A base is a negative number and an exponent is also a negative number is explained in two ways:
(a) if the negative exponent is an even number, then the result will be a positive number.
(b) if the negative exponent is an odd number, then the result will be a negative number.
What is the required negative exponential formula?The required negative exponential formula is
a⁻ᵇ = 1/aᵇ or 1/a⁻ᵇ = aᵇ
Calculation:Consider two negative numbers '-x' as the base and '-n' as the exponent.
So, the given statement in mathematical form is as below:
⇔ (-x)⁻ⁿ
Then, we can evaluate them in two ways by considering 'n' to be an even and an odd number.
(a) If 'n' is an even number:
from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write
(-x)⁻ⁿ = 1/(-x)ⁿ
Since 'n' is an even number (-x)ⁿ = xⁿ
So, the result will be a positive rational or decimal number.
I.e., (-x)⁻ⁿ = 1/xⁿ
(b) If 'n' is an odd number:
from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write
(-x)⁻ⁿ = 1/(-x)ⁿ
Since 'n' is an odd number (-x)ⁿ = -xⁿ
So, the result will be a negative rational or decimal number.
I.e., (-x)⁻ⁿ = -1/xⁿ
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demonstrate how you would employ fourier analysis to determine the frequencies of any other particular chords at varying volumes of your own choosing
The use of Fourier analysis in the chords of varying volumes is explained below .
What is Fourier Series ?
The Fourier Series can be defined as a expansion of a periodic function f(x) in terms of infinite sum of sine and cosine .
The Fourier Series make use of orthogonality relationship of sine and cosine function.
The process in which the Fourier Series analysis helps in determine the frequencies of any other particular chords at varying volumes is :
the Fourier series convert the time-domain input signal into a frequency-domain representation which is analyzed for the intensities of specific pitches.
and the relationship between the pitches at a particular given time is then analyzed to find the chord that is being played.
Therefore , the process of Fourier series in music is explained above .
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Questionaire below Image
Answer: the first one is 30 ml
Please help me with this question
Answer:
2093pi/90 cm
Step-by-step explanation:
You want the exact length of the arc subtended by a 182° central angle in a circle of radius 23 cm.
Arc lengthThe length of an arc of a circle is given by ...
s = rθ
where θ is the central angle in radians.
ApplicationThe radian measure of an angle of 182° is ...
182°(π/180°) = 91π/90 . . . . radians
Then the arc length is ...
s = (23 cm)(91π/90) = 2093π/90 cm
If f(a)=3a+5 and g(a) =a^2+4, find f(-2)-g(-2)
The value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.
What is function?In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.
Given function:
f(a) = 3a + 5 and g(a) = a² + 4
Calculate the f(-2) - g(-2) by putting value -2 in both function
f(-2) = 3(-2) + 5 = -6 + 5
f(-2) = -1
g(-2) = (-2)² + 4
g(-2) = 4 + 4
g(-2) = 8
Hence, f(-2) - g(-2) = -1 - 8 = -9
Therefore, the value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.
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What is the length hypotenuse of a right triangle with legs 8 units and 6 units?; What is the length of the hypotenuse for a right triangle with leg a 8 and leg B 15?; How do you find the length of one leg of a right triangle?; How do you find the length of the legs of a right triangle with the hypotenuse?
The length of the hypotenuse with legs 8 units and 6 units is 10 units and with leg 8 units and 15 units is 17 units. We calculate the length of a leg of the right triangle by using formula [tex]h ^ {2} = p ^ {2} + b ^{2}[/tex]
What is a right-angle triangle?If one of the angles in a triangle is 90 degrees, the triangle is said to have a right angle. The term "right angle" refers to angles in right triangles that are 90 degrees. The side opposite in a 90° angle is the hypotenuse. The hypotenuse is always the longest side. The sum of the other two inner angles is 90 degrees.
What is the Pythagorean theorem for right angle triangle?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
length of legs = 8 units and 6 units
hypotenuse = [tex]\sqrt {8 ^ {2}+6 ^ {2}}[/tex] = 10 units
length of legs = 8 units and 15 units
hypotenuse = [tex]\sqrt {8 ^ {2}+15 ^ {2}}[/tex] = 17 units
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Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar field or a vector field.a. curl f b. grad f c. div F d. curl(grad f) e. grad F f. grad(div F) g. div(grad f) h. grad(div f) i. curl(curl F) j. div(div F) k. (grad f) x (div F) l. div(curl(grad f))
Let f be a scalar field and F a vector field.
a) False- can not take the curl of a scalar field.
b)True- it is a vector fields.
c)True- it is a scalar fields.
d)True- it is a vector fields.
e)False- can not take grad of a vector field.
f)True- vector fields.
g)True- - scalar fields.
h)False- can not take div of a scalar field.
i)True- - scalar fields.
j)False- can not take div of a scalar field.
k)False- can not cross product a vector with a scalar.
l)True- vector fields.
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Flour is sold in 3-pounds bags.how many pounds are in 7 bags.
Answer: 21
Step-by-step explanation: multiply 7 by 3, which = 21
Match each of the following planar vector fields with the corresponding plot. Note that the vectors are scaled to avoid overlap. A
nswer Bank F(x, y)=(8,8) F(x, y)=(8,0) F(x, y)=(0,8) F(x, y)=(-8,0)
The vector are quantity that has both magnitude and direction. they are normally visualized in graph.
A vector - values function F : R² ---> R² can be visualized as a vector field. At a point (x,y) , we plot a value of F(x,y) as a vector with the tail anchored as (x,y)
If we visualize the vector field it will look like an explosion emanating from the origin.
At each point (x,y) , the vector F(x,y) points precisely away from the origin.
If you drew the arrows to scale they would be as long as the distance to the origin but again the drawn arrows are shorter than the actual values of the vector field
The graph of a vector field is created by pointing arrows one at a time of substituting points into the plane to determine what error to draw at the point
The question is incomplete so, I have answered in general
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the left-moving pulse could be described by the following type of equation: yleft(x,t)
The equation y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second.
i) Direction of wave propagation is negative x-axis.
ii) The wave speed is 1.25m/s.
iii)The maximum displacement from the mean position (i.e., the amplitude of the wave) is 0.16 m.
iv)The wave pulse is symmetric.
We compare the given wave equation from the standard wave equation. On comparing, direction and wave speed is found out. The Remaining two parts are found by maxima concept and changing x by −x at t=0 to get a wave is symmetric.
Moving pulse is given by
⇒y(x,t)=0.8[(4x+5t)2+5]
Comparing (4x+5t) with (ax+bt) then we get,
⇒a=4 and b=5 ⋯⋯⋯(1)
(i) When coefficients of x and t are positive then the wave pulse is moving negative x-direction. So, given an equation with coefficients a = 4 and b= 5 are positive. Therefore, the direction of the given equation will be negative x axis.
(ii) After getting the coefficient a and b, we can calculate the speed by determining the value of b/a. And we have value of a =4 and b =5 from the equation (1) .Then speed of the wave will be
=> b/a=5/4
=> speed of the wave =1.25m/s
(iii) To get the maximum displacement from the mean position we put (4x+5t)=0. As the denominator is minimum, the fraction will be maximum. Therefore displacement will be
=> y=0.85, putting the (4x+5t) is equal to zero.
After simplify we get,
=> y=0.16 m
Hence maximum displacement is 0.16m from the mean position,
(iv) We replace x by −x and also put t= 0 in the given equation. If the equation does not change, replacing the x by −x, it will be symmetric otherwise not.
Putting t=0 in the given equation y(x,t) we get,
=> y=0.8(4x)2+5
Now replace x by −x on the above equation we get, y=0.8(4x)2+5
there will not be any change. Therefore, the given equation is symmetric.
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Complete question:
If y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second. Find
(i) Direction of wave propagation.
(ii) The wave speed.
(iii) The maximum displacement from the mean position (i.e., the amplitude of the wave)
(iv) Whether the wave pulse is symmetric or not.
melissa has $5000 and adds $20 each week to it. chris has $6820 and spends $50 from it each week. after how many weeks will both melissa and chris have the same amount
Answer:
It will take approximately 36.4 weeks for Melissa and Chris to have the same amount of money.
Step-by-step explanation:
To determine how many weeks it will take for Melissa and Chris to have the same amount of money, you can set up an equation based on the information given. Let W be the number of weeks it takes for Melissa and Chris to have the same amount of money.
Melissa's total amount of money after W weeks will be 5000 + 20W.
Chris's total amount of money after W weeks will be 6820 - 50W.
Therefore, you can set up the equation 5000 + 20W = 6820 - 50W and solve for W.
First, you can add 50W to both sides of the equation to get 50W + 5000 = 6820.
Next, you can subtract 5000 from both sides of the equation to get 50W = 1820.
Finally, you can divide both sides of the equation by 50 to get W = 36.4.
the regression equation is Y = 29.29 -0.88X, the sample size is 25, and the standard error of the slope is 0.22.
The test statistic for the test of whether the slope is of zero is given as follows:
t = -20.
How to calculate the test statistic?The equation that gives the test statistic is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The value tested of the slope is of:
[tex]\mu = 0[/tex]
The regression line in this problem is of y = 29.29 - 0.88x, hence the mean slope is of:
[tex]\overline{x} = -0.88[/tex]
The standard error and the sample size are given as follows:
s = 0.22, n = 25.
Then the test statistic is calculated as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-0.88 - 0}{\frac{0.22}{\sqrt{25}}}[/tex]
t = -20.
Missing InformationThe problem asks for the test statistic regarding whether the slope assumes a value of zero or different of zero.
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How do you determine if a given graph represents a quadratic equation?
A function's graph will always be quadratic if the equation includes the variable x2.
What is quadratic equation?Any equation that can be written in standard form, with x denoting an unknown value and a, b, and c denoting known integers, is referred to as a quadratic equation in algebra. In general, it is assumed that a > 0; equations with a = 0 are thought to be degenerate since they become linear or even more basic.
Examining the graph's data plotting will help you distinguish between a linear and a quadratic graph. A linear graph depicts a direct link between two variables when it follows a straight line. Parabolas are used to graph quadratic equations, on the other hand. As a result, the data will be represented graphically as a "open" or "upside-down" U-shaped curve.
A function's graph will always be quadratic if the equation includes the variable x2.
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How many line segments does a triangle have?
There are three line segments in a triangle. Since there are three vertices in a triangle, they form three line segments.
What is a line segment?A line segment is formed by two endpoints. It has a certain length or distance between its endpoints.A line segment is represented by a line without arrows over two ends of a line segment.Example: A line segment formed by the two points A and B is represented as [tex]\overline{AB}[/tex].Line segments in a triangle:Consider a triangle ABC. It has three vertices A, B, and C.
And it has three angles ∠A, ∠B, and ∠C.
So, the line segments formed by these three vertices are [tex]\overline{AB}[/tex], [tex]\overline{BC}[/tex], and [tex]\overline{CA}[/tex].
So, a closed figure will form by connecting these three vertices. That closed figure is said to be a triangle.
Therefore, there are 3 line segments in a triangle.
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an advantage of the exponential smoothing method over the moving average method is that it assigns exponentially weights as the observations get older.
Exponential smoothing of time collection records assigns exponentially lowering weights for latest to oldest observations.
In different words, the older the records, the much less priority (“weight”) the records is given; more moderns records is visible as extra applicable and is assigned extra weight. Smoothing parameters (smoothing constants),denoted through α, decide the weights for observations.
The simple formulation is:
St = ayt-1 + (1 - a) S-1
Where:
α = the smoothing constant, a fee from zero to 1. When α is near zero, smoothing takes place extra slowly. Following this, the satisfactory fee for α is the only that outcomes withinside the smallest suggest squared error (MSE).and t = time period.
One of the blessings of Exponential smoothing is ,the forecast may be built the use of most effective 3 values.
Only 3 portions of records are required for exponential smoothing methods.
1. It desires the forecast for the maximum latest time period.
2. It desires the real fee for that point period.
3. It desires the fee of the smoothing constant, a weighting thing that displays the load given to the maximum latest records values.
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suppose that and use phasors to reduce the sum to a single term of the form draw a phasor diagram, showing and state the phase relationships between each pair of these phasors
Answer:
I hope the best for you
Step-by-step explanation:
have a good day :)!!
The table to the right shows binned data for the percentages of high school graduates who took a national ___ in 2016 among the 50 states and the District of Columbia. Make a histogram of the data.Test Takers by State Percentage of high school graduates Number of states s 20% 2 21-40% 13 41-60% 4 61-80% 7 81-100% 25 O A. 0 B. O C. D. 30- a Number of states Number of states 0 0 100 Percentage of students 100 Percentage of students 0 100 Percentage of students 0- 0 100 Percentage of students
Number of states , 100 Percentage of students 0- 0 100 Percentage of students 20 21- 40 41- 60 61- 80 81- 100
1. Draw a horizontal axis with percentages of students (0 - 100%) marked along the axis.
2. Draw a vertical axis with number of states (0 - 25) marked along the axis.
3. Divide the horizontal axis into sections, with each section corresponding to one of the percentage ranges in the table (20%, 21-40%, 41-60%, 61-80%, 81-100%).
4. For each section, draw a rectangle with a height that corresponds to the number of states in that range. For example, for the 81-100% section, the rectangle should have a height of 25.
5. Label each rectangle with the corresponding percentage range.
The final result should be a histogram that shows the percentage of high school graduates who took a national test in 2016 among the 50 states and the District of Columbia.
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Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P.x+y=96 and P=x^2y is maximizeda. Solve x+y=96 for y.y=b. Substitute the result from part a into the equation P=x2y for the variable that is to be maximized.P=c. Find the domain of the function P found in part b.= ? (Simplify your answer. Answer in interval notation.)d. Find dP/dx. Solve the equation dP/dx=0.dP/dx=Solve the equationx=? (Use a comma to separate answers as needed.)e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0).P(0)=? (Simplify your answer.)Determine P(64)=? (Simplify your answer.)Find P(96)=? (Simplify your answer.)f. Give the maximum value of P, as well as the two numbers x and y for which x2y is that value.The maximum value of P is =?The values of x and y are x= and y=
the two numbers x and y for which x2y is that value, as well as the highest possible value .P at any solutions found in part d, as well as the endpoints of the domain found as The maximum value of P is =4092, The values of x and y are x=64, y=32.
a. Solve x+y=96 for y.
y=96-x
b. In the equation P=x2y, replace the variable to be maximized with the outcome from part a.
P=x^2(96-x)
c. Find the domain of the function P found in part b.
Dom(P)=[0,96]
d. Find dP/dx. Solve the equation dP/dx=0.
dP/dx=2x(96-x)-x^2=0
Solve the equation
x=0,96
e. Evaluate P at any solutions identified in part d, as well as the endpoints of the domain found in part c.
P(0)=0
P(64)=4096
P(96)=0
f. provide the maximum value of P, as well as the two numbers x and y for which x2y is that value.
The maximum value of P is 4096
The values of x and y that maximize P are x=64, y=32
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Find the length of side AC in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and
The length of AB is equal to 12cm
How to find the length of a triangle?
If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)
Leg b = √(c² - a²) if leg b is unknown.
The equation is c = √(a² + b²) for the hypotenuse c that is absent.
What is the side length of a triangle?According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition. This indicates that a triangle with the dimensions 3, 4, and 9 is impossible because 3 + 4 =7 < 9.
a = √(c² - b²)
a=?,b=5,c=13
a=√169-25
a=12cm
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what is 3 divided by 1/3; 9 divided by 1/4; 1/8 divided by 4; 12 divided by 1/3
12 divided by 1/3 is 1
9 divided by 1/4 is 2.25
1/8 divided by 4 is 0.5
12 divided by 1/3 is 4
Division:
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer.
given that
3 divided by 1/3
3× 1/3 = 1
9 divided by 1/4
9 × 1/4 = 2.25
1/8 divided by 4
4 × 1/8 = 0.5
12 divided by 1/3
12 × 1/3 = 4
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Eli wants to combine 0.5 gallons of a 10% acid solution with a 35% solution to make a 15% acetic acid solution. He needs to determine how many gallons of 35% solution are needed.
Eli decides to let v represent the volume of the 35% solution and makes a table to help solve the problem.
Help Eli by completing the table.
Drag each tile to the correct cell in the table.
The required volume of the 35% acetic acid solution that will combine with the 0.5 gallons of the 10% acetic acid solution to make a solution that is 15% acetic acid solution is 0.125 gallons, which indicates, using the dilution formula, that the correct options for the completed table are;
[tex]{}[/tex] Amount of Solution Acid Concentration Amount of Acid
10% Acid[tex]{}[/tex] 0.5 0.10 (0.10)·(0.5)
35% Acid [tex]{}[/tex] v 0.35 0.35·v
Mixture v + 0.5 [tex]{}[/tex] 0.15 0.15·(v + 0.5)
What is the dilution formula?The dilution formula indicates that the product of the concentration and volume of the initial solution is equivalent to the product of the concentration and volume of the intended solution to be made.
The volume of the 10% acetic acid solution in the mixture = 0.5 gallons
The volume of the 35% acetic acid solution = v
The concentration of the acetic acid solution Eli wants to make = 15%
The dilution formula for mixtures is; C₁·V₁ = C₂·V₂
Therefore; 0.1 × 0.5 + 0.35 × v = (v + 0.5) × 0.15
0.35 × v - (v + 0.5) × 0.15 = -0.1 × 0.5 = -0.05
0.2·v - 0.075 = -0.05
v = (0.075 - 0.05)/0.2 = 0.125
The volume of the 35% solution required, v = 0.125 gallons
The completed table is therefore;
[tex]{}[/tex] Amount of Solution Acid Concentration Amount of Acid
10% Acid [tex]{}[/tex] 0.5 0.10 (0.10)·(0.5)
35% Acid [tex]{}[/tex] v 0.35 0.35·v
Mixture v + 0.5 [tex]{}[/tex] 0.15 0.15·(v + 0.5)
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test the series for convergence or divergence. if the series is convergent, use the alternating series estimation theorem to determine how many terms we need to add in order to find the sum with an error less than 0.0001?
By using the alternating series estimation theorem we found that the number of terms we need to add in order to find the sum with an error less than 0.0001 is 7.
We must employ one of the convergence tests to determine whether the provided series is convergent or divergent. The alternating series test, which states that a series converges if it takes the form ∑ [tex](-1)^{n}[/tex] x an, where 'an' is a decreasing sequence of positive terms, is the most applicable test for this series.
∑ [tex](-1)^{n}[/tex] x an
a n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex]
by taking the derivative of the expression for a n, this sequence is decreasing and showing that it is always negative. given by a'n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex] [tex]- \frac{(n + 1) X 2)}{(n^2 + 2n + 3)^2}[/tex]
= [tex]\frac{(-2n - 2)}{(n^2 + 2n + 3)^2}[/tex]
for all values of n it is negative, therefore the sequence a n is decreasing. Thus, given series satisfies the conditions of the alternating series test. Therefore, the series is convergent.
The alternating series estimation theorem can be used to determine how many terms are required to be added in order to find the total with an error of less than 0.0001. This asserts that the first disregarded term in an alternating series is smaller than the error in the series' sum. The error in the sum of the series with N + 1 terms is therefore smaller than the value of the (N + 1)th term in the series if we add N terms to the series and the error is less than E.
Find the first term in the series that is less than 0.0001 in order to calculate the number of terms we must add to the series in order to find the total with an error smaller than 0.0001.
given series that a 1 = [tex]\frac{2}{4}[/tex] = 0.5, a 2 = [tex]\frac{3}{9}[/tex] = 0.333, a 3 = [tex]\frac{4}{16}[/tex] = 0.25, and a 4 = [tex]\frac{5}{25}[/tex] = 0.2. Since the first term that is less than 0.0001 is a 7 = [tex]\frac{8}{64}[/tex] = 0.125, Adding, 7 terms to the series in order to find the sum with an error less than 0.0001.
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The wholesale price for a shirt is 5.50. A certain department store marks up the wholesale price by 90%. Find the price of the shirt in the department store.
Round your answer to the nearest cent, as necessary.
The price of the shirt if The wholesale price for a shirt is 5.50 and A certain department store marks up the wholesale price by 90% is $10.45.
What is the Wholesale price?The cost price of a certain product plus the profit margin earned by the manufacturer equals the wholesale price.
Given:
The wholesale price for a shirt is $5.50,
The markup price = 90%
Calculate the markup price as shown below,
The markup price = 90% of $5.50
The markup price = 90 / 100 × 5.50
The markup price = $4.95
Calculate the price of the shirt as shown below,
The price of a shirt = The markup price + The wholesale price of the shirt
The price of a shirt = $5.50 + $4.95
The price of a shirt = $10.45
Therefore, the price of the shirt if The wholesale price for a shirt is 5.50 and A certain department store marks up the wholesale price by 90% is $10.45.
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Angle M has a measure of 47°. What is the measure of angle PNL? 43° 47° 86° 94°
As angle M has a measure of 47°, then the measure of angle PNL is 43°
To find: the measure of ∠ PNL .
To proof
As given
∠ M = 47°
In ΔLMN
If the two sides of a triangle are equal and you use the property, the diagonals are also equal.
As given MN = LN
∠ M =∠ L = 47°
and ∠ MPN = 90 °
∠ MPN + ∠ NPL = 180° (Linear pair)
∠ NPL = 180° - 90°
∠ NPL = 90°
Now by using the angle sum property of a triangles.
in Δ NPL
∠NPL +∠PNL + ∠NLP = 180°
90 + 47 + ∠PNL = 180
137+ ∠PNL = 180
∠PNL = 180 - 137
∠PNL = 43 °
Therefor the Measure of angle PNL is 43°.
Hence proved
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1. Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists. (a) A relation R on N that is reflexive and symmetric but not transitive. (b) A relation S on N that is reflexive and transitive but not symmetric. (c) A relation T on N that is transitive and symmetric but not reflexive.
A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .
Given :
Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists.
a )
A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .
b )
A relation S on N that is reflexive and transitive but not symmetric is { MA , CT , RI } .
c )
A relation T on N that is transitive and symmetric but not reflexive is { ME , NH , VT } .
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the following expression is being factored. select the two values(with the correct signs) that will fill in the gaps of the parentheses.
x^2 - 10x + 24 = (x ) (x )
-4
+2
+12
-12
+4
+6
-2
-6
Answer:
-4, -6
Step-by-step explanation:
You want the constants that go into the binomial factors of x² -10x +24.
FactorsThe binomial constants used in the factors must have ...
a product of +24
a sum of -10.
The positive product means the two factors have the same sign. The negative sum tells you both signs are negative. The negative answer choices are -2, -4, -6. The only pair with a sum of -10 and a product of +24 is -4 and -6.
= (x -4)(x -6)
A student is ordering a flower arrangement. She can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30.
If roses cost $3 each and carnations cost $2 each, which inequality represents all possible combinations of x roses and y carnations?
The inequality represents all possible combinations of x roses and y carnations is 3x+2y≤30.
What is meant by inequality?Different types of inequalities can be represented by a number of different notations. A relationship between two expressions or values that is not equal in mathematics is referred to as an inequality. To correct an inequality, take the following actions: Prior to subtracting any fractions, multiply each phrase by the sum of the least common denominators of all the fractions. Step 2: To make the inequality simpler, combine related terms on both sides. Step 3: To calculate the value of the unknown, subtract or add the amounts from the numbers on either side.
The cost of each rose flower is $3
The cost of each carnation is $2
The cost for x roses will be 3x$
The cost for y carnations will be 2y$
The overall cost must be less than or equal to $30
Therefore, 3x+2y≤30.
Hence, the inequality represents all possible combinations of x roses and y carnations is 3x+2y≤30.
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TT D (t) = 10 + 4.9 cos ~t 6 The function D defined above models the depth, in feet; of the water t hours after 12 A.M. in a certain harbor: Which of the following presents the method for finding the instantaneous rate of change of the depth of the water; in feet per hour; at 6 AM ? A D(6)_D(O) 6_0 S 1.633 B D (6) = 0 D"' (6) = 1.343 D(6) = 5.100'
The method for finding the instantaneous rate of change of the depth of the water; in feet per hour; at 6 AM is B. D' ( 6 ) = 0 .
Given :
The function D ( t ) = 10 + 4.9 cos ( pi/6 * t )
D is defined above models the depth, in feet, of the water t hours after 12 am. Which of he following shows the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 am .
Differentiate :
D'( t ) = -4.9 sin ( πt / 6 ) ( π / 6 )
D'( 6 ) = -4.9 sin ( π ) ( π / 6 )
we know that
sin ( π ) = 0
so D'( 6 ) = 0
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Roberto's employer offers a sliding paid vacation. when he started work, he was given three paid days of vacation. For each six-month period he stays at the job, his vacation is increased by two days. Let x represent the number of 6-month periods worked and y represent the total number of paid vacation days. Write an equation that modes the relationship between these two variables.
Answer:
telecomunication of te following
The water in the swimming pool was as blue as the sky.
True or false. The author uses this figurative language to help the reader understand the color of the water.
True
False
Answer:
true
Step-by-step explanation:
the author compares the color of the water to the color of the sky. so that makes it figurative language.
hope this helps.
find total amount to be repaid. round to nearest cent as needed.
The total amount to be repaid by Neema will be $4135.50
How to calculate the total amount?It was illustrated that Neema bought appliances that cost $3805 at an interest charge of 5% and she will pay back in two years.
Since there is a $500 down payment, the remaining amount will be:
= $3805 - $500
= $3305
Therefore, the interest will be:
= PRT
= $3305 × 5% × 2
= $330.50
Therefore, total amount will be:
= $3305 + $500 + $330.50
= $4135.50
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