Let the first of the two consecutive integers be n. Then the next consecutive integer is n+1.
From the given information, we can form an inequality, which is:2n + (n+1) ≥ 25
The above inequality is formed from the statement "Twice the smaller of two consecutive integers increased by the larger integer is at least 25". Now, let's solve this inequality and find the values of n that satisfy it.2n + (n+1) ≥ 25Simplifying the above inequality, we get:3n + 1 ≥ 25
Subtracting 1 from both sides, we get:3n ≥ 24
Dividing both sides by 3, we get:n ≥ 8
Hence, the first of the two consecutive integers is greater than or equal to 8.
Therefore, the two consecutive integers that satisfy the given information are 8 and 9.
Now, we need to check which of the given values, 7, 8, or 9, satisfy the above inequality. Let's check for
n=7.2n + (n+1) = 2(7) + (7+1) = 15 < 25
Therefore, n=7 is not a solution.
Let's check for n=8.2n + (n+1) = 2(8) + (8+1) = 25 ≥ 25
Therefore, n=8 is a solution. Let's check for n=9.2n + (n+1) = 2(9) + (9+1) = 28 ≥ 25
Therefore, n=9 is also a solution.
Thus, we have found that the solutions to the given problem are n=8 and n=9.
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identify f(1) and (f2)
Answer:The vowels in the left column are called "front vowels." Tongue body is in the front of the mouth. All vowels show a "gap" in frequency between F1 and F2. ... A traditional "vowel diagram" can be obtained by plotting the vowel formants in a graph where the horizontal axis is (F2-F1) and the vertical axis is inverse F1.
Step-by-step explanation:
Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)
On which interval is y = sin(x) strictly increasing?
Answer: 0, pi/2
Step-by-step explanation:
I guessed tbh
The interval in which the function y = sin( x ) will strictly increase is ( 0, π/2 ).
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The graph is attached with the answer below in the graph we can see the maximum and minimum values of the function y = sin ( x ).
In the graph the maximum limit of the function π/2 it means that the strict increment in the graph is in the interval of ( 0, π/2 ).
Therefore, the interval in which the function y = sin( x ) will strictly increase is ( 0, π/2 ).
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6 Kyle is creating a frame for a model car. He begins by plecing two rods together, as shown in the diagram. Justify why AB- 10. O Segment Addition Postulate O Addition Property O Definition of Collinear Points O Definition of Midpoint
According to the diagram provided, Kyle is creating a frame for a model car by placing two rods together. To justify why AB equals 10, we can use the Segment Addition Postulate.
The Segment Addition Postulate states that if three points A, B, and C are collinear (meaning they lie on the same line), then point B is between points A and C if and only if the sum of the lengths of segments AB and BC is equal to the length of segment AC. In this case, the diagram shows points A, B, and C on a line, where A is the left endpoint, B is the midpoint, and C is the right endpoint. Since point B is the midpoint of segment AC, it divides the segment into two equal parts. Therefore, the length of segment AB is equal to the length of segment BC, and since the lengths are equal, we can conclude that AB is equal to 10 units. Hence, the justification for AB being 10 is based on the Segment Addition Postulate, as it guarantees that point B is the midpoint of segment AC.
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Complete question:
Kyle is creating a frame for a model car. He begins by plecing two rods together, as shown in the diagram. Justify why AB- 10. O Segment Addition Postulate O Addition Property O Definition of Collinear Points O Definition of Midpoint
3 t-shirts and 2 hats costs £14.
2 t-shirts and 7 hats costs £15.
Find the cost of a t-shirt.
Find the cost of a hat.
t-shirt: £
o
hat: £
Write an equation in point-slope form of the line that passes through the point (4,7) and has a slope of -1.
Answer:
y - 7 = - 1(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 1 and (a, b) = (4, 7) , thus
y - 7 = - (x - 4)
The equation of line in the point-slope form is y = -1x + 11
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the point be P = P ( 4 , 7 )
Let the slope of the line be m = -1
So , the equation of line is given by the formula
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 7 = -1 ( x - 4 )
On simplifying the equation , we get
y - 7 = -1x + 4
Adding 7 on both sides of the equation , we get
y = -1x + 11
y = -x + 11
Therefore , the value of A is y = -x + 11
Hence , the equation of line is y = -x + 11
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Five less than twice a number is greater than 13. Then solve.
Answer: The answer should be -4
Step-by-step explanation:
i need help with these questions !
Answer:
See below:
Step-by-step explanation:
A. y = 30 + 12.50x
Let x be the number of people. It costs 12.50 per person, so y = 12.50x. Notice how the delivery fee is not per person, meaning that the delivery fee is not impacted by the amount of people buying it. Thus, y = 12.50x + 30
B. c = 0.12m + 8.00
See explanation of A:
C. 2
The slope of a line in y-intercept form ( y = mx + b ), is the number before the x. In this case, there is a 2 before the x.
D. y = 2/3x - 3
In slope intercept form, y = mx + b. Plug in the values of m ( slope ) and b( y-intercept ) and you get y = 2/3x - 3
E. y = 1/2x
The slope can be found by dividing the change of y by the change of x. Our points are (0,0) and (2,1). The change in y is 0-1, which is -1; the change in x is (0 - 2), which is -2. -1/-2 is 1/2 so the slope of the line is 1/2. Because when x = 0, y = 0 too, there is no y-intercept, so the equation of the line is y = 1/2
Answer:
The answer is B.
Step-by-step explanation:
Y = the holiday meal costs
If they’re charging a holiday meal per person the equation would be 12.50x = y
But we also have a $30 delivery fee so it would be
12.50x + 30 = y
So the equation represents
A holiday meal costing 12.50 is ordered for an x amount of people. There is also a $30 delivery fee. The meal costed y amount of dollars.
Write an equation that would represent the following statement: The difference of three times a number and 7 is 39.
b1=10
b2=8
b3-a=15
b3-b=10
b4=9
i want to ask... now in question i want to calculate
the time needed..i should take the lomgest way?
i mean 10 + 8 +15 + 9=42
or i need to take the average i
The total Distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them
In order to calculate the time needed, we need to consider the distances between each point.
This can be done using the Pythagorean Theorem, which states that the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides.
For this problem, we can treat each segment as the hypotenuse of a right triangle, where the other two sides are the distances between each point.Using this method,
we can calculate the distances between each point:b1 to b2: distance = sqrt((b2 - b1)^2) = sqrt((8 - 10)^2) = 2b2 to b3: distance = sqrt((b3 - b2)^2) = sqrt((15 - 8)^2) = 7b3 to a: distance = sqrt((a - b3)^2) = sqrt((15 - 15)^2) = 0b3 to b: distance = sqrt((b - b3)^2) = sqrt((10 - 15)^2) = 5b4 to b: distance = sqrt((b - b4)^2) = sqrt((10 - 9)^2) = 1
Now that we have the distances,
we can add them up to get the total distance:2 + 7 + 0 + 5 + 1 = 15
Therefore, the total distance between all points is 15. This is the shortest distance between all points, so it is the time needed to travel between them.
So, the answer is we should take the shortest way, not the longest way.
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CAN SOMEONE PLEASE HELP ME?? I NEED ANSWERS FAST!!!
Answer:
hi
Step-by-step explanation:
hello
What is the full form of PDF ?
Answer:
portable document format
Answer:
Portable document format
Luke weight 90 pounds on earth and when he recheas the moon he weight twice lesser, why?
Answer:
he doesn't weight as much because he doesn't have gravity helping keep him to the ground
Prove, or disprove by means of a counterexample, each of the following statements. (i) The sum of a finite number of convex subsets of R n is convex. (ii) The collection of all convex subsets of R 2 a linear space. (iii) The sum of two closed subsets of R n is closed. (iv) Does the sentence in (iii) above make sense if (X,d) is substituted for R n ? If so, prove it. If not, justify the claim that it is incoherent. (v) The projection onto any particular coordinate of a closed subset of a metric space R n is closed. [Recall that for any A⊆R n , its projection on to the i th -cordinate, i=1,⋯,n, is denoted by proj i A={y i ∈R:(y 1 ,y 2 ,⋯,y n )∈A}.]
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
Proof: Let A_1, A_2, ..., A_k be convex subsets of R^n. We want to show that the set B = A_1 + A_2 + ... + A_k (which is the set of all possible sums of elements from each A_i) is convex.
Let x, y ∈ B and let α ∈ [0, 1]. Since x and y are in B, there exist vectors a_1, a_2, ..., a_k and b_1, b_2, ..., b_k such that x = a_1 + a_2 + ... + a_k and y = b_1 + b_2 + ... + b_k, where a_i, b_i ∈ A_i for each i = 1 to k.
Now consider the point z = αx + (1 - α)y. We need to show that z is also in B.
z = αx + (1 - α)y
= α(a_1 + a_2 + ... + a_k) + (1 - α)(b_1 + b_2 + ... + b_k)
= (αa_1 + (1 - α)b_1) + (αa_2 + (1 - α)b_2) + ... + (αa_k + (1 - α)b_k)
Since each A_i is convex, we have αa_i + (1 - α)b_i ∈ A_i for all i = 1 to k. Therefore, z belongs to the set B = A_1 + A_2 + ... + A_k.
Hence, the sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
Counterexample: Consider two convex subsets of R^2, A = {(x, y) ∈ R^2 : x > 0} (the right half-plane excluding the y-axis) and B = {(x, y) ∈ R^2 : x < 0} (the left half-plane excluding the y-axis). Both A and B are convex subsets of R^2.
Now, let's consider their sum, A + B. For any point (x, y) in A + B, there exist points (a, b) from A and (c, d) from B such that (x, y) = (a, b) + (c, d). However, (a + c, b + d) must lie on both the right half-plane and the left half-plane simultaneously, which is not possible. Therefore, A + B is not a valid convex subset of R^2.
Hence, the collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
Counterexample: Consider the closed subsets A = [0, 1] and B = [2, 3] of R. Both A and B are closed intervals in R.
The sum A + B = [0, 1] + [2, 3] = [2, 4]. However, [2, 4] is not closed since it does not contain its limit points, specifically the point 3.
Therefore, the sum of two closed subsets of R^n is not always closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
The concept of "closed" subsets relies on the notion of limits and convergence, which is defined in the context of metric spaces. If (X, d) is a general metric space, the idea of closed subsets and their properties may vary depending on the specific metric and topology of the space. Therefore, it is not meaningful to discuss the closure of subsets in a general metric space without further specifying the properties of that particular space.
Hence, the claim is incoherent unless additional information about the specific metric space (X, d) is provided.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
Proof: Let A be a closed subset of R^n, and consider its projection onto the i-th coordinate, proj_i(A) = {y_i ∈ R : (y_1, y_2, ..., y_n) ∈ A}.
We need to show that proj_i(A) is closed. To do this, we can show that its complement, proj_i(A)^c, is open.
Let x ∈ proj_i(A)^c. This means that x is not in proj_i(A), so there exists some (a_
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you are required to push a 180 pound ball to a storage platform 15 feet higher than where you are now. you can use a 45 foot long ramp to push the ball up. how much effort is required to push the ball up the platform using the ramp?
60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.
To determine the effort required to push the 180-pound ball up a 15-foot high platform using a 45-foot long ramp, we need to consider the forces involved and apply the principles of work and energy.
The work done to raise the ball to the platform is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is the effort required to push the ball up the ramp, and the distance is the length of the ramp.
First, we need to calculate the mechanical advantage of the ramp. The mechanical advantage is the ratio of the length of the ramp to the vertical height it lifts the object. In this case, the mechanical advantage is 45/15 = 3.
Next, we calculate the weight of the ball, which is 180 pounds.
The effort required can be determined using the formula:
Effort = (Weight of the ball) / (Mechanical advantage)
Effort = 180 pounds / 3 = 60 pounds
Therefore, approximately 60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.
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How do you determine where to place the decimal point in the product?
Let's look at an example:
2.24 x 21.6
[tex]2.24\\ 21.6\\ ______[/tex]
Do normal multiplication and get
48384 This is not correct, until we put the decimals in. To know how to do this, count the number of decimal spaces from the factors. In 2.24, there are 2, because .24. In 21.6 there are 1 because of .6. This mean three places, so 48384 becomes
48.384
~theLocoCoco
please give answer it is very small
Answer:
Answer is 3^4/5*a^2*b*c^2
How do I solve... a for this equation? What steps should I take to solve it?
2B(F+a)=H
3[tex]\sqrt{x} 9\\[/tex]
Answer: x^4X\sqrt{x}
Step-by-step explanation: x9" was replaced by "x^9".
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x9) = x4 • SQRT(x)
Simplified Root :
x4 • sqrt(x)
(a^2 + b^2)^2 + (a^8 + b^8)^2
Answer:
a^4+2ab^2+b^4+a^16+2ab^8+b^16
Step-by-step explanation:
(a^2+b^2)^2+(a^8+b^8)^2
(a^2+b^2)^2=(a^2+b^2)(a^2+b^2)
=a^2(a^2+b^2)+b^2(a^2+b^2)
=a^4+(ab)^2+(ba)^2+b^4
=a^4+2ab^2+b^4
(a^8+b^8)^2=(a^8+b^8)(a^8+b^8)
=a^8(a^8+b^8)+b^8(a^8+b^8)
=a^16+(ab)^8+(ba)^8+b^16
=a^16+2ab^8+b^16
(a^2+b^2)^2+(a^8+b^8)^2=(a^4+2ab^2+b^4)+(a^16+2ab^8+b^16)
the answer is a^4+2ab^2+b^4+a^16+2ab^8+b^16
i think it is simplified answer
A train leaves Boston at 10:20 AM and arrives in Stamford at 1:00 PM. Find the distance between the stations if the average speed of the train is 60 mph. help
Answer:
average speed = distance / time
60 = distance / (13.20 - 10.40)
13.20 - 10.40 = 2 hours 40 minutes = 2 2/3 hours
60 = distance / 8/3 = 3 d / 8 (where d = distance)
3d = 480
d = 480/3 = 160 miles
The distance between the station in Boston and the one in Stamford is 160 miles.
Distance is calculated by the formula:
= Speed x Time
The Speed is 60 mph as given.
The time is:
= 1:00 pm - 10:20AM
= 2 hrs 40 minutes
In decimals this is:
= 2 + 40/60 minutes
= 2 + 2/3
= 2.67 hours
The distance is therefore:
= Speed x Time
= 60 x 2.67
= 160 miles
In conclusion, the distance between the stations is 160 miles.
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What is the best method to separate a mixture of staples and salt?
Answer:
A filter.
Step-by-step explanation:
The given table of values represents a linear equation. What is the slope?
Answer:
2
Step-by-step explanation:
slope=∆y/∆x
thus values of y and x at any point in the table can be used.
slope= (7-5)÷(2-1)
slope=2.
Solve for r.
K= 2r-35
Answer:
r = k/2 + 35/2
multiply the square root of 20 and the square root of 63
Answer:
36.0555
Step-by-step explanation:
Answer:
= square root of 7 i believe
Step-by-step explanation:
QUESTION 5 Let u = (1, 2, -1), v = (6, 4, 2) € R³. 5.1 Write w = (-3,2,-5) as a linear combination of u and u. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is
1. The vector w = (-3, 2, -5) can be written as a linear combination of u and v.
2. The set {u, v} is linearly independent.
3. The vector w is not in the span of the set {u, v}.
1. To write w as a linear combination of u and v, we need to find scalars a and b such that w = au + bv. By solving the system of equations, we get:
-3 = a1 + b6,
2 = a2 + b4,
-5 = a*(-1) + b2.
Solving these equations, we find a = 2 and b = -1. Therefore, w = 2u - v.
2. The set {u, v} is linearly independent if the only solution to the equation au + bv = 0 is a = b = 0. We can write this equation as a system of equations:
a + 6b = 0,
2a + 4b = 0,
-a + 2b = 0.
Solving this system, we find that the only solution is a = b = 0. Therefore, the set {u, v} is linearly independent.
3. To determine if the vector w is in the span of {u, v}, we need to check if there exist scalars a and b such that w = au + bv. However, from the previous calculation, we found that w can be expressed as a linear combination of u and v with a = 2 and b = -1. Therefore, w is not in the span of {u, v}.
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Which statement compares the two numbers correctly? (2 points) 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 ________ 73.293 Group of answer choices 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 < 73.293 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 = 73.293 73.293 > 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 > 73.293
Answer:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Step-by-step explanation:
Given: Numbers are 7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 and 73.293
To compare: the two given numbers
Solution:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 is equal to [tex]73.385[/tex]
Compare the numbers [tex]73.385[/tex] and 73.293
Digits at the ones pace and tens place in both the numbers are same.
Observe the digit at the tenth place in both the numbers.
Digit at the tenth place in 73.385 is 3
Digit at the tenth place in 73.293 is 2
As [tex]3>2[/tex],
73.385 > 73.293
So,
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Answer: 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 > 73.293
Step-by-step explanation: ik this bc i have this same quiz so gl on the rest of the questions
The ratio of girls to boys in one of Mr. Pryslak's grade 9 Mathematics dasses is 4:3. If there are 9
boys in the class, how many girls are there?
Help me
Answer:
12 girls
Step-by-step explanation:
So the ratio of girls to boys is 4:3 and if there are 9 boys you multiply the number 3 by 3 to get 9 and do the same to the other side to get 12
Select the correct answer.
A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of
. What is the approximate distance from the playground to the road along the other path?
The picture shows an upside-down right-angle triangle. The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 mi and the swing stands on the downside of the triangle
A.
2.6 mi
B.
1.5 mi
C.
3.1 mi
D.
1.3 mi
The approximate distance from the playground to the road along the other path is 1.3 miles.
How to find the side of a right triangle?The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 miles and the swing stands on the downside of the triangle.
Using trigonometric ratios, let's find the approximate distance from the playground to the road along the other path as follows:
cos 50 = adjacent / hypotenuse
cos 50° = x / 2
cross multiply
x = 2 cos 50°
x = 2 × 0.64278760968
x = 1.28557521937
x = 1.3 miles
Therefore,
distance from the playground to the road along the other path = 1.3 miles
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what is the base of a triangle if the height is 6mm and the area is 36
Answer:
b=1.2×107mm
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
