Solve: -1/3 (5x +3) < 14
x > - 9
x ∈ ( - 9 : + oo)
Step-by-step explanation:[tex]-\frac{1}{3}(5x+3)<14\\ \\-(5x+3)<42\\\\-5x-3<42\\\\-3-42<5x\\\\-45<5x\\\\5x>-45\\\\x>-9\\\\[/tex]
x∈ ( - 9 ; + oo)
Answer:
x > -9
Step-by-step explanation:
you want to multiply both sides of the inequality by 3/1 to make
-1/1 (5x+3) < 42/1
any expression divided by 1 remains the same
-1 (5x+3) < 42/1 ⇒ - (5x+3) < 42/1 ⇒ - (5x+3) < 42
Where there is a - in front of an expression in parentheses, change the sign of each term in the expression
-5x -3 <42
Then move the constant to the right-hand side and change its sign
-5 < 42 + 3
Add the numbers and you'll get
-5x < 45
Divide both sides of the inequality by -5 and flip the inequality sign and your answer would be
x > -9
Which function has an inverse that is also a
function?
{(-1, -2), (0, 4), (1, 3), (5, 14), (7,4)}
{(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Given:
Different functions in the ordered pairs.
To find:
The function which has an inverse that is also a function.
Solution:
A relation is a function, if there exist unique output for each input.
The inverse of a function is a function, if there exist unique input for each output in the function.
It means, the inverse of a function is a function if each y value has unique x-value.
In {(-1, -2), (0, 4), (1, 3), (5, 14), (7,4)},
For y=4 we have x=0 and x=7, therefore, the inverse of this function is not a function.
In {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} ,
For y=4 we have x=0 and x=5, therefore, the inverse of this function is not a function.
In {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} ,
For all y value we have unique x values, therefore, the inverse of this function is a function.
In {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)},
For y=4 we have x=-1 and x=0, therefore, the inverse of this function is not a function.
Therefore, the correct option is C.
Answer:C
Step-by-step explanation:
A car manufacturer provides six exterior colors, five interior colors, and three different trims. How many different color-trim schemes are available?
Answer:
90
Step-by-step explanation:
take one interior color and multiply by 5 for every interior color. then multiply by three for each trim. you get 15. multipy 15 by 6 for every exterior color and you get 90. there are 90 combinations.
the letters of the word combine are placed at random in a row in how many ways can an arrangement occur such that all vowels are placed together
==========================================================
Explanation:
The word "combine" has three vowels o, i, and e.
One grouping of the three vowels together leads to oie, which we'll replace with Z for now.
So we have the "word" Zcmbn after taking out the vowels and replacing with Z temporarily. There are 5 letters in Zcmbn making 5! = 5*4*3*2*1 = 120 different permutations.
Within any permutation of Zcmbn, there are 3! = 3*2*1 = 6 ways to arrange the sequence oie
So overall there are 6*120 = 720 different ways to arrange the word "combine" such that all the vowels stick together.
whats is the answer for 2y-x=5
Answer:
That's the answer in the photo.
18. A shelf holds fewer than 50 cans. If all of the
cans on this shelf were put into stacks of
five cans each, no cans would remain. If the
same cans were put into stacks of three cans
each, one can would remain. What is the
greatest number of cans that could be on
the shelf?
Answer:
40
Step-by-step explanation:
Given that the number of cans are fewer than 50.
Let the number of cans = [tex]x[/tex]
It is given that no cans remain if they are put in the stacks of five cans each.
i.e. number of cans are a multiple of 5.
Let us have a look at the numbers in decreasing order which are multiples of 5 and are lesser than 50.
45, 40, 35, 30, ......
Now, let us check the numbers one by one.
If [tex]x=[/tex] 45,
Now, they are placed on stacks of three each and one can remains.
So, the remainder when [tex]x[/tex] is divided by 3 will be 1.
But when 45 is divided by 3, remainder is 0.
Now, let us check next greatest number, which is 40.
When 40 is divided by 3, the remainder is 1.
Therefore, greater number of cans can be 40.
5x+2/6-2x-7/11_>-4
What’s the answer?
Answer:
Inequality Form: x > − 122 /99
Interval Notation: ( − 122/ 99 , ∞ )
Step-by-step explanation:
You have a bag with 30 fireballs and another bag with 42 jolly ranchers. For a party, you want to repackage the candy into smaller bags, and you want each bag to have the same number of fireballs and jolly ranchers and. How many bags will you be able to make without any leftover?
Solve for a
2(a+5)=-2 Steps too please ❤️
Answer:
a=-6
Step-by-step explanation:
2(a+5)=-2 Step 1 distribute
2a+10=-2 Step 2 minus 10 on both sides
2a=-12 Step 3 divide but 2 on both sides
a=-6
Answer:
a=-6
Step-by-step explanation:
In order to solve for a, we must isolate a on one side of the equation.
[tex]2(a+5)=-2[/tex]
2 is being multiplied by (a+5). The inverse of multiplication is division. Divide both sides of the equation by 2.
[tex]2(a+5)/2=-2/2[/tex]
[tex](a+5)=-2/2[/tex]
[tex](a+5)=-1[/tex]
5 is being added to a. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.
[tex]a+5-5=-1-5[/tex]
[tex]a=-1-5[/tex]
[tex]a=-6[/tex]
Let's check our solution. Plug -6 in for a and solve.
[tex]2(a+5)=-2[/tex]
[tex]2(-6+5)=-2[/tex]
[tex]2(-1)=-2[/tex]
[tex]-2=-2[/tex]
This checks out, so we know our solution is correct.
The solution to the equation 2(a+5)=-2 is a=-6
what are the coordinates of the midpoint of the line segment with endpoints (2,5) and (4,-7)
Answer:
(3, -1)
Step-by-step explanation:
Let A be the midpoint and (x,y) its coordinates
● x = (2 + 4)/2 = 6/2 = 3
● y = (5 +(-7))/2 = -2/2 = -1
So the coordinates are (3, -1)
If you sell ice cream cones at the football game you must sell 25 to make a profit. You have already sold 15 cones. Write an inequality that can be solved to show all the numbers of cones, c, that you will still need to sell
Answer:
The inequality to describe the problem is 15 +c >25.
We must sell more than 5 cones to make a profit
Step-by-step explanation:
From this problem, we can see that we need to sell a number of cones (c), that when added to the 15 cones that we have already sold, the result will be greater than 25.
To set up the inequality sign, we need to, first of all, know the inequality sign that we will be using. From the preceding statement, we can see that we need to sell greater than a certain number of cones.
This should tell us that we will be needing the greater-than sign (>).
The next step is to know the format the equation should take:
We have sold 15 cones; We need to sell c more to make it greater than 25.
This will be 15 +c >25.
The inequality to describe the problem is 15 +c >25.
from this, we can see that c > 5 cones.
We must sell more than 5 cones to make a profit
What is 5+x+11x=11x+11
Answer:
x = 6
Step-by-step explanation:
Solve for x:
11 x + x + 5 = 11 x + 11
Hint: | Add like terms in 11 x + x + 5.
x + 11 x = 12 x:
12 x + 5 = 11 x + 11
Hint: | Move terms with x to the left hand side.
Subtract 11 x from both sides:
(12 x - 11 x) + 5 = (11 x - 11 x) + 11
Hint: | Combine like terms in 12 x - 11 x.
12 x - 11 x = x:
x + 5 = (11 x - 11 x) + 11
Hint: | Look for the difference of two identical terms.
11 x - 11 x = 0:
x + 5 = 11
Hint: | Isolate terms with x to the left hand side.
Subtract 5 from both sides:
x + (5 - 5) = 11 - 5
Hint: | Look for the difference of two identical terms.
5 - 5 = 0:
x = 11 - 5
Hint: | Evaluate 11 - 5.
11 - 5 = 6:
Answer: x = 6
Answer:
x = 6
Step-by-step explanation:
5 + x + 11x = 11x + 11
5 + 12x = 11x + 11
5 + 1x = 11
1x = 6
x = 6
help with number 14! it’s due tomorrow.
Answer:
23 is you number move it that many times right see what it gives you
Step-by-step explanation:
Which would the phrase "two times the quotient of a number and 3" look like as a variable expression? 3n2 3(n−2) 2n3 2(n−3)
Answer:
the answer here would be 2(n-3)
Step-by-step explanation:
Complete the equation of the line through ( 3 , − 1 ) (3,−1)left parenthesis, 3, comma, minus, 1, right parenthesis and ( 4 , 7 ) (4,7)left parenthesis, 4, comma, 7, right parenthesis.
Answer:
[tex]y=8x-25[/tex]
Step-by-step explanation:
Given the coordinates:
(3,−1) and (4,7)
To find:
The equation of line passing through the given points.
Solution:
Let us have a look at the slope intercept form of a line:
[tex]y=mx+c[/tex]
c is the y intercept.
Where [tex]m[/tex] is the slope of the line passing through the points [tex](x_1,y_1),(x_2,y_2)[/tex]
Formula for slope is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]x_1 = 3\\y_1 = -1\\x_2 = 4\\y_2 = 7[/tex]
[tex]m=\dfrac{7-(-1)}{4-3}\\\Rightarrow m = 8[/tex]
So, equation of line becomes:
[tex]y=8x+c[/tex]
Let us put (4, 7) to find the value of c:
[tex]7=8\times 4 +c\\\Rightarrow c = -25[/tex]
So, the equation is:
[tex]y=8x-25[/tex]
The equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].
Given information:
The given line passes through the points (3.-1), and (4,7).
It is required to write the equation of the line.
Use the two-point form of a line to write the equation of the line:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-(-1)=\dfrac{7-(-1)}{4-3}(x-3)\\y+1=8(x-3)\\y+1=8x-24\\y=8x-25[/tex]
From the above equation of the line, the slope is equal to 8.
Therefore, the equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].
For more details, refer to the link:
https://brainly.com/question/19082942
Solve for y. I REALLY NEED HELP ON THIS!! 2(3y+6x)=2(5y-2x)
Answer:
y = 4x
Step-by-step explanation:
2(3y + 6x) = 2(5y - 2x)
Divide both sides by 2.
3y + 6x = 5y - 2x
Subtract 5y from both sides. Add 2x to both sides.
-2y = -8x
Divide both sides by -2.
y = 4x
2. Miss. Mead pays Miss. Brown $125.00 per week. How much money must Miss. Brown take in for
services if Miss. Mead is to realize $50.00 profit on her work? (Conditions on salary are the same
as in problem 1)
ODS
a. $275.00 b. $325.00 c. $250.00 d. $300.00
The question is incomplete:
1. A cosmetologist must double his/her salary before the employer con realize any profit from his/her work, Miss, Mead paid Miss, Adams $125,00 per week to start.
2. Miss. Mead pays Miss. Brown $125.00 per week. How much money must Miss. Brown take in for services if Miss. Mead is to realize $50.00 profit on her work? (Conditions on salary are the same as in problem 1)
ODS
a. $275.00 b. $325.00 c. $250.00 d. $300.00
Answer:
d. $300.00
Step-by-step explanation:
Given that a cosmetologist must double her salary before the employer can realize any profit from his/her work, for Miss. Mead to realize $50.00 profit on her work, you would have to determine the amount that doubles the salary of the cosmetologist and add the $50 needed as profit:
Salary= $125*2=$250
$250+$50= $300
According to this, the answer is that for Mead to realize $50.00 profit on her work, Miss. Brown must take $300.
2.2.115
The per capita (per person) income from 1980 to 2010 can be modeled by
f(x) = 2000(X – 1980) + 10,000
where x is the year. Determine the year when the per capita income was $18,000.
The per capita income was $18,000 in the year N.
Answer:
X= 1984
Step-by-step explanation:
f(x) = 2000(X – 1980) + 10,000
Where,
f(x)= per capita income
x= year
Find x when f(x)= $18,000
f(x) = 2000(X – 1980) + 10,000
18,000 = 2000(X - 1980) + 10,000
18,000 = 2000X - 3,960,000 + 10,000
18,000 = 2000X - 3,950,000
Add 3,950,000 to both sides
18,000 + 3,950,000 = 2000X
3,968,000 = 2000X
Divide both sides by 2000
X= 3,968,000 / 2000
= 1984
X= 1984
Therefore, the per capita income was $18,000 in the year 1984
simply the question please
Answer: -2²¹
Step-by-step explanation:
Convert each term into a power of 2.
Use the product rule of adding the exponents and the quotient rule of subtracting the exponents.
[tex]\dfrac{(-2)^3\times 4^4}{16^{-1}\times 8^{-2}}\quad =\dfrac{(-1)^3(2)^3(2)^{2(4)}}{(2)^{4(-1)}(2)^{3(-2)}}\qquad =-1^3\bigg(\dfrac{2^32^8}{2^{-4}2^{-6}}\bigg)[/tex]
[tex]=-1(2^{3+8-(-4)-(-6)})\qquad =-1(2^{3+8+4+6})\qquad =-2^{21}[/tex]
Answer:
-2^21
Step-by-step explanation:
(-2)^3*4^4=-8*(2^2)^4=-1*2*4*2^8=-1*2^9*2^2=
=-1*2^11
(16)^-1*8^-2=2^-4*2^-6=2^-10
-1*2^11/2^-10=-1*2^11*2^10=-2^21
6x + 2 = 9x - 4 help me please
Answer:
x=2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
6x + 2 = 9x - 4
We want terms with x on the left side and numbers on the right side.
Subtract 9x from both sides.
6x - 9x + 2 = 9x - 9x - 4
-3x + 2 = -4
Subtract 2 from both sides.
-3x + 2 - 2 = -4 - 2
-3x = -6
Divide both sides by -3.
-3x/(-3) = -6/(-3)
x = 2
3. The volume of a cylinder is V = trh. If the radius of the cylinder is 1.5 feet and the height is 2.7 feet, what is the volume of the cylinder? (Use 3.14 for pi.)
28.6 cubic feet
6.1 cubic feet
12.7 cubic feet
19.1 cubic feet
Answer:
the volume of the cylinder = 19.08 ft³
Step-by-step explanation:
given:
If the radius of the cylinder is 1.5 feet and the height is 2.7 feet,
find:
what is the volume of the cylinder? (Use 3.14 for pi.)
Volume of a cylinder = π r² h
where π = 3.14
radius (r) = 1.5 ft.
height (h) = 2.7 ft.
plugin values into the formula:
V = π r² h
V = 3.14 (1.5)² 2.7
V = 19.08 ft³
therefore,
the volume of the cylinder = 19.08 ft³
round the following number to 2 decimal places 17.422
Answer:
17.42
Step-by-step explanation:
Because the third place is less than 5 you have to round it to smaller number and that is 2.
If by any chance the third number was for example six you would have to round it to 3.
- Use your ruler and protractor to draw an isosceles obtuse triangle ZAP with and vertex angle B. base angles A and Z.
Answer:
In the diagram, the obtuse isosceles is what you need.
For your problem, the angle F is the vertex angle B
The base angles A and Z go on both sides.
Step-by-step explanation:
1.08 x 10^-3 in standard form?
If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f '(5).
Answer:
f(5) = 2
f'(5) = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Tangent line to a function y = f(x) on a point (5, 2) passes through two points (5, 2) and (0, 1)
Let the equation of the line is,
y - y' = m(x - x')
Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2-1}{5-0}[/tex]
= [tex]\frac{1}{5}[/tex]
Therefore, equation of the line passing through (0, 1) and slope = [tex]\frac{1}{5}[/tex] will be,
y - 1 = [tex]\frac{1}{5}(x-0)[/tex]
y = [tex]\frac{x}{5}+1[/tex]
Function representing equation will be,
f(x) = [tex]\frac{x}{5}+1[/tex]
At x = 5,
f(5) = [tex]\frac{5}{5}+1[/tex]
= 1 + 1
= 2
f(5) = 2
f'(x) = [tex]\frac{d}{dx}(\frac{x}{5}+1)[/tex]
= [tex]\frac{1}{5}[/tex]
Therefore, f'(5) = [tex]\frac{1}{5}[/tex] will be the answer.
Point T is on line segment \overline{SU} SU . Given ST=2x+6,ST=2x+6, TU=4,TU=4, and SU=4x,SU=4x, determine the numerical length of \overline{ST}. ST
Answer: The numerical length of [tex]\overline{SU}[/tex] is 20 units.
Step-by-step explanation:
Given: Point T is on line segment [tex]\overline{SU}[/tex] .
i.e. [tex]\overline{SU}=\overline{ST}+\overline{TU}[/tex] (i)
Since , it is given that ST=2x+6,TU=4, and SU=4x
Substitute these values in (i), we get
[tex]4x= 2x+6 + 4\\\\\Rightarrow\ 4x-2x=10\\\\\Rightarrow\ 2x=10\\\\\Rightarrow\ x=5[/tex]
Now, the numerical length of [tex]\overline{SU}= 4(5)=20\ units[/tex]
Hence, the numerical length of [tex]\overline{SU}[/tex] is 20 units.
Answer:
Step-by-step explanation:
ST = 16
find h(-4 ) given h(x)=3x2 +2x -16
Answer:
2x-10
Step-by-step explanation:
3x2+2x-16
6+2x-16
2x-10
Solve the equation for x.
answer:
x=-2
Step-by-step explanation:
my suggestion for this problem and all problems like it would to turn everything into 6ths. 1/3 would become 2/6. and 2 would become 12/6. leave the negatives. now you'll add 2/6 to -12/6. which will equal 10/6. divide 10/6 by 5/6 and youll get -2. x=-2
Answer:
x = -2
Step-by-step explanation:
● (5/6)x - (1/3) = -2
Add (1/3) to both sides
● (5/6)x - (1/3) + (1/3) = -2 + (1/3)
-2 is (-6/3)
● (5/6)x = (-6/3) + (1/3)
● (5/6)x = -5/3
Move 5/6 to the other side and switch the places of 5 and 6
● x = (-5/3) × (6/5)
● x = -30/15
● x = -2
Can someone help me on this?
I believe the difference is 5 degrees Fahrenheit.
A student artist randomly selected two media from among: charcoal sketches, pencil drawings, and oil paintings, and then submitted all of her works in that media for a gallery showing.
Complete question is;
A student artist randomly selected two media from among: charcoal sketches, pencil drawings, and oil paintings, and then submitted all of her works in that media for a gallery showing. Identify the kind of sample that is described.
Answer:
Cluster sample
Step-by-step explanation:
Looking at the question, we can see that the media has already been grouped into 3 parts namely charcoal sketches, pencil drawings, and oil paintings. It has already been grouped into multiple groups for easy selection or identification.
Now this type of grouping is synonymous with cluster sampling because cluster sampling is a probability sampling technique in which the researchers divide the population into multiple groups known as clusters for research and this question clearly shows that the media has been grouped.