Question 4
Solve the equation x² - 4x+6=0 by completing the square.
BIUX² X₂ 15px help!!p
Answers
The solution of the equation x² - 4x + 6 = 0 using completing the square is x = 2 ± √(-2)
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial can be classified based on degree of two as a quadratic equation.
Given the equation:
x² - 4x + 6 = 0
Solving using completing the square method:
subtract 6 from both sides:
x² - 4x = -6
add to both sides the square of half the coefficient of x:
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
Taking square root of both sides:
x - 2 = ±√(-2)
x = 2 ± √(-2)
The solution is x = 2 ± √(-2)
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Related Questions
A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?
O 31 units
O 39 units
O 41 units
O 49 units
Mark this and retum
Save and Exit
Next
Submit
rs/AssessmentViewer/Activit.
Answers
Answer:
41 units
Step-by-step explanation:
Use the Pythagorean Theorem
c^2 = a^2 + b^2
c^2 = 9^2 + 40^2
c^2 = 81 + 1600
c^2 = 1681
Take the square root of both sides
c = 41
The length of the diagonal is 41 units
What is Pythagoras' rule?The Pythagoras' rule states that the sum of the hypotenuse squared is equal to the sum of both the opposite squared and the adjacent squared.
i.e
hyp² = opp² + adj²
The shape of the rectangle takes a right angle triangle with the:
hypotenuse = diagonal of the rectangleopposite = length of the rectangleadjacent = width of the rectanglehyp² = 40² + 9²
hyp² = 1600 + 81
hyp² = 1681
hyp = [tex]\mathbf{\sqrt{1681}}[/tex]
hyp = 41 units
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solve right tringle if BC = 83 and A = 40
Answers
Answer:
Step-by-step explanation:
In Ronna’s class, the ratio of boys to girls is 2:3. In Suzie’s class, there are half as many girls as in Ronna’s class. If there are 12 boys in Ronna’s class, how many girls are in Suzie’s class?
Answers
Answer:
4
Step-by-step explanation:
2:3
4:6
6:9
8:12
8 girls in Ronna’s class
Half of 8 is 4
Consider the line y = 8x-2.
Find the equation of the line that is parallel to this line and passes through the point (3, -2).
Find the equation of the line that is perpendicular to this line and passes through the point (3,-2).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Answers
Answer:
parallel line: y = 8x - 26
perpendicular line: y = -1/8 x - 13/8
Step-by-step explanation:
1.
Lines are parallel, so slopes are equal, and y-intercepts are different.
Given line:
y = 8x - 2
New line:
y = 8x + b
Use point (3, -2) and solve for b.
-2 = 8(3) + b
-2 = 24 + b
b = -26
Equation: y = 8x - 26
2.
Lines are perpendicular, so slopes are negative reciprocals.
Given line:
y = 8x - 2
New line:
m = -1/8
y = -1/8 x + b
Use point (3, -2) and solve for b.
-2 = -1/8 × 3 + b
-2 = -3/8 + b
b = -16/8 + 3/8
b = -13/8
Equation: y = -1/8 x - 13/8
The figure shown is a rectangle with a semicircle on each end. What is the area of the
figure? Use 3.14 for 7 and round your answer to the nearest tenth.
Answers
9514 1404 393
Answer:
(c) 76.3 in^2
Step-by-step explanation:
From the offered selections, you can make an informed choice with a simple estimate.
The overall length of the figure is 8+6 = 14 inches, and its width is 6 inches. The area will be smaller than a 14 × 6 = 84 square inch rectangle, and larger than the central rectangle of 8 × 6 = 48 square inches.
The only choice in the range 48 to 84 square inches is the correct one:
76.3 square inches
__
If you'd like to figure it out, the area is the sum of the 48 square inch central rectangle and the (π/4)(36 in^2) ≈ 28.26 square inch circle. That total, rounded to tenths, is 76.3 square inches.
he heights of young women aged 20 to 29 follow approximately the N(64, 2.7) distribution. Young men the same age have heights distributed as N(69.3, 2.8).Height is measured in inches.A young woman in that age group is randomly selected; independently, a young man in that age group is randomly selected. What is the probability that the young man is taller than the young woman by more than 5 inches
Answers
Answer:
0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Distribution of the difference in height between men and woman:
Applying the concept above:
[tex]\mu = 69.3 - 64 = 5.3[/tex]
[tex]\sigma = \sqrt{2.7^2 + 2.8^2} = 3.89[/tex]
What is the probability that the young man is taller than the young woman by more than 5 inches?
Probability of the difference being more than 5 inches, that is, 1 subtracted by the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 5.3}{3.89}[/tex]
[tex]Z = -0.08[/tex]
[tex]Z = -0.08[/tex] has a pvalue of 0.4681
1 - 0.4681 = 0.5319
0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches
Which shows how to use similar right triangles to find the equation of the line through (0,b) and any point (x, y), on the line?
Answers
Answer: b
Step-by-step explanation:
Esh
Given K (9,-9), L(2,-2), M(-9,-5), and N (5, y). Find y such that
KL_|_MN.
Answers
On solving the provided question, we cans say that - here in coordinates S is given by: [tex](-2,4)[/tex]
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
x-coordinate of [tex]X = -2[/tex]
y-coordinate of[tex]S = 4.[/tex]
S is given by: [tex](-2,4)[/tex]
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On solving the provided question, we cans say that - here in coordinates S is given by: (-2,4)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
x-coordinate of -2
y-coordinate of 4
S is given by: (-2,4)
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What is sin 30°?
60°
2
2
1
90°
30°
3
Answers
According to the property of cofunctions, [tex]$\sin 30^{\circ}$[/tex] exists equivalent to
[tex]$\cos 60^{\circ} \cdot \sin 30^{\circ}=1 / 2$[/tex].
What is cofunction?A trigonometric function whose value for the complement of an angle exists equivalent to the value of a given trigonometric function of the angle itself the sine exists the cofunction of the cosine.
According to the property of cofunctions, [tex]$\sin 30^{\circ}$[/tex] exists equivalent to
[tex]$\cos 60^{\circ} \cdot \sin 30^{\circ}=1 / 2$[/tex].
Therefore, the correct answer is option B. 1/2.
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What type of correlation does the following have? The age of a person vs. The
last four digits of their phone number.
Answers
Answer:
no correlation
Step-by-step explanation:
make this equation true using grouping symbols.
39 + 5 - 3^2 = 13
Answers
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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Estimate how many liters of air you breathe in one year. To calculate your estimate, you must make assumptions.
1. Assume it takes 10 breathes to blow up a balloon the size of a two-liter bottle.
2. Assume 10 breathes per minute.
A)
500,000 liters
B)
1,000,000 liters
)
2,500,000 liters
D)
10,000,000 liters
Answers
Answer: 1,000,000
Step-by-step explanation: USA test prep
Find the median of the following data set. 1 1/4,5/8 ,3/5 ,1/2 ,1 1/2, 1 3/4
1. 7/8
2. 15/16
3. 5/6
Answers
Answer:
1. 7/8
Step-by-step explanation:
7, 12, 15
Right traingle????
Answers
Answer:
No, it is not a right triangle.
Pls help me, if you get it right I will give you Brainlist!
Answers
Answer:
370 m²
Step-by-step explanation:
Front and back
a = 2(11 * 6)
a = 132 m²
Right and left sides
a = 2(7 * 6)
a = 84 m²
Top and bottom
a = 2(11 * 7)
a = 154 m²
______________________
total
a = 132 + 84 + 154
a = 370 m²
Practice Test
Flashcards
Stu
Question 4 Mathematics Practice Test for the TEAS
Solve the equation and choose the best answer:
9
6
6
4
7
C
6
Answers
Answer:
Where is the equation??
A truck spilled 1000 gallons of asphalt on the 5 freeway. Come up with a way to approximate the cost of the clean up
Answers
HELP PLS!!! Determine the type of triangle that is drawn below.
Answers
Answer:
Isosceles right triangle
Step-by-step explanation:
Right isosceles has a 90° degree angle with two other sides 45° each
===========================================================
Explanation:
Sides AB and AC are the same length (5.61), so the triangle is isosceles. If all three sides were the same, then it would be equilateral, but side BC is a different length of the first two sides mentioned. If all sides were different, then the triangle would be scalene.
Angle A is 90 degrees, making it a right angle. That means triangle ABC is also a right triangle. The triangle would be acute only when all three angles are less than 90. If any angle is greater than 90, then the triangle is obtuse.
So put together, triangle ABC is both isosceles and a right triangle, or in short we could say "triangle ABC is an isosceles right triangle".
In the school cafeteria there are 20 seats at each table.
How many tables are needed for 250 students?
Answers
Answer:
12.5
Step-by-step explanation:
you can solve this by dividing 250/20=12.5
anoheeeeeeeeeeeerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Answers
Answer: [tex]\frac{29}{6}[/tex]
Step-by-step explanation:
To make an improper fraction, make the whole number into a fraction with the denominator 6. We do this because we want the fraction and the whole number to have the same denominator, so we can later add them together.
To do this, multiply 4 by 6:
[tex]\frac{4 }{6}[/tex] * [tex]\frac{6}{1}[/tex] = [tex]\frac{24}{6}[/tex]
Then, add [tex]\frac{24}{6}[/tex] and [tex]\frac{5}{6}[/tex] together
[tex]\frac{24}{6}[/tex] + [tex]\frac{5}{6}[/tex] = [tex]\frac{29}{6}[/tex]
PLEASE HELP ME, EASY MATH QUESTION !!!! (no links), beainliest xtra points profile thanks, thanks, 5star rating ((IF CORRECT))
This data set shows all of the scores Jane earned on her math tests.
{80, 90, 90, 92, 94,95, 95, 97, 98, 98, 100, 100}
Jane removes her lowest score from the data set.
How are the mean and median test scores affected?
Select from the drop-down menus to correctly complete the statements.
The mean score ____.
A) Increases
B) Decreases
C) Stays the same
The median score ____.
A) Increases
B) Decreases
C) Stays the same
Answers
Answer:
1) A) Increases
2) C) Stays the same
Step-by-step explanation:
1) A) Increases (94 to 95)
2) C) Stays the same (95)
parallel abcd is similar to parallelogrem efgh. what is the lenght of gh?
Answers
The value of side GH as shown in the parallelogram is 2 units
What is an parallelogram?Parallelogram is a polygon that has four sides (quadrilateral) and opposite sides are always equal and parallel to each other
Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are proportional. Also, their corresponding angles are equal to each other.
Parallelogram abcd is similar to parallelogram efgh, hence:
FG/BC = GH / CD
substituting:
7/21 = GH / 6
GH = 6 * 7/21 = 2
GH is 2 in
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Find the x of =3(x+1)=12
Answers
Answer:
x = 3
Step-by-step explanation:
Answer:
it’s in the picture
Step-by-step explanation:
I hope it helps
HEEEELPPPP IT IS FOR TODAY!!!
Write the equation of a line that goes through the points (12, 22) and (7, 12). Type your slope and y-intercept into the blanks below to complete the equation. Do not use any spaces.
Answers
Answer:
Step-by-step explanation:
1. Find the slope of the line using the formula (change in y/change in x)
(12-22)/(7/12)=2
2. Find the y intercept by plugging in one coordinate point and the slope into the slope-intercept form.
Formula: y=mx+b Coordinate: (12, 22)
22=2(12)+b
22=24+b
b=-2
3. Put the equation together given slope and y-intercept.
y=2x-2
Find the value of x.
Answers
Answer:
76 don't know how to explain it
when finding the exterior angle, a good thing to keep in mind would be the exterior angle theorem: m<1 = m<2 + m<3z
if you are given the measurements of the angles INSIDE the triangle, it would equal the exterior angle.
hope this helped!
After a 40% discount, The price of a T-shirt with $30. What was the price before the discount?
Answers
Answer:
Mizuki is on the way to help!
The original price was $50!
Step-by-step explanation:
This is the way I did it, I don't know if your going to do it this way so use it as an refrence!
10 - 4 = 6
30 ÷ 6 = 5
5 x 10 = 50
Answer:
$50.00
Step-by-step explanation:
This is because 30 is 60% of 50. (100% - 40% = 60%)
You can verify this answer by calculated 40% of 50, which is 30.
Hope this helps!
Elizabeth went to the candy store and wanted to use the dimensional analysis she had learned in class that day. She only had a certain amount of money to spend. In terms of price, she figured out the following conversion factors: 2 lollipops = 8 gumballs 11 gumballs = 8 lemonheads 14 lemonheads = 16 redhots If Elizabeth knows she could buy 18 lollipops, how many redhots could she buy for the same amount of money?
Answers
Answer: 315,392
Step-by-step explanation: this took me some time but I multiplied multiple times each time and I got this I hope it’s correct.
Btw I multiplied 2 times 8 then multipled with 11 then multipied 172 times 8 then multiplied by 14 and got 19,712. Then, I multiplied 19,712 by 16 and got 315,392
I had to edit cause I miscalculated :/ anyways I hope this is correct
Which of the points (s, t) is inside the shaded region of the set of inequalities
shown below?
SS10 -0.331
s 2 10 - 1
s 25 - 7
s20
t20
A. (-5,5)
B. (12,5)
C. (3,2)
D. (12,-9)
Answers
Answer: (12,5)
Step-by-step explanation: For that class you can't do
The points (s, t) is inside the shaded region of the set of inequalities shown is, (3, 2)
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
All the inequalities are,
S < 10 - 0.33t
S < 12 - t
S > 5 - t
S > 0
t > 0
From option B;
Point = (3, 2) = (s, t)
Put s = 3 , t = 2, we get;
S < 10 - 0.33t
3 < 10 - 0.33 x 2
3 < 10 - 0.66
3 < 9.34
Hence, The points (s, t) is inside the shaded region of the set of inequalities shown is, (3, 2)
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Simplify (- -)--).
- | D)
21
32
© 21
|
32
Answers
Answer:
(- -)--).- | D)2132© 21|32 is not an equation i'm pretty sure
Step-by-step explanation:
Find the inverse of the function.
y = x + 1
Write your answer in the form ax + b. Simplify any fractions.
y =
Answers
that’s what i got, i’m not too sure