Answer:
To solve the quadratic equation 3w^2 - 12w = -12, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -12, and c = -12. Plugging these values into the formula, we get:
w = (-(-12) +/- sqrt((-12)^2 - 43(-12))) / (2*3)
Simplifying, we get:
w = (12 +/- sqrt(144 + 144)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- 16.97) / 6
w = (12 +/- 16.97) / 6
w = 28.97/6 or -4.97/6
w = 4.828 or -0.828
Therefore, the solutions to the equation 3w^2 - 12w = -12 are w = 4.828 and w = -0.828.
Answer:
w = 2
Step-by-step explanation:
[tex]3w^{2} -12w=-12\\3w^{2} -12w+12 = 0\\[/tex]
[tex]\frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\frac{-(-12) + \sqrt{(-12)^{2} - 4(3)(12) } }{2(3)} = 2[/tex]
Please help it about calculus
The total distance travelled by the particle is 24 units.
What is displacement?
Displacement is defined as a change in an object's position. An object's displacement is defined as how far it has moved from its starting point. The dependent variable in the displacement time graph is displacement, which is represented on the y-axis, and the independent variable is time, which is represented on the x-axis. Position-time graphs are another name for displacement time graphs.
The displacement curve is given for 0 ≤ t ≤ 18.
We need to find the total distance of the curve, it will be the positive sum of all displacements.
So, total distance = (7-0) + (3-0) + (2+3) + (2+4) + (7-4)
= 7 + 3 + 5 + 6 + 3
= 24
Hence, the total distance is 24 units.
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what is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)?
The surface area, A, is changing at a rate of 288 km/min decreasing.
Given,
Base length, l = 6 km
Height, h = 10 km
dl/dt = -9 km/min
dh/dt = 12 km/min
Surface area of a prism, A = 2 × (lw + lh + wh)
For a square prism,
Length, l = width, w = 6km
A = 2 × (l² + lh + lh)
= 2(l²) + 4lh
A = 2(l²) + 4 lh
= 2 × (l² + 2lh)
dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)
dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)
= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))
= 2 × (- 108 + -180 + 144)
= 2 × -144
= -288 km/min
The rate of change of the surface area, A is decreasing by 288 km/min.
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Question is incomplete. Completed question is given below;
The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?
DJ was going to meet his family at the beach in NC. He looked on a map and saw that the beach he was going to was 800 km from his house and he knew he would average 110 km/hr on the highway. How long is it going to take him to get to the beach?
On average, it is going to take DJ 7.27 hours to get to the beach.
What is the average?Average refers to the quotient when a numerator is divided by a denominator.
In this situation, the average refers to the time, which is the quotient of the distance and speed.
The total distance going to the beach from his family = 800 km
The average speed = 110 km/hr
The time to cover the distance of 800 km at 110 km/hr = 7.27 hours (800/110).
Thus, DJ will take 7.27 hours to cover 800 km at 110 km/hr.
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A class measure the radius and circumference of various
It can be seen that the radius and circumferance are not proportional.
What is a expression? What is a mathematical equation? What is constant of proportionality?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.The general equation of a straight line is y = mx + c. The equation can also be used to represent direct proportionality as -
y = mx
m = y/x
[m] is called constant of proportionality.
Given is a graph as shown in the figure.
For the proportional relationship -
(25 - 18)/(4 - 3) should be equal to (38 - 25)/(6 - 4)
7/1 = 13/2
7/1 = 6.5
7 ≠ 6.5
Therefore, it can be seen that the radius and circumferance are not proportional.
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If m is a real number such that m² + 1 = 3m , the value of [tex]\frac{2m^{5} - 5m^{4} + 2m^{2} - 8m^{2} }{m^{2} + 1 }[/tex]
The required solution of the given expression is 1/3 [m²-2m-6].
Given that,
To simplify the [2m⁵ -5m₄ +2m² -8m²]/[m²+1], when m² + 1 = 3m.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= [2m⁵ -5m₄ +2m² -8m²]/[m²+1]
When substituting the value m² + 1 = 3m in the above expression we get.
= m/3 [m²-2m-6]
Thus, the required solution of the given expression is 1/3 [m²-2m-6].
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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 ft
The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
What is a semicircle?A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.
What is a formula for the area of a semicircle?The formula for finding the area of a semicircle is half of the area of a circle with the same radius.
area of semicircle = [tex]\frac{\pi r^{2} }{2}[/tex] square units
Given:
A table with a round top is cut in half so now its shape is a semicircle.
After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft
Diameter = 6 ft
Radius = diameter / 2
Radius = 6/ 2
Radius = 3 ft
Therefore now we can calculate the area of the table after it is cut in half
Area of the semicircle table after it is cut in half =
[tex]=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi[/tex]
The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.
Please help with ixl
Answer:
<AFC
Step-by-step explanation:
Vertical angles are pairs of opposite angles that are created by two intersecting lines. As an example, the other pair of vertical angles are <CFD and <AFE.
The Pythagorean Theorem, given by the formula a² + b² = c², relates the
three sides of a right triangle. Solve the formula for the positive value of b in
terms of a and c.
Answer:
Below
Step-by-step explanation:
a^2 + b^2 = c^2 subtract a^2 from both sides
b^2 = c^2 - a^2
take the positive sqrt of both sides ( since you can't have a negative length)
b = sqrt (c^2 - a^2)
For the function: y = startroot x minus 7 endroot minus 1 the domain is : x ≥ the range is: y ≥
The domain the function is In interval notation [7, ∞). The range of the function is in the interval (-1, ∞).
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph can be used to draw a vertical line that crosses the relation twice.
Here,
y=√(x-7)-1
x-7≥0
x≥7
at x=7
y=√(7-7)-1
y=-1
The function's domain is represented by the interval notation [7, ∞). The function's range falls within the range [-1, ∞).
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Find the sum of all three - digit numbers which give a remainder of 5 when they are divided by 7 immediately
Answer: As Devansh Sehta has calculated, there are 82 terms and 82=7×11+5. When each term of S is divided by 7, the remainders, in order are 6, 3, 0, 4, 1, 5, 2, and these repeat.
Step-by-step explanation:
For any arithmetic sequence, record the remainders when successive terms are divided by n. Then the sum of every set of n consecutive remainders is divisible by 7. In this case, the first 77 terms add to a multiple of 7 as do the 5 remaining terms.
Write the equation of the line passing through the points (10,3) and (-2,-3).
The equation of the line is
Answer:
[tex]y=\frac{1}{2} x-2[/tex]
A rectangle has an area of 943 square feet. Its width is five feet less than twice the length. Find the measures
of the length and width of the rectangle.
Answer: the rectangle is 23 x 41
Step-by-step explanation:
x = length
2x - 5 = width
A = length x width = (x)(2x-5) = 943
2[tex]x^{2}[/tex] - 5x - 943 = 0
use quadratic equation to solve for x:
a = 2, b = -5, c = -943
roots are 23, -20.5
x = 23 (length)
2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)
Verizon charges $0.50 per minute plus a monthly base fee. In October, Noah used 200 minutes and his bill was $100
The monthly base fee of the situation is $0
How to determine the monthly base fee of the situationFrom the question, we have the following parameters that can be used in our computation:
Charges per minute = $0.50 per minute
Number of minutes = 200 minutes
Total charges = $100
The above parameters mean that
Total charges = Monthly Base fee + Charges per minute x Number of minute
Substitute the known values in the above equation, so, we have the following representation
Monthly base fee + 0.50 * 200 = 100
This gives
Monthly base fee + 100 = 100
Subtract 100 from both sides
Monthly base fee = 0
Hence, the monthly base fee is $0
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Express the following fraction in simplest form using only positive exponents.
The fracion 12k⁸/4(k⁵)² expressed in its simplest form is the expression 3/k².
How to simply the expression in fractionTo simplify fraction, we need to factorise the denominator and numerator, and then look for common factors in the numerator and denominator and cancel.
Given the fraction;
12k⁸/4(k⁵)² = 3 × 4 × k⁸/k² × 4 × k⁸ {expressed to get a common factor}
12k⁸/4(k⁵)² = 3 × 4k⁸/k² × 4k⁸
4k⁸ is a common factor to the numerator and denominator, so we cancel it out
12k⁸/4(k⁵)² = 3/k²
Therefore, the simplest form of the fracion 12k⁸/4(k⁵)² is derived as the expression 3/k.
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Ariane borrow $500 on a 3−year loan. She i charged 5% imple interet per year. How much interet i he charged for 3 year? What i the total amount he ha to pay back?
The interest charged for 3 years would be $75 ($500 x 0.05 x 3). The total amount Ariane has to pay back would be $575 ($500 + $75).
What does a simple interest mean?Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.
How is a simple interest calculated?To calculate simple interest, multiply the principal sum by the time period, interest rate, and time period. Simple interest is calculated as follows: "Simple Interest = Principal x Interest Rate x Time." This equation provides the simplest method for calculating interest.
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help pls
Write the equation of the line in slope-intercept form that is perpendicular to
y = -x – 18 and passes through (-6, 11).
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
The line in slope-intercept form that is perpendicular to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex].
As we know the slope of line is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y intercept.
Given points are [tex](-6,11)[/tex].
If we want to describe the perpendicular line to the original line then the slope of line is
[tex]m_2=-\frac{1}{m_1}[/tex]
In our given slope of line
[tex]y = -x -18[/tex]
where [tex]m_1=-1[/tex]
So,
[tex]m_2=-\frac{1}{m_1}\\\\m_2=-\frac{1}{-1}\\\\m_2=1[/tex]
Now for the slope of second line we use the point slope from the construct equation then,
[tex]y-y_1=m_2(x-x_1)\\\\y-11=1(x-(-6))\\\\y-11=x+6\\\\y=x+6+11\\\\y=x+17[/tex]
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
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slope of a line that passes through the points (-4,-7) and (-2,-19) in simplest form
Answer:
m=-6
Step-by-step explanation:
use slope formula to solve
m= rise/run=y2-y1/x2-x1
what is the answer i need answers now I will fail
The amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups. So, option D is correct.
What is meant by mixed fraction?A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance.
You can write mixed numbers with or without the word "and," for example, 5 and 3/4 . The mixed number must have a valid fraction as its fractional component. A correct fraction, such as 37, has a numerator that is less than the denominator.
Given,
The amount of orange juice= 3 [tex]\frac{1}{3}[/tex] cups
The amount of grape juice=6 [tex]\frac{1}{2}[/tex] cups
The amount of cherry juice= 4 [tex]\frac{1}{8}[/tex] cups
The amount of club soda=1 [tex]\frac{1}{4}[/tex] cups
So, 3 [tex]\frac{1}{3}[/tex]+6 [tex]\frac{1}{2}[/tex] + 4 [tex]\frac{1}{8}[/tex]
=(10/3)+(13/2)+(33/8)
=(10/3)+(13/2)+(33/8)
=(80+156+99)/24
=335/24
=13.95
≈14 cups approximately
Therefore, the amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups.
So, option D is correct.
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Pls help fast i need help right neow.
[tex]\angle R \cong \angle STV[/tex]: Alternate interior angles theorem
[tex]\angle TSV \cong \angle U[/tex]: Alternate interior angles theorem
[tex]\angle R \cong \angle TSV[/tex]: Transitive property of congruence
[tex]\angle R \cong \angle U[/tex]: Transitive property of congruence
I need help on these questions.
can someone help with this thank you so much .
Answer:
NO=6
Step-by-step explanation:
If MP=16 and NP=13 that means MN=3 and MO=9 so that makes NO=6
the pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams. true false
the Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams: True.
What is Pearson product moment correlation?A measure of the degree and direction of relationship between two variables assessed on at least an interval scale is the Pearson product-moment correlation coefficient, or Pearson's correlation.
If you want to determine whether there is a linear relationship between two quantitative variables, you may use Pearson's correlation. The expectation of a linear relationship between those variables is the sole part of the study hypothesis.
This approach finds the precise amount or degree of correlation between any two variables and tells if there is or is not any correlation between them.
Thus, the given statement is true.
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The polynomial p(x)=-2x+3x+4 is given. Which conclusion is valid if p(1)=5
The value of the polynomial p(x) = -2x + 3x + 4 when x is 5 will be 9
How to calculate the value of the polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.
A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.
p(x) = -2x + 3x + 4
when x = 5
= -2x + 3x + 4
= -2(5) + 3(5) + 4
= -10 + 15 + 4
= 9
Note that the information you gave wasn't complete.
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A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downtream 70 mile in 2 hour. Write a ytem to repreent the ituation. Then find the peed of the boat and the peed of the current. Ue b for boat and c for current
The speed of boat is 14 miles per hour and the speed of current 35 mile per hour
Speed:
The general formula to calculate the speed is written as
Speed = Distance/Time
Given,
A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downstream 70 mile in 2 hour.
Here we need to find the speed of boat and the speed of current.
While we looking into the given question, we have identified the following values,
Distance = 42 mile
time = 3 hour
Then the speed is calculated as,
=> speed = 42/3
=> speed = 14 miles per hour
Similarly, for the current is
distance = 70 miles
time = 2 hour
Then the speed is calculated as,
=> speed = 70/2 = 35 miles per hour.
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Madison is reeling in her string at a steady rate the linear equation 3y - 9x = -81 can be used to find y the number of feet of kite string she still needs to reel in after x seconds after the points (0, -27). And (-9,0) on the line? Show your work
Point ( 0 , -27 ) on the line and ( -9 , 0 ) are not on the line
Given :
Madison is reeling in her string at a steady rate the linear equation 3y - 9x = -81 can be used to find y the number of feet of kite string she still needs to reel in after x seconds .
Points ( 0 , -27 )
when x = 0
3y - 9 * 0 = -81
3y - 0 = -81
3y = -81
y = -81 / 3
y = -27
so point ( 0 , -27 ) on the line .
when y = 0
3 * 0 - 9x = -81
0 - 9x = -81
-9x = -81
x = 81/9
x = 9
so ( -9 , 0 ) are not on the line
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a sample of size 115 will be drawn from a population with mean 48 and standard deviation 12 . use the ti-83 plus/ti-84 plus calculator. (b) find the 25th percentile of x . round the answer to at least two decimal places. the 25th percentile is
Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.
what is mean ?A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.
calculation
a) µ = 48
σ = 12
n= 115
X = 45
Z =(X - µ )/(σ/√n) = (45-48)/(12/√115)= -2.68
P(X<45) = P(Z<-2.68) = 0.0037
b) µ = 48.00
σ = 12.00
n= 115.00
P(X ≤ x) = 0.2500
z value at 0.25= -0.674 (excel formula =NORMSINV(0.25))
z=(x-µ)/(σ/√n)
X=z * σ/√n +µ= -0.674*12/√115+48= 47.25
Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.
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In a race, Jason's position was −11 1/5 feet relative to the leader after 1 3/4 minutes. On average, how much did Jason's position relative to the leader change per minute? Enter your answer as a mixed number, in simplified form, in the box.
The way Jason's position relative to the leader changed per minute is; 6²/₅ ft/minute
How to solve fractions?We are told that Jason's position was 11 ¹/₅ feet relative to the leader after 1 ³/₄minutes.
Now, the fractions are in mixed fraction form and so let us convert them to improper fractions to get;
⁵⁶/₅ and ⁷/₄
Thus, the way Jason's position relative to the leader changed per minute is; ⁵⁶/₅ ÷ ⁷/₄
= ⁵⁶/₅ * ⁴/₇
= 32/5
= 6²/₅ ft/minute
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Why do you need to state restrictions on the variable when dividing rational expressions?.
It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original.
What is rational expressions?
The ratio of two polynomials is a rational expression. F can be expressed in the form p/q, where p and q are polynomials, if f is a rational expression.
Fractional terms are seen in rational expressions. We include constraints because with some x values, the equation may become undefined. Undefined inquiries are hypothetical or ideal. The seven expressions for undefined words are (∞-∞),∞^∞, N/0, 0⁰, 1^∞, ∞/∞ and 0×∞ respectively. N/0 is the most typical constraint on rational expressions. Any number divided by 0 is therefore undefined. For instance, if you substitute 0 for x in the case of the function f(x) = 6/x2, the outcome is 6/0, which is undefined. If you graphed this function, you would see a break at x=0.
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if the equation x^2 + 16x + c = 0 has only one real solution, the value of c must equal
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
Discriminant:The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.
The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by
Discriminant Δ = b² - 4acHere we have
x² + 16x + c = 0 equation has only one real solution
Compare given equation with ax²+ bx + c = 0
=> a = 1, and b = 16
As we know when an equation has only one real solution
then its Discriminant will be equal to zero
=> b² - 4ac = 0
By the above values,
=> 16² - 4(1)c = 0
=> 256 - 4c = 0
=> 4c = 256
=> c = 256/4
=> c = 64
Therefore,
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
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Is 4,6,8 a right triangle
Answer: It is an obtuse triangle.
Answer: No
Step-by-step explanation:
To know if a triangle is a right triangle, we can use Pythagorean Theorem to test.
Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
[tex]4^2+6^2=8^2[/tex] [exponents]
[tex]16+36=64[/tex] [add]
[tex]52\neq 64[/tex]
Therefore, this is not a right triangle.