Solving proportions-what’s 3 over 7 and 12 over 21? do the ratios from a proportion

Answer:

5^9 or 1,953,125

Step-by-step explanation:

5^22 / 5^13

Using the law of exponents we have 5^22-13 = 5^9

Answer:

Step-by-step explanation:

coffee=c

cakes=d

c+2d=8

2c+3d=14

c=8-2d

2(8-2d)+3d=14

16-4d+3d=14

-d=-2

d=2

c+4=8

c=4

coffee=4 dollars each

cakes=2 dollars each

The price of coffee is $4 and price of slice of cake is $2.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

One coffee and two slices of cake cost 8 dollars in total.

Two coffees and 3 slices of cake cost 14 dollars in total.

let the price of coffees sold be x

let the price of slices of cake sold be y

Then, the system of equations are

x+ 2y = 8

2x+ 3y = 14

On solving

2(8- 2y)+ 3y= 14

16 - 4y + 3y= 14

-y= -2

y= 2

and, x = 8- 2(2)= 8- 4= 4

Hence,  price of coffee is $4 and price of slice of cake is $2.

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The solution to the given linear function at f(1) when calculated gives an output value of; 8

We are given the linear function represented by the equation;

f(x) = 7(x - 1) + 8

Now, to find f(1) simply means we substitute 1 for x in the given expression to obtain;

f(1) = 7(1 - 1) + 8

f(1) = 8

Thus, the solution is; f(1) = 8

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Answer:

0.75

Step-by-step explanation:

hope this helps you

Step-by-step explanation:

step 1. The first equation 4x - y = 5 has a slope of 4. The 2nd equation simply cannot have the same slope for there to be 1 solution.

step 2. -y = 4x + 5. This has a slope of -4 so "yes" it could work.

step 3. y = 4x - 5. "no".

step 4. 2y = 8x - 10. The slope is 8/2 = 4. "no".

step 5. -2y = 8x - 10. The slope is 8/-2 = -4. "yes".

Answer:

5.62 - 0.32= 5.3 or 5.30

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

We are given that

Angle ,[tex]\theta=\frac{\pi}{2}[/tex]radian

Length of an arc=[tex]\pi[/tex]

We have to find the radius of circle in simples form.

We know that

[tex]\theta=\frac{l}{r}[/tex]

Where l=Length of arc

r=Radius of circle

Using the formula

[tex]\frac{\pi}{2}=\frac{\pi}{r}[/tex]

[tex]r=\frac{2\times \pi}{\pi}[/tex]

[tex]r=2[/tex]units

Hence, the radius of the circle=2 units

Answer:

3 3/5 meters (B)

Step-by-step explanation:

Since this is perimeter, you must find the "outside".

The top side: 1/4 * 4 = 1

Left side: 1/5 * 4 = 4/5

Bottom: 1

Right side: 4/5

Add them up!

1 + 1 + 4/5 + 4/5

2 8/5

3 3/5

B!

Answer:

4y=48

y=48/4

y=12

therefore,the value of y is 12

Answer:

180

Step-by-step explanation:

36, 72, 108, 144, 180

90, 180

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Answer:

$285

Step-by-step explanation:

57 by 4 is 228 then add 57 to 228 which is 285

Sorry this took a while; calculated a lot of things.

Step-by-step explanation:

A.

Combined:

2.67 times 23.76 = 63.4392

2.67 times - 21 and 5/6 = -58.295

63.4392 - 31.85 -58.295 = -26.7058

If you mean do both separate:

63.4392 - 31.85 = 31.5892

-58.295 - 31.85 = -90.145

B.

Combined:

11 and 3/4 times 23.76 = 279.18

11 and 3/4 times 21 and 5/6 = 256.541666667

279.18 + 256.541666667 + 56 and 3/8 = 592.096666667

If you mean do both separate:

279.18 + 56 and 3/8 = 335.555

256.541666667 + 56 and 3/8 = 312.916666667

Answer:

the submarine travels 26.8 km. from its base

Answer:

The answer is 19.1

Step-by-step explanation:

[tex]z = \sqrt{ {x}^{2} + {y}^{2} } = \sqrt{ {12}^{2} + {14.8}^{2} } = 19.1[/tex]

Answer:

d

Step-by-step explanation:

Answer:

(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.

(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.

(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.

(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.

Step-by-step explanation:

The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is defined by the following formula:

[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, measured  in centimeters.

[tex]h[/tex] - Height, measured in centimeters.

From statement, we understand that volume of the cylinder is directly proportional to its height. That is:

[tex]V \propto h[/tex]

[tex]V = k\cdot h[/tex] (2)

Where [tex]k[/tex] is the proportionality constant, measured in square centimeters.

In addition, we eliminate this constant by constructing the following relationship:

[tex]\frac{V_{2}}{V_{1}} = \frac{h_{2}}{h_{1}}[/tex]

[tex]V_{2} = \frac{h_{2}}{h_{1}} \cdot V_{1}[/tex] (3)

Based on (3) and knowing that [tex]V_{1} = 48\pi[/tex], we calculate the volumes for each height ratio:

(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.

(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.

(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.

(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.

Answer:

1st is 1/4 and 2nd is 1/10

Answer:

It will be 1/4

Step-by-step explanation:

Hope this helped

Answer:

First, develop an equation for this scenario. The formula to find the perimeter of a quadrilateral is 2l+2w. Because the length is 4 less than twice the width, this would be translated to (2w-4). Plug this into the variable for the length to get 2(2w-4)+2w=40. Distribute the 2 to get 4w-8+2w=40. Add the like terms to get 6w-8=40. Add 8 to both sides and get 6w=48. Divide 6 to result with w=8.

Now that we know w, we can substitute 8 into the variable to solve for the length. 2l+2(8)=40. Multiply 8 and 2 to get 2l+16=40. Subtract 16 to both sides to get 2l=24. Divide 2 to both sides to result with l=12.

Length = 12 feet

Width = 8 feet

Answer:

Step-by-step explanation:

(-3 + 1)/(2 + 2)= -2/4= -1/2 is the slope

Answer:

merhaba ben yeni geledimde adın ne

Answer:

Step-by-step explanation:

Answer:

ST =6.9

SR =15.9

Step-by-step explanation:

A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.

Speed is the time rate at which an object is moving along a path,

Given that car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.

We have to check whether the statement is true or false.

To check, we can use the formula:

distance = rate x time

Substituting the given values, we get:

distance = 60 x 4.5 = 270 miles

Therefore, the statement is true.

Hence, A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.

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Answer:

x=2/5y+6/5

Step-by-step explanation

5x-2y=6

5x-2y+2y=6+2y

5x=2y+6

step 2

5x/5=2y+6/5

x=2/5y+6/5

Answer:

34 cm

Step-by-step explanation:

The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.

Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm

Then, T₃/T₁ = ar²/a = r²

r² = T₃/T₁

r² = 64 cm/121 cm

r = √64/121

r = 8/11

So, the height of our fifth bounce T₅ = ar⁵⁻¹

= ar⁴

= 121 cm × (8/11)⁴

= 121 × 4096/14641

= 4096/121 cm

= 33.9 cm

≅ 34 cm to the nearest cm

Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

[tex]a_n = a_1r^{n-1}[/tex]

[tex]64 = 121r^{2}[/tex]

[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]

[tex]r = \frac{8}{11}[/tex]

Hence:

[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]

The height of the fifth bounce is of [tex]a_5[/tex], hence:

[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]

The height of the fifth bounce is of 33.85 cm.

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The elevator of  John Hancock Center in Chicago travels at a faster rate.

For the equation represented by the height of the elevator of  John Hancock Center in Chicago given as y = 30x, the rate of change is 30 ft/s which is equivalent to 1800 per minute.

Since the express elevator in the Empire State Building in New York City travels nonstop from  the ground floor to the top floor at a rate of 1,400 feet per minute, hence the elevator of  John Hancock Center in Chicago travels at a faster rate.

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Answer:

8*29=232

Step-by-step explanation:

if you take 8*20 you get 160

if you take 8*9 you get 72

Add them and you get 232

Answer:

20.1 feet

Step-by-step explanation:

We solve the above question using the Pythagoras Theorem

The Pythagoras Theorem =

Opposite² + Adjacent ² = Hypotenuse²

From the above question,

Opposite side = Height of the wall = x

Adjacent side = Distance from the base of the building = 9 feet

Hypotenuse = Length of the ladder = 22 feet

Hence:

x² + 9² = 22²

x² = 22² - 9²

x = √22² - 9²

x = √403

x = 20.0748599 feet

Approximately = 20.1 feet

Therefore, the height of the wall = 20.1 feet