The numeric values of each function at x = 3 are given as follows:
f(3) = 50.
g(3) = 10.
The division is given as follows: f(3)/g(3) = 5.
The space of f(x)/g(x) is given as all genuine values with the exception of x = - 7, as the function g(x), which is the denominator of the division, expects a worth of 0 at x = - 7.
To track down the numeric worth of a function or of articulation, we supplant each example of the variable in the function or in the articulation with the worth at which we need to track down the numeric worth.
Subsequently, the numeric values are found to supplant the solitary example of x by 3 in each function, as follows:
f(3) = 5(3) + 35 = 15 + 35 = 50.
g(3) = 3 + 7 = 10.
Subsequently, the division is given as follows:
(f/g)(3) = f(3)/g(3) = 50/10 = 5.
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Which statement is the converse of the following conditional? If a polygon has three sides, then it is a triangle. A. If a polygon does not have three sides, then it is not a triangle. B. If a polygon is not a triangle, then it does not have three sides. C. If a polygon is a triangle, then it does not have three sides. D. If a polygon is a triangle, then it has three sides.
Answer:
Step-by-step explanation:
The converse of the conditional statement "If a polygon has three sides, then it is a triangle" is:
D. If a polygon is a triangle, then it has three sides.
In the original conditional statement, the "if" part is "a polygon has three sides," and the "then" part is "it is a triangle." The converse switches the positions of the "if" and "then" parts, resulting in the statement "If a polygon is a triangle, then it has three sides."
The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie?
This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:
$$
\begin{aligned}
x + y &= 87.18 \\
x &= y - 2.12
\end{aligned}
$$
Substituting x into the first equation, we get:
$$
\begin{aligned}
(y - 2.12) + y &= 87.18 \\
2y - 2.12 &= 87.18 \\
2y &= 89.30 \\
y &= 44.65
\end{aligned}
$$
Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:
$$
\begin{aligned}
x &= y - 2.12 \\
x &= 44.65 - 2.12 \\
x &= 42.53
\end{aligned}
$$
Therefore, the price of the tie is $42.53.
Answer:
42.53
Step-by-step explanation:
write equation
tie + pants = 87.18
since ties cost 2.12 less than pants,
tie = pants -2.12
now substitute back into first equation
pants - 2.12 + pants = 87.18
solve for pants by adding 2.12 to the other side
divide by 2 since there are 2 pants on one side
find pants and then substitute value into the tie equation to find the price of the tie
Which system is equivalent to
O
O
O
[5-x=9x²
y = 5-x
[y=9y²-90y+225
1x=y-5
[5+x=9x²
y = 5+x
y = 3x
x+3x=5
y=9x²?
x+y=5
The first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The system that is equivalent to:
O
O
O
[5-x=9x²
y = 5-x
is: x = -2, y = 7
In the given system, the first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
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hey i have a question about this assignment and want to check if my answers are right
The value of x from the given triangle with angle 55° and side 27 units is 15.5 units.
A) By using Pythagoras theorem,
x²=16²+6²
x²=292
x=17.1 units
B) By using Pythagoras theorem,
23²=x²+9²
x²=529-81
x²=448
x=21.2 units
C) By using Pythagoras theorem,
10²=x²+8.5²
x²=100-72.25
x²=27.75
x=5.3 units
D) By using Pythagoras theorem,
x²=12²+15²
x²=369
x=19.2 units
E) Here, cos60°=6√3/x
1/2=6√3/x
x=12√3 units
F) Here, cos45°=√10/x
1/√2=√10/x
x=10 units
G) Here, sin60°=30/x
2/√3=30/x
x=15√3 units
H) Here, cos30°=x/16
2/√3=x/16
x=32/√3 units
I) Here, sinx=25/26
x=74°
J) Here, sin45°=x/16√2
1/√2=x/16√2
x=16 units
K) tan34°=x/28
0.6745=x/28
x=18.886
L) tanx°=17/18.5
tanx°=0.9189
x=42.5°
M) Here, cosx=9/12
x=41.4°
N) Here, sin16°=4/x
0.2756=4/x
x=4/0.2756 units
x=14.5
O) Here, cos55°=x/27
0.5735=x/27
x=15.4845
Therefore, the value of x from the given triangle with angle 55° and side 27 units is 15.5 units.
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PLEASE HELP WITH SURFACE AREA!! This is my project and I need the awnser quick!! Pls help me marking brainliest if the awnsers r right !
The surface areas and volumes of the solids are listed below:
Case 1: A = 118 cm², V = 70 cm³
Case 2: A = 121.5 in², V = 91.125 in³
Case 3: A = 192 m², V = 144 m²
Case 4: A = 480 ft², V = 576 ft³
Case 5: A = 87.965 yd², V = 62.832 yd³
How to determine the surface area and the volume of solidsIn this problem we need to determine the surface area and the volume of each solid. The surface area is the sum of the areas of all faces. The area and volume formulas required to answer this question are shown below:
Area
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Circle
A = π · r²
Lateral face of a cylinder
A = 2π · r · h
Volumes
Prism
V = A · h
Where:
w - Widthl - Lengthh - Heightr - RadiusA - Base area.Now we proceed to determine the surface areas and volumes of the solids:
Case 1
A = 2 · [(5 cm) · (7 cm) + (5 cm) · (2 cm) + (7 cm) · (2 cm)]
A = 2 · (35 cm² + 10 cm² + 14 cm²)
A = 2 · 59 cm²
A = 118 cm²
V = (5 cm) · (7 cm) · (2 cm)
V = 70 cm³
Case 2
A = 6 · (4.5 in)²
A = 121.5 in²
V = (4.5 in)³
V = 91.125 in³
Case 3
A = 2 · 0.5 · (8 m) · (6 m) + (6 m) · (10 m) + (6 m)² + (8 m) · (6 m)
A = 192 m²
V = 0.5 · (8 m) · (6 m)²
V = 144 m²
Case 4
A = 2 · 0.5 · (12 ft) · (8 ft) + 2 · (10 ft) · (12 ft) + (12 ft)²
A = 480 ft²
V = 0.5 · (12 ft) · (8 ft) · (12 ft)
V = 576 ft³
Case 5
A = 2π · (2 yd)² + 2π · (2 yd) · (5 yd)
A = 87.965 yd²
V = π · (2 yd)² · (5 yd)
V = 62.832 yd³
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An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected malpractice suits, a 99% confidence interval was constructed for the true proportion of medical malpractice lawsuits that are dropped or dismissed. The confidence interval was (0.6633, 0.7308) find the Margin of error.
Answer: I have this same exact question
Step-by-step explanation: So someone please help this person, or animal which ever you perfer
You Draw two marbles (without replacement) from a bag containing 4 green 2 yellow and 6 red marbles.what is the probability that both marbles are yellow? round to the nearest thousand
The probability of drawing two yellow marbles is 0.015 to the nearest thousandth.
What is the probability?The probability of drawing two yellow marbles after drawing a yellow marble on the first draw and without replacement drawing another yellow marble is determined as follows:
Total number of marbles in the bag = 4 + 2 + 6
Total number of marbles in the bag = 12 marbles in the bag.
P(Yellow on first draw) = 2/12 or 1/6
P(Yellow on second draw | Yellow on first draw) = 1/11
The probability of both marbles being yellow will be:
P(Both marbles yellow) = (1/6) * (1/11)
P(Both marbles yellow) = 1/66 or 0.015
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please help! math: find the perimeter of the polygon below. use the correct formula!
the width is 3.8 and the length is 6.3
The perimeter of the rectangular polygon is given by P = 20.2 units
Given data ,
Let the perimeter of the polygon be represented as P
Now , the value of P is
Perimeter P of rectangle = 2 ( Length + Width )
Now , width is 3.8 and the length is 6.3
On simplifying , we get
P = 2 ( 3.8 + 6.3 )
P = 20.2 units
Hence , the perimeter is P = 20.2 units
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A head teacher shared 27 notebooks among 9 students.one of them students found that each of his books combined 155 pages.how many pages were in the books he received
The number of pages that each book contained is given as follows:
465 pages.
How to obtain the number of pages?The number of pages that each book contained is obtained applying the proportions in the context of the problem.
A head teacher shared 27 notebooks among 9 students, hence the number of the notebooks per student is given as follows:
27/9 = 3 notebooks per student.
One of them students found that each of his books combined 155 pages, hence the number of pages on the book is given as follows:
155 x 3 = 465 pages.
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4. The wheels of a bicycle have a
diameter of 22 inches. How many
full revolutions will the wheels need
to make to travel 300 feet? Use 3.14
for .
A 105 revolutions
B 10 revolutions
C164 revolutions
D 53 revolutions
no
53 revolutions will be needed by the wheels to make it travel 300 feet.
Option D is the correct answer.
We have,
To solve this problem, we can use the formula:
Number of revolutions = Distance / Circumference of the wheel
First, let's convert the distance from feet to inches:
300 feet = 300 x 12 = 3600 inches
Next, we need to calculate the circumference of the wheel using the given diameter:
Circumference = π x diameter
Circumference = 3.14 x 22 inches
Circumference ≈ 69.08 inches
(rounded to two decimal places)
Now we can calculate the number of revolutions:
Number of revolutions = 3600 inches / 69.08 inches
= 52.14 revolutions
Rounding to the nearest whole number.
= 52 revolutions.
Therefore,
53 revolutions will be needed by the wheels to make it travel 300 feet.
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The bicycle wheels will need 53 full revolutions to travel 300 feet.
The circumference of a wheel can be calculated using the formula:
circumference = π x diameter
So, circumference = 3.14 x 22
= 69.08 inches
Now, converting feet to inches
300 feet = 300 x 12 inches
300 feet = 3600 inches
So, number of revolutions:
revolutions = distance / circumference
= 3600 / 69.08
≈ 52.11
Therefore, the bicycle wheels will need 53 full revolutions to travel 300 feet.
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Below are two inequalities and the graphs of their without the shading. By imagining where the shading should be, identify which point would satisfy BOTH
inequalities
Answer: C
Step-by-step explanation:
Answer:
D. (-2, 10)
Step-by-step explanation:
Given inequalities:
[tex]y > -\dfrac{5}{3}x+2[/tex]
[tex]y > 3x+2[/tex]
Both inequalities have been given in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The first equation has a negative slope, which means that as x increases, y decreases. Therefore, it is the dashed line that begins in quadrant II and ends in quadrant IV.
The second equation has a positive slope, which means that as x increases, y increases. Therefore, it is the dashed line that begins in quadrant III and ends in quadrant I.
When graphing inequalities, the inequality sign ">" indicates a dashed line and shading above the line.
As both inequalities should be shaded above the lines, the region where the shaded regions overlap is the upper "V" of the graph (see attachment).
A point that satisfies both inequalities is any point that is located in the overlapping shaded region, but not found on the dashed lines.
Therefore, the point that satisfies both inequalities is (-2, 10).
Focus: (-5,3); Directrix: y = 1
The equation of the parabola is: y = (1/4)(x-3)²+ 2
In Parabola mathematics, it is defined as a set of points that are equidistant from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.
To find the equation of the parabola, we first need to determine the vertex. The vertex is the midpoint between the focus and the directrix, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of symmetry passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the axis of symmetry is x=3.
Next, we need to find the distance between a point on the parabola and the focus, as well as the distance between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)
The distance between (x,y) and the directrix is simply the absolute value of the difference between y and 1: |y-1|
Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|
Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)
Therefore, the equation of the parabola is: y = (1/4)(x-3)²+ 2
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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.
Complete Question : Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1
Mrs. Garcia invests a total of $6331 in two savings accounts. One account yields 8.5% simple interest and the other 8% simple interest. Find the amount placed in each account if she receives a total of $517.68 in interest after one year.
Mrs. Garcia invested $2240 in the 8.5% account and $4091 in the 8% account.
Let x be the amount invested in the 8.5% account, and y be the amount invested in the 8% account. Since the total investment is $6331, we have x + y = 6331.
The total interest received is $517.68, which can be expressed as 0.085x + 0.08y = 517.68, where 0.085 and 0.08 are the decimal equivalents of the interest rates.
We can now solve this system of equations to find x and y. One possible method is to use substitution, where we solve for one variable in terms of the other from one of the equations, and substitute it into the other equation. From x + y = 6331, we have y = 6331 - x. Substituting this into the second equation, we get:
0.085x + 0.08(6331 - x) = 517.68
Simplifying and solving for x, we get:
0.005x + 506.48 = 517.68
0.005x = 11.2
x = 2240
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When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive
(–∞, 0)
(0, 2)
(2, ∞)
(–∞, ∞)
Answer:
They are both positive on (2, ∞)
Step-by-step explanation:
g(x) > 0
log(2x + 1) > 0
2x + 1 > 0
x > –1/2
(-1/2, ∞)
PLEASSE HELP!!! MARKING AS BRAINLIST
The area of the figure as shown in the diagram is 24 in².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the figure, we use the formula below
Formula:
A = lw+l'w'+l''w''.................. Equation 1Where:
A = Area of the figurel, l', l'' = Length of the first, second and third rectangle respectivelyw, w', w'' = Width of the first second and third rectangle respectiveyFrom the question,
Given:
l = 4 inw = 2 inl' = 2 inw' = 4 inl'' = 4 inw'' = 2 inSubstitute these values into equation 1
A = (4×2)+(2×4)+(2×4)A = 8+8+8A = 24 in²Learn more about area here: https://brainly.com/question/25092270
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Consider this equation.
cos(0) = 4/41
If 0 is an angle in quadrant IV, what is the value of sin(0)
Answer: sin(0) = 40.804/41
Step-by-step explanation:
if 4.2 pounds of strawberry sells for an income of $12 what is 24,990 pounds income
Answer: $71,400
Step-by-step explanation:
We will set up a proportion with income in the numerator and pounds in the denominator.
[tex]\displaystyle \frac{\$12}{4.2\;lbs} =\frac{\$x}{24,990\;lbs}[/tex]
Then we will cross-multiply.
4.2 * x = 12 * 24,990
4.2x = 299,880
Lastly, we will divide both sides of the equation by 4.2.
x = $71,400
The income from 24,990 pounds of strawberries would be approximately $71,690.14.
To find the income from 24,990 pounds of strawberries, we need to use a proportion:
4.2 pounds of strawberries sells for $12, so 1 pound of strawberries sells for $12/4.2 = $2.86 (rounded to two decimal places).
Therefore, 24,990 pounds of strawberries would sell for:
$2.86 x 24,990 = $71,690.14 (rounded to two decimal places).
In AABC, AB=32, AC = 23, and BC= 20. What is mZA?
The measure of m∠A in the triangle is:
m∠A = 38.44°
How to find the measure of m∠A?The cosine rule is used for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula for angles:
cos(A) = (b² + c² − a²)/2bc
cos(B) = (c² + a² − b²)/ 2ac
cos(C) = (a² + b² − c²)/2ab
Where a, b and c are the length of the sides, and A, B, and C are the measures of the angles
We have:
a = BC = 20
b = AC = 23
c = AB = 32
Substituting into:
cos(A) = (b² + c² − a²)/2bc
cos(A) = (23² + 32² − 20²)/(2*23*32)
cos(A) = 0.7833
A = cos⁻¹(0.7833)
A = 38.44°
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According to the graph, what is the value of the constant in the equation
below?
Constant/ Width=Height
O A 3
OB. 75
O C. 15
OD. 25
The calculated value of the constant in the equation is 75
How to determine the value of the constant in the equationFrom the question, we have the following parameters that can be used in our computation:
The graph
Where we have
(3, 25) and (5, 15)
The value of the constant in the equation is calculated as
Constant = Width * Height
So, we have
Constant = 3 * 25
Evaluate
Constant = 75
Hence, the value of the constant in the equation is 75
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Find the area of a triangle with the base of 3x²y2 and a height of 4x4y³. Use the formula: A=bh
The area of the triangle is 6x³y⁵
What is area of a triangle?The space enclosed by the boundary of a plane figure is called its area.
A triangle is a polygon with three sides having three vertices.
There are different types of triangle, scalene triangle, equailteral triangle, isosceles triangle, right triangle e.t.c
The area of a triangle is expressed as ;
A = 1/2 bh
where b is the base and h is the height of the of the triangle.
Base = 3x²y²
height = 4x4y³
A = 1/2 × 3x²y² × 4x4y³
A = 1/2 × 12x³y⁵
A = 6x³y⁵
Therefore the area of the triangle is 6x³y⁵
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The area of the Triangle is [tex]48x^{3} y^{4}[/tex]
What is Triangle?Triangle is a two-dimensional three-sided polygon, which has three vertices, three sides and three angles. It is a shape formed when three straight lines meet.
How to determine this
Area of triangle = 1/2 base * height as given
Where area of triangle = ?
Base = [tex]3x^{2} y2[/tex]
i.e 3 * 2 [tex]x^{2} y[/tex]
Base, b = [tex]6x^{2} y[/tex]
Height = [tex]4x4y^{3}[/tex]
i.e [tex]4x[/tex] * [tex]4y^{3}[/tex]
Height,b = [tex]16xy^{3}[/tex]
Area of triangle = 1/2 * [tex]6x^{2} y[/tex] * [tex]16xy^{3}[/tex]
Area = 1/2 * 96* [tex]x^{2+1}[/tex] * [tex]y^{1+3}[/tex]
Area = 1/2 * 96 * [tex]x^{3}[/tex] * [tex]y^{4}[/tex]
Area = 48 * [tex]x^{3} y^{4}[/tex]
Area of the triangle = [tex]48x^{3} y^{4}[/tex]
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Find the median and mean of the data set below: 9,23,38,45,14
Answer:
mean, 25.8 median 23
Step-by-step explanation:
Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
The mean of a set of numbers is the sum divided by the number of terms.
Alfred has a coupon for 35 cents off a 32-ounce bottle of detergent that sells for $1.39. Another brand offers a 20-ounce bottle for 79 cents. If he uses the coupon, which will be the better buy?
The detergent with the coupon is the better buy since it has a lower price per ounce.
To determine which option is the better buy, we need to compare the prices per ounce for each detergent brand.
First, let's calculate the price per ounce for the 32-ounce bottle of detergent after applying the coupon:
Price per ounce = (Price - Coupon) / Ounces
Price per ounce = ($1.39 - $0.35) / 32
Price per ounce = $1.04 / 32
Price per ounce ≈ $0.0325
Next, let's calculate the price per ounce for the 20-ounce bottle of the other brand:
Price per ounce = Price / Ounces
Price per ounce = $0.79 / 20
Price per ounce = $0.0395
Comparing the two price per ounce values, we can see that the price per ounce for the detergent with the coupon is approximately $0.0325, while the price per ounce for the other brand is $0.0395.
Therefore, the detergent with the coupon is the better buy since it has a lower price per ounce.
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Plsss help plsss help
Answer:
It's B
Step-by-step explanation:
Look at the sides with the number compare them with each other and you will find they are the most similar ones with each other.
Apples cost $1.29 per pound. How much would a bag of apples weighing 4.7 pounds cost? (Round your answer to the nearest cent.)
Answer:
$6.06
Step-by-step explanation:
$1.29 x 4.7 = 6.063
Round: 6.06
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
Karen measures the width of a garden plot and records that it is 40 meters. Its actual width is 42 meters.
What is the percent error in the measurement?
A: 2%
B: 3%
C: 4%
D: 5%
Explanation:
The error is 42-40 = 2 meters
Divide this over the actual width
2/42 = 0.0476 = 4.76% approximately
This rounds to 5%
Answer:
D. 5%
Step-by-step explanation:
Percent Error = (|40 - 42| / 42) × 100
Percent Error = (2 / 42) × 100
Percent Error ≈ 4.76%
Can anyone help me answer this question?
Define y as an explicit function of x; x + y + y^2 = x^2
We have two explicit functions of x for y:
[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]
To define y as an explicit function of x, we need to solve for y in terms of x in the given equation:
[tex]x + y + y^2 = x^2[/tex]
First, let's simplify the equation by moving all the terms to one side:
[tex]y^2 + y + (x - x^2) = 0[/tex]
Now, we can use the quadratic formula to solve for y:
[tex]y = (-b + \sqrt{(b^2 - 4ac)} ) / 2a[/tex]
where a = 1, b = 1, and [tex]c = x - x^2.[/tex]Substituting these values, we get:
[tex]y = (-1 + \sqrt{(1 - 4(x - x^2)} )) / 2[/tex]
Simplifying further:
[tex]y = (-1 + \sqrt{(1 - 4x + 4x^2)} ) / 2\\y = (-1 + \sqrt{(4x^2 - 4x + 1)} ) / 2\\y = (-1 + 2\sqrt{(x^2 - x + 1/4)} ) / 2\\y = -1/2 + \sqrt{(x^2 - x + 1/4)}[/tex]
Therefore, we have two explicit functions of x for y:
[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]
Either of these expressions represents y as an explicit function of x.
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Find the 9th term of the geometric sequence 4 , − 16 , 64 , . . . 4,−16,64,...
The 9th term of the geometric sequence 4, -16, 64, ... is 262144.
To find the 9th term of the geometric sequence 4, -16, 64, ... , we need to determine the common ratio (r) of the sequence.
To do this, we can divide any term by its preceding term:
-16 / 4 = -4
64 / -16 = -4
We see that the common ratio (r) is -4.
To find the 9th term, we can use the formula for the nth term of a geometric sequence:
Tn = a * r^(n-1)
Where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number.
In this case, the first term a is 4, the common ratio r is -4, and we want to find the 9th term.
T9 = 4 * (-4)^(9-1)
T9 = 4 * (-4)^8
T9 = 4 * 65536
T9 = 262144
Therefore, the 9th term of the geometric sequence 4, -16, 64, ... is 262144.
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Given that ∅ = 12.2° , calculate the area of the triange below
give your answer to 2 d.p.
Answer:
A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)
A = (1/4)√29√21√7
= about 16.32 mm²
Answer:
16.27 mm² (see comment)
Step-by-step explanation:
You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.
AreaThe area is given by the formula ...
A = 1/2ab·sin(C)
A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²
The area of the triangle is about 16.27 square millimeters.
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Additional comment
If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)
s = (4 +11 +14)/2 = 14.5
A = √(s(s -a)(s -b)(s -c))
A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375
A ≈ 16.32
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Enter the correct answer in the box.
Solve the quadratic equation by completing the square.
2x² + 12x = 66
Fill in the values of a and b to complete the solutions.
x=a-√b
x=a+√b
The values of a and b are a = -3 and b = 42. The solutions for x can be written as:
x = -3 - √42
x = -3 + √42
To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:
Step 1: Move the constant term to the right side:
2x² + 12x - 66 = 0
Step 2: Divide the equation by the leading coefficient (2):
x² + 6x - 33 = 0
Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x² + 6x + (6/2)² = 33 + (6/2)²
x² + 6x + 9 = 33 + 9
x² + 6x + 9 = 42
Step 4: Rewrite the left side as a perfect square:
(x + 3)² = 42
Step 5: Take the square root of both sides:
√(x + 3)² = ±√42
x + 3 = ±√42
Step 6: Solve for x:
x = -3 ± √42.
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