Answers
We have then:
x ^ 2 + 20x + 100 = 36
Rewriting:
x ^ 2 + 20x + 64 = 0
The values of the roots are:
x1 = -4
x2 = -16
Remember that the values of the roots are what make the polinome zero
Answer:
x1 = -4
x2 = -16
Related Questions
find the inverse of y=x2-10x
Answers
y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Answer:
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Step-by-step explanation:
We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].
We know that to find inverse, we interchange x and y values and then solve for y.
After interchanging x and y values, we will get:
[tex]x=y^2-10y[/tex]
Switch sides:
[tex]y^2-10y=x[/tex]
[tex]y^2-10y-x=x-x[/tex]
[tex]y^2-10y-x=0[/tex]
Now, we will use quadratic formula to solve for y.
[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]
[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]
[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].
how would I solve for x?
Answers
Acute scalene triangle.Sides: a = 15 b = 13 c = 14
Area: T = 84
Perimeter: p = 42
Semiperimeter: s = 21
Angle ∠ A = α = 67.38° = 67°22'49″ = 1.176 rad
Angle ∠ B = β = 53.13° = 53°7'48″ = 0.927 rad
Angle ∠ C = γ = 59.49° = 59°29'23″ = 1.038 rad
Height: ha = 11.2
Height: hb = 12.923 <- Answer
Height: hc = 12
Median: ma = 11.236
Median: mb = 12.971
Median: mc = 12.166
Inradius: r = 4
Circumradius: R = 8.125
Vertex coordinates: A[14; 0] B[0; 0] C[9; 12]
Centroid: CG[7.667; 4]
Coordinates of the circumcenter: U[7; 4.125]
A 45° sector in a circle has an area of 13.75π cm². What is the area of the circle? Use 3.14 for pi.
Enter your answer as a decimal in the box.
cm²
Answers
you know the area of 45° of the part.
now if you divide 360 by 45 you'll get numbers of 45° sector that circle will have.
360/45=8
multiply the given area with8
i.e. 8×(13.75×3.14)
=345.4 answer
Area of circle is 345.4 cm²
Area of sector:Given that;
Angle of sector = 45°
Area of sector = 13.75π cm²
Find:
Area of the circle
Computation:
Area of sector = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75π = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
43.175 = 0.125[Area of circle]
Area of circle = 345.4 cm²
Find out more information about 'Area of circle'
https://brainly.com/question/1238286?referrer=searchResults
The length of a football field is 100 yards and the width is 53 yards. in the first game of the season, joe don catches the opening kickoff at the corner of the goal line and runs straight as a string the diagonal length of the field to score a touchdown. the next day, the local paper credits joe for a 100 yard touchdown run, but how far did he actually run?
Answers
.. diagonal = √((53 yd)^2 +(100 yd)^2) = (√12809) yd ≈ 113.2 yd
Joe Don's run was 113.2 yards.
Answer:
Joe Don actually ran 113.2 yards
Step-by-step explanation:
Length of the football field = 100 yd
Width of the football field = 53 yd
The football field is rectangular in shape. So in order to find the diagonal of the field, we need to split it up into two right triangles.
In one of the right triangles, the length and width becomes the two sides of it and diagonal is the third side.
In order to find the third side (diagonal), we need to apply the Pythagoras theorem.
So,
Diagonal² = 100² + 53²
Diagonal² = 10000 + 2809
Diagonal² = 12809
Taking square root on both sides
[tex]\sqrt{Diagonal^{2} } =\sqrt{12809}[/tex]
Diagonal = 113.17 yd
Diagonal = 113.2 yd (approx)
Thus Joe Don actually ran 113.2 yards
Write and solve an equation to find the value of each variable
Answers
as you can see in the picture, the "near arc" is x°, and the "far arc", is the leftover from subtracting the arc of 120° and x°, therefore then
[tex]\bf 44=\cfrac{\stackrel{far~arc}{(360-x-120)~~-~~\stackrel{near~arc}{x}}}{2}\implies 88=240-2x \\\\\\ 2x=152\implies x=\cfrac{152}{2}\implies x=76[/tex]
Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition?
A. 2 + x + 3y
B. (2 + x) + 3y
C. 2x + (3 + y)
D. x + (2 + 3y)
Answers
(2 + x) + 3y ...>Associative Property of Addition
hope it helps Plz give Brainliest
B. (2 + x) + 3y
Step-by-step explanation:
First of all you must know how the associative property of addition looks like. Example: (1 + x) + y = 1 + (x + y)
Ok so now really we have to make the two ( ) on the outside of 2+x so then it looks like these ( ) have been reversed. So then (2+x)+3y would be your answer. Also I did this on FLVS so I know that the answer I said is correct. I hope this helps you.
Can someone help me?
Answers
= 6² + 2
= 36 + 2
= 38
= 6^2 + 2
= 36 + 2
= 38
helpppppppppppppppppppppp
Answers
Second Option
Solution:
A geometric series converges when the value of its common ratio is between -1 and 1. Else the series will diverge. So we find the common ratio for each of the given options, the series with common ratio between -1 and 1 will be converging series.
For first option, common ratio = 1/3 divided by 1/9 = 3
Common ratio is not between -1 and 1, so this series is diverging.
For second option, common ratio = 1/2 divided by 1 = 1/2
Since the common ratio is between -1 and 1, this series is converging.
For third option, common ratio = -4
This series is also diverging.
For Fourth option, common ratio = 2
This series is also diverging.
The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. Which segments appear to be equal in length? Check all that apply. XP = YP for an acute triangle XP = ZP for an acute triangle YP = ZP for an obtuse triangle ZP = XP for a right triangle XP = YP for an obtuse triangle
Answers
XP=YP for an acute triangle
YP=ZP for an obtuse triangle
XP=YP For an obtuse triangle
YP=ZP for an obtuse triangle
XP=YP for an obtuse triangle
this is right
For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}
Answers
the formula is a(r)^(n-1)
a------------- >a is the first term------------ > -4
r--------------- > is the common ratio------- > 12/(-4)=(-36/12)=-3
n--------------- > is the number of terms
The fifth term is -4[(-3)^(5-1)]=-4[(81]=-324
the answer is -324
r = [tex] t_{n+1} / t_{n} [/tex]
where r is the common ratio
[tex] t_{n} [/tex] is any term in the sequence
[tex] t_{n} [/tex] is the term preceding [tex] t_{n} [/tex]
In your case the common ratio will be
12/-4 = -3
The recursive formula of a geometric sequence is:
An = [tex] A_{n-1} [/tex] x r
Where : An is the nth term
[tex] A_{n-1} [/tex] is the erm preceding the nth term
r = common ratio
For this case it is:
An = [tex] A_{n-1} [/tex] x -3
Now let us use this formula to find the 5th term:
[tex] A_{5} [/tex] = [tex] A_{5-1}[/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4}[/tex] x -3
Since you do not know the 4th term, you can use that by using our reclusive formula:
[tex] A_{4} [/tex] = [tex] A_{4-1} [/tex] x -3
[tex] A_{4} [/tex] = [tex] A_{3} [/tex] x -3
[tex] A_{4} [/tex] = [tex] -36 [/tex] x -3
[tex] A_{4} [/tex] = [tex] 108 [/tex]
Now that you know your fourth term, you can use the same formula:
[tex] A_{5} [/tex] = [tex] A_{5-1} [/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4} [/tex] x -3
[tex] A_{5} [/tex] = [tex] 108 [/tex] x -3
[tex] A_{5} [/tex] = [tex] -324 [/tex]
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. How many more jumps (j) do they need to match the record? Show your work!
Answers
We have then:
Lindsay has gotten 14 jumps in a row and Lorraine has gotten 13:
14 + 13 = 27
Then, we must find the remaining amount:
j = 48-27
j = 21
Answer:
they need 21 more jumps to match the record
Jacqueline's piggy bank contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?
Answers
In the two triangles below, all angles equal 60 degrees and ab = ef. are the two triangles congruent?
Answers
Write an expression for the following situation and solve it. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students.
Answers
1/4 of 20 pencils are 5 pencils.
Since he gave away 4 pencils,
Total = 5 + 4 = 9
Mr. Simms use and give away total 9 pencils.
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. y = 2.5 when x = 9 answer asap plaese
Answers
2. xy=k
Answer:
k = 22.5; xy = 22.5
your welcome
XD
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 5 7.5 15 7.5 11 13.8 6.4
HS 16 0 9.5 14.5 5 13 . 10.7 5.3
Which of the choices below best describes how to measure the spread of this data? (Hint: Use the minimum and maximum values to check for outliers.) (2 points) A:Both spreads are best described with the IQR.
B:Both spreads are best described with the standard deviation.
C:The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D:The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answers
Answer:
Option A is correct
Step-by-step explanation:
Given is a table which shows data from a survey about the amount of time students spend doing homework each week.
College HS
High 50 16
Low 5 0
Q1 7.5 9.5
Q3 15 14.5
IQR 7.5 5
Median 11 13
Mean 13.8 10.7
Std dev 6.4 5.3
1.5IQR 11.25 7.5
Q1-1.5IQR -9.38 -12
Q3+1.5IQR 37.5 29.5
WE find that there is only one outlier in college with 50 as high.
Except that all others are well within IQR range. Hence outliers are minimum
So option A is right.
Final answer:
To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.
Explanation:
To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.
When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.
Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.
1. Billy had 40 songs on his MP3 player. If he deleted 8 songs, what is the ratio of songs he kept to songs he deleted?
1 point
8:40
32:40
40:32
40:8
2. A vendor sold 63 hotdogs during a football game. If the ratio of hotdogs to hamburgers sold was 9:5, how many hamburgers did the vendor sell? *
1 point
Your answer
3. Paul had sold 24 orange fish. If the ratio of blue fish to orange fish is 3:8, how many fish did he sell in total?
1 point
Your answer
4. Jack has a collection of toy cars. If there are 2 blues, 5 black, 7 red and 3 purple cars, what is the ratio of purple to all the cars?
1 point
3:14
3:17
5. At an ice cream shop the ratio of sugar cones to waffle cones sold is 2:1. If there are 15 cones altogether, how many sugar cones are there?
1 point
3
5
15
10
6. There is a total of 72 total students. If the ratio of boys to girls is 4 to 5, how many of the students are girls?
1 point
32
40
8
7. Paul can walk 15 steps in 5 minutes. How long does it take Paul to walk 75 steps?
1 point
25
225
3
8. If the ratio of pink flower to blue flower is 2 to 7 and there are 12 pink flowers, how many blue flowers are there?
1 point
6
12
42
36
Other:
9. If the ratio of white pens to green pens is 1 to 4 and there are 6 white pens, how many are green?
1 point
6
20
24
36
10. Jennifer and Melissa are both making lemonade. Melissa uses 3 cups water to 1 cup lemon juice. Jennifer uses 5 cups water to 2 cups lemon juice. Which mixture will have more lemon flavor?
1 point
Jennifer's
Melissa's
11. Nicholas has a collection of pens. He has 4 red, 9 blues, 2 white and 3 black pens. What is the ratio of black to the total amount of pens in simplified form?
1 point
1:3
1:6
3:1
6:1
Answers
3- 9
4- 3:17
5- 10
6- 40
7- 25 minutes
8- 42
9- 24
10- Jennifer
11- 1:6
hope this helps (I don't know the first answer )
Ginny has a sheet of plywood that is 4 feet by 8 feet. She wants to saw the plywood into pieces 1 foot high and 2 feet long for signs. How many signs can she make with the sheet of plywood?
Answers
Answer: 16 signs
Step-by-step explanation: i not saying this cause the other person said it i am saying it because i tookthe question
Eric borrowed $1,800 for 9 months at 13.5% simple interest under an
add-on plan. What was his monthly payment?
a. $15.63
b. $220.25
c. $187.50
d. $1,982.25
ANSWER IS NOT C
Answers
You know the monthly repayment of $1800 over 9 months will be at least $200 per month. Since the interest is about 10% of the loan amount (3/4 of 13.5%), the amount added on for interest will be on the order of $20 per month.
If you work out the math, you find the payment is exactly $220.25 (selection B). You don't need to do that to make a sensible choice.
_____
Payment = ($1800 + 9/12*0.135*1800)/9 = $220.25.
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
Answers
There are 10 different ways to select a committee of 2 people from a group of 5 candidates.
Explanation:To calculate the number of ways to select a committee of 2 people from a group of 5 candidates, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
Here, n is the total number of candidates (5) and r is the number of people to be selected for the committee (2). Plugging in the values, we get:
5C2 = 5! / (2!(5-2)!)
Simplifying this expression:
5C2 = (5 * 4) / (2 * 1)
Therefore, there are 10 different ways to select the committee.
can someone answer this?
Answers
All the right triangles are similar, so
.. hypotenuse/(short side) = x/6 = 6/(x -9)
Multiplying by the product of denominators gives
.. x(x -9) = 36
Two factors of 36 that differ by 9 are 12 and 3, so we have
.. x = 12
For y, we can use the Pythagorean theorem.
y^2 +6^2 = 12^2
y^2 = 144 -36 = 108
y = √108 = √(36*3)
y = 6√3
Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 Which polynomial represents the standard form of the original polynomial?
a.x^3/2 – 2x^5 + x/4 + 1
b.–2x^5 + x^3/2 + x/4 + 1
c. –2x^5 + x/4 + x^3/2 + 1
d. 1 – 2x^5 + x^3/2 + x/4
Answers
Answer:
b. –2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
In the given expression, the degrees of the terms, in the order given, are ...
1, 5, 3, 0
When the terms are properly arranged in standard form, they will be ...
5, 3, 1, 0 . . . . descending order
The standard form of this expression is ...
-2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B
Answer: b.–2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
The expression below is the factorization of what trinomial?
(2x + 7)(4x - 3)
A. 8x2 + 22x + 4
B. 8x2 + 28x - 21
C. 8x2 + 28x + 4
D. 8x2 + 22x - 21
Answers
= (2x)(4x) + (2x)(-3) + (7)(4x) + (7)(-3)
= 8x^2 - 6x + 28x - 21
= 8x^2 + 22x - 21 (Answer D)
Someone pleaser help me !
Answers
.. $80,000 * 4/(3 +4) = 45,714.29
The closest answer is the 4th selection, but it doesn't really agree with the conditions of the problem statement.
_____
If Steve invests the balance after Elizabeth contributes 45,600, the ratio of their contributions will be 43:57, about 0.7544, not 3:4 = 0.7500.
30 POINTS!!! WILL MARK BRAINLIEST! : )
1. Name the property the equation illustrates.
8 x 1/8 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
2. Name the property the equation illustrates.
–5 + (8 + 10) = (–5 + 8) + 10
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
3. Name the property the equation illustrates.
-4 x -1/4 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
4. Name the property the equation illustrates.
(ab)3 = a(b3)
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
Answers
2. B) Inverse Property of Addition
3. C) Inverse Property of Multiplication
4. Your answer is not listed (The answer is Associative Property of Multiplication)
Answer:
1. C) Inverse Property of Multiplication
2. None of these. The answer is Associative property of Addition
3. C) Inverse Property of Multiplication
4. None of these. The answer is Associative property of Multiplication
Step-by-step explanation:
1.
Given a number a , the inverse property of multiplication states that
a * 1/a = 1
and 1/a is called the multiplicative inverse of a.
So 8 * 1/8 = 1 features the inverse property of multiplication where a = 8.
2.
Given three numbers a,b,c , the associative property of addition states that a + (b + c) = (a + b) + c
In this case, a = -5, b = 8 and c = 10
3.
-4 x -1/4 = 1 features the inverse property of multiplication where a = -4.
4.
Given three numbers a,b,c , the associative property of multiplication states that (a * b) * c = a * (b * c)
In this case, a = a, b = b and c = 3
What is 4 equal parts
Answers
Suppose there are 7 dimes, and someone gives you 4 of them. Each dime they gave you represents a part of the whole amount of dimes, and each of those dimes is equal to the others in size, weight, color, value. They are 4 equal parts of the whole amount of dimes. (The four equal parts don't have to add up to the whole--except when we say the whole is divided into 4 equal parts.)
Usually, we talk about equal parts when we are dividing something into shares. If we have a pizza that four people want to share in such a way that each person gets as much as possible without any fighting, it would usually be divided into four equal parts. Each share would be the same as the others in every aspect that matters. Each of those parts would be 1/4 of the pizza. The "4" in that fraction tells you the number of equal parts. The "1" tells you the number of those parts any one person gets in this scenario.
_____
Each of the words in that phrase "4 equal parts" has its usual dictionary meaning.
The name of a triangle whose angles are all more that 90 degrees?
Acute
Obtuse
Right
Isosceles
None of the above
Answers
Answer:
Option B is correct.
Obtuse triangle.
Step-by-step explanation:
Acute triangle:
In acute triangle, all angles are less than 90 degree.
Obtuse triangle:
In obtuse triangle, the triangle has an angle more than 90 degree.
Right triangle.
In right triangle, it has a right angle 90 degree.
Isosceles triangle.
In isosceles triangle, it can be acute, right or obtuse depends only on the apex angle.
Therefore, the triangle whose angles are all more that 90 degree is, Obtuse triangle.
A sidewalk forms the diagonal of a square park. The sidewalk is 30 meters long. To the nearest tenth of a meter, how long are the sides of the park ?
Answers
900 = 2A²
A^2 = 450
Taking the square root of 450, we find that the lengths of A and B are roughly 21.2 meters.
Length of the Diagonal l = 30 m
Formula for the length of the diagonal of a square l = square root of 2 x s; s being the side.
Therefore square root of 2 x s = 30 => s = 30 / square root of 2 = 30 / 1.414 Side of the Square s = 21.21 m
What is the total number of rectangles and triangles used for the net of this solid?
a. 3
b. 4
c. 5
d. 6
Answers
The total number of rectangles and triangles used for the net of this solid is 4.
Explanation:To find the total number of rectangles and triangles used for the net of a solid, we need to examine the shape of the solid. If the given solid has 4 faces, like a regular tetrahedron or a pyramid, then it will have 3 triangles and 1 rectangle. Hence, the total number of rectangles and triangles used for the net of this solid is 4, so the answer is option b.
Learn more about Rectangles and Triangles here:https://brainly.com/question/21681499
#SPJ12
Factor the quadratic equations W^2-W-12
Answers
W^2-W-12 = w^2+bW+c
b=-1,
c=-12
We look for m, n so that m+n=b=-1, m*n=c=-12, where m,n are integer factors of -12.
Now enumerate all possibilities for m*n=12
m n m*n m+n
1 -12 -12 -11
2 -6 -12 -4
3 -4 -12 -1 ....... so m*n=-12, m+n=-1
The factorization is then
W^2-W-12=(W+3)(W-4)