Mathematics High School

The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21

Answers

Answer 1
Cube Root 1113 = 10.36
Cube Root 53 = 3.76

The ratio is 10.36/3.76 = 2.76
Cube Root (21) = 2.76 to 3 places. 

D <<<<<<<answer.

There is another way to do this (much better I think).
1113/53 = 21

A solid has 3 dimensions. Each dimension of the big solid will be k times bigger than the little one.

Therefore the volumes are related by a factor of cube root(large one ) to small one = cube root (21)

Related Questions

Hi could u plz help me anyone please

Answers

Hello,

To find this solution, you have to write an inequality. We want the new plan to be less than the old plan of $175.

So our inequality would be:
94 + 4.5x < 175
Solving it gives:
4.5x < 81
x < 18

So the number of devices must be less than 18. Draw an open circle at 18 with a ray going to the left to show those numbers.

Good luck,
MrEQ

f(x) = x3 - 3x2 + 4 = 0 For the equation given, 2 has a multiplicity of? 1, 2, 3

Answers

3 It's the highest power.
Multiplicity is how many times
a certain solution to the function.
In this case, we are finding out how many times 2 appears in the function, meaning you’ll have to solve for it when it equals 0. You may use a calculator or use the rational roots method. I will simply derive the answer from the calculator. If you’d like to know about the rational roots method, comment.

x^3 - 3x^2 + 4 = 0 // Given
0 = (x + 1)(x - 2)(x - 2) // Calculator skills
0 = (x + 1)(x - 2)^2 // Simplify

Therefore, 2 has a multiplicity of 2

Two sides of a triangle have lengths 5 in. and 16 in. Describe the possible lengths of the third side.


5 < x < 21


5 < x < 16


16 < x < 21


11 < x < 21

Can you construct a triangle that has side lengths 11 cm, 12 cm, and 15 cm?


no


yes


Answers

yes, 3rd one please help me out too

Answer:

11 < x < 21

Yes

Using your knowledge of circles, label the following on the given diagram: chord, tangent, radius, secant, point of tangency and diameter. Name a minor arc and a major arc.

Answers

The purple line is tangent. Tangent line intersects a circle in only 1 point
The yellow dot is the point of tangency. It is the point where tangent line touches the circle
The light blue line is secant. Secant line intersects a circle in 2 points
The red line is the radius. Radius is the distance from center to the outer rim of the circle.
The green line is the diameter. It is the line passing through the center of a circle. It measures twice the radius
The gray line is the chord. Chord is the line whose endpoints lie on the circle.
Arc AB is a minor arc
Arc ABCD is a major arc

Marge orders the following items and would like to leave a 20 percent tip based on her bill. There is no tax on her meal. What is the total cost of her dinner including gratuity? Item Amount Soup $3.75 Shrimp scampi $15.00 Iced tea $2.60 Dessert $4.25.

Answers

3.75+15+2.6+4.25=$25.60 *1.2 = $30.72

Answer:

The total cost of her dinner including tip would be $30.72

Step-by-step explanation:

Marge orders the following items on her meal.

Soup = $3.75

Shrimp scampi = $15.00

Iced tea = $2.60

Dessert = $4.25

The total cost of her dinner including gratuity is

3.75 + 15.00 + 2.60 + 4.25 = $25.60

She would like to leave a 20% tip based on her bill

Therefore, 20% of $25.60

= 0.20 × 25.60 = $5.12

Now add this tip amount to the bill amount.

$25.60 + $5.12 = $30.72

The total cost of her dinner including tip would be $30.72

If a fictional shrinking man shrinks proportionately to 1/10 his original height, his weight will be multiplied by

Answers

The final weight will be reduced by 1/10 of its original weight.

What is equation modelling? What is a mathematical equation and expression?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.

Given is a fictional shrinking man shrinks proportionately to 1/10 his original height.

Assume the weight to be [W]. Then -

W = mg

m = ρV     {ρ is density}

Then -

W = ρVg

Assume the body to be cylinder of radius [r] and height [h], we can write-

W =  πr²ρgh

Than, the initial weight will be -

W = πr²ρgh

After Shrinking -

W' = πr²ρgh/10

Then -

W'/W = {πr²ρgh/10}/{πr²ρgh}

W'/W = πr²ρgh/10  x  1/πr²ρgh

W'/W = 1/10

W' = W/10

Therefore, the final weight will be reduced by 1/10 of its original weight.

To solve more questions on equations, expressions and polynomials, visit the link below -

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In a drawing of the solar system, the scale is 1 mm = 500 km. for a planet with a diameter of 6,000 km, what should be the diameter of the drawing of the planet?
12 mm
120 mm
6,000 mm
3,000,000 mm

Answers

1 mm : 500 km
Multiply the above equation by 12 to get
12 mm : 6000 km

The 1st selection is appropriate.

Company A can produce 100 CPUs in 3 days while Company B can produce 150 CPUs in 4 days. If the two companies join forces, how many days would it take them to produce 1000 CPUs?

Answers

I'm guessing it's about 16 days.

Hope this helped!

Answer: They would need 15 days

Step-by-step explanation:

The data is:

Company A produce 100 CPUs in 3 days, so the rate per day is:

Ra = 100/3 CPUs per day: 33.33 CPUs per day.

Company B produce 150 CPUs in 4 days, then it produces:

Rb = 150/4 = 37.5 CPUs per day.

Then, if both companies work toggeter, they produce

Ra + Rb = 33.33 + 37.5 CPUs per day =  70.83 CPUs per day.

We want to know the number X of days needed to make 1000 CPUs, then we need to solve:

70.83*X = 1000

X = 1000/70.83 = 14.11 days, we could round it up to 15 days if we want to have a whole number.

Expressed powers are those that aref(x) = 5x + 3; g(x) = 6x - 5 Find f/g. (f/g)(x) = Quantity six x minus five divided by five x plus three. domain {x|x ≠ Five over six. } (f/g)(x) = Quantity five x plus three divided by six x minus five. domain {x|x ≠ Three over five } (f/g)(x) = Quantity five x plus three divided by six x minus five.domain {x|x ≠ Five over six. } (f/g)(x) = Quantity six x minus five divided by five x plus three. domain {x|x ≠ - Three over five. }

Answers

Answer: (f/g)(x) = Quantity five x plus three divided by six x minus five.domain {x|x ≠ Five over six. }

Explanation:

1) (f/g)(x) = f(x) / g(x)

2)

  f(x)         5x + 3
-------- = ------------
  g(x)        6x - 5

3) Since the division by 0 is not defined, the domain is restricted to 6x - 5 ≠ 0.

Therefore you must solve 6x - 5 = 0 to exclude the value of x for which the denominator becomes 0:

6 x - 5 = 0 => 6x = 5 => x = 5 / 6.

So, the domain is all x | x ≠ 5/6.

Answer:

(f/g)(x) = Quantity five x plus three divided by six x minus five.domain {x|x ≠ Five over six. }

Step-by-step explanation:

Given functions,

[tex]f(x)=5x+3[/tex]

[tex]g(x) =6x-5[/tex]

[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]

[tex]=\frac{5x+3}{6x-5}[/tex]                        ( By substitution )

Let [tex]h(x)=\frac{5x+3}{6x-5}[/tex]    

Which is the rational function,

Since, a rational function is defined for all real number except those for which denominator = 0,

[tex]6x-5=0[/tex]

[tex]6x=5[/tex]

[tex]x=\frac{5}{6}[/tex]

Thus, h(x) is defined on all real numbers except 5/6,

Hence, domain of [tex]\frac{f}{g}(x)[/tex] is {x| x ≠ [tex]\frac{5}{6}[/tex] }

The area of a rectangular hotel room is 209 square feet. the perimeter is 60 feet. what are the dimensions of the room?

Answers

A) x * y = 209
B) 2x + 2y = 60

A) y = 209 / x   putting this into equation B

B) 2x + (2 * 209 / x) = 60
2x + 418 / x = 60  multiplying by x
2x^2 + 418 = 60x
2x^2  -60x + 418 = 0
Solving by quadratic formula
x = 19
y = 11








A sign standing 6 feet tall is situated 18 feet away from a flag pole. at a certain time of day the sign's shadow is 3 feet long and the flagpole's shadow is 24 feet long. how tall is the flagpole?

Answers

Observe attached picture.

On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft

When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.

We can apply trigonometry rules to find height of flagpole.

From small triangle containing sign we can find tangens function:
[tex]tan \alpha = \frac{C}{D} [/tex]
Similarly we can do for large triangle containing flagpole:
[tex]tan \alpha = \frac{A}{B} [/tex]

We see that these two equations have same left sides. This means that their right sides must also be same:
[tex]\frac{C}{D} = \frac{A}{B}[/tex]
We can solve for A:
[tex]CB=AD \\ A= \frac{CB}{D} \\ A= \frac{6*24}{3} \\ A=48 ft[/tex]

Height of flagpole is 48 feet.

10 POINTS + BRAINLIEST ANSWER!!!

65x + y = 455

A grocery store receives a shipment of oranges and consistently sells the same number of oranges each day. The equation above models the number of oranges, y, that remain x days after the shipment is received. What does it mean that (7, 0) is a solution to the equation?

A. It takes 7 days after the shipment until none of the oranges are remaining.

B. There are 7 oranges in the shipment.

C. It takes 7 days for orange to be sold to 455 customers.

D. After the shipment, 7 oranges are sold each day.

Answers

A. It takes 7 days after the shipment until none of the oranges are remaining.
A. it takes 7 days after the shipment until none of the oranges are remaining. 

If PQRS is a parallelogram, what is the value of Y

Answers

1/4(y) = 13
y = 13 * 4
y = 52

answer
C. 52

Answer:

52

Step-by-step explanation:

did the question

Please show me the steps on how to do this.


Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.

I'm learning about vectors right now.
Options:
o 54 degrees
o 36 degrees
o 46 degrees
o 44 degrees,

Answers

You can consider the tree perpendicular to its shadow, therefore you get a triangle rectangle of which you know the two legs and you need to find the angle between the shadow and the hypothenuse, opposite to the tree.

In this case, the angle α can be easily found with trigonometry:
tan α = (opposite side / adjacent side) 

Therefore:
α = tan⁻¹ (tree / shadow) = tan⁻¹ (10 / 14) = 35°

NOTE:
tan⁻¹ is sometimes found written as arctan.


please help asap! 54 points

Answers

slope = (2+2)/(6-3) = 4/3
a)
point slope intercept
y + 2 = 4/3(x - 3)

standard form
y + 2 = 4/3(x - 3)
3y + 6 = 4x - 12
- 4x +  3y = -18 ..........this is standard form

Answer is C
y + 2 = 4/3(x - 3);  -4x + 3y = -18 


slope =  (2 - (-2)) /  (6-3)  = 4/3

point-slope from  is 

y - (-2) = (4/3)(x - 3)

y + 2 = (4/3) (x - 3) is the equation in point slope form

Standard form is  -4x + 3y = -18 

The answer is C

answer asap Malia created a correct function table using the equation g = 4f.

Which table could be Malia's?


A.

B.

C.

Answers

answer is A.
hope I helped

laura budgets $54 each month for annual expenses. she nets $1820 semimonthly. what percent of her net monthly income does she budget for annual expenses?


1%

3%

6%

8%

Answers

Answer: The correct answer is 1%.

If she is getting $1820 semimonthly. That means that she is getting $3640 per month. 1820 x 2 = 3640

Now, we just need to find the percent of that which goes for the annual expenses.

Divide 54 by 3640 and multiply by it 100 to get a percent of 1.4% which can be rounded to 1%.
Answer:

Explanation: 

Since the income known in the problem is for semi-monthly (meaning every half of the month), we should compute for the monthly income because we what know is the amount of money Laura allots on a monthly basis for her annual expenses. 

Since semi-monthly income is received twice per month, the monthly income of Laura is two times her semi-monthly income (= $1820). That is,

monthly income
= 2 × semi-monthly income
= 2 × $1820
monthly income = $3,640

Because $54 is budgeted each month for annual expenses, the percentage of the monthly income that is allocated for annual expenses is computed as

percentage of the monthly income
= ((monthly income allocated for annual expenses) ÷ (monthly income)) × 100%
= ($54 ÷ $3,640) × 100%
≈ 0.0148351648 × 100%
percentage of the monthly income ≈ 1%

helppppppppppppppppppppppppp

Answers

Slope formula is 

[tex] \frac{y2-y1}{x2-x1} [/tex]
[tex] \frac{5-1}{-2-3} [/tex]
[tex] \frac{4}{-5} [/tex]

So -4/5 is the right answer.

Hope this helps :)

Write the expression as either the sine, cosine, or tangent of a single angle

Answers

We'll use this trig identity
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
where in this case,
x = pi/3
y = pi/5

So,
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(pi/3-pi/5) = cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(pi/3-pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(5pi/15-3pi/15)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(2pi/15)

------------------------------------------------------------

The answer is cos(2pi/15) which can be written as [tex]\cos\left(\frac{2\pi}{15}\right)[/tex]

Sonya has four straws of different lengths: 2cm,8cm,14cm,and 16cm. How many triangles can she make using the straws?

Answers

You cant make a triangle with the combination 2,8 and 14,  nor 2, 8 and 16 nor 2 , 14 and 16.
You can make a triangle with  6, 14 and 16 straws.

The answer is one triangle

Im assuming you are not allowed to stick together any of the straws


There is no way to make a triangle with numbers 2,8,14, nor 2,8,16, nor 2,14, and 16.  Using 6, 14, and 16 straws, you can form a triangle.

I'm guessing you're not supposed to stick any one of the straws together.  Kindly see the accompanying document for more information. As a result, B is represented by one triangle. All two sides add up to more than the third side. As a result, the difference between the two sides is less than the difference between the first and third sides.

Therefore, the final answer is "one triangle".

Learn more:

brainly.com/question/3528787

1. 16y + 0 = 16y
Associate Property of Addition
Zero Property of Multiplication
Commutative Property of Addition
Identity Property of Addition
2. d • r = r • d
Commutative Property of Multiplication
Identity Property of Multiplication
Zero Property of Multiplication
Commutative Property of Addition
3. 27a • 0 = 0
Associative Property of Multiplication
Commutative Property of Multiplication
Zero Property of Multiplication
Identity Property of Multiplication
4. 16x + 5y = 5y + 16x
Commutative Property of Addition
Zero Property of Addition
Ident

Answers

1) Identity Property of addition
2) Commutative Property of Multiplication
3) Zero property of multiplication
4) Commutative property of addition
Hope this helps!

A room's length is 3 feet less than twice its width. The area of the room is 135 square feet. What are the room's dimensions?

Answers

A room's length is 3 feet less than twice its width. The area of the room is 135 sq feet. What are the room's dimensions?

Hope this helps:

A= L x W
135 = (2w-3)(W)
135 = (2w squared - 3W)
135 = 2w^2-3w
2w^2-3w-135 = 0
-----

Use the quadratic formula to get:
w = [3 +- sqrt(9 - 4*2*-135)]/4

Positive solution:
w = [3 + sqrt(1089)/4
w = [3 + 33]/4
w = 9 ft
L = 2W-3 = 2*9-3 = 15 ft.





If the width is w, the length is l = 2w-3.
The total area is length x width = w*(2w-3)
Solve
w*(2w-3)=135 to find w.
2w^2-3w-135=0

w = (3 +/- sqrt ( 9 +8*135))/4

The positive solution is
w = ( 3 + 33) /4 = 9 and then l = 15.

The dimensions of room are: Length = 15 feet and Width = 9 feet.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

we have,

A room's length is 3 feet less than twice its width.

The area of the room is 135 square feet.

let the width be x then length = 2x - 3.

So, Area of Room

135 = l w

135 = x (2x- 3)

2x² - 3x - 135= 0

2x² + 15x - 18x - 135 = 0

x (2x+ 15) - 9 (2x- 15)= 0

(2x+ 15)(x- 9)=0

x= -15/2 or x= 9.

Thus, the dimensions of room are:

Length = 2(9)-3 = 15 feet

Width = 9 feet

Learn more about algebra here:

https://brainly.com/question/24875240

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What is the measure of angle S?

Answers

subtract 86-42... the answer is 44 degrees

A student's home is 3.25 miles from the school. A soda shop is located 900 feet farther down the road from the school. What is the total distance from the student's home to the soda shop?

Answers

3.42mi miles because if you convert 3.25 miles into feet it gives you 17160 ft so if you add 900 to that then you get 18060 after that you can convert it back into miles and it gives you 3.42mi or 18060ft                                                                                                     

Answer:

18060

Step-by-step explanation:

.

which equation has (2, -1) as a solution?

A. y = 2x - 1
B. y = x + 3
C. y = x - 3
D. y = -2x + 1

If someone could explain this to me it would be greatly appreciated. Thank you.

Answers

(x,y) is a solution to an eqn when y = mx + c

A. 2(2)-1 = 3 <>-1

B. 2+3 = 5<>-1

C. 2-3 = -1 = y

so C has (2,-1) as a solution

Mark went to the store and spent a total of $18.90. What is the cost of 5 items is if one item cost $2.95?

Answers

18.90 - 2.95= 15.95 ÷4= 3.99

item #1 was 2.95 the rest of the items were 3.99

the diameter of a bike is 90cm. How far would it travel after 5 revolutions?

Answers

we know that
[length of a circumference]=2*pi*r
diameter=90 cm-------------> r=d/2--------> r=45 cm
[length of a circumference]=2*pi*45----------> 90*pi cm

with 1 revolution will go the length of the wheel

if 1 revolution is-------------------> 90*pi cm
 5 revolution is--------------------> X
X=5*90*pi----------> 1413 cm

the answer is 1413 cm

A bicycle store costs $1700 per month to operate. The store pays an average of $75 per month. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?

Answers

The formula in computing the break-even point is:

Break-even = fixed cost / contribution margin

The fixed cost is already given which is $1700 per month. To compute for the contribution margin, you have to deduct the average cost per month ($75) to the selling price of each bicycle ($95). The contribution margin is $20 ($95 - $75).

Substituting the amounts to the formula:

Break-even = $1,700/$20

                     = 85

Therefore, the store must sell 85 bicycles each month to break even.

Three fourths of the students in class said they like word problems . If fewer than 30 students said they like word problems , how many students are there ?

Answers

x < 40. 

Since there are less than 30 students that say they like that and that represents 3/4, you can start by trying to solve the equation. 

3/4x < 30

Where x is the total number of students in the class. 

Please Help!!!

(x-3)^2/64 + (y+5)^2/100 = 1

a. Identify the coordinates of the center of the ellipse.
b. Find the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. Label the center and foci.,

Answers

Your ellipse is given in the form:
[tex]\frac{(x - xc)^{2} }{ a^{2} } + \frac{(y - yc)^{2} }{ b^{2} } = 1[/tex]

Indeed, you have:

[tex]\frac{(x-3)^{2} }{64} + \frac{(y+5)^{2} }{100} = 1[/tex]

Therefore you can easily find:

a) the coordinates of the center:
in your case xc = 3 and yc = -5
hence C(3 , -5)

b) lenght of the major and minor axis:
in your case a² < b²:
a² = 64  ⇒ a = 8 (ATTENTION! This is the semi-minor axis)
b² = 100 ⇒ b = 10 (again, this is the semi-major axis)
Therefore,
minor axis 2a = 16 and major axis 2b = 20

c) coordinates of the foci:
Since you have a² < b², foci have the generic coordinates F₁₂ (xc , yc+/-c)
where c = √(b² - a²)

Let's compute c = √(100 - 64) = √36 = 6
yf₁ = -5 - 6 = -11
yf₂ = -5 + 6 = -1
Therefore:
F₁ (3, -11) and F₂(3, +1)

d) the graph is in the picture attached

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