Simplified each expression of (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.
First, let's factor the polynomials:
(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)
Now, let's plug these back into the expression and cancel out any common factors:
((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))
= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))
= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))
= (5x(x-24)(x-1))/(-2(3+x)(x-8))
Finally, let's simplify the expression by multiplying the constants:
= (-5x(x-24)(x-1))/(2(3+x)(x-8))
So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
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An amusement park charges an admission fee of 25 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following.
C = 25 p
What is the cost of admission for a group of 3 people?
Answer:
75 dollars.
Step-by-step explanation:
Each person costs 25 dollars and p=3 we just put this into a equation.
25 × 3 = 75
C = 75
Springfield avenue is 3 miles long. there are 8 sets of stop signs along Springfield avenue. the stop signs are the same distance apart . how far apart are the stop signs
The distance between the stop signs is 0.375 miles or roughly 0.6 kilometers.
distance between stop signs = 3 miles / 8
= 0.375 miles
What is the distance?
While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."
Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
The scalar quantity known as distance measures "how much ground an object has traversed" while moving.
From the question:
We can use the following calculation to calculate the separation between the stop signs:
distance between stop signs = total distance/number of intervals
There are 8 spaces between the stop signs and a total distance of 3 miles in this instance. As a result, we can determine the separation between the stop signs as:
distance between stop signs = 3 miles / 8
= 0.375 miles
As a result, there are 0.375 miles (or 0.6 kilometers) between each stop sign.
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question in the photo please help me im begging lol
Water turning to blood will be the first plague that will be present.
What are plagues?Both humans as well as mammals can contract the plague. The protozoan parasite is the bacterium that causes it. The most common ways for humans to contract the plague are through handling a plague-infected animal or by getting bitten by a rodent bug that is carrying the disease.
The 10 plagues in the correct order are:
Water turning to bloodFrogsLiceFliesTerrible BoilsLivestock dyingHail & fireLocustsThree days of darknessDeath of the firstbornLearn more about plagues, here:
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Does someone mind helping me with this problem? Thank you!
Starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To find the future amount of the investment after 40 years, we can use the formula for compound interest:
Future Amount = Present Value x (1 + Interest Rate/Compounding Frequency)^(Compounding Frequency x Time)
In this case, the present value (PV) is $500, the interest rate (r) is 15%,
the compounding frequency (n) is 1 (since the interest is compounded every 2 years).
The time (t) is 40 years.
Plugging in the values, we get:
Future Amount = [tex]500 \times (1 + 0.15/1)^{(1 \times 40/2)}[/tex]
Future Amount = [tex]500 \times (1.15)^{20}[/tex]
Future Amount = [tex]500 \times 13.591409[/tex]
Future Amount = $6,795.70 (rounded to the nearest cent)
Therefore, starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.
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Evaluate sin(A-B), if sinA=12/13 where A is in Quadrant II and
cosB= 8/17 where B is in Quadrant IV.
Answer with a fraction. No decimals
Sin(A-B) =
The result of sin (A - B) is 21/221.
To evaluate sin (A - B), we can use the formula:
sin (A - B) = sin A * cos B - cos A * sin B.
We are given that sin A = 12/13 and cos B = 8/17. We need to find cos A and sin B to use the formula.
Since A is in Quadrant II, cos A is negative. We can use the Pythagorean identity, sin²A + cos²A = 1, to find cos A:
cos²A = 1 - sin²A
cos²A = 1 - (12/13)²
cos²A = 1 - 144/169
cos²A = 25/169
cosA = -5/13
Similarly, since B is in Quadrant IV, sin B is negative. We can use the Pythagorean identity to find sin B:
sin²B = 1 - cos²B
sin²B = 1 - (8/17)²
sin²B = 1 - 64/289
sin²B = 225/289
sinB = -15/17
Now we can plug in the values into the formula:
sin (A-B) = (12/13)*(8/17) - (-5/13)*(-15/17)
sin (A-B) = 96/221 - 75/221
sin (A-B) = 21/221
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64200x0.12 with work!
Answer: 7704
Step-by-step explanation:
( see image !)
If S is a vertex matrix, which transformation does S + [\begin{array}{ccc}-1&-1&-1\\-3&-3&-3\end{array}\right] represent? a. translation of 3 units left and 1 unit down b. translation of 3 units left and 1 unit up c. translation of 1 unit left and 3 units down d. translation of 1 unit left and 3 units up
The correct answer is option c. translation of 1 unit left and 3 units down.
The transformation represented by S + [\begin{array}{ccc}-1&-1&-1\\-3&-3&-3\end{array}\right] is a translation of 1 unit left and 3 units down. This can be seen by examining the values in the matrix. The -1 in the first row represents a translation of 1 unit left, while the -3 in the second row represents a translation of 3 units down. Therefore, the correct answer is option c. translation of 1 unit left and 3 units down.
To summarize, the transformation represented by the given matrix is a translation of 1 unit left and 3 units down. This is indicated by the values of -1 and -3 in the matrix.
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HURRY!!!
The height of a tower on a scale drawing is 12 centimeters. The scale is 2 cm : 25 m. What is the actual height of the tower?
Answer:
Step-by-step explanation:
300
Answer:150 m
Step-by-step explanation:
2cm/25 m = 2 cm: 2500 cm= 1cm:1250 1250x12=15000 convert back to meters 150 m
18. Find m/BCA.
(9x + 1)
A
(5x + 12)
B
(10x-37)
C
Answer:
∠BCA 57 degrees
Step-by-step explanation:
∠ABC + (5x + 12) = 180
=> ∠ABC = 180 - (5x + 12)
∠BAC + (9x + 1) = 180
=> ∠BAC = 180 - (9x + 1)
∠BCA + (10x - 37) = 180
=> ∠BCA = 180 - (10x - 37)
∠ABC + ∠BAC + ∠BCA = 180
Substitute to find x
[180 - (5x + 12)] + [180 - (9x + 1)] + [180 - (10x - 37)] = 180
180 + 180 + 180 - 5x - 9x - 10x - 12 - 1 + 37 = 180
564 - 24x = 180
24x = 564 - 180
24x = 384
x = 384/24 = 16
Substitue x = 16
∠BCA = 180 - (10x - 37)
∠BCA = 180 - 10(16) + 37 = 57
Answer:
m∠BCA = 57°
Step-by-step explanation:
To find the measure of angle BCA we must first find the value of x.
The diagram gives expressions for the exterior angles of the triangle.
The exterior angles of a triangle sum to 360°. Therefore, to calculate the value of x, equate the sum of the exterior angles to 360° and solve for x.
⇒ (9x + 1)° + (5x + 12)° + (10x - 37)° = 360°
⇒ 9x + 1 + 5x + 12 + 10x - 37 = 360
⇒ 9x + 5x + 10x + 1 + 12 - 37 = 360
⇒ 24x - 24 = 360
⇒ 24x - 24 + 24 = 360 + 24
⇒ 24x = 384
⇒ 24x ÷ 24 = 384 ÷ 24
⇒ x = 16
Each interior and exterior angle of a triangle form a linear pair.
As the sum of angles of a linear pair is always equal to 180°, to find the measure of angle BCA, equate the sum of ∠BCA and its exterior angle to 180°:
⇒ (10x - 37)° + m∠BCA = 180°
Substitute the found value of x and solve for the angle:
⇒ (10(16) - 37)° + m∠BCA = 180°
⇒ (160 - 37)° + m∠BCA = 180°
⇒ 123° + m∠BCA = 180°
⇒ 123° + m∠BCA - 123° = 180° - 123°
⇒ m∠BCA = 57°
Therefore, the measure of angle BCA is 57°.
What is the following Factor for these two rational expressions:
22x + 11 x2 – 3x – 10 1 – 2c 20c2 + 10c
To find the factor of these two rational expressions, we need to factor each expression separately and then compare them to find any common factors.
First, let's factor the expression 22x + 11 x2 – 3x – 10:
(22x + 11 x2) + (-3x - 10)
11x(2 + x) - (3x + 10)
(11x - 10)(x + 2)
Next, let's factor the expression 1 – 2c 20c2 + 10c:
(1 - 2c) + (20c2 + 10c)
(1 - 2c) + 10c(2c + 1)
(1 - 2c)(10c + 1)
Now, we can compare the factors of each expression to see if there are any common factors. In this case, there are no common factors between the two expressions.
Therefore, the factor for these two rational expressions is 1.
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roshan and Isha share a reward of 250 rs. in the ratio 1:4. Find the amount shared by each of them. pls tell the answer. I will mark you as the brainlist
Answer: Roshan: 250/5 = 50 Rs.
Isha: 250 - 50 = 200 Rs.
Step-by-step explanation:
Question content area top
Part 1
In a race, 17 out of the 50 finished in less than 56 minutes. What percent of finished the race in less than 56 minutes? Write an equivalent fraction to find the percent
The percentage of people who participated in the race finished in less than 56 minutes is 34%. This can also be written as the equivalent fraction 34/100
To find the percentage of people who finished the race in less than 56 minutes, we can use the following formula:
percentage = (part/whole) x 100%
where "part" is the number of people who finished in less than 56 minutes, and "whole" is the total number of people who participated in the race.
In this case, we know that 17 people finished in less than 56 minutes, and there were 50 people in total. So we can plug these values into the formula:
percentage = (17/50) x 100%
percentage = 34%
Therefore, 34% of the people who participated in the race finished in less than 56 minutes.
To write an equivalent fraction for this percentage, we can write:
34% = 34/100
This is an equivalent fraction because 34/100 can be simplified to 17/50
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Find the value of AC and BD
The values are given as follows:
AC = 25.BD = 12.4.How to obtain the values?The value of AC can be obtained applying the Pythagorean Theorem, as follows:
(AC)² = 20² + 15²
AC = sqrt(20² + 15²)
AC = 25.
Then there are two similar triangles, with dimensions given as follows:
BC = 15 and DC = x.AB = 20 and AD = 25 - x.Then the value of x is obtained as follows:
15/20 = x/(25 - x)
3/4 = x/(25 - x)
4x = 3(25 - x)
7x = 75
x = 10.7.
Then the altitude BD is obtained with the geometric mean theorem as follows:
BD² = 10.7 x (25 - 10.7)
BD² = 153
BD = sqrt(153)
BD = 12.4.
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help me i don't understand
The volume of the fully inflated balloon is [tex]\frac{19652}{3}[/tex]π inch³ and volume of half inflated balloon is [tex]\frac{19652\pi }{6}[/tex].
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Diameter of a fully inflated balloon = 34 inch
Radius is half the diameter.
Radius of fully inflated balloon = 34 / 2 = 17 inches
Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³, where r is the radius.
(a) Volume of fully inflated balloon = [tex]\frac{4}{3}[/tex] π (17)³
= [tex]\frac{19652}{3}[/tex]π inch³
(b) Volume of the half inflated balloon = Half of the fully inflated volume
= ([tex]\frac{19652}{3}[/tex]π / 2) inch³
= [tex]\frac{19652\pi }{6}[/tex] inch³
(c) Volume of half inflated balloon = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] π r³ = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] r³ = [tex]\frac{19652}{6}[/tex]
r³ = [tex]\frac{19652}{8}[/tex]
r = 13.49 inch
Hence the volume and radius are found.
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20 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Answer:
.7x 63 = 90 (.7 is the same as 70%. If they took off 30%, they left on 70%)
90 ÷ 3 = 30
Jennifer originally paid $30.00 a shirt.
Check
30 x .3 = 9 This is the amount of the discount per shirt.
30 - 9 = 21 Discounted cost per shirt.
21 x 3 = 63 The cost of three shirts.
This checks.
Helping in the name of Jesus.
A parallelogram has a height of 2 units. One side of the parallelogram is AB¯¯¯¯¯. The paralleogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment on the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (5, 3) labelled: B.
It is a unique variety of quadrilateral called a parallelogram that has both pairs of opposite sides parallel and equal.
What is quadrilateral?A polygon with has four sides, four angles, and four vertices is called a quadrilateral. The Latin words 'Quadri', which denotes four, and latus, which means side, were combined to form the English word quadrilateral.
Given, Height of the Parallelogram = 2 units
Each segment on the grid is represented as = 1 unit.
So, One side of the Parallelogram = 3 units
Properties of Parallelogram
a. Opposite sides are equal.
b. Opposite sides are parallel.
c. Diagonals Bisect each other.
Also, Every Rectangle is a Parallelogram.
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Write a division expression that reporesetns the weight of the steel structure divided bythe total weiught of the briudges material
The division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials is 400 tons ÷ (1,000 tons + 400 tons + 200 tons) = 25%.
The total weight of the bridge's materials is the sum of the weight of concrete, steel structure, glass, and granite, which is:
1,000 tons + 400 tons + 200 tons = 1,600 tons
Simplifying the expression by dividing both numerator and denominator by 400 tons gives:
Weight of steel structure / Total weight of bridge's materials = [tex]\frac{1}{4}[/tex]
Weight of steel structure / Total weight of bridge's materials
[tex]= \frac{400 tons}{1,000 tons + 400 tons + 200 tons}[/tex]
[tex]= \frac{400 tons}{1,600 tons}[/tex] = 0.25
Therefore, the weight of the steel structure is one-fourth (or 25%) of the total weight of the bridge's materials.
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The complete question is:
Write a division expression that represents the weight of the steel structure divided by the total weight of the bridge's materials. Concrete weighs 1,000 tons, Steel structure weighs 400 tons and glass and granite weighs 200 tons.
Jamie works twice as many hours on the weekend as he does during the week. He earns $7.75 per hour. This week, he wants to earn at least 279 dollars. Will Jamie meet his goal by working 10 hours during the week? Show your work.
Using algebra, we can conclude that, if Jamie only works 10 hours during the week, he will not be able to meet his goal of earning at least $279, because the total pay he will earn, which is $232.50, is less than the amount he wants to earn.
How to Use Algebra to Solve Problems?The method to use to solve this problem would be algebra. We will use variables to represent the number of hours that Jamie works during the week and on the weekend, and we used equations to express the relationship between the total pay Jamie earns and the number of hours he works.
Let's first find out how many hours Jamie works during the week and on the weekend.
Let's say Jamie works x hours during the week. Then, he works 2x hours on the weekend.
The total amount of money Jamie earns is given by:
Total pay = Pay for week hours + Pay for weekend hours
Pay for week hours = $7.75 per hour * x hours
Pay for weekend hours = $7.75 per hour * 2x hours = $15.50 per hour * x hours
Total pay = $7.75x + $15.50x = $23.25x
Now let's substitute x = 10, since Jamie wants to work 10 hours during the week, to see if he can meet his goal of earning at least $279:
Total pay = $23.25 * 10 = $232.50
Since $232.50 is less than $279, Jamie will not meet his goal by working 10 hours during the week alone. He will need to work more hours during the week and/or on the weekend to reach his goal.
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7
The final answer of Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]
To determine the possible numbers of positive and negative real zeros of f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7 using Descartes's Rule of Signs, we must first count the number of sign changes in the polynomial.
For positive real zeros, we look at the original polynomial: f(x)=8x^(4)-7x^(3)-4x^(2)-2x+7.
There are two sign changes: from 8x^(4) to -7x^(3) and from -2x to +7.
Therefore, there are either 2 or 0 positive real zeros.
For negative real zeros, we look at the polynomial with x replaced by -x: f(-x)=8(-x)^(4)-7(-x)^(3)-4(-x)^(2)-2(-x)+7.
Simplifying, we get [tex]f(-x)=8x^4+7x^3-4x^2+2x+7[/tex]. There are no sign changes in this polynomial, so there are 0 negative real zeros.
In conclusion, Using Descartes's Rule of Signs, we can determine that there are either 2 or 0 positive real zeros and 0 negative real zeros of [tex]f(x)=8x^4-7x^3-4x^2-2x+7[/tex]
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A professor records the following final grades in one course. Construct a frequency table for the grades.
A
A
A
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
D
D
D
D
F
Complete the table.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Grade Frequency Relative Frequency Cumulative Frequency
A. ____ ____% _____
B ____ _____% ______
C ____ _____% ______
D ____ _____% ______
F ____ _____% ______
TOTAL. ____. 1=100%. _______
The frequency table when constructed is
Grade Frequency Relative Frequency Cumulative Frequency
A 3 12.5% 3
B 8 33.3% 11
C 8 33.3% 19
D 4 16.7% 23
F 1 4.2% 24
Total 25 1 or 100%
How to construct the frequency tableThe grades A to F represent the given parameter
From the given grade, we have the following frequencies
A = 3
B = 8
C = 8
D = 4
F = 1
From the above frequency, we have the relative frequency to be
A = 3/24 = 12.5%
B = 8/24 = 33.3%
C = 8/24 = 33.3%
D = 4/24 = 16.7%
F = 1/24 = 4.2%
From the above frequency, we have the cumulative frequency to be
A = 3
B = 11
C = 19
D = 23
F = 24
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y = 4* Reflect it across the y-axis, translate it to the right 3 units, and vertically stretch it by a factor of 2
y = -2x + 14
To reflect the equation y = 4 across the y-axis, we need to change the sign of the x-term. Since there is no x-term in the original equation, we can simply add a negative x-term to get the reflected equation: y = -x + 4.
Next, to translate the equation to the right 3 units, we need to subtract 3 from the x-term. This gives us the translated equation: y = -(x - 3) + 4.
Finally, to vertically stretch the equation by a factor of 2, we need to multiply the entire equation by 2. This gives us the final transformed equation: y = 2(-x + 3) + 8.
In summary, the equation y = 4 reflected across the y-axis, translated to the right 3 units, and vertically stretched by a factor of 2 is y = -2x + 14.
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Apparently i got a 40 but i can redo it again, any help?
2- Not J
3- Not B
4- Not F
7- Not 6
8- Not J
9- Not C
URGENT PLEASE HELP 30 POINTS!!!
Answer:
angle 1 will be 32
angle 2 will be 2
hope it helps u mark me BRAINLIST
You go out for a long walk. You walk 3/4 mile and then sit down to take a rest. Then you walk 3/8 of a mile. How far did you walk altogether?
*
(0, 1x4 – 1⁄2x³) ³
[tex](0.1x4 - \frac{1}{2} {x}^{3}) ^{3} [/tex]
The expanded form of the expression [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex] is,
[tex]0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9[/tex]
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
We know, (a - b)³ = a³ - 3a²b + 3ab² - b³.
Given, [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex].
Here, [tex]a = 0.1x^4[/tex] and [tex]b = \frac{1}{2}x^3[/tex].
Therefore, [tex](0.1x^4 - \frac{1}{2}x^3)^3[/tex].
[tex]= (0.1x^4)^3 - (\frac{1}{2}x^3)^3 - 3.(0.1x^4)^2.\frac{1}{2}x^3 + 3.(0.1x^4).(\frac{1}{2}x^3)^2[/tex].
[tex]= 0.001x^{12} - 0.125x^9 - 0.015x^{11} - 0.15x^{10}[/tex].
[tex]= 0.001x^{12} - 0.015x^{11}- 0.15x^{10}-0.125x^9[/tex].
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Could anyone explain the steps to this problem?
Answer:
Step-by-step explanation:
Both angles are equal so,
1+16x =17x-3
16x-17x= -3-1
-x = -4
x = 4
In the drawing, >ℎ
. Which statement about the volumes of the two cylinders is true?
The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
The volume of the cylinder is given by:
V = π r² h
where r = radius
h = height
Consider the left-hand side cylinder.
radius = h
height = g
Then the volume is V1 = π h²g
Now consider the right-hand side cylinder
radius = g
height = h
Then the volume is V2 = π g²h
It is given that g > h
Taking V1/V2 = π h²g/π g²h = h/g = k
where k is a constant.
Now V1 = k V2
This means that V2 will be k times V1.
So right-hand side cylinder has the largest volume among the two.
Therefore the volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
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Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=2 ?
The value of z when t=2 is 24
The value of z varies inversely with t, which means that the product of z and t is a constant. We can write this relationship as:
zt = k
Where k is the constant. We are given that z=6 when t=8, so we can plug these values into the equation to find k:
6*8 = k
k = 48
Now we can use this value of k to find the value of z when t=2. Plugging in these values gives us:
z*2 = 48
Solving for z gives us:
z = 48/2
z = 24
Therefore, the value of z when t=2 is 24.
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find the perimeter of the given circle
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the hub. The radius of a rotation is the distance between the center and the rim.
Let r be the radius of the circle. The circumference of the circle will be given as,
C = 2πr units
The diameter of the circle is 28 cm. Then the radius is calculated as,
r = d / 2
r = 28 / 2
r = 14 cm
Then the circumference of the circle is given as,
C = 2 · π · 14
C = 28 × 3.14
C = 87.92 cm
The circumference of the circle with a diameter of 28 cm will be 87.92 cm.
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#5 ( List all methods that can possibly be used to solve a quadratic equation. (ii) Solve each equation for the unknown variable. State the method used and briefly explain why you decide to use that method. a. 2x^2 - 7x + 3 = 0 b. x^2 + 10x + 1 = 0 c. x² – 18=0
The solutions are x = 3√2 and x = -3√2.
There are several methods that can be used to solve a quadratic equation. The most commonly used methods are:
1. Factoring
2. Completing the square
3. Quadratic formula
4. Graphing
Now, let's solve each equation using one of the methods listed above.
a. 2x^2 - 7x + 3 = 0
We can use the factoring method to solve this equation. First, we need to find two numbers that multiply to give us 3 and add to give us -7. The numbers are -3 and -1. So, we can factor the equation as follows:
(2x - 1)(x - 3) = 0
Now, we can set each factor equal to zero and solve for x:
2x - 1 = 0 => x = 1/2
x - 3 = 0 => x = 3
So, the solutions are x = 1/2 and x = 3.
b. x^2 + 10x + 1 = 0
We can use the quadratic formula to solve this equation. The quadratic formula is:
x = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values of a, b, and c, we get:
x = (-(10) ± √((10)^2 - 4(1)(1)))/(2(1))
Simplifying, we get:
x = (-10 ± √96)/2
So, the solutions are x = (-10 + √96)/2 and x = (-10 - √96)/2.
c. x² – 18=0
We can use the square root method to solve this equation. First, we need to isolate the x^2 term on one side of the equation:
x^2 = 18
Now, we can take the square root of both sides:
x = ±√18
Simplifying, we get:
x = ±3√2
the solutions are x = 3√2 and x = -3√2.
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