find the number by which 5400 must be multiplied so that the product is a perfect cube.
Also find the cube root of the number obtained.
( Show workings )
Answer:
Step-by-step explanation:
The easiest way (or the most reliable way) is to factor the given number into primes
5400 = 2 * 2 * 2 * 3 * 3 * 3 * 5 * 5
I cheated a little bit. 54 = 2 * 27 which is 2 * 3 * 3 * 3
100 = 2 * 2 * 5 *5
Combine the two parts and you get the factors I gave you.
Now you have to have the numbers go into groups of three. The only adjustment needed is 5 * 5 and one more 5
So the perfect cube is 5400 * 5 = 27000
Does that work? It should
27000^(1/3) = 3 * 10 = 30
So the cube root of 27000 is 30.
Frito lay mix variety in pack 28 bags for 9.88 cost per bag
Answer:
Each bag costs 0.35 cents
Step-by-step explanation:
divide 9.88 by 28 and that gives you the total for each bag of chips
Find the value of the variable
X=
Answer:
X=20º
Step-by-step explanation:
This is a vertical angle meaning both sides are congruent to each other.
Meaning: (x+100)º= 6x
Solve:
(x+100)º= 6x
-x -x
100º=5x
/5 . /5
x=20º
I don't understand how to do this. If someone can help me understand how to do this I would be very grateful.
Step-by-step explanation: ok do 10 - y2 then it will be 8 so whats left is y divide 8 by 2 and thats the answer for 2y. Reapet this patern for 3z and all the other questions
hope this helps
what is (c+d) to the power of 3
Answer:
c³ + cd³ + 3c²d + 3cd²
Step-by-step explanation:
(c+d)^3 is worded as c plus d quantity cubed which doesn't mean you cube everything inside. It means you multiply the quantity by itself 3 times.
(c+d)(c+d)(c+d)
You can only multiply 2 at a time so do the first two then the result and the third one.
Distribute everything in one quantity to the other so c*c = c^2 and c*d = cd
= (c^2 + 2cd + d^2)(c+d)
= c^3 + c^2d + 2c^2d + 2cd^2 + cd^2 + cd^3
Combine like terms
= c³ + 3c²d + 3cd² + cd³
Solve both the formula for the circumference of a circle and the formula for the area of a circle for π. Use these equations to write a proportion comparing the circumference and the area of a circle.
Answer:
ósea un momento
Step-by-step explanation:
........,...
Factorise : a²+b²-c²+2ab
Answer:
Step-by-step explanation:
a²+b²-c²+2ab
=a²+b²+2ab-c²
=(a+b)²-c²
=(a+b+c)(a+b-c)
Given congruent triangles ABC and MNL, which of
the following are corresponding parts? Check all that
apply.
2,5,6 2)AB and MN 5)B and N 6)CB and LN
Step-by-step explanation:
Edge 2021
Write the equation of the line in fully simplified slope-intercept form.
What is the value of y in the sequence below?
2,y,18, -54,162,
First, let's check if the sequence is geometric or arithmetric.
If arithmetric, the sequence will have common difference.
Arithmetric
[tex] \displaystyle \large{a_{n + 1} - a_n = d}[/tex]
d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.
Geometric
[tex] \displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}[/tex]
r stands for a common ratio.
To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.
Let's check by dividing sequences.
We have:
2,y,18,-54,162,...Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.
[tex] \displaystyle \large{ \frac{ - 54}{18} = - 3 } \\ \displaystyle \large{ \frac{ 162}{ - 54} = - 3} [/tex]
Hence, the sequence is geometric.
Because the common ratio is -3. Let these be the following:
[tex] \displaystyle \large{ a_{n + 1} = y } \\ \displaystyle \large{ a_n = 2 } \\ \displaystyle \large{ r = - 3 }[/tex]
From the:
[tex] \displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}[/tex]
Substitute the values in.
[tex] \displaystyle \large{ \frac{y}{2} = - 3}[/tex]
Multiply the whole equation by 2 to isolate y.
[tex] \displaystyle \large{ \frac{y}{2} \times 2 = - 3 \times 2} \\ \displaystyle \large{ y = - 6}[/tex]
Therefore, the value of y is -6.
Graph y - 4x + 3 = 0 and {(x , y ): x ≤ 1}. Click on the graph until the correct graph appears.
definition of a quadratic function
Answer:
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
Step-by-step explanation:
Answer:
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero
Step-by-step explanation:
Find the missing angle
Step-by-step explanation:
119°+29°+n°=180°. (Sum of all the angles of triangle)
So,
158°+n= 180°
n= 180°-158°
n= 22°
Answer:
n = 22°
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Roko paid $12.50 for 25 game tickets. Louisa paid $17.50 for 35 game tickets. What is the constant of proportionality?
Answer:
1 ticket = $0.50
Step-by-step explanation:
hope this helps and have a great day
pew pew.
The diagonals of a rhombus are 30cm and 16cm. Find its area, the length of a side and its perimeter.
Answer:
Area = 1/2 × product of diagonalsso area = 1/2 × 30 ×16 = 240 cm²
also diagonals bisect each other at right angles so 1/2×30= 15cm,, 1/2× 16 = 8cm
therefore by pythagoras theorem,
[tex] {15 }^{2} [/tex]+ [tex]{8}^{2} [/tex]= [tex] {side}^{2} [/tex][tex] \sqrt{289 = side} [/tex]
side = 17
Perimeter = 4×17 =68 cm.
Answer:
Step-by-step explanation:
[tex]\large \boldsymbol {} \tt Formulas : \\\\d_1^2+d_2^2=4a^2 \\\\S=\dfrac{1}{2} d_1d_2 \\\\ \ where \ S \ is \ the \ area \ of \ the \ rhombus \ ;\\\\\ and \ d_1 \ and \ d_2 \ are \ its \ diagonals \ ; \ and \ a \ , \\\\\\ respectively, \ is\ the \ side \ of\ the rhombus \\\\ then : \\\\ 4a^2=16^2+30^2 \\\\ 4a^2=1156 \\\\a^2=289 \\\\a=17 \ \ then \ P=4a=17*4=\boldsymbol {68} \\\\ \tt S=\dfrac{1}{2} \cdot 30 \cdot 16 =\boldsymbol {240 } \\\\ Answer : S=240 \ ; a=17 \ ; \ P=68 \ ;[/tex]
You are installing a fence around your yard. In the figure,
your yard is rectangle ABCD. Each unit in the coordinate
plane represents 10 feet.
a. What is the perimeter of your entire yard
b. You consider only installing a fence around your backyard represented by rectangle ABEF what is the perimeter of your backyard?
c. The cost of fencing is $50 for each 6 foot section how much do you say by only installing a fence in the backyard?
Perimeter of a shape can be determined by the sum of its individual sides. Thus, the answers to the given questions are:
(a) 360 feet
(b) 240 feet
(c) $1000.0
Perimeter can simply be defined as the sum of all sides of a given figure or shape. Thus, the solutions required can be determined as follows:
(a) Side AB = CA = (7 - 1) x 10 feet
= 6 x 10 feet
= 60 feet
Side AD = BC = 13 - 1
= 12 x 10 feet
= 120 feet
The perimeter of the entire yard = 60 + 120 + 60 + 120
= 360
Perimeter of the entire yard = 360 feet
(b) Side AB = EF = 60 feet
Side FA = BE = (7 -1) x 10 feet
= 60 feet
So that,
The perimeter of the backyard = 60 feet x 4
= 240
Perimeter of the backyard = 240 feet
(c) The cost of installing a fence in the entire yard = [tex]\frac{360}{6}[/tex] x $50
= $3000.0
The cost of installing a fence in the back yard = [tex]\frac{240}{6}[/tex] x $50
= $2000.0
The amount saved by only installing a fence in the back yard = $3000.0 - $2000.0
= $1000.0
Thus, the amount saved by only installing a fence in the back yard is $1000.0
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NEED ANSWERS FAST!! please
What is 8y squared+7y+4-3(2y squared-5y-8)?
Answer: 2 • (y2 + 11y + 14)
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((8•(y2))+7y)+4)-(3•((2y2-5y)-8))
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2y2-5y-8
The first term is, 2y2 its coefficient is 2 .
The middle term is, -5y its coefficient is -5 .
The last term, "the constant", is -8
Step-1 : Multiply the coefficient of the first term by the constant 2 • -8 = -16
Step-2 : Find two factors of -16 whose sum equals the coefficient of the middle term, which is -5 .
-16 + 1 = -15
-8 + 2 = -6
-4 + 4 = 0
-2 + 8 = 6
-1 + 16 = 15
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
(((8•(y2))+7y)+4)-3•(2y2-5y-8)
STEP
3
:
Equation at the end of step
3
:
((23y2 + 7y) + 4) - 3 • (2y2 - 5y - 8)
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
2y2 + 22y + 28 = 2 • (y2 + 11y + 14)
Trying to factor by splitting the middle term
5.2 Factoring y2 + 11y + 14
The first term is, y2 its coefficient is 1 .
The middle term is, +11y its coefficient is 11 .
The last term, "the constant", is +14
Step-1 : Multiply the coefficient of the first term by the constant 1 • 14 = 14
Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is 11 .
-14 + -1 = -15
-7 + -2 = -9
-2 + -7 = -9
-1 + -14 = -15
1 + 14 = 15
2 + 7 = 9
7 + 2 = 9
14 + 1 = 15
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Help me please i don’t have my notes and I forget how to do this
Answer:
AC = AB + BC
18 = (2X - 4) + (3X + 2)
18 = 5X - 2 ( add/subtract like terms)
20 = 5X (-2 take over otherside - 18 + 2)
X = 4
SUB X INTO AB AND BC
AB = 2(4) - 4 = 4
BC = 3(4) + 2 = 14
18)
Christopher's cell phone company
charges a monthly'rate of $56 plus
$0.95 per gigabyte of data used,
and $0.08 per text message sent.
Christopher sent 55 text messages
messages in April and received a bill
for $68.00. How much data did he
use?
Answer:
8 GB
Step-by-step explanation:
Cost = sum of fees 1, 2, and 3
C = 56 + .95g + .08t
so
68 = 56 + .95g + .08(55)
68 = 56 + .95g + .08(55)
68 = 56 + .95g + 4.4
68 - 56 - 4.4 = .95g
7.6 = .95 g
7.6/.95 = g
8 = g
Hi, I need help with this story problem.
Zach has the following partial bags of sugar in his pantry; 2 c., 1.5 c., 0.5 c., 3 c., and 1.5 c. If he uses 1 c. of sugar for his baking, how many cups of sugar will he have left?
Answer: 7.5 cups of sugar.
Step-by-step explanation:
Add all of the above:
2+1.5+0.5+3+1.5= 8.5 cups of sugar
Since Zach only needs 1 cup of sugar, subtract 1 from 8.5.
Therefore, your answer is 7.5 cups of sugar.
3 divided by 45 I need help I stink at division
Answer:45 divided by 3 is 15
Step-by-step explanation:
Answer:
its 15
I'm bad at explaning
To find 15, Beau found 32 = 9 and 4 = 16. He said that since 15 is between 9 and 16,15 must be between 3 and 4. He thinks a good estimate for 15 is 3+4 = 3.5. Is Beau's estimate high, low, or correct? Explain.
Answer:
Answer: His estimate was low
Step-by-step explanation:
It's true that √16 is 4 and that √9 is 3
for √15 :
[tex] \sqrt{15} = 3.9[/tex]
It's true that √15 lies between 3 and 4
[tex] \sqrt{15} : 3 < x < 4[/tex]
Estimated answer :
[tex] = 3.5[/tex]
Exact answer :
[tex] = 3.9[/tex]
Therefore, the error:
[tex] \delta x = 3.9 - 3.5 \\ \\ = 0.4[/tex]
Since error is less than 0.5, his estimation was moderate, [ low ]
The mass of an object is measured to be 5.55g. The actual weight of the object is 6.00g. What is the percent error?
Answer:
. The actual mass of the object was 9.98 X 10-3 g.
Step-by-step explanation:
yeah
I don't know this please help
What is the image point of (-8,9)(−8,9) after a translation right 3 units and down 1 unit?
Answer:
(-5,8)
Step-by-step explanation:
The left number represents the x-axis, the right one the y-axis. A translation to the right means in the positive direction on the x-axis, which is why we add 3 to -8 which gives us -5. Down on the y-axis is in the negative direction, which means we have to subtract 1 from 9, giving us 8.
Answer:
the answer is the same since it is the same numeral so in terms of y=mx+c and x1/y1 would be inversely proportional to x2/y2 which is perfectly direct proportional to x3/y3×2 and then dy over dx is the problem of integration so you use (x2/x3÷y2/y3)×x1^y1
I need help….. please help me
1). 3x-8 for x=5
2). 5(x+7)-1 for x = -3
Can someone help me!!!
4x+3=3x+13(Alternative interior angles)
4x-3x=13-3
x=10
Value of each angle=43 each
Write 7.12 as a mixed number in simplest form.
Work Shown:
7.12 = 7 + 0.12
7.12 = 7 + (12/100)
7.12 = 7 + (3/25)
7.12 = 7 & 3/25
The notation 7 & 3/25 means we have the whole part 7 and fractional part 3/25.