The standard form of polynomial is to write the polynomial so that the term with the highest power of the variable comes first, followed by the other terms in order of descending powers of the variable.
A polynomial in standard form requires that the polynomial be written in descending order of exponents. Polynomials are written in standard form for ease of computation. A polynomial is in its canonical form when it is expressed with the highest order term first, followed by the higher order terms, and so on. For example: 14x⁴ - 5x³ - 11x² - 11x + 8. You can see that in this standard form polynomial, the exponents are ordered in descending powers. These algebraic equations are called polynomials. Procedure for writing polynomials in standard form:
Write the terms Make the groups of all similar terms.The highest exponent write the as first term.Write the rest of the terms with small exponents in descending order.Write the constant term.The normal form polynomial of degree 'n' is : aₙxⁿ + aₙ₋₁ x⁽ⁿ⁻¹⁾ + ... + a₁ x + a₀
Let us assume a polynomial, p(x) = x² + 8x - 9 + 7x³ - 6x + x⁴ , using the above steps we can write the standard form of p(x).
x² + 8x - 9 + 7x³ - 6x + x⁴ x² - 9 + 7x³ - 6x + 8x+ x⁴ = x² - 9 + 7x³+ 2x + x⁴x⁴ + 7x³ + x² + 2x - 9 ( standard form)To learn more about Standard form polynomial, refer:
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Which expression is equivalent to the given expression?
√45
A. 5√9
B. 3√5
C. 9√5
D. 5√3
Steven has a rope that is 6 ft long. He cuts it into 9 pieces, as shown in the model.
The model shows that there are 9 pieces that are each 2/3 ft long.
Which division equation represents the situation?
Answer: 6 divided by 2/3 = 9
Step-by-step explanation:
For division always take the first number in the word problem so in this question the answer would be 6 then you take the 2/3 and divide it by 6. So it would be 6 divided by 2/3. then you take the 9 from the word problem and do 6 divided by 2/3 equals 9. So in this question the answer would be option 2 or could also be called option B. And if this is it that means the answer is, 6 divided by 2/3 = 9.
The division equation which representant this situation is 6 ÷ 2/3 = 9.
What is an division equation?Division equations are mathematical equations with the division operator in them. Division equations are useful not only in math class, but in everyday life as well. For example, if we wanted to evenly distribute a bag of candies among our friends, we could use division to find our answer. Assume we have 100 candy bars and four friends. Divide 100 by 4 to find out how many candies each person gets. We discover that our answer is 25, which means that each of our friends receives 25 candies.
It's our job to figure out what the division equals. This can be represented by a variable, such as x. As a result, our total division equation will be: 100/4=x. On both sides of the equals sign, we have things.
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Find (fog)(x) where f(x)=x²+2, g(x)=x-3.
Step-by-step explanation:
fog(x)=f(x-3)
=(x-3)²+2
=x²-6x+9+2
=x²-6x+11
What is the differentiation of log 7 x?.
The derivative of log₇(x) is 1/(xln(7))
To find the derivative of log₇(x), we can use the chain rule and the properties of logarithms.
The chain rule states that if we have a composite function, such as y = f(g(x)), then the derivative of y with respect to x is given by
dy/dx = dy/dg * dg/dx.
In this case, y = log_7(x) and g(x) = x, so
dy/dx = d/dx (log_7(x))
As by logarithmic property log₇x = ln(x)/ ln(7)
dy/dx = d/dx (ln(x)/ln(7))
To find the derivative of ln(x), we can use the property that the derivative of ln(x) is 1/x. This is because the natural logarithm function is the inverse of the exponential function eˣ, and the derivative of eˣ is eˣ. Therefore, the derivative of ln(x) is the reciprocal of x, or 1/x.
The differentiation of log₇(x) is given by:
d/dx (log₇(x)) = (1/x) * (d/dx (x)) * (1/ln(7))
= (1/x) * 1 * (1/ln(7))
= 1/(x ln(7))
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Drag each tile to the correct box.
Match each type of insurance to its description.
life insurance
property and casualty insurance
health insurance
disability insurance
Description
provides for the replacement of earned income
lost because of a person's inability to work
covers damages to property
provides benefits to a policyholder's beneficiary
(or beneficiaries) when the policyholder dies
pays for medical treatment in the event of an
illness
Type of Insurance
This type of insurance is designed to provide financial protection for the policyholder's loved ones in the event of their death.
Explain about types of Insurance:Life insurance: provides benefits to a policyholder's beneficiary (or beneficiaries) when the policyholder dies.Property and casualty insurance: covers damages to property. This type of insurance provides protection for the policyholder's property, such as a home or car, from losses due to accidents, theft, or natural disasters.It also covers the policyholder's liability in the event that they are found responsible for damages to someone else's property.Health insurance: pays for medical treatment in the event of an illness. Disability insurance: provides for the replacement of earned income lost because of a person's inability to work. It can also cover preventive care and certain preventive treatments.To learn more about insurance refer to:
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D is the midpoint of AC, AE CF, AB IDE and BC L DF.
Prove AB=BC
HELP PLEASE ASAP!!! PRECAL!!
The average rate of change from x = 1 to x = 5 is given as follows:
-1.25.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The numeric values for the function graphed are given as follows:
f(1) = 7.5.f(5) = 2.5.Hence the change in the output is given as follows:
2.5 - 7.5 = -5.
The change in the input is given as follows:
5 - 1 = 4.
Hence the average rate of change is given as follows:
-5/4 = -1.25.
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helppp
i don't understand any of this
Here you go mate!
7x + 10 = -11
answer : x = -3
-12(x + 5) = -144
Answer : x = 7
-9x - 9 = 27
Answer : x = -4
x/4 + 2 = 10
Answer : x = 32
How to solve systems of linear equation in two variables by substitution?.
Solving systems of linear equations in two variables by substitution involves isolating one of the variables and substituting its value into the other equation.
This can be done by adding or subtracting the same term from both sides of one equation and then using that result to substitute into the other equation.
For example, consider the system of equations below:
2x + 3y = 8
3x + 2y = 7
Start by solving for x in the first equation by subtracting 3y from both sides:
2x + 3y = 8
2x = 8 - 3y
x = (8 - 3y)/2
Now substitute this expression for x in the second equation:
3(8 - 3y)/2 + 2y = 7
24 - 9y + 2y = 7
11y = 17
y = 17/11
Finally, solve for x, add y = 17/11 to the first equation as follows:
2x + 3(17/11) = 8
2x + 51/11 = 8
2x = 8 - 51/11
x = (8 - 51/11)/2
x = 21/22
The solution is x=21/22 and y=17/11.
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what is 3 and 1/6 as an improper fraction
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer
Is molar mass equal to Avogadro's number?.
Yes, The molar mass of a substance is defined as the mass of 1 mol of that substance, expressed in grams per mole, and is equal to the mass of 6.022 × 10²³(Avogadro's number) atoms, molecules, or formula units of that substance.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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I will give Branley
A rectangular flag is 80 centimeters by 92 centimeters. What are the dimensions of a scale drawing of the flag using the scale 1:4?
20 cm by 23 cm
320 cm by 360 cm
8 cm by 9.2 cm
1.15 cm by 4.35 cm
The dimensions for the scale drawing of the flag is 20 cm by 23 cm
What is scale?A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.
Given that, A rectangular flag is 80 centimeters by 92 centimeters. we need to find dimensions of a scale drawing of the flag using the scale 1:4,
Therefore,
80 / 92 = 20 / 23
Hence, the dimensions for the scale drawing of the flag is 20 cm by 23 cm
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Answer:
20cm by 23cm
Step-by-step explanation:
Triangle ABC is a right triangle with the right angle at angle B. If the sine of angle A is ? and the longer leg is 52 inches, what is the length of the shorter leg of the triangle?
Answer:
The length of the shorter leg of the triangle can be calculated using the Pythagorean Theorem. The formula is a^2 + b^2 = c^2, where a is the length of the shorter leg, b is the length of the longer leg and c is the length of the hypotenuse. In this case, a^2 + 52^2 = c^2. The hypotenuse can be calculated by using the sine formula. c = (52/sinA). Substituting this value into the Pythagorean Theorem equation, a^2 + 52^2 = (52/sinA)^2. Solving for a, a = sqrt(52^2 - (52/sinA)^2).
3/4 ( x + 8 ) = 1/2 ( x - 6) what is the solution to this equation?
The solution for this equation is x = -36
3/4 ( x + 8 ) = 1/2 ( x - 6)
(Opening the brackets)
(3x + 24)/4 = ( x - 6)/ 2
By cross multiplication,
2(3x + 24) = 4( x - 6 )
6x + 48 = 4x - 24
(Taking the Variable to one side)
6x - 4x = - 24 - 48
2x = - 72
x= - 72/2
x = -36
Hence, the solution for this equation is x = -36
Sam can paint an apartment living room in 3 hours, and Pam can paint the same room in 2 hours. The solution to the equation §+ £ = 1 describes how long it will take them to paint the living room if they work together. Before solving this problem, make a guess about the answer. Then solve the equation. How did your guess compare?
Answer:
sorry its so long
Step-by-step explanation:
We multiply the entire equation by the number
6
6 in order to get rid of the fractions.
2
�
+
3
�
=
6
5
�
=
6
�
=
6
5
=
1
1
5
1
1
5
ℎ
=
1
hour
12
minutes
2x+3x
5x
x
1
5
1
h
=6
=6
=
5
6
=1
5
1
For the following dilation, do, k = (5, 0) (10, 0), the scale factor is equal to ______. 10 2 5 0. 5.
The scale factor is equal to 2.
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
as given, K =(5,0) (10,0)
Solution:
Initial Coordinates=(5,0)=(xi,yi)→xi=5, yi=0
Final Coordinates=(10,0)=(xf,yf)→xf=10, yf=0
Scale factor=xf/xi=yf/yi
We divide the final coordinates by the initial coordinates. In this case the ordinates (yf and yi) are zero and we can't divide by zero, but the abscissas (xf and xi) are different of zero, then we can use them:
Scale factor=xf/xi=10/5
Scale factor=2
Therefore, the scale factor is equal to 2.
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PLEASE HELP!!!!!!
Which expression is equal to 511√
Answer:
[tex]\frac{5\sqrt{11} }{11}[/tex]
Step-by-step explanation:
To cancel out a square-rooted number at the denominator, we can multiply the square-rooted number by multiplying the square root number over again:
[tex]\frac{5}{\sqrt{11}}[/tex] * [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]
Now, any same number of square root times another same number of a square root will cancel out the root. So [tex]\sqrt{11}[/tex] * [tex]\sqrt{11}[/tex] will equal 11.
With this information, we can now go back to the problem, so we will get:
[tex]\frac{5\sqrt{11}}{11}[/tex]
15n2 - 7n - 2
Algebra. Factoring Trinomials.
Please help.
Factor the following trinomials. Helpful Hint: Use the Sum/Product and Factoring
by Grouping method for trinomials with a leading coefficient other than one.
Check your answers using the FOIL method
Answer:
(5n + 1)(3n - 2)
Step-by-step explanation:
Find what number multiplies into -7 and adds into -2, including the coefficient in 15n^2
How do you solve complex fractions with rational expressions?.
To solve a complex fraction, which is a fraction that contains one or more fractions in its numerator and/or denominator, you can follow these steps:
Factor the numerator and denominator of the complex fraction if possible. This will make it easier to cancel common factors.
Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator. This will eliminate the fraction(s) in the denominator, leaving a simplified expression.
Simplify the resulting expression by combining like terms, if possible.
Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.
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ZA and ZB are vertical angles. If m
-
then find the value of x.
The value of X of the vertical angles would be = 1.36
What is a vertical angles?The vertical angles are the type of angles that are known to be directly opposite each other which are also equal angles.
The given vertical angles are ZA and ZB.
If m A = (8x – 20)°
m B = (3x – 5)º
The vertical angles are equal, to find X;
mA = mB
8x -20 = 3x - 5
Bring the like terms together;
8x + 3x = 20- 5
11x = 15
X= 15/11
X= 1.36
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Complete question:
ZA and ZB are vertical angles. If m A = (8x – 20)° and m B = (3x – 5)º, then find the value of x.
Place these events from "Let George Do It!" in the right sequence by choosing the correct step from each blue box.
A strange feeling developed in his stomach.
"George, come with us for a ride," the boys called.
They looked toward the shore and saw the large sand dunes.
"George, do you want to be like this always?"
Tall, lanky George walked along the dusty path in Alderdale, Washington.
George reached the boys, and with one quick jump, leaped into the boat.
They were now approaching home.
The events from "Let George Do It!" in the right sequence will be:
Tall, lanky George walked along the dusty path in Alderdale, Washington."George, come with us for a ride," the boys called.George reached the boys, and with one quick jump, leaped into the boat.They looked toward the shore and saw the large sand dunes.They were now approaching home.A strange feeling developed in his stomach."George, do you want to be like this always?"What is the program about?From 1946 to 1954, Owen and Pauline Vinson produced the radio drama series Let George Do It in the United States.
In 1954, Olan Soule voiced the role of private eye George Valentine, which was portrayed by Bob Bailey. The scripts by David Victor and Jackson Gillis were directed by Don Clark.
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PLS HELPPP (algebra 2)
Given f(x)=4(2)^x
a. find f(4)
b. write your answer as a logarithmic expression
a) The numeric value at x = 4 is given as follows: f(4) = 64.
b) The logarithmic expression is given as follows: x = log2(16).
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 4(2)^x.
At x = 4, the numeric value is found replacing the lone instance of x by 4, hence:
f(4) = 4(2)^4 = 64.
For the logarithmic expression, we obtain the inverse function, hence:
64 = 4(2)^x.
2^x = 16
x = log2(16).
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Find The coordinate of the interection of the diagonal of a parallelogram with the vertical WXYZ
The coordinate of the intersection is (k, m*k + b).
A parallelogram is a four-sided shape with opposite sides that are parallel. The diagonal of a parallelogram cuts the shape into two congruent triangles. The coordinates of the intersection of the diagonal of a parallelogram with the vertical line of the parallelogram can be found by solving the equation of the line that forms the diagonal and the equation of the vertical line.
If the diagonal of the parallelogram is given by the equation y = mx + b, where m is the slope of the diagonal and b is the y-intercept, and the vertical line is given by the equation x = k, where k is the x-coordinate of the vertical line.
To find the x-coordinate of the intersection point, we can substitute x = k into the equation of the diagonal:
x = k
Then, we can substitute this value of x into the equation of the diagonal:
y = mx + b
This will give us the y-coordinate of the intersection point.
So, the coordinate of the intersection is (k, m*k + b)
Note: You need the equation of the diagonal and the equation of the vertical line to find the intersection point.
Therefore, The coordinate of the intersection is (k, m*k + b).
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x = k
Then, we can substitute this value of x into the equation of the diagonal:
y = mx + b
This will give us the y-coordinate of the intersection point.
So, the coordinate of the intersection is (k, m*k + b)
You need the equation of the diagonal and the equation of the vertical line to find the intersection point.
Therefore, The coordinate of the intersection is (k, m*k + b).
Which of the following reasons states why line
segment TV is congruent to line segment VT?
Vertical Angles
Reflexive Property
Transitive Property
Complementary Property
Answer:
complementary property
Step-by-step explanation:
©Thank You
Answered By Solution 49
What are the coordinates of the vertex for f/x )= 3x 2 6x 3?.
The coordinates of the vertex for f(x) = 3x²+6x+3 are (-1, 0).
For any equation of the type y=ax²+bx+c, the vertex is given by (h, k)
Where, h = -b/2a and k = (4ac - b²)/4a.
Given, the equation is y = 3x²+ 6x+3
Here, a = 3, b = 6 and c = 3
So, h = -6/2(3)
h = -6/6
h = -1
4ac = 4(3)(3)
4ac = 36
So, k = [36 - (6)2]/4(3)
k = (36 - 36)/12
k = 0
Therefore, the coordinates of the vertex are (h,k) = (-1, 0).
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If a block is drawn from the box as shown above 200 times with replacement, predict the number of times the block drawn will have
the vowel A.
The letter E would be drawn roughly 40 times, but probably not exactly 20 times.
What does probably mean?The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are connected, but probability is necessary for odds to exist.
Statistical formula
P(A) stands for the likelihood that event A will occur.
f = Number of possible outcomes of an event (frequency)
N stands for the total number of outcomes.
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What is the product of X+ a and x b )?.
The product of (X + A) + (X + B) is- [tex]x2 + xb + ax + ab[/tex]
The information provided in the question,
The outcome of multiplying two numbers together is known as the product. 12 is the result of the addition of 3 and 4, 20 is the sum of 4 and 5, and so on. Discovering the Product A multiplication problem has a solution in the product.
We must determine the of (x + a) and (x + b).
The product is the result of multiplying two numbers, as we all know.
So,
[tex]( x+ a)[/tex] x [tex]( x + b)[/tex]
[tex]x( x+b) + a( x + b)[/tex]
[tex]x[/tex]²[tex]+ bx + ax + ab[/tex]
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Given the following practical problem, what is the y-intercept of the linear function?
Desmond decided to babysit for extra money over the summer. He decided to charge a flat rate of $15 to babysit and then charged $10 for every hour he babysat.
A( 3
B(10
C(15
D(5
step by step pleaseee!
The y-intercept of the linear function is: C. 15.
What is the Y-intercept of a Linear Function?The y-intercept of a linear function is defined as the starting or initial value, which is also the point on the y-axis where the line of the equation crosses.
In a given function represented as y = mx + b, the y-intercept is the value of b.
From the information given above, we have:
Initial value/y-intercept (b) = flat rate = $15
Slope/unit rate (m) = $10
Therefore, the y-intercept of the function is: C. 15.
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An oven is being preheated . The temperature starts at 75F and increases at a constant rate for 8 minutes until it reaches the desired temperature , 350F . it remains the same temperature for 27 minutes . then the temperature decreases at a constant rate for 5 minutes until it reaches 175 , where it remains steady to keep the food warm , sketch a graph to represent the situation .
Answer:
The required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.
Step-by-step explanation:
Given that,
An oven is turned on and set to reach the desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes.
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
At time m = 1 min, temperature T = 134 °F
At time m = 5 min. temperature T = 450 °F
Slope of the equation M = 450 - 134 / 5 - 1
= 216 / 4
= 54
Linat relationship can be given as,
T - 134 = 54 (m - 1)
T = 54m -54 + 134
T = 54m + 80
Thus, the required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.
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The royals softball team played 75 games and won 55 games what percent of the games did they louse round to the nearest tenth
The percent of the games that was lost is 26.7%.
What is the percentage of games that were lost?Percentage is the ratio of two numbers expressed as a number out of 100. The sign that is used to represent percentage is %.
Percentage of the games lost = (number of games lost / total number of games) x 100
Number of games lost = total number of games - number of games won
75 - 55 = 20
Percentage of the games lost = (20 / 75) x 100 = 26.7%
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