a) The equation is therefore; x³ + 3x² + 2x = 336
b) Solving for the length, we get the length to be; x = 6.
c) All workings are as shown below;
According to the question;
When the height of a rectangular prism was halved, the volume was 168 cubic cm.In essence, the volume of the original prism is;
Volume = 168 × 2.Volume = 336cm³Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.
Therefore, length = xwidth = (x +1)height = (x +2)Volume = x (x+1) (x+2) = 336a) The equation is therefore;
x³ + 3x² + 2x = 336b) Solving for the length, x is as follows;
(x-6) (x² + 9x + 56) = 0By testing values and checking;
Upon solving the polynomial, x = 6.c) All workings are as shown above.
Read more on cubic equation:
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Manny has a garden that is 12 feet long and 9 feet wide. What is the perimeter of
Manny's garden?
Use the formula for perimeter, P =
2 (1 + w).
432 feet
O 33 feet
O 42 feet
216 feet
Answer:
42 ft
Step-by-step explanation:
2(L + W ) = P
2 (12 + 9) = P
2 (21) = P
42 = P
P = 42
please helppppppppppppp ASAP. please ensure to use step by step explanation. thanks.
I'll do the first two parts to get you started.
=====================================================
Part (i)
We can show that the operation [tex]\nabla[/tex] is not commutative by picking two random and different real numbers for a,b. In other words, I'm using a counter-example.
Let's say we go for a = 1 and b = 2
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\1 \nabla 2 = \frac{3*1+2}{5} - 1\\\\1 \nabla 2 = \frac{5}{5} - 1\\\\1 \nabla 2 = 1 - 1\\\\1 \nabla 2 = 0\\\\[/tex]
Now let's swap the values. We'll try a = 2 and b = 1
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\2 \nabla 1 = \frac{3*2+1}{5} - 1\\\\2 \nabla 1 = \frac{7}{5} - 1\\\\2 \nabla 1 = 1.4 - 1\\\\2 \nabla 1 = 0.4\\\\[/tex]
We can see that [tex]1 \nabla 2[/tex] and [tex]2 \nabla 1[/tex] are not the same value. In general, [tex]a \nabla b \ne b \nabla a[/tex] Therefore, the operation [tex]\nabla[/tex] is not commutative.
The only time [tex]a \nabla b = b \nabla a\\\\[/tex] is true is when [tex]a = b[/tex], since,
[tex]\frac{3a+b}{5}-1 = \frac{3b+a}{5}-1\\\\\frac{3a+a}{5}-1 = \frac{3a+a}{5}-1\\\\\frac{4a}{5}-1 = \frac{4a}{5}-1\\\\[/tex]
It's when [tex]a \ne b[/tex] is where the operation becomes noncommutative.
Another way to arrive at the [tex]a = b[/tex] condition is to solve the original equation for either 'a' or b.
=====================================================
Part (ii)
Using the previous part as inspiration, we'll do a counter-example to show that the operation is not associative. Pick 3 random values for a,b,c. Here are the values I'll pick.
a = 1b = 2c = 3Then,
[tex]d = b \nabla c = \frac{3b+c}{5}-1 = \frac{3*2+3}{5}-1 = 0.8\\\\a \nabla (b \nabla c) = a \nabla d = \frac{3a+d}{5}-1 = \frac{3*1+0.8}{5}-1 = -0.24\\[/tex]
Next, we can say:
[tex]d = a \nabla b = \frac{3a+b}{5}-1 = \frac{3*1+2}{5}-1 = 0\\\\(a \nabla b) \nabla c = d \ \nabla c = \frac{3d+c}{5}-1 = \frac{3*0+3}{5}-1 = -0.4[/tex]
Let's compare the two outputs:
[tex]a \nabla (b \nabla c) = -0.24\\\\(a \nabla b) \nabla c = -0.4[/tex]
They don't match up, so [tex]a \nabla (b \nabla c) \ne (a \nabla b) \nabla c[/tex] when (a,b,c) = (1,2,3).
In general, the operation is not associative in R.
What is the slope of the line
Answer:
-1.5
Step-by-step explanation:
if g(x)=x^2-x then what is g(2)-2
Answer:
0Step-by-step explanation:
[tex]g(x) = {x}^{2} - 2[/tex]
To find g(2) - 2 first find g(2) by substituting the value of x that's 2 into the original expression after that subtract 2 from the final answer obtained.
We have
[tex]g(2) = {2}^{2} - 2 \: \: \: \: \: \: \: \: \: \: \\ = 4 - 2 = 2 \\ \\ \\ g(2) - 2 = 2 - 2 = 0[/tex]
We have the final answer as
0Hope this helps you
Cynthia gave 15 of her toys to her little sister. If she had 25 toys, how many did she give away?
5
she gave her sister 5 toys.
Correction to the question - It is not 15 it 1/5th.
According to the given question Cynthia had 25 toys and she gave 1/5th of her toys to her little sister.
So, The total number of toys is 25 to find 1/5th of it we need to multiply the total number of toys she had and the fraction she gave.
(25 x 1/5) = 5. so the number of toys she gave away to her little sister is 5.
To solve more of these kind of arithmatic and alzebraic word problems just search on web for word problems on arithmatic and alzebra.Learn more about word problems here :
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Randy can run six-tenths of a mile every 4 minutes, but it takes Julie 5 minutes. By the time Julie has run for 20 minutes, how far has Randy run?
A
1.8 miles
B
2.4 miles
C
2.6 miles
D
3 miles
Answer:
D!!!
Step-by-step explanation:
you have to make a table to see that randy has run 3 miles.!!!
Answer: D is the correct answer!
Step-by-step explanation: Like the one above me!
(-7,-4) (-11,-2) slope
Answer:
1/3
Step-by-step explanation:
-2-4 = -6
-7-11 = -18
1) Use the distributive property to write an expression that is equivalent to 8(a + 4).
8(a + 4) = _a + _
Where us point c on the number line
Answer: - 0.3
Step-by-step explanation:
Correct me if I am incorrect.
Which of the following is a proper fraction? A7001/6 B 9/4 C 31/99 D3/2
Answer:
31/99
Step-by-step explanation:
Becuase the numerator is lesser than the denominator
Answer:
C. 31/99
Step-by-step explanation:
It's C because a proper fraction is a fraction with a numerator that is less that it's denominator in its lowest terms
factorise this
12a²+20a
Answer:
4a(3a+5)
We take H.C.F of both number and the variables then we compare the HCF number and variable with our question and equate and write the answer about how much should be multiplied from the H.C.F answer to get the question.
Carpet Company A
c = 1.35y + 100
where c is the cost and y is the number of square yards.
Carpet Company B
This company charges $2.05 per square yard for the carpet and the installation.
Identify the unit rate in dollars per square yard for each carpet company.
Answer:
2.45
Step-by-step explanation:
Help help math math math please
Answer:
x = 5
Step-by-step explanation:
2x+15 = 4x+5 (because they are corresponding angles)
10 = 2x
x = 5
Answer:
x = 5
Step-by-step explanation:
The set-up cost for a machine that attaches snaps on clothing is $1,100. After set-up,
it costs $0.12 for each snap to be attached. A newer machine has come out that has
a set-up cost of $1,520. With the new machine, it only costs $0.09 for each snap to
be attached. How many snaps would the company have to attach to make the
purchase of the newer machine worthwhile?
Answer:
14,001
Step-by-step explanation:
old machine: 1,100+.12x
new machine: 1,520+.09x
if you plug in 14,000 for x, you get
old machine: 2,780
new machine: 2,780
therefore, you need 1 over 14,000 for it to be worth it because
if you plug in 14,001 for x, you get
old machine: 2,780.12
new machine: 2,780.09
which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)
hope this helps!
Image attached giving 25 points please help
Answer:
Rational
Step-by-step explanation:
It isnt whole because its a decimal,
It isnt an Integer because its a decimal
It isnt natural because its a decimal
Meaning it can only be rational
Need help
Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed?
Answer:
it is A bacause the fractions for that one are correct
Step-by-step explanation:
The largest lollipop ever made had a mass of 2158.7kg and was made for a festival in Granna, Sweden on July 27, 2003, If a spherical lollipop with radius 2 cm has a mass of 50 g, what was the radius of this giant lollipop?
Answer:
Step-by-step explanation:
Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.
Small Lollipop
r = 2cm
V=4 /3πr^3
V = 33.51 cm^3
Mass is 50 g in 33.51 cm^3, so the density is:
50g/(33.51 cm^3) = 1.492 g/cm^3
We have 2158.7kg in the larger lollipop. That is 2158700 grams.
Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3. :
(2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3
V=4 /3πr^3
1446775 cm^3 = (4/3)*π*r^3
r = 70.12 cm
Please somebody help me with this
Answer: call 911
Step-by-step explanation: call 911
find the following integrals. need help plssss
Answer:
1) -15/4
2) -15/2
Step-by-step explanation:
1) Let u=4t. Then the limits become u=4(0)=0 and u=4(4)=16. Also du=4 dt upon differentiating the equation.
So the integral can be written as
Integral( 1/4 f(u) , u=0 to u=16)
We are given Integral( f(u) , u=0 to u=16) is -15. So a fourth of that is our answer for the first question.
2) Let u=t^2. Then the limits become u=(0)^2=0 and u=(4)^2=16. Also upon differentiating we obtain equation du =2 t dt.
So the integral becomes
Integral( 1/2 f(u) , u=0 to u=16).
We are given Integral( f(u) , u=0 to u=16) is -15. So a half of that is our answer for the second question.
Can anyone help thanks
Answer:
First Option, log 3x is equivalent to the expression shown
A jet plane can carry up to 200,000 liters of fuel. It used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight?
Answer:
Step-by-step explanation:
65%
Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.
Answer:
65%.
Step-by-step explanation:
(130,000/200.000) * 100
= 0.65 * 100
= 65%.
5c + 7c simplify fytdtdecxsts
Answer:
12c
Step-by-step explanation:
Note that when simplifying through adding or subtracting, the terms must have the same amount of the same variables to combine them.
In this case, all given terms have the same variable, denoted by c. Combine the given coefficients:
5c + 7c = 12c
12c is your answer.
~
5) Using the formula A=652
find the surface area of a
cube with sides measuring 8
inches.
Answer:
81.5
Step-by-step explanation:Cube has all sides of equal dimensions and like that it has 6 faces.
So total surface area of cube is equal to the combined area of all the six faces.
Now each face has equal dimensions so same area
Therefore,
area of a single face =side²
Therefore, area of entire cube = 6 times the area of a single face
= 6 * side²
.
SOMEBODY HELP ME NO LINKS PLEASE
If Amari had 15 apples and 14 got taken away how many would there be??
Answer:
15-14=1
Step-by-step explanation:
1 apple left
Answer:
1 apple
Step-by-step explanation:
15-14=1
Hope the helps!
1 1/2 - 1/2 pls helpppppppppp
Answer:
It would be 1 whole
Step-by-step explanation:
1/2 - 1/2 is 0 the only thing left is one whole
Need a little help on this
Answer:
Step-by-step explanation:
This is an isosceles triangle. You can tell because 2 of the sides are equal and the third is not equal to either of the other two.
x + x + 56 = 180 Combine the left
2x + 56 = 180 Subtract 56 from both sides.
2x = 180 - 56
2x = 124 Divide by 2
x = 124/2
x = 62
Need answer to the question in the picture above
Answer:
solution given :
Since opposite side and side of a congruent triangle are equal.
Now
the statement which is true is:
<HDG=~ <HFE
Hemp bell bell help math
Answer:
This is indeed a function!
Step-by-step explanation:
After a party there is 3/4 of a pizza left. You split it evenly between you and 3 friends. What fraction of a pizza does everyone get?
Answer:
3/16
Step-by-step explanation:
3/4÷4=3/16
Since there are 4 people, not 3, divide the remaining pizza by 4.