Two architectural models are pyramids with bases of equal area. The smaller model has a height of 10 centimeters, and the larger model has a height of 30 centimeters. How many times greater than the smaller model is the larger model’s volume?

Answer:

53:2 Im sure.

Ratio is a comparison of two quantities. Online Simplifying ratios calculator is a ratio simplifier that simplify ratios in to its simplest form. For that ones should know the greatest common factor of both numerator and denominator. And then divide these two by the common factor. By using ratio in simplest form calculator one can simplify ratio from the high value to lower value in an easy way.

Answer:

Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

40 ÷ 5 = 8

25 ÷ 5 = 5

The ratio 40 : 25 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

40 : 25 = 8 : 5

Therefore:

5 : 3 1/8 = 8 : 5

Step-by-step explanation:

Answer:

-69.19x + 38.2

Step-by-step explanation:

–9.2(8x – 4) + 0.7(2 + 6.3x)

= -73.6x + 36.8 + 1.4 + 4.41x

= -69.19x + 38.2

Answer:

The paths between the three cities DO NOT form a right triangle.

Step-by-step explanation:

For a right triangle to be formed, the Pythagorean Theorem (a2+b2=c2, with a and b being the legs that form the right angle, and c being the hypotenuse) needs to apply correctly to the distances. In a right triangle, the longest distance is always the hypotenuse, or the slanted side that doesn't touch the right angle. The question is to suggest that the hypotenuse is 400 km. long and the legs being 200 km. and 300 km. long respectively. So, to solve this, all we have to do is plug these distances into the Pythagorean Theorem and see if it comes out correct. When plugged in, the equation should be 2002+3002=4002. Then, you solve! It should go like this: 2002+3002=4002, then 40,000+90,000=160000, then add the numbers on the left side to get 130,000=160,000, but, hang on a second. 130,000 does not equal 160,000. This means that the Pythagorean Theorem does not work with the proposed right triangle, which means that the paths between the three cities do NOT form a right triangle!

  Paths between the three cities do not form a right triangle.

"In a right angle triangle, square of the hypotenuse is equal to the sum of squares of the other two sides"

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Given in the question,

If ABC is a right triangle, sides of the triangle will follow Pythagoras theorem.

AC² = AB² + BC²  [By Pythagoras theorem]

(400)² = (200)² + (300)²

160000 = 40000 + 90000

160000 = 130000

But 160000 ≠ 130000.

Therefore, ΔABC is not a right angle triangle.

Learn more about the use of Pythagoras theorem here,

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Answer:

-2

Step-by-step explanation:

2x + y = 10               Subtract 2x from both sides.

2x-2x + y = 10 - 2x  Combine the left.

y = 10 - 2x

The slope is the number in front of the x -- in this case - 2

The answer is - 2

So, 1 cube equals 1/4 unit.

4 cubes will equal 1 whole unit.

If the volume of the rectangular prism is 3 cubic units, all you have to do is multiply.

4*3=12

So it would take a total of 12 cubes to fill the prism.

Hope this helps.

Answer:

x-6

Step-by-step explanation:

Let the number be x

Then the algebraic expression  “six less than a number” can be represented as:

x - 6

So, "six less than a number” can be represented as: x - 6

Answer:

1/6 * 1/6 = 1/36 or 0.027%

Step-by-step explanation:

This is because there is a 1/6 chance the cubes will land on 3. Sincer there is 2 of them, multiply them by each other. Do not add.

Hope this helps!

Answer: 42.5

Step-by-step explanation:

The answer is 42.5

Answer: 42.5 cm

Step-by-step explanation: Its really simple. You multiply 8.5 cm and 5 cm to get 42.5 cm.

Answer:

60

Step-by-step explanation:

124−4(3−5(17−14)+2(9+5))

=124−4(3−(5)(3)+2(9+5))

=124−4(3−15+2(9+5))

=124−4(−12+2(9+5))

=124−4(−12+(2)(14))

=124−4(−12+28)

=124−(4)(16)

=124−64

=60

Answer:

1/5 *3 = 15

You have to do Keep, Change, Flip. When you do that it becomes 1/5*3/1.

That equals 15.

Answer:

x = 3

x = -5

Step-by-step explanation:

(9)(x+1)(x+1) = 144

(9)(x²+2x+1) = 144

9x²+18x+9 = 144

9x²+18x = 135

x²+2x = 15

x(x+2) = 15

x = 3

x= -5

Answer: [tex]x_1=3\\x_2=-5[/tex]

Step-by-step explanation:

Divide boht sides of the eqeuation by 9:

[tex]\frac{9(x+1)^2}{9}=\frac{144}{9}\\\\(x+1)^2=16[/tex]

Remembert that:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Then, applying this, you get:

[tex]x^2+2(x)(1)+1^2=16\\x^2+2x+1=16[/tex]

Subtract 16 from both sides:

[tex]x^2+2x+1-16=16-16\\x^2+2x-15=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 2 and whose product be -15, then:

[tex](x-3)(x+5)=0\\x_1=3\\x_2=-5[/tex]

Answer:

option D is correct.

Step-by-step explanation:

We need to find the value of

[tex]\sum_{n=1}^{6} 4(3)^{n-1}[/tex]

Here value of n starts from 1 and goes on till 6

And we need to add the values of all the terms by putting value of n from 1 to 6

This can be written as:

[tex]=4(3)^{1-1}+4(3)^{2-1}+4(3)^{3-1}+4(3)^{4-1}+4(3)^{5-1}+4(3)^{6-1} \\    Solving\\=4(3)^0+4(3)^1+4(3)^2+4(3)^3+4(3)^4+4(3)^5\\=4(1)+4(3)+4(9)+4(27)+4(81)+4(243)\\=4+12+36+108+324+972\\=1456[/tex]

So, option D is correct.

Answer:

1456

Step-by-step explanation:

This is the sum of a geometric sequence

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

4[tex](3)^{n-1}[/tex] ← is in this form

with a = 4 and r = 3

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex], hence

[tex]S_{6}[/tex] = [tex]\frac{4(3^6-1)}{3-1}[/tex] = [tex]\frac{4(729-1)}{2}[/tex] = 2 × 728 = 1456

Answer:

Step-by-step explanation:

6+2 = 8 your welcome or 4 x 2 = 8 :)

Answer:

B. 28 minutes

Step-by-step explanation:

According to the given statement,

William weeds the whole garden in 45 minutes, then in one minute he will weed 1/45 of the garden

and

similarly, 1/75 of the garden in one minute.

When they both will work together, they will weed (1/45+1/75) of the garden in one minute

Solving the equation:

= [tex]\frac{1}{45}+ \frac{1}{75}\\= \frac{75+45}{3375}\\ =\frac{120}{3375}\\ = 0.036[/tex]

Garden weeded in one minute by both = 0.036

So, number of minutes to weed whole garden = 1/0.036

= 27.77 minutes

Rounding off will give us: 28 minutes

So,

Option B is the correct answer ..

The answer is:

The domain for the function is all the real numbers,

Domain:(-∞,∞)

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

[tex]f(x)=\frac{1}{x^{2}-5x+25 }[/tex]

Where, the denominator is given by the expression:

[tex]x^{2}-5x+25[/tex]

For the given expression (quadratic equation), we have that:

[tex]a=1\\b=-5\\c=25[/tex]

Calculating the discriminat of the quadratic function, in order to know if the denominator of the function has roots (zeroes) at the real numbers, we have:

[tex]Discriminant=b^{2} -4ac[/tex]

[tex]Discriminant=-5^{2} -4(1)(25)[/tex]

[tex]Discriminant=25 -100=-75[/tex]

Now, as we know, if the discriminant of a quadratic function is less than 0, the quadratic function has no roots in the real numbers.

Therefore, since the denominator (quadratic function) has no roots in the real numbers, the domain for the function will be equal to all the real numbers.

Domain:(-∞,∞)

Hence, the answer is the third option, the domain for the function is all the real numbers,

Domain:(-∞,∞)

Have a nice day!

For line A,

if we increase x by 1 unit then y increases by 4 units i.e. (1,3) and similarly another point becomes

(2,7).

For line B,

if we increase x by 1 uni then y also increases by 1 unit i.e ( 1,1) and similarly another points becomes (2,2),(3,3),(4,4), etc.

For line C,

if we increase x by 3 units then y increases by 1 units i.e.(3,1) and similarly another points becomes

(7,2) and so on.

In above lines, the value of x is exactly equal to that of y in line B.

therefore, line B has constant proportionality between x and y.

To find the line with a constant of proportionality of 111 between y and x, we calculate the slope for each line. Line A has a slope of 111, making it the correct answer.

To determine which line has a constant of proportionality of 111, we need to examine the slope of each line. The slope represents the ratio of the change in the y-values to the change in the x-values for any two points on the line. If the slope is the same for all points on the line, then it has a constant of proportionality. Let's calculate the slopes for lines A, B, and C:

Line A: Let's choose two points: (0, 0) and (1, 111). The slope is (111 - 0) / (1 - 0) = 111 / 1 = 111.

Line B: Let's choose two points: (0, 0) and (1, 1110). The slope is (1110 - 0) / (1 - 0) = 1110 / 1 = 1110.

Line C: Let's choose two points: (0, 0) and (1, 11100). The slope is (11100 - 0) / (1 - 0) = 11100 / 1 = 11100.

Therefore, the line with a constant of proportionality of 111 is Line A.

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Answer:

The length of side AB is 5 units

Step-by-step explanation:

* Lets revise how to find the distance between two points

- If there are two points their coordinates are (x1 , y1) and (x2 , y2),

 then we can find the distance between them by this rule:

 d = √[(x2 - x1)² + (y2 - y1)²]

- Now lets solve the problem

∵ A = (4 , -5)

∵ B = (7 , -9)

- To find the length of AB use the rule of the distance above

- Let point A is (x1 , y1) and point B is (x2 , y2)

∵ x1 = 4 and x2 = 7

∵ y1 = -5 and y2 = -9

∴ AB = √[(7 - 4)² + (-9 - -5)²]

∴ AB = √[(3)² + (-4)²]

∴ AB = √[9 + 16] = √25 = 5

* The length of side AB is 5 units

Answer:

D

Step-by-step explanation:

Supplementary angles sum to 180°

Subtract the given angle from 180 for the supplement, that is

180° - 89° = 91° ← the supplementary angle

Final answer:

The supplement of an 89° angle is found by subtracting it from 180°, giving us 91°. Therefore, the correct answer is 91°, which is option D.

Explanation:

To find the supplement of an angle, we need to know that supplementary angles add up to 180 degrees. Given an angle that measures 89°, we can find its supplement by subtracting the given angle from 180°.

So, 180° - 89° = 91°.

The supplement of an angle that measures 89° is 91°, which corresponds to option D.

Answer:

Add 8 to both sides of the equation

Step-by-step explanation:

We have been given the quadratic equation;

x^2 - 14x +41 = 0

we are required to complete the square in order to express it in the form;

(x - p)^2 = q

In order to do this we need to find a constant c, such that;

[tex]c=(\frac{b}{2})^{2}[/tex]

where b is the coefficient of x in the quadratic equation. In our case b = -14. Therefore,

[tex]c=(\frac{-14}{2})^{2}=49[/tex]

Therefore, for us to complete the square, the left hand side of the quadratic equation should be;

x^2 - 14x +49

Since we already have 41, we can simply add 8 to make it 49. Thus, the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers is to Add 8 to both sides of the equation

Separate the kite into two triangles.

The base of the triangles would be 6 ( half the width is given as 3, so the full width would be 3 x 2 = 6).

The height of the bottom triangle is given as 10.

The area of a triangle is 1/2 x base x height.

Bottom triangle = 1/2 x 10 x 6 = 30 square units.

For the top triangle you need to find the height using the Pythagorean theorem.

Height = √(5^2 - 3^2) = √(25-9) = √16 = 4

Now the area of the top triangle is 1/2 x 4 x 6 = 12 square units.

Total area = Bottom + top = 30 + 12 = 42 square units.

Step 1: Set the two equations equal to each other and solve for x.

3x -5 = 6x - 8

3x + (-5+5) = 6x -8 + 5

(3x - 6x) = (6x - 6x) - 3

-3x/-3  = -3/-3

x = 1

Step 2: To solve for y take one of the given equation of your choice (for the purpose of this explanation I will only do y = 3x - 5) and replace x with 1, then solve for y

y = 3(1) - 5

y = 3 - 5

y = -2

(1,-2)

Check:

-2 = 3(1) - 5 ---> - 2 = -2

-2 = 6(1) - 8 ---> -2 = -2

Hope this helped!

Answer:

x=1

and y= -2

Step-by-step explanation:

y=3x-5 y=6x-8

On equating the two equations:

3x-5= 6x-8

Taking terms of x on one side and constant terms on the other

6x-3x= 8-5

3x= 3

Dividing both sides by 3, we get

x=1

Now, putting value of x in y=3x-5, we get

y=3-5

 = -2

Hence, Solution is:

x=1 and y= -2

Answer:

C=175-35t

Step-by-step explanation:

Each week - $35

After the 1st week - has $140 left

So, at the beginning of the first week he has $140+$35=$175 on the card.

Now,

Initial amount of monay = $175

Spent each week= $35

Number of weeks = t

Spent in t weeks =$35t

The cash balance C on his card after t weeks =$175-$35t (left)

So, the equation is

[tex]C=175-35t[/tex]

The equation that represents the cash balance on Rodolpho's prepaid gas card after t weeks is Balance = 175 - 35t, where t is the number of weeks.

The equation that represents the cash balance on Rodolpho's prepaid gas card after t weeks can be derived from the information given. We know that every week, he spends $35 on gas, which decreases the balance on his card by that amount. If he starts with $140 after the first week, we can establish the initial balance (before any purchase) as $175. Thus, the formula to calculate the remaining balance after t weeks would be:

Balance = Initial balance - (Weekly spending × Number of weeks)

Balance = 175 - (35 × t)

So, the equation that represents the balance on the card after t weeks is:

Balance = 175 - 35t

Answer:

Option "A" might be the correct option

Step-by-step explanation:

By the Angles of Intersecting Chords Theorem, When two chords intersect inside a circle, then the measure of the angle formed is one half the sum of chord's intercepted arcs.

In the diagram : -

⇒ ∠ 1 = 38°

Now, again by the diagram,

∠1 and ∠2 are linear pairs,

⇒ ∠1 + ∠2 = 180°

⇒ 38° + ∠2 = 180°

⇒ ∠2 = 142°

Answer:

38,142.

Step-by-step explanation:

The measure of angle 1 = the sum of the measure of the 2 arcs / 2

= (36 + 40) / 2

= 38 degrees.

Answer:

36 watts.

Step-by-step explanation:

Power is calculated from

W = E^2/R

E = 24 volts.

R = 16 ohms

W = 24^2 / 16

W = 576 / 16

W = 36 watts.

You are basically just working this problem backwards; the way you would find the zeros of the function.

Therefore, to start, make each equal to zero and do the opposite (+ or -) to each side.

-2=x and 2/3=x

0=x+2 and 0=x-2/3

In a function like this, we are usually given an equation like (x+#)(x+#) then we would set these to zero. However, since we are working backwards we are trying to get it in that (x+#)(x+#) form.

(x+2)(x-2/3)

2+2/3 = 2 2/3 or 2.667

2 x 2/3 = 4/3 or 1.334

Your quadratic function is now x^2+2.67x+1.334

or x^2+2 2/3x+4/3.

Hope I helped!

Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition

x = 2 when y = 2

k = yx = 2 × 2 = 4, hence

y = [tex]\frac{4}{x}[/tex] ← equation of variation

11 • 55 = 55

The starfish had 55 arms all together.

Hope this helps!

Answer:

I may not be completely sure but I am 85% confident the answer is B

Answer:

(9,-6)

Step-by-step explanation:

4x+3y=18

3x+4y=3

Multiply the first equation by 3

3(4x+3y)=18*3

12x+9y = 54

Multiply the second equation by -4

-4(3x+4y)=3*-4

-12x -16y = -12

Add these two new equations together to eliminate x

12x+9y = 54

-12x -16y = -12

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

    -7y = 42

Divide each side by -7

-7y/-7 = 42/-7

y = -6

Now we can find x

3x+4y =3

3x +4(-6) = 3

3x -24 =3

Add 24 to each side

3x-24+24 = 3+24

3x = 27

3x/3 = 27/3

x = 9

(9,-6)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x+3y=18&(1)\\3x+4y=3&(2)\end{array}\right\\\\(1)\\4x+3y=18\qquad\text{subtract}\ 4x\ \text{from both sides}\\3y=-4x+18\qquad\text{divide both sides by 3}\\y=-\dfrac{4}{3}x+6\qquad\text{substitute it in (2):}\\\\3x+4\left(-\dfrac{4}{3}x+6\right)=3\qquad\text{use the distributive property}\\\\3x+(4)\left(-\dfrac{4}{3}x\right)+(4)(6)=3\\\\3x-\dfrac{16}{3}x+24=3\qquad\text{multiply both sides by 3}\\\\9x-16x+72=9\qquad\text{subtract 72 from both sides}\\\\-7x=-63\qquad\text{divide both sides by (-7)}\\\\\boxed{x=9}[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-\dfrac{4}{3}(9)+6\\\\y=(-4)(3)+6\\\\y=-12+6\\\\\boxed{y=-6}[/tex]

[tex]\bf \begin{array}{llll} term&value\\ \cline{1-2} a_5&36\\ a_6&36\left( \frac{1}{3} \right)\\ a_7&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_8&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_9&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_{10}&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right) \end{array}[/tex]

[tex]\bf a_{10}=36\left( \frac{1}{3} \right)^5\implies a_{10}=36\cdot \cfrac{1^5}{3^5}\implies a_{10}=\cfrac{36}{243}\implies a_{10}=\cfrac{4}{27}[/tex]