Answers
The correct value of m = 6 and b = -9.
The function f(x) is differentiable at x = 3 and we know that if a function is differentiable at some point means that it is continuous at that point also.
Here function is continuous at x = 3 piecewise
m(3) + b = (3)²
3m + b = 9 .....(1)
and function is differentiable at ( x = 3 ) piecewise
d/dx ( m * x + b ) = d/dx (x)² at ( x= 3 )
( m + 0 ) = 2x at ( x = 3 )
m = 2 * 3
m = 6
By placing the value of m in equation (1)
3m + b = 9
3 * 6 + b = 9
18 + b = 9
b = 9 - 18
b = -9
Therefore, the value of m = 6 and b = -9.
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Related Questions
1. Suppose we have two consecutive odd integers. If the smaller one is “x” ; what would we call the large one?
2. We are told there are two consecutive odd integers and the smaller one is 12 more than one third the large one. Use the answer to problem 1 to write a clean equation then find the integers
Answers
Main Answer:1) (x + 2)
2) The numbers are 19 and 21.
Concept and definitions should be there:
An odd integer n is an integer which is not a multiple of 2 (or equivalently one more than a multiple of 2). The odd integers are ..., -5, -3, -1, 1, 3, 5, ... Every odd integer can be written in the form 2k + 1 for some unique integer k.
The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are even.
The sum and difference of an even integer and odd integer are odd. Besides 2, all prime numbers are odd. Also, odd integers are really cool
This article is a stub. Help us out by expanding it.
Given data:
1) We have two consecutive odd integers.
Solving part:
Remember that the distance between any two consecutive odd numbers is 2.
5 - 3 = 2
7 - 5 = 2
13 - 11 = 2
etc.
So if the smaller of the two odd numbers is x, then the larger one will be (x + 2).
Given that:
2) We have two consecutive odd numbers, let's write them as:
Solving part:
(2*n + 1) and (2*n + 3)
Where n is an integer number.
We know that the smaller one is 12 more than one third of the larger one, so we have:
(2*n + 1) = 12 + (2*n + 3)/3
Now we can solve this for n
2*n + 1 = 12 + (2/3)*n + 1
2*n - (2/3)*n = 12 + 1 - 1
(4/3)*n = 12
n = (3/4)*12 = 9
n = 9
Then the two consecutive odd integers are:
(2*n + 1) = (2*9 + 1) = 19
(2*n + 3) = (2*9 + 3) = 21
Final Answer:1) (x + 2)
2) The numbers are 19 and 21.
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Which fraction is greater, 35/109 or 36/104?? To explain your answer, use our definition of fraction along with reasoning other than finding common denominators, common numerators, cross-multiplying, or converting to decimals.
Answers
The fraction that is greater is 36/104 since 34.62% is greater than 32.11%
Percentages and ratioFractions are written as the ratio of two integers. For instance a/b is a fraction.
In order to determine which of the fractions is greater, we will express them as percentage as shown:
35/109 * 100
3500/109
32.11%
Similarly;
36/104 * 100
3600/104
34.62%
Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%
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18x - 3
6 + 25x
does anyone know?
Answers
2. 6+25x=31
What are all the solutions to the equation 10x4 + 30x3 + 35x2 = 0? 0, StartFraction 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, StartFraction negative 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction negative 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, 6 + 2 i StartRoot 5 EndRoot, 6 minus 2 i StartRoot 5 EndRoot. 0, negative 6 + 2 i StartRoot 5 EndRoot, negative 6 minus 2 i StartRoot 5 EndRoot.
Answers
The solutions to the equation 10x⁴ + 30x³ + 35x² as required in the task content are; 0, (-3 + i√5)/2, and (-3 - i√5)/2.
What are all the solutions to the equation 10x⁴ + 30x³ + 35x² = 0 as given in the task content?It follows from the task content that the given equation is; 10x⁴ + 30x³ + 35x² = 0.
Hence, to find all the solutions of the equation, one must factorise the expression on the left hand side so as to obtain the factors as follows;
10x² (x² + 3x +3.5) = 0
Hence, we have;
10x² = 0; x = 0 OR
x² + 3x +3.5 = 0.
Hence, it follows from the quadratic formula that the roots/zeroes of x in the equation above can be evaluated as follows;
x = {-b±√(b²-4ac)}/2a
hence, by comparison, we have;
x = {-3±√(9-14)}/2
x = (-3 ± √-5)/2
x = (-3 ± i√5)/2
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can someone please explain this
Answers
Answer: x=-3-[tex]\sqrt{7}[/tex] or x=-3+[tex]\sqrt{7}[/tex]
Step-by-step explanation:
f(x)=x+1. g(x)=x+5
(f * g)(x)=
f(x)*g(x)=
(x+1)(x+5)=
x^2+5x+x+5=x^2+6x+5
x^2+6x+5=3
x^2+6x+9=7 ==> Add 4 on both sides of the equation
(x+3)^2=7
x+3=[tex]\sqrt{7}[/tex]
x=-3+[tex]\sqrt{7}[/tex]
x+3=-[tex]\sqrt{7}[/tex]
x=-3-[tex]\sqrt{7}[/tex]
NEEEEED HELP ASAP!!!
Answers
Area= 8,104mm^2
Perimeter=460mm
Explanation:
For area: find area for both rectangles and add together
You’ll get 6370 and 1734 because (49x130) and (51x34) add and get 8104mm^2 (squared because it’s area
Perimeter: add all outside lengths
51+34+100+130+49+96=460mm
I just need the answer for C. Please answer quick this is due tmr morning!! worth 20 points and brainliest
Answers
Answer:
The answer is 7 for C.
Step-by-step explanation:
7+7=14 and 7x7=49
The diamond just asks for numbers that make up a pattern for the two given numbers.
Please help I will give you brainliest
Answers
Answer:
$7.4
each bag of milk cost $7.4
Answer: $7.4
Step-by-step explanation: i did this and i remember it!
Need help with this problem
Answers
Answer:
I could be wrong, but I think you got right in the beginning 107°, but go with your gut feeling. Wish you the very best <3
Answer: x=73 degrees, z=73 degrees, y=107 degrees
Step-by-step explanation:
y=107 degrees because y and 107 degrees are congruent angles
z=x because z and x are congruent angles
x+y=180 ==> x and y are supplementary angles that are placed on a straight line(the straight line is 180 degrees and is called a straight angle.)
x+107=180
x=73 degrees
z=x
z=73 degrees
You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answers
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
Find the ending
balance:
$2,500 for 25 years at
2.75% annual simple
interest
Show work
Answers
Answer:
$4,218.75
Step-by-step explanation:
The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by
I = Prt
The ending balance amount is found by adding the principal to the interest computed
Ending balance = P + I
Here r is the interest rate in % converted to a decimal. This is done by dividing by 100
r = R/100 = 2.75%/100 = 0.0275 per year
I = 2500 x 0.0275 x 25 = 1718.75
So interest I = $1718.75
Ending balance = $2,500 + $1718.75 = $4,218.75
Carlos is paid $17.90 per hour regularly. If he worked 45 hours last week, what was his gross pay? Carlos is paid at time-and-a-half for overtime.
Answers
Answer:
$ 850.25
Step-by-step explanation:
I will assume anything over 40 hours is 'overtime'
total pay will be
regular pay + overtime pay
17.90 * 40 hr + (17.90 * 1.5)(5hr) = $ 850.25
Which shows (3^2)^-2 in standard form
Answers
Answer:
1/81
Step-by-step explanation:
[tex](3^2)^{-2}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]
An online poll of 6,000 residents of Washington, DC showed that 79% agreed with the statement "Employers should be required to pay men and women the same salary for the same job." An online poll of 4,800 residents of Atlanta revealed that 74% agreed with the same statement.
A button hyperlink to the SALT program that reads: Use SALT
(b)
How many successes were there in the Washington sample?
How many failures were there in the Washington sample?
(c)
Calculate a 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement (DC − Atlanta). (Use a table or technology. Round your answers to three decimal places.)
Answers
Step-by-step explanation:
Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.
b. The number of successes in the Washington sample were 4740 .
The number of failures in the Washington sample is 1,260
c. the 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement "Employers should be required to pay men and women the same salary for the same job" is 0.018 to 0.068.
How do we calculate?(b) Number of successes and failures in the Washington sample:
Total number of respondents in the Washington sample: 6,000
Percentage who agreed with the statement: 79%
Number of successes = 79% of 6,000
= 0.79 * 6,000
= 4,740
Number of failures = Total - Number of successes
= 6,000 - 4,740
= 1,260
(c)
confidence interval = (p1 - p2) ± Z * √((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
p1 = Proportion of successes in the Washington sample
p2 = Proportion of successes in the Atlanta sample
n1 = Size of the Washington sample
n2 = Size of the Atlanta sample
Z = Z-score for the desired confidence level = 1.96
confidence interval = (0.79 - 0.74) ± 1.96 * √((0.79 * (1 - 0.79) / 6000) + (0.74 * (1 - 0.74) / 4800))
confidence interval = 0.05 ± 1.96 * √((0.79 * 0.21 / 6000) + (0.74 * 0.26 / 4800))
confidence interval = 0.05 ± 1.96 * √(0.00013815 + 0.0001244583)
confidence interval = 0.05 ± 1.96 * √(0.0002626083)
Lower bound of the confidence interval (DC - Atlanta)
= 0.05 - 0.0317226549
= 0.018
Upper bound of the confidence interval (DC - Atlanta)
= 0.05 + 0.0317226549
= 0.068
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based on the equation 5×x+860=2×x+380, you can say
Answers
The value of x is -160.
An equation in which the power of any variable is not more than one is called a linear equation.
Here, we are given a linear equation as follows-
5 × x + 860 = 2 × x + 380
⇒ 5x + 860 = 2x + 380
Let us solve the given equation-
Subtracting 2x from both sides, we get
5x - 2x + 860 = 2x - 2x + 380
3x + 860 = 380
Subtracting 860 from both sides-
3x + 860 - 860 = 380 - 860
3x = -480
dividing both sides by 3,
3x/3 = -480/3
x = -160
Thus, the value of x comes out to be -160.
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Which table represents y as a function of x?
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.
i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.
And as we can see in the given tables,
1.) 12.23 is the value of x for both 5.4 and 6.4
2.) 0.31 is the value of x for both 55 and 59
4.) 20 is the value of x for both 245 and 255
So, the only table representing y as a function of x is table 3.
Answer:
table 3 is correct i took the test
Step-by-step explanation:
Random means by chance.
O True
O False
Answers
Answer:
True
Step-by-step explanation:
Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".
Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)
and maybe the question has more chance to be false because if a statement is false at least in one case it is false.
Express 60 of its prime factors in assessing order and answer in index form
Answers
Answer:
2^2×3×5
Step-by-step explanation:
hope this works :)
Need help asap math !
Answers
Answer:
7/10 = 0.7 = 70%
25/100 = 0.25 = 25%
56/100 = 0.56 = 56%
Step-by-step explanation:
One-stray Problem Solving
POSSIBLE POINTS: 5.88
A rectangular playground is to be fenced in using a wall on one side and 210 meters of fencing for the other three sides. The area A(z) in square meters
of the playground is a function of the length z in meters of the side parallel to the wall.
What is the area of the playground when z = 50?
square meters
Answers
b) A(x) = x(200 -2x)
c) 0 < x < 100
Step-by-step explanation:
b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:
A(x) = x(200 -2x)
__
a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²
__
c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.
Find the area of the triangle
3 m
8 m
Answers
area - 1/2 x 3 x 8
Answer:
3×8 =24
24÷2=12
Area of triangle=12m²
Step-by-step explanation:
3×8 =24
24÷2=12
what is the value of x?
help would be so appreciated
Answers
Answer:
x = 23
Step-by-step explanation:
The two angles are supplementary angles.
Supplementary angles sum 180°
(6x+4) + 38 = 180
6x + 42 = 180
6x = 180 - 42
6x = 138
x = 138/6
x = 23
Check:
6*23 + 4 + 38 = 180
138 + 42 = 180
Answer:
x = 23Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.
[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)
[tex]\bf 6x+42=180[/tex] (Simplify)
[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)
[tex]\bf 6x=138[/tex] (Simplify)
[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)
[tex]\bf x=23[/tex]
Therefore, x = 23.
_____________________
Hope this helps!
Have a great day!
Find an equation for the line which passes through (-2,8) and is perpendicular to the line containing (0,1) and (4,5).
Answers
The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
Let the equation of line passes through the point (-2, 8) be y = mx + b.
Where m is the slope of the line and b is the y intercept of the line.
According to the given question.
A line passes through the points (-2, 8).
And it is also perpendicular to the line containing (0, 1) and (4, 5).
Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).
So, the slope of the line whose equation is to be find is given by
m = -1/(5 - 1/4-0)
⇒ m = -1/4/4 = -1
Thereofre, the equation of line with slope -1 is
y = -1x + b
Also, it passes through (-2, 8)
So,
8 = -1(-2) + b
⇒ 8 - 2 = b
⇒ b = 6
Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
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50 POINTS The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A=h(a+b)/2
Solve for b.
Answers
Answer:
[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]
Translation:
Option C.
Find the quotient.
h6 ÷ h
Answers
Answer:
6
Step-by-step explanation:
Possibly 6 but if not let me know
Answer:
6
Step-by-step explanation:
the h's cancel out
6) Convert the following equivalent scales to ratios.
(i) 1cm=20m
Answers
Answer:
[tex]1cm = 20 \times 100 \\ = 2000cm \\ 1cm = 2000cm[/tex]
Hall dimensions 200m by 85m. Diagram office wall scale 1:40. What are the dimensions of floor space in cm
Answers
The dimensions of floor is 500 cm by 212.5 cm
HOW TO FIND DIMENSION OF HALL ?Multiply the width and length of each rectangle to find its area. The areas of each rectangle are then added up to determine the total area. In the event that your room is L-shaped, for instance, this can be split into two rectangles. Additionally, this method still works in a complicated room.
CALCULATION500 cm by 212.5 cm
Given :
The main arena hall has dimensions 200 m by 85 m.
On a large diagram on the office wall the scale is 1:40.
Length of arena hall = 200 m
Scale is 1:40
So, the length of the floor =
Since 1 m = 100 cm
So, 5 m = 100*5 = 500 cm
Width of arena hall = 85 m
So, width of floor =[tex]\frac{85 * 1}{40}[/tex] = 2.125m
Now 1 m = 100 cm
So, 2.125 m = 212.5 cm
Thus the dimensions of floor is 500 cm by 212.5 cm
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China generated 237.188 billion kilowatt-hours (kWh) of wind energy in 2018. The population in China in 2018 was 1.379 billion. What was the wind energy generated per capita? Give your answer to the nearest hundredth.
Answers
Answer:
172 kilowatts.
Step-by-step explanation:
Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹
People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹
Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.
PLEASE HELP I WILL GIVE BRAINLIST Graph the line with slope 1/3 passing through the point (2, -3)
Answers
Answer:
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Factor as the product of two binomials. x 2 + 3 x − 4
Answers
Answer:
[tex](x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]x^2+3x-4[/tex]
The best way to write a polynomial with three terms as a product of binomials is to FACTOR!
The middle number is 3 and the last number is -4.
Factoring means we want something like
[tex](x+?)(x+?)[/tex]
We need two numbers that...
ADD together to get 3 and
MULTIPLY together to get -4
Test the numbers -1 and 4:
[tex]-1+4=3\\(-1)4=-4[/tex]
These are the right numbers! Now, I can write them as factored binomials!
[tex](x-1)(x+4)[/tex]