The polynomial we get after solving this is (x+6).
To simplify this expression, we need to use the rules of algebra. First, we can factor the numerator to get (x-6)(x+6) so the expression becomes:
(x-6)(x+6)÷ (x-6)
Now we can cancel out the (x-6) terms in the numerator and denominator to get:
(x-6)(x+6)÷(x-6) = (x+6)
This is the simplified form of the expression. Note that this result is only valid when x is not equal to 6, since division by zero is undefined.
What is a Polynomial?
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
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COMMON IDENTITIES IN VECTOR ANALYSIS
How do i prove that .......... if F, G, and H are scalar fields?
The cross product or the curl of F, G, and H are zero so they are scaler fields.
What are dot products and cross products?The cosine of the angle between the vectors and their magnitude are combined to form the dot product.
The dot product is represented by A.B = ABCos θ.
The sine of the angle between the vectors and their magnitude are combined to form the cross-product.
The cross product is represented by A×B = ABSin θ.
Given, F × (G × H) = (F . H)G - H(F .G).
∴ F × (G × H) = (FHcosФG) - H(FGcosФ).
F × (G × H) = FGHcosФ - FGHcosФ.
F × (G × H) = 0.
We know that cross-product is the curl of a vector field and if the curl is zero it is a scalar field.
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Lines h and j are parallel and cut by transversal k. What is the measure of angle x ?
A. 109°
B. 119°
C. 161°
D. 171°
The value of angle x is 161 degree. So the option B is correct.
In the given question, lines h and j are parallel and cut by transversal k.
We have to find the measure of angle x and choose the correct option.
The diagram of the given question is given below:
From the given diagram using the corresponding angle theorem
x = y
As we know that the angle of straight line is 180 degree.
So x+19 = 180
Subtract 19 on both side, we get;
x = 161 degree
Hence, the value of angle x is 161 degree. So the option B is correct.
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Khalid has 2 bags of cornmeal that each contain 25 servings. One serving is 3/4 cup. Khalid is making muffins that require 2.5 cups of cornmeal per batch. What is the maximum number of batches of muffins that Khalid can make using cornmeal?
Using ratios and proportions, he can make 15 batch of muffins from 2 bags of cornmeal
What are Ratios and ProportionsRatio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.
Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.
In this problem, we know that he has 2 bags of cornmeal
1 bag of cornmeal = 25 serving
2 bags = x
x = 2 * 25 = 50 servings
When making muffins, he needs 2.5 cups in a batch
But 3/4 cup = 1 serving
x cups = 50 serving
x = 50 * 3/4
x = 37.5 cups
1 batch = 2.5 cups
x batch = 37.5 cups
x = 37.5 / 2.5
x = 15 batch
He can make a 15 batches
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Find −0.5D. with options [9 8] [-7 -4], [9 8] [14 8], [-18 -16] [7 4], [9 8] [7 4]
The evaluation of −0.5D of the matrix gives
[9 8]
[-7 -4]
How to determine -0.5D of the matrix?
A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
Given: the matrix
D = [-18 -16]
[14 8]
To find −0.5D, multiply every number in the matrix D by -−0.5. Thus:
−0.5D = −0.5 × [-18 -16]
[14 8]
−0.5D = [9 8]
[-7 -4]
Therefore, the 1st option is the answer
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plot the image of triangle ABC under a reflection across line l
The image of the triangle ΔABC under a reflection across the line l can be obtained my making use of the laws of reflection, and the rules of a reflection transformation, to obtain the triangle ΔA'B'C', with vertices at A'(10, -5), B'(13, -6), and C'(12, -3)
Please find attached the plot of the image of the triangle ΔABC, created with MS Excel
What is a reflection transformation?A reflection transformation is one that forms a mirror image of the object across the line of reflection, such that lines joining corresponding points on the pre-image and the image are perpendicular to the line of reflection, and the corresponding points on the pre-image and the image are equidistant from the line of reflection.
Taking the coordinate of the vertices of the triangle ΔABC as A(10, 5), B(13, 6), C(12, 3), and the line l as coinciding with the x-axis, we get:
The coordinates of the image of a point (x, y) following a reflection about the x-axis is the point (x, -y)
Therefor, the coordinates of the vertices of the image of the triangle under a reflection across the line l are;
A'(10, -5), B(13, -6), C'(12, -3)Please find attached the plot of the image of the triangle ABC under a reflection, across line l, created with MS Excel.
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100 points and will mark brainliest
Answer:
The x-intercept is 40, which represents the number of monthly payments needed to repay the loan.
Step-by-step explanation:
The x-axis can be represented as y = $0, and in this graph y represents remaining balance. So, the x-intercept represents when no more money needs to be paid back on the loan.
My Truck Takes 50 Gallons of gas. I used 20⅔ gallons on Monday. 9¼ on Tuesday. And 2½ on Wednesday. How many Gallons of gas do i still have in my truck?
Answer:
17 7/12 gallons of gas.
Step-by-step explanation:
Set the fractions to like denominators. It'll make it a hell of a lot easier to add.
20 2/3rds = 20 8/12
9 1/4ths = 9 3/12
2 1/2 = 2 6/12
Adding those together gets you 31 17/12 which is 32 5/12 simplified.
Take that fraction and subtract it from your 50 gallons and it'll get you 17 7/12
identify the terms in the algebraic expression 4x2 - 5y + 7
Terms in Algebraic Expression are [tex]4x^{2}[/tex] , -5y , 7
What is an Algebraic Expression ?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Example of Algebraic Expression - 4x + 5y +8
Hence the term is the algebraic expression are -4x , 5y 8
According to the given information
The Algebraic Expression given to us
[tex]4x^{2} -5y+7[/tex]
Hence
The algebraic expression has three terms.
Terms are [tex]4x^{2}[/tex] , -5y , 7
Terms in Algebraic Expression are [tex]4x^{2}[/tex] , -5y , 7
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0.0000000536 in scientific notation
Answer: 5.36 × [tex]10^{-8}[/tex]
Step-by-step explanation:
5.36 × [tex]10^{-8}[/tex]
1. Shelby had $33.00. Then,
Now, she wants to spend all of her
money on some ice cream cones
that cost $3.00. How many ice
cream cones can she buy?
Answer:11 cones
Step-by-step explanation: She can by 11 since $3x 11 =$33
Please help me on this.
a coach took his team out for pizza after their last game. there were 14 players so they had to sit in smaller groups at different tables. six players sat at one table and got 4 small pizzas to share equally. the other 8 players sat at a different table and got 6 small pizzas to share equally. afterwards one of the players said it wasnt fair because some kids got more pizza do u agree?
Yes, it wasn't fair because some kids got more pizza.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A coach took his team out for pizza after their last game.
There were 14 players, so they had to sit in smaller groups at different tables.
Six players sat at one table and got 4 small pizzas to share equally.
Each of them got = 4/6 = 0.67
The other 8 players sat at a different table and got 6 small pizzas to share equally.
Each of them got = 6/8 = 0.75
0.75 > 0.67
Therefore, some kids got more pizza.
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Tom wants to know whether a new chest of drawers will fit next to his bed. The chest of drawers would like to buy is 70 centimeters wide.He knows that the room is 86 inches wide. The bed is 67
inches wide. Will the chest fit next to bed?
Answer:
no
Step-by-step explanation:
Tom wants to know if a 70 cm chest will fit in the space left by a 67 in bed in a room 86 in wide.
Available spaceThe space available is 86 in -67 in = 19 in.
Space neededAn approximate conversion between cm and inches is that 10 cm corresponds to about 4 in. Then 70 cm will correspond to 7×4 = 28 inches, much too wide for a 19-inch space.
The chest will not fit next to the bed.
IMAGE ATTACHED PLEASE HELP PLEASE
Answer: first one
Step-by-step explanation: when u divide the equation to (x+2) and (x-1)
Write down the equation in slope intercept form if slope m=4 and y intercept is (0,-5). Do not leave spaces.
Answer:
y=4x-5
Step-by-step explanation:
y=mx+c
m=4
c = y-intercept = -5
y=4x-5
What is the remainder when 7x^4+6x^3−9x^2−32x+95 is divided by x+1?
Only enter a number
The required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}[/tex] .
What is synthetic division?It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
When performing synthetic division of polynomials, the terms in the product that remain as fractions are referred to as the division's remainder, whereas the polynomial is referred to as the division's quotient.
[tex]= \frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}\\=7x^3-x^2-8x-24+\frac{119}{x+1}[/tex]
Thus, the required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
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I think of a number,take away 4 and multiply the result by 2.
The number that is thought in the form of expression will be 2x - 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let the number be 'x'. Then the expression is given as,
⇒ (x - 4) × 2
Simplify the expression, then we have
⇒ (x - 4) × 2
⇒ 2x - 4
The number that is thought in the form of expression will be 2x - 4.
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PLEASE I REALLY NEED HELP!!! 100 points if answer right
y=1/3x+4 is perpendicular to y=-3x-4,
y=2/5x-7 is perpendicular to y=-5/2x+7,
y=-5/2x+8 is perpendicular to y=2/5x+6,
y=-2x+6 is perpendicular to y=1/2x+3 and
y=7/5x-9 is perpendicular to y=-5/7x-11.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We know that the product of slopes of perpendicular lines is -1.
mM=-1
m is slope of one line and M is the slope of perpendicular line.
M=-1/m
y=1/3x+4
The perpendicular line is y=-3x-4
y=2/5x-7
The perpendicular line is y=-5/2x+7
y=-5/2x+8
The perpendicular line is y=2/5x+6
y=-2x+6
The perpendicular line is y=1/2x+3
y=7/5x-9
The perpendicular line is y=-5/7x-11.
Hence, the lines with corresponding perpendicular lines are
y=1/3x+4---> y=-3x-4
y=2/5x-7-----> y=-5/2x+7
y=-5/2x+8----->y=2/5x+6
y=-2x+6---->y=1/2x+3
y=7/5x-9-----> y=-5/7x-11.
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A line passes through the points (4, -1) and (2, 3). What is the slope of the line?
Answer:
-2
Step-by-step explanation:
We can find slope by using change in y over change in x, as shown:
3-(-1) = 4, and 2-4=-2, and 4/-2 = -2, so our answer is -2.
The display summarizes grades on a World History exam.
100
95
90
85
80
75
70
65
60
55
50
World History Exams
Which of the following describes the data set?
The data is univariate and categorical.
O The data is univariate and numerical.
O The data is bivariate and categorical.
O The data is bivariate and numerical.
The data set is the data is univariate and numerical.
What is set ?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
The display summarizes grades on a World History exam.
100,95,90,85,80,75,70,65,60,55, 50
The data is univariate and numerical.
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Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $6,000, annual interest: 6%, interest periods: 6, number of years: 18
The investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher.
What is compound interest?
Compound interest is a type of interest that is calculated on the initial principal of an investment as well as any accumulated interest. In other words, compound interest is interest that is earned on both the original principal and on the accumulated interest from previous periods.
To compare the investment you described to an investment of the same principal at the same rate compounded annually, we need to calculate the final value of each investment after 18 years.
For the investment you described, the final value can be calculated using the formula:
FV = P(1 + r/n)^(nt)
Where FV is the final value, P is the principal, r is the annual interest rate, n is the number of interest periods per year, and t is the number of years.
Plugging in the values given in the problem, we get:
FV = $6,000(1 + 0.06/6)^(6*18) = $6,000(1.01)^108 = $12,688.80
For the investment compounded annually, the final value can be calculated using the same formula, but with n = 1:
FV = $6,000(1 + 0.06/1)^(1*18) = $6,000(1.06)^18 = $15,848.75
Hence, the investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher. The difference in final value between the two investments is $15,848.75 - $12,688.80 = $3,159.95.
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2y+x=-15 and x=3y substitution method
Answer:x = -9, y = -3
Step-by-step explanation:
Point B with coordinates (95, 71) is mapped onto B' through a translation by vector (2,-4). What are the coordinates of B'?
(91,73)
(93,75)
(97,67)
(99,69)
The translated coordinates of B is B'(97,69).
What is translation?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation may alternatively be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Given, point B with coordinates (95, 71) is mapped onto B' through a translation by vector (2,-4).
That means, the translation is 2 units right and 4 units down.
A positive number means moving to the right and a negative number means moving to the left.
The number at the second term represents up and down movement. A positive number means moving up, and a negative number means moving down.
So, B (95, 71) → B' (95 + 2, 73 -4)
B (95, 71) → B' (97, 69)
Therefore, the coordinates of B' is (97, 69).
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A TPN solution contains 8.25 % amino acids it. If the patient needs 75 grams of protein per day, how much of the TPN solution should the patient receive per day?
The patient should receive 909 mL of the TPN solution per day.
To determine the amount of the TPN solution the patient should receive per day, we need to use the following formula:
amount of TPN solution = (grams of protein needed / percentage of amino acids in TPN solution) × 100
In this case, we are given that the TPN solution contains 8.25% amino acids and that the patient needs 75 grams of protein per day. Substituting these values into the formula, we get:
amount of TPN solution = (75 / 8.25) × 100
amount of TPN solution = 9.09 × 100
amount of TPN solution = 909 mL
Therefore, the patient should receive 909 mL of the TPN solution per day.
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In the following lever system, what is the clockwise torque? 40 N. 9m. 3m. 80 N.
Answer:
Counter Clockwise Torque = 360 Nm
Clockwise Torque = 240 Nm
Step-by-step explanation:
(Answer both please will give a brainlest )
To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the
shoreline, and that a-2.92 miles and b-3.91 miles. Round your answer to two decimal places)
A parallelogram has sides of lengths 5 and 4, and one angle is 60°. Find the lengths of the diagonals. (Round your answers to two decimal places. Enter your answers as a comma-separated list
Answer:
Dang this is hard
Step-by-step explanation:
PLS HELP!!!
Radical functions
Answer:
B
Step-by-step explanation:
Reverse the first and second elements of each ordered pair.
Solve equation:
0=2n+6n
Answer: 0=8n
Step-by-step explanation: Add 2n+6n = 8n, so 0=8n
Answer:
0
Step-by-step explanation:
0=2n+6n
add 2n + 6n =8n
0=8n
divide both sides by 8 and you get 0
I'm not sure though unless it's 0=8n
n baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
a. Tasha, because she has the lowest ratio since 0.9 > 0.8
b. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
c. Jana, because she has the lowest ratio since 0.9 > 0.8
d. Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
The player that has a ratio that means they have a better batting average is B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
How to illustrate the ratio?From the information Illustrated, the ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.
For the season so far, Jana has hit the ball 12 times out of 15 attempts. This will be:
= 12/15
= 0.8
Tasha has hit the ball 9 times out of 10 attempts. This will be:
= 9/10
= 0.9
The player that has a ratio that means they have a better batting average is Tasha.
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PLEASE HELP 15 POINTS I'M GIVING BRAINLIEST!!!
Answer:
sec^2(a) - sin(a)
Step-by-step explanation:
Hope it helps!
Answer:
Step-by-step explanation:the answer is (sin2 A+cos2)/cos A
tan A+cot A =? =sin A/cos A + cosA/sinA. = (sin^2 A+cos^2 A)/cos A.