The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,
x³ - 4x² - 7x + 10 = 0
x³ - 3x² - 10x - x² + 3x + 10 = 0
( x² - 3x - 10) ( x - 1 ) = 0
( x² -5x + 2x - 10 ) ( x- 1) = 0
( x - 5 )( x + 2 )( x - 1 ) = 0
Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
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PLEASE HELP ME RUNNING OUT OF TIME Determine if the point (3, 1) is a solution to the system of inequalities shown below and use the characteristics of inequality graphs to justify your answer
Answer:
nope
Step-by-step explanation:
aight so basically . you see how the line , that the point is , on is dotted ? that means that nothing on the line is included aka ">" or "<" . and the line that solid , that means if a point is on that line , you can include it . aka "[tex]\leq[/tex]" or "[tex]\geq[/tex]" cause that means or equal to or whatever . so overall if we were only looking at the lil triangle that both of the colors intersect on , ( 3 , 1 ) wouldnt work . sorry if my explaination sucks :)
What is the value of the expression below when x=5x=5?
8x+9
The value of the expression below when x=5x=5?
8x+9 is equal to [tex]7^{2}[/tex] (or) 49.
Substitute [tex]\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)[/tex]
The expression,
y = 8x + 9
If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:
So, we can substitute x = 5,
Then, y = 8 * 5 + 9
Calculate the product or quotient,
y = 40 + 9
Calculate the sum or difference,
y = 49
We can write alternative form,
y = [tex]7^{2}[/tex]
Therefore,
Hence the value of the expressions if x = 5 is [tex]7^{2}[/tex] (or) 49.
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Simon wanted to find the equation of a line that passes through (–6, 5) and is perpendicular to the graph of 3x + 2y = –11. His work is shown below.
1. 3x + 2y = –11 written in slope-intercept form is y = x , so the slope is .
2. The slope of the perpendicular line is .
3. Substitute the point and the new slope into point-slope form to get y – 5 = (x – (–6)).
4. Simplifying, the line is y – 5 = (x + 6).
Is Simon’s work correct?
No, the slope of the line 3x + 2y = –11 is not .
No, the slope of the line perpendicular to the line 3x + 2y = –11 should be .
No, he did not substitute the point and the slope into point-slope form correctly.
Yes, the work is correct.
The answer would be: B. No, the slope of the line perpendicular to the line 3x + 2y = –11 should be 2/3.
What if the Slope of Perpendicular Lines?The equation in slope-intercept form of a line is, y = mx + b, where we have the slope value as m. If two lines are perpendicular, the value of their slope (m) will be negative reciprocals to each other.
Rewriting the equation, 3x + 2y = -11 in slope-intercept form, we would have:
2y = -3x - 11
y = -3/2x - 11/2
The slope (m) is, -3/2. The negative reciprocal is, 2/3.
Therefore, the slope of the line that is perpendicular to the given line would be: 2/3.
Thus, the answer would be: B. No, the slope of the line perpendicular to the line 3x + 2y = –11 should be 2/3.
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Answer:
b. No, the slope of the line perpendicular to the line 3x+ 2y = –11 should be .
Step-by-step explanation:
its right on edge
As a race is finished the amount of elapsed time for the racer is recorded. what measurement scale is this?
The answer is Numeric.
What is a measuring scale?Items are weighed on a scale to determine their weight. In order to ensure that the components are utilized exactly as specified in the recipe, they are frequently used in cooking.The four common scales of measurement—nominal, ordinal, interval, and ratio—were created by psychologist Stanley Stevens.The type of measurement scale to be used for statistical measurement depends on the type of data being collected. There are various types of measurement scales. The nominal, ordinal, interval, and ratio scales are the four measurement scales that make up this set.What measurement scale is this?
There are mainly two types of variables
Numerical(quantitative): observations that can be measured in numerical form
Agin two types: ratio scale and interval scale
Categorical(qualitative ): named categories
Again two types: Ordinal or nominal
Her in the given an example,
Measured time of race have numerical observations
The measurement scale is Numeric.
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can someone help me with this? Thank you!
Answer:
4 5/6
Step-by-step explanation:
1/2 -> 3/6
2/3 -> 4/6
? 3/6 - ? 4/6 = ? 5/6
10 - 5 ( Take away one because you needed to do 3/6-4/6 which results in a negative number )
4 5/6
please help. two other ppl have answered with wrong answers pls only reply if you know it !!!!!!!!!!!!! high points and brainily for the people who know it fr
Answer:
-12
i hope this helps;/
Answer:
The answer is -12.
Step-by-step explanation:
Basically when it says, "when h = -1 ", we need to substitute t for -1.
So, here's what the equation would look like now,
h(-1) = (-1 + 7) (-1 - 1)
= (6)(-2)
= -12
So, our answer is -12.
Hope this helps!
I need help asap and explain if you can if not it’s okay
The tables 2, 3 and 4 represent linear equations. (Correct choice: D)
Which tables do represent linear functions?
Algebraically speaking, linear functions are represented by a expression of the form y = m · x + b, where m is the slope of the function and b is the y-intercept of the line. Slope can be interpretated in accordance with the secant line formula:
m = Δy / Δ x
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.In other words, a table represents a linear function if for all difference between two consecutive values in x means the same change for two corresponding values in f(x).
After a quick inspection, we find that tables 2, 3 and 4 represent linear as they show the following features:
Table 2: Δx = 1, Δy = 3, Table 3: Δx = 1, Δy = 4, Table 4: Δx = 1, Δy = 2
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Translate each rule into a formula.
The Average of 4 numbers a, b, c, d is equal to the sum of the numbers divided by 4.
The average of 4 numbers a, b, c, d is equal to the sum of the numbers divided by 4 is (a + b + c + d) / 4
How to illustrate the information?From the information, the average of 4 numbers a, b, c, d is equal to the sum of the numbers divided by 4.
It should be noted that this can be illustrated as:
(a + b + c + d) / 4
It should be noted that average simply means the addition of the numbers and then dividing them.
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2x² - y
if x = 3 and y = 8
Answer:
10
Step-by-step explanation:
2(9)-8
10
Hey there!
2x^2 - y
= 2(3)^2 - 8
= 2(3^2) - 8
= 2(3 * 3) - 8
= 2(9) - 8
= 18 - 8
= 10
Therefore, your answer should be:
10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
For each equation, find the center and radius of the circle.
(x+2)²+(y-10)²=4
The equation of the circle (x + 2)^2 + (y - 10)^2 = 4 has a radius of 2 and a center located at (-2 , 10).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 2)^2 + (y - 10)^2 = 4, is in standard form, then
h = -2
k = 10
r = 2
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What is the equation of the line that passes through the point (-1,6)and has a slope of −1
Answer:
y = -x + 5
Step-by-step explanation:
slop m = -1, x = -1, y = 6
y = mx + b
6 = (-1)(-1) + b
6 = 1 + b
b = 5
so y = -x + 5
The cross-section of a lean-to shelter is in the shape of a triangle. The base of the
triangle is 6 feet more than twice its height. If the area of the triangle is 88 square feet,determine the length of the base and the height of the triangle in feet
Answer:
Step-by-step explanation:
Givens
Let the height = x
Let the base = 2*x +6
Let the area = 88 square feet.
Formula
A = Base * height / 2
Solution
88 = (2x + 6)*x/2 Multiply both sides by 2
88*2 = (2x+6)*2*x/2 Combine
176 = (2x + 6)*x Remove the brackets
176 = 2x^2 + 6x Subtract 176 from both sides
0 = 2x^2 + 6x - 176 This factors without the quadratic
0 = (2) (x^2 + 3x - 88)
0 = 2 (x +11)(x - 8)
Note: x + 11 has no meaning. Measurements of this type cannot be minus. What is - 11 feet.
x - 8 =0
x = 8
Answer
height = 8 feet
base = 2*8 + 6
base = 22
please answer i will give 100 extra points if correct
Answer:
-6, -5, -5.9, -1, 0, 1, 5, 5.9, 6, 6.1, 7, 11
Step-by-step explanation:
Its basically saying that all values of x must be greater than or equal to -6. So, we can substitute -6, -5, -5.9, -1, 0, 1, 5, 5.9, 6, 6.1, 7, 11
-6.1, -7, and -11, is wrong because it is less than -6,
hope this helped
I have a crush on a Virgo dude and I’m a Libra . Should I ask if I can kiss him or just do it , or just wait . I’m in love with this guy and he says im pretty too
Explain how you decided what to draw on your place value chart. Be sure to include reasoning about
how the value of each digit was affected by the division.
Write an example from daily life that uses each type of real number.
whole numbers
Whole numbers are defined as a set of natural numbers plus the integer zero. There exists no fractions, decimals, or negative integers in whole numbers, which are actual numbers.
What are whole numbers?Whole numbers are defined as a set of natural numbers plus the integer zero. In mathematics, the set of whole numbers is denoted by the letter W and is given as 0, 1, 2, 3, etc.
Examples:
1. Learning geometry and trigonometry can help people who desire to get better at sports.
2. The ability to compute an area is useful since it will be useful when we renovate our homes and rental properties.
3. When making many purchases, we must decide which retailer gives the best price or financing.
4.People use ratios or proportions to calculate the right amount of each item when they cook.
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Karen stops at starbucks every weekday (M-F). She is very excited for the fall season and mobile orders a venti pumpkin spice latte every time she visits and leaves a one dollar tip. At the end of the week, she spent a total of $39.15. How much does one latte cost?
Based on the total amount that Karen spent in one week at the Starbucks, the cost of one latte was $6.83
What was the cost of one latte?Karen left a tip of a dollar every day she bought a Latte so this comes to:
= 1 x 5 days
= $5
The cost of a single latte is therefore:
= (Total amount spent - Total tips) / Number of days
= (39.15 - 5) / 5
= 34.15 / 5
= $6.83
In conclusion, a single latte at the Starbucks to Karen for the weekdays was $6.83.
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Solve the System of Equations:
y = [tex]\frac{1}{6}[/tex]x + 6
y = [tex]\frac{1}{3}[/tex]x + 2
Answer:
(x;y)=(24;10)
y = 1/6 * x + 6; y = 1/3 * x + 2
Substitute the given value of y into the equation y = 1/3 * x + 2
1/6 * x + 6 = 1/3 * x + 2
Solve the equation for x
x = 24
Substitute the given value of x into the equation y = 1/3 * x + 2
y = 1/3 * 24 + 2
Solve the equation for y
y = 10
What else is needed to prove these triangles congruent using the SAA postulate? I NEED THE ANSWER
To prove triangles ACB and ECD to be congruent using SAA we need
A. Both ∠B and ∠D need to be congruent and ∠A and ∠E need to be congruent.
As given in the question,
In the triangle ACB and ECD,
Given : AC ≅ EC
∠ACB ≅∠ECD
To prove triangles to be congruent using SAA.
Two angles need to be congruent.
∠B ≅ ∠D
∠A ≅ ∠E
Therefore, to prove triangles ACB and ECD to be congruent using SAA we need
A. Both ∠B and ∠D need to be congruent and ∠A and ∠E need to be congruent.
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Important need help fast!
The function of correct growth or decay factors are,
[tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.
[tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.
[tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor related to growth factor 15%.
[tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor related to growth factor 5%.
[tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to 20%.
We know that,
Exponential Decaying factor is [tex]y = ab^{x}[/tex]
Where, 0<b<1
The decay rate is expressed as a percentage. We convert it to a decimal by simply reducing the percent and dividing it by 100.
Growth factor is the factor by which a quantity multiplies itself over time. Growth rate is the addend by which a quantity increases (or decreases) over time.
Here,
Option(1) : [tex]y = (0.3)(0.5)^{x}[/tex]
Then, 0.5 < 1 (0.5 means 50%)
So, [tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor .
Hence, [tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.
Option(2) : [tex]y = 2000(\frac{4}{5}) ^{x}[/tex]
Then, 4/5 < 1
⇒ 0.8 < 1
So, [tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor.
Hence, [tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.
Option(3) : [tex]y = 800 (1.15)^{x}[/tex]
Then, 1.15 > 1
So, [tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor.
Hence, [tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor of 115%, so it is not decay factor, then the related to growth factor 15%.
Option(4) : [tex]y = 1200 (1.05)^{x}[/tex]
Then, 1.05 > 1
So, [tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor.
Hence, [tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor of 105%, so it is not decay factor, then the related to growth factor 5%.
Option(5) : [tex]y = 3(0.85)^{x}[/tex]
Then, 0.85 < 1
So, [tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor.
Hence, [tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to 20%.
Therefore,
[tex]y = (0.3) (0.5)^{x}[/tex] is an exponential decay factor of 50%.
[tex]y = 2000(\frac{4}{5} )^{x}[/tex] is an exponential decay factor of 15%.
[tex]y = 800 (1.15)^{x}[/tex] is an not exponential decay factor related to growth factor 15%.
[tex]y = 1200 (1.05)^{x}[/tex] is an not exponential decay factor related to growth factor 5%.
[tex]y = 3(0.85)^{x}[/tex] is an exponential decay factor of 85%, then the related to 20%.
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12 + 3[18 - 5(16 - 13)]
Answer:
algebra = 21
Step-by-step explanation:
the answer is 21
branbliest, please
2-inch candle burns down in 8 hours. At what rate does the candle burn, in inches per hour?
Answer:
1/4 inches/hour
Step-by-step explanation:
We need inches per hour, which means inches divided by hours, so we divide the number of inches by the number of hours.
2 inches / 8 hours = 2/8 inches/hour = 1/4 inches/hour
b. Do transformations of the form y=|x|+k affect the axis of symmetry? Explain.
A line that bisects or cuts an objects into two equals parts is called the axis of symmetry for that object. The axis of symmetry creates a mirror-like reflection of each side of the object.
The function f(x) = |x| is called an absolute value function. The highest or lowest point on the graph of the absolute value function is called the vertex. The absolute value graph has an axis of symmetry through the vertices.
The axis of symmetry (x=0 or y-axis) is the line that divides the graph into two congruent halves. Translate is a transformation that moves the graph horizontally or vertically, but does not change its overall shape or orientation.
So, it does not affect the axis of symmetrical. Is symmetrical about the Y axis (axis of symmetry).
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i need help again yall..............................
Answer:
the answer is c !!!!!!!!!!!!!!!!!!
Back in 1997, Sally paid $11,448 for a new automobile. This amount included
the 6% sales tax. What was the price of the automobile without the tax?
Draw a line representing the rise and representing the run of the line. State the slope of the line in simplest form.
Answer:
See below
Step-by-step explanation:
See graph below
just an addition to the great reply above by jsimpson11000
Check the picture below.
What is the key phrase?
The formula for the volume of a cone is V=1/3x3.14xr^2h, where V is the
volume, r is the radius of the base, and h is the height.
a. Solve the formula for h.
b. What is the height of a cone with a volume of 1017.36 square inches and
a radius of 6 inches? Use 3.14 to approximate
Answer: a. h=3V/(πr^2)
b. h=27 inches
Step-by-step explanation:
a. V=1/3 π r^2 h
V*3=3*1/3 π r^2 h
3V=3/3 π r^2 h
3V=π r^2 h
3V/π=π/π r^2 h
3V/π=r^2 h
h=3V/(πr^2)
b. h=3(1017.36)/(3.14(6^2))
h=3052.08/(3.14(36))
h=3052.08/(3.14(36))
h=3052.08/113.04
h=27 inches
what is 8 to the 6 power?
(8⁶) who ever answers first gets brainiest
Answer:
262144
Step-by-step explanation:
8*8*8*8*8*8
64*8*8*8*8*8
512*8*8*8*8
4096*8*8*8
32,786*8
262144
Evaluate each expression for the given value of the variable. 3(2 a+5)+2(3-a) ; a=4
The value of the expression 3(2 a+5)+2(3-a) at a=4 is 37 .
An Algebraic expression is defined as an expression that consists of variables and constants linked with mathematical operators (+,-,x,÷).
According to the question
=3(2 a+5)+2(3-a)
Substituting the value a=4 in the above expression.
We get,
=3(2(4)+5)+2(3-4)
=3(8+5)+2(3-4)
Solving terms in bracket first ,
=3(13)+2(-1)
=39-2
=37
Therefore , The value of the expression 3(2 a+5)+2(3-a) at a=4 is 37 .
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