The graph of y = 4x? - 4x - 1 is shown.
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x - 1 = 0
1%C
ii) 4x2 - 4x - 1 = 2
Answers
Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075 and x = (4 - 5.66) / 8 = -0.2075
What is meant by Bhaskara's equation?The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.
Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.
Here we have the equation:
y = 4 × x² - 4 × x - 1
And the graph should be available (you can see it below this answer)
Now, we're seeking answers to:
4 × x²- 4 × x - 1 = 0
The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.
The next step is to identify the two x values where our graph crosses the x-axis.
We can estimate the solutions in the graph as follows:
x = -0.2
x = 1.2
The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:
[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}[/tex]
Then the two solutions are:
x = (4 + 5.66) / 8 = 11.2075
x = (4 - 5.66) / 8 = -0.2075
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Related Questions
Solve for X. Please solve this.
Answers
Answer:
32
Step-by-step explanation:
Opposite angles are congruent, so Angle BAC is 58 degrees.
Line KL and FG are perpendicular (forms a 90 degree angle), so Angle ABC is 90 degrees.
Points ABC form a triangle, and the interior angles of a triangle must add up to 180 degrees.
Thus, 58 + 90 + Angle BCA = 180. Solving for BCA, we get 32 degrees. Since Angle GCJ is opposite to BCA, x is 32 degrees.
Analyzing the Discrim
Which values of c will cause the quadratic equation-x²+3x+c=0 to have no real number solutions? Check all that
apply.
0-5
0 0 0
9
Intro
ant of a Quadratic Equation
Done
Answers
The values of x that will give the quadratic equation no real number solutions are -5 and 9
What are real roots of a quadratic equation?Real roots of a quadratic equation are values of x, whose numbers can be represented on a number line.
Analysis:
We have -[tex]x^{2}[/tex] +3x +c = 0
[tex]b^{2}[/tex] - 4ac is called the discriminant of a quadratic equation.
if [tex]b^{2}[/tex] - 4ac < 0, then the quadratic equation has no real root.
where a = -1, b = 3 c = c
[tex](3)^{2}[/tex] -4(-1)c < 0
9 + 4c < 0
4c < -9
c < -9/2
Which means values lower than -9/2 would give the solution no real root.
From, the options, only -5 would give no real solution, since it is lower than -9/2.
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What is the solution to the equation? 2(z-4)^3/2 = 54
5
13
22
no solution
Answers
2(z-4)^3/2=54
(z-4)^3/2=27
(z-4)^3=27^2
(z-4)^3= 729
(z-4)= cube root 729
z-4= 9
z=13
A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
Answers
The width of the box is 3 ft that can be produced using the minimum amount of material.
What are the volume and surface area of a box?Consider a box with length 'l', width 'w' and height 'h',
Volume V = l × w × h
Surface area S = 2(lw + wh + hl)
Calculation:It is given that,
Volume of the box V = 36 cubic feet and l = 2w
Using the formulae,
V = 2w × w × h = 2w²h ...(1)
S = (2w² + 2wh + 4wh) = 2w² + 6wh ... (2) (here only single lw is considered since it is open top)
From equation (1),
36 = 2w²h
⇒ w²h = 18
⇒ h =18/w²
equation (2) becomes
S = 2w² + 6w(18/w²) = 2w² + 108/w ...(3)
So, for a minimum amount of material, the width of the box is,
On differentiating the surface area w.r.t 'w'
S' = 4w - 108/w²
For a minimum amount, substituting S' = 0 we get,
0 = 4w - 108/w²
⇒ 4w = 108/w²
⇒ 4w³ = 108
⇒ w³ = 27
∴ w = 3 feet
Therefore, the width of the given box is 3 feet.
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1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answers
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20
POSSIBLE OUTCOMES!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
Answers
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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what is the rule for the following sequence:
-1; -4; -9; -16; -25
Answers
Answer:
It´s an exponential rule. where one of the factors is negative
Step-by-step explanation:
1 * -1 = -1
2 * -2 = -4
3 * -3 = -9
4 * -4 = -16
5 * -5 = -25
Nancy left a bin outside in her garden to collect rainwater. she notices that 1 over 2 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin. show your work. explain your answer in words.
Answers
[tex]\frac{3}{4}[/tex] gallons of water fill the bin.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Given: Nancy left a bin outside in her garden to collect rainwater.
She notices that 1 over 2 gallons of water fills 2 over 3 of the bin.
To Find: Write and solve an expression to find the amount of water that will fill the entire bin.
Let's say the amount of Water to fill the bin = W gallon
Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{2W}{3}[/tex]Water required to fill the [tex]\frac{2}{3}[/tex] bin = [tex]\frac{1}{2}[/tex] gallonEquate both:
[tex]\frac{2W}{3} =\frac{1}{2}[/tex] is the expression to find the amount of water that will fill the entire bin.
[tex]\frac{2W}{3} =\frac{1}{2} \\2W=\frac{3}{2} \\W=\frac{3}{4}[/tex]
Therefore, [tex]\frac{3}{4}[/tex] gallons of water fill the bin.
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Question is in the pic.
Answers
Answer is C as all other choices are even numbers therefore make the equation non-integer.
Answer:
C)7
Step-by-step explanation:
Due to the fact that all other options are even numbers so it Wii make the equation non-integer.
The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) f(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. f(x) is an odd degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a positive leading coefficient.
Answers
Last option. The correct statement about the graph is g(x) is an odd degree polynomial with a positive leading coefficient.
How to solve the questionWe have the function as
[tex]f(x) = x^2 - 2x + 1[/tex]
The polynomial that we have here is of an even degree. The highest degree we have here is 2. The coefficient that has the highest degree is 1.
Hence all of the options that have f(x) are incorrect.
The answer to the question is option 4.
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Total area=
Help asap please thank u so much
Answers
The total area of the figure shown is 320 square units.
How to get the total surface area?
We can see that we have 4 triangular faces and one square face.
The area of a square of side length S is:
A = S²
Here we can see that the side length of the square is 10 units, then the area of the base is:
a = (10)² = 100
For a triangle of base B and height H, the area is:
[tex]A = B*H/2[/tex]
Here we can see that the base measures 10 units and the height 11 units, so the area of each triangular face is:
A' = (10)*(11)/2 = 55
Then the total area is:
area = 100 + 4*55 = 320
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Comparing Ratios Using Fractions
Compare 4:10 and 12:20 using fractions. Which ratio is
smaller? How do you know?
Answers
Answer:
4:10
Step-by-step explanation:
4:10 = 4/10 = 2/5
12:20 = 12/20 = 6/10 = 3/5.
So 4:10 is smaller than 12:20 because 2/5 is less than 3/5.
Answer:
4:10
Step-by-step explanation:
First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.
11. Write four solutions for each of the following equation: (i)7x + 2y = 9 (ii) 2x = -5y
Answers
The solutions of the equations are (0,4.5), (1, 1), (2, -2.5) & (3, -6) and (0,0), (1, -0.4), (2, -0.8) & (3, -1.2)
How to determine the solutions?Equation 1
7x + 2y = 9
Make y the subject
2y = 9- 7x
Divide by 2
y = 4.5 - 3.5x
Let x = 0, 1, 2 and 3
y = 4.5 - 3.5 * 0 = 4.5
y = 4.5 - 3.5 * 1 = 1
y = 4.5 - 3.5 * 2 = -2.5
y = 4.5 - 3.5 * 3 = -6
Hence, the solutions of the equation are (0,4.5), (1, 1), (2, -2.5) and (3, -6)
Equation 2
2x = -5y
Make y the subject
y = -0.4x
Let x = 0, 1, 2 and 3
y = -0.4 * 0 = 0
y = -0.4 * 1 = -0.4
y = -0.4 * 2 = -0.8
y = -0.4 * 3 = -1.2
Hence, the solutions of the equation are (0,0), (1, -0.4), (2, -0.8) and (3, -1.2)
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The graph of a sinusoidal function intersects its midline at (0,−3)and then has a maximum point at (2,-1.5). Write the formula of the function, where x is entered in radians. f(x)= Please answer fast
Answers
The sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.
How to derive a sinusoidal function
In this question we must derive a sinusoidal function based on two given points. Sinusoidal functions are periodic functions that uses trigonometric functions and have the following form:
y = A · cos (2π · x/T) + B (1)
Where:
A - AmplitudeT - Period B - Vertical midpointThe horizontal distance between the midline and the maximum point is equal to a quarter of the period. Hence,
T = 4 · (2 - 0)
T = 8
The vertical midpoint and amplitude of the sinusoidal function are now calculated:
Vertical midpoint
B = - 3
Amplitude
A = - 1.5 - (- 3)
A = 1.5
Then, the sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) - 3.
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Solve for xxx in the diagram below.
Answers
Answer:
x = 34
Step-by-step explanation:
The three angles form a straight line and are thus supplementary angles. The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:
180 = 2x + 112
68 = 2x
x = 34
Find the perimeter and area of the figure shown in the picture.
Answers
Answer:
52 units
Step-by-step explanation:
Perimeter = sum of it sides =
15 + 8 + 6 + 17 + 6
= 52
f(x) is a function. O A. True 0 False 6 12 9 f(x) 3 4 7
Answers
Answer:Answer: true
Step-by-step explanation: f(x) is a function because each x value (left oval) has one y value (right oval)!
Which of the following statements about angles is NOT correct?
Complementary angles are two angles whose sum is 90 degrees.
The measure of an obtuse angle is always greater than the measure of an acute angle.
The measure of an acute angle and the measure of an obtuse angle added together will always
be supplementary.
Two right angles that share a leg are supplementary.
Answers
ANSWER: The third statement appears to be incorrect.
The area of the triangle shown is represented by A=s(s−12)(s−9)(s−7)−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle? Round your answer to the nearest hundredth. (25 points to answer!! please))
Answers
The height h of the triangle is 5.42 ft
How to find height of a triangle?The height of the triangle can be found using the formula below:
Area = 1 / 2 bh
where
b = baseh = heightTherefore,
A = √s(s - a)(s - b)(s - c)
Hence,
s = 14 + 7 + 11 / 2 = 32 / 2 = 16
A = √16(16 - 11)(16 - 7)(16 - 14)
A = √1440
A = 37.947331922
A = 37.95 ft²
37.95 = 1 / 2 × 14 × h
h = 37.95 / 7
h = 5.42104741743
h = 5.42 ft
Therefore, the height h of the triangle is 5.42 ft
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When y = -8, x = 8, what is x when y = -6?
Answers
Answer:
x = 6
Step-by-step explanation:
y = -8
x = 8
-x = -8 = y
-x = y
now, when y is -6
-x = y = -6
-x = -6
x = 6
Solve the following system of equations:
3x-5y=-11
7x+2y=-12.
Express your answer as an ordered pair. (x, y)
Answers
Answer: (-2, 1)
Step-by-step explanation:
We will graph the given equations. The point of intersection is the solution to the system of equations. See attached.
They intersect at the point (-2, 1) giving us an answer of x = -2 and y = 1, but this question asks for the answer as an ordered pair so we leave it as is.
Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
-Write the piecewise function for 0 to 2 miles.
f(x) = ?
Answers
The piecewise function is
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
How to determine the piecewise function?From the question, we have:
Fares = $2.00 ⇒ up to (and including) 1/2 miles
Fares = $0.70 increment ⇒ greater than 1/2 miles
Let x represent the number of miles, and f(x) the fares.
So, we have:
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
The above represents the piecewise function
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these box plots show the basketball scores for two teams.
Answers
The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.
What is a box plot ?A box plot is used to study the distribution and level of a set of scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
A box plot is symmetric when the median is at the center of the box and negatively skewed if the median is closer to the upper quartile.
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Which statement is true of the graph on the
right?
The average salary doubled between year 1
and 2.
The average salary tripled between year 1
and 3.
The average salary increased by the same
amount each year.
DONE
Answers
1. The TRUE statement about the graph, which is represented here by the data table, is D. The average salary increased by some irregular amount each year.
2. The average salary per year between 2001 and 2006 is $3,600?
What is an average?An average number is the mean of a total value.
The average is computed as the total value of observations divided by the number of observations.
Data for the graph and Calculations:Year Salary
2001 $1,500
2002 2,600
2003 3,200
2004 4,100
2005 5,000
2006 5,200
Total $21,600
Average = $3,600 ($21,600/6)
Thus, the graph or the data table shows that D. The average salary increased by some irregular amount each year.
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Question Completion:1. Option D: The average salary increased by some regular amount each year.
2, What is the average salary per year between 2001 and 2006?
Answer: C-The average salary increased by the same amount each year.
NEXT ANSWER-B
Step-by-step explanation:
Helllllllppppppppppp what Is 20 divided by 8
Answers
Answer:
2.5
Step-by-step explanation:
IVE BEEN WATCHING YOUR ACCOUNT STOP STEALING POINTS OR YOUR ACCOUNT WILL BE TERMINATED.
Hi, can you help me with this math problem?
The equation of a hyperbola is shown.
[tex]\frac{(y-7)^2}{3}-\frac{(x+13)^2}{12}=1[/tex]
Determine the area of the central rectangle.
Answers
Answer:
24
Step-by-step explanation:
The semi-axis lengths are 'a' and 'b' in the equation ...
(y -k)²/a² -(x -h)²/b² = 1
AreaThe area of the central rectangle will be ...
A = LW
The axis lengths are 2a and 2b, so the area is ...
A = (2a)(2b) = 4ab
In terms of the numbers in the given equation, this is ...
A = 4√(a²b²) = 4√(3×12)
A = 4×6 = 24
The area of the central rectangle is 24 square units.
What are the solutions of sin(2theta)+sin(theta)=cos(theta) on the interval [0, 360]
Answers
The solutions are: θ = 90º, 270º, 30º, and 150º
Given,
sin2θ = cosθ
sin2 θ = 2sinθ cosθ
2sinθ cosθ = cosθ
2sinθ cosθ - cosθ = 0
factor
cosθ(2sinθ-1) = 0
cosθ = 0 or 2sinθ - 1 = 0
cosθ = 0 when θ=90º or θ=270º (look on the unit circle)
2sinθ - 1 = 0
2sinθ = 1
sinθ = 1/2
look at the unit circle and see that sinθ=1/2 when θ=30º
sin is positive in Quadrant2 as well as Quadrant 1
180º-30º=150º
θ=150º
answers: θ=90º, 270º, 30º, and 150º
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Joe and Sue were trying to calculate the square inches of paper needed to create a cone for the cotton candy. The radius
was 2 in and the height was 6 inches and there was a 1/2 in of overlap for the glue.
Calculations
Joe
2π√10+ √10
Sue
12π + 3
choose the correct statements below.
select one or more:
Sue was correct.
Joe was correct.
Sue used the correct height and radius and calculated the overlap by adding the area for the strip of glue.
Neither were correct.
Joe used the height and radius to calculate the slant height.
Answers
The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
How to find the square inches of paper needed.The square inches of paper needed A = surface area of cone + area of overlap
Surface area of cone
The surface area of the cone is given by A = πr[r + √(h² + r²)] where
r = radius of cone = 2 in and h = height of cone = 6 in.So, A = πr[r + √(h² + r²)]
A = π × 2 × [2 + √(6² + 2²)]
A = π × 2 × [2 + √(36 + 4)]
A = π × 2 × [2 + √40]
A = π × 2 × [2 + 2√10]
A = 2π[2 + 2√10]
A = 4π + 4π√10
The area of overlap
The area of overlap A' = wL where
w = width of overlap = 1/2 in and L = slant height of cone = √(h² + r²)So, A' = wL
A' = w[√(h² + r²)]
A' = 1/2[√(6² + 2²)]
A' = 1/2[√(36 + 4)]
A' = 1/2[√40]
A' = 1/2 × 2√10
A' = √10
So, the number of square inches of paper needed is A" = A + A'
= 4π + 8π√10 + √10
Since the number of square inches of paper needed is 4π + 4π√10 + √10
So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.
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Can someone pls pls PLS, help me out? ASAP!! (Geometry)
“Complete the proof”
Answers
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)
4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)
5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)
Solve the polynomial congruence x^2-3x+2 is congruent to 0 mod 5. Solve for x=? or x=?,when k is any integer
Answers
The solutions of x² - 3x + 2 ≡ mod 5 does not exist.
How to solve Polynomial Congruence?
We are given the Polynomial;
x² - 3x + 2 ≡ mod 5
Finding the roots of the equation gives;
x² - 2x - x + 2 = 0(mod 5)
x(x - 2) - 1(x - 2) = 0(mod 5)
Thus, RHS = 0(mod 5) = 0
The roots of the equation are;
x = 1 and x = 2
Thus, the solutions of x² - 3x + 2 ≡ mod 5 does not exist.
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