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.
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What is the prime factorization of 32?
A. 32 = 2 x 4x4
B. 32 = 2x2x2x2x2
C. 32 = 2x2x2x2
D. 32 = 2 * 2 * 2 * 4
Answer:
2nd option
Step-by-step explanation:
Repeatedly divide by 2 until the value 1 is reached
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 ← finish here
Then
32 = 2 × 2 × 2 × 2 × 2
A rectangular cube of iron is a side 8 cm. What is it volume.
[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]
Answer:
The volume is 512 cube centimetres.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Find the intersection point for the following linear functions.
Rx) = 2x + 3
8(x) = -4x - 27
Answer:
(-5, -7)
Step-by-step explanation:
Answer:
[tex](-5,-7)[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3[/tex]
[tex]g(x)=-4x-27[/tex]
[tex]2x+3=-4x-27[/tex]
[tex]6x+3=-27[/tex]
[tex]6x=-30[/tex]
[tex]x=-5[/tex]
[tex]f(-5)=2(-5)+3[/tex]
[tex]f(-5)=-10+3[/tex]
[tex]f(-5)=-7[/tex]
Therefore, the point of intersection is [tex](-5,-7)[/tex]
Help help help math math
Answer:
Function
Step-by-step explanation:
Hope it help !!
What is the value of x in the equation 4
.
+
2
Answer:
x=-3
Step-by-step explanation:
"When I started here, there were 500 employees. Since then, we have
added 35% more employees, so we now have a total of employees."
Answer:
Assuming that the question is asking how many employees there are, your answer would be 675.
Step-by-step explanation:
First, to find 35% of 500, you can use this equation (35 x 500) / 100 Second, solve the equation (The answer is 175) Third, you add 500 + 175 to get 675Rewrite in simplest terms: (-9x + 7y) - (-9x + 5y)
Answer:
3y
Step-by-step explanation:
(-9x+7y)-(-9x+5y)
Distribute the negative(-)
-9x+7y+9x-5y
-9 and 9 cancel each other
3y
The simplest terms of the given expression (-9x + 7y) - (-9x + 5y) will be 2y.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
(-9x + 7y) - (-9x + 5y)
Open the bracket
-9x + 7y + 9x - 5y
Combined likely terms together
-9x + 9x + 7y - 5y
0 + 2y = 2y
Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".
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QUESTION 21 PLEASE HELPPP
Answer:
one solution
Step-by-step explanation:
Since both are y-isolated equation, we can write as:
[tex]\displaystyle \large{6x-2=4x-2}[/tex]
Solve for x, first move 4x to subtract with 6x and -2 to add with -2
[tex]\displaystyle \large{6x-4x=-2+2}\\\displaystyle \large{2x=0}\\\displaystyle \large{x=0}[/tex]
Then substitute x = 0 in any of these equations which we receive y = -2.
And the solution is (0,-2) which only has one solution.
Need answer to the question
Answer:
B) Symmetric property of congruenceStep-by-step explanation:
The angles 1 and 2 are marked as congruent
If a ≅ b, then b ≅ a, this is called the symmetric property of congruence:
The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first.Correct choice is B
Answer:
Symmetric property of similarity
Step-by-step explanation:
If a=a then that's reflexive propertyIf a=b and b=c then a=c, transitive propertyrewrite in simplest terms -6(-7u+6)+2u
Answer:
44u-36
Step-by-step explanation:
42u-36+2u
44u-36
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is your total bill
Answer:
$4.32
Step-by-step explanation:
If you are splitting it evenly, just divide 12.96 by 3
12.96 / 3 = $4.32
7362*637 help please
Answer:
4689594
Step-by-step explanation:
help plsssssssssssssss
Answer:
Last answer, height is 150 ft
Step-by-step explanation:
from the graph, you can clearly see, when T=3, H=150
Which means The firework is at a height of 150 feet
Answer:
D
Step-by-step explanation:
At 3 seconds, the firework is at a height of 150 feet
Answer is D. third option
The firework is at a height of 150 feet
ST
16. (26)
A bag contains 3 green marbles and
7 yellow marbles. Find the probability of
drawing a green marble, keeping it, and
drawing another green marble. Write the
probability as a fraction in simplest form.
17.
Answer:
the probability would be 30% but as a fraction it would be 3/10
Step-by-step explanation:
Answer:
7/15
Step-by-step explanation:
The probability of the first one is 7/10 and the second one is 6/9. Multiply them together and you get 42/90, which simplifies to 7/15.
What is the percent decrease from 16 to 0
Help with this please?
find three solutions for 9x - 2y = 18
Answer:
[tex](x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)[/tex]
Step-by-step explanation:
In a parking lot 30% of the cars are white write this as a decimal
Answer:
0.3
Step-by-step explanation:
Answer:
[tex]{ \tt{30\% = 0.3}} \\ [/tex]
David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $4.45 per pound, and type B coffee costs $5.85 per pound. This month, David made 123 pounds of the blend, for a total cost of $643.95. How many pounds of type B coffee did he use?
Step-by-step explanation:
x = pounds A
y = pounds B
x + y = 123
4.45x + 5.85y = $643.95
from the first equation we get
x = 123 - y
and we use that in the second equation :
4.45×(123 - y) + 5.85y = 643.95
547.35 - 4.45y + 5.85y = 643.95
1.4y = 96.6
y = 69
x = 123 - y = 123 - 69 = 54
so, he used 69 pounds of B coffee.
Mrs Ang bought k apples at 50% each from a supermarket. How much
change did she receive if she paid $10 to the cashier? Express your answer
in cents.
Answer:
The apples may have costed 0.50 cents each, and she may have bought 10, which would result in her paying 10 dollars, and receiving 5 dollars in change.
Step-by-step explanation:
Multiply 10 (the amount she gave to the cashier) by 0.50%, it equals 5, so that's how much she paid, and since she gave a 10 dollar bill, she should get 5 dollars in change.
T^T
I thought of a number. This number double is 7 less than 29. What is my number? hurry please
Answer:
11
Step-by-step explanation:
11*2=22
29-7 =22
Answer:
11
Step-by-step explanation:
Let x be your number
Is means equals
2x = 29-7
2x= 22
2x/2 = 22/2
x =11
Which story represents the equation six-sevenths times one-fourth?
A: Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more milk. How much milk did she drink in all?
B: Mike walked one-fourth mile and then he took the bus for six-sevenths miles to school. How many miles did he travel in total?
C: Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
D: Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left?
Answer:
C I think.
Step-by-step explanation:
I don't know for sure, but A, B and D all talk about adding or subtracting the answers together, while C tells us to find the fraction of a fraction so I'm pretty sure you multiply. Hope this helps!
Solve 3-x/2<18.
A. X>-42
B. x > -30
C. X< -30
D. X<42
The solution of the given equation will be C -x< 30
What does it mean to solve an equation?An equation represents the equality of two or more mathematical expressions.
A Solutions to an equation are those values of the variables, involved in that equation for which the equation is true.
We have been given the equation as 3-x/2<18.
Now solving for x
3-x/2<18.
Eliminate 3
-x/2 < 18 - 3
-x/2 < 15
Multiply by 2 on both sides;
-x/2 < 15 (2)
-x< 30
Therefore, the solution of the given equation will be C -x< 30
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Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
that is 64% acid?
Step-by-step explanation:
Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
is 64% acid
There should be 40 L of solution A and 60 L of solution B should be added in order to make 100 L of a solution that is 64% acidic.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, solution A is 40% acidic and solution B is 80% acidic, they are mixed to get a 100 L solution which is 64% acidic.
Establishing the equations,
A+B = 100
A = 100-B.......(i)
40% of A + 80% of B = 64% of 100
0.4A + 0.8B = 64......(ii)
Solving the equations,
0.4(100-B) + 0.8B = 64
40 - 0.4B + 0.8B = 64
0.4B = 24
B = 24/0.4
B = 60
Putting, B = 60 in Eq(i)
A = 100-60
A = 40
Hence, The amount of solutions needed is A = 40 L and B = 60 L.
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Using the table find then relative frequency of each color, to 3 decimal places
Explanation:
For each row, divide the color counts over the total. For example, we have 9 red in bag one out of 61 total. This leads to a relative frequency of 9/61 = 0.1475 which rounds to 0.148; so approximately 14.8% of the items in bag one are red. This represents the top left corner of the table.
As another example, we have 5 brown out of 60 total in bag ten. That leads to a relative frequency of 5/60 = 0.0833 = 0.083 (see the bottom right corner of the table).
Take note that for any given row, adding up the relative frequencies will yield the value of 1 (though there might be some slight rounding error along the way).
please help I am so lost rn
(please put step by step if you can)
thanks!
Answer:
x=-5 and y= 4
Step-by-step explanation:
To eliminate x, add up both equations
9y= 36
divide both sides by 9
y=36/9
y= 8
To eliminate y, multiply the first equation by 8
-16x + 8y = 112
2x+ 8y= 22
Subtract equation 2 from equation 1
-18x = 90
Divide both sides by -18
x= 90/-18
x= -5
Ben currently has $70 in his trip fund. He makes $45 per week doing yard work for his neighbors. He keeps $18 of the $45 for weekly expenses. The remaining amount goes into his trip fund. Which function can be used to determine the amount of money (y), in dollars, that Ben has in his trip fund at the end of xx weeks?
y=70+27x
Answer:
he starts with 70 and $45-18=27 so he makes $27 to add to those $70
Step-by-step explanation:
In a group of workers, 16 belonged to a lottery syndicate and 4 did not.
What fraction of the workers did not belong to the syndicate?
1: 4/16
2: 1/5
3: 1/4
4: 3/4
Answer:
HI THEREthe answer is number 1 !!
• correct me if I'm wrong
Express the following surds in the simplest form
a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]
[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]
[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]
[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
HELPPPP PLEASEEEEE