The solution set of the inequalities given in the task content is described as; (-infinity, -17) U [ -9, infinity).
What is the solution set for the given pair of inequalities?It follows from the task content that the solution set containing values of w which render the pair of inequalities true be determined.
On this note, since the inequalities given are;
-14 > w + 3 or 3w ≥ -27
By solving the inequalities individually; we have;
-14 > w + 3
Subtract 3 from both sides of the equation so that we have;
-14 - 3 > w; Therefore, -17 > w.
Also, 3w ≥ -27
Therefore; w ≥ -9.
On this note, it follows that; w < -17 or w ≥ -9.
Consequently, the solution set of the inequalities can be represented using interval notation as;
(-infinity, -17) U [ -9, infinity)
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Which number sentence is true?
A.
B.
C.
D.
Answer: D
Step-by-step explanation:
The square root of 50 is less than 8.34, the square root of 15 is less than the absolute value of 4.32, 2.3x10^1 is greater than 2 2/5.
The absolute value of 5.43 is less than 2.1x10^1.
HELP ASAP PLEASE
The following angles are supplementary to each other.
m∠A = (2x − 27)° and m∠B = (3x + 27)°
Determine x.
55
36
18
9
Two angles A and B are supplementary when the value of x is 36°.
What are supplementary and complementary angles?Two angles are said to be supplementary if their sum is 180°.
Two angles are said to be complementary if their sum is 90°.
Given, m∠A = (2x − 27)° and m∠B = (3x + 27)° are supplimentary to each other.
∴ (2x - 27)° + (3x + 27) = 180°.
2x + 3x - 27 + 27 = 180°.
5x = 180°.
x = 36°.
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7.25% as a fraction?
Answer:
29/400
Step-by-step explanation:
6. Simplify (x + 7)(x + 5).
Answer:
[tex]x^{2} +12x+35[/tex]
Step-by-step explanation:
Distribute
(X+7)(X+5)
x^2+5x+7x+35
X^2+12x+35
Hopes this helps please mark brainliest
Answer:
x^2 + 12x + 35
Step-by-step explanation:
Hi! I solved this using the FOIL, or firsts, outsides, insides, and lasts, to simplify:
The firsts, or F, would be: x*x which equals x squared (x^2)
The outsides, or O, would be: x*5 which equals 5x
The insides, or I, would be 7*x which equals 7x
The lasts, or L, would be 7*5 which equals 35
Then, the FOIL method says to add up all the answers you got together:
x^2+5x+7x+35
and then you simplify and get:
x^2+12x+35
I hope this made sense! :)
The sales tax on a laptop is $30.00 that cost $800.00. What is the percent of sales tax?
Answer:
3.75%
Step-by-step explanation:
800+3.75%=830
18. Herman decides to take up golf. His golf club membership will cost $450 for the season and he will
be charged $18 for each round of golf that he plays. Herman has decided not to spend more than
$1000 on golf for the season. Write an inequality that describes the relationship between the maximum
amount Herman wants to spend and the total golf costs for the season.
The inequality that describes the relationship between the maximum amount Herman wants to spend and the total golf costs for the season is 450 + 18x ≤ 1000.
Herman can play for a maximum of 30 rounds, which will cost $990 in total.
Herman decides to take up golf. His golf club membership will cost $450 for the season, and he will be charged $18 for each round of golf that he plays. Herman has decided not to spend more than $1000 on golf for the season.
Let the number of rounds of golf Herman plays be represented by the variable "x". We can write the inequality as given below.
450 + 18x ≤ 1000
We can further simplify and solve this inequality.
18x ≤ 1000 - 450
18x ≤ 550
x ≤ 30.56
Hence, the maximum number of rounds of golf is 30. The total cost is calculated below.
C = $450 + $18*30
C = $450 + $540
C = $990
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Differentiate the function with respect to x. Shot steps
The differentiation of the function f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
What is function?Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is,
f(x) = sin⁻¹(3x⁵)
Differentiate the given function with respect to x
f'(x) = d/dx(sin⁻¹(3x⁵))
The differentiation of sin⁻¹x is [tex]1/\sqrt{1-x^2}[/tex],
f'(x) =[tex]1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)[/tex]
= [tex]1/\sqrt{1-9x^{10}}\cdot 15x^4[/tex]
= [tex]15x^4/\sqrt{1-9x^{10}}[/tex]
The differentiation of f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
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5x+3y=25, 2x+12y=37
x=3.5 and y=2.5
First, combine the equations in such a way that you can eliminate a variable. Then solve for the variable. Insert this value into one of the original equations and solve for the unknown variable.
See details:
Find the common difference of the arithmetic sequence: { 8, 5, 2, -1, -4, ...}
d=
Answer:
d=3
Step-by-step explanation:
because
8-5=3
5-2=3
2--1=3
-1--4=3
A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t) = -16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ___ second(s) after launch.
(Simplify your answer.)
The rocket reaches its maximum height at 1.25 second(s) after launch
The maximum height reached by the object is 32 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 40t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 40
Set to 0
-32t + 40 = 0
So, we have
32t = 40
Divide by 32
t = 1.25
Hence, the time is 1.25 seconds
The maximum heightIn (a), we have
t = 1.25
Substitute t = 1.25 in h(t) = -16t² + 40t + 7
h(1.25) = -16(1.25)² + 40(1.25) + 7
Evaluate
h(1.25) = 32
Hence, the maximum height is 32 feet
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Solve 6x + 2 = 2x - 14
Answer:
x = - 4
Step-by-step explanation:
6x + 2 = 2x - 14 ( subtract 2x from both sides )
4x + 2 = - 14 ( subtract 2 from both sides )
4x = - 16 ( divide both sides by 4 )
x = - 4
We move all terms to the left:
6x + 2 - (2x - 14) = 0We get rid of the parentheses.
6x- 2x + 14 + 2 = 0We add all the numbers and all the variables.
4x + 16 = 0We move all terms containing x to the left hand side, all other terms to the right hand side
4x = -16x= -16/4x=-4Write an explicit function to represent each pattern.
Angelo sells cookies in packages, where each package contains the same number of cookies. The total number of cookies he has after 1, 2, 3, 4, and
5 packages are sold are 110, 88, 66, 44, and 22, respectively.
f(x) =
The explicit function of the packages is f(x) = a +(n-1)d.
What is explicit function?
An explicit function is a function in algebra in which the output variable (dependent variable) can be explicitly written only in terms of the input variable (independent variable). An explicit function usually involves two variables - dependent and independent variables.
the given numbers are 110,88,66,44,22.
This is an AP (arithmetic progression)
f(x) = a +(n-1)d
were,
a is the first term, n is the number of terms, d is the difference.
n= 5, d = 22, a =110
f(x) = 110 +(5-1)22
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Part 2: Using Your Results
How could you estimate the minimum speed of the car that made the skid marks in this picture? What additional information do you need to know?
A helpful fact is that each dashed line on any road or highiway is 10 feet long, with 30 feet in berween dashes.
Why do the dashed road lines appear smaller near the top of the picture? How will you adjust for this in making your measurement?
Once you have determined a seale (or scales) for the picture, measure the skid marks.
Given the length of the slcid marks, what was the approximate minimum speed of the vehicle when the brakes were applied? Was the driver speeding? Explain your answer.
Answer:
I c Phil and the way u are u 3AM u are u and tahsin will u be happy so we will be crazy for a different time to kick in hamtramck tomorrow so we will have
9/14 as a decimal rounded to nearest hundredth
Answer:
0.64
Step-by-step explanation:
9/14 is 0.642
rounding that decimal to the nearest hundredth would get you 0.64 because the 2 next to the 4 is below 5 so it would keep it the same.
........hELP pLEASE........
The total amount that Ms. Henderson must pay, given the penalty and the amount of taxes is $1, 478.75
How to find the total amount to be paid?First, find the total penalty on the taxes, to Ms. Henderson.
= Tax amount x Penalty percentage
= 1, 400 x 11 ¹ / ₄%
= $157.50
Because she paid in 6 months, but the penalty is for a year, Ms. Henderson's tax penalty is:
= 157.50 / 2
= $78.75
The total amount to be paid is:
= Taxes owed + Penalty
= 1, 400 + 78. 75
= $1, 478.75
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I really need help on this math assignment it’s about probability and if work can be shown that would be great I will give 35 points
1)1000
2) 4.4%
3) 4.4
4) 9%
5)4.4%
6) 0.6%
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12y^2-17y-5 to factor it
After factoring the given expression [tex]12y^2-17y-5[/tex], we get (4y+1)(3y-5).
The breakdown of a thing into a product of other objects, or factors, which when multiplied together provide the original, is known as factorization or factoring in mathematics. Factorization can be done using middle term splitting method in which the middle term of the expression is broken down to factor.
Factoring the given expression by splitting the middle term -17y to -3y and 20y as product of 12 and 5 is 60 and also the product of 3 and 20 is 60.
[tex]12y^2-17y-5=12y^2+3y-20y-5\\=3y(4y+1)-5(4y+1)\\[/tex]
Now, factoring out [tex](4y+1)[/tex],
[tex]=(4y+1)(3y-5)[/tex]
Therefore, After factoring the given expression, we get [tex](4y+1)(3y-5)[/tex].
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You used 8 cups of sugar while baking
three dozen cookies and one cake. If you
used 1.25
cups of sugar for the cake and
the same amount of sugar for each dozen
of cookies, how much sugar was used for
each dozen of cookies?
Answer:
2.25 cups of sugar per dozen cookies
Step-by-step explanation:
8 - 1.25 = 6.75
6.75 ÷ 3 = 2.25
DUE TOMORROW HELP PLEASE!
Answer:
57°
Step-by-step explanation:
Vertical angels are congruent. They have the same measurements.
Answer:
57
Step-by-step explanation:
<PQS and <RQN are vertical angles and thus are congruent by the Vertical Angles Theorem. If m<PQS = 57, then m<RQN = 57.
Complete (assume $60,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 10,000 A B Dept. B 30,000 C D
The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:
Ratio Amount
Department A 0.25 $15,000
Department B 0.75 $45,000
What is the ratio?The ratio is the proportion of the whole shared by two or more numbers.
Ratios are fractional values like proportions.
Ratios, depicted in fractions, decimals, and percentages, show how much a value or variable is contained in another.
Total distributable overhead = $60,000
Ratios = 10,000:30,000
= 1:3
Sum of Ratios = 4
OR
= 0.25:0.75
Sum of Ratios = 1
Overhead Allocation:Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 10,000 A = 1 B = $15,000 ($60,000 x 0.25)
Dept. B 30,000 C = 3 D = $45,000 ($60,000 x 0.75)
Thus, based on the cost driver ratios, Department A bears $15,000, while Department B will be allocated $45,000 of the distributable overheads.
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Help me with this math homework
You could buy 1 box, 14 bags and 4 single marbles and you could buy 2 box, 4 bags and 14 single marbles.
What is fundamental operation?
The fundamental operations are expressed in an order. Generally, the order will be in the format of “DMAS” where “D” stands for “Division”, “M” stands for “Multiplication”, “A” stands for “Addition”, “S” stands for “Subtraction”. This order is considered and sequentially performed from left to right.
Given, 1 box contains 10 bags of marbles
1 bag contains 10 marbles
Hence, 1 box contains 10 × 10 = 100 marbles.
Total numbers of marbles = 254
First condition is,
you can buy one box of marble = 1× 100 = 100
4 single marbles,
To find the number of bags, let x be the number of bag and one box contains 10 marbles,
therefore, x bags contains 10x marbles.
According to question,
100 + 4 +10x =254
104 +10x = 254
10x = 254- 104
10x = 150
x = 150÷10
= 15
Similarly in case of second condition,
2 boxes = 100×2 = 200
4 bags = 10× 4 = 40
Single marbles =?
200 + 40 +? =254
the single marble = 14
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What is the midpoint of the segment shown below?
-10
(-4, 6)
10
-10
(4,-2)
10
Answer:
Step-by-step explanation:
PLEASE HELP!!!:
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60% pure antifreeze. The company wants to obtain 180 gallons of a mixture that contains 20% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The volume of premium antifreeze to be used is 60 gallons.
The volume of water to be used is 120 gallons
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Let the volume of 60% pure antifreeze be used to make 20% pure antifreeze.
= x gallons
The volume of 20% pure antifreeze = 180 gallons
For 60% pure antifreeze:
C₁ = 60% , V₁ = x gallons
For 20% pure antifreeze :
C₂ = 20% , V₂ = 180 gallons
Applying,
C₁V₁ = C₂V₂
60 × x = 20 × 180
x = 60 gallons
The volume of 60% pure antifreeze used = 60 gallons.
The volume of water to be used.
= 180 - 60 gallons
= 120 gallons
Thus,
The volume of premium antifreeze to be used is 60 gallons.
The volume of water to be used is 120 gallons
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Factor the difference of cubes.
Zx^{3} -125
Answer:
you cannot factor it anymore
therefore, there is no solution
Can you find the inverse of the function y = 4x^2 + 12x + 9? Why or why not?
What domain restrictions are necessary to allow the function to have an inverse?
Find the inverse of the domain restricted function.
Inverse of the given function y= 4x² +12x + 9 is given by x=(1/2) (√y -3).
Restricted domain is required to make function one -one so that its inverse exist.
Domain of the inverse function is y ≥ 0.
As given in the question,
Given function is equal to :
y = 4x² +12x + 9
Inverse of the function exist if and only if it is one to one.
x₁ ≠ x₂
⇒2x₁ +3 ≠ 2x₂ + 3
⇒f(x₁) ≠ f(x₂)
It is one -one. Inverse exist.
y = (2x +3)²
⇒ 2x + 3 = √y
⇒x = (1/2) ( √y -3)
Restricted domain of the inverse of the function is y ≥0.
Therefore, Inverse of the given function y = 4x² +12x + 9 is given by
x = (1/2) (√y -3)
Restricted domain is required to make function one -one so that its inverse exist.
Domain of the inverse function is y ≥ 0.
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Can someone help me please I need to check this answer in equations. I have the answer I just need someone to help me check it correctly. There is a way to check them as per Math equations check. 5 pts
8(4 – a) = 2a
32-8a=2a
-2a from both sides
32-10a=0
-32 from both sides
-10a=-32
A=-32/-10
Answer: 16/5=3 1/5 =3.2
Answer:
3.2
Step-by-step explanation:
8(4-a)=2a
32-8a=2a
collect like terms
32=2a+8a
32=10a
divide both sides by 10
a=3.2
Your solution is correct
In a marching band maneuver, the marcher at the left spins 180° in place with arms spread, and hands the horn to the marcher at the right, who spins 180° with arms spread, and stops.
a. How far from the initial position is the horn?
The initial position is the hor from inch b.
What composition maps the horn from the initial position to the final position?
Answer: B
Step-by-step explanation:
B
Please help it would make my day.
Answer:
part A=329.99=25.72+23.50x
part B=12.95=13 weeks
Step-by-step explanation:
need=329.99
have=25.72
save=23.50 per week
equation329.99=25.72+23.50x
23.50x=(329.99-25.72)
23.50x=304.24
x=12.95
=x =13
I really need help!! These fractions are confusing me !
The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.
We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.
The first composition is f(g(x)). The composite function is solved below.
f(g(x)) = f((4/x) + 3)
f(g(x)) = 1/([(4/x) + 3] - 3)
f(g(x)) = 1/(4/x)
f(g(x)) = x/4
The second composition is g(f(x)). The composite function is solved below.
g(f(x)) = g(1/(x - 3))
g(f(x)) = (4/[1/(x - 3)]) + 3
g(f(x)) = 4(x - 3) + 3
g(f(x)) = 4x - 12 + 3
g(f(x)) = 4x - 9
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Solve the following quadratic equation by using the definition of a square root and write the solutions in simplified radical form. 3(y-7)² = 24
Answer:
y = 7 + 2√2, y = 7 - 2√2
Step-by-step explanation:
We need to solve for y to find the solutions of the quadratic equation:
3(y-7)^2 = 24
(y-7)^2 = 8
y-7 = ±√8 = ±√(4*2) = ±2√2
y = 7 + 2√2
y = 7 - 2√2
2√2 is the simplified radical form because 4 is the highest factor of 8 that is a perfect square.
