Answer:
[tex]a=1,\ 2,\ 3,\ 6.[/tex]
Step-by-step explanation:
A whole number is any number of a set [tex]\{0,\ 1,\ 2,\ 3,...\}[/tex]
The equation [tex]ax=6[/tex] has a solution [tex]x=\dfrac{6}{a},\ a\neq 0.[/tex]
If [tex]a=1,[/tex] then [tex]x=\dfrac{6}{1}=6[/tex] is a whole number.
If [tex]a=2,[/tex] then [tex]x=\dfrac{6}{2}=3[/tex] is a whole number.
If [tex]a=3,[/tex] then [tex]x=\dfrac{6}{3}=2[/tex] is a whole number.
If [tex]a=6,[/tex] then [tex]x=\dfrac{6}{6}=1[/tex] is a whole number.
For all other values of [tex]a[/tex] equation [tex]ax=6[/tex] will have solution that is not a whole number.
The top deck of a boat is 9.5 feet above the surface of a lake, while the bottom of the boat is 24 feet below the surface of the lake. What is the vertical distance between the top deck and the bottom of the boat? Drag and drop the correct value into the box to complete the statement
The vertical distance is___________________ feet.
A. -33.5
B. -14.5
C. 14.5
D. 33.5
Answer:
The answer would D.) 33.5 because 9.5+24 is 33.5 and since vertical distance is always an absolute value, it will never be a negative number.
The vertical distance between the top and bottom of the boat is calculated by summing the distances above and below the lake's surface, which total 33.5 feet, making option D correct.
To calculate this, we consider that the top deck of the boat is 9.5 feet above the surface of the lake, while the bottom of the boat is 24 feet below the surface. The total vertical distance would be the sum of these two values, as one needs to account for the entire distance the boat covers from top to bottom.
So, the calculation would be as follows: 9.5 feet + 24 feet = 33.5 feet. Therefore, the vertical distance between the top deck and the bottom of the boat is 33.5 feet. This makes option D the correct answer.
The formula for the circumference of a circle is C = 2r. What is one-fourth of the circumference of a circle that measures 12 centimeters around? If necessary, use 3.14 for .
The formula of a circumference is:
[tex]C=2\pi r[/tex]
r - radius
or
[tex]C=d\pi[/tex]
d - diameter
We have d = 12cm. Substitute:
[tex]C=12\pi\ cm[/tex]
One-fourth of the circumference:
[tex]\dfrac{1}{4}C=\dfrac{1}{4}\cdot12\pi=3\pi\ cm\approx3\cdot3.14=9.42\ cm[/tex]
Answer: 9.42 cm.Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
A) graph of line going through 1, 2 and 3, 4
B) graph of line going through 1, 1 and 3, 3
C) graph of line going through 1, 4 and 3, 10
D) graph of line going through 1, 2 and 2, 5
Answer:
Option C) graph of line going through 1, 4 and 3, 10
Step-by-step explanation:
Let y equal to Margo's coin collection
Let x equal to number of years
At the begining x=0, y=1 → Point=(x,y)→Point=(0,1)
She adds 3 coins per year, then y=1+3x
At x=1, y=1+3(1)=1+3→y=4→Point=(x,y)→Point=(1,4)
At x=3, y=1+3(3)=1+9→y=10→Point=(x,y)→Point=(3,10)
The graph of line going through (1, 4) and (3, 10), then the option C is the correct.
what is the midpoint of ab with endpoints A(3,2) and B (8,14
Answer:
( [tex]\frac{11}{2}[/tex], 8)
Step-by-step explanation:
Find the midpoint using the midpoint formula
midpoint = [ [tex]\frac{1}{2}[/tex](3 + 8), [tex]\frac{1}{2}[/tex](2 + 14)] = ( [tex]\frac{11}{2}[/tex], 8)
Answer: (5.5, 8)
Step-by-step explanation:
We know that midpoint (x,y) of a line XY having points having points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by :-
[tex]x=\dfrac{x_1+x_2}{2}\ ;\ y=\dfrac{y_1+y_2}{2}[/tex]
Then similarly, the midpoint of AB with endpoints A(3,2) and B (8,14) will be :_
[tex]x=\dfrac{3+8}{2}\ ;\ y=\dfrac{2+14}{2}\\\\\Rightarrow\ x=\dfrac{11}{2}\ ;\ y=\dfrac{16}{2}\\\\\Rightarrow\ x=5.5\ ;\ y=8[/tex]
Hence, the midpoint of AB with endpoints A(3,2) and B (8,14) = (5.5, 8)
identify an equation in point-slope form for the line parallel to y=5x+2 that passes through (-6,-1)
Answer:
y = 5x + 29
Step-by-step explanation:
y=5x+2
Given equation is in the form of y=mx+b
Where m is the slope = 5
and b is the y intercept = 2
When the lines are parallel then their slopes are equal
So the slope of parallel line is also 5 (m=5)
Given that the line passes through (-6,-1)
We use point slope formula
y-y1= m (x-x1)
m=5, x1= -6, y1=-1
Plug in all the values
y - (-1) = 5(x-(-6))
y + 1= 5 (x+6)
y + 1= 5x + 30
Subtract 1 on both sides
y = 5x + 29
Solve equation for z
Answer:
z = 7
Step-by-step explanation:
9z + 4 / 5 - 8 = 5.4
Add 8 to both sides.
9z + 4 / 5 = 13.4
Multiply 5 by both sides.
9z + 4 = 67
Subtract 4 from both sides.
9z = 63
Divide both sides by 9.
z = 7
Answer:
7 (rounded up)
Step-by-step explanation:
9z+4/5=13.5
Multiply both sides by 5
9z+4=67.5
Subtract both sides by 4
9z=63.5
Divide both sides by 9
z=7 (rounded up)
The box plots below show the ages of college students in different math courses
Answer:
4. The mean and median age are most likely to be same for the students in Math 1.
Step-by-step explanation:
We have been given two box plots that show the ages of college students in different math courses. We are asked to choose the true statement about these box plots.
1. The median age of the students in math 1 is greater than the median age of the students in math 2.
We can see from our given box plots that median age for both Math 1 and Math 2 is 19 that is represented by vertical middle line of box, therefore, 1st statement is not true.
2. The median age of the students in math 1 is less than the median age of the students in math 2.
Since median ages for students in Math 1 and Math 2 are same (19), therefore, 2nd statement is not true.
3. The mean and median age are most likely same for both sets of data.
We can see that box plot for ages of Math 1 students is symmetric, therefore, both mean and median will be same for Math 1 students.
The box plot representing ages of Math 2 students is skewed right as it has an outlier as 23, therefore, its mean age will be greater than median age.
Therefore, 3rd statement is not true either.
4. The mean and median age are most likely to be same for the students in Math 1.
We can see that box plot representing ages for Math 1 students is symmetric and its whiskers are equidistant from median. So both mean and median age are same that is 19, therefore, 4th statement is true.
Answer:
in shorter terms, the answer is d
Step-by-step explanation:
A hudson valley farmer has 26 employees.He pays each employee $410 per week.After paying his workers for one week,the farmer has $162 left in his bank account.how much money did he have at first?
Hi there!
A valley farmer has 26 employees and he pays each of them $410 per week.
After paying them for one week he has $162 dollars left. We need to find how much money he had at first.
So the first step is to multiply $410 on 26 since he gives 410 dollars to each employee, which he has 26.
$410 · 26 = $10,660
So he had $10,660 before he paid the workers, but he still had $162 left. To find out his overall total of money he had we need to add $10,660 and $162 which will be $10,822.
The farmer had $10,822
Hope this helped!~
10 is increased to 35
What is the percent increase?
SUPER EASY AND URGENT!
Answer:
The percent increase is 250 percent
Step-by-step explanation:
To find the percent increase we use the formula
percent increase = (new-original)/original * 100
= (35-10)/10 * 100
= 25/10 *100
250
The percent increase is 250 percent
There is a 250% increase.
Work is attached in the image provided.
Select all that apply question! See picture
Either table C or Table D shows a proportional relationship. Plot all the points from the table that shows a proportional relationship. I'll post a picture of the graph. Table C is ( X= 2,4,6,8) and Y= ( 1,3,5,7). Table D is ( X= 2,6,8,10) and Y= ( 1,3,4,5).
Answer:
Step-by-step explanation:
A proportional relationship is a straight line through the origin that grows at a constant rate
For table C
The constant of proportionality is y/x
2/1 = 4/3 = 6/5 = 8/7 This is not true so this is not proportional
For table D
The constant of proportionality is y/x
1/2 = 3/6 = 4/8 = 5/10 This is true so this is proportional
Which of the following is a complex number?
-7
2 + √3
4 + 9i
pie (no symbol available)
Answer:
The correct answer is option C , 4 + 9i
Step-by-step explanation:
A complex number is the one which has a real number and an imaginary number.
In all the example given , option C 4 + 9i has "i" which signifies the imaginary number which nothing but a negative square root.
please help 5 pts
The Questions
An item sells for $40. the sales tax on the item is 8%. What is the sales tax and total cost?
What value for the constant,h, in the equation shown below will result in an onfinite number of solutions? Equation: 6x+18=h(3x+9) Answer choices: a. -2 b.-3 c.2 d.3
Answer:
c.2
Step-by-step explanation:
6x+18=h(3x+9)
To have an infinite number of solutions, the left and right side must be equal
Distribute the h
6x+18 = 3xh +9h
6x = 3xh
Divide by x
6x/x = 3xh/x
6 = 3h
Divide by 3
6/3 =3h/3
2 =h
Lets verify
18 = 9h
Divide by 9
18/9 = 9h/9
2 =h
h must be 2
simplify this expression
17-a-2a-6+5a
please solve
Answer:
Answer: 2 a + 11
Step-by-step explanation:
Simplify the following:
5 a - a - 2 a - 6 + 17
Grouping like terms, 5 a - a - 2 a - 6 + 17 = (-a - 2 a + 5 a) + (17 - 6):
(-a - 2 a + 5 a) + (17 - 6)
-a - 2 a + 5 a = 2 a:
2 a + (17 - 6)
17 - 6 = 11:
Answer: 2 a + 11
The expression 17-a-2a-6+5a simplifies to 2a+11. This involves combining similar terms and simplifying the arithmetic.
Explanation:
In order to simplify the expression 17-a-2a-6+5a, we first need to gather like terms. In this expression, the like terms are -a, -2a, and +5a. When you add these together, you get 2a. Now, substitute this back into the expression. You now have 17+2a-6. If you simplify further by adding the plain numbers together, you get 2a+11. Therefore, the simplified expression is 2a+11.
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I think the answer is is either B or C
Confused
Answer:C
Step-by-step explanation:If she studies for 10 munites and t equals munite t would go next tp 10 then d would go under it.
PLEASE HELP WILL GIVE BRAINLIEST the number of students at north middle school is 1240 and is decreasing by 25 students per year. The number of students at south middle school is 800 and it is decreasing by 30 students per year. in how many years will the two schools have the same number of students?
Answer:
-88
Step-by-step explanation:
Let N(x) be the number of students at NMS for a certain number of years.
Let S(x) be the number of students at SMS for a certain number of years.
Let x be the number of years.
N(x)=1240-25x
S(x)=800-30x
When # of students is equal, N(x)=S(x). Therefore, we are looking for the value of x (# of years) when 1240-25x=800-30x
Subtract 1240 from each side
-25x=-440-30x
Add 30x
5x=-400
x=-88 years
Check your numbers.
The height of a rectangular prism is found by dividing volume, V, by the base area, B. If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height? 3x + 5 – 3x – 7 + 3x + 5 + 3x – 7 –
Answer:
[tex](3x+5)+\frac{28}{2x-4}[/tex]
Step-by-step explanation:
Since,
The volume of a rectangular prism = Base area × Height,
Given,
Volume of the rectangular prism = [tex]6x^2-2x+8[/tex]
Base area = 2x - 4
Let h be the height,
[tex]\implies 6x^2-2x+8=(2x-4)h[/tex]
[tex]\implies h = \frac{6x^2-2x+8}{2x-4}[/tex]
By long division ( shown below ),
[tex]h=(3x+5)+\frac{28}{2x-4}[/tex]
Which is the required expression that represents the height.
Answer:
[tex](3x+5) + \frac{14}{x-2}[/tex]
Step-by-step explanation:
We are given the following information in the question:
Volume of rectangular prism =
[tex]6x^2 - 2x + 8[/tex]
Area of base of prism =
[tex]2x -4[/tex]
Formula:
[tex]\text{Volume of Prism} = \text{Area of base}\times \text{Height of prism}\\\\\text{Height of prism} = \displaystyle\frac{\text{Volume of Prism} }{\text{Area of base}}[/tex]
Putting the values we, get,
[tex]\text{Height of prism} = \displaystyle\frac{6x^2 - 2x +8}{2x-4} = \frac{2(3x^2-x+4)}{2(x-2)}= (3x+5) + \frac{14}{x-2}[/tex]
Hence, the height of the prism is given by the expression [tex](3x+5) + \frac{14}{x-2}[/tex]
Boots: $59.00, discount: 10 percent sales tax 5.5 percent
Answer:
Total cost of boots = $56.02
Step-by-step explanation:
$59 x 0.90 = $53.10
$53.10 x 1.055 = $56.02
or
59 x 0.10 = 5.9
59 - 5.9 = $53.10
53.10 x 0.055 = $2.92 tax
$53.10 + $2.92 = $56.02
identify the property that the statement illustrates
Answer:
6 units away from 0.
Step-by-step explanation:
when move to 6 you count the units.
Dmitri brought 28 ounces of trail mix for $3.92. What is the unit rate?
Answer:
The unit rate is 0.14 cents per ounce.
Step-by-step explanation:
Divide 3.92 by 28 to find out how much the trail mix is per ounce.
The unit rate of Dmitri's trail mix purchase is $0.14 per ounce, calculated by dividing the total cost by the total weight.
To find the unit rate of Dmitri's trail mix purchase, we divide the total cost of the trail mix by the total weight of the trail mix. Dmitri bought 28 ounces of trail mix for $3.92, so we perform the following calculation:
Unit Rate = Total Cost / Total Weight
Unit Rate = $3.92 / 28 ounces
Unit Rate = $0.14 per ounce
Therefore, the unit rate is $0.14 per ounce. This means that for every ounce of trail mix, Dmitri paid $0.14.
how do i simplfy 2/56
Answer:
1/28
Step-by-step explanation:
think what two can be divided by it can only be divided by two
think if 56 can, it could so 2 divided by 2 is 1 and 56 divided by two is 28 so the answer is 1/28
Solve for x in the equation?
a/(2x-c) = -1
Answer:
[tex]\frac{c-a}{2}[/tex]
Step-by-step explanation:
given [tex]\frac{a}{2x-c}[/tex] = - 1 ( cross- multiply )
- (2x - c ) = a ( distribute left side )
- 2x + c = a ( subtract c from both sides )
- 2x = a - c ( multiply both sides by - 1 )
2x = c - a ( divide both sides by 2 )
x = [tex]\frac{c-a}{2}[/tex]
Answer:
x = [tex]\frac{(a - c)}{-2}[/tex]
Step-by-step explanation:
a/(2x-c) = -1
The first step is to multiply both sides by (2x - c)
(2x - c)a/(2x-c) = -1(2x - c)
a = -2x + c
a - c = -2x + c - c
a - c = -2x
Divide both side by -2
(a - c)/-2 = x
∴ x = [tex]\frac{(a - c)}{-2}[/tex]
Marcia uses 5 ounces of chicken stock to make one batch of soup.She has a total of 400 ounces of chicken stock.How many batches of soup can Marcia make
Answer:
Marcia can make a total of 80 batches of soup
Step-by-step explanation:
400(total ounces)/5(ounces per batch)=80 batches
Answer:
80 batches of soup can Marcia .
Step-by-step explanation:
Given : Marcia uses 5 ounces of chicken stock to make one batch of soup.She has a total of 400 ounces of chicken stock.
To find : How many batches of soup can Marcia make.
Solution : We have given
Marcia uses 5 ounces of chicken stock = 1. batch of soup
Marcia uses 1 ounces of chicken stock = [tex]\frac{1}{5}[/tex].
Marcia uses 400 ounces of chicken stock = [tex]\frac{400}{5}[/tex].
= 80 batch of soup.
Therefore, 80 batches of soup can Marcia .
what is an interger?
An integer is any whole number and it can be positive or negative. Integers cannot be fractions!
A few examples of integers are...
21, 4, -6666
Solve the equation 7h-5(3h- 8) = -72
Answer: h=14
Step-by-step explanation:
7h-5(3h-8)=-72
7h-15h+40=-72 > I distributed the -5(3h-8) to get rid of parenthesis
-8h+40=-72 > I combined the like terms 7h-15h
-8h=-112 > I subtracted 40 from both sides
h=14 > I divided -8 from both sides
The solution is h = 14.
What are Equivalent Expressions?These are the expressions which give the same or the equivalent result.On solving, both the expressions will get the same value.Given: Equation
7h - 5(3h - 8) = -72
Now, we will solve the equation for the value of h.
⇒ 7h - 5(3h - 8) = -72
⇒ 7h - 15h + 40 = -72
⇒ 7h - 15h = -72 - 40
⇒ -8h = -112
Dividing both sides by -8, we get:
⇒ h = 14
Therefore, the solution of the given equation is h = 14.
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HELP!!
a student finished 45 of her homework problems in class. if the ratio of problems she finished to problems she had left was 9:4, how many homework problems did she have total?
Answer:
60
Step-by-step explanation:
45 divided by 9 is 5. So you multiply 4 times 5. Which equals 20. So 20 plus 45 is 65. Hope you understand it.
8.1 + -3.5 = what?
Please help this is due soon! Thank youu
Answer:
4.6
Step-by-step explanation:
8.1 + (-3.5) = 8.1 - 3.5
4.6
Used paperback books are $0.25 and hardback books are $0.50. If you buy 3 paperback book and 5 hardback books, how much money do you spend
Answer:3.25$
Step-by-step explanation:
If one paperback book is 0.25 and you buy 3 of them, (0.25 x 3) is 0.75 and a hardcover is 0.50 per book, (0.50 x 5) is 2 dollars and 50 cents and if you add the two, you will get 3.25$
The amount of money to spend to buy 3 paperback books and 5 hardback books is,
⇒ $3.25
Given that,
The cost of Used paperback books is $0.25.
And, cost of hardback books is $0.50
Here, the cost to buy 3 paperback books is,
⇒ [tex]3 \times 0.25[/tex]
⇒ $0.75
And, the cost of 5 hardback books is,
⇒ [tex]5 \times 0.50[/tex]
⇒ $2.50
So, the total cost of 3 paperback books and 5 hardback books is,
⇒ $0.75 + $2.50
⇒ $3.25
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Katherine is considering two new cell phone plans she doesn’t want to spend more for minutes she won’t use one plan allows up to 250 minutes per month for $49 and the other plan allows up to 350 minutes per month for $65 in the last six months she used 1470 minutes use estimating an exact answer to you to determine the best cell phone plan for Katherine
Answer: The plan with 250 minutes is best because she Maximus uses only 245 minutes per month so just 5 min to spare. Also i used mental math
Step-by-step explanation:
1470 divided by 6 equals= 245 minutes exactly unless Katherine had rounded her answer
Final answer:
To determine the best cell phone plan for Katherine, compare the cost per minute for each plan. The second plan, which allows up to 350 minutes per month for $65, has a lower cost per minute.
Explanation:
To determine the best cell phone plan for Katherine, we need to compare the cost per minute for each plan.
For the first plan, Katherine gets 250 minutes for $49, which means the cost per minute is $49/250 = $0.196 per minute.
For the second plan, Katherine gets 350 minutes for $65, which means the cost per minute is $65/350 = $0.1857 per minute.
Since the cost per minute is lower for the second plan, Katherine should choose the plan that allows up to 350 minutes per month for $65.