The sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70
How to find the real roots of the polynomials?Using Vieta's formulas, the sum of the roots of the polynomials is 1, so the sum of the two non-positive roots is -1. Let's call these roots r and s. Then we have:
Let r and s be the non-positive roots of the polynomial P(x) = x³ - x² - 18x + k. Then we have:
r + s = -1
rs + k = 18
The sum of the squares of these roots:
r² + s² = (r + s)² - 2rs = 1 - 2(18 - k) = -35 + 2k
For the non-positive roots to be real, the discriminant of the polynomial must be non-negative, i.e.,
D = 18² - 4(1)(-k) = 72 + 4k ≥ 0
Solving for k, we get:
4k ≥ -72
k ≥ -18
So, the smallest value of k that makes the non-positive roots real is -18, and the sum of their squares is:
r² + s² = -35 + 2(-18) = -71
Finally, the sum of the roots of P(x) = 1 (by Vieta's formulas).
Therefore, the sum of the squares of all the real roots of the polynomials = 1² + (-71) = -70
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If you were to graph 9x + 5y > 1 , where would you shade according to the slope of the line? The shading would occur above the solid line of the slope The shading would occur below the solid line of the slope. The shading would occur below the dashed line of the slope. The shading would occur above the dashed line of the slope.
The requried shading would appear above the solid line of the slope.
To graph the inequality 9x + 5y > 1, we first require to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.
To graph this line, we can solve for y in terms of x:
9x + 5y = 1
y = (-9/5)x + 1/5
Although the slope of the line is negative, the shading should occur above the line, which means the correct answer is, the shading would occur above the solid line of the slope.
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A dog runs 100 feet in 30 seconds. How many meters per hour is this? Use the fact that 1 meter is about 3.28 feet.
Answer:
60.96 meters per hour.
Answer:
3658.53658537 meter per hour
Step-by-step explanation:
[tex]\frac{100ft}{30sec}[/tex] · [tex]\frac{1meter}{3.28feet}[/tex] · [tex]\frac{60sec}{1min}[/tex] ·[tex]\frac{60min}{hour}[/tex] You can cross cancel works like you can numbers
[tex]\frac{100}{30}[/tex] · [tex]\frac{1meter}{3.28}[/tex] · [tex]\frac{60}{1}[/tex] · [tex]\frac{60}{1hour}[/tex]
[tex]\frac{360000meters}{98.4hours}[/tex]
3658.53658537 meter per hour
Find each angle and arc measure.
mBC⌢ = degrees
(60 POINTs will give BRAINIEST FOR EFFORT)
The angle is 47 degrees while the arc measure is solved to be 94 degrees
How to find the arc measureThe arc measure of the figure labelled AC is solved using the relationship between arcs and inscribed angles.
The relationship goes with formula below
angle B = 1/2 arc measure AC
where
angle B is the inscribed angle and it is equal to 47 degrees
arc measure AC is the unknown
plugging in the values will result to
47 degrees = 1/2 arc measure AC
arc measure AC = 2 * 47 degrees
arc measure AC = 94 degrees
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Mia and Allen have been married for 3 years. They both have well-paying jobs
that allow them to live comfortably and pay their bills. They are trying to live on
a budget. They have a $1,000 emergency fund, and they are paying down $28,000
worth of combined student loan debt. Each year for the past 3 years, they have
received a large tax refund -- which they call their "celebration fund" - and use it
to take a nice vacation each summer. They are receiving a large refund, rather
than one close to zero. Why is this kind of tax refund problematic?
Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.
We have,
While receiving a large tax refund each year may seem like a positive thing, it actually means that Mia and Allen are overpaying their taxes throughout the year.
This means that they are essentially giving the government an interest-free loan by allowing them to hold onto their money instead of having it available to them throughout the year to use for things like paying down debt or investing in their future.
By overpaying their taxes,
Mia and Allen are essentially missing out on the opportunity to use their money in ways that could benefit them in the long run.
Additionally, the large tax refund they receive each year may create a sense of false security, leading them to believe that they are in a better financial situation than they actually are.
Rather than receiving a large tax refund each year, it may be more beneficial for Mia and Allen to adjust their tax withholdings so that they are receiving more money in each paycheck.
This way, they can use the extra money to pay down debt, build up their emergency fund, or invest in their future, rather than giving the government an interest-free loan.
Thus,
Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.
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Find the volume of the composite solid
6 cm.
14 cm.
120 cm*
460 cm³
1462 cm³
980.2 cm³
The volume of the composite solid is 980.2 cm³.
What is a composite solid?
A composite solid is a solid made of two or more well-defined solid objects.
To calculate the volume of the composite solid, we use the formula below
Formula:
V = (πr²h/3)+(2πr³/3)...................... Equation 1Where:
V = Volume of the composite solidr = Radius of the cone and the hemisphereh = Height of the coneFrom the question,
Given:
r = 6 cmh = 14 cmπ = 22/7Substitute these values into equation 1
V = (6²×14×22/7)/3+(2×6³×22/7)/3V = 528+452.2V = 980.2 cm³Learn more about composite shape here: https://brainly.com/question/8370446
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Simply 4(2y-4)-11y????
Answer:
[tex]\mathrm{-3y-16}[/tex]Step-by-step explanation:
[tex]\mathrm{4(2y-4)-11y}[/tex]
Apply the distributive property:-
[tex]\mathrm{8y-16-11y}[/tex]
Combine like terms:-
[tex]\mathrm{8y-11y=\bf-3y}[/tex]
[tex]\mathrm{-3y-16}[/tex]
_________________________
Hope this helps! :)
Suppose Manuela flips a coin three times. What is the theoretical probability of flipping tails at least two times? Express your answer as a fraction in simplest form.
The probability of flipping tails at least two times in three flips is 1/2.
When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).
To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:
P(x ≥ k) = 1 - P(x < k)
where P(x < k) is the probability of getting tails fewer than k times in three flips.
To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:
P(x < 2) = P(0 tails) + P(1 tail)
P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8
P(1 tail) = 3 x (1/2) (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)
P(x < 2) = 1/8 + 3/8 = 1/2
Therefore, the probability of flipping tails at least two times in three flips is:
P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2
So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.
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James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the
________ movement.
O Color Field
Aesthetic
Impressionist
Avant-Garde
James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aesthetic movement is: B. Aesthetic.
What is The Falling Rocket?The art for art's sake movement which began to form in the late 19th century as a response against the utilitarian and moralistic attitude to art that had predominated in previous centuries is exemplified by The Falling Rocket.
The movement emphasized the value of art as a self sufficient and independent field, free from politics, religion and other outside influences.
Therefore the correct option is B.
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Out of 100 people sampled, 12 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Give your answers as decimals, to three places
< p
The true population proportion of people with kids is between 0.0565 and 0.1835.
We are given that;
Number of people= 100
Percent= 95%
Now,
To construct a 95% confidence interval for the true population proportion of people with kids. Here are the steps to do so:
Find the sample proportion p. This is the ratio of the number of successes (people with kids) to the sample size. In this case, p = 12 / 100 = 0.12.
Find the z-value that corresponds to the 95% confidence level. You can use a table or a calculator to find this value. The z-value for a 95% confidence level is 1.96.
Find the standard error of the sample proportion. This is the standard deviation of the sampling distribution of p. You can use the formula √p (1-p) / n to find this value. In this case, the standard error is √0.12 (1-0.12) / 100 = 0.0324.
Plug these values into the formula for the confidence interval and simplify. You get:
Confidence interval = 0.12 +/- 1.96*0.0324 Confidence interval = 0.12 +/- 0.0635 Confidence interval = [0.0565, 0.1835]
Therefore, by proportions the answer will be 0.0565 and 0.1835.
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Compound Area mathsss
Answer:
The answer for Area is 189.29in²
Step-by-step explanation:
Area of compound =Area of semi circle +Area of rectangle
r=d/2=10/2=5in
A=1/2pir² + L×B
A=1/2×5² + 10×15
A=25pi/2+150
A=39.29+150
A=189.29in²
Round your answer to the nearest hundredth.
Answer:
∠ A ≈ 75.96°
Step-by-step explanation:
using the tangent ratio in the right triangle
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then
∠ A = [tex]tan^{-1}[/tex] ( 4 ) ≈ 75.96° ( to the nearest hundredth )
What is the value of x?
Enter your answer in the box.
x =
Find the sum of the first 6 terms of the following sequence. Round to the
nearest hundredth if necessary,
12,
4,
4
3
Sum of a finite geometric series:
Sn
-
1-r
Тhе sum оf thе first 6 tеrms оf thе given sеquеncе is аpproximаtely 14.56.
Determining the sum of the first 6 termsFirst detеrmine thе common rаtio (r) аnd thе first tеrm (а1).
Eаch tеrm is obtаined by multiрlying thе prеvious tеrm by 1/3. Тherefоre, thе common rаtio is r = 1/3.
Тhe first tеrm is а1 = 12.
Now wе cаn use thе fоrmulа fоr thе sum оf а finite geоmetric series:
Sn = а1(1 - r^n) / (1 - r)
whеrе n is thе number оf tеrms.
Plugging in thе vаlues, wе gеt:
Sn = 12(1 - (1/3)^6) / (1 - 1/3) ≈ 14.55
Rounding to thе neаrest hundredth, wе gеt:
Sn ≈ 14.55 ≈ 14.56
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4. Marcy makes $19 an hour working as a librarian. She gets a 5% raise.
Which of the following statements are true about Marcy's new rate of pay? Select the 3 correct answers.
A Marcy will make an additional 1/20 of her salary an hour.
B Marcy will make an additional $0.95 an hour.
C Marcy’s new hourly rate is $19.50 an hour.
D After working 10 hours at the new rate, Marcy will make $195.
E After working 15 hours at the new rate, Marcy willmake $299.25.
You are given an image of a panda to create a custom shirt. The original image is 9mm tall and 16mm wide. You need to enlarge the image by a scale factor of 6. What is the new height?
The height of the image after the dilation with scale factor of 6 is given by the relation H = 54 mm
Given data ,
Let the image be an image of a panda to create a custom shirt
Now , original image is 9mm tall and 16mm wide
Let the dilation scale factor of enlargement be k = 6
So , the new image is 6 ( 9mm tall and 16mm wide )
On simplifying the equation , we get
The new image is 54 mm tall and 96 mm wide
Hence , the height of the image is 54 mm
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Find the value of x in the isosceles triangle shown below
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 8^2 - 2^2}\implies x=\sqrt{ 64 - 4 } \implies x=\sqrt{ 60 }[/tex]
Two households are saving money each month to go towards the shared costs of a vacation trip. One household has $700 saved and will continue saving $400 each month. The other household has $1,000 saved and will continue saving $300 each month.
Use the system of equations, where y represents total saved and x represents number of months, to answer the question.
y = 400x + 700
y = 300x + 1,000
At what point would the two lines intersect if graphed?
The two lines will intersect after 3 months.
How to explain the equationWe can set the two expressions for y equal to each other:
400x + 700 = 300x + 1,000
100x + 700 = 1,000
100x = 300
x = 3
So the two lines will intersect after 3 months. In this case, to find the corresponding value of y, we can substitute x = 3 into either of the equations:
y = 400x + 700
y = 400(3) + 700
y = 1,500
Therefore, the two lines will intersect after 3 months, at a point with coordinates (3, 1,500).
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how long would it take a car going 20 mph to real 528 feet?
The time will take the car to reach it's destination is 0.005 hours
The first step is to convert 528 feet to miles
1 foot= 0.000189394 miles
528= x
cross multiply
= 528 × 0.000189394
= 0.1
Time= distance/speed
distance= 0.1 miles
speed= 20
Time= 0.1/20
= 0.005 hours
Hence it will take the car 0.005 hours to reach its destination
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Line 1: y=x
System A
1 9
Line 2: y=-- x+
2
12.5
This system of equations is:
O consistent dependent
O consistent independent
O inconsistent
This means the system has:
O a unique solution
Solution:
D
O Infinitely many solutions
Ono solution
Line 1: y=-
Line 2: y=-
System B
This system of equations is:
O consistent dependent
O consistent independent
inconsistent
This means the system has:
O a unique solution
Solution: D
Infinitely many solutions
Ono solution
System C
Line 1: y=-
-x-1
Line 2: -x+4y=-4
This system of equations is:
O consistent dependent
consistent independent
O inconsistent
This means the system has:
O a unique solution
Solution: D
Infinitely many solutions
no solution
The equations are classified as follows
System A
consistent and independent this means that the system as a unique solution at (3, 3)
How to classify system B and CSystem B
inconsistent this means that the system as a no solution
A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
System C
consistent and dependent this means that the system as infinitely many solution
A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.
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Help its urgent i need to get these done
The planes that are parallel in the cube shown would be C. NOR and LMP.
What are parallel planes ?Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.
From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.
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Sarah has 14 cupcakes she gives 3/7 away how many cupcakes did she give away
Answer:
she gave away 6 cupcakes
Step-by-step explanation:
3/7 is the same as 6/14.
if she gave away 6/14 cupcakes, she gave away 6 cupcakes
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. at the end of one year, the two accounts earned $220 in interest. how much money was invested at 3%
The amount of money is 4000 was invested at 3%.
Let x be the amount of money invested at 3%.
Then, the amount of money invested at 5% is 6000 - x.
The interest earned on the amount invested at 3% is 0.03x.
The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.
The total interest earned is given as $220.
So, we can write the equation:
0.03x + (300 - 0.05x) = 220
Simplifying and solving for x, we get:
0.03x + 300 - 0.05x = 220
-0.02x + 300 = 220
-0.02x = -80
x = 4000
Therefore, $4000 was invested at 3%.
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HELP PLS ILL PUT MAX POINTS AS I CAN ALSO CHECK PICTURE
The expression which has the greatest value is 1 7/8 divided by 1/12
• For the first question, [tex]\frac{3}{4} /\frac{1}{3} =2 \frac{1}{4}[/tex]
• For the second question, [tex]\frac{3}{4} / \frac{1}{12} = 9[/tex]
• For the third question, [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{12} = 22 \frac{1}{2}[/tex]
• For the fourth question, [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{3} = 5 \frac{5}{8}[/tex]
—————
Please remember to revise this and make it in your own words if you want! I tried to speed this up a lot! I hope this helps you. -Doodle
—————
Answer:
1 7/8 / 1/ 12 has the greatest value
Step-by-step explanation:
Fast will give Brainliest.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Answer:
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Step-by-step explanation:
To reflect a point over a line, we can use the following steps:
Find the distance between the point and the line.
Construct a perpendicular line from the point to the given line.
Extend this perpendicular line to the same distance on the other side of the given line.
The intersection of the extended perpendicular line with the given line is the reflected point.
Alternatively, we can use the fact that reflecting a point over a line is equivalent to reflecting the coordinates of the point across the line. In this case, we are reflecting over the line y = -2, so we can simply negate the y-coordinate of each point to find its reflection.
Using this method, the reflected vertices are:
N'(-5, -4)
M'(-2, -3)
O'(-3, -1)
′(Therefore, the correct answer is option D: N−5, −6), M′(−2, −5), O′(−3,-7)
dividing 1/9 is equal to multiplying by
Answer: 9
Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:
10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.
Now lets try it with 1/9.
X divided by 1/9 = X times 9/1.
So dividing by 1/9 is equal to multiplying by 9.
Use substitution!!!
Pt. a
truck a costs $20,345. You can expect to pay an average of $1230 per year for repairs. truck b costs about 16,000. It will cost an average of $1425 for repairs per year. After how many years are the total costs for cars the same?
(I can solve it, can you just turn the words into an equation for me?)
Pt. B
You have 56 coins that are all nickles and dimes. The value of the coins is $2.05. Find the number of nickels and dimes.
(Can you also just make an equation out of this for me?)
The system of equations are t = 22.28 years , number of nickles and dimes are solved
Given data ,
a)
Let the number of years be represented as t
For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck A = 20345 + 1230t
For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck B = 16000 + 1425t
when the total costs are equal , we get
20345 + 1230t = 16000 + 1425t
On simplifying , we get
195t = 4,345
t = 22.28 years
b)
Let the number of nickels be n and number of dimes be d
The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)
The total value of the coins = $ 2.05
And , the total number of coins = 56
0.05n + 0.10d = 2.05
And , n + d = 56
Hence , the system of equations are solved
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if P = (4,2), Find: Rx=3 (P). Pls help!!
The coordinates of the reflected point P' will be (4, -3).
When a point is reflected over the x-axis, its y-coordinate changes sign.
In this case, the point P has coordinates (4,3).
To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.
So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.
Therefore, the coordinates of the reflected point P will be (4, -3).
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Answer:
Step-by-step explanation:
Which comparison is true? (Homework)
A) 8 x 2 5/6 < 8
B) 2 x 1 2/5 > 2
C) 5 x 1 1/3 < 5
D) 7 x 3/7 > 7
B.
B, is the true comparison
In the figure, m<1 = (3x + 12) degrees, m<2 = (3x + 18) degrees and m<3 = (7x + 10) degrees. What is m<3 in degrees?
The measure of the angle m∠3 of the triangle is m∠3 = 150°
Given data ,
Let the triangle be represented as ΔABC
Now , the measures of the angles are
m∠1 = ( 3x + 12 )°
m∠2 = ( 3x + 18 )°
m∠3 = ( 7x + 10 )°
m∠3 = 180° - ( m∠1 + m∠2 )
Now , for a triangle , the total angles = 180°
So , m∠1 + m∠2 = m∠3
On simplifying , we get
( 3x + 12 ) + ( 3x + 18 ) = ( 7x + 10 )
6x + 30 = 7x + 10
Subtracting 6x on both sides , we get
x + 10 = 30
Subtracting 10 on both sides , we get
x = 20
m∠3 = 150°
Hence , the measure of m∠3 = 150°
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The complete question is attached below :
In the figure, m<1 = (3x + 12) degrees, m<2 = (3x + 18) degrees and m<3 = (7x + 10) degrees. What is m<3 in degrees?
Look at the scatter plot below.
Which statement is true about data?
A The data shows a strong linear association
B There is no association
C There is a nonlinear association
D There is week negative association
Answer:
there is no associstaion
Step-by-step explanation: