The non-real solutions of the polynomial expression are x = 2 + i√11 and x = 2 - i√11
How to determine the non-real solutions?The equation of the polynomial expression is given as:
x^4 – 7x^3 + 23x^2 – 29x – 60 = 0
Also, we have the following points
(-1, 0), (0, -60), (2.5, -60), (4, 0)
Write out the x-intercepts
(-1, 0) and (4, 0)
This means that
x = -1 and x = 4
So, we have
x + 1 = 0 and x - 4 = 0
Multiply
(x + 1)(x - 4) = 0
Divide the polynomial equation x^4 – 7x^3 + 23x^2 – 29x – 60 = 0 by (x + 1)(x - 4) = 0
Using a graphing calculator, we have
x^4 – 7x^3 + 23x^2 – 29x – 60/(x + 1)(x - 4) = x^2 - 4x + 15
So, we have
x^2 - 4x + 15
Next, we solve the quadratic expression using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 1 * 15))/2 * 1
So, we have
x = (4 ± √-44)/2
This gives
x = (4 ± 2√-11)/2
Divide
x = 2 ± √-11
So, we have
x = 2 ± i√11
Split
x = 2 + i√11 and x = 2 - i√11
Hence, the non-real solutions are x = 2 + i√11 and x = 2 - i√11
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What is the distance between the points A(-1,3) and point B(-8,3)?
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the standard deviation is 3.1 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a gorilla living longer than 23.9 years
The probability of a gorilla living less than 23.9 years is 0.84 (84%) if the lifespans of gorillas in a particular zoo are normally distributed.
How does probability work?A probability is also called as a numerical representation of the likelihood or chance that any kind of specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Probability refers to potential.
Any random event's occurrence is the exact subject of this area of mathematics. The range of the value varies from 0 to 1. Mathematics has been incorporated probability to forecast the likelihood of various types of events.
How is probability determined?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas.
We need to find the z-score herein of 23.9 years in the kind of standard normal distribution of the lifespans of gorillas in this particular zoo.
z score can be further be calculated using the equation
z = (X-M)/s
and it has been given that X is 23.9 years
M is also called the average gorilla life (20.8 years)
s is given as the standard deviation (3.1 years)
Thus, putting up the values, we have
Z = 1
The Empirical rule that is present here states that 68% of the total lifespans lie within 1 standard deviation from the other mean.
Then Half of it, 68/2 = 34 % lies right side of 1 standard span of the mean.
Since this lifespan is less than mean is 50%, 50%+34% =84% lies less than total z-score 1, that is the probability of a gorilla living less than 23.9 years.
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8 ÷ 2(2 + 2)
what is the answer
Answer: 16
Step-by-step explanation: 8 ÷ 2(2 + 2)
850' of #2 wire is sent to your job. On Monday, you cut 3 pieces, each 175' long. On Tuesday, you cut 3 pieces, each 88' long, and 3 pieces, each 20' long. How much wire is left on the reel?
The remaining wire (W) is just the original wire (850') minus the cut wire on Monday, Tuesday...
[tex]W=850^{\prime}-3\cdot175^{\prime}-3\cdot88^{\prime}-3\cdot20^{\prime}=1^{\prime}[/tex]There is merely 1' of wire in the reel.
i..i
哈!
Natalie used 2 1/2 tubes of blue paint to
paint the sky in her picture. Each tube
holds 4/5 ounces of paint. How many
ounces of blue paint did Natalie use?
3) A clock is set correctly at 1pm. If it loses 3 minutes every hour, what will the clock show
when the correct time is 10 am the next day?
Based on the time the clock is set to, and the minutes lost every hour, the time the clock would show the next day at 10 am is 8:57 am
How to find the time shown?To find the time that the clock would show the next day, first find the difference between the 1 pm and 10 am the next day:
This difference is:
= 10 am the next day - 1 pm
= 10 + (12 - 1)
= 10 + 11
= 21 hours
The number of minutes lost is:
= 21 x 3 minutes per hour
= 63 minutes
The time the clock would be showing is:
= 10 am - 63 minutes
= 8:57 am
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Zoe is making a rectangular box with measurements as shown below 5 inches 3 inches 3 inches what is the surface area of the box
Surface area of rectangular box is 78 inches².
What is surface area?The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
Given Data
rectangular box with measurements as shown below 5 inches 3 inches 3 inches
Length = 5 inches
Width = 3 inches
Height = 3 inches
Surface area formula
2lw + 2lh+2hw
Equating values
2(5)(3) + 2(5)(3) +2(3)(3)
30 + 30 + 18
78
Surface area of rectangular box is 78 inches².
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Question
A golden retriever weighing 85 lb was prescribed a medication. If the dosage is 1 mg for every 5 lb, how much medicine was
the dog given?
A store has 18 cell phones in stock. The manufacturer ships cell phones to the store to sell in boxes that contain four cell phones each. If the store is preparing for a big sale and would like to have 30 cell phones in stock for the sale, how many boxes should they order from the manufacturer?
A. 3
B. 4
C. 8
D. 12
Answer:
The answer is A, 3
Answer:
4 is the answer
Find the slope and the y-intercept of the line with the equation 9y - 6x + 8 = 0.Select the correct choice below and fill in any answer boxes within your choice. A. The slope is(Type an integer or a simplified fraction.)B. The slope is undefined.Select the correct choice below and fill in any answer boxes within your choice.A. The y-intercept is(Type an integer or a simplified fraction. Type an ordered pair.)B. There is no y intercept
Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.
Rewrite the given equation as follows:
[tex]\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}[/tex]Simplify the equation:
[tex]y=\frac{6}{9}x-\frac{8}{9}[/tex]Compare to the equation y=mx+c, to get:
[tex]\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}[/tex]Hence, the slope is 6/9 and the y-intercept is -8/9.
You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.
How to get the equation of a parabola with 3 pointsy- intercept : (0, -1.4)x-intercept : (0.905,0)3rd point: (2,0.6)
he standard form of a quadratic efunctionis:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Where } \\ a,b,\text{ and }c\text{ are real constants such that }a\ne0. \end{gathered}[/tex]Since the y-intercept is (0, -1.4), it follows that:
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ \text{ Therefore,} \\ c=-1.4 \end{gathered}[/tex]Substitute c = -1.4 into the equation:
[tex]y=ax^2+bx-1.4[/tex]Since the x-intercept is (0.905, 0), it follows that:
[tex]\begin{gathered} a(0.905)^2+b(0.905)-1.4=0 \\ \text{Therefore,} \\ 0.819025a+0.905b=1.4-------(1) \end{gathered}[/tex]Since the graph passes through the third point (2, 0.6), it follows that:
[tex]\begin{gathered} 0.6=a(2)^2+b(2)-1.4 \\ \text{Therefore} \\ 4a+2b-1.4=0.6 \\ 4a+2b=0.6+1.4_{} \\ 4a+2b=2 \\ \text{Divide both sides by }2 \\ 2a+b=1 \\ \text{Hence} \\ b=1-2a---------(2) \end{gathered}[/tex]Substitute equation (2) into equation (1):
[tex]\begin{gathered} 0.819025a+0.905(1-2a)=1.4 \\ 0.819025a+0.905-1.81a=1.4 \\ \text{ Collect like terms:} \\ 0.819025a-1.81a=1.4-0.905 \\ -0.990975a=0.495 \\ \text{ Therefore,} \\ a=\frac{0.495}{-0.990975} \\ a\approx-0.5 \end{gathered}[/tex]Substitute a = -0.5 into equation (2), therefore,
[tex]b=1-2(-0.5)=1+1=2[/tex]Therfore the function is given by:
[tex]y=-0.5x^2+2x-1.4[/tex]The equation of the parabola is y = -0.5x² + 2x - 1.4
.
Find MK.
08
04
O 14
06
L
4x-2
O
x+2
K
Il
Answer:
14
Step-by-step explanation:
well, the logic is simply that the sum of the parts must be the same as the whole.
so,
8 + (x + 2) = 4x - 2
10 + x = 4x - 2
12 = 3x
x = 4
therefore,
MK = 4x - 2 = 4×4 - 2 = 16 - 2 = 14
Evaluate a³ - b + 7, if a = 3 and b
=4
⇒Plug in the given values of the variables in order and then simplify the expression
Given that a= 3 and b=4
⇒[tex]=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30[/tex]
⇒The expression evaluated at the given known variables gives 30.
evaluate 4.141414 as a rational number
we'll start by moving the recurring part to the left of the decimal point hmmm so the recurring part is 0.14 so if we just multiply that by 100, that'll give us 14.141414...., now let's make the recurring part a variable
[tex]x=0.\overline{14}\hspace{5em} \begin{array}{llll} 100x&=&14.\overline{14141414}\\\\ &&14+0.\overline{14141414}\\\\ &&14+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x=14+x\implies 99x=14\implies x=\cfrac{14}{99}[/tex]
Answer:
2070707/500000
Step-by-step explanation:
rational no. simply means a fraction.
Please help me solve question
In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.
What we can find here first is the rate of the increase of the salary of the workers. We can use the equation
[tex]y=y_0e^{rt}[/tex]We are looking for the value of r. We have to derive an equation solving for r. We have
[tex]\begin{gathered} \frac{y}{y_0^{}}=e^{rt} \\ rt=\ln \frac{y}{y_0} \\ r=\frac{1}{t}\ln \frac{y}{y_0} \end{gathered}[/tex]Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get
[tex]\begin{gathered} r=\frac{1}{15}\ln (\frac{29.59}{6.70}) \\ r=0.099yr^{-1} \end{gathered}[/tex]The doubling time is computed as
[tex]d=\frac{\ln 2}{r}[/tex]Substitute the value of r on the equation above and solve, we get
[tex]d=\frac{\ln 2}{0.099}=7.00yr[/tex]Hence, the doubling time for this problem is equal to 7 years.
Answer: 7 years
Show your work here. Use the pen as needed. North High School is selling game tickets for one of their football games. Adult tickets (x) cost $7 each and student tickets (y) cost $4 each. Write and graph an inequality to represent the combination of tickets sold, assuming they estimate to make at most $280 in ticket sales for this game.graph it
Adult tickets cost $7 each
Student tickets cost
A number, n, is multiplied by 5/8 The product is -0.4. What
is the value of n?
Answer:
n= -16/25
Step-by-step explanation:
Expert hel
me Give example of 6 types of factoring polynomials with Solution
Answer:
1 Greatest Common Factor
We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law.
2. Grouping
This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros.
3. Using Identities
The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
a2 – b2= (a + b)(a – b)
4. Zero Factor Property :The Zero Factor Property (also called the Zero Product Property) says that if the product of two quantities is zero, then at least one of those quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.
5. Greatest Common Factor (GCF) Method:
This is almost always the first method applied to factoring polynomials. Look at all of the terms and see if they all have something in common that can be removed.
6. Sum or Difference in Two Cubes
A cube is a term that has been multiplied by itself twice.
[tex] {3}^{3} {x}^{3} and \: \: \: {27x}^{3} [/tex]
are all cubed terms. The trick to remembering how to factor cubed terms is S.O.A.P. S = same sign, O = opposite sign A.P. = always positive.
A cement walkway is to be poured .it is consists of the two rectangles with dimensions and a circle with radius 1.5 yards use 3.14 as an approximate value.how many square yards will the walkway be?If a painter it for 3.75 per square yard,how much will the painting cost?
The area of the walkway in square yards is 22.77 yards²
The cost of painting the walkway will be $85.37.
What is the area of the walkway?The square yards of the walkway can be determined by adding the areas of the two rectangles and the area of the quarter of a circle together.
Area of a rectangle = length x width
Area of the first rectangle = 9.5 x 1.5 = 14.25 yards²
Area of the second rectangle = 4.5 x 1.5 = 6.75 yards²
Area of a circle = πr²
Area of quarter of a circle = 1/4 × πr²
Where:
π = pi = 3.14
r = radius
1/4 x (3.14 x 1.5²) = 1.77 yards²
Area of the walkway = 1.77 yards² + 6.75 yards² + 14.25 yards² = 22.77 yards²
The cost of the painting can be determined by multiplying the area of the walkway by the cost per square yard.
Total cost = 22.77 yards² x 3.75 = $85.37
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Find the measure of each angle indicated
Answer:
68°
Step-by-step explanation:
Alternate exterior angles have the same measurement.
Identify Linear Function from Points Which table of Values REPRESENTS a linear Functions?draw the problems on the table Please.
Linear functions from tables
I'll draw the calculations directly on the tables as required. The table that has the same slope represents a linear function.
Table A has different values for the slope, this table is not a linear function.
Table C is not a linear function since the slope is not constant
Table B does not have a constant slope, so it's not a linear function
Table D has a constant slope of 1/3, thus this table represents a linear function
Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{1}{10}+\frac{11}{20}
10
1
+
20
11
The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.
What is a fraction?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.
It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.
In this case, we want to add 1/10 + 11/20. This will be illustrated thus:
= 1/10 + 11/20
= 2/20 + 11/20
= 13/20
Therefore the addition is 13/20.
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Sara bought 7 red peppers for $5.60.
Find the unit rate. Then use the unit rate to write an equation relating the cost in dollars c to the number of red peppers p.
The unit rate of what Sarah bought is 0.8 dollars per pepper.
The equation relating cost in dollars, c to the number of red peppers is c = 0.8p
How to find unit rate?A unit rate describes the ratio of two different units for the quantity of one.
In other words, the unit rate can be defined as the ratio between two measurements with the second term as 1.
Therefore, the unit rate when Sara buys 7 red peppers for $5.60 can be calculated as follows
unit rate = cost of pepper / number of pepper
unit rate = 5.60 / 7
unit rate = 0.8 dollars per pepper
Let's use the unit rate to write an equation relating the cost in dollars c to the number of red peppers, p.
Therefore,
c = 0.8p
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I need help with the following question
The values of the trigonometry formulas are sin(240) = -sin(60), cos(225) = -cos(45) and tan(225) = tan(45)
How to determine the values of the trigonometry formulas?The trigonometry ratios are given as
sin(180 - ∅) = sin(∅)
cos(180 - ∅) = -cos(∅)
tan(180 - ∅) = -tan(∅)
Also, we have the following trigonometry ratios are given as
sin(180 + ∅) = -sin(∅)
cos(180 + ∅) = -cos(∅)
tan(180 + ∅) = tan(∅)
Using the above trigonometry ratios, we have
sin(240) = sin(180 + 60)
By comparison, we have
sin(240) = sin(180 + 60)
sin(180 + ∅) = -sin(∅)
This gives
∅ = 60
So, we have
sin(180 + 60) = -sin(60)
Evaluate
sin(240) = -sin(60)
Using the above trigonometry ratios, we have
cos(225) = cos(180 + 45)
By comparison, we have
cos(225) = cos(180 + 45)
cos(180 + ∅) = -cos(∅)
This gives
∅ = 45
So, we have
cos(180 + 45) = -cos(45)
Evaluate
cos(225) = -cos(45)
Using the above trigonometry ratios, we have
tan(225) = tan(180 + 45)
By comparison, we have
tan(225) = tan(180 + 45)
tan(180 + ∅) = tan(∅)
This gives
∅ = 45
So, we have
tan(180 + 45) = tan(45)
Evaluate
tan(225) = tan(45)
Hence, the value is tan(225) = tan(45)
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Why is it important the order we write the vertices of a triangle in a congruent statement? SELECT ALL THAT APPLY!
A The middle letter is the vertex of the angle.
B The order tells us what sides are congruent.
C The order does not matter
D The order tells us what angles are congruent.
It is important the order we write the vertices of a triangle in a congruent statement as
B. The order tells us what sides are congruent.
D. The order tells us what angles are congruent.
How to illustrate the information?A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.
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f(-3) = -1, f(-2) = 4
Answer:
1(-3) = -3, 1f(-2) = -2
Step-by-step explanation:
The sum of the forth and thirteen terms of an arithmetic progression is 80. find the sum of the first sixteen terms.
The most appropriate choice for Arithmetic Progression will be given by-
The sum of the first sixteen terms of the Arithmetic Progression is 640
What is Arithmetic Progression?
A series of numbers are said to be in Arithmetic Progression if the difference between consecutive terms of the series are same.
If [tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the series, a be the first term and d the common difference,
[tex]a_n = a+(n-1)d[/tex]
If [tex]S_n[/tex] is the sum of first n terms of the series,
[tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]
Here,
Let the first term be a and the common difference be d
The sum of the fourth and thirteen terms of an arithmetic progression is 80.
[tex]a_4 + a_{13} = 80[/tex]
[tex]a + (4-1)d + a + (13-1)d = 80[/tex]
[tex]a + 3d +a +12d =80\\2a+15d =80[/tex]
[tex]S_{16} = \frac{16}{2}(2 \times a + (16 -1) \times d)\\[/tex]
[tex]= 8(2a+15d)[/tex]
[tex]= 8 \times 80[/tex]
[tex]= 640[/tex]
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Two shops rent pairs of skis for a rental fee plus a fee per hour. Write and solve an equation to
find how many hours must a pair of skis be rented for the total costs to be the same?
Shop A Equation:
Shop B Equation:
Solution:
Rental Fee
Hourly Fee
Shop A
$3
$9
Shop B
$9
$6
For the total costs to be the same a pair of skis must be rented for 3 hours.
Two shops rent pairs of skis for a rental fee plus a fee per hour.
Let, the number of hours must a pair of skis be rented = x
Equation for Shop A,
3 + 9x equation 1
Equation for Shop B,
9 + 6x equation 2
Total cost for Shop A and Shop B is same so we can equate equation 1 and equation 2 as mentioned below:
3 + 9x = 9 + 6x
3x = 6
x = 3
Thus we can write, for the total costs to be the same a pair of skis be rented for 3 hours.
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Identify the correct description of the values in both the domain and range of the function
Domain is number of minutes water has been added .
Range is amount in the pond
What are domain and range ?The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then
Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.
The set of all y-coordinates in the range is equal to 2, 3.
Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.
Range : a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).
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50÷2 and 5÷3solve the question and tell the remainder
Step-by-step explanation:
the perimeter of a triangle is 84 cm and its area is 36 CM square if one its side is 30 cm find the length of remaining two side