what is the length of h in the following composite figure? all angles are right angles. 5 m 3 m 4 m 2 m
The length of h in the attached composite figure where all the angles are right angles is equal to 4m.
In the attached diagram of composite figure,
All are right angles.
Composite figure consist two rectangles,
Upper and lower rectangles.
length of the upper rectangle is equal to 5m
Width of the upper rectangle is equal to 'h' m
Width of the lower rectangle is equal to 2m
Length of each dash '-' mark is equals to 1m.
length of 'h'm is equals
= 2 m + 2 dash marks
= 2m + 2m
= 4m
Therefore, the length of the h in the composite figure ( attached diagram ) is equals to 4m.
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The above question is incomplete, the complete question is:
What is the length of h in the following composite figure? All angles are right angles.
5 m
4 m
3 m
2 m
Diagram is attached.
Answer:
4 m is ur answer
Step-by-step explanation:
hope this helps
Factor the polynomial completely:
78¹ - 148³ - 560s²
Answer: 2s²(39 - 74s - 280s)(s - 2)(s + 7/2)
Step-by-step explanation:
To factor the polynomial 78s - 148s³ - 560s² completely, we can first factor out a common factor of 2s²:
2s²(39 - 74s - 280s)
Then, we can factor the quadratic expression inside the parentheses using the quadratic formula:
s = [-(-74) ± √((-74)² - 4(39)(-280))] / 2(39)
s = [74 ± √(54724)] / 78
s = [74 ± 2√13681] / 78
s = [74 ± 2×117] / 78
Therefore, the roots of the quadratic expression are:
s = 2 or s = -7/2
Substituting these values back into the factored expression, we get:
2s²(39 - 74s - 280s) = 2s²(39 - 74(2) - 280(2)) = -1240s²
2s²(39 - 74s - 280s) = 2s²(39 - 74(-7/2) - 280(-7/2)) = 2450s²
So the completely factored form of the polynomial is:
2s²(39 - 74s - 280s)(s - 2)(s + 7/2)
Write the function for the table in standard form?
I tried to work out the problem and got y = -x^2 -6x + 2 not sure if that is correct. Please see steps on the attached file.
The value of the quadratic equation in the standard form is y = -x² -6x + 2.
What is quadratic equation?y = ax² + bx + c, where a, b, and c are constants and an is not equal to 0, is a quadratic equation in standard form. A parabolic function's vertex, axis of symmetry, and intercepts with the x- and y-axes are all expressed by the quadratic equation in standard form. While the positions of the vertex and intercepts are determined by the factors b and c, the direction and form of the parabola are determined by the coefficient a. Every quadratic equation may be changed into standard form by applying the quadratic formula or the square method, which simplifies the analysis and comparison of various functions.
The standard form of the quadratic equation is given by:
y = ax² + bx + c
Substituting the values of x and y from the table we have:
For (-4, 10):
10 = a(-4)² + b(-4) + c
10 = 16a - 4b + c......(1)
For (-3, 11):
11 = a(-3)² + b(-3) + c
11 = 9a -3b + c......(2)
For (-2, 10):
10 = 4a - 2b + c .........(3)
Equation 1 can be written as follows:
10 = 16a - 4b + c
c = 10 - 16a + 4b
Substitute the value of c in equation 2 and 3:
11 = 9a -3b + c
11 = 9a - 3b + 10 - 16a + 4b
1 = - 7a + b .........(4)
And,
10 = 4a - 2b + c
10 = 4a - 2b + 10 - 16a + 4b
0 = -12a + 2b
12a = 2b
b = 6a .......(5)
Substitute the value of b in equation 4:
1 = - 7a + 6a
1 = -a
a = -1
Substitute the value of a in equation 5:
b = -6
Now, substitute the value of a and b in equation 1:
10 = 16a - 4b + c
10 = 16(-1) - 4(-6) + c
10 = -16 + 24 + c
10 = 8 + c
c = 2
Substituting the value in the quadratic equation we have:
y = -x² -6x + 2
Hence, the value of the quadratic equation in the standard form is y = -x² -6x + 2.
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Find X using the picture of the triangles below.
Answer:
x = 37.5
Step-by-step explanation:
the top triangle has 2 congruent sides and is therefore isosceles with base angles being congruent, then
base angles = (180 - 75) ÷ 2 = 105 ÷ 2 = 52.5
the angle on the left of the outer triangle is right , then
x + 52.5 = 90 ( subtract 52.5 from both sides )
x = 37.5
this is just a quick addition to the superb reply above by "jimrgrant1"
Check the picture below.
I will mark you brainiest!
What is the length of BC?
A) 1.7
B) 2.1
C) 3.8
D) 4.6
Answer:
B. 2.1
Step-by-step explanation:
If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.
For △ACD, AC is hypotenuse so sinA = CD/AC
=> CD = 5 x sin(20) = 5 x 0.342 = 1.71
then we have AB = AD + BD
Pythagorean theorem: c^2 = a^2 + b^2
for △ACD, 5^2 = 1.71^2 + AD^2
AD^2 = 5^2 - 1.71^2 = 22.0759
AD = 4.70
BD = AB - AD = 6 - 4.70 = 1.30
for △BCD, BC is hypotenuse
BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61
BC = √4.61 = 2.1
You applied for k40 000.00 for a bank loan and you where given a flat rate interest of 9% for 2½ years. What is the amount he will pay the bank?
Answer:
The formula to calculate the amount of loan with flat rate interest is:
Amount = Principal + (Principal x Rate x Time)
Where,
Principal = the amount of loan
Rate = the interest rate per year
Time = the time period in years
Given,
Principal = K40,000.00
Rate = 9% per year
Time = 2.5 years
Substituting the values in the formula, we get:
Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)
Amount = K40,000.00 + K9,000.00
Amount = K49,000.00
Therefore, the amount he will pay the bank is K49,000.00.
find the value of the derivative (if it exists) at
each indicated extremum
Answer:
The value of the derivative at (2, 3) is zero.
Step-by-step explanation:
Given function:
[tex]g(x)=x+\dfrac{4}{x^2}[/tex]
To differentiate the given function, use the power rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\textsf{Rewrite\;the\;function\;using\;the\;exponent\;rule\;\;$a^{-n}=\dfrac{1}{a^n}$}:[/tex]
[tex]\implies g(x)=x+4x^{-2}[/tex]
Apply the power rule:
[tex]\implies g'(x)=1+(-2) \cdot 4x^{-2-1}[/tex]
[tex]\implies g'(x)=1-8x^{-3}[/tex]
[tex]\implies g'(x)=1-\dfrac{8}{x^3}[/tex]
An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (2, 3).
To determine the value of the derivative at the minimum point, substitute x = 2 into the differentiated function.
[tex]\begin{aligned}\implies g'(2)&=1-\dfrac{8}{2^3}\\\\&=1-\dfrac{8}{8}\\\\&=1-1\\\\&=0\end{aligned}[/tex]
Therefore, the value of the derivative at (2, 3) is zero.
These two triangles are similar. What is the missing side measure?
X
5
O x = 9.5
0 x = 2
Ox=7
Ox=4
3.5
20
8
14
According to the given information, the missing side measure is 14.
What is triangle?
A triangle is a polygon with three sides, three angles, and three vertices. It is the simplest polygon and the fundamental shape used in geometry. A triangle can be classified based on the length of its sides and the measure of its angles.
To find the missing side measure, we can set up a proportion between the corresponding sides of the two similar triangles:
(x + 5) / x = 9.5 / 7
We can then solve for x by cross-multiplying:
7(x + 5) = 9.5x
7x + 35 = 9.5x
35 = 2.5x
x = 14
Therefore, the missing side measure is 14.
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6u^2+17u-10
factor please
Answer:
(2u - 1) (3u + 10)
Step-by-step explanation:
Let's Check
(2u - 1) (3u + 10)
6u² + 20u - 3u + 10
6u² + 17u + 10
So, (2u - 1) (3u + 10) is the correct answer.
BANK2 For 4 months, you have withdrawn $25 a month from your savings account. Your account
balance is now $75. Write an equation to represent your money(y) at any time(x).
The equation representing the money or balance (y) in your savings account any time (x) is y = z - 25x.
What is an equation?An equation is an algebraic statement showing the equality of two or more mathematical expressions.
Mathematical expressions combine variables with numbers, values, and constants without the equal symbol (=).
The monthly withdrawals = $25
The number of months (x) = 4
Account balance (y) = $75
Let z = the initial balance in the savings account.
Equation:y = z - 25x
75 = z - 25x
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A line passes through points (5,3) and (-5,-2). Another line passes through points (-6,4) and (2,-4). Find the coordinates (ordered pairs) of the intersection of the two lines.
Step 1: Find the slope of each line
Step 2: Find the y-intercept of each line
Step 3: Write each line in slope-intercept form (y = mx + b)
Step 4: Solve for the system. Find the point of intersection for the system
Please help I will mark brainliest!!!
The point of intersection of the two lines is (-3.4, -1.2).
How to find the slope of each line?Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:
m = (y2-y1)/(x2-x1)
Using this formula, we can find the slope of the first line:
m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2
And the slope of the second line:
m2 = (−4−4)/(2 -(-6)) = -8/4 = -2
Step 2: Find the y-intercept of each line
The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:
For the first line passing through points (5,3) and (−5,−2):
y = mx + b
3 = (1/2)(5) + b
b = 3 - 5/2
b = 1/2
So the first line can be written as y = 1/2x + 1/2
For the second line passing through points (−6,4) and (2,−4):
y = mx + b
4 = (-2)(−6) + b
b = 4 - 12
b = -8
So the second line can be written as y = -2x - 8
Step 3: Each line in slope-intercept form (y = mx + b):
First line: y = 1/2x + 1/2
Second line: y = -2x - 8
Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:
1/2x + 1/2 = -2x - 8
(x + 1)/2 = -2x - 8
x + 1 = -4x - 16
5x = -16 - 1
5x = -17
x = -17/5
x = -3.4
Now that we know x, we can find y by substituting x=10 into one of the two equations:
y = -2x - 8
y = -2(-3.4) - 8
y = - 1.2
Thus, the point of intersection of the two lines is (-3.4, -1.2).
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In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Step-by-step explanation:
See Venn diagram below
The rate at which a rumor spreads through a town of population N can be modeled by the equation dt/dx = kx(N−x) where k is a constant and x is the number of people who have heard the rumor. (a) If two people start a rumor at time t=0 in a town of 1000 people, find x as a function of t given k=1/250. (b) When will half the population have heard the rumor?
(a) The function x as a function of t is t = 250ln(499x/998)
(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.
(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate
dt/dx = kx(N−x)
dt/(N-x) = kx dx
Integrating both sides, we get
t = -1/k × ln(N-x) - 1/k × ln(x) + C
where C is the constant of integration.
To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:
0 = -1/k * ln(N-2) - 1/k * ln(2) + C
C = 1/k * ln(N-2) + 1/k * ln(2)
Substituting C back into the equation, we get:
t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)
Simplifying, we get
t = 1/k * [ln((N-2)x/(2(N-x)))]
Substituting k=1/250 and N=1000, we get:
t = 250ln(499x/998)
(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get
t = 250ln(499(500)/998) = 250ln(249/499)
t ≈ 109.86
Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.
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Find a negation for each of the statements in (a) and (b). (a) This vertex is not connected to any other vertex in the graph. No vertex is connected to any other vertex in the graph. All vertices are connected to all other vertices in the graph. This vertex is connected to at least one other vertex in the graph. All vertices are connected to at least one other vertex in the graph. This vertex is connected to all other vertices in the graph.
(a) Negation: C) This vertex is connected to at least one other vertex in the graph. (b) Negation: D) This number is related to at least one even number.
(a)
A) Some vertex is connected to some other vertex in the graph.
B) At least one vertex is not connected to any other vertex in the graph.
C) This vertex is connected to at least two other vertices in the graph.
D) There exists at least one vertex that is not connected to at least one other vertex in the graph.
E) This vertex is connected to some other vertices in the graph, but not necessarily to all of them.
(b)
A) This number is related to at least one odd number.
B) There exists at least one number that is not related to any even number.
C) All numbers are related to at least one even number.
D) This number is not related to at least one even number.
E) All numbers are related to at least one even number.
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Complete question:
Find a negation for each of the statements in (a) and (b).
(a) This vertex is not connected to any other vertex in the graph.
A) No vertex is connected to any other vertex in the graph.
B) All vertices are connected to all other vertices in the graph.
C) This vertex is connected to at least one other vertex in the graph.
D) All vertices are connected to at least one other vertex in the graph.
E) This vertex is connected to all other vertices in the graph.
(b) This number is not related to any even number.
A) This number is not related to any odd number.
B) All numbers are related to at least one even number.
C) All numbers are not related to any even number.
D) This number is related to at least one even number.
E) No number is related to any even number.
PLEASE HELP ME ON THIS QUESTION
0-24- Tally (1)
25-49 Tally (4)
50-74 Tally (5)
75-99 Tally (2)
Determine all real numbers s associated with the following point (x, y) on the unit circle. Write the exact radian answer in [0, 2pi) indicate remaining answers by using n to represent any integer.
If we cοnsider (x, y) tο be a pοint οn the unit circle, we get:
[tex]x^2 + y^2 = 1[/tex] (because the pοint is οn the unit circle) (since the pοint is οn the unit circle)
Hοw are real numbers determined?All real numbers must be determined in such a way that:
tan(s) = y / x
The trigοnοmetric identity can be applied:
Tan is equal tο Sin / Cοs.
We thus have:
Y/X = Tan(S), Sin(S), and Cοs (s)
Using the identity cοs(s) + sin(s) = 1, we square bοth sides tο οbtain:
[tex](y/x)^2 = sin^2(s) / cos^2(s) = 1 - cos^2(s)[/tex]
Rearranging and applying the equatiοn x2 + y2 = 1 results in:
cοs2(s) equals 1 - (y/x).
[tex]^2 = x^2[/tex]
Given that (x, y) is in the first οr fοurth quadrant and that x is pοsitive, we can take the square rοοt tο get the fοllοwing result:
cοs(s) = ± x
Sο, s is determined by:
S equals arccοs(x) + n, where n is any pοsitive integer.
The range οf x's value is limited tο [-1, 1] because it is οn the unit circle. As a result, the values οf s are prοvided by:
S = arccοs(x) + n, where n is any pοsitive integer and x is within the range [-1, 1].
The pοssible values οf s in exact radian measure in [0, 2] are as fοllοws:
S = arccοs(-1) + = S = arccοs(1) = 0
S is equal tο arccοs(0) + n + (n + 1/2)
where any integer n is used.
As n can be any integer, the pοssible pοssibilities οf s are s = 0,, and (n + 1/2).
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NEED HELP ASAP Writing Quadratics From A Table
Answer: In the table x part, it increases from -2 all the way to 4. In the table y part, it decreases from 17 to -1, but then increases back from -1 to 17.
the level of confidence of a test of hypothesis is denoted by
PLS HELP I WILL MARK BRAINILEST
Answer:
Let's assume the original price of the stock was x.
When the company announced it overestimated demand, the stock price fell by 40%.
So, the new price of the stock after the first decline was:
x - 0.4x = 0.6x
A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.
So, the new price of the stock after the second decline was:
0.6x - 0.6(0.6x) = 0.24x
Given that the current stock price is $2.40, we can set up the equation:
0.24x = 2.40
Solving for x, we get:
x = 10
Therefore, the stock was originally selling for $10.
If f(a)=a squared plus 7 for all real values of a, which of the following are possible values of a: square root of 5, square root of 7 or 100 times the square root of 3
100 times the square root of 3 is also a possible value of a for this function.
What is a square root?In mathematics, the square root of a non-negative real number "a" is a non-negative real number that, when multiplied by itself, gives the original number "a". It is denoted by the symbol "√".
According to question:We can substitute each of the given values into the function f(a) = a² + 7 to determine if they are possible values of a.
Substituting the square root of 5:
f(√(5)) = (√(5))² + 7 = 5 + 7 = 12
So, the square root of 5 is not a possible value of a for this function.
Substituting the square root of 7:
f(√(7)) = (√(7))² + 7 = 7 + 7 = 14
So, the square root of 7 is a possible value of a for this function.
Substituting 100 times the square root of 3:
f(100√(3)) = (100√(3))² + 7 = 30000 + 7 = 30007
So, 100 times the square root of 3 is also a possible value of a for this function.
Therefore, the possible values of a for the given function are:
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HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Answer:
[tex]\textsf{To\;add\;(or subtract)\;in\;Scientific\;Notation,\;you\;must\;have\;the\;same\;$\boxed{\sf power\;of\;10}$\:.}\\\textsf{Then\;you\;can\;$\boxed{\sf add\;or\;subtract}$\;the\;coefficients\;and\;$\boxed{\sf keep}$\;the\;power\;of\;10.}[/tex]
[tex]\textsf{To\;multiply\;in\;Scientific\;Notation,\; you\;must\;$\boxed{\sf multiply}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf add}$\;the\;powers\;of\;10.}[/tex]
[tex]\textsf{To\;divide\;in\;Scientific\;notation,\;you\;must\;$\boxed{\sf divide}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf subtract}$\;the\;powers\;of\;10.}[/tex]
Step-by-step explanation:
To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add or subtract the coefficients and keep the power of 10.
Example expression:
[tex]2.3 \times 10^3 +3.2 \times 10^3[/tex]
Factor out the common term 10³:
[tex]\implies (2.3 +3.2) \times 10^3[/tex]
Add the numbers:
[tex]\implies (5.5) \times 10^3[/tex]
[tex]\implies 5.5\times 10^3[/tex]
Therefore, we have added the coefficients and kept the power of 10.
[tex]\hrulefill[/tex]
To multiply in Scientific Notation, you must multiply the coefficients and add the powers of 10.
Example expression:
[tex]2.3 \times 10^3 \times 3.2 \times 10^3[/tex]
Collect like terms:
[tex]\implies 2.3 \times 3.2 \times 10^3 \times 10^3[/tex]
Multiply the numbers (coefficients):
[tex]\implies 7.36 \times 10^3 \times 10^3[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 7.36 \times 10^{(3+3)}[/tex]
[tex]\implies 7.36 \times 10^{6}[/tex]
Therefore, we have multiplied the coefficients and added the powers of 10.
[tex]\hrulefill[/tex]
To divide in Scientific notation, you must divide the coefficients and subtract the powers of 10.
Example expression:
[tex]\dfrac{8.6 \times 10^6}{2.15 \times 10^2}[/tex]
Collect like terms:
[tex]\implies \dfrac{8.6}{2.15} \times \dfrac{10^6 }{10^2}[/tex]
Divide the numbers (coefficients):
[tex]\implies 4\times \dfrac{10^6 }{10^2}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]\implies 4\times 10^{(6-2)}[/tex]
[tex]\implies \implies 4\times 10^{4}[/tex]
Therefore, we have divided the coefficients and subtracted the powers of 10.
Answer the question below: *
The area of a playground is 108 yd². The width of the playground is 3 yd longer than its length. Find the
length and width of the playground.
•length = 9 yards, width = 12 yards
•length = 12 yards, width = 15 yards
•length = 12 yards, width = 9 yards
•length= 15 yards, width = 12 yards
Solving a system of equations we the length and width of the playground is length = 9 yards, width = 12 yards
How to find the length and the width?Remember that the area of a rectangle of length L and width W is:
Area = L*W
Here we know that the area is 108 square yards, and we know that he width is 3 yards longer than the length, then we can write a system of equations:
W =L + 3
108 = L*W
Replacing the first equation into the second one we will get:
108 = (L + 3)*L
108 = L² + 3L
Then we have the quadratic equation:
L² + 3L - 108 = 0
Using the quadratic formula we get the solutions:
[tex]L = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]
We only care for the positive solution, which is:
L = 9
Then the width is:
W = L + 3 = 9 + 3 = 12
Then the correct option is:
•length = 9 yards, width = 12 yards
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prove that the absolute value of x-y is greather than the absolute value of x minus the absolute value of y
Using the properties of absolute value function, proved that |x - y| > |x| - |y| is true for all x and y.
To prove that |x - y| > |x| - |y|, we can consider two cases
Case 1
x >= 0 and y >= 0
In this case, |x - y| = x - y and |x| - |y| = x - y. So we have
|x - y| = x - y
| x | - | y | = x - y
Substituting these expressions into the original inequality, we get:
x - y > x - y
This inequality is true for all x and y where x >= 0 and y >= 0, since the difference between x and y is always greater than or equal to zero.
Case 2
x < 0 and y < 0
In this case, |x - y| = -(x - y) and |x| - |y| = -x + y. So we have:
|x - y| = -(x - y)
| x | - | y | = -x + y
Substituting these expressions into the original inequality, we get
-(x - y) > -x + y
Simplifying both sides, we get
y - x > -x + y
Adding x to both sides, we get
y > 0
This inequality is true for all x and y where x < 0 and y < 0, since both x and y are negative and the difference between x and y is always less than or equal to zero.
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3. The total number of Democrats and Republicans in the US House of Reps during the 115th
year was 434. There were 46 fewer Democrats than Reps. How many were there of each
party?
Answer:
Step-by-step explanation:
subtract 434-46
evaluate f(0) when f(x)=5x. if it's impossible to do so, enter "dne" (with no quotes) in the answerbox.
The value of function f(0) after putting the value of x = 0 we get the value o which is not DNE.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).
Given function is
f(x)=5x
we have to find the value of the f(0)
so putting the value of 0 as x we get,
f(x)=5x
f(0) = 5(0)
f(0) = 0
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Find the error. Select choice options are step 1, 2, 3 and x-coordinates and y-coordinates
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
What is the slope?
In mathematics, the slope is a measure of the steepness of a line.
The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).
Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.
Therefore, the change in y-coordinates is 6 - 8 = -2.
Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.
Therefore, the change in x-coordinates is 4 - (-2) = 6.
Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.
Since all the steps are correct and properly executed, there is no error.
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
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what is the largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$?
the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.
One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.
A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.
Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:
[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]
This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).
Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.
To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.
There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.
There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.
There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.
Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:
[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]
[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]
Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
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If f(7) = 9 and f’(7) = 3, estimate f(7.3).
Answer:
[tex]f(7.3)\approx9.9[/tex]
Step-by-step explanation:
Use point-slope form
[tex]y-y_1=m(x-x_1)\\y-9=3(x-7)\\y-9=3x-21\\y=3x-12[/tex]
[tex]f(7.3)=3(7.3)-12=21.9-12=9.9[/tex]
X man can complete a work in 40 days.If there were 8 man more the work should be finished in 10 days less the original number of the man
Step-by-step explanation:
Original job = x men * 40 days = 40x man days to complete
now add 8 men = x+8 men
man days now is (x+8) (30) to complete job
so 40x = (x+8)(30)
40x = 30x + 240
10 x = 240
x = 24 men originally
what is the distance between the points (-9, 4)and(3,-12) ? a. 12 units b. 16 units c. 20 units d. 28 units
Answer:
20 units
Step-by-step explanation:
Point 1 (-9, 4)
Point 2 (3, -12)
Distance Formula
d=√((x2-x1)²+ (y2-y1)²)
d=√((3+9)²+ (-12-4)²)
d=√(12²+ (-16)²)
d=√(144+ 256)
d=√400
d=20