The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
What are quadratic equations?Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0
How to determine the other roots of the equation?The equation of the function is given as:
f(x) = x^2 - 93987
The above equation is a quadratic equation
Express the equation as a difference of two squares
f(x) = (x - √93987)(x + √93987)
Set the equation of the function to 0
(x - √93987)(x + √93987) = 0
Split the factors of the above function equation as follows
x - √93987 = 0 and x + √93987 = 0
Solve for x in the above equations
x = √93987 and x = -√93987
Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
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Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. y = ex, y = x2 − 1, x = −1, x = 1
[tex]e-\frac{1}{e} +\frac{4}{3} 0r 3.687[/tex] is the value when the equation is to integrate with respect to x or y
we integrate with respect to x
Area = [tex]\int\limits^b_a{(f(x)-g(x))} \, dx[/tex]
= [tex]\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx[/tex]
=[tex]e^{x} -\frac{x^{3} }{3} +x[/tex]
substitute 1 and -1 in place of x
= [tex](e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)[/tex]
= [tex]e-\frac{1}{e} + \frac{4}{3} or 3.6837[/tex]
The diagram was attached in the given below.
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Select all of the values of x that are solutions to 17-7x> 3(10x-4) + 61.
-2
-4
-1
2
5
0
Answer: -2, -4, -1
Step-by-step explanation:
[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]
So, the values of x are -2, -4, -1.
Fiona wrote the linear equation y = 2/5x -5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s?
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
This question is incomplete, the missing answer choices are;
A. x- 5/4y =25/4
B. x-5/2y=25/4
C. x-5/4y =25/4
D. x- 5/2y=25/2
Which equation could be Henry’s?Given the linear equation written by Fiona; y = 2/5x - 5.
From the answer choices provided, they are in the form of x - (m)y = b.
We will transform Fiona's equation into that form.
y = 2/5x - 5
Divide each term by the coefficient of x.
y(5/2) = (5/2)2/5x - (5/2)5
5/2y = x - 25/2
25/2 = x - 5/2y
x - 5/2y = 25/2
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
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possible roots math related olds helppp
In accordance with the Ferrari's method, all the roots of the quartic polynomial are complex numbers.
What kind of roots does a quartic polynomial have?
By fundamental theorem of algebra quartic polynomials have four roots. Based on characteristics of the quadratic formula, use for the solution of quadratic polynomials, there are three possible sets of roots:
All roots are real numbers.Two roots are real numbers and two roots are complex numbers.All roots are complex numbers.There are several methods to solve quartic polynomials. In this case, we decide to use the Ferrari's method to determine all roots of the polynomial:
[tex]x_{1} = \frac{1 + i \sqrt{3}}{2}[/tex], [tex]x_{2} = \frac{1 - i\,\sqrt{3}}{2}[/tex], [tex]x_{3} = - \frac{5}{3} + i\,0.471[/tex], [tex]x_{4} = -\frac{5}{3} - i\,0.471[/tex]
All the roots of the quartic polynomial are complex numbers.
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10. A circular Harkness table is placed in a comer of a room so that it touches both walls. A mark is made on the
edge of the table, exactly 18 inches from one wall and 25 inches from the other wall. What is the radius of the
table?
The radius of the table can be either 13 inches or 73 inches.
How to estimate the radius of the table?Let the radius of the table be r inches and the corner be the origin.
The coordinates of the center of the table exist (r, r).
The equation for the circumference of the table exists (x−r)²+(y−r)²=r².
The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.
As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.
(18−r)² + (25−r)² = r²
324−36r+r²+625−50r+r² = r²
r²−86r+949 = 0
(r − 13)(r − 73) = 0
r = 13 inches and r = 73 inches
Therefore, the radius of the table can be either 13 inches or 73 inches.
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1/2 to the 2nd power in fraction form
Answer: [tex]\frac{1}{4}[/tex]
Work Shown:
[tex]\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)*\left(\frac{1}{2}\right) = \frac{1*1}{2*2} = \frac{1}{4}[/tex]
When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. patasitism
B. Mutualism
C. Commensalism
D. Predation
When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. Parasitism
B. Mutualism
C. Commensalism
D. Predation
Answer:
Step-by-step explanation:
a
PLS HALP ASAP
A vertical slice through a three-dimensional solid produces a two-dimensional shape.
tall rectangle
Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Answer:
the answer is B
a 3d rectangle slided vertically can produce a 2d rectangle
What percent of zachary's pay do his deductions comprise? round your answer to the nearest whole percent.
The percentage of Zachary's pay due to his deductions comprise exists 18.724%.
How to estimate the deduction percentage for Zachary?Zachary exists supposed to earn a paycheck of $20,160.00 but instead, he acquires a lesser amount of money due to deductions. The money he acquires after deductions exists at $16,385.31.
Money deducted = Original paycheck amount - deductions
= $20,160.00 - $16,385.31
= $3,774.69.
So Zachary obtains a deduction of $3,774.69.
To estimate the percent of deductions in terms of his pay we divide the deduction cost with the original paycheck amount and multiply it by 100 to transform it into a percentage.
Deduction % = ($3,774.69 / $20,160.00) [tex]*[/tex] 100
= 0.1872366 [tex]*[/tex] 100
= 18.72366%
We obtain the deduction percentage as 18.724%.
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Find the shaded area. Round to the nearest 10th, if necessary.
Answers:
16 cm²
24 cm²
40 cm²
Step-by-step explanation:
The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.
[1] First shaded area
A = L * W
A = (4 cm) * (12 cm - 5 cm - 3 cm)
A = (4 cm) * (4 cm)
A = 16 cm²
[2] Second shaded area
A = L * W
A = (2 cm) * (12 cm)
A = 24 cm²
Lastly, we add them together.
16 cm² + 24 cm² = 40 cm²
A substance is tested and has a ph of 7.0. how would you classify it? a. a strong acid b. a strong base c. a weak acid d. neutral
A substance is tested and has a Ph of 7.0. It would be a weak acid.
The correct option is (c) a weak acid .
What is the nature of substance if the pH is less than 7?
Acidity is defined as pH below 7. More than 7 pH is considered basic. Each whole pH number below 7 is ten times more acidic than the next higher value since the pH scale is logarithmic. For instance, pH 4 is 100 times (10 times 10) more acidic than pH 6, while pH 5 is ten times (10 times) more acidic than pH 4.What is pH?
The pH scale determines how acidic or basic water is. The range is 0 to 14, with 7 representing neutrality. Acidity is indicated by pH values below 7, whereas baseness is shown by pH values above 7. In reality, pH is a measurement of the proportion of free hydrogen and hydroxyl ions in water.Learn more about pH
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Which description best fits this picture?
Answer:
Accurate AND Precise
NASA launched another space probe, Voyager 2 on August 20, 1977. Voyager 2 is a bit slower than Voyager 1 only traveling 15.4 km/s (34,449 miles per hour). Voyager 2 is 19.3 billion kilometers or 1.93 x 10^10 km (1.2 billion miles) away from the Earth. How many years will it take Voyager 2 from its location to travel to the second closest star (Proxima Centauri) which is 4.24 light years away from Earth? Include all your calculations in your answer. Recall that a light year is 9.5 x 10^12 kilometers.
Using proportions, it is found that it will take Voyager 2 82,900 years from its location to travel to the second closest star.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the Voyager 2 travels 15.4 km/s. In kilometers per year, considering that one hour has 3600 seconds, the measure is given by:
15.4 x 365 x 24 x 3600 = 485,654,400 km/year.
The distance to Proxima Centauri in km is given by:
d = |1.93 x 10^10 km - 4.24 x 9.5 x 10^12 km| = 4.02607 x 10^13 km.
Hence the time in years is given by:
t = d/v = 4.02607 x 10^13/485,654,400 = 82,900.
It will take Voyager 2 82,900 years from its location to travel to the second closest star.
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Part D Now use GeoGebra to measure the length of each side of ABC, and use those lengths to calculate the perimeter of ABC. Do you get the same result that you obtained in part C? Take a screenshot of your work, and paste it be
FROM EDMENTUM.........Using Coordinates to Compute Perimeters and Areas: Tutorial
The perimeter of quadrilateral ABCD will be 26 units.
How to illustrate the perimeter?It should be noted that we want to measure the length of each side of ABC, and use those lengths to calculate the perimeter of ABC.
This will be 10, 5, 5, and 6. Therefore the perimeter will be the addition. This will be:
= 10 + 5 + 5 + 6
= 26 units.
This also was identical to the result gotten. This is attached below.
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At a school 45% of the students are boys; 30% of the boys and 40% of the girls play soccer. What percentage of the whole school plays soccer?
The percentage of the whole school that plays soccer is 35.5%
How to determine the percentage of the whole school plays soccer?The percentage of the boys is given as
Percentage boys = 45%
This means that the percentage of the girls is given as
Percentage girls = 55%
Also, from the question, we have:
30% of the boys and 40% of the girls play soccer
So, the percentage of the whole school that plays soccer is
P = Boys * Percentage Boys + Girls * Percentage Girls
This gives
P = 45% * 30% + 55% * 40%
Evaluate the product
P = 13.5% + 22%
Evaluate the sum
P = 35.5%
Hence, the percentage of the whole school that plays soccer is 35.5%
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What are the restricted values for x2−3x−2−4y⋅2x−2−xy2+2y2?
The restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
How to determine the restricted values for the function?The complete question is added as an attachment
The equation is given as:
(x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2)
Set the products of the denominators to 0
-4y * (-xy^2 + 2y^2) = 0
Split the equation
-4y = 0 or (-xy^2 + 2y^2) = 0
Remove the bracket
-4y = 0 or -xy^2 + 2y^2 = 0
Divide both sides by -4 in -4y = 0
y = 0
Factor out y^2 in -xy^2 + 2y^2 = 0
y^2(-x + 2) = 0
This means that y^2 = 0 or -x + 2= 0
This gives y = 0 or -x + 2 = 0
Solve for x in -x + 2 = 0
x = 2
Hence, the restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
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A bag has marbles labeled ‘4’ and ‘7’ and a spinner has 3 options, What is the probability of drawing a number less than 8 or spinning a 4?
Answer:2
Step-by-step explanation:
im just guessing
The answers are :
P (Drawing a number < 8) = 1
P (Spinning a 4) = 0
There are only 2 numbers in the bag, 4 and 7, both of which are less than 8. Hence, as it is a sure event, the probability of the event is 1.
There are only 3 numbers on the spinner, 1, 2, and 3. As 4 is not on the spinner, it is an impossible event, hence the probability of the event is 0.
A ladder is leaning against a building and makes a 28 degree angle with the ground. the top of the ladder reaches up the building. what is the length of the latter
The length of the ladder is 75ft.
What is hypotenuse?The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.
According to the information:The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft
Therefore, we have:
Sineα = opposite/hypotenuse
Where:
Opposite = 35
Hypotenuse = Length
α = 28°
substitute values and solve for the length, as following:
Sine(28) = 35/Length
Length = 35/Sine(28)
Length = 75ft
Therefore,
The length of the ladder is 75 ft.
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find unknown angles, value of 'x' and unknown sides:
Please help with this question!
Answer:
NONE of these statements are true
[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]
b) False[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]
Im assuming this is an absolute valuec) True[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]
Option Cwhat part of an hour passes between 11:24 am and 415 am
Using proportions, it is found that 1685% of an hour passes between 11:24 am and 415 am.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
One hour is composed by 60 minutes. Between 11:24 am and 4:15 am, there are 16 hours and 51 minutes, hence the number of minutes is given by:
M = 16 x 60 + 51 = 1011 minutes.
As a percentage of one hour = 60 minutes, we have that this measure is:
1011/60 x 100% = 1685%.
Hence 1685% of an hour passes between 11:24 am and 415 am.
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Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 k.
The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
What is an equivalent function?Two functions are equivalent if they share the same domain and codomain and have the same values for all domain components.To complete the square to transform the expression:
The given expression is [tex]x^{2} -2x-2[/tex].Then the expression can be written as, add and subtract one.Then we have:[tex]x^{2} -2x+1-1-2\\x^{2} -2x+1-3\\(x-1)^{2} -3[/tex]Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
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The correct question is shown below:
Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.
(A) (x − 1)2 + 3
(B) (x − 1)2 − 3
(C) (x − 2)2 − 3
(D) (x − 2)2 + 3
Find the circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j , 0 ≤ t ≤ 2π
The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is 2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.
The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.
r (t) = cost i + sin t j = dr( sin ti + cos t)dt
F = -xi -yj = -costi - sin tj
Flux = F .dr = [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex]j)-( sin ti + cos t)dt
[tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex] -( sin ti + cos t)dt
2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
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Daria pays x dollars for a pair of shoes. the tax on shoes is 5%. the expression representing her total cost is x+0.05x.
witch expression is equivalent and why?
A 1.05x because adding $5 to the cost of the shoes is the same as multiplying the cost by 1.05
B 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
C x(0.05) because the cost of the shoes can be factored out
D 1.5x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.5
The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
PercentageAmount paid for shoes = $xTax = 5%Total cost = x + (5% of x)
= x + (0.05 × x)
= x + (0.05x)
Total cost = 1.05x
Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
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What is the answer ?
∠ADB + ∠BDC = ∠ADC
39° + (3x - 4) = 8x + 5
3x - 4 = 8x + 5 - 39
3x - 4 = 8x - 34
34 - 4 = 8x - 3x
5x = 30
x = 6
∠ADC = 39° + (3(6) - 4) = 39 + 14 = 53°
Hope it helps!
Please use elimination method to solve
The answer is x = 4, y = -1 or (4, -1).
We are given :
2x + 7y = 13x + 4y = 8Multiply the 1st equation with 3 and 2nd equation with 2.
3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3
4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16
Now, subtract : Equation 3 - Equation 4.
6x + 21y - 6x - 8y = 3 - 1613y = -13y = -1Substitute in the 1st equation.
3x + 4(-1) = 83x - 4 = 83x = 12x = 4Answer:
(4, - 1 )
Step-by-step explanation:
2x + 7y = 1 → (1)
3x + 4y = 8 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate x
6x + 21y = 3 → (3)
- 6x - 8y = - 16 → (4)
add (3) and (4) term by term to eliminate x
0 + 13y = - 13
13y = - 13 ( divide both sides by 13 )
y = - 1
substitute y = - 1 into either of the 2 equations and solve for x
substituting into (1)
2x + 7(- 1) = 1
2x - 7 = 1 ( add 7 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
solution is (4, - 1 )
The growth of a strain of bacteria can be modeled by the function graphed, where the x-values are the time in seconds and the y-values are the number of bacteria. how many bacteria are there initially? 0 2.7 2.8 4
There are (A) 2.7 bacterias initially.
What is a function?A function is an expression that establishes the relationship between the dependent and independent variables.A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To find the number of bacteria:
The graph shows that the function follows an exponential curve, and the starting point is at ( 0,2.7 ). The starting number of bacteria is then 2.7.Therefore, there are (A) 2.7 bacterias initially.
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The correct question is given below:
The growth of a strain of bacteria can be modeled by
the function graphed, where the x-values are the time
in seconds and the y-values are the number of
bacteria. How many bacteria are there initially?
(A) 2.7
(B) 2.8
(C) 4
Answer:
mine was b 2.7
Step-by-step explanation:
What is the area of this figure?
14 km
8 km
9 km
8 km
5 km
4 km
4 km
4 km
The Area of the composite figure as shown in the image below is: 105.57 km².
What is the Area of a Composite Figure?Referring to the diagram given below, the shape can be decomposed into one rectangle, one square, and one quarter circle.
The area of the composite figure = area of rectangle + area of square + area of quarter circle.
Area of the Rectangle = length × width
Length = 12 km
Width = 7 km
Area of the Rectangle = 12 × 7
Area of the Rectangle = 84 km²
Area of the square = (s)²
s = 3 km
Area of the square = 3²
Area of the Rectangle = 9 km²
Area of the quarter circle = 1/4(πr²)
r = 4 km
Area of the quarter circle = 1/4(π × 4²)
Area of the quarter circle = 12.57 km²
Area of the composite figure = 84 + 9 + 12.57
Area of the composite figure = 105.57 km².
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Can someone help me solve this currently stuck on it please do explain how you get the answers properly Thank you!
Area of semi circle + area of rectangle!
please help and thank you
Answer: 138.63 mm²
Step-by-step explanation:
First, we will solve for the area of the rectangle.
A = L * W
A = 15 mm * 5 mm
A = 75 mm²
Next, we will solve for the area of the semi-circles. Since there are two equivalent semi-circles, I will find the area of one circle with the same radius as these two.
First, we need to find the radius.
15 mm - 3 mm - 3mm = 9mm, 9 mm / 2 = 4.5 mm
A = πr²
A = π(4.5)²
A ≈ 63.62 mm²
Lastly, we will add them together.
75 mm² + 63.62 mm² = 138.63 mm²
i just need explanations on how to solve this. i have an upcoming test. please help.
[tex]\frac{3x}{6y} x\frac{7}{12y}[/tex]
The product of the given expression is 7x/24y²
Product of fractionsGiven the product of the fractions below
3x/6y * 7/12y
Simplify
x/2y * 7/12y
Multiply the numerator and denominator to have:
7x/24y²
Hence the product of the given expression is 7x/24y²
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