Answers
Related Questions
f (x) = (x - 6)2(x + 2)2
DONE
Answers
The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.
What is the root of function?The root of the function is calculated by setting the function equal to zero.
The given function is f (x) = ( x - 6 )²( x + 2 )²
we will separate the two equation and set them equal to zero.
( x - 6 )² = 0 ---- equation ( 1 )
or
( x + 2 )² = 0 -------- equation ( 2 )
from the first equation, x = 6
from the second equation, x = - 2
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The complete question is below:
Find the roots of f(x) = (x - 6)² (x + 2)²
Tina would like to withdraw an annual salary of $35,756 from an account paying 2.2% compounded annually for 35 years once she retires. Given this information, determine the amount needed in her account in order for her to reach her goal. Round to the nearest cent.
Answers
Amount needed in account = Annual salary / (Interest rate / 100)^(Years of compounding)
Amount needed in account = 35756 / (2.2/ 100)^35 Amount needed in account = $737,939.36
What is the equation of the line that passes through the point (-3,1)(−3,1) and has a slope of \frac{2}{3}
3
2
?
Answers
Answer:
y = (2/3)x + 3
Step-by-step explanation:
first we need to find the y-intercept
we can do this by using what is given, the point (-3,1) and the slope (2/3)
using the slope-intercept formula: y = mx + b.
m = slope
b = y intercept
we can plug in the x and y values we were given
so,
1 = (2/3)(-3) + b
we can now easily solve for b
1 = (2/3)(-3) = b
first multiply
1 = -2 + b
then add 2 to both sides, this way we isolate b
3 = b
now that we have the y intercept we can write the equation of the line
y = (2/3)x + 3
if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.
1 = (2/3)(-3) + 3
multiply first
1 = -2 + 3
add the like terms
1 = 1
Classify the following triangle as acute, obtuse, or right.
50°
80°
50⁰
Answers
Answer: acute
Step-by-step explanation:
This triangle does not have any right angles (90°), or any angles larger than a right angle, so it is an acute triangle.
An approximate solution to an equation is found using this iterative process
Answers
a) The values are given as follows:
i) x1: -0.5.
ii) x2: -0.280125.
b) The solution of the equation is of: -0.25410169644.
How to calculate the valueThe equation in this problem is given as follows:
y = (x³ - 1)/4.
The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.
Then the values are given as follows:
x1 = -1 -> attributed.
x2 = ((-1)³ - 1)/4 = -0.5.
x3 = ((-0.5)³ - 1)/4 = -0.28125.
x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.
x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837
x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385
x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.
x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.
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An approximate solution to an equation is found using this iterative process.
Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1
a)
(i) Work out the value of x₂
(ii) Work out the value of x₃
b) Work out the solution to 6 decimal places
Need answers stat trigonometry
Answers
The value of x to the nearest tenth are as follows;
x = 47.0 units.
x = 25.1 units.
x = 23.8 units.
x = 29.7 units.
x = 21.1°.
x = 39.6°.
x = 58.0°.
x = 72.9°.
How to determine the value of x?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = x.
Adjacent side = 25.
Therefore, we would determine the value of x by using Tan trigonometric function:
Tanθ = Opposite side/Adjacent side
Tan45 = 25/x
x = 25Tan62
x = 47.0 units.
For right-angled triangle 3, we have:
Sin26 = 11/x
x = 11/0.4384
x = 25.1 units.
For right-angled triangle 4, we have:
Sin48 = x/32
x = 32sin48
x = 23.8 units.
For right-angled triangle 5, we have:
Cos12 = 29/x
x = 29/0.9782
x = 29.7 units.
For right-angled triangle 6, we have:
Cosθ = 14/15
θ = cos⁻¹(0.9333)
θ = 21.1°.
For right-angled triangle 7, we have:
Tanθ = 19/23
θ = tan⁻¹(0.8261)
θ = 39.6°.
For right-angled triangle 8, we have:
Cosθ = 9/17
θ = cos⁻¹(0.5294)
θ = 58.0°.
For right-angled triangle 9, we have:
Sinθ = 43/45
θ = sin⁻¹(0.9556)
θ = 72.9°.
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help pls
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)n+1
n=1
Submit Answer
Answers
S = a / (1 - r)
where "a" is the first term, and "r" is the common ratio.
In this case, "a" is 900 and "r" is 1.04, so the sum of the series can be calculated as:
S = 900 / (1 - 1.04) = 900 / -0.04 = -22,500
Rounding to the nearest integer, the answer is -22,500 rounded to -22500, which is approximately equal to -22,500
The reading group checked out 36 library books. 17 books are fiction, 10 are biographies, and some are science. How many books are science?
Answers
36-27= 9
so 9 books are science
Answer:
9 science books
Step-by-step explanation:
Step 1) 36 - 17 = 19
Step 2) 19 - 10 = 9
g questions: if a set of grades for a class has a large range and a small standard deviation, what can you say about the class? include an interpretation that is specific to grades in a class.
Answers
If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.
Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.
If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.
Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.
So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.
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the riverton high rockets won their regional basketball tournament and were awarded this trophy. what is the approximate volume of the trophy?
Answers
V Prism is V = B × h=9.5*4=38
the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47
V=10.47+38=48.476
A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.
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PLEASE HELP!!! Will give brainliest.
Answers
Answer:
The system of equation is y=12x+5
Step-by-step explanation:
Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
GIVING 70 POINTS FOR RIGHT ANSWER NEED ASAP (please and ty)
Answers
Answer:
m∠A = 45°;m∠B = 65°;m∠C = 70°.-----------------------------------
Recall triangle angle sum property, the sum of three interior angles is 180°.
Add up the three angle measures, then solve the equation for x:
m∠A + m∠B + m∠C = 1803(x + 5) + 5x + 15 + 7x = 1803x + 15 + 12x + 15 = 18015x + 30 = 18015x = 150x = 10Substitute the value of x and find the value of each angle:
m∠A = 3(10 + 5) = 3(15) = 45m∠B = 5*10 + 15 = 50 + 15 = 65m∠C = 7*10 = 70What is the area of the shaded region? Round to the nearest tenth of a centimeter.
Answers
The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters
What are trigonometric ratios?Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.
Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;
Interior angle of a regular hexagon = 120°
The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;
sin(60) = s/(5·√3) = (√3)/2
Where;
s = The side length of the regular hexagon
(5·√3)/s = (√3)/2
s = (5·√3)/((√3)/2) = 10
The side length of the regular hexagon, s = 10
The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a
Where;
a = The apothem = 5·√3
Therefore; A = ((3·√3)/2) × 10² = 150·√3
A = (1/2)×6 ×10 × 5·√3 = 150·√3
Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3
Area of the shaded region = Area of the hexagon - Area of the quadrilateral
Therefore;
Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6
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PLS HELP! Write 5x = -2y + 6 in slope intercept form and explain your answer
Answers
Answer: 5/2x-3
Step-by-step explanation: you would subtract 6 from both sides.
5x = 2y + 6
-6 -6
6-6=0 so they would cross out. and you can't subtract 5x from 6 because they aren't like terms. Your new equation would look like 5x-6 = 2y.
Now you need to get the y alone. To do that you need to divide everything by 2 so that the 2y crosses out. 5x-6 = 2y
-----------------
2 2 2
I'm trying to visually show it sorry if it looks weird. one you divide everything. (5/2) (-6/2) (2/2) you'll need to clean everything up.
Since you can't simply 5/2 leave it as a fraction. Which makes your answer: 5/2x - 3 = y or y = 5/2x - 3
what are 3 ways to solve 26x14
Answers
Answer:
i think this the answer
Step-by-step explanation:
26×14=ans
20×14+6×14=the same answer
10×26+4×26=same answer
a company made 500 flashlights and found five that were defective.if the company makes 12,500 flashlights how many do you predict will be defective
Answers
Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.
The formula for this problem is: Number of Defects = (total number of items)*(percent of defects)For this problem, we know that the total number of items is 12,500 and the percent of defects can be found by taking the 5 defective items out of the 500 items produced, which is 1%.Plugging these numbers into the formula, we get :Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.
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Directions - Solve the following equation:
12 =2 (x - 6)
X =
Answers
Answer:
x=12
Step-by-step explanation:
12 =2 (x - 6)
Solve for x.
Divide each side by 2
12/2 =2/2 (x - 6)
6 = x-6
Add 6 to each side
6+6 = x-6+6
12 = x
Answer:
x = 12
Step-by-step explanation:
Simplify both sides of the equation
Turn the equation around
Add 12 to both sides
Divide both the sides by 2
Need this for a math lesson
Answers
Answer:
maximum score = 92
Step-by-step explanation:
the maximum score is the largest value in the data set.
maximum score = 92
how many slices of pizza did he eat
Answers
Answer: The answer is 3 slices
Step-by-step explanation:
if you cut a pizza into 12 peices and devide it by 4 people each person gets 3
the sum of two numbers is 2490.if 65% of one number is equal to 85% of the other, the smallest is?
Answers
Answer:
the smallest number is 1079
Step-by-step explanation:
Let the numbers be x and y
We have two equationsx + y = 2490 (1)
0.65x = 0.85y (2)
Take the first equation
[tex]x + y = 2490[/tex]Move y to the right side:
[tex]x=2490-y[/tex]
Substitute for x in the second equation:
[tex]0.65x=0.85y[/tex]
[tex]0.65\left(2490-y\right)=0.85y[/tex]
[tex]1618.5-0.65y=0.85y[/tex]
Multiply throughout by 100:
[tex]161850 - 65y = 85y[/tex]
Move 161850 to the right side:
[tex]-65y=85y-161850[/tex]
Move 85y to the left side:
[tex]-65y=85y-161850[/tex]
[tex]-150y=-161850[/tex]
Divide both sides by -150
[tex]\dfrac{-150y}{-150}=\dfrac{-161850}{-150}[/tex]
[tex]y=1079[/tex]
Substitute for y in x = 2490 -y
[tex]x=2490-1079[/tex]
[tex]x=1411[/tex]
So the smaller number is 1079 and the larger number is 1411
Solve using substitution
3x-2y=3
y=6+4x
Answers
The system using substitution has its solution to be (-1.8, -1.2)
How to solve the system using substitutionFrom the question, we have the following parameters that can be used in our computation:
3x-2y=3
y=6+4x
By susbstitution, we have the following equation
3x - 12 - 8x = 3
Evaluate the like terms
so, we have the following representation
-5x = 9
Divide by 5
x = -1.8
So, we have
y= 6 + 4 * -1.8
Evaluate
y = -1.2
Hence, the value of y is -1.2
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2. If 3x² - 2x - 16 = 0, then x = ?
F. -8/3 or -2
G. 3/8 or 2
H. -2 or 8/3
J. -2 or 3/8
K. 2 or 8/3
Answers
Answer: H. -2 or 8/3
Step-by-step explanation:
3x^2-2x-16=0
Multiply 3 times 16
x^2-2x-48=0
find two numbers that will add up to equal -2 and will be multiplied to get -48. (-8 and 6)
(x-8)(x+6)
divide both numbers by 3 but since you cannot divide 8 and 3 you will move the 3 in front of the x.
(3x-8)(x+2)
Set both equal to 0.
3x-8=0 x+2=0
x= 8/3 x=-2
In order to keep the numbers in the proper place-value column
Answers
The order of the place value in increasing order is equal to units , tens , hundreds , thousands , ten-thousand and so on.
The value of every digit present in any number depends on the position of the digit in a number.The place of the digit in the number represents its place value of the digit in a number.Starting position of a digit is ones or units.After unit the place value is tens.In ascending order the place value of all the digit in any given number is represented as units , tens , hundreds , thousands , ten- thousands, so on.Therefore, the order of the place value in ascending order of the place of the digit is given by units , tens , hundreds , thousands , ten-thousand and so on.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the order of the place value ?
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Which value of x makes the equation
5(x - 2) - 4 = 6 true?
A. 2
B. 3
C. 4
D. 5
Answers
Answer:
Step-by-step explanation:
5x - 10 - 4 = 6
5x - 14 = 6
5x = 20
x = 4
Option C is the solution
What is 5’7 in cm
Please can I have help
Answers
Step-by-step explanation:
Sure, I'd be happy to help!
5 feet 7 inches is equivalent to 170.18 cm.
a committee of 3 is to be selected to plan the annual company picnic. how many different committees are possible that contain at least 2 secretaries?
Answers
There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.
Assume that there are n total secretaries employed by the business.
Either we can select 2 secretaries and 1 non-secretary member, or we can select all 3 members to be secretaries in order to form a committee with at least 2 secretaries.
Out of n, there are binom n2 ways to select two secretaries, and binom n-21 ways to select a non-secretary member from the remaining n-2 non-secretaries.
This means that there are binom n ways to form a committee with 2 secretaries and 1 non-secretary member.
There are binom ways to select each of the three members to serve as a secretary.
There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.
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What is the value of x for each question? Step by step please.
-1/2-4x/5=1/2-2x
7x²+9x²=-6x²-7x
-7x²+6=x²-7x²
Answers
Answer:
-1/2-4x/5=1/2-2x
Starting from the left side, we can simplify:
-1/2 - 4x/5 = 1/2 - 2x
Next, we can isolate x by adding 2x to both sides:
-1/2 - 4x/5 + 2x = 1/2 - 2x + 2x
-1/2 + 2x/5 = 1/2
Adding 1/2 to both sides:
0 + 2x/5 = 1
Finally, solving for x:
2x/5 = 1
Multiplying both sides by 5:
2x = 5
Dividing both sides by 2:
x = 5/2
7x² + 9x² = -6x² - 7x
Combining like terms:
16x² = -6x² - 7x
Adding 6x² to both sides:
22x² = -7x
Dividing both sides by -7:
-22x²/-7 = 7x/-7
-22x²/7 = -7x/7
-22x²/7 = -x
Multiplying both sides by -7:
22x² = x
Dividing both sides by 22:
x² = x/22
Since this equation states that x² equals x divided by 22, it has no real solutions for x.
-7x² + 6 = x² - 7x²
Combining like terms:
-8x² + 6 = 0
Adding 8x² to both sides:
-8x² + 8x² + 6 = 0 + 8x²
6 = 8x²
Dividing both sides by 8:
6/8 = 8x²/8
3/4 = x²
Taking the square root of both sides:
sqrt(3/4) = sqrt(x²)
x = +/- sqrt(3/4)
These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Table A represents a multiplicative relationship because y is 2.5 times x, O and Table B represents an additive relationship because y is 2 more than O X. Table A represents an additive relationship because y is 1.5 more Othan x, and Table B represents a multiplicative relationship because y is 3 times x. Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X. Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x.
Answers
Answer:
Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X
Step-by-step explanation:
Self-explanatory
Every value of y in Table A is 2.5 times x value
and
every value of y in table B is 3 times x value
Question 1 of 5
Drag each value to the correct location on the circle. Not all values will be used.
Circle F has radius of 4 inches with a central angle of 120°. Determine the measure of the central angle in radians, the arc length of RS
, and the area of sector RFS.
Answers
The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.
What is the central angle?
A central angle is an angle with endpoints and located on a circle's circumference and a vertex located at the circle's center. A central angle in a circle determines an arc.
To determine the measure of the central angle in radians, we can use the formula:
radians = degrees * (π / 180)
So, for the central angle of 120°:
radians = 120 * (π / 180) = 2 * π / 3
The measure of the central angle in radians is approximately 2 * π / 3 radians.
To find the arc length of RS, we can use the formula:
arc length = (central angle / 360) * circumference
The circumference of the circle is given by 2 * π * r, where r is the radius:
circumference = 2 * π * 4 = 8 * π
So the arc length is:
arc length = (120 / 360) * (8 * π) = 4 * π / 3
The arc length of RS is approximately 4 * π / 3 inches.
To find the area of sector RFS, we can use the formula:
area = (central angle / 360) * π * r²
So the area of sector RFS is:
area = (120 / 360) * π * (4)² = 8 * π
Therefore, The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.
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Answer:
Arch length = 8pi/3
Area of sector = 16pi/3
Central angle in radians = 2pi/3
Step-by-step explanation: see picture-
A charity needs to report its typical donations received. The following is a list of the donations from one week.
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.
Answers
The measure of center should the charity use to accurately represent the data is The mean of 49 is the most accurate to use to show that they have plenty of money, the correct option is C,
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that;
The list of donation is as follows
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
Now,
Mean is the middle term of the data
Here,
Middle term of data=49
Therefore, the mean of the given list will be 49.
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