Answer: 1.9
Step-by-step explanation:
[tex]f(x)=\dfrac{14}{7+2e^{-0.6x}}\\\\\\f(3)=\dfrac{14}{7+2e^{-0.6(3)}}\\\\\\.\qquad =\dfrac{14}{7+2e^{-1.8}}\\\\\\.\qquad =1.9\qquad \quad need\ to\ use\ a\ calculator\ after\ replacing\ x\ with\ 3[/tex]
Which equation gives the length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in.?
Answer:
12 in
Step-by-step explanation:
the arc length formula is s = rФ, where Ф is the central angle in radians.
Here, the arc length is s = (4 in)(3 radians) = 12 in
Answer:
D on edge
Step-by-step explanation:
Given the following system of equations:
−4x + 8y = 16
2x + 4y = 8
What action was completed to create this new equivalent system of equations?
−2x + 4y = 8
2x + 4y = 8
A.Multiply the second equation, 2x + 4y = 8, by −1.
B.Multiply the first equation, −4x + 8y = 16, by −1.
C.Divide the second equation, 2x + 4y = 8, by 2.
D.Divide the first equation, −4x + 8y = 16, by 2.
Answer:
D.Divide the first equation, −4x + 8y = 16, by 2.
Step-by-step explanation:
All you have to do is look at the effect of the proposed action on the constant on the right to tell which answer choices are incorrect.
A: you would get -8 on the right. Neither equation has that.B: you would bet -16 on the right. Neither equation has that.C: you would get 4 on the right. Neither equation has that.D: you would get -2x +4y = 8, matching the first equation of the new system exactly.Answer:
D.Divide the first equation, −4x + 8y = 16, by 2.
Step-by-step explanation:
−4x + 8y = 16
2x + 4y = 8
Take the first equation and divide it by 2
−4x/2 + 8y/2 = 16/2
-2x + 4y = 8
What equation can be written from this sequence -50,-33,-16,1
Answer: [tex]a_n=-50+(n-1)17[/tex]
Step-by-step explanation:
The Arithmetic Sequence Formula is:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
[tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the sequence.
[tex]a_1[/tex] {a_1} is the first term of the sequence.
[tex]n[/tex] is the term position.
[tex]d[/tex] is the common difference of any pair of consecutive numbers.
We can observe that the first term is:
[tex]a_1=-50[/tex]
Now, we need to find "d". This is:
[tex]d=-16-(-33)\\d=-16+33\\d=17[/tex]
Then, substituting, we get the following equation:
[tex]a_n=-50+(n-1)17[/tex]
One side of a triangle is 2 feet shorter than the second side. The third side is 4 feet shorter than the second side. The perimeter of a triangle is 15 feet. Find the length of each side.
The length of first side is 5 feet, the length of second side is 7 feet, the length of third side is 3 feet.
What is perimeter?The perimeter is the sum of measurement of all sides of a triangle. It is done by a ruler.
How to calculate perimeter?let the second side be x
according to question first side will be (x-2) feet and the third side will be (x-4) feet.
We know that the perimeter is equal to the sum of all sides of a triangle.
so
x+x-2+x-4=15
3x=6=15
3x=21
x=7
The length of first side=7-2=5 feet
The length of second side=7 feet
The length of third side=3 feet
Hence the sides of the triangle is 5 feet, 7 feet, and 3 feet.
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An air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu). The unit has a maximum variance of y Btu. If x is the air conditioning unit’s actual capacity, which graph could be used to determine variance levels that would cause a unit to be rejected because of its cooling capacity?
Answer:
ITS 100% A
Step-by-step explanation:
Answer:
Option 2.
Step-by-step explanation:
Let as consider x be the air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).
It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).
We need to find the graph that could be used to determine the variance levels that would cause a unit to be rejected because of its cooling capacity.
It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.
[tex]y\leq |x-6000|[/tex]
The related equation of this inequality is
[tex]y=|x-6000|[/tex]
It is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000).
The related curve is a solid V-shaped curve because the points on curve included in the solution set.
The shaded region lie below the curve because the sign of inequality is ≤.
Therefore the correct option is 2.
Solve the following equation for . A. y = 3 B. y = 18 C. y = 6 D. y = 36
Your answer is D. y = 36
We can find this by just rearranging the equation firstly:
2 + √4y - 3 = 11
√4y - 1 = 11
√4y = 12
Now we can simplify √4y, because 4 2², so you get 2√y :
2√y = 12
√y = 6
We can now square both sides to get the equation as "y ="
y = 36
I hope this helps! Let me know if you have any questions :)
At how many points does the graph of the function below intersect the x-
axis?
y = 4x^2 - 6x + 1
Answer:
Option B is correct.
Step-by-step explanation:
y=4x^2-6x+1
Solving the quadratic equation:
4x^2-6x+1
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a=4, b=-6 and c=1
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(4)(1)}}{2(4)}\\x=\frac{6\pm\sqrt{36-16}}{8}\\x=\frac{6\pm\sqrt{20}}{8}\\x=\frac{6+\sqrt{20}}{8} \,\,and\,\, x=\frac{6-\sqrt{20}}{8}[/tex]
So, it has 2 solutions,
Option B is correct.
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1 /4 square foot. How many squares is the wall divided into?
Answer:
96 squares
Step-by-step explanation:
The number of squares is ...
(wall area)/(square area) = (24 ft²)/(1/4 ft²) = 24×4 = 96 . . . . squares
Answer:
96 squares
Step-by-step explanation:
There are 7 people on a cycling team. Their coach mush pick two of them to be Co - Captain. How many different pairs can the couch choose?
Graph the solution to the following system of inequalities in the coordinate plane.
Answer:
see below
Step-by-step explanation:
The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.
The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.
Suppose that y varies inversely with x, and y = 2 when x = 4. What is an
variation?
Answer:
xy=8
Step-by-step explanation:
The equation for inverse variation is
xy = k where k is the constant of variation
4*2 = k
8=k
The equation is
xy=8
Need help with a math question
ANSWER
P'(2,7)
EXPLANATION
When we reflect a point in the y-axis, we negate the x-coordinates.
The rule for reflection across the y-axis is
[tex](x,y)\to (-x,y)[/tex]
The given point, P has coordinates (-2,7)
To obtain the coordinates of the image P', we negate the x-coordinate of P(-2,7).
[tex]P( - 2,7) \to \: P'( - - 2,7)[/tex]
[tex]P( - 2,7) \to \: P'(2,7).[/tex]
Answer:
(2, 7)
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y) → (- x, y)
Hence
P(- 2. 7) → P'(2, 7)
Solve the formula I = Prt, in general, to find the principal, P.
By substitution of formula, the expression of principle P is P = I/(r*t) .
What is substitution of formula ?Substitution of formula is a method to find any parameter from the given expression by substituting the required value from the expression or equation mentioned.
Given expression is I = Prt .
Substituting the parameter of principle(P) from the above expression -
P = I/(r * t)
Thus, by substitution of formula, the expression of principle P is P = I/(r*t) .
To learn more about substitution of formula, refer -
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Identify the slope and y-intercept of the line: PLEASE HELP ME IT WOULD ME SO MUCH THANK YOU!!!!!
y =– (¾)x - 2
Answer:
slope: -3/4y-intercept: -2 . . . . or point (0, -2)Step-by-step explanation:
Slope-intercept form is ...
y = mx + b
Comparing your equation to this pattern, you can see that your equation is already in this form, with ...
m = -3/4b = -2In this form, the coefficient of x (which is m) is the slope of the line. Thus your slope is -3/4. The added constant (which is b) is the y-intercept, the value of y when x=0. Your y-intercept is -2. Expressed as the coordinates of a point, the y-intercept is (x, y) = (0, -2).
How many real and imaginary solutions does the equation X^2+x=11 contains?
Answer:
Two
Step-by-step explanation:
x² + x = 11
The degree of a polynomial will always tell us the maximum number of solutions
You have a second degree polynomial, so there are two possible solutions.
They are
[tex]x = \dfrac{1}{2} \left (-1 - 3\sqrt{5} \right )[/tex]
and
[tex]x = \dfrac{1}{2} \left (-1 + 3\sqrt{5} \right )[/tex]
The diagram below shows that the zeros are at (-3.854,0) and (2,854, 0), which are the decimal equivalents of the roots.
One angle of a triangle measures 76" more than the smallest, while a third angle is twice the smallest. Find the
measure of each angle
The triangle has angles of
degrees
Answer:
26,102,52
Step-by-step explanation:
Let x be the smallest angle
x+76 is the second angle
2x is the third angle
The sum of all three angles is 180 degrees
x+ (x+76) + 2x = 180
Combine like terms
4x+76 = 180
Subtract 76 from each side
4x+76-76 = 180-76
4x =104
Divide by 4
4x/4 =104/4
x =26
x+76 =26+76 =102
2x = 2*26 = 52
find f’(x).
1. f(x)=x^2-5x+1
2. f(x)=10/x
Answer:
1) 2x-5 2) -10/x^2
Step-by-step explanation:
Use power rule and constant rule for the first one:
1) f(x)=x^2-5x^1+1 (x^n)'=nx^(n-1) and (c)'=0
f'(x)=2x^1-5(1)x^0+0
f'(x)=2x-5(1) x^0=1
f'(x)=2x-5
Use just power rule for last one after a rewrite
2) f(x)=10/x
f(x)=10x^(-1) now use power rule
f'(x)=-10x^(-2) =-10/x^2
The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2. Obi spent ?20 that day. Obi now had ?8 less than Rudy. How much did they have initially altogether?
Answer:
Altogether, they had ?28
Step-by-step explanation:
Had Obi spent only ?12, they would have been even. Thus ?12 is the same as 5-2 = 3 "ratio units". So, each "ratio unit" is worth ?12/3 = ?4.
Then Obi started the day with 5·4 = 20, and Obi started the day with 2·4 = 8. Obi ended with 0, which is 8 less than Rudy.
Altogether, they started with 20 + 8 = 28 of whatever a ? is.
Answer:
Money they have initially altogether = 28
Step-by-step explanation:
The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2.
Money Obi has = 5 r
Money Rudy has = 2 r
Obi spent 20 that day and bi now had 8 less than Rudy
5r -20 = 2r - 8
3r = 12
r = 4
Initial money they have
Obi = 5r = 5 x 4 = 20
Rudy = 2 x 4 = 8
Altogether they have 20+8 = 28
Money they have initially altogether = 28
The table shows values for the functions f(x) and g(x). What are the solutions of X where f(x) = g(x)?
Step-by-step explanation:
You need to look for where f(x) and g(x) have the same value. That's at x=0 and x=2.
Answer: If you want to see in what value of x there is true that f(x) = g(x), you need to see in the table when f(x) and g(x) has the same value, this is lock in in table when the second and third values are the same.
This is true for x = 2, where f(2) = 0 and g(0) = 2, and for x = 0, wher f(0) = -3 and g(0) = -3.
Michael has never taken a foreign language class, but is doing a story on them for the school newspaper. The school offers French and Spanish. Michael has a list of all 25 kids in the school enrolled in at least one foreign language class. He also knows that 18 kids are in the French class and 21 kids are in the Spanish class. If Michael chooses two kids at random off his list and interviews them, what is the probability that he will be able to write something about both the French and Spanish classes after he is finished with the interviews? Express your answer as a fraction in simplest form.
Answer:
112/125
Step-by-step explanation:
If we know all 25 are in at least one foreign language class then we can assume that exactly 4 of the 18 kids in French only take French to add up to 25 and this means that the 14 left take both classes. Now we can create three fractions for each case which are 7/25 (Spanish only) 4/25 (French only) and 14/25 (Both) and we can know say that if he goes down the route of getting a Spanish only as his first he needs one of the 18 other students the chances of this happening are 7/25 * 18/25 = 126/625 the same thing is done with the French only and we get 4/25 * 21/25 = 84/625 and then we have the possibility of just getting a student that does both which is 14/25 or 350/625. now we add them all together to get 560/625 which is simplified to 112/125.
Hope this helps please mark brainliest :)
what is the illustrated property of the statement
if 5n=15,then 15=5n ?
BRAINLIEST
This would be the symmetric property!
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
The property illustrated here is symmetric property .
Explanation:
Symmetric Property of Equality. The following property: If if a = b then b = a. This is one of the equivalence properties of equality. See also. Reflexive property of equality, transitive property of equality, transitive property of inequalities.
PLEASE HELP ME
3x - 8y = 29
3x + y = -2
Question 4 options:
(0.5, -3.5)
(0, -2)
(0.75, -2.25)
(0, -3.75)
Answer:
Solution to pair of linear equations
Step-by-step explanation:
Subtract second equation from the first
[tex]3x-8y=29\\3x+ y=-2\\[/tex]
subtraction eqn 2 from 1 we get
[tex](3x-3x)+(-8y-y) = (29-(-2))\\-9y=31\\y=-\frac{31}{9} \\y= - 3.44[/tex]
In order to find the value of x we will put this value of y in anyof the above equation and solve it for x
[tex]3x-\frac{31}{9} = -2\\3x=-2+\frac{31}{9} \\3x=\frac{-18+31}{9} \\3x=\frac{13}{9} \\x=\frac{13}{9*3} \\x=\frac{13}{27} \\x=0.4814[/tex]
The Correct answer which is solution two the above linear pair of equations is
x=0.4814
y=-0.344
What is the area of the figure? The diagram is not drawn to scale.
A. 528 in^2
B. 1,056 in^2
C. 1184 in^2
D. 1,221 in^2
Answer: The answer is B.
Step-by-step explanation:
Area of parallelogram = B*H (base times height)
Here, the base is 32 inches and the height is 33 inches.
32*33=1,056in^2
Answer:b
Step-by-step explanation:
We multiply base and height
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = 2x3 + 8x2 + 7x - 8
Answer:
The list is -1,1,-2,2,-4,4,-8,8,-1/2,1/2
Step-by-step explanation:
Possible rational zeros are the constant factors/leading coefficient factors
So factors of -8: -1,1,-2,2,-4,4,-8,8
So factors of 2: -1,1,-2,2
Now put every number in the first list over every number in the second list:
The possible rational zeros are:
-1/1=-1
1/1=1
-2/1=-2
2/1=2
-4/1=-4
4/1=4
-8/1=-8
8/1=8
-1/2
1/2
I didn't write any number twice.... like -8/2 is just -4 which I already wrote
The list is -1,1,-2,2,-4,4,-8,8,-1/2,1/2
Answer:
±1/2, ±1, ±2, ±4 and ±8
Step-by-step explanation:
The Rational Zeros Theorem is defined as when a polynomial has all coefficients integer, then any rational zeroes of the polynomial have to be in the form ±p/q, where q is the coefficient of the highest power of the variable and p is declared as the constant term.
Furthermore, a rational "zero" is for a polynomial. when the polynomial is p(x), a "zero" is a value of x when p(x) = 0
Secondly, we have to know what a "rational zero" is. A "rational zero" is a zero that its number is rational. Some polynomials have some rational zeros and some irrational zeros, and some only have zeros that are rational numbers.
By applying this theorem, all possible factors of the constant term must be considered . In this example they are 1, 2, 4, and 8. After that Then you consider all possible factors of the coefficient of the highest power of the variable. we take the x³ term, whose coefficient is 2. the the possible factors of 2 are 1 and 2.
Therefore, the possible list of rational zeroes are given below
±1/1 = ±1
±1/2
±2/1 = ±2
±2/2 = ±1
±4/1 = ±4
±4/2 = ±2
±8/1 = ±8
±8/2 = ±4
By removing the duplicates, we arrive at the following,
±1/2, ±1, ±2, ±4 and ±8
The parabola opens: y=√x-4 (principal square root) up down right left
Answer:
right towards positive x axis
Step-by-step explanation:
In order to find the orientation of the parabolas we can follow following steps.
1. if in the equation x is squared , the parabola opens up. Also if its coefficient is negative it opens down.
2. If y is squared , the parabola opens right , and its coefficient is negative , it opens left
but before that we have to convert our function in standard form of the parabola. Our equation is
[tex]y=\sqrt{x-4}[/tex]
hence we square on both sides
[tex]y^2=x-4[/tex]
which is now into one of the standard form of a parabola. here y is squared and its coefficient is not negative hence it opens towards right.
Consider the quadratic function shown in the table below. x y 0 0 1 3 2 12 3 27 Which exponential function grows at a faster rate than the quadratic function for 0
Answer:
Graph D last graph
Step-by-step explanation:
please help asap urgent brainliest
Answer:
24 units cubed
Step-by-step explanation:
Volume is just length x width x height
so the width is 2 units and the height is 2 units and the length is 6 units: 2 x 2 = 4
4 x 6 = 24 units cubed
One unit cube = 1 by 1 by 1.
In the long picture, we have 2 by 2 by 6.
Volume = 2 x 2 x 6
Volume = 4 x 6
Volume = 24 units^3
HELP ME PLEASE MATH
Which graph represents the following system of inequalities?
y > 5x-1, because it is just a greater than sign, the shaded area would be to the left of a dotted line.
y ≤ x +3, because the sign is less than or equal to, the line is solid and the shaded area would be to the right.
Combine the shaded areas would make Graph B. the correct answer.
Brainliest!, write an algebraic expression to represent the verbal expression
the cube of the quotient of a number and 24
Answer:
(n/24)^3
Step-by-step explanation:
If "n" represents "a number," then "the quotient of a number and 24" means ...
(n/24)
The cube of that is ...
(n/24)^3
Ms. Clint is comparing the sales of sweaters and gloves at her store for the past ten winter weeks. Select the true statement based on the graph.
Answer:
i would say b
Step-by-step explanation:
Answer:
The correct option is B.
Step-by-step explanation:
The given graph represents the sales of sweaters and gloves at her store for the past ten winter weeks.
If the scatter points lie near to a straight line and the slope of the line is positive, then there is a strong positive linear correlation between two variables.
r=1 means strong positive correlation.
r=0 means no correlation.
r=-1 means strong negative correlation.
From the figure it is clear that the scatter points lie near to a straight line and the slope of the line is positive. So, there is a positive linear correlation between the sales of sweaters and gloves.
Therefore the correct option is B.