The function that is positive for the entire interval [-3, -2] is given as follows:
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0).
When is a function positive over an entire interval?A function is positive over an interval if the values of y of the function are above zero for the entire interval.
A function is negative over an interval if the values of y of the function are below zero for the entire interval.
For the function in this problem, we have that:
It is a concave up parabola with roots at x = -1 and x = 5.The minimum value is at x = 2.As the function is concave up, it is positive to the left of the smaller root at x = -1, that is, positive for all x < -1, hence the correct option.
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cylinder has a volume of 2,034.72 cubic millimeters and a radius of 6 mm, whats the height?
Answer:
2,260.80 cubic millimeters
Step-by-step explanation:
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters
Explain how you can check to see if your prime
factorization is correct.
Answer:
The simplest algorithm (a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.) to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, by prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, and 5/5 = 1. Since we received the remainder, it cannot be further factorized.
Step-by-step explanation:
pls tell me if wrong have a good day/night<3
There are two typical approaches to prime factorization. The Prime Factor Tree and the Upside-Down Division are the first and second, respectively.
How many ways can you find prime factorization?There are two typical approaches to prime factorization. The Prime Factor Tree and the Upside-Down Division are the first and second, respectively. I'll also demonstrate two approaches to prime-factorize 40 using this. Divide the supplied number by the smallest prime, 2, to begin.To factorize an equation is to write it as the product of its factors. An irreducible factor is one that cannot be further represented as the product of other factors, much like prime factors. Every algebraic term also has the number 1 as a factor, however this is only indicated when it is necessary.Factorization is the technique of representing an expression as the sum of two or more factors.First, imagine that the given number is the tree's root. Step 2: Draw a tree with the two elements as its branches. Step 3: Refactor the composite factors and make a branching list of the factor pairs. Method 4: Repeat the previous step until all of the composite factors' prime factors have been identified.To learn more about prime factorization refer to:
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A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon
(A) 41
(B) 46
(C) 43
(D) 45
(E)Other
A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure
(A) 40
(B) 25
(C) 60
(D) 35
(E)Other
A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q
(A) 5
(B) 19
(C) 37
(D) 47
(E)Other
The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence
(A) 25/12
(B) 9/4
(C) 7/4
(D) 2
(E)Other
sorry if there's any spelling errors
Answer:
C. 43
A. 40
C. 37
E. Other
A rectangle with sides of length 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon
Ans:
The perimeter of a rectangle is given by 2length + 2width. In this case, the perimeter of the rectangle is 284 + 245 = 258.
Since the perimeter of the hexagon is the same as the rectangle, and the sides of the hexagon are all the same length, we can find the length of a side of the hexagon by dividing the perimeter by the number of sides.
A hexagon has 6 sides, so the length of a side of the hexagon is 258/6 = 43.
So the answer is (C) 43.
A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure.
Ans:
The perimeter of the new figure would be 40. The original square had a side length of 5, so when two opposite sides were tripled, the new side length became 15. The perimeter of a rectangle is the sum of all four sides, so it would be 2 * (15) + 2 * (15) = 40.
(A).40
A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q.
Ans:
The probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 can be found by comparing the areas of the two triangular regions formed by the point and the two sides. The area of the triangular region formed by the point and the side of length 25 is (1/2) * 6 * (distance from point to side of length 25) while the area of the triangular region formed by the point and the side of length 6 is (1/2) * 25 * (distance from point to side of length 6).
For the point to be closer to the side of length 25, the area of the triangular region formed by the point and the side of length 25 must be greater than the area of the triangular region formed by the point and the side of length 6. This means (1/2) * 6 * (distance from point to side of length 25) > (1/2) * 25 * (distance from point to side of length 6). Therefore, the probability that the point is closer to the side of length 25 is (1/2) * (6/25) = 3/25. The sum of p and q is 3 + 25 = 28.
Therefore, the answer is (C) 37.
The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence.
Ans:
It is not possible to determine the sum of the possible values of the common ratio of the geometric sequence without more information about the values of m and n in the equation X^3 + mx = 37x^2 +n. In order to solve for the common ratio, the values of x would need to be found and it requires the values of m and n.
7 x + 4 y = 17 3 x + 4 y = 5
Answer:
make the x and y variables to each other variables by addition or subtraction
173x-7x +4y-4y=5
166x + 0y=5
166x =5
x= 166/5
x=33.2
The following scenario represents a proportional relationship.
Jason bought 4 pounds of bananas for $3.16.
What is the constant of proportionality?
The constant of proportionality will be $0.79
What is constant of proportionality?It is defined as the rate or the ratio of two proportional values which are known to be at the same value.
The two variable values are said to have a proportional association if or when either of their ratio or their product are known to bring about a constant.
Hence, the proportionality constant's value is known by the proportion between the two said quantities.
Jason bought 4 pounds of bananas for $3.16.
k = $3.16/4
k = $0.79
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Joshua drove 22 miles in 55 minutes. If he drove at a constant rate, how far did he travel in one hour?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, whole numbers, or decimals.
If Joshua drove at a constant rate, he drove 24 miles in one hour since he could drive 22 miles in 55 minutes or 0.4 miles per minute (driving speed).
What is the speed?Joshua's driving speed is the quotient of the total distance and the time.
The quotient is the result of a division operation, where a numerator (distance) is divided by the denominator (time) to obtain the unit rate or constant rate.
This constant rate (speed) is multiplied by the time (one hour), according to the distance, time, and speed formula, to obtain the distance to be covered.
The distance covered in 55 minutes = 22 miles
Constant driving speed or rate = 0.4 miles per minute (22/55)
1 hour = 60 minutes
For one hour, the distance Joshua could cover = 24 miles (60 x 0.4)
Thus, we can assert that in one hour, Joshua traveled 24 miles, given his constant driving rate.
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NO LINKS!!!
Find the area of the shaded region of the shapes below. (Label Units.)
Answer:
1) 216 units², 2) 138 units²-------------------------------------
Top figureWe know that the area of a rectangle with same dimensions is twice the area of a triangle.
The shaded area is half the area of the rectangle:
A = ab/2 = 18*24/2 = 216 units²Bottom figureYou already divided it to rectangle and triangle.
Area of rectangle:
A = ab = 10*12 = 120 units²The triangle have same base, 12 units. It height is 16 - 10 = 6 units.
Its area is:
A = bh/2 = 12*6/2 = 36 units²Area of the small rectangle in the middle:
A = 6*3 = 18 units²The shaded area is the difference of the total area and the small rectangle:
Shaded area = 120 + 36 - 18 = 138 units²ANYONE GOOD AT MATH! PLEASE HELP!
Answer:
To find f(2), we substitute 2 for x in the equation of the parabola F(x) = x^2 - 2x - 3:
F(2) = 2^2 - 2(2) - 3 = 4 - 4 - 3 = -3
So f(2) = -3
To find g(-3), we substitute -3 for x in the equation of the line g(x) = x - 2:
g(-3) = -3 - 2 = -5
So g(-3) = -5
The correct solution to this question is as follows:
f(2)= -3 & g(-3)=-5
Step-by-step explanation:
[tex]f(x)=x^{2} -2x-3[/tex]
[tex]f(2)=2^{2} -2(2)-3[/tex]
[tex]f(2)=4 -4-3[/tex]
[tex]f(2)=-3[/tex]
[tex]g(x)=x-2[/tex]
[tex]g(-3)=-3-2[/tex]
[tex]g(-3)=-5[/tex]
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Let f(x)=e^x and g(x). What are the domain and range of (gxf)(x)?
domain: x > 0 range: y > 0
domain: x > 6 range: y > 0
domain: all real numbers range: y > 6
domain: all real numbers range: all real numbers
Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
What are the domain and range?
The domain and range of a function are the set of all the inputs and outputs a function can give respectively. The domain and range are important aspects of a function. The domain takes all the possible input values from the set of real numbers and the range takes all the output values of the function.
We have the functions, f(x) = eˣ and g(x) = x+6
So, their composition will be g(f(x)).
Then, g(f(x)) = g(eˣ) = eˣ+6
Thus, g(f(x)) = eˣ+6.
Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.
Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.
Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.
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What is the slope of the line?
m =
Answer:
1/3
Step-by-step explanation:
Everytime x increases by 3 units, y increases by 1 unit.
Hence, when Δx=3, Δy=1 (Δx = change in x)
m=Δx/Δy
m=1/3
(Y-9)²/4÷(4y-36)/16 what is solver
Answer:
y - 9
Step-by-step explanation:
(y-9)²/4÷(4y-36)/16
is a fraction divided by a fraction.
When you have one or two fractions with a division, use Keep-Change-Flip.
Keep the first term:
(y-9)²/4
then Change the ÷ to a times.
(Y-9)²/4•
then Flip the second term.
(y-9)²/4 • 16/(4y-36)
You can factor the term (y-9)² into
(y-9)(y-9).
The other term (4y-36) can also be factored into
4(y-9).
see image.
The 4's and the y-9 terms can be "cancelled".
see image. The only term left is y-9.
A group of people were asked how many people live in their household. How many said they have 3 or more in their household?
Answer:
11
Step-by-step explanation:
we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7
In the Olympic Games, Michael Phelps won eight gold medals in swimming. Following are some of the events he won, along with his margin of victory, in seconds
The median margin for victory will be 1.89.
What defines median?The median of the data is the value of the middle observation discovered after the data are organized in ascending order. The median is useful in situations where it is difficult to express anything while taking into account all of the data.
One of the easy to calculate statistical summary metrics is the median. Since it bases its value on the data that is in the middle of a sequence, the median is often referred to as the place average.
Given Data:-
1.89,2.32,0.08,4.74,0.30
Mean margin of victory= 1.866
Median margin of victory= 1.89
So the median margin for victory will be 1.89.
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Complete question -
A computer and printer cost a total of $1056. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
Hope This Helps <3
Step-by-step explanation:
Printer cost 265
Computer cost 795
What is the meaning of the absolute value of a number?
A.the direction a number is located with respect to zero
B. the distance a number is located from zero
C.the value of a number after it has been rounded up
D.the value of a number after it has been rounded down
Which reason completes the proof for step 6? A. Definition of slope B. Definition of midsegment C. Definition of median D. Definition of midpoint
The reason that completes the proof for step 6 is given as follows:
D. Definition of midpoint.
How to obtain the midpoint of a segment?The midpoint between two points is the halfway point between them, hence it is found obtaining the mean of the coordinates of each endpoint.
Thus the coordinates of P' are obtained as follows:
x: (2r + 0)/2 = r.y: (2s + 0)/2 = 2.(applying the mean of the coordinates of x and y for the endpoints of the segment P').
The coordinates of R' are obtained as follows:
x: (0 + 2t)/2 = t.y: (0 + 0)/2 = 0.The coordinates of Q' are obtained as follows:
x: (2r + 2t)/2 = 2(r + t)/2 = r + t.y: (2s + 0)/2 = s.Meaning that the correct option is given by option D.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Vanessa picked 12 strawberries. She divided the strawberries and gave 1/3 to her brother. She kept the rest for herself. How many strawberries did she give her brother.
Answer: 4 strawberries
Step-by-step explanation:
First, we can change the total number of strawberries into a fraction, that way it makes the division process easier. 12 is really equivalent to 12/1 since it is a whole number. Now, we can set up an equation: (12/1) * (1/3) will solve to give us the number of strawberries the brother has. Since there is a one in both the numerator and the denominator, they will cancel, leaving us with (12/3). This is now just division, which gives us 4. Therefore, the brother will receive 4 strawberries. Hope this helps!
FInd the half-life of a radioactive element, which decays according to the function A(t)= A0e^-0.0372t, where t is the time in years
Answer:
below
Step-by-step explanation:
1/2 = e^(-.0372t) ln both sides to get :
-.693147 = - .0372t then t = 18.6 yrs
3. Copy these equations and add brackets so that the answers are correct. 42-8x3-22=80 b) 75+5x4-70=25 160÷4x3 + 2 = 200 d) 120÷2x3+5=25
The correct brackets for the equations are added as follows:
a) (42 - 8) x 3 - 22 = 80
b) 75+ (5 x 4) -70 = 25
c) (160 ÷ 4) x (3 + 2) = 200
d) 120 ÷ (2 x 3) + 5 = 25.
What are equations?Equations are mathematical statements that equate or show that two or more mathematical expressions are equivalent or equal.
Equations use the equation symbol (=) to show the equality of the algebraic expressions.
Using parentheses in equations enable the use of the distributive property to solve the equation.
Thus, the correct parentheses have been added to the equations to prove them correct when solved.
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please help very important
Answer:
x = 18.3
Step-by-step explanation:
You want the length of the hypotenuse of a right triangle given the side opposite the 41° angle is 12 units.
SineThe sine relation is ...
Sin = Opposite/Hypotenuse
This can be rearranged to ...
Hypotenuse = Opposite/Sin
x = 12/sin(41°) ≈ 18.3 . . . . units
The value of x is about 18.3.
__
Additional comment
This is the SOH relation from the mnemonic SOH CAH TOA, which is intended to remind you of the relation between trig functions and sides of a right triangle. The others tell you ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
In the attached, note the calculator mode is set to DEG (degrees) so the argument of the Sin( ) function will be interpreted properly.
Please look at the picture and answer the question, thank you!
Which angle is vertical to 1?
Answer:
Have a good day!:)
Step-by-step explanation:
When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Help please
The amount of fencing is ___\
The perimeter of the fencing in terms of 'x' will be 13x + 3.
What is the perimeter of the shape?The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
The perimeter of the fencing in terms of 'x' is given as,
P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)
Simplify the equation, then we have
P = x + x + x + x + (3x + 1) + (3x + 1) + (3x + 1)
P = x + x + x + x + 3x + 1 + 3x + 1 + 3x + 1
P = 13x + 3
The perimeter of the fencing in terms of 'x' will be 13x + 3.
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Find the values of a, b, and]e if lines m and n are parallel.
The angles are 36,118,62
What happens when a transversal intersects parallel lines?If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
Given: m and n are parallel lines with 3 transversals
We can observe that a=36 (vertically opposite angles)
and b =180-(36+26) ∵ They all lie on a line .
=118
and c= 180-118 ∵They all lie on a line.
=62
Hence, The angles are 36,118,62
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12 People fit comfortably in a 5 feet by 11 feet area. Use this value to estimate the size of a crowd that
is 10 feet deep on both sides of the street along a 3-mile section of a parade route.
Answer:
Step-by-step explanation:
Assuming that there are no sidewalks or other obstructions, the estimated size of the crowd along a 3-mile section of the parade route would be approximately 3,780,400 people. This calculation is based on the assumption that people will be standing shoulder to shoulder and that each person will take up an area of 5 feet by 11 feet. This would mean that for each mile of the parade route, there would be 1,260,800 people standing (12 people x 10 feet x 5280 feet). Multiplying this by 3 gives us 3,780,400 people.
Answer:
12 people fitting in an area of 5*5 = 25 ft². Area of the street: 3 miles = 3*5280 ft = 15840 ft 25 feet on both sides. So, the total area in which the crowd is sparsed is: A = 15840*25*2= 792000 ft². Now we apply the ratio: People over area. Applying cross multiplication: 25x = 12*792000 x = (12*792000)/25 x = 380160
Step-by-step explanation:
DUE SOON! PLEASE HELP!
QUESTIONS ARE BELOW!
MANY THANKS!
An equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y= 1/4 ((x-3)²-6).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Translation rules:
When the shape is moved towards the left by k units, then replace x with x - k.
When the shape is moved up by k units, then replace y with y + k.
3) Given that, the equation of the parabola is y=(x-3)²-7
The equation is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter.
Here, 1/4 ((x-3)²-7-4+5)
y= 1/4 ((x-3)²-6)
4) The given equation is h=-4.9t²+180t+2
a) the maximum height of the rocket
Use the formula
x =-b/2a to find the maximum and minimum.
(18.36734693,1655.06122448)
b) the time required for the rocket to reach its maximum height
Find where the first derivative is equal to 0 to find the local maxima and minima.
(18.36734693, 1655.06122448) is a local maxima
c) the time required for the rocket to reach the ground
Solve the equation for t by finding a, b, and c of the quadratic then applying the quadratic formula.
t=900+3.16227766√(81098−49h)/49
t=900-3.16227766√(81098-49h)/49
Therefore, an equation of a given parabola that is translated by 4 units left, 5 units up and is compressed by a factor of one-quarter is y= 1/4 ((x-3)²-6).
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find the interval(s) of numbers that are at least a distance of 3 away from "-7"
Answer:
x ≥ - 4 and x ≤ - 10 - as inequality( - ∞, - 10] ∪ [ - 4, ∞) - as intervals-----------------------------
The numbers that are at least a distance of 3 away from -7 are the numbers 3 units or more away from -7 either side on the number line :
x ≥ - 7 + 3 = - 4or
x ≤ - 7 - 3 = - 10This is same as:
( - ∞, - 10] ∪ [ - 4, ∞)PLSSS HEPP MEEE THYYY
In November 2018, the frequency tree shows us that 35 students aged 15 years old had part-time work.
That number 35 drops to 23 a year later in 2019. There are two reasons for this:
The student lost their job. They got fired or quit their job.The 15 year old student had a birthday and turned 16.Case (2) mentioned above only works if the student's birthday is before April 2019.
how to identify what type of shape ABCD is if A is (-3,0), B (1,5), C(-3,10) and D(-7,5) the slope of BC=-5/4 and the length of DA=6.4
The shape of the ABCD is a rhombus. The diagonals are not equal to each other.
What is the 2-dimensional shape?
A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.
Given the vertices of ABCD are A(-3,0), B (1,5), C(-3,10) and D(-7,5).
The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4
The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4
The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10
The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8
The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of AB is (5-0)/(1-(-3))=5/4
The slope of BC is (10-5)/(-3-1)=-5/4
The slope of CD is (5-10)/(-7-(-3))=5/4
The slope of AD is (5-0)/(-7-(-3))=-5/4
The number of vertices of the quadrilateral is 4.
Thus it is either a square or rectangle or rhombus or parallelogram.
Since the length of all sides is equal thus it is either a square or rhombus.
Since the diagonals are not equal it is a rhombus.
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The sum of an A.P. is 340, the first term is 7 and the common difference is 6.
Calculate the number of terms in the sequence
The number of terms (n) in the sequence = 10.
We know that,
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
Where,
S = Sum of A. P. series
n = number of terms in A. P. series
a = first term of the series
d = common difference
According to the question,
Sum of the series, S = 340
First term, a = 7
Common difference, d = 6
S = [tex]\frac{n}{2\\}[/tex] {2a + (n-1)d}
340 = [tex]\frac{n}{2}[/tex] {2*7 + (n-1)6}
340 = [tex]\frac{n}{2}[/tex] {14 + 6n - 6}
340*2 = n( 6n + 8)
680 = 6n^2 + 8n
6n^2 + 8n - 680 = 0
2 (3n^2 +4n - 340) = 0
3n^2 +4n - 340 = 0
3n^2 + 34n - 30n - 340 = 0
n (3n+ 34) - 10 (3n + 34) = 0
(3n + 34) (n - 10) = 0
if we take, 3n + 34 = 0
3n = - 34
n = -34/3
which is not possible, as the number of terms can not be negative
if we take, n- 10 = 0
n = 10
Hence, the number of terms in the given A. P. series is 10.
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