.
During the day, the sand's radiation from the sun's energy superheats the air, causing temperatures to rise. And, because the desert air is so dry, heat escapes quickly at night, according to NASA. The desert biomes are the driest of all biomes.
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A university will spend at most $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250, and each keyboard will cost $50.
Which inequality represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab?
fifty x plus two hundred fifty y, symbol, four thousand five hundred
two hundred fifty X, plus fifty Y, symbol, four thousand five hundred
two hundred fifty X, plus fifty Y, symbol, four thousand five hundred.
fifty X plus two hundred fifty Y, symbol, four thousand five hundred
...
The inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500
Which inequality represents all possible combinations?
The given parameters are:
Spending = At most $4,500
Cost of monitor (x) = $250 per unit
Cost of keyboard (y) = $50 per unit
The total spending is represented as
Total = 250 * x + 50 * y
This gives
Total = 250x + 50y
The spending is at most $4,500 i.e less than or equal to
So, we have
250x + 50y <= 4500
Hence, the inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500
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HELP PLEASE ?! HURRY
Only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.
What is a expression? What is a mathematical equation? What is constant of proportionality?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.The general equation of a straight line is y = mx + c. The equation can also be used to represent direct proportionality as -
y = mx
m = y/x
[m] is called constant of proportionality.
Given is a graph as shown in the figure.
The graph represents a proportional relationship. The possible coordinates that can be plotted are (x, y) and not (y, x). Only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.
Therefore, only a line that goes from (0, 0) and (3.6, 14.4) satisfy the given relationship.
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how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
A small change in x can change the conclusion of our test.
Given :
how would your conclusion change if your sample mean had been 1.355 mg/l.
t - test :
A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.
if x = 1.355
t = 1.355 - 1.3 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 * [tex]\sqrt{30}[/tex] / 0.18
= 1.67
df = n - 1
= 30 - 1
= 29
P - value from t table :
p = 0.525
fail to reject [tex]H_0[/tex]
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Full question :
The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 mg/liter of copper. You are testing water from a new source, and take 30 water samples. The mean copper content in your samples is 1.36 mg/l and the standard deviation is 0.18 mg/l. There do not appear to be any outliers in your data .
how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
In this diagram, the area of the large square is equal to the combined areas of the tilted square and the four right triangles.
(the picture)
When written as an equation, this relationship can be simplified algebraically, as shown in these 4 steps.
Step 1: (a + b) (a + b) = c2+ 2ab
Step 2: a2 + 2ab + b2 = c2 + 2ab
Step 3: a2 + 2ab ─ 2ab + b2 = c2 + 2ab ─ 2ab
Step 4:
What equation fits in the box in Step 4 to complete the proof
(part B)
Builders use the equation from Part A to determine the number, height, and depth of stairs necessary to extend from the first floor to the second floor of a building.
Given that the ceiling is 12 feet high, stairs are 8 inches high and the stairwell is 16 feet long, describe in detail how a builder could use the equation to determine the number, height, and depth of the stairs.
Answer:
Step-by-step explanation:
The number of beads in a jar is 50 to the nearest ten.
(a) What is the minimum possible number of beads in the jar?
(b) What is the maximum possible number of beads in the iar?
Answer:
a) 45
b) 54
Step-by-step explanation:
a) To be able to round up to the nearest 10, the number in the "ones column" needs to be 5 at the minimum.
You could argue it could be a decimal point however, you shouldn't really have a decimal of a bead ( it's possible but it over complicates the answer ) and, it's to the nearest 10, not nearest one decimal point for example.
Therefore, the min is 45 beads
b) ( The above poster was correct oops, I made a silly mistake )
The max is 54 beads as if anything in the ones column is under 4, you can't round up to the nearest 10. Hence it remains as 50 when rounding
Therefore, the max is 54 beads
What is the value of K?
After solving the quadratic equation, the value of k will be equal to 71.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given equation in the question,
4x² - 5x = -6
4x² - 5x + 6 = 0
k = b² - 4ac
⇒ (-5)² - 4(4)(6)
k = 25- 96
k = -71 or,
k = i(71)
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What is the slope of the line?
5(y+2)=4(x-3)5(y+2)=4(x−3)
Answer:
4/5
Step-by-step explanation:
Jane had 5 1/6 pecan pies. Marge had 4 3/6 pecan pies. How much pie do they had all together?
Answer:
9 4/6
Step-by-step explanation:
5 + 4 = 9
1/6 + 3/6 = 4/6
9 4/6
Hope this helps! :)
Find the area of the trapezium.
Answer:
68 cm^2
Step-by-step explanation:
A = ((a+b)/2) x h
A = ((6+11)/2) x 8
A = 68 cm^2
I hope my answer helps you.
Answer:
Area of the trapezium is 68[tex]cm^{2}[/tex]
Step-by-step explanation:
[tex]Given[/tex],
[tex]Parallel side\\[/tex] [tex]A[/tex]= 6cm
[tex]Parallel[/tex][tex]sideB=11cm[/tex]
[tex]Height = 8[/tex]
Formula to find the area of the trapezium
[tex]Area[/tex] [tex]of[/tex][tex]Trapezium[/tex]=[tex]\frac{1}{2}(a+b)h[/tex]
[tex]\frac{1}{2}[/tex][tex](6+11)8[/tex]
[tex]\frac{1}{2}[/tex] X[tex]136\\[/tex]
[tex]68[/tex]
Hence the area of the trapezium is 68
the graph shoes the value a stock( to the nearest dollar) over an 8-hour period. FInd the average rate of change in the stock from hour 3 to hour 7. Round to the nearest cent if necessary.
The average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.
What is average rate of change in stock?
By subtracting the price of a security at time B from the price of the same security at time A and dividing the result by the price at time A, the price rate of change can be calculated. The indicator is a technical analysis tool that measures unbounded velocity versus a zero-level middle.We need to find the average rate of change of stock from 1 hour to 6 hours.
The value of stock was $11 in hour 1 and $10 in hour 6.
Average rate of change = Δy/ Δx
= $10 - $11 / 6-1
= - $1/5
= -$0.20 /hr
Hence, the average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.
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PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Solve for x. Round your answer to the nearest tenth.
A. 11.5
B. 10.2
C. 12.0
Answer: 11.5
Step-by-step explanation:
[tex]\sin 35^{\circ}=\frac{x}{20}\\\\x=20 \sin 35^{\circ}\\\\x=11.5[/tex]
Members of a softball team raised $2089.50 to go to a tournament. They rented a bus for $1087.50 and budgeted $41.75 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament would be = 24 players
What is softball game?The softball game is the type of game that involves two teams which is made up of 9. - 10 players.
The total amount of money raised by a softball team=
$2089.50
The amount of money spent on rented bus = $1087.50
The amount left after rent deductions= 2,089.50 - 1,087.50 = 1,002
The amount budgeted for meals for each player= $41.75
The number of players that would be brought for tournament= 1,002/41.75
= 24 players.
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What is the value of x in the solution of systems below?
The solution for this system of equation will be [tex]x=4, y=-3.[/tex]
We will solve the given system of equation by the method of substitution. Now we label the equations as [tex]2x+y=5....(i)[/tex] and [tex]-3x-5y=3....(ii)[/tex].
Now from equation [tex](i)[/tex] we will find the value of [tex]y[/tex] which is [tex]5-2x[/tex]. Then we will substitute the value of [tex]y[/tex] in equation [tex](ii)[/tex].
So, [tex]-3x-5\times(5-2x)=3[/tex]
⇒ [tex]-3x-25+10x=3[/tex]
⇒ [tex]7x-25=3[/tex]
⇒ [tex]7x=28[/tex]
[tex]\therefore x =\frac{28}{7}=4....(iii)[/tex]
Now we will take the value of [tex]x[/tex] from equation equation [tex](iii)[/tex] and substitute in equation [tex](i)[/tex] to get the value of [tex]y[/tex].
So, [tex](2 \times 4)+y=5[/tex]
⇒ [tex]8+y=5[/tex]
⇒ [tex]y=8-5[/tex]
[tex]\therefore y=3[/tex]
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You have two instruments with which to measure the height of a tower. If the true height is 100 meters, measurements with the first instrument vary with mean 100 meters and standard deviation 1. 2 meters. Measurements with the second instrument vary with mean 100 meters and standard deviation 0. 85 meter. You make one measurement with each instrument. Your results are X1 for the first and X2 for the second, and are independent. A) To combine two measurements, you might average them, Y=(X1+X2)/2. What are the mean and standard deviation of Y? b) It makes sense to give more weight to the less variable measurement because it is more likely to be close to the truth. Statistical Theory says that to make the standard deviation as small as possible you should weight X2 is very close to half the variance of X1, so X2 should get twice the weight of X1. That is, use W=1/3X1 + 2/3X2 What are the mean and standard deviation of W?
(a) The mean of Y is 100 meters, and the standard deviation of W is approximately 0.7348 meters.
(b) The mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
a) To find the mean and standard deviation of Y, where Y = (X₁ + X₂) / 2, we use the properties of the mean and variance of a sum of independent random variables.
Mean of Y:
The mean of Y is simply the average of the means of X₁ and X₂, as the measurements are independent and have the same true height of 100 meters.
Mean(Y) = (Mean(X₁) + Mean(X₂)) / 2 = (100 + 100) / 2 = 100 meters
The standard deviation of Y:
When adding or subtracting independent random variables, the variances add up. Since the measurements are independent, we can use the formula:
Var(Y) = Var((X₁ + X₂) / 2) = (Var(X₁) + Var(X₂)) / 4
Now, calculate the variance of Y:
Var(Y) = (1.2² + 0.85²) / 4 ≈ 0.54
Standard deviation(Y) = √Var(Y)
≈ √0.54
≈ 0.7348 feet
b) Now, let's find the mean and standard deviation of W, where W = (1/3)X₁ + (2/3)X₂.
Mean of W:
Mean(W) = (1/3) * Mean(X₁) + (2/3) * Mean(X₂)
= (1/3) * 100 + (2/3) * 100
= 100 meters
The standard deviation of W:
To calculate the standard deviation of W, we need to find the variance of W and then take its square root.
Var(W) = (1/3)² * Var(X₁) + (2/3)² * Var(X₂)
= (1/9) * 1.2² + (4/9) * 0.85²
Now, calculate the variance of W:
Var(W) = 0.0181 + 0.1956 =0.481
Standard deviation(W) = √Var(W)
≈ √0.481
≈ 0.6935 meters
So, the mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
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Will give 5 stars and give thanks
Answer:
x=36
Step-by-step explanation:
The length of a secant segment and a tangent segment drawn to a circle drawn from an external point is:
whole secant * external secant = tangent^2
(12+x)*12=24^2
144+12x=576
12x=432
x=36
A frying pan has a diameter of 13 inches. What is the area to the nearest whole square inch of the smallest cover that will fit on top of the frying pan
Answer:
176cm
Step-by-step explanation:
area of a circle(cover)= pie r squaretherefore r=13÷2 =r=7.5. and pieces =22÷7
then we substitute
22÷7×(7.5 ×7.5)
=3.14×56.25
=176.58
to the nearest whole =176cm
the volume of a rectangular prism is represented by the expression (x^3-2x^2-20x-24). if the length is (x-6) and the height and width are equal, what is the width of the prism?
The width of the prism is x+2. The smallest dimension of an item or figure on a planar surface is its width.
How do you find volume in rectangular prisms?When calculating the volume of a rectangular prism, we multiply the prism's length, width, and height.
A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section.
Given, the volume of the prism
= x³ + 2x²+ 20x - 24
length = (x- 6 )
height and width are equal then
h * w = x³ + 2x²+ 20x - 24 / (x - 6)
= (x + 2 ) (x + 2)
h = (x +2 )and
w = (x+2)
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what is (-4x² + 3x + 3)(x² - 2x + 2) as a polynomial
The given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial expression is, (-4x² + 3x + 3)(x² - 2x + 2)
We have to simplify the expression by multiplying the expression as,
=-4x²(x² - 2x + 2)+3x(x² - 2x + 2)+3(x² - 2x + 2)
=-4x⁴+8x³-8x²+3x³-6x²+6x+3x²-6x+6
= -4x⁴+11x³-5x²+6
Thus, the given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
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PLSS HELP MEEE!! It'll be very appreciated
$35.82 total. He gives the cashier $50. How much change should Rishank receive?
Answer: $14.18
Step-by-step explanation:
Because total change is the amount the cashier is giving back to us,
we can do
$ amount given - $ price of order = $ total change
So:
50 - 35.82 = $14.18
The cashier will give us $14.18 back in change.
Damian was out at a restaurant for dinner when the bill came. His dinner came to $26. He wanted to leave a 31% tip. How much was his meal plus the tip, before tax, in dollars and cents?
Answer:
34 dollars and 6 cents
Step-by-step explanation:
1 percent = 0.26
0.26 x 31 = 8.06
26 + 8.06 = 34 dollars and 6 cents
I believe it is 34.06
justin purchased a lawn sprinkler costing 9.23. If Justin recived 9.07 in change, how much money did he give the cashier
Answer: $18.30
Step-by-step explanation:
The sprinkler cost 9.23, and the change is 9.07, so adding both of them equal $18.30
Answer 18.3
eeeeeeeeeeeeeeeeeeeeeeee
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 9x2 − 3xy + 5. The friends have already collected the following number of cans:
Jessa: 5xy + 2
Tyree: 6x2 − 5
Ben: x2
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Answer:
Part A
7x² + 5xy – 3
Part B
2x² – 8xy + 8
Step-by-step explanation:
Part A
the canned food collected so far is the sum of the canned food the three friends have by combining the expression
5xy + 2 + 6x² – 5 + x²
= 6x² + x² + 5xy + 2 – 5
= 7x² + 5xy – 3
Part B
The total of cans the friend need to collect to meet their goal is the canned food collected so far minus their targeted goal
= 9x² – 3xy + 5 – (7x² + 5xy – 3)
= 9x² – 3xy + 5 – 7x² – 5xy + 3
= 9x² – 7x² – 3xy – 5xy + 5 + 3
= 2x² – 8xy + 8
i hope this helps
what are two square roots of 484
Answer:
22, and -22
Step-by-step explanation:
22x22=484
-22x(-22)=484
PLEASE HELP ME PLS ......
Answer:
1 = 45
2 = 75
3 = 60
4 = 41
5 = 71
6 = 109
Step-by-step explanation:
This may seem tricky at first, but if you follow the order of the numbers, you can find them fairly quickly using the values already given.
For angle 1:
The angle above it of 45 degrees is similar to angle 1, so that it automatically going to be 45
For angle 2:
The same concept for angle 1 applies for angle 2, so it will be 75 degrees.
For angle 3:
All triangles add up to 180 degrees. So, since we have angles 1, and 2, solve to find 3:
180 - 45 - 75 = 60
For angle 4:
All straight lines add up to 180 degrees. So solve to find angle 4 using the value we found for angle 3:
180 - 60 - 79 = 41
For angle 5:
Angle 5 is part of another triangle and we have two of the angles already. So solve to find angle 5 using the logic used to find angle 3:
180 - 41 - 68 = 71
For angle 6:
angles 5 and 6 are part of a straight line, so use the same logic for angle 4 and solve for angle 6:
180 - 71 = 109
what do you add to 4 5/8 to make 6
Answer: 1 3/8
Step-by-step explanation:
6 - 4 5/8 = 1 3/8
Since you are missing a part to the sum, you use subtraction to find the missing part.
Does anyone know the area of this figure in square inches
The area is 120 [tex]cm^{2}[/tex].
What is area?Area is the size of a two-dimensional surface, usually expressed in square units, such as square feet or square meters. It is the amount of two-dimensional space enclosed within a given set of boundaries. Area can be calculated for various shapes, including squares, rectangles, triangles, circles, and more complex shapes. Area is also a measure of the amount of space an object occupies. In mathematics, area is used to measure the size of a shape or region in a plane. It can also be used to calculate the size of a figure, such as the area of a triangle, or to measure the area of an enclosed space, such as a garden or a room.
Given:
AB = CD = 8cm
AD = BC = 12cm
EF = DH = 4cm
So, the required area is A = Area (ABCEFD) = Area (ABCD) + Area (CEFD)
Area of ABCD = Area (ABCD) = AB × BC
⇒ 12 × 8 = 96 [tex]cm^{2}[/tex]
Area of CEFD = Area (CEFD) = 0.5 (CD + EF) × HD
⇒ 0.5 × (8 + 4) × 4 = 24[tex]cm^{2}[/tex]
Now, the required area is
⇒ A = 96 [tex]cm^{2}[/tex] + 24 [tex]cm^{2}[/tex] = 120 [tex]cm^{2}[/tex]
Hence, the required area of the figure is 120 [tex]cm^{2}[/tex].
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help me please!!! :)
Answer:
A
(will be continued)
Step-by-step explanation:
this is an exponential graph
The original mass is 7.71 because it is being multiplied by the percentage.
0.9333 in percentage form is 93.33
Since it is being multiplied, by the original mass this means that 93.33% of it is the amount being left over.
100% - 93.33% = 6.67%
this is the decrease in the amount of the thing
***tell me if i explained it clearly i'm not sure if i did