The non real roots of the polynomial x³ – 7x² + 15x – 25 = 0 are; 1 + 2i, 1 – 2i
What is the non - real root?
Non real roots are simply imaginary roots.
We are told that the real roots of the equation x³ – 7x² + 15x – 25 = 0 is 5.
Now, it means that (x - 5) is a factor of the given polynomial. Thus, we can factorize the polynomial as;
(x - 5)(x² - 2x + 5) = 0
Now, to find the non - real roots, we will use quadratic formula on (x² - 2x + 5) to get;
x = [-(-2) ± √((-2)² - (4 * 1 * 5))]/2(1)
x = (2 ± √(-16))/2
x = 1 ± 2i
x = 1 + 2i, 1 – 2i
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Answer:
c
Step-by-step explanation:
|x - 3|= 2x - 15
8 - 2|6 - x|= 20
By solving both equations we get x =:
1. x = 12
2. x = 28/3
solution1. |x - 3| = 2x - 15
|x - 3| - 2x = 2x - 15 - 2x
by simplifying,
- 2x + |x - 3| = -15
- 2x + x -3 = -15 and -2x - (x - 3) = -15
by solving equation ,
= -x -3 = - 15
= -x = -12
x = 12
2. 8 - 2|6 - x|= 20
6 |6 - x| = 20
6 |-x + 6| = 20
dividing both side with 6,
(6 |-x + 6|)/6 = 20/6
| -x + 6| = 10/3
add 6 on both sides,
x - 6 + 6 = 10/3 +6
x = 28/3
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Which pair or pairs of polygons are congruent?2624-2220-18pair 116pair 21412-10-86-4pair 3
Congruent polygons are those that have equal measurements. Since we are given their graphs, we simply inspect each pair of polygons to determine which among them are congruent.
I have made an example using the first pair. I rotated the first polygon (the red one) to show that they are indeed congruent.
Following the same process, we can see that pairs 3 and 4 are also congruent.
Pair 2 are not congruent because the green rectangleis longer.
So the answer is pairs 1, 3, and 4.
8x^2 - 9 when x = -4
Answer:
119
Step-by-step explanation:
substitute x = - 4 into the expression
8x² - 9
= 8(- 4)² - 9
= 8(16) - 9
= 128 - 9
= 119
Can you please do this step by step.
The resulting exponent form is, 1/9¹⁰
Exponent:
Exponent is used to show repeated multiplication of a number by itself. For example,
7 × 7 × 7 can be represented as 7³
Here, the exponent is ‘3’ which stands for the number of times the number 7 is multiplied.
Given,
Here we have the exponent form is,
9⁻⁸x9⁻²
Here we have to use the product property and then we have to get rid of negative exponents.
First step is to use the product property,
We know that, the product property states that,
for any non-zero term a,
yᵃ x yᵇ = yᵃ⁺ᵇ
where a and b are real numbers.
So, the given expression is written as,
=> 9⁻⁸⁺⁽⁻²⁾
=> 9⁻⁸⁻²
=> 9⁻¹⁰
Now the second step is to get rid of the negative components,
As per the rule, the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.
So, the value is,
=> 9⁻¹⁰ = 1/ 9¹⁰
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The function g(r) represents the shift of the
function f(x) five units to the right. If f(x)=
It +5, which of the following is g(x)?
Carter is jogging with a velocity of 3.8 m/s when he accelerates at 3.7 m/s² for 3 s. How
fast is Carter running now?
Uniformly Varied Rectilinear Motion.
When we start to solve a physics exercise, we get the exercise data:
Initial Speed = 3.8m/s
Acceleration (a)= 3.7 m/s²
Time (t) = 3 sec.
He tells us that Carter treats at a speed of 3.8 m/s, this is the speed, since he asks us, at what speed does he treat now. Then we must calculate the final speed.
The formula to calculate the final velocity is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=V_{o}+a*t} \end{gathered}$} }[/tex]
We substitute the data in the formula used and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+3.7 \ \frac{m}{\not{s^{2}} }*3 \ s } \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+11.1 \ \frac{m}{s} } \end{gathered}$} }[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=14.9 \ m/s} \end{gathered}$} }}[/tex]
Carter now runs a new speed of 14.9 m/s.What different types of funding sources are available to businesses? Explain why a business should use a particular type of fund. Most companies use a mix of these funds, however. Provide examples that justify this business decision.
The types of funding sources that are available to businesses include:
Family and FriendsEquity ProvidersDebt Providers Institutional Investors.A business can use a particular type of fund that meets its goals.
A reason why companies van use a mix of different funding is to improve a company's financial strength.
What is funding about?Providing resources to finance a need, a program, or a project is the act of funding. While usually in monetary form, this can also refer to an organization or company's time or effort.
Having adequate funding enables your firm to seize any possibilities that present themselves, such as investing in new goods and services that can advance your company. Working capital can act as a safety net when your company requires additional funding.
Although there are many diverse reasons why businesses want financing, there are certain frequent ones. Business grants and loans may be used for working capital, equipment purchases, staff expansion, or even the refinancing of existing debt to lower monthly payments.
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When solving the following system of equations, which variable would be the easiest to solve for? 5x+3y=22 4x-2y=16
Variable x would be easier to solve for.
Step - by - Step Explanation
What to find?
• The value of x.
,• The value of y.
,• The variable that was easier to solve.
Given:
5x+3y=22
4x-2y=16
Using elimination method,
First solve for x.
To solve for x, multiply through the first equation by 2 and then multiply through the second equation by 3.
10x + 6y = 44 _____________(3)
12x - 6y = 48 ______________(4)
Add (3) and (4)
22x = 92
Divide both-side of the equation by 22
x = 92/22
Reduce the fraction by 2.
x =46 / 11
To solve for y,
Multiply through the first equation by 4 and through the second equation by 5.
20x + 12y = 88 _________________ (5)
20x - 10y = 80 __________________(6)
Subtract equation 6 from 5.
22y= 8
Divide both-side of the equation by 22.
y = 8/22
We can reduce the fraction by 2.
y = 4 / 11
Judging from the steps above, we can deduce that the variable that was easier to solve is x.
Answer: x of first equation
Step-by-step explanation:
A shipping box is 36 inches by 24 inches by 18 inches; how many cubic ft. can it hold?
A) 8 D) 12
B) 9 E) 15
C)10
The volume that the shipping box which measure 36 inches by 24 inches by 18 inches can hold is 9 cubic feet.
What is the volume of the shipping box with the given dimensions?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Given the data in the question;
Length l = 36 in = ( 32/12 )ft = 3ftWidth w = 24 in = ( 24/12 )ft = 2ftHeight h = 18 in = ( 18/12 )ft = 1.5ftVolume V = ?Plug the given values into the formula above and solve for the volume V.
V = w × h × l
V = 2ft × 1.5ft × 3ft
V = 3ft² × 3ft
Volume V = 9ft³
Therefore, the volume of the rectangular prism is 9 cubic feet.
Option B is the correct answer.
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What is the answer to this
Answer:
b
Step-by-step explanation:
the square root of 9 is 3 because 3*3=9
3+6=9
Need this answer in 1 minute
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{8^3}{2^4}}[/tex]
[tex]\mathsf{= \dfrac{8\times8\times8}{2\times2\times2\times2}}[/tex]
[tex]\mathsf{= \dfrac{64\times8}{4\times4}}[/tex]
[tex]\mathsf{= \dfrac{512}{16}}[/tex]
[tex]\mathsf{= 512\div16}[/tex]
[tex]\mathsf{= 32}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{32}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Power of fractions, with numerator and denominator.
The power is composed of a base and an exponent, so the exponent indicates how many times the base is multiplied, then,
[tex]\boldsymbol{\dfrac{8^{3} }{3^{4} }=\dfrac{8\times8\times8}{2\times2\times2\times2} =\cfrac{512}{16}=32 }[/tex]
What is the area of this face?
4 in.
4 in.
4 in.
1 in.
1 in.
16 in²
15 in²
17 in²
12 in²
The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.
The area of the face is 17 in²/17 inches2.
How to find the area of the face?The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area.
Draw a square on a piece of paper using a pencil. A 2-D figure, that is.
The term "Area" refers to the area that a shape occupies on paper.
By squaring the side's length, the area of each face may be calculated.
To determine the overall surface area of the cube, multiply the area of each face by the number of faces.
For big square,
a = 4 in
a*a = 4 * 4 inches
[tex]a^{2}[/tex] = 16 in²
For another small square,
a = 1 in
[tex]a^{2}[/tex] = 1*1 = 1 in²
In total,
[tex]a^{2}[/tex] = 16 + 1 = 17 in²
Therefore, the area of the face is 17 in²
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Help please need answer
17Given:
The smaller triangle is,
Find the length of the hypotenuse,
[tex]\begin{gathered} \text{hypotenuse}^2=4^2+1^2 \\ =16+1 \\ =17 \\ \text{hypotenuse}=\sqrt[]{17} \end{gathered}[/tex]The larger traingle is,
[tex]\begin{gathered} \text{Hypotenuse}^2=12^2+3^2 \\ =144+9 \\ =153 \\ \text{Hypotenuse}=3\sqrt[]{17} \end{gathered}[/tex]Now, find all the trigonometric functions for a smaller triangle.
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}=\frac{1}{\sqrt[]{17}} \\ \cos \theta=\frac{Adjacent\text{ side}}{\text{hypotenuse}}=\frac{4}{\sqrt[]{17}} \\ \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}=\frac{1}{4} \\ co\sec \theta=\frac{\text{hypotenuse}}{opposite\text{ side}}=\frac{\sqrt[]{17}}{1}=\sqrt[]{17} \\ \sec \theta=\frac{\text{hypotenuse}}{adjacent\text{ side}}=\frac{\sqrt[]{17}}{4} \\ \cot \theta=\frac{adjecent\text{ side}}{\text{opposite side}}=\frac{4}{1}=4 \end{gathered}[/tex]For the larger triangle,
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}=\frac{3}{3\sqrt[]{17}}=\frac{1}{\sqrt[]{17}} \\ \cos \theta=\frac{Adjacent\text{ side}}{\text{hypotenuse}}=\frac{12}{3\sqrt[]{17}}=\frac{4}{\sqrt[]{17}} \\ \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}=\frac{3}{12}=\frac{1}{4} \\ co\sec \theta=\frac{\text{hypotenuse}}{opposite\text{ side}}=\frac{3\sqrt[]{17}}{3}=\sqrt[]{17} \\ \sec \theta=\frac{\text{hypotenuse}}{adjacent\text{ side}}=\frac{3\sqrt[]{17}}{12}=\frac{\sqrt[]{17}}{4} \\ \cot \theta=\frac{adjecent\text{ side}}{\text{opposite side}}=\frac{12}{3}=4 \end{gathered}[/tex]Therefore, the value of the function is the same because the triangles are similar so, corresponding sides are proportional.
You purchase $7,000 from a store offering 10% down, no interest if paid in full by three months.
$5,000 is paid before deadline, how much is owed if monthly interest is 2.49%?
Owed: $____________
The $7,000 worth of purchase and payment of $5,000 before the three months deadline gives the amount owed at 2.49% monthly compound interest rate as $2,153.15
Owed: $2,153.15
What is a compound interest rate?Compound interest accounts for the interest that is earned on an interest, such that the interest rate is compounded on an initial amount.
The given parameters are;
The amount of the items purchased from the store = $7,000
The amount of down payment required = 10%
The amount paid in three months = $5,000
Monthly interest on amount owed after three months = 2.49%
Required;
The amount owed after payment of $5,000 before three months
Solution;
Using the compound interest formula, we have;
[tex] \displaystyle{A = P \cdot \left(1 + r \right)^{n} }[/tex]
Where;
A = The amount owed
P = The amount loaned = $7,000 - $5,000 = $2,000
r = Monthly interest rate = 2.49%
n = The number of months = 3 months
Which gives;
[tex] \displaystyle{A = 2000 \times \left(1 + 0.0249 \right)^{3} \approx 2153.1509}[/tex]
The amount owed (for the 3 months period) is approximately $2,153.15
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57⁰
Diagram not
drawn accurately
(i) Work out the size of the angle marked p.
The measure of angle p is 213 degrees
How to determine the measure of the angle?The possible question is added at the end of the solution and as an attachment
From the attached figure, we have the following angles
Angle 1: Angle pAngle 2: Angle with a measure of 57 degreesAngle 3: Angle with a measure of 90 degrees i.e. a right-angled triangleAlso, from the attached figure:
We can see that the three angles named above are formed by lines that meet at a point (say the point of origin)
When multiple lines meet at a point, the sum of the angles formed at this point is 360 degrees
This means that
Angle 1 + Angle 2 + Angle 3 = 360
Substitute the known values in the above equation
So, we have
p + 57 + 90 = 360
Evaluate the sum in the above equation
So, we have
p + 147 = 360
Evaluate the like terms in the above equation
So, we have
p = 213
Hence, the value of the angle with the name p is 213 degrees
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Possible question
Diagram not drawn accurately
Work out the size of the angle marked p.
See attachment
How to do this problem
From the graph, the y-intercept is the point (0,40). We can calculate the slope of the line, given two points, using the following formula
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2)_{} \\ \Rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} (x_1,y_1)=(0,40),(x_2,y_2)=(2,0) \\ \Rightarrow m=\frac{0-40}{2-0}=-20 \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line is
[tex]\begin{gathered} y=mx+b \\ \Rightarrow y=-20x+40 \end{gathered}[/tex]The answer is y=-20x+40
The city is issuing bonds to raise money for a building project. You obtain a $4100 bond that pays 6% interest annually that matures in 8 years. How much interest will you earn?
rather its multiplication,division,adding, and subtraction I will give four answers
Answers: I think its 718320000
Four students, Naomi, Nathan, Jonathan, and Carson, line up one behind the otherHow many different ways can they stand in line?
This is a Permutations of 4 people in a line
The answer is 24
[tex]4!=4\cdot3\cdot2\cdot1=4\cdot3\cdot2=12\cdot2=24[/tex]Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the distance in 4.5 h. Car B traveled 5 mph slower than Car A. (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) How fast did Car B travel? Enter your answer in the box.
Car B travelled with the rate of speed of 40mph .
In the question ,
it is given that ,
Car B travelled 5mph slower than Car A .
let the rate of speed at which Car B travelled be x mph.
So , the rate of speed of Car A is = (x+5) mph
Car A travelled the distance in 4 h , with the speed of (x+5) mph ,
the value of T = 4 h and R = (x+5) mph
So, by the formula R*T=D ,
we get ,the distance travelled by Car A = 4(x+5) miles .
Car B travelled the distance in 4.5 h , with the speed of x mph .
the value of T= 4.5h and R = x mph
So, by the formula R*T=D,
we get , the distance travelled by Car B = 4.5*x = (4.5x) miles .
Since , both the cars travelled the equal distance ,
we get ,
4(x+5) = 4.5x
4x+20=4.5x
4.5x-4x = 20
0.5x= 20
x = 40
Therefore , the rate of speed of Car B is 40 mph.
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If you plot the point -8.85 on anumber line. would you place it to the left or right of -8.8? explain
Explanation:
Think of -8.8 as -8.80
We're comparing -8.85 to -8.80, which means we're comparing the stuff after the decimal 85 and 80
Since 85 > 80, this places -8.85 to the left of -8.80
It's like saying how -85 is to the left of -80
I recommend drawing out a number line to see what's going on.
A truck is carrying tomato juice, orange juice, and cherry juice bottles in a ratio of 4:3:4. If there are 30 orange juice bottles, then how many juice bottles in total are there.
We know that there are tomato juice, orange juice, and cherry juice bottles in a ratio of 4:3:4, respectively.
As you can observe in the given ratio, to get 30 orange juice, we have to multiply it by 10. So, if we multiply the whole ratio, we obtain the following
[tex]\begin{gathered} 4\times10\colon3\times10\colon4\times10 \\ 40\colon30\colon40 \end{gathered}[/tex]This means that 30 orange juice bottles are in the same ratio as 40 tomato juice bottles and 40 cherry juice bottles.
Hence, the total number of juice bottles is 40+30+40 = 110.Find the standard form of the graph
The Standard form is y = [tex]x^{2}[/tex] + 6x - 16
Given,
A quadratic function n standard form whose graph has the given characteristics.
and, passes through (-8, 0), (-6, -16), (2,0).
To find the y =?
Now, According to the question:
Because the graph of a quadratic goes through point (-8 ,0) and point (2, 0)
So, supposing the equation of the quadratic function is
y = a [x - (-8)] (x - 2) = a (x + 8)(x - 2)
The graph passes through the point (-6, 16)
So, -16 = a(-6 + 8)(-6 -2)
=> -16 = a x 2 x (-8)
=> a = 1
So, y = (x + 18)(x - 2)
y = [tex]x^{2}[/tex] + 8x - 2x - 16
y = [tex]x^{2}[/tex] + 6x - 16
Hence, The Standard form of y = [tex]x^{2}[/tex] + 6x - 16
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A plot of land measure 25m by 12cm .A portion of this plot measuring 8m by 8m is used for cultivation of vegetable find the area of the plot not cultivated.
Answer
is ur question right
What is the gradient of the straight line shown
below?
Answer:
Gradient = 1.
Step-by-step explanation:
Note that it passes through the points (6, 6) and (0, 0)
So, the gradient is (6-0)/(6-0)
= 1.
Calculate the Pressure
300N divided 5m²equals? Nper m²
<<<<< >>>>
How much is +7 - 4?
Number line: -15 to +15
A.3
B.11
C.-11
D.-3
_________
What is the value of +3 - 8?
Number line: -15 to +15
A.-11
B.-5
C.5
D.11
________
What is the value of 5 - 12?
Number line: -15 to +15
A.7
B.-17
C.17
D.-7
______What integer is the result of moving 10 units in a positive direction, starting at -6?
Number line: -15 to +15
A.-16
B.4
C.16
D.-4
Answer:
1. 3
2. -5
3. -7
4. 4
Step-by-step explanation:
prove me wrong
Solve for x: (round your decimal to 4 places)
In(x + 2) = 4
The value of x is 52.5981
The given equation is:
In(x + 2) = 4
Taking log on the right hand side of the equation, we get
x + 2 = [tex]e^{4}[/tex]
The value of [tex]e^{4}[/tex] is 54.59815
⇒ x + 2 = 54.59815
Subtract 2 on both the sides of the equation
⇒ x = 54.59815 - 2
⇒ x = 52.59815
Rounding 52.59815 to 4 places, we get
⇒ x = 52.5981
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The following sequence is a geometric sequence
17
,
51
,
153
,
459
,
1377
,
...
Find the sum of the first 13 terms of this sequence.
What is the common ratio for this sequence?
r
=
What is the index of the final term of this sum?
last index =
What is the sum?
Sum =
Answer:
13,551,737
Step-by-step explanation:
You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....
Common ratioThe common ratio is found by dividing a sequence term by the one before it:
r = 51/17 = 3
The common ratio is 3.
IndexThe index of the 13th term of the sequence is n = 13.
SumThe sum of n terms of a geometric sequence with first term a1 and common ratio r is ...
Sn = a1·(r^n -1)/(r -1)
For a1 = 17, r = 3, and n = 13, the sum is ...
[tex]S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}[/tex]
Please help me with my calculus homework, thanks so much!
SOLUTION:
Step 1:
In this question, we are given the following:
Use geometry to evaluate:
[tex]\int ^2_0(\sqrt[]{4-x^2}\text{ ) }dx[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
[tex]\pi\text{ -- OPTION B}[/tex]N=65 p=0.5 X=39 binomial formula
The binomial formula with the given parameters has a value of 0.0272
How to evaluate the binomial formula?The given parameters are
N = 65
p = 0.5
X = 39
The interpretation of the above parameters are
Sample size, N = 65
Probability of success, p = 0.5
Number of success, X = 39
The binomial probability states that
P(x) = ⁿCₓ * pˣ * (1 - p)ⁿ⁻ˣ
Where n, p and x are the same as the parameters described above
When the values are substituted in the binomial probability formula, we have
P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (1 - 0.5)⁶⁵⁻³⁹
Evaluate the difference
P(39) = ⁶⁵C₃₉ * (0.5)³⁹ * (0.5)²⁶
Evaluate the products
P(39) = ⁶⁵C₃₉ * (0.5)⁶⁵
This gives
P(39) = 0.0272
Hence, the value of the binomial formula is 0.0272
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