The equation is y=mx+b
so it would be y=2/7(x)-12
Half of the product of two consecutive numbers is 105. which equation can be used to solve for n, the smaller of the two numbers
Givens
The numbers are n and n + 1
Average = Av = 105
Equation
Av = (n)(n + 1)/2
Solution
Av = 105
n(n +1)/2 = 105 Multiply both sides by 2
n(n + 1) = 105 * 2
n(n + 1) = 210 Remove the brackets.
n^2 + n = 210 Subtract 210 from both sides
n^2 + n - 210 = 0
factor
(n+15)(n - 14)
n + 15 = 0
n = - 15
n = - 15 which is the smallest of the two answers.
n + 1 = - 14
Check
(-15)*(-14)/2 =
210/2
105 It does check.
Answer:
The numbers are n and n + 1
Average = Av = 105
Step-by-step explanation:
Multi step linear inequality
c > -13/10
The > should have _ under it.
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x=29 and s=3.6 . Which statement must be true?
z37 is within 1 standard deviation of the mean.
z37 is between 1 and 2 standard deviations of the mean.
z37 is between 2 and 3 standard deviations of the mean.
z37 is more than 3 standard deviations of the mean.
Answer:
Option 3 is right
z37 is between 2 and 3 standard deviations of the mean.
Step-by-step explanation:
Let X be a random variable which represents the mean number of miles that the employees in a department live from work
X is normal (N(29,3.6)
WE have to find Z score for X
Z =[tex]\frac{x-29}{3.6}[/tex]
=2.22
i.e. 37 is 2.22 std deviations from the mean.
In other words, z37 is between 2 and 3 standard deviations of the mean.
The z-score for z37 is approximately 2.22. This indicates that it lies between 2 and 3 standard deviations of the mean. Hence, the correct statement is: z37 is between 2 and 3 standard deviations of the mean.
To determine which statement is true regarding the z-score for the value z37, we need to calculate the z-score using the given mean and standard deviation.
We know the mean ( ext{x}) = 29 and the standard deviation (s) = 3.6.The z-score formula is z = (X - mean) / standard deviation. Here, X = 37.This means that z37 is approximately 2.22 standard deviations away from the mean. Therefore, the correct statement is:
z37 is between 2 and 3 standard deviations of the mean.
In a normal distribution, about 95 percent of the x values lie within two standard deviations, and about 99.7 percent lie within three standard deviations of the mean.
What is the slope of the line passing through the points (2, −5) and (4, 1)?
A. 3
B. 2
C. -4/5
D. 5/4
Answer:
The slope is 3 (answer choice A).
Step-by-step explanation:
Take a look at the two given points, (2, -5) and (4, 1). As we move from the first point to the second, x increases by 2 and y increases by 6, so that the slope is m = 6/2, or 3.
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.
Step-by-step explanation:
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival
0.75 per ticket. So cost of 18 tickets= 0.75 * 18 = $13.5
Kendall spent $13.50 for tickets . Total spent = $33.50
Total spent = ticket cost + admission cost
33.50 = 13.50 + admission
Admission cost = 33.50 - 13.50 = $20
(a) y to represent the total cost , x to represent the number of ride tickets.
'b' represents the admission cost
(b) General form of linear equation is y=mx+b
m = 0.75 and b = admission cost = 20
So equation becomes y = 0.75x + 20
(c) Initially, she has to pay the admission price $20. then 0.75 per ticket.
The value of x changes depends on the number of tickets she wants to buy.
y is the total cost she has to pay for x tickets with admission price
carlos is arranging books on shelves he has 40 novels and 16 autobiographies. each shelf will have the same number of novels and autobiographies. If carlos must place all of the books on shelves, what are the possible numbers of shelves carlos will use?
two people begin traveling at the same time from opposite ends of a 20 mile trail. one person travels 3 miles per hour faster than the other. if they meet after 2 hours, what are the rates of the 2 people
Let us assume rate of other person = x miles per hour.
Rate of first person is 3 miles per hours faster than other.
Therefore, rate of first person = (x+3) miles per hour.
Total distance between them = 20 miles.
And total time taken by them is 2 hours.
We know, distance, time and rate relation:
Distance = Rate × Time.
Therefore, distance covered by other person = x * 2 = 2x.
Distnace covered by first person = (x+3)*2.
Total distance covered by both = 20 miles.
We can setup an equation
Total distance covered by both = Distnace covered by first person + distance covered by other person.
2(x+3) +2x = 20.
Now, we can solve the eqation for x.
2x +6 +2x = 20.
4x +6 =20.
Subtracting 6 from both sides, we get
4x +6-6 =20-6
4x = 14.
Dividing both sides by 4, we get
x=3.5
Rate of first person = (x+3) = 3.5+3 = 6.5 miles per hour.
Therefore, the rate of first person is 6.5 miles per hour and rate of second person 3.5 miles per hour.A magazine can layout 1/16 of an issue in 3 days.How many days dies it take to layout one issue?
To determine the time needed to layout a full magazine issue, multiply the time taken to layout 1/16 of an issue (3 days) by 16, resulting in 48 days total.
If a magazine can layout 1/16 of an issue in 3 days, then to calculate how many days it takes to layout one entire issue, we simply multiply the number of days it takes to layout 1/16 of the issue by 16.
This is because if 1/16 takes 3 days, then 1/8 (which is twice the amount of 1/16) would take twice as long
(3 days * 2 = 6 days),
and similarly, we can scale up to the full issue (1/1) by multiplying 3 days by 16.
The calculation would be:
Identify the portion of the issue completed: 1/16.
Identify the time taken for this portion: 3 days.
Calculate the time for the whole issue: 3 days * 16 = 48 days.
So, it would take 48 days to layout one full issue.
Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units
Answer:
7/4 < x < 11/2
Step-by-step explanation:
PLATO
Inequality which ensure triangle exists is 22 > 4x > 7.
What is inequality ?
" Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Theorem used
In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get,
[tex]AB + BC > AC[/tex]
⇒[tex]2x + 4 + 6x > 18[/tex]
⇒[tex]8x > 18 - 4[/tex]
⇒ [tex]8x > 14[/tex]
⇒ [tex]4x > 7[/tex] ___(1)
[tex]AC + AB > BC[/tex]
⇒ [tex]18 + 2x + 4 > 6x[/tex]
⇒ [tex]22 > 6x-2x[/tex]
⇒[tex]22 > 4x[/tex] ____(2)
From (1) and (2) inequality of triangle we get,
[tex]22 > 4x > 7[/tex]
Hence, Inequality which ensure triangle exists is 22 > 4x > 7.
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Two number that are equivalent to 0.20 and 0.30
Name all of the angles in these polygones (info in picture) FAST!!
First of all this is a very poor question, and you should question it a bit. What are these figures? Are they regular? (first 2). Is the last one a parallelogram. I'm going to assume that the yellow one is a rectangle and the middle one is a pentagon and the last one is a parallelogram.
Yellow
A has 4 right angles (That's the property of a rectangle).
Green
B has 5 angles that are equal to 108 degrees. If you draw a 2 lines from any vertex you get 3 triangles. The size of the interior angles totals 3 triangles * 180 degrees = 540 degrees.
540/3 = 108.
Each angle in the interior is 108 degrees.
B has 5 angles all equal 108 degrees. All 5 are obtuse.
Red
Just by sight and assumption C has 2 obtuse angles, and 2 acute angles.
Consider the following graph of an absolute value function
A
The domain is -∞ < x < ∞
B
The range is -∞ < x ≤ 3
C
The graph is increasing from -∞ < y < 3
D
The graph is decreasing from 3 > y > -∞
E
The local maximum is at ( - 2, 3 )
F
There are no local minimums
The graph of an absolute value function is a V or inverted V. The x-coordinate of the V's vertex provides the function's line of symmetry, and the y-coordinate of the V's vertex shows the minimum or maximum value of the function.
Explanation:An absolute value function is a function that contains an algebraic expression within absolute value symbols. The graph of an absolute value function is a symmetrical V or inverted V, depending on the direction of the opening. The vertex of the V, which is the minimum or maximum point of the graph, provides two important pieces of information: the x-coordinate of the vertex gives us the equation's line of symmetry, and the y-coordinate represents the minimum or maximum value of the function, depending on the opening direction.
Let's say, for example, we have the graph of the function |x - 3| + 2. The vertex of this function is at the point (3, 2). Therefore, the line of symmetry is x = 3, and the minimum value of the function is 2.
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You and nine friends have decided to take a few days to go camping. You plan a budget of $50 per day for activities. On one of the days you will rent canoes and tubes to explore the river. Tube rentals cost $5 and canoes cost $10. Each person would need a tube, but canoes hold up to three people. In order to budget for your day on the river, write an equation that shows how many tubes (t) and canoes (c) you would need to accommodate your group, then write an equation that expresses how much the tubes and canoes will cost and remain within the confines of your budget. Using the equations, find how many tubes and canoes can be rented.
y=10x+5 because x=3 so 10*3=30 and 30+5=35 which would mean that $35 is the lowest amount you can spend.
To stay within a $50 daily budget for activities, equations are created to determine the number of tubes (t) and canoes (c) that can be rented. With tube rentals at $5 and canoe rentals at $10, the group of ten can only rent tubes (t = 10), as renting canoes would exceed the budget (c = 0).
The question involves creating and solving a budget constraint problem similar to the examples provided for Janet Bain and Mr. Higgins. To accommodate the group of 10 people with a budget of $50 per day for activities, we need to write equations to determine how many tubes (t) and canoes (c) can be rented. We know that tube rentals cost $5 and canoe rentals cost $10. Each canoe holds up to three people.
First, we write an equation that represents the number of tubes and canoes needed:
Everyone needs a tube: t = 10
Canoes can hold three people: 3c ≥ 10 (since not everyone needs to be in a canoe at the same time)
Next, we write an equation for the total cost to remain within the budget: 5t + 10c ≤ 50 (cost of tubes plus canoes must be less than or equal to $50)
Using t = 10, we can substitute t in the cost equation: 5(10) + 10c ≤ 50
50 + 10c ≤ 50
10c ≤ 0
From the final inequality, c = 0; meaning you cannot rent any canoes if you're buying a tube for each person and staying within a $50 budget. Therefore, the group can only rent tubes, with 0 canoes.
She found that the area of the garden will be 127 1/2 square feet by using the equation Area=bh. I'd the height, h, of the parallelogram-shaped garden is 8 1/2 feet, what is the base, b, in feet?
To solve this problem yo must apply the proccedure shown below:
1. You must use the formula applied to calculate the area of the garden.
[tex]A=bh[/tex]
2. You know the value of the area ([tex]127^{\frac{1}{2}}ft^{2}=127.5ft^{2}[/tex] and the value of the heigth ([tex]8^{\frac{1}{2}}ft=8.5ft[/tex] , therefore, you only need to solve for the base:
[tex]b=\frac{A}{h}\\b=\frac{127.5ft}{8.5ft}\\b=15ft[/tex]
The answer is: 15 feet.
Classify each scale factor as a contraction or an expansion. 5, 0.9, -6, 8/5, 3/8
The numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.
The scale factors are given which are 5, 0.9, -6, 8/5, 3/8
We have to find which one has a contraction or expansion.
What do you mean by contraction and expansion on a scale ?
If the scale factor is larger than 1 then it would be an expansion whereas the scale factor between 0 and 1 would be a contraction.
As per the question ;
The scale factors given are ;
5, 0.9, -6, 8/5, 3/8
We can also write it as ;
5 , 0.9 , -6 , 1.6 , 0.375
We know that ;
If the scale factor is larger than 1 , it would be an expansion.
So ;
The factors we have listed that are larger than 1 are 8/5 and 5.
Also ;
If the scale factor is between 0 and 1 , it would be a contraction.
So ;
The factors we have listed that are between 0 and 1 are 0.9 and 3/8.
Also ;
A negative scale factor will result in a larger, inverted value.
So ;
The scale factor of -6 will also be an expansion.
Thus , the numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.
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The sum of five times a number and -6 is -2.
Answer:
5x + (-6) = -2
Step-by-step explanation:
Times is used in multiplication
Sum is used in addition
Twice the difference of a number and six is negative six, find the number
Let x = a number
3(6 - x) = -9
Divide both sides of equation by 3.
6 - x = -3
Subtract 6 on both sides of equation.
-x = -9
Divide both sides of equation by -1.
x = 9
The number is 9.
The difference between a number and six is [tex] x-6 [/tex]. Twice this difference is [tex] 2(x-6) [/tex]. If you want this difference to be negative, six, you have
[tex] 2(x-6)=-6 [/tex]
Divide both sides by 2:
[tex] x-6 = -3 [/tex]
Add 6 to both sides:
[tex] x = 3 [/tex]
At the dog show there are 4 times as many boxes as spaniels. if there are a total of 30 dogs how many dogs are spaniels
Is |-6| a negative integer
Answer:
NO. |-6| = 6 - a positive integer
Step-by-step explanation:
|a| = a for a ≥ 0
examples
|2| = 2, |0| = 0, |0.56| = 0.56
|a| = -a for a < 0
examples
|-2| = -(-2) = 2, |-100| = -(-100) = 100, |-0.25| = 0.25
Therefore your answer:
|-6| = 6 > 0
Need help on this kinda lost on it
A translation moves the image up, down and/or right, left. It does not change its size or shape.
Try this: Move your pencil up and to the right. Did its size or shape change? no
Answer: D
Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thunderstorm for the last 16 mi. She drives 18 mi slower through the thunderstorm than she does in clear weather. If the total time for the trip is 1.5 hr, determine her speed driving in nice weather and her speed driving in the thunderstorm.
Answer:
Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.
Step-by-step explanation:
Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.
Suppose, her speed in nice weather is [tex]x[/tex] mph.
As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: [tex](x-18) mph[/tex]
We know that, [tex]Time = \frac{Distance}{Speed}[/tex]
So, the time of driving in clear weather [tex]=\frac{50}{x}[/tex] hours
and the time of driving in thunderstorm [tex]=\frac{16}{x-18}[/tex] hours.
Given that, the total time for the trip is 1.5 hours. So, the equation will be......
[tex]\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0[/tex]
Using zero-product property.........
[tex]x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12[/tex]
We need to ignore [tex]x=12[/tex] here, otherwise the speed in thunderstorm will become negative.
So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph
Answer:
Drive Faster!
Step-by-step explanation:
What is the solution set of the following equation? 3x^2 - 6x = 0
Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn costs $4. She needs to buy at least 7 tubs of popcorn, but she only has $24 in her wallet.
If the solution region represents the number of small and large tubs of popcorn that Katie can buy, determine which graph represents the solution set to the system of inequalities representing this situation.
The correct solution is shown in the graph (D)
Given that the budget is $24 and the minimum is 7 tubs, the fourth graph shows the area in which both constraints are satisfied: triangular area between the points
7 small tubs
8 small tubs
3 large and 4 small tubs
Lets x = # of small tub of popcorn and y = # of large tub of popcorn
She needs to buy at least 7 tubs of popcorn: x + y >= 7
Each small tub of popcorn costs $3 and each large tub of popcorn costs $4 but she only has $24 in her wallet.
3x + 4y <= 24
So now you have the system of inequalities
x + y >= 7
3x + 4y <= 24
Find x and y intercepts of blue line
x + y = 7
x = 0 then y = 7
y = 0 then x = 7
The inequality sign is >= so it's above.
The blue line, B and D are matching the results
Find x and y intercepts of red line
3x + 4y = 24
x = 0 then 4y = 24; y = 6
y = 0 then 3x = 24; x = 8
The inequality sign is <= so it's below.
The red line, Only B is matching
Answer
D is the solution of the system of inequalities.
What is another way to show 3+3+3+3+3+3?
3 x 6 is the simplest way of saying it
Answer: 3x6 because there are 6 3's so it's 3x6
Find the slope of the line passing through each of the following pairs of points. (−10, 4), (2, −5)
M= change in y /change in x
(−10, 4), (2, −5)
M= -5-4/2-(-10)
M= -9/12
M- 3/4
Slope is - 3/4
answer: [tex]m = -\frac{3}{4}[/tex]
work:
slope formula ==> [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
plug the points in according to the formula
[tex]m = \frac{-5-4 }{2-(-10)}[/tex]
[tex]m = -\frac{9}{12}[/tex]
[tex]m = -\frac{3}{4}[/tex] <== simplified, and final answer :)
hope this helps! ❤ from peachimin
Which set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20?
A. (2, -7)
B. (1, -6)
C. (5, 0)
D. (0, -7.5)
Answer:
easy 5 ,0 c the x axis is run 5 then you rise on the positive y axis 0 and theres your awnser
Step-by-step explanation:
The set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20 is (5, 0).
Option C is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
3x - 2y = 15 _____(1)
4x - y = 20 _____(2)
The point of intersection of (1) and (2).
3x - 2y = 15
3x = 15 + 2y
x = (15 + 2y) / 3 _____(3)
4x - y = 20
4x = 20 + y
x = (20 + y) / 4 ______(4)
From (3) and (4) we get,
(15 + 2y) / 3 = (20 + y) / 4
4(15 + 2y) = 3(20 + y)
60 + 8y = 60 + 3y
8y - 3y = 0
5y = 0
y = 0
Now,
y = 0 in (1) or (2) we get,
3x = 15
x = 5
(5, 0)
4x = 20
x = 5
(5, 0)
Thus,
The coordinates (5, 0) satisfy the equations.
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I need the answer for 16 and 17
Son proporciones.
cual es el resultado de :x/2,5=y/5 si x+y=6
Respuesta: x/2,5=y/5=4/5=0,8
x/2,5=y/5
Multiplicando ambos lados de la ecuación por 5:
5(x/2,5)=5(y/5)→2x=y→y=2x
Sustituyendo y por 2x en la ecuación x+y=6:
x+2x=6
Resolviendo para x: Sumando términos semejantes:
3x=6
Dividiendo ambos lados de la ecuación entre 3:
3x/3=6/3
x=2
Sustituyendo x por 2 en la formula y=2x
y=2(2)→y=4
Determinando la proporción:
x/2,5. Sustituyendo x por 2:
2/2,5
Multiplicando numerador y denominador por 2:
2*2/(2,5*2)=4/5
La proporción es 4/5=0,8
Si lo hacemos con y:
y/5
Reemplazando y por 4:
4/5=0,8 (la misma proporción)
Zoe had a board 5 1/4 feet long she cut off a piece now the board is 3 5/6 feet long how long was the piece she cut off
Least common denominator is 24
What is the value of s?
0.7(3s+4)−1.1s=7.9
5.1=s. Use the distributive property and add like terms