The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.
What is algebra?According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.
Here,
According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.
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what is the slope of the line represented by the equation 10x + 5y=4
Answer:
10x
Step-by-step explanation:
Answer: The slop is -2 and the y-intercept is (0,4/5)
Step-by-step explanation:
Here is the graph, I hope this helps, have a great school day! :D
Juan has a summer job delivering newspapers. He is paid $15 per hour and a $10 bonus when he completes his daily route.
If h represents the number of hours he works, which expression can be used to find out how much money Juan makes each day?
Alicia had $375 in her savings account. She withdraws $12 a week to buy lunch. Assuming she does not deposit any more money. Write a linear function to represent how much money (y) Alicia will have after x weeks. A y = 375 + 12x B y = 375 − 12x C x = 375 + 12y D x = 375 − 12y
please help with the question above.
Answer: D
Step-by-step explanation:
Find the coordinates of B! PLEASE
Answer:
C ( -1, 1)
Step-by-step explanation:
(5+x)/2= 2
x = -1
(-3+y)/2= -1
y= 1
Please help I will give brainliest
Answer:
Rectangular
Step-by-step explanation:
I would be rectangular if you listened in class you would know.
What are the 4 method of quadratic equation?
The four methods to solve quadratic equations are factorising, quadratic formula, graphing and completing the square.
Factorising is nothing but the method of equating the given equation to zero.
Quadratic formula method is by placing the coefficients of the given quadratic equation into the formula and obtaining the solutions.
Completing the square method is when a quadratic equation has a square term. We would once more have a linear equation if we could place two square terms on either side of the quality sign.
We can find the solution of a quadratic equation using a graph. Rearrange the equation so that one side corresponds to the graphed function. Plot this function and write y = the other side of the equation. To obtain the answers, draw vertical lines from the intersection spots down to the x-axis.
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What is horizontal line test answer?
The horizontal line test is a method used in mathematics to determine if a given function is one-to-one. A function is one-to-one if for every unique x-value, there is a unique y-value.
The horizontal line test is used to determine if a function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.
The horizontal line test is based on the idea that if a horizontal line intersects the graph of a function more than once, then there must be at least one pair of x-values that correspond to the same y-value.
This means that the function is not one-to-one and therefore, not invertible. A function that is not invertible is not a function in strict mathematical sense.
It's important to note that the horizontal line test can only be applied to functions that are defined on a closed interval or on all real numbers.
Also, It is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.
In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.
If it does, the function is one-to-one, if not, the function is not one-to-one and therefore not invertible. The test is only sufficient and should be used with caution.
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Octagon Towers is an octagon-shaped condominium building in Miami, Florida. Assuming the base of Octagon Towers is a regular octagon, find the measure of each interior angle of the base of Octagon Towers.
Each interior angle measures ?
Answer: The measure of each interior angle of a regular octagon can be found using the formula:
(n-2) x 180 / n
Where n is the number of sides in the polygon.
For Octagon, n=8
So we can substitute 8 for n in the formula:
(8-2) x 180 / 8 = 6 x 180 / 8
Therefore, each interior angle of the base of Octagon Towers measures 135 degrees.
Step-by-step explanation:
PLEASE HELP! Matthew uses this scale model of a design he plans to paint on a wall. He uses the key 1 cm = 2.5 ft. One gallon of paint will cover 400 square feet of wall.
How many gallons of paint will Matthew use?
Enter your answer as decimal in the box.
Answer: Matthew will use 12.25 Gallons of Paint. (I'm not sure if I have the correct amount of cm so if you think/know it's a different amount, use the step by step explanation to figure it out. Good luck :D)
Step-by-step explanation: 28x2.5 = 70. 70 Feet to Square Feet = 4900 square feet. 4900 divided by 400 = 12.25.
Use the diagram and the Exterior Angle Theorem to solve for y.
Y= ______
Hello there!
Answer:
15
Step-by-step explanation:
According to Exterior Angle Theorem for ∠С in ∆ ABC:
∠BAC + ∠ABC = ∠ACD
(5y + 3)° + (4y + 8)° = 146°
5y + 3 + 4y + 8 = 146
9y + 11 = 146
9y + 11 - 11 = 146 - 11
9y = 135
y = 15
A blue whale can weigh up to 400,000 pounds. A standard school bus has a gross weight of 25,000 pounds. How many school buses are equivalent to the weight of a blue whale?
Answer:
16 school buses
Step-by-step explanation:
400,000/25,000 = 16
25,000*16 = 400,000
Mr. Eng brought different kinds of fruit drinks to his class picnic.
How many more orange drinks than apple and grape drinks did Mr. Eng bring?
(A) 4
(B) 5
(C) 9
(D) 11
(E) 15
Answer:
Simply add apple and grape together you get 10, and orange is 14, so 14 - 10 = 4, answer is a
Step-by-step explanation:
Convert this equation into standard form
The standard form of the linear function in this problem is given as follows:
-4x + 5y = -25.
How to convert the linear function in standard form?The linear function for this problem is defined in point-slope form as follows:
y + 1 = 4/5(x - 5).
To convert to standard form, we leave the coefficients of x and y on the left side and the constant on the right side, hence:
y + 1 = 4x/5 - 4.
-4x/5 + y = -5.
Multiplying everything by 5, we have that:
-4x + 5y = -25.
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What is fifth formula?
Answer: It is not clear what you are asking for when you say "fifth formula". There are many formulas in mathematics, and it could be referring to different things in different context.
Formulas can be found in different branches of mathematics and science, such as geometry, algebra, physics, chemistry, etc. Can you please provide more context or specify what area of mathematics or science you are interested in?
It is important to note that any formula needs to be referenced in order to understand what it represents and how to use it.
Step-by-step explanation:
find the length of the hypotenuse if both legs of the right triangle are 3
Answer:
h = 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 legs.
let h represent the hypotenuse , then
h² = 3² + 3² = 9 + 9 = 18 ( take square root of both sides )
h = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] ← exact value
or h ≈ 4.24 ( to 2 decimal places )
What are the determinants for solving this linear system?
5x + 3y = 17
−8x − 3y = 9
The determinants for solving the linear system is given as follows:
|A| = 9.|Ax| = -78.|Ay| = 91.How to obtain the determinant of the matrices?The system of equations for this problem is defined as follows:
5x + 3y = 17−8x − 3y = 9The matrix A is composed by the coefficients of x and y, hence:
A = [5 3]
= [-8 -3]
The determinant of a 2 x 2 matrix is the multiplication of the principal diagonal subtracted by the multiplication of the secondary diagonal, hence:
|A| = 5 x (-3) - 3 x (-8)
|A| = -15 + 24
|A| = 9.
For the matrix Ax, the coefficients of x are replaced by the results of the equalities, hence:
Ax = [17 3]
= [9 - 3]
|Ax| = 17 x (-3) - 3 x 9
|Ax| = -51 - 27
|Ax| = -78.
For the matrix Ay, the coefficients of y are replaced by the results of the equalities, hence:
Ax = [5 17]
= [-8 -9]
|Ay| = 5 x (-9) + 17 x 8
|Ay| = 91.
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If sarah can blow up three balloons in one minute , how long will it take her to blow up 21 balloons?
Sarah can blow 7 minutes to blow 21 balloons
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Sarah can blow 3 balloons in 1 minute
Then unit rate of sarah is 3 balloons per minute
Thus the time she would take to blow 21 balloons is 21/3=7 minutes
Hence, Sarah can blow 7 minutes to blow 21 balloons
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5
Give the coordinates of the point obtained from each reflection.
(a) Reflect the point (0, 3) across the X-axis:
(b) Reflect the point (0, 3) across the y-axis:
0-D
OD
X
Reflect the X-axis at the position (0, 3): ( 0 , - 3 ) , Reverse the y-axis at the position (0, 3): ( 0 , 3 )
How do you find coordinates in math?In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.
A group of values that exhibit precise positioning On graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up. a pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane.
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At noon, a tank contains 5 in of water. After several hours, it contained 3 in of water. What is the percent decrease of water in the tank?
Answer: To calculate the percent decrease of water in the tank, we can use the following formula:
Percent decrease = (Initial value - Final value) / Initial value x 100%
In this case, the initial value of water in the tank is 5 inches and the final value is 3 inches. So, the percent decrease is:
(5 - 3) / 5 x 100% = 2 / 5 x 100% = 40%
So, the percent decrease of water in the tank is 40%.
Step-by-step explanation:
A local bank is advertising that you can double your money in eight years if you invest with them. Suppose you have $1,000 to invest. What interest rate is the bank offering? Show both compound and simple.
a) The compound interest rate is 75%
b) The simple interest rate is 12.5%
What is the interest?
We know that the interest is the money that accrues to an investment that have been made. We know that we can be able to determine the simple interest by the use of the formula.
A = P(1 + r/n)^nt
A = amount
P = principal
r = rate
n = Number of times compounded
Then we have;
2(1000) = 1000(1 + r)^8
Where n = 1
2 = (1 + r)^8
0.693 = 8 ln(1 + r)
e^0.693/8= (1 + r)
r = 1 - e^0.693/8
r = 0.75 or 75%
For the simple interest rate;
I = PRT/100
I = A - P
I = 2000 - 1000 = 1000
1000 = 1000 * R * 8/100
R = 1 * 100/8
R = 12.5%
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roberto is building a rainbow for the set of the school play. he draws the sketch shown to find the amount of paint he needs to make the rainbow. he says he needs to buy enough green paint to cover at least 15.7 square feet.
Answer:
what is the question
Step-by-step explanation:
Match the reasons to the statements. ( 50 POINTS PER PERSON + BRAINLIEST )
[ Please look at the photos below! Must match ALL the statements to the reasons ]
Answer:
a) Reflexive Property => 7
b) Angle Congruence Postulate => 8
c) Definition of Supplementary => 4
d) Segment Addition Postulate => 5
e) Definition of Right Angle => 6
f) Symmetric Property => 11
g) Substitution Property of Equality => 2
h) Definition of Complementary => 1
i) Segment Congruence Postulate => 9
j) Angle Addition Postulate => 3
k) Linear Pair Postulate (maybe 10)
Step-by-step explanation:
Hope this helps and sorry for taking so long!
"Write an equation in slope-intercept form for the trend line that is drawn."
Answer:
y = - 3x--------------------------------
The line passes through the origin, therefore one point on the line is sufficient to determine the equation:
y = kx, is the form of this equationThe point on the line is (1, - 3), so the line is:
y = - 3xAnswer:
[tex]y=-3x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
From inspection of the given graph, two points on the line are:
(1, -3)(2, -6)Substitute the two points into the slope formula to calculate the slope of the line:
[tex]\implies m=\dfrac{-6-(-3)}{2-1}=\dfrac{-3}{1}=-3[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and one of the points on the line into the point-slope formula:
[tex]\implies y-(-3)=-3(x-1)[/tex]
[tex]\implies y+3=-3x+3[/tex]
[tex]\implies y=-3x[/tex]
Select all the group of number that are ordered correctly from leat to greatet. 2,−4,6,−8
−13,−16,12,1
−110,0. 2,310,14
−112,−0. 75,−0. 25,112
−8,−34,−3,14
The correct group is 3rd. (Option C)
The groups of numbers that are ordered correctly from least to greatest are :
-13,−16,12,1
-110,0.2,310,14
-112,−0.75,−0.25,112
The first group has -13, -16, 12 and 1. -13 and -16 are the smallest numbers and 1 is the largest, so it is ordered incorrectly from least to greatest.
The second group has -110,0.2,310,14 and -110 is the smallest number and 310 is the largest, so it is ordered incorrectly from least to greatest.
The third group has -112, -0.75, -0.25 and 112. -112 is the smallest number and 112 is the largest, so it is ordered correctly from least to greatest.
The last group has -8,-34,-3,14 and -34 is the smallest number and 14 is the largest, so it is not ordered incorrectly from least to greatest.
Therefore, the correct group is 3rd. (Option C)
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An Internet media and market research firm measured the amount of time an individual spends viewing a specific Webpage. The data in the accompanying table represent the amount of time, in seconds, a random sample of 40 surfers spent viewing a Webpage.
Create the graphical summary.
Write a sentence that describes the data. Write a sentence that describes the data. Choose the correct answer below.
O The distribution is bell shaped.
O The distribution is skewed right.
O The distribution is uniform.
O The distribution is skewed left.
The distribution of the data is skewed right, which means that the data is not evenly distributed across the range of values.
To calculate the skewness, we can use the formula Skewness = (Mean - Mode) / Standard Deviation. In this case, the mean is 599.2 seconds, the mode is 590 seconds, and the standard deviation is 110.88 seconds. Plugging these values into the formula, we get Skewness = (599.2 - 590) / 110.88 = 0.8094. This indicates that the data is skewed right, as the skewness is greater than 0. A right-skewed distribution typically occurs when the majority of data points are closer to the minimum value, while there are fewer data points near the maximum value. This can be seen in the graphical summary, where the majority of the data points are clustered around the lower end of the range and the tail extends to the right.
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Which of the following is the discriminant of the quadratic equation 2x² 6x 3 0?
Answer:
The discriminant of a quadratic equation ax² + bx + c = 0, is the value of b² - 4ac.
Given the equation 2x² + 6x + 3 = 0, the discriminant is:
b² - 4ac = (6)² - 4(2)(3) = 36 - 24 = 12
So the discriminant is 12.
Step-by-step explanation:
This is due tomorrow, please help!!
Answer:
x > -20/7
Step-by-step explanation:
[tex]\frac{2x-4+5x}{8} > -3[/tex]
multiply both sides by 8 to remove the denominator
2x-4+5x > -24
7x - 4 > -24
add 4 to both sides to isolate the variable and its coefficient
7x > -20
divide both sides by 7 to isolate x
x > -20/7
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{2x - 4 + 5x}{8} > -3}[/tex]
[tex]\mathsf{= \dfrac{7}{8}x - \dfrac{1}{2} > -3}[/tex]
[tex]\text{Add } \rm{\dfrac{1}{2}\text{ to both sides of the equation}[/tex]
[tex]\mathsf{\dfrac{7}{8}x - \dfrac{1}{2} + \dfrac{1}{2} > -3 + \dfrac{1}{2}}[/tex]
[tex]\text{Simplify it}[/tex]
[tex]\mathsf{\dfrac{7}{8}x > -3 + \dfrac{1}{2}}[/tex]
[tex]\mathsf{\dfrac{7}{8}x > - \dfrac{5}{2}}[/tex]
[tex]\text{Multiply }\rm{\dfrac{8}{7}\text{ to both sides of the equation}[/tex]
[tex]\mathsf{\dfrac{8}{7}\times\dfrac{7}{8}x > \dfrac{8}{7} \times - \dfrac{5}{2}}[/tex]
[tex]\text{Simplify it}[/tex]
[tex]\mathsf{x > \dfrac{8}{7}\times -\dfrac{5}{2}}[/tex]
[tex]\mathsf{x > \dfrac{8\times -5}{7\times 2}}[/tex]
[tex]\mathsf{x > \dfrac{-40}{14}}[/tex]
[tex]\mathsf{x > \dfrac{-40\div 2}{14\div2}}[/tex]
[tex]\mathsf{x > -\dfrac{20}{7}}[/tex]
[tex]\mathsf{x > -2 \dfrac{6}{7}}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x > -\dfrac{20}{7} \ or \ \mathsf{x > -2 \dfrac{6}{7}}}}\huge\checkmark[/tex]
[tex]\textsf{It is an o.p.e.n circle shaded to the right}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Write an equation that represents the
situation. Use x to represent the number of roast beef sandwiches. Then determine how many sandwiches the customer buys.
Amount Used for Payment $50
Change Received
$16.25
An equation that represents this situation is
The customer buys sandwiches.what is an equation that represents this situation? How many sandwiches did the customer buy?
The equation that represent the situation is 16.25 = 50 - 6.75x.
The number of sandwich bought by the customer is 5.
How to represent a situation with an equation?A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Let x represent the number of roast beef sandwiches.
Then we will find the how many sandwiches the customer buys when the amount Used for Payment is $50 and change received is $16.25.
Therefore, using equation,
16.25 = 50 - 6.75x
where
x = the number of roast beef sandwichesTherefore, let's find the number of sandwich bought using the equation.
16.25 = 50 - 6.75x
16.25 - 50 = - 6.75x
-33.75 = -6.75x
divide both sides by -6.75
x = -33.75 / -6.75
x = 5
Hence,
number of roasted beef sandwich bought = 5
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The perimeter of a rectangle is 172 feet. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.
The length of the rectangle is 28 feet, and the width is 58 feet.
How to find the length and width of the rectangle?We know that for a rectangle of length L and width W, the perimeter can be written as:
P = 2*(L + W)
Here we know that the perimeter is 172 ft, then we can write:
172 ft = 2*(L + W)
And we know that the length is an integer:
L = x
And the width is two times the next integer:
W = 2*(x + 1)
Then we can replace these two in the perimeter equation so we get:
172 = 2*(x + 2*(x + 1))
172 = 2*(x + 2x + 2)
172 = 6x + 4
172 - 4 = 6x
168 = 6x
168/6 = x
28 = x
So we have:
Length = x = 28 ft
Width = 2*(x + 1) = 2*(29) ft = 58ft
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The the length and width of the rectangle are 43 feet and 129 feet
What is a perimeter?Perimeter is the distance round an object, The rectangle is a polygon that has four sides and some of its angles is equal to 360 degrees
The given parameters that will help us to find the values of the length and width of the rectangle are
Perimeter = 172
The length is an integer = 2
The width is 2 times the next consecutive integer = 2(3) = 6
The ratio of the sides of the rectangle is
W = 2/8 *172 = 43
Length = 6/8*172 = 129
Therefore length and the width of the rectangle are 43 feet and 129 feet
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Jerry tarted doing it-up every day. The firt day he did 15 it-up. Every day after that he did 2 more it-up than he had done the previou day. Today Jerry did 33 it-up. Write an equation that could be olved to find the number of day Jerry ha been doing it-up, not counting the firt day
Jerry has been doing it-up for number of 10 days , not counting the first day.
n + 14 = 33
n = 19 days
We know that Jerry did 15 it-up on the first day and 33 it-up today. Therefore, we can subtract 15 from 33 to get the total number of it-up that Jerry did over the past few days.
33 - 15 = 18e
We know that Jerry did 2 more it-up each day, so we can divide 18 by 2 to get the number of days.
18 / 2 = 9
Finally, we need to add 1 to the result to account for the first day.
9 + 1 = 10 days
Jerry has been doing it-up for 10 days, not counting the first day.
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