Step-by-step explanation:
-3(6 - 2x) > 4x + 12
-18 + 6x > 4x + 12
2x > 30
x > 15
The solution set is (15, ∞).
The interval that includes all possible values of x that satisfy the inequality is (15, infinity), which can be written as [15, oo) in interval notation.
The answer is (d) [15,00)
What are intervals?The intervals are numbers or values between two given point
The intervals are denoted as:
Closed intervals = [a, b]
This interval includes a and b.
Open intervals = (a, b)
This interval does not include a and b.
We have,
We can solve the inequality as follows:
-3(6 - 2x) > 4x + 12
Distribute the -3 on the left side:
-18 + 6x > 4x + 12
Subtract 4x from both sides:
2x > 30
Divide both sides by 2:
x > 15
Therefore,
The interval that includes all possible values of x that satisfy the inequality is (15, infinity), which can be written as [15, oo) in interval notation.
Learn more about intervals here:
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if a cubic container has a side length of 50.0cm, what is the volume in liter?
Answer:
The answer is
125 litresStep-by-step explanation:
To find the volume in liter we must first find the volume in cm³
Since the container is cubic
Volume = l³
where l is the length of one side
From the question
l = 50.0 cm
Volume = 50³
= 125000 cm³
Next we use the conversion
1cm³ = 0.001 L
If 1 cm³ = 0.001 L
Then 125,000 cm³ = 125,000 × 0.001 L
We have the final answer as
125 litresHope this helps you
Using the volume of a cube, and conversion of units, it is found that the volume of the cube is of 125 liters.
---------------------
The volume of a cube of side s is given by:
[tex]V = s^3[/tex]
---------------------
Side length of 50cm means that [tex]s = 50[/tex].Thus, the volume, in cubic centimetres, is given by:
[tex]V = 50^3 = 125000[/tex]
---------------------
To convert the volume from cubic centimetres to liters, it is divided by 1000.Then:
[tex]\frac{125000}{1000} = 125[/tex]
The volume of the cube is of 125 liters.
A similar problem is given at https://brainly.com/question/23514867
A rock is dropped off the edge of a cliff and its distance s (in feet) from the top of the cliff after t seconds is s(t) = 16t2. Assume the distance from the top of the cliff to the water below is 96 ft.
A) When will the rock strike the water?
B) Make a table of average velocities and approximate the velocity at which the rock strikes the water.
Answer:
A) 2.45 seconds
B)[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]
Step-by-step explanation:
Distance [tex]s[/tex] (in feet) from the top of cliff after [tex]t[/tex] seconds when a rock is dropped off the edge of a cliff is given as:
[tex]s(t)=16t^2[/tex]
Distance from the top of cliff to water = 96 ft
To find:
A) When will the rock strike the water
i.e. The time taken by the rock to travel the distance of 96 ft.
B) Table of Average Velocity and approximate velocity at which the rock strikes the water ?
Solution:
A) Given that distance traveled = 96 ft
To find the value of [tex]t[/tex]
Putting the value of [tex]s[/tex] in formula: [tex]s(t)=16t^2[/tex] to find [tex]t[/tex]:
[tex]96 = 16t^2\\\Rightarrow t^2=6\\\Rightarrow \bold{t = 2.45\ sec}[/tex]
B) The velocity at which the rock hits the water:
We need to differentiate [tex]s(t)[/tex] w.r.to [tex]t[/tex] in order to find the velocity at any instant.
[tex]s'(t) =\dfrac{d}{dt}s(t) = \dfrac{d}{dt}(16t^2)\\\Rightarrow v = 2\times 16t^{(2-1)}\\\Rightarrow v = 32t[/tex]
The time taken to reach the water is 2.45 seconds.
Putting [tex]t[/tex] = 2.45 seconds to find the velocity:
[tex]v = 32\times 2.45 = 78.4\ ft/sec[/tex]
Average velocity is given as total distance traveled and total time taken.
[tex]\text{Average Velocity = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}[/tex]
[tex]\text{Average Velocity = }\dfrac{96}{2.45}\\\text{Average Velocity = 39.18\ ft/s}[/tex]
[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]
Find the factors of the following numbers.
a) 15
b) 22
c) 34
d) 45
e) 50
Answer:
1,3,5,15
1,2,11,22
1,2,17,34
1,3,5,9,15,45
1,2,5,10,25,50
Step-by-step explanation:
Hope it will help u
Which expression has the same value as -18-(-9)?
0 - 18+2
-12-(-3)
- 1945
O-8-(-4)
Answer:
the answer is -12-(-3)
Step-by-step explanation:
The expression equivalent to -18-(-9) is -12-(-3)
What are expressions?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, -18-(-9), we are given to find the expression equivalent to it,
-18-(-9) = -18+9 = -9
1) -18+2 = -16 (not equivalent)
2) -12-(-3) = -12+3 = -9
Therefore, we see, the value of expressions -12-(-3) and -18-(-9) are equivalent,
Hence, the expression equivalent to -18-(-9) is -12-(-3)
For more references on expressions, click;
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Which property is used in the problem below?
2 (x + 4) = 2 x + 8
the associative property
the commutative property
the distributive property
the additive identity property
Answer:
Distributive property
Step-by-step explanation:
2(x+4)
We can write it as:-
=>2(x)+2(4)
=>2x+8
Answer:
the awnser is c the distributive proporties
Step-by-step explanation:
2. Which of the following is not an example of
a perfect square?
a. 9 +
b. 200
c. 4
.
d. 64
Answer:
B. 200
Step-by-step explanation:
A perfect square is the multiplication of two equal integers such as 1*1=1, 2*2=4, 3*3=9. From the examples, 1, 4, 9 are perfect square.
Non perfect square numbers are 1*2=2,
3*1=3,
5*1=5,
3*2=6,
6*1=6,
7*1=7
Examples of perfect squares:
1*1=1
2*2=4,
3*3=9,
4*4= 16,
5*5=25,
6*6=36,
7*7=49,
8*8=64,
9*9=81,
10*10=100,
11*11=121,
12*12=144,
13*13=169,
14*14=196,
15*15=225 and so on
Farmer Hank has fewer than 100 pigs on his farm. If he groups five to a pen, there are always three pigs left over. If he groups the pigs seven to a pen, there is always one left over. However, if he groups the pigs three to a pen, there no pigs left. What is the greatest number of pigs that Farmer Hank could have on his farm?
Answer:
the answer is 99
Step-by-step explanation:
How much of the circle is shaded? simply your answer
Answer:
The part that is shaded is 5/14
Step-by-step explanation:
The total circle is 1
1/2 + 1/7 + x = 1 where x is the shaded area
Multiply each side by 14 to get rid of the fractions
14(1/2 + 1/7 + x) = 1*14
7 + 2 + 14x = 14
9+14x = 14
Subtract 9 from each side
14x = 5
Divide by 14
x = 5/14
The part that is shaded is 5/14
Use the distributive property and add like terms 5(3x-4) -8x
Answer:
[tex] \huge{ \fbox{ \sf{7x - 20}}}[/tex]
Step-by-step explanation:
[tex] \star{ \sf{ \: 5(3x - 4) - 8x}}[/tex]
[tex] \text{Step \: 1 \: : Distribute \: 5 \: through \: the \: parentheses}[/tex]
[tex] \mapsto{ \sf{5 \times 3x - 5 \times 4 - 8x}}[/tex]
[tex] \mapsto{ \sf{15x - 20 - 8x}}[/tex]
[tex] \text{Step \: 2 \: : Collect \: like \: terms}[/tex]
[tex] \sf{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}[/tex]
[tex] \mapsto{ \sf{15x - 8x - 20}}[/tex]
[tex] \mapsto{ \boxed{\sf{7x - 20}}}[/tex]
[tex] \sf{Hope \: i \: helped!}[/tex]
[tex] \sf{Best \: regards!!}[/tex]
~[tex] \rm{TheAnimeGirl}[/tex]
Fatima highlighted columns 3 and 8 in the multiplication table below to find equivalent ratios.
1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9
22 4 6 8 10 12 14 16 18
3 3 6 9 12 15 18 21 24 27
4 4 8 12 16 20 24 28 32 36
5 5 10 15 20 25 30 35 40 | 45
6 6 12 18 24 30 36 42 48 54
7 7 14 21 28 35 42 49 56 63
8 8 16 24 32 40 48 56 64 72
9 9 18 27 36 45 54 63 72 81
Which ratio is equivalent to 8:32
O 12:32
24:3
40:15
64:9
Save and Exit
Answer:
the answer is 40:15
Step-by-step explanation:
Answer:
answer 40:15
Step-by-step explanation:
Factorise
a) 2ax + 6ay
Answer:
2a(x + 3y)
Step-by-step explanation:
2ax + 6ay
factor out a 2a
2a(x + 3y)
What is an algebraic equation?
Answer:
algebraic equation is an equation of the form
Juan pays $15 per hour to rent a paddle boat. He can rent a wetsuit for $5 a day. What amount will he pay if he rents the paddle boat for 6 hours
Answer:
90
Step-by-step explanation:
15*6=90...
You meet with the financial aid office to discuss your costs for attending MGA next semester. Tuition is $113.67 per credit hour, and fees are a flat cost of $660. You have a grant of $350 and a scholarship of $400. If you are taking 15 credit hours, what amount will you need to pay for your classes next semester?
Answer:
$1615.05
Step-by-step explanation:
First the cost. We know that tuition per credit hour is 113.67 and there is a flat fee of 660. This can be represented by 113.67h + 660, where h is equal to the number of credit hours.
Next, the amount paid. There are two constants of 350 and 400 already there. We can represent the remaining amount that needs to be paid by another variable, x.
Now, the cost needs to be equal to the amount you pay. We can replace h with 15 for 15 hours and solve for x.
113.67h + 660 = 350 + 400 + x
113.67(15) + 660 = 350 + 400 + x
1705.05 + 660 = 750 + x
2365.05 = 750 + x
1615.05 = x
Help i don’t know the answer to this
Answer:
95°
Step-by-step explanation:
∠SRW is a vertical angle with respect to the one marked 95°. As such, it will have the same measure: 95°.
m∠SRW = 95°
A baseball pitcher has pitched 89 innings. What is the number of innings written as a decimal?
3
2
The number of innings 89 written as a decimal is
Answer:
I think its 0.89
Step-by-step explanation:
1 Which proputy is illustrated by the equation
ax +ay=a(x+y)?
1) associative
2 2) commutative
3) distributive
4) identity
Answer:
its a distributive property..
Two minor league baseball players got a total of 314 hits. Washington had 4 more hits than Sanchez. Find the number of hits for each player.
Answer:
Washington has 159 hits and Sanchez has 155 hits.
Step-by-step explanation:
First, divide 314 by 2 (the number of players), then add 2 for Washington and subtract 2 for Sanchez.
3/4 x - 1/2 - 4 = 12
Answer: x=22
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Add 9/2 to both sides.
Step 3: Multiply both sides by 4/3.
NEED HELP ASAP
given m||n find the value of x
The alternate interior angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
This means that [tex]6x-8=5x+14[/tex]
[tex]x=22[/tex]
Hope this helps. 頑張って!
The coordinates of the vertices of a triangle are 2,3 5,1 and 6,4 after one reflection the coordinates of the vertices of the triangle’s image are (2,-3) (5,1) and (6,-4). Over what line has the triangle been reflected?
Answer:
it is being reflected by the x axis
i need help plsss ;(((
Answer:
Look below
Step-by-step explanation:
1) x = 14, because 14 * 14 = 196
2) x = 3 / 16, because ( 3 / 16 ) * ( 3 / 16 ) = 9 / 256
3) x = 8, because 8 * 8 * 8 = 512
4) x = 4 / 7, because ( 4 / 7 ) * ( 4 / 7 ) * ( 4 / 7 ) = 64 / 343
Simple geometry equation
Answer:
106 or 4x+18
Step-by-step explanation:
Since Ray QR is a bisector you can determine that PRQ and QRS are equal angles (def. of a bisector). Then, what I chose to do is graph them and find where they intercept which was 22. We now know 22 is x so we can substitute it into the equation and solve to deterine that our answer is 106.
how do you solve (5^{2} - 1) ÷ 6
[tex]( {5}^{2} - 1) \div 6 = [/tex]
[tex](25 - 1) \div 6 = [/tex]
[tex]24 \div 6 = 4[/tex]
Note:
Do the square first, and then you do mathematic operation between the parentheses. And, then do the
mathematic operation in the outside of parentheses.
Thank you.
Answer:
4Step-by-step explanation:
[tex]\left(5^2-1\right)\div \:6\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(5^2-1\right)\::\quad 24\\=24\div \:6\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:24\div \:6\:\\:\quad 4[/tex]
Jacki evaluated the expression below. 2 cubed (3 minus 1) + 4 (8 minus 12) = 2 cubed (2) + 4 (4) = 8 (2) + 16 = 16 + 16 = 32. What was Jacki’s error? Jacki should have simplified the exponent first. Jacki should have multiplied 4 and 8 first. Jacki did not subtract 12 from 8 correctly. Jacki should not have multiplied
Answer:
jacki did not subtract 8 minus 12 properly.8 minus 12 equals -4
Answer:
its c
Step-by-step explanation:
on edunuity
Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches
Answer:
V = πr²(h/3)
Step-by-step explanation:
83.74 = πr²(5/3)
R = 4.00 in
Diamater = 2r = 2 x 4.00 = 8 inches
y=-4x - 8
6x + 2y=-10
I need the equation solved by substitution
Please show work :)
Answer:
x =1.28571428571
Step-by-step explanation:
6x + 2y = -10
y = -4x - 8
6x + 2(4x - 8) = -10
6x + 8x - 8 = -10
14x - 8 = 10
(we put together the like terms)
14x = 10 + 8
14x = 18
x = [tex]\frac{18}{14}[/tex]
x = 1.28571428571
Solve the inequality. A. >> O B. x >7 C. x>-5 ) D. x
Answer:
A. [tex] x > \dfrac{7}{3} [/tex]
Step-by-step explanation:
[tex] 8(\dfrac{1}{2} x - \dfrac{1}{4}) > 12 - 2x [/tex]
Distribute the 8 on the left side.
[tex] 4x - 2 > 12 - 2x [/tex]
Add 2x to both sides. Add 2 to both sides.
[tex] 6x > 14 [/tex]
Divide both sides by 6.
[tex] x > \dfrac{14}{6} [/tex]
Reduce 14/6 by dividing the numerator and denominator by 2.
[tex] x > \dfrac{7}{3} [/tex]
Anyone can help me?
Answer:
see the work pictured please
9(Y+2)=
Distributive Property & Combining Like
Answer:
9y+18
Step-by-step explanation:
Distribute the 9 to the terms in the parentheses.
9(y)+9(2)
9y+18