The required value of c is 9 so that [tex]f(c) =20[/tex] is true, where the function is defined by the equation f(x)=3x-7.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
To determine the value of c such that [tex]f(c) = 20[/tex], we can simply substitute in the given equation and solve for c.
So, we have:
[tex]f(c) = 3c - 7[/tex]
And, we know that [tex]f(c) = 20[/tex], so we can substitute to get:
20 = 3c - 7
Adding 7 to both sides, we get:
27 = 3c
Dividing both sides by 3, we get:
c = 9
Therefore, the value of c that satisfies the equation [tex]f(c) = 20[/tex] is 9.
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If a hexagon represents 1 whole, what fraction does each of the following shapes represent? Be prepared to show or explain your reasoning
The triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole trapezoid.
Determine the fractionEach of the shapes represent a different fraction of the whole trapezoid.
The triangle represents 1/4 of the whole trapezoid. This is because there are four triangles in the trapezoid, and each one is equal in size. Therefore, each triangle is 1/4 of the whole trapezoid. The rhombus represents 1/2 of the whole trapezoid. This is because there are two rhombuses in the trapezoid, and each one is equal in size. Therefore, each rhombus is 1/2 of the whole trapezoid.
The hexagon represents 1/1 of the whole trapezoid. This is because there is only one hexagon in the trapezoid, and it is equal in size to the whole trapezoid. Therefore, the hexagon is 1/1, or the whole trapezoid.
In conclusion, the triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole Hexagon. These fractions can be used to determine the value of each shape in relation to the whole trapezoid.
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A polynomial f (x) has the given zeros of 7, –1, and –3.
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form. Show all necessary calculations. (3 points)
Part B: Divide the polynomial f (x) by (x2 – x – 2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote. (4 points)
Part C: List all locations and types of discontinuities of the function g(x). Be sure to check for all asymptotes and holes. Show all necessary calculations. (3 point
The answers to all parts are shown below.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
Given:
The polynomial zeros are given as:
x = 7, x = -1 and x = -3
x - 7 = 0, x + 1 = 0 and x + 3 = 0
So, f(x) = (x - 7)(x + 1)(x + 3)
f(x) = (x - 7)(x² + 4x +3)
f(x) = x³ -3x² -25 x -21
Now, Rational function g(x)
g(x) = f(x) / (x² - x + 2)
After Factorizing
g(x) = (x-2) - 25x+ 25 / (x² - x + 2)
The slant asymptote is the quotient i.e. x - 2
Hence, the slant asymptote of the function g(x) is x - 2
So, the discontinuities of g(x)
g(x) = (x³ -3x² -25 x -21) / (x² - x + 2)
Set the denominator to 0
x² - x + 2 = 0
(x - 2)(x + 1) = 0
x= 2 or x= -1.
So, the discontinuities and their types are:
Essential discontinuity at x = 2
Removable discontinuity at x = -1
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Find f(4) for f(x) = x3 - 2x2 + 3x - 7
I'm not sure how to find out the x in f(x) in equations like this. Any help understanding this would be appreciated.
Answer:37
Step-by-step explanation:
just write 4 instead of x
f(4)=[tex]4^{3} -2*4^{2} +3*4-7=64-32+5=37[/tex]
A fifth-degree polynomial function has a zero at r = -3 with a multiplicity
of 2. It also has a zero at r = 2 with a multiplicity of 3. The value of the
function is negative when I = −4.
Which graph could model this polynomial function?
Answer:
The graph that could model this polynomial function will be a fourth-degree function.Step-by-step explanation:
It will have two roots at r = -3 and r = 2, and it will cross the x-axis twice at both those roots.It will also be negative for all values below -4, which means that it will also cross the x-axis two times above r = -4.World War II began in the year 1939.
Let x represent any year. Write an inequality in terms
of x and 1939 that is true only for values of x that
represent years before the start of World War II.
The Inequality to represent year is x < 1939.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Let x represent any year.
If we want years before 1939, then x must be less than 1939.
Then, the Inequality can be
x < 1939.
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Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their hcf is 101.
The smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101 are 1010 and 1313.
HCF (Highest Common Factor) of two numbers, which is the largest number that divides both numbers evenly.
Let's call the smaller of the two numbers "x". The larger number would be "x + 303".
The HCF of these two numbers must be 101, which means that 101 must be a factor of both x and x + 303.
To find the smallest possible value of x, we need to find the smallest number that is divisible by 101 and also a 4-digit number.
The smallest multiple of 101 that is a 4-digit number is
=> 101 x 10 = 1010.
Therefore, x = 1010.
The larger number would be
=> x + 303 = 1010 + 303 = 1313.
To check if the HCF of these two numbers is indeed 101, we can use the Euclidean Algorithm or the Prime Factorization method to find the HCF.
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Solve by substitution
**Pls explain answer
y = -6x + 5
-2x + y = 5
Answer: 0,5
x = 0
y = 5
Answer: (0,5)
Step-by-step explanation:
Since "y" is equal to -6x+5 everywhere you see a "y" you can replace it with -6x+5.
-2x-6x+5=5
Combine like terms
-8x+5=5
Isolate x (subtract 5 from both sides)
-8x=0
Solve for x
x=0
Now that you have the value for "x" you can substitute the value into either equation and solve for y
-2(0)+y =5
y=5
or
y=-6(0)+5
y=5
Exactly $9 was used to purchase an equal number of each of the three types of tokens
$0.10, $0.15 and $0.20, how many of each type of tokens were purchased?
A)45
B)30
C)25
D)20
E)15
Answer:
The answer is 20, so the answer is (D) 20.
Step-by-step explanation:
Let's say x is the number of tokens purchased for each of the three types. Then, the total amount spent is 0.10x + 0.15x + 0.20x = $9.
Combining like terms, we get 0.45x = $9.
Finally, dividing both sides by 0.45, we get x = 20.
So, 20 tokens were purchased for each of the three types.
The answer is 20, so the answer is (D) 20.
PLEASE HELPPPP I DONT UNDERSTAND ITTT
According to the information, we need 107.42ft of black cord and 26 yards of fabric to make the design.
How to find the amount of black cord we need?To find the amount of black cord that we need in this design we must calculate the perimeter of all the figures as shown below:
rectangle
16ft + 16ft + 10ft + 10ft = 52ftSquare
7ft + 7ft + 7ft + 7ft = 28fttriangle
2ft + 2ft + 2ft = 6ftCircle
2*3.14*1.5=9.42ftTotal
9.42ft + 24ft + 28ft + 52ft = 107.42ftHow much fabric do we need?To calculate the amount of fabric, we must find the visible area of the figures and calculate what the area is in yards.
rectangle:
16ft*10ft=160ftSquare:
7ft*7ft=49ftTriangle:
1.73ft * 2ft / 2 = 1.73ft1.73*4=6.92ftCircle:
3.14*1.5²=7.06ft160ft - 49ft = 11ft49ft - 8ft - 6.92ft = 34.08ft160ft * 0.11 = 17.6 = 18 yards49ft * 0.11 = 5.39 = 6 yards6.92ft * 0.11 = 0.76 = 1 yard7.06ft * 0.11 = 0.77 = 1 yardLearn more about inches in: brainly.com/question/16311877
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Are the lines with the equation y = -5x + 1 and y = -5x + 8 parallel? (use a graph, might help)
Answer:
Yes, the lines y = -5x + 1 and y = -5x + 8 are parallel. This is because they have the same slope (-5) but different y-intercepts (1 and 8). Parallel lines have the same slope, and different y-intercepts.
Answer:
For y = -5x + 1
x = [tex]\frac{1-y}{5}[/tex].
And
y = 1 - 5x.
Put on a graph: look at picture 1.
The for y = -5x + 8
x = [tex]\frac{8-y}{5}[/tex]
And
y = 8 - 5x.
Put on a graph: look at picture 2.
These two lines are parallel.
Can a continuous random variable take all values in an interval?
A continuous random variable can take all values in an interval, assuming that the interval is unbounded.
This is because a continuous random variable has an infinite number of possible outcomes, and the probability density function (PDF) of a continuous random variable is defined over a range of values rather than specific values.
For example, consider the normal distribution, which is a common continuous probability distribution. The PDF of a normal distribution is a bell-shaped curve that extends from negative infinity to positive infinity.
This means that a continuous random variable following a normal distribution can take any value on the real number line, with some values being more likely than others.
However, if the interval is bounded, then it is possible for a continuous random variable to not take all values within the interval. In this case, the probability density function is zero outside of the interval, and the random variable is restricted to the range of values within the interval.
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Which display is most likely to reveal association between X and Y ? A. Dot plot B. Scatter plot C. Histogram D. Pareto chart
Scatter plot Answ
Step-by-step explanation:
Does someone mind helping me with this? Thank you!
The required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.
What is point-slope form?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
To understand more about it and see some instances, watch this video.
Both the slope-intercept form and the point-slope form can be used to write the equation of a straight line.
The slope and ANY point on the line are highlighted using the point-slope form.
Slope intercept form merely shows the slope and the y-intercept of a line.
So, we have:
m = 1
And points are (12, -2) and (6, -8)
We need to use the points: (12, -2)
Now, form the equation as follows:
y - (-2) = m (x-12)
y + 2 = 1(x-12)
y+2 = x-12
Therefore, the required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.
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the product of permutation matrices is again a permutation matrix. True/False
The statement which is given as , "The product of permutation matrices is again a permutation matrix." is True.
A permutation matrix is a square matrix whose entries are either 0 or 1 and has exactly one "1" in each row and each column. In other words, it is a matrix that represents a permutation of the rows (or columns) of the identity matrix.
When two permutation matrices are multiplied, the result is another square matrix with exactly one "1" in each row and each column. To see why this is true, consider two permutation matrices, A and B. Suppose that A is a m x m matrix and B is a m x m matrix. The product of these two matrices is another m x m matrix, C = AB.
Each entry in the matrix C is given by the dot product of the corresponding row in A and the corresponding column in B. If the row in A has a "1" in the i-th position and the column in B has a "1" in the j-th position, then the i,j-th entry in C will be "1".
Since both A and B are permutation matrices, each row in A and each column in B has exactly one "1". This means that each row in C will have exactly one "1", and each column in C will also have exactly one "1". Hence, C is also a permutation matrix.
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2. In a bag of fruit Skittles, the ratio of strawberry to orange to lemon-lime is 4: 3:7. There are 56 Skittles in a bag.
Find the number of lemon-lime Skittles in the bag.
Answer:
28
Step-by-step explanation: 4+3+7=14
56/14=4
7*4=28
Answer:
28
Step-by-step explanation:
4x+3x+7x = 56
14x=56
x=4
7x ---> 7(4) ---> 28
So there are 28 lemon lime skittles in a bag
10. Sleeping 8 hours a day is the same as sleeping 10 days a month. How many days is this per year?
If there are 10 days of sleeping a month then in a year there are 120 days of sleeping.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Sleeping 8 hours a day is the same as sleeping 10 days a month.
In according to hours the number of hours sleeping in month will be
= 8 x 30
= 240 hours
= 240 / 24
= 10 days
So, in a year the number of days of sleeping is
= 10 x 12
= 120 days
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fuel pressure in the fuel tank of the space shuttle is decreasing at a rate of r(t)= 17e^-0.1t psi per second at time t in seconds. at what rate is pressure decreasing at 15 seconds
The pressure is decreasing at a rate of approximately 0.26 psi/s at t = 15 seconds.
What is pressure ?
In physics, pressure is the amount of force applied per unit area. It is a scalar quantity, which means that it has a magnitude but no direction. Pressure is typically denoted by the symbol P, and its units are commonly expressed in pascals (Pa), which is the SI unit of pressure.
Pressure can be defined as the amount of force F applied per unit area A:
P = F / A
For example, if a force of 100 newtons (N) is applied to an area of 2 square meters (m^2), then the pressure would be:
P = 100 N / 2 m^2 = 50 Pa
Pressure is an important concept in many areas of physics, including fluid dynamics, thermodynamics, and atmospheric science. It is commonly used to describe the behavior of gases and liquids under different conditions, such as changes in temperature or volume. Pressure can also be used to calculate other physical properties, such as the flow rate of a fluid or the speed of sound in a gas.
According to given condition :
The rate of change of the fuel pressure in the fuel tank of the space shuttle is given by the derivative of the function [tex]r(t) = 17e^(-0.1t)[/tex]psi per second with respect to time t. Taking the derivative of r(t), we get:
[tex]r'(t) = (-0.1) * 17e^(-0.1t)[/tex]Simplifying this expression, we get:
[tex]r'(t) = -1.7e^(-0.1t)[/tex]
To find the rate at which the pressure is decreasing at t = 15 seconds, we substitute t = 15 into the expression for r'(t):
[tex]r'(15) = -1.7e^(-0.1*15)[/tex]
r'(15) ≈ -0.26 psi/s
Therefore, the pressure is decreasing at a rate of approximately 0.26 psi/s at t = 15 seconds.
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what is the answer to this?
Answer:
Step-by-step explanation:
If I see this correctly it would be about 16 minutes he played football.
pls help me on all questions if you can
All the answers to the questions except which are impossible are illustrated below.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments are referred to as its edges or sides.
9. We know, The sum of all the interior angles of a 'n' sided polygon is,
= 180(n - 2).
= 180(10 - 2).
= 180×8.
= 1440°.
11. 180(n - 2) = 1260.
180n - 360 = 1260.
180n = 1620.
n = 9.
13. Mesure of exterior angles is,
= 360/n.
= 360/5.
= 72°.
14. 360/60 = 6 sides, As EA = 360/n, n = 360/EA.
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What are the outliers in this data set?
26, 51, 53, 57, 57, 62, 65, 71, 93
Select EACH correct answer.
Answer:
What are the outliers in this data set?
26, 51, 53, 57, 57, 62, 65, 71, 93
Select EACH correct answer.
26, 71, 93Step-by-step explanation:
Tell me if I'm wrong, You're welcome.
The radius of a circle is 21 m. Find its area to the nearest whole number.
Answer: A≈1385.44m²
Step-by-step explanation:
A=πr2=π·212≈1385.44236m²
Can somebody help me on this? I answered all of them on the right side but I don’t know if it’s right. The answer choices are- additive property of angle measure / additive property of length / all right angles are congruent / alternate interior angles theorem / angle side angle / definition of angle bisector/ definition of equilateral triangle / definition of midpoint / given/ and reflexive property of congruence. I know this a lot but that is all the answer choices.
The completed two-column table that proves ΔQTU is congruent to ΔRSU can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{RS}[/tex] ⊥ [tex]\overline{RT}[/tex] [tex]{}[/tex] Given
2. [tex]\overline{QT}[/tex] ⊥ [tex]\overline{QS}[/tex] [tex]{}[/tex] Given
3. [tex]\overline{QU}[/tex] ≅ [tex]\overline{RU}[/tex] [tex]{}[/tex] Given
4. ∠Q ≅ ∠R [tex]{}[/tex] All 90° angle are congruent
5. ∠QUT ≅ ∠RUS [tex]{}[/tex] Vertical Angle Theorem
6. ΔQTU ≅ ΔRSU [tex]{}[/tex] ASA
What are congruent triangles?Congruent triangles are triangles that have the same size and shape.
The details of the reasons that are used to prove that the triangles ΔQTU and ΔRSU are congruent, can be presented as follows;
All 90° angle are congruent
The segments [tex]\overline{RS}[/tex] and [tex]\overline{RT}[/tex] are perpendicular, which indicates that the angle ∠R is a 90° angle. Similarly, segments [tex]\overline{QT}[/tex] and [tex]\overline{QS}[/tex] are perpendicular, therefore, ∠Q is a 90° angle, which indicates that we get;
m∠Q = m∠R = 90°
The definition of congruent angles, indicates; ∠Q ≅ ∠R
Vertical Angle Theorem
The vertical angle theorem states that the vertical angles formed by two intersecting lines are congruent.
ASA
The Angle-Side-Angle, (which can be abbreviated as ASA) congruence postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
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Help please helpppppppppppppppp
15x = 180
divide both by 15, and you get
x = 12
I'm unsure if this is correct
Answer: Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees
3 cm
20 cm
8 cm
5 cm
Find the lateral surface area of the solid above.
Answer:
Step-by-step explanation: 320 cm sq
I need help with this please and thank you.
Answer:
(3x -4 ) (x^2 -5x -1) multiply the binomial by trinomial3×^3 -15x^2 -3x -4x^2 +20x +4group like terms , then get your answer as3x^3 -19x^2 +17x +4what are 2 equations for d 2 miles and t 30 minutes
two equations are: v = u + 0.5a and (v)² = (u)² + 4a.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, the distance traveled by an object in t = 30 minutes is 2 miles
Let "v" be the final velocity of an object,
"u" be the initial velocity of an object,
and "a" be the acceleration of an object.
From the standard velocity equation:
final velocity = initial velocity + acceleration * time.....(1)
(final velocity)² = (initial velocity)² + 2*acceleration * distance....(1)
From equation (1)
v = u + a*30 minutes
time in hours,
v = u + 0.5a
From equation (2)
(v)² = (u)² + 2*a* 2
(v)² = (u)² + 4a
therefore, two equations are: v = u + 0.5a and (v)² = (u)² + 4a.
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The legs of a right triangle have lengths of
2x + 3 and 4x - 1. Which polynomial is equivalent
to c²?
A 6x + 2
B 4x² + 12x + 9
C 20x² + 4x + 10
D 36x² + 24x + 4
mai poured 2.6 of water into a partially-filled pitcher. the pitcher now contains 10.4.mai wants to know how many liters of water was originally in the pitcher.
Answer:
Step-by-step explanation:
Let's call the original volume of water in the pitcher "V". Then, after Mai added 2.6 liters, the total volume of water in the pitcher became V + 2.6 = 10.4 liters.
To find the original volume of water in the pitcher, we can isolate V by subtracting 2.6 from both sides of the equation:
V + 2.6 = 10.4
V = 10.4 - 2.6
V = 7.8 liters
So the original volume of water in the pitcher was 7.8 liters.
Answer: 7.8
Step-by-step explanation:
really sorry if im wrong
How do you use logarithmic differentiation to find the derivative of the function?
Answer: Logarithmic differentiation when the logarithm of an expression can be written in a form for which we can find the derivative more simply. Or, for which we can find the derivative at all.
HELP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answers and solutions
Step-by-step explanation: