How to find the volume of a rectangle

9514 1404 393

Answer:

  $2400

Step-by-step explanation:

The question is asking the amount invested in fund B. We can let 'b' represent that amount. Then the amount invested in fund A is (6000-b). The total profit from the investments is ...

  0.02(6000 -b) +0.07(b) = 0.04(6000)

  120 +0.05b = 240 . . . . . simplify

  0.05b = 120 . . . . . . . . . subtract 120

  b = 2400 . . . . . . . . . . .divide by 0.05

Alonzo invested $2400 in fund B.

9514 1404 393

Answer:

  (i) 55.59 km/h

  (ii) 3600 nautical miles ≈ 6670.8 km

  (iii) 30°N 29.3°E

Step-by-step explanation:

(i) The speed in km/h requires a units conversion.

  (30 kt/h)(1.853 km/kt) = 55.59 km/h

__

(ii) Here, we assume we're interested in the distance traveled. If the course is "due east", we presume that means it follows the 30° latitude line, so is not the shortest route between A and B. That is, the distance from A to B will be different from the distance traveled. (The shortest route from A to B is along a great circle.)

  distance = speed × time

  distance = (30 kt/h)(120 h) = 3600 nautical miles

  = (55.59 km/h)(120 h) = 6670.8 km

__

(iii) The radius of the 30° latitude line is ...

  (6370 km)(cos(30°)) = 3185√3 km ≈ 5516.58 km

The relationship between arc length (s) and central angle (α) is ...

  s = rα

So, the change in the vessel's longitude is ...

  α = (6670.8 km)/(5516.58 km) ≈ 1.20923 radians ≈ 69.28°

Then town B has longitude ...

  40°W -69.3° = -29.3°W = 29.3°E

The position of town B is about 30°N 29.3°E.

_____

Additional comment

The route supposedly taken by this sea vessel is from the middle of the North Atlantic to a town in northern Egypt, through the northern Sahara desert. The eastern end point is shown in the attachment.

Some spherical trigonometry is involved if you want to find the end point of the great-circle route of the same length.

Answer:

ITS 80,000,000

Answer: the slope of perpendicular lines are opposite and reciprocal.

First line slope is 3/2. The slope of the second line is - 2/3

First line slope is 2. The other line slope is -1/2

Step-by-step explanation:

Answer:

7.9000 × [tex]10^{-4}[/tex]

Step-by-step explanation:

0.0014 - 0.00061 = 0.00079

0.00079 in scientific notation = 7.9000×10^-4

Answer:

2 1/2 in.

Step-by-step explanation:

6 - 3 1/2 this is the answers

Answer:

Test Results indicate that a woman is not pregnant when she is.

Test Results indicate that a woman is pregnant when she is not

Answer:

168

plssss mark brainliestt

Step-by-step explanation:

28×27=756 in

756÷ 4.5=168

9514 1404 393

Answer:

  3p +24 +162/(p-6)

Step-by-step explanation:

The result of the division can be found using polynomial long division, or using synthetic division. The latter requires less writing and gives the same answer:

  [tex]\dfrac{3p^2+6p+18}{p-6}=3p+24+\dfrac{162}{p-6}[/tex]

Answer:

∠DAC is 35°

Step-by-step explanation:

Given:

Measure of ∠DAB = 64°

Measure of ∠CAB = 29°

Solution:

∠DAB shows the value of the overall angle.

∠CAB shows the value for almost half of the angle.

∠DAB - ∠CAB = ∠DAC

64° - 29° = ?

∴ 64° - 29° = 35°

Hence, the value of ∠DAC is 35°

Answer:

Step-by-step explanation:

Given,

Length of the rectangle = 12 meters = 1200 cm

Width of the rectangle = 400 cm

Therefore,

Perimeter of the rectangle = 2(l+w)

= 2(1200+400) cm

= 2 × 1600 cm

= 3200 cm (Ans)

Answer:

3200 cm

Step-by-step explanation:

12m = 12,000 cm so therefore the answer is 3200cm

Chau rode the scooter for 69 minutes.

Given that :

Initial fee paid = $8

Fee per minute = 6 cents = 6/100 = $0.06

Hence,

Total ride cost = $8 + (fee per minute × number of Minutes)

If total Cost of ride = $12.14

Let number of minutes = m

Hence, we have :

12.14 = 8 + 0.06m

12.14 - 8 = 0.06m

4.14 = 0.06m

m = 4.14 / 0.06

m = 69

Hence, he rode the scooter for 69 minutes

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Answer:

fhfgb

Step-by-step explanation:

ffhfdhdd

Here we want to make a system of equations and solve it for the smallest angle of a triangle.

We will find that the smallest angle is 5.625°

First, let's define the variables:

a₁ = smallest angle

a₂ = middle angle

a₃ = largest angle.

We know that the sum of all interior angles of a triangle is equal to 180°, then we can write:

a₁ + a₂ + a₃ = 180°

We also know that:

"the largest angle of a triangle is the sum of the other two angles"

This can be written as:

a₃ = a₁ + a₂

And we know that:

"The smallest angle is one 16th of the largest angle"

Then:

[tex]a_1 = \frac{a_3}{16}[/tex]

Writing together these 3 equations we get our system:

a₁ + a₂ + a₃ = 180°

a₃ = a₁ + a₂

[tex]a_1 = \frac{a_3}{16}[/tex]

Now we want to solve this for a₁

To do it we need to replace equations into other equations.

How do we do this?

Notice that in the third equation we have:

a₃ = a₁ + a₂

Then we can replace it in the first equation:

a₁ + a₂ + a₃ = 180°

(a₁ + a₂) + a₃ = 180°

a₃ + a₃ = 180°

2a₃ =  180°

a₃ =  180°/2 = 90°

a₃ = 90°

Now we can use the last equation:

[tex]a_1 = \frac{a_3}{16}[/tex]

To get the value of the smallest angle:

[tex]a_1 = \frac{90 \°}{16} = 5.625 \°[/tex]

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Answer:

Let x=Width

Length = 7x-22 (22m less the 7 times width)

A=L*w

A=(7x_22)x

7805=7x^2-22x

7x^2-22x-7805=0

(7x-223) (7x+223)=0

7x-223=0

7x=223

x=223%7

x=35

Now,

Length =7x-22

=7(35)-22

=223

therefore,length =223

If the area of the rectangle is 7805 square meters, The length of the rectangle will be 223 units

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that, A rectangle has a length of 22 meters less than 7 times its width. If the area of the rectangle is 7805 square meters,

Suppose the width of the rectangle is x.

Length = 7x-22 (22m less the 7 times width)

A=L*w

A=(7x_22)x

7805=7x²-22x

7x²-22x-7805=0

(7x-223) (7x+223)=0

7x-223=0

7x=223

x=223/7

x=35

As a result

Length =7x-22

=7(35)-22

=223 units.

Thus, if the area of the rectangle is 7805 square meters, The length of the rectangle will be 223 units

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Answer:

x = -7

Step-by-step explanation:

2x+2-x+5=0

x+2+5=0

x+7=0

x = -7

So the answer is -7

Given:

[tex]\to \bold{ (2x+2)-(x+5)=0}[/tex]

To find:

x=?

Solution:

[tex]\to \bold{ (2x+2)-(x+5)=0}\\\\\to \bold{ (2x+2-x-5)=0}\\\\\to \bold{ (x-3)=0}\\\\\to \bold{ x-3=0}\\\\\to \bold{ x=3}\\\\[/tex]

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Answer:

answers are:

7 and 14

The factors of 7 is:  1, 7

The factors of 14 is:  1, 2, 7, 14

28 and 7

Factors of 28:  1, 2, 4, 7, 14, 28

Facotrs of 7:  1, 7

Step-by-step explanation:

others:  

21, 3 is GCF is 3

The factors of 3 are: 1, 3

The factors of 21 are: 1, 3, 7, 21

7, 1 is GCF is 1

The factors of 1 are: 1

The factors of 7 are: 1, 7

9514 1404 393

Answer:

  n(B) = 4

Step-by-step explanation:

There are four (4) elements in set B.

  n(B) = 4

Answer:

The coefficient of x is 1.

Step-by-step explanation:

If the question had asked for the coefficient of x^2 then it would be 3.

The coefficient of a variable is the number that is attached to it (the big number, not the exponent).

Answer:

1/2

Step-by-step explanation:

1/3 + 1/6

Get a common denominator of 6

1/3 *2/2  + 1/6

2/6 + 1/6

3/6

Simplify the fraction

1/2

Answer:

[tex]yasmin \: = \frac{1}{3} \\ alex = \frac{1}{6} \\ yasmin \: = \frac{1}{3} \times \frac{2}{2} = \frac{2}{6} \\ they \: togather \: eat \: \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \\ c \: ic \: your \: answer \\ thank \: you[/tex]

Answer:

i dont really understand this question though but ill try. Ok so 50 times, to say this you would have to take a number then multiply that number by 50 and you would get your answer. but this is the only way i think you could say 50 is  times as much as.

Step-by-step explanation:

I hope this helped you in some way or form. :)

Answer:

B

Step-by-step explanation:

Recall that [tex]7^a\cdot 7^b = 7^{a+b}[/tex]

So now

[tex]7^{2/3} \cdot 7^{1/3}\\= 7^{\frac{2}{3}+\frac{1}{4}}\\=7^{\frac{8}{12}+\frac{3}{12}}\\=7^{11/12}[/tex]

The equivalent value of the expression is A = 7^ ( 11/12 )

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the first number be p = 7 ^ ( 2/3 )

Let the second number be q = 7 ^ ( 1/4 )

And , A = pq

On simplifying , we get

A = 7 ^ ( 2/3 ) . 7 ^ ( 1/4 )

From the laws of exponents , we get

mᵃ×mᵇ = mᵃ⁺ᵇ

So , A = 7 ^ ( 2/3 + 1/4 )

A = 7 ^ ( 11/12 )

Hence , the equation is 7^ ( 11/12 )

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The GCF of 10 and 6 is 2. May this will help you.

Hope it helps... Mark me brainliest

Answer:

x + y + z = 49

2.50x + 7y + 1.50z = 147

y + 7 = z

Step-by-step explanation:

Before you even start setting up the equations, create variables for information needed, but not given in the problem:

Variable x = number of tacos

Variable y = number of burritos

Variable z = number of sodas

The first piece of information we are given is the number of items so make this into an equation:

x + y + z = 49

Next we are told how much everything cost in total so make this into an equation:

2.50x + 7y + 1.50z = 147

Lastly, we are informed Rosa bought 7 more sodas than burritos so form an equation using this information:

y + 7 = z

Answer:

Step-by-step explanation:

g(f(x)) = g(x²) = x²- 3

f(g(x)) = f(x-3) = (x-3)² = x²+ 6x + 9

The composition of two functions will be ; f(g(x)) = x²+ 6x + 9 and g(f(x)) = x² - 3.

Two functions f(x) and g(x) are given in the question.

We have to find the composition of the two functions.

What is a function ?

The function is the description of how the inputs relate to the output. Each input has only one output.

As per the question ,

f(x) = x²

g(x) = x - 3

The composition of these two functions can be defined as ;

   g(f(x)) = g ( x² )  

⇒ g(f(x)) = x²- 3

and

   f(g(x)) = f(x-3)

   f(g(x)) = (x-3)²

⇒ f(g(x)) = x²+ 6x + 9

Thus , the composition of two functions will be ; f(g(x)) = x²+ 6x + 9 and g(f(x)) = x² - 3.

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Answer:

2400.036 or 4.875 × 10^5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

528/16=33

165/33=5

Answer:

[tex] log_{2}(x) \times \frac{1}{3} log_{2}(x) \\ \\ = log_{2}x + log_{2}(x) {}^{ \frac{1}{3} } \\ \\ { \boxed{ \boxed{= log_{2} \{x + ({x})^{ \frac{1}{3} } \}}}}[/tex]