The value of a , b and c in the quadratic equation 5x² - 4x + 8 = 0 is given by 5 , -4 and 8 respectively
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
5x² - 4x + 8 = 0 be equation (1)
On factorizing the equation , we get
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0.
Substituting the values in the equation , we get
a = 5
b = -4
c = 8
Hence , the quadratic equation is 5x² - 4x + 8 = 0
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Can anyone help with categorizing these polynomials?
The given polynomials are discussed and grouped into each given category as given below.
What is a polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
We can now look into each polynomial.
a) x³ + 125
125 is a cube of 5 and also x³ is the power of x.
So this is a perfect cube.
b) 8p³ - 27
8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.
So it is a perfect cube.
c) 12x³-9
This is neither a cube nor a square.
d) a²-100
100 is a perfect square and so is a².
So this is a difference of perfect squares.
e) 4m² + 25
4m² is a square of 2m and 25 is a square of 5.
But the operator is +
So this is neither a cube nor a difference of a perfect square.
f) 16x²-9
16x² is a square of 4x and 9 is a square of 3.
Also, the operator is -
So this is a difference of perfect squares.
Therefore the above polynomials are discussed and grouped into each given category accordingly.
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Which equation represents the graph?
y = - 1/2x + 6
y = 1/2x - 3
y = 2x − 3
y = −2x + 6
The correct equation of the linear graph is; y = 1/2x - 3
How to find the equation of a linear graph?Linear graph is usually represented in the form of a straight line. To show a relationship between two or more quantities we use a graphical form of representation.
The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given graph, we can tell that the y-intercept is c = -3
Now, the slope will be calculated with two coordinates using the formula;
m = (y2 - y1)/(x2 - x1)
Coordinates are (2, -2) and (4, -1)
m = (-1 - (-2))/(4 - 2)
m = 1/2
Thus, equation is;
y = 1/2x - 3
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According to a research study, parents with young children slept 6.4 hours each night last year, on average. A random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. This data has a sample standard deviation of 0.9. (Assume that the scores are normally distributed.)
Researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year.
The null and alternative hypotheses are H0:μ=6.4 and Ha:μ>6.4, which is a right-tailed test.
The test statistic is determined to be t0=1.89
Using the partial t-table below, determine the critical value(s). If there is only one critical value, leave the second answer box blank.
df t0.10 t0.05 t0.025 t0.01 t0.005
... … … … … …
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
The critical value for a one-tailed test at the 5% significance level with 18 degrees of freedom is 2.878.
To determine this value, the researcher can use the partial t-table above. The first row of the table contains the degrees of freedom (df) and the last column (t0.005) contains the C. To find the critical value, the researcher would look for the row with df=18 and the column with t0.005. The value at the intersection of these two values is 2.878. Therefore, the critical value for this test is 2.878.
To compare the test statistic to the critical value, the researcher would subtract the test statistic from the critical value. If the difference is greater than 0, then the test statistic is greater than the critical value and the null hypothesis can be rejected. In this case, the difference is -0.988, which is less than 0. Therefore, the test statistic is less than the critical value and the null hypothesis cannot be rejected.
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Solve for x. 6x² + 1 = 20 Round to the nearest hundredth.
Answer:
x = 1.78
Step-by-step explanation:
6x² + 1 = 20
6x^2 = 19
x^2 = 19/6
x = 1.78
Answer:
1.78
Step-by-step explanation:
6x² + 1 = 2
6x²=19
x²=19/6=3.167
x=√3.167 = 1.78
Scenario: Your friend kara recently decided to start a skateboard business. She just spent $50 on the assembly kit, but she makes $20 in profit for every skateboard she sells. Shes asked you to help her think about her potential finances for this month. In that time period, she said she can make 15 skateboards at most.
Answer: If she makes 15 skateboards she will make $250
Step-by-step explanation:
$20(15) - $50=
Multiply the $20 by the 15 skateboards: $20 x 15= 300
300 - $50 = $250
May or may not be correct
What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
In accordance with the above, the scale that relates these two figures is 1:4, that is to say that each unit of the large figure is reduced four times.
How to find the scale that relates these two figures?To find the scale that relates these two figures we must know the measures of one of its sides. In this case we have the measure of the side of the rectangle, which in the large rectangle is equal to 6 and in the small rectangle is equal to 1.5
Based on the above information, we must divide the larger number into the smaller number and the result of this operation will be the scale of the model.
6 / 1.5 = 4So, the scale would be 1:4 because the distances of the small model represent a quarter of the original distance of the figure.
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a standing wave is set up in a pool 24 m long which contains six loops. what is the wavelength? a) 24 m b) 48 m c) 8 m d) 4 m
Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.
Wavelength = Length of Pool / Number of Loops
24 m / 6 loops
= 4 m
Wavelength
= 4 m
Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.
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in a game a player throws a dart at the object shown here. if the player throws two darts, what is the probability they both land in a shaded region
The probability of an event happening is represented as a fraction, with the numerator being the number of favorable outcomes and the denominator being the total number of outcomes.
In this case, if the player throws two darts, the probability that both land in a shaded region is equal to the product of the probabilities of each dart landing in the shaded region.
If the shaded region is a circle with radius r and the darts are randomly thrown onto a larger circle with radius R, then the probability of a dart landing in the shaded region is given by:
P = (Area of shaded region) / (Area of larger circle) = (πr^2) / (πR^2)
So, the probability that both darts land in the shaded region is given by:
P = (πr^2 / πR^2) * (πr^2 / πR^2) = (πr^2 / πR^2)^2
Note that the specific values of r and R would depend on the particular game and the dimensions of the object.
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let v1 = (1, 1, 1), v2 = (1, 1, 0), v3 = (1, 0, 0), and w = (2, −3, 4). determine whether w can be expressed as a linear combination of v1, v2, and v3. if it can, write the linear combination.
We can solve this equation by setting up a system of equations and solving for the constants a, b, and c. Hence, w = 2v1 - 3v2 + 4v3.
Yes, it can.
w = 2v1 - 3v2 + 4v3
We can express w as a linear combination of v1, v2, and v3 by writing the equation w = ax1 + bx2 + cx3, where x1, x2, and x3 are the vectors v1, v2, and v3, respectively, and a, b, and c are constants.
We can solve this equation by setting up a system of equations and solving for the constants a, b, and c.
The equations we need to solve are:
2 = a + b + c
-3 = a + b
4 = a
From this, we can solve for a, b, and c to get a = 2, b = -1, and c = 2.
Hence, w = 2v1 - 3v2 + 4v3.
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consider the dimensions implied by the formula
whether the formula could be for a length , an area , a volume or none of these
d2 + hw
Answer:
The formula d2 + hw could be for an area. The formula is the sum of two terms, d2 and hw. The first term, d2, is the area of a square with side length d. The second term, hw, is the area of a rectangle with length h and width w. Therefore, the formula is for the total area of the square and the rectangle combined.
Step-by-step explanation:
(a) What 3 by 3 matrix E₁₃ will add row 3 to row 1? (b) What matrix adds row 1 to row 3 and at the same time adds row 3 to row 1? (c) What matrix adds row 1 to row 3 and then adds row 3 to row 1?
The process of adding the matrix is explained blow.
Matrices are powerful tools used to analyze data and solve complex equations.
A 3x3 matrix, or E₁₃, is a matrix composed of 3 rows and 3 columns. It can be used to perform various operations, including adding two rows together.
(a) To answer the first question, a 3x3 matrix E₁₃ can add row 3 to row 1 by performing a row operation. This involves taking the second row and adding it to the first, thus adding the values on each row together.
(b) To answer the second question, a 3x3 matrix E₁₃ can add row 1 to row 3 and at the same time add row 3 to row 1 by performing a row exchange operation. This results in a 3x3 matrix where each value in the first row is equal to the corresponding value in the third row.
(c) To answer the third question, a 3x3 matrix E₁₃ can add row 1 to row 3 and then add row 3 to row 1 by performing two separate row operation and then taking the third row and adding it to the first, thus adding the values of each row together again.
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you have 3/4 yard of wire. you use 1/3 yard to make an electric circuit. how much wire do you have left?
Answer: 5/12th or 0.41666666666 yards of wire
Step-by-step explanation:
this is my math... not an explanation
3, 6, 9, 12,
4, 8, 12,
4/12-9/12=5/12
Answer:
Step-by-step explanation:
x/10 = 2/8 solve answer for x
Answer:
To solve for x, we need to isolate x on one side of the equation. We can start by multiplying both sides of the equation by 8:
8 * (X/10) = 8 * (2/8)
Expanding and simplifying the right side:
8 * (X/10) = 2
And multiplying out the left side:
8X/10 = 2
Next, we can multiply both sides by 10 to isolate x:
8X = 20
Finally, dividing both sides by 8:
X = 2.5
Answer:
X = 2.5.
express each set using roster notation. then give the cardinality of the set. (a) p(∅) (b) p(p(∅)) (c) p(p(p(∅)))
The cardinality of the sets p(∅), p(p(∅)), and p(p(p(∅))) are 1, 2, and 4 respectively.
a)p(∅) = {x | x ⊆ ∅}
Cardinality of the set is 1, since there is only one subset of the empty set, which is the empty set itself.
b)p(p(∅)) = {x | x ⊆ {∅}}
Cardinality of the set is 2, since there are two subsets of the set containing the empty set, which are the empty set itself and the set containing the empty set.
c)p(p(p(∅))) = {x | x ⊆ {{∅}}}
Cardinality of the set is 4, since there are four subsets of the set containing the set containing the empty set, which are the empty set itself, the set containing the empty set, the set containing the set containing the empty set, and the set containing the empty set and the set containing the empty set.
The cardinality of the sets p(∅), p(p(∅)), and p(p(p(∅))) are 1, 2, and 4 respectively.
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The function is continuous and So f(u)du = 6 What is the value of $xf(x2 – 1)dx? (A) 3/2(B) 3(C) 6(D) 12 (E) 24
If the function is continuous function and ∫0 to 8 f(u) du = 6, the value of ∫ 1 to 3 xf(x² - 1) dx is B) 3.
Given ∫0 to 8 f(u) du = 6 and we need to find the value of ∫ 1 to 3 xf(x² - 1) dx
We can say, u = x² - 1
Differentiating both sides
du = 2x dx
dx = du/2x
When x = 1,
u = 1² - 1 = 0
and when x = 3
u = 3² - 1 = 8
So, ∫ 1 to 3 xf(x² - 1) dx can be written as
∫ 1 to 3 xf(x² - 1) dx = ∫ 0 to 8 xf(u) du/2x
= 1/2∫ 0 to 8 f(u) du
It is given that ∫0 to 8 f(u) du = 6
So, ∫ 1 to 3 xf(x² - 1) dx = 1/2 x 6 = 3
Hence, the value of ∫ 1 to 3 xf(x² - 1) dx is 3.
The question is incomplete. The complete question is
" The function f is continuous and ∫0 to 8 f(u) du=6. What is the value ∫ 1 to 3 xf(x² - 1) dx? (A) 3/2 (B) 3 (C) 6 (D) 12 (E) 24 "
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Question4,5,6
(4) Ndidi rides y km at 10 km/h, then walks 0.5y km at 3 km/h. she is away from home less than 4 hours. find the range of value of y.
Answer:
y < 15
Step-by-step explanation:
Check attachment for explanation
Melissa buys framing to go around the perimeter of her rectangular painting that measures inches by 8 1/4 inches. 10 1/4 Each inch of framing costs $0.45. What is the total cost for the framing? Show your work.
The total cost of the framing measuring 8 1/4 inches by 10 1/4 is $16.65
How to determine the cost of the framingThe total perimeter of the framing is solved by the formula
= perimeter of the frame * price of each framing
perimeter of the framing is equal to perimeter of rectangle
= 2 * (length + width)
= 2 * (10 1/4 + 8 1/4)
= 37 inch
The cost of the framing
Since the unit cost of the framing is $0.45 per inch then the total cost is
= 0.45 * 37
= $16.65
The framing will cost $16.65
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Which expression is equivalent to 1/5 (150x-80y+50-50x-25y+20)?
20x-21y+14
20x+11y+14
20x-11y+6
20x+21y+6
Answer: [tex]20x-21y+14[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}(150x-80y+50-50x-25y+20)\\\\=\frac{1}{5}(100x-105y+70)\\ \\ =20x-21y+14[/tex]
help please!!!
Fill in the table below. Round your answers to the nearest thousandth.
(1) From Latoya's results, compute the experimental probability of landing on white. ~
(2) Assuming that the spinner is fair, compute the theoretical probability of landing on white.
(3) Assuming that the spinner is fair, choose the statement below that is true:
a. The experimental and theoretical probabilities must always be equal.
b. As the number of spins increases, we expect the experimental and theoretical
c. probabilities to become closer, though they might not be equal. As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
1) The experimental probability of landing on white is; 18/50
2) The theoretical probability of landing on white is; 1/3
3) Assuming that the spinner is fair, the statement that is true is; probabilities to become closer, though they might not be equal.
How to find experimental probability?Theoretical probability is the term that is used to describe what we expect to happen based on math theory, whereas experimental probability refers to what actually happens when the actual situation is tried out as an experiment.
A) Total number of spins = 18 + 14 + 18
= 50
Thus, experimental probability of landing on white = 18/50
B) The theoretical probability of landing on white as there are only three colors is;
Prob = 1/3
C) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
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The graph above is a graph of what function? (It's not a parabola)
The function graphed in this problem is a secant/cosecant function.
What are the secant and cosecant functions?The secant of an angle is given by the division of one and the cosine of the angle, as follows:
sec(x) = 1/cos(x).
As the cosine is a periodic function varying between -1 and 1, the secant function is periodic, with values with absolute value greater than 1.
The secant function has vertical asymptotes at the values of x for which
cos(x) = 0.
The cosecant of an angle is given by the division of one and the sine of the angle, as follows:
csc(x) = 1/sin(x).
With vertical asymptotes at the values of x for which
sin(x) = 0.
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NEED HELP WITH 2 QUESTIONS WILL MARK BRAINLIEST!!!
Graph the curves y = x^5 and x = y(y - 1)^2 Find their points of intersection correct to one decimal place. find the smallest x-value and the largest x-value
The points of intersection are (-0.4, -0.2) and (2.8, 16.8). The smallest x-value is -0.4 and the largest x-value is 2.8.
To graph the curves y = x^5 and x = y(y - 1)^2, first plot the points on the graph for y = x^5. This can be done by substituting in values for x and then finding the corresponding values for y. For example, when x = -3, y = -3^5 = -243. When x = 0, y = 0^5 = 0. When x = 3, y = 3^5 = 243. After plotting the points, draw a smooth curve connecting them. Next, plot the points on the graph for x = y(y - 1)^2. This can be done by substituting in values for y and then finding the corresponding values for x. For example, when y = -2, x = -2(-2 - 1)^2 = -2(-3)^2 = 18. When y = 0, x = 0(0 - 1)^2 = 0(-1)^2 = 0. When y = 4, x = 4(4 - 1)^2 = 4(3)^2 = 36. After plotting the points, draw a smooth curve connecting them. The curves intersect at two points. The points of intersection are (-0.4, -0.2) and (2.8, 16.8). The smallest x-value is -0.4 and the largest x-value is 2.8.
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find the surface area of 9 3 3 pyramid
The surface area of the pyramid is 1377 square units
What is surface area of a pyramid?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
To find the surface area of a pyramid, we use the formula SA=B+12ps, where B is the area of the base, p is the perimeter of the base, and s is the slant height
height = 9
length = 3
width = 3
therefore s = √9²+3²
s = √81+9
s = √90
s = 9.5 units
Base area = l×w = 3 × 3 = 9 units
perimeter of the base = 2( 3+3) = 2×6 = 12
Surface Area = 9 + 12× 12× 9.5
SA = 9 + 1368
SA = 1377 square units
Therefore the surface area of the pyramid is 1377 square units
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What’s the value of X?
Assuming these triangles are similar, first find the standard ratio between them by dividing the corresponding sides of triangle VUT by RSQ:
[tex]R=\frac{36}{54} =\frac{2}{3}[/tex]
Now we know that if we multiply any side of triangle RSQ by the ratio (2/3), we can find the corresponding side of triangle VUT. Using this logic, multiply side RQ by our common ratio to find what UT should equal:
[tex]24*\frac{2}{3} =UT[/tex]
[tex]16=UT[/tex]
Finally, set up an equation for this side:
[tex]x+5=16[/tex]
Solve for x:
[tex]x=11[/tex]
Help me please I need this problem answered
To solve this equation for v, we need to get v by itself on one side of the equation. To do this, we can subtract 6 from both sides of the equation:
[tex]\displaystyle -\frac{5}{8} - 6= v \\\\-\frac{5}{8} - \frac{48}{8} =v\\\\-\frac{53}{8} =v[/tex]
To convert a fraction in the form of a/b to a mixed fraction, we can divide a by b and then write the quotient as the whole number part of the mixed fraction and the remainder as the numerator of the fractional part, with the denominator being the same as the denominator of the original fraction.
In this case, we have a/b = -53/8. To convert it to a mixed fraction, we can divide -53 by 8: -53/8 = -6 R 5
So, -53/8 as a mixed fraction is -6 5/8.
In circle P shown, the measure of PQS is 20°.
What is the measure of PRS?
A. 20°
B. 40°
C. 60°
D. 70°
The measure of PRS is 70°, So correct option is D.
What do you mean by circle?A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, away from a given central point. Circles are unique among shapes because they have no corners, sides, or edges and are continuous, meaning that they have no gaps or breaks. The circumference of a circle is the distance around its outer edge and is equal to 2π times the radius. The area of a circle is the amount of space contained within its circumference and is equal to π times the square of the radius. Circles are used in a variety of applications, from mathematics and science to engineering, design, and art. In mathematics, circles are used to understand concepts such as angles, arc lengths, and curvature. In science and engineering, they are used to model physical phenomena, such as the motion of planets and the flow of fluids. In design and art, circles are used to create visually appealing patterns, logos, and symbols. The circle is considered a symbol of unity, wholeness, and completeness.
In triangle QRS, angle SQR is 20°, so angle QSR is 180° - 20° = 160°. Since point P is the midpoint of side QR, angle QRP is equal to half of angle QSR, or 160° / 2 = 80°. Therefore, angle PRS = 180° - 80° = 100°. So the measure of angle PRS is 100°, making the answer D. 70°.
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5. Maggie spent $2.90 on 3½ pounds of peanuts. How much did she spend per pound?
If the sum of three consecutive integers is less than 75, find the cube of the largest possible integer.
Answer:
The cube of the largest number is < 19683
Step-by-step explanation:
let the three integers be :- x, x+1, x+2
x + (x+1) + (x+2) < 75 (given)
x + x + x + 1 + 2 = 75 (considering that the sum is 75)
3x + 3 = 75
3(x + 1) = 75
x + 1 = 75/3 = 25
x = 24
The largest number is x + 3
x + 3 = 27
(x + 3)^3 = 27^3
= 19683
The instantaneous rate of change of the vector-valued function f(t) is given by r(t) = (evė, 10 cos(t + Vě)). 17 f(2) = (2e, 7 – 7), what is the value of f(6) ? A. (11.582, -5.609) B. (12.906, 0.163) C. (30.170, 9.141) D. (35.606, 5.283)
The value of function f(6) is (35.606, 5.283). Therefore, option D is the correct answer.
What is constant rate of change?When something has a constant rate of change, one quantity changes in relation to the other.
We are given that, f(t) rate of change = df(t)/dt =r(t)
df(t)/dt =r(t) = <[tex]e^\sqrt{t}[/tex], 10cos(t+√t)>
Let us solve for x component as all options have different x components.
x component of r(t)
df(t)/dt =[tex]e^\sqrt{t}[/tex]
∫df(t) = ∫[tex]e^\sqrt{t}[/tex] dt
f(t) = ∫[tex]e^\sqrt{t}[/tex] dt
Let us substitute t=x^2 -----(1)
dt=2xdx
f(t)=∫eˣ × 2xdx
Using integration by parts formula
f(t)=2[x ∫eˣdx- ∫∫ eˣ dx d(x)/dx .dx ∫eˣ+c
f(t) =2[xeˣ-∫eˣdx]+c
f(t) = 2[xeˣ-eˣ]+c
f(t)=2eˣ[x-1]+c
From equation (1) we have x=rtt
f(t)=2[tex]e^\sqrt{t}[/tex][√t-1]+c -----(2)
Substituting t=2
We have f(2)=<2e, π-7>
2e=[tex]2^\sqrt{t}[/tex][√t-1]+c
2e=[tex]2^\sqrt{t}[/tex]2[√2-1]+c
2e=8.226[0.414]+c
2e=3.407+c
c=2.029
Now solving for f(6) (x-component only)
f(6)=2[tex]e^\sqrt{t}[/tex]6(√6-1)+2.029
= (23.165×1.45)+2.029
= 33.589+2.029
= 35.618
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The instantaneous rate of change of the vector-valued function f(t) is given by r(t)=<[tex]e^\sqrt{t}[/tex], 10cos(t+√t)>. If f(2)=<2e, π-7>, what is the value of f(6)?
a) <11.582, -5.609>
b) 12.906, 0.163>
c) <30.170, 9.141>
d) <35.606, 5.283>
ASAP I need a quick answer pls
Answer:
62 square feet.
Step-by-step explanation:
7*5=35, 9*3=27, 35+27=62
