What is the difference between a Rate and a Ratio? Explain

Answer:

The speed of plane = 40 m/s

The speed of the wind = 300 m/s

Step-by-step explanation:

Let the speed of the plane = Y

And the speed of the wind = X

If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,

X + Y = 340 ..... ( 1 )

Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,

X - Y = 260 ..... ( 2 )

Solve the two equations simultaneously by addition. That will eliminate Y

X + Y = 340

X - Y = 260

2X = 600

X = 600/2

X = 300 m/s

Substitutes X in equation (1)

300 + Y = 340

Make Y the subject of formula by collecting the like terms

Y = 340 - 300

Y = 40 m/s

Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.

Answer:

Step-by-step explanation:

Given that f(x) = 3x + 21

Plug in 3 for x

F(3)= 3(3) +21

F(3) = 9+21

f(3) = 30

Plug in 7 for x

F(7)= 3(7) +21

F(7) = 21+21

f(7) = 42

Answer:

irrational

Step-by-step explanation:

If a square root is not a perfect square, then it is considered an irrational number.

The square root of the number 34 is not a rational number

From the question, we have the following parameters that can be used in our computation:

The square root of the number 34

When evaluated, we have

The square root of the number 34 = √34

So, we have

The square root of the number 34 = 5.83.....

The above number cannot be represented by the quotient of 2 integers

Using the above as a guide, we have the following:

We can conclude that the number is an irrational number

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Answer:

9 cm

Step-by-step explanation:

Pythagorean's Theorem: a^2+b^2=c^2

x^2+6^2=117 (the square root of 117, squared)

X^2+36=117

x^2=117-36

x^2=81

x=9

Answer:

x = 9 cm

Step-by-step explanation:

Use the Pythagorean Theorem to find the length of the missing side.

a² + b² = c²

a² + (6)² = (√117)²

a² + 36 = 117

a² = 81

a = √81

a = 9

X is equal to 9 cm.

Hope this helps.

Answer:

25 houses on prince street

Step-by-step explanation:

add them up and bam

Answer:

25 houses

Step-by-step explanation:

You need to add up all the houses and u will get the ans..

Have a good day !!

Hope this helps..

Hello!

Answer:

12 cm, 12 cm, 10 cm.

Step-by-step explanation:

Given:

Perimeter, or P = 34 cm

Ratio of sides = 6 : 6 : 5

To find the length of each side, we can use a variable in the ratio to find the perimeter:

34 = 6x + 6x + 5x

Combine like terms:

34 = 17x

Solve for x:

34/17 = 17x/17; x = 2

Plug in this value of "x" into each expression for the side-lengths:

6(2) = 12 cm

6(2) = 12 cm

5(2) = 10 cm

Therefore, the lengths of each side of the triangle are 12 cm, 12 cm, 10 cm.

Hope this helped you! :)

Answer:

12, 12 and 10 cm.

Step-by-step explanation:

6 + 6 + 5 = 17

So one side = 6/17 * 34 = 12 cm

One other side is also 12 cm

The third side = 5/17 * 34 = 10 cm.

Answer:

8sqrt(2)

Step-by-step explanation:

An isosceles is a triangle with 2 45 degree angles and one 90 degree angle.

if the hypotenuse side=4sqrt(2) than that means the other 2 sides have to be just 4 units.

the formula for a triangle is than (base×height)÷2

4×4sqrt(2)=16sqrt(2)

(16sqrt(2))/2=8sqrt(2)

Answer:

19.595 units²

Step-by-step explanation:

Find length of other sides:

An isosceles triangle has 2 sides equal. It has two 45 degrees angles and one  90 degrees angle. We can use Pythagorean theorem.

[tex](4\sqrt{2} )^2 =a^2 +a^2[/tex]

[tex]32 =2a^2[/tex]

[tex]16=a^2[/tex]

[tex]4=a[/tex]

The 2 equal sides measure 4 units.

Find area:

base × height × 1/2

The height can be found by Pythagorean theorem.

height² = 4² + 4sqrt(2)²

height²  = 16 + 32

height² = 48

height = 6.928

base is given

4sqrt(2) × 6.928 × 1/2

= 19.595343

Answer:

  A) 2 m/s

Step-by-step explanation:

The ball increases from its thrown height of 3 meters to its maximum height of 7 meters in 2 seconds. That's an average rate of increase of ...

  (4 m)/(2 s) = 2 m/s

The average rate of change of height is 2 meters per second.

Answer:  2m/sec

Step-by-step explanation:  From the graph we see that the ball went from 3 meters to 7 meters, a difference of 4m.  It took 2 seconds to reach that height.

The average is found by dividing 4m/2sec

The result is 4m/sec

Answer:Área y perímetro de figuras compuestas

por Luz | Dic 5, 2014 | Geometría, Matematicas | 39 Comentarios

Obtener el área o perímetro es de las habilidades más fáciles y básicas en geometría. Sin embargo, al momento de combinar varias figuras planas se forma figuras compuestas, que pueden incluir: cuadrados, círculos, triángulos, rectángulos, trapecio, etc.

Answer: D

Step-by-step explanation:

There’s a trapezoid a rectangle and two squares at the bottom

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

[tex]\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm[/tex]

The volume of the frustrum is given by:

[tex]V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3[/tex]

Answer:

the answer is C

Step-by-step explanation

I am guessing you mean (x-y)^4 and this expanded is [tex]x^4+4x^3y+6x^2y^2+4xy^3+y^4\\[/tex] and the first three coefficients are 1,4,6

The required first three coefficients of the expression (x - y)⁴ is 1, -4, 6. Option b is correct.

Given that,
To determine the coefficients of the first three terms in the expansion of (x – y)⁴.

The coefficient is defined as the number present former to any variable is called a coefficient.

Here,
[tex]\left(x-y\right)^4=\quad x^4-4x^3y+6x^2y^2-4xy^3+y^4[/tex]
First three coefficients from the above equation,
= 1, -4 and 6

Thus, the required first three coefficients of the expression (x - y)⁴ is 1, -4, 6. Option b is correct.

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Answer:

x = ---------- = 1

Step-by-step explanation:

The formula for the axis of symmetry is x = -b/(2a).  In this case b = -4 and a = 2, and so the axis of symmetry is

        -(-4)

x = ---------- = 1

       2(2)

Answer:

x=1

Step-by-step explanation:

because I said so

Answer:

1)

[tex]\text{ Slope = -3}[/tex]

2)

[tex]y+4=-\frac{7}{8}(x-7)[/tex]

3)

[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

[tex]m=\frac{3-(-4)}{-1-7}[/tex]

Subtract. So, our slope is:

[tex]m=\frac{7}{-8}=-7/8[/tex]

2)

Now, let's use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

[tex]y-(-4)=-\frac{7}{8}(x-7)[/tex]

Simplify. So, our point-slope equation is:

[tex]y+4=-\frac{7}{8}(x-7)[/tex]

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

[tex]y+4=-\frac{7}{8}x+\frac{49}{8}[/tex]

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

[tex]y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}[/tex]

Subtract. So, our slope-intercept equation is:

[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]

And we're done!

Answer: Shown Below

Step-by-step explanation:

1. -7/8

2. y+4= (-7/8)(x-7)

3. y=(-7/8)x+ (17/8)

Just did it

Answer:

x ≈ 15.59

Step-by-step explanation:

We need to use the Pythagorean Theorem to solve for x. The equation for that is a^2 + b^2 = c^2. Side a is 9. Side b is x. Side c is 18 and 18 is also the hypotenuse. Let's solve for x(side b):

a^2 + b^2 = c^2

9^2 + x^2 = 18^2

81 + x^2 = 324

Subtract 81 from both sides to get x^2 alone on one side.

x^2 = 243

Square root both sides to isolate x.

x = 9sqrt3)

x ≈ 15.59

Answer:

7/8 of the game is left. The game lasts for 592 minutes.

Step-by-step explanation:

It is halfway through the first quarter so it is 1/8. So that's 7/8 part of the game left. if 74 minutes of playing time has past, then you do 74*8 so that's 592 minutes.

Answer:

4) 1/8

3)74x8=592

6)592-74= 518

Step-by-step explanation:

Step-by-step explanation:

[tex]diameter \: = \sqrt{ { 24}^{2} + {7}^{2} } = 25 [/tex]

[tex]shaded \: area \: = circle - tringle[/tex]

[tex]shaded \: area = ( \frac{\pi}{4} \times {25}^{2} ) - ( \frac{1}{2} \times 7 \times 24)[/tex]

[tex]shaded \: area \: = (490.6) - (84) = 406.6 \: = 407 \: {cm}^{2} [/tex]

Answer:

Ok so im in 7thgrade so ima try to help answer is x= 8x9

Answer:

rational (I think

Step-by-step explanation:

Answer: 32/345 wall per gallon

Step-by-step explanation:

Rate is defined as ratio between two quantities with different units.

Gallons of paint used by Martin = 8 5/8 gallons = 69/8 gallons

Portion of wall Martin wishes to pint = 4/5 wall

Rate at which Martin paints the wall:

= Portion of wall covered / paint used

=

4/5 / 69/8 = 32/345 wall per gallon

Answer:

Martin paints 0.093 walls per gallon of paint

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of paint used by Martin = 8 5/8 of a gallon

Ratio of wall painted by Martin with 8 5/8 of a gallon = 4/5

2. What is the unit rate at which Martin paints in walls per gallon?

Let's convert the mixed fractions to decimals this way:

8 5/8 = 8 + 0.625 = 8.625

4/5 = 0.8

Now, let's use the Direct Rule of Three, this way:

Gallons                      Walls

8.625                          0.8

x                                   1

Solving for x :

0.8x = 8.625 * 1

x = 8.625/0.8

x = 10.78125

x = 10.8 (rounding to next tenth) gallons

For painting a wall, we will use 10.8 gallons of paint. Now, we can calculate the unit rate at which Martin paints in walls per gallon, this way:

Gallons                      Walls

10.8                               1

 1                                  x

Solving for x :

10.8x = 1

x = 1/10.8

x = 0.09259

x = 0.093 (rounding to the next hundredth) walls per gallon of paint

Answer:

80$

Step-by-step explanation:

total amount of needed=200

Total =Tef +Angelina+Jason

200=90+30+Angelina

Angelina=200-120

Angelina=80$

Answer:

.06x

Step-by-step explanation:

So 20 percent of x has to first be represented. So would do .2x. So then we have to find 30% of that number. So we multiply .2x*.3 and we get 0.06x.

I believe this is correct but tell me if I'm wrong

Answer:

0.06x

Step-by-step explanation:

.2x*.3=0.06x

Answer: 240

Step-by-step explanation:

5/6x=200

(6/5)5/6x=200(6/5)

1x=40(6/1)

x=40(6)

x=240

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]

Multiply both sides by r :

[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]

Subtract the latter sum from the first, which eliminates all but the first and last terms:

[tex]S_n-rS_n=a-ar^n[/tex]

Solve for [tex]S_n[/tex]:

[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]

Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with

[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

Answer:

22-26: frequency = 3

27-31: frequency = 4

32-36: frequency = 5

37-41: frequency = 3

42-46: frequency = 4

100 total numbers.

20 Numbers divisiblae by 5: 5, 10, 15, 20, 25, 30, 35,40,45,50,55,60,65,70,75,80,85,90,95,100

Probability = 20/100 = 2/10

Answer:

1/5

Step-by-step explanation:

There are total 100 numbers.

Numbers divisible by 5 through 1-100 are:

5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

There are 20 numbers that are divisible by 5.

20/100 = 1/5

Answer:

A

Step-by-step explanation:

Answer:

Option 4

Step-by-step explanation:

=> [tex]\frac{4}{5} x^{-9}y^6z^8[/tex]

If there is any variable having a negative exponent, we should move it to its opposite side (Denominator to numerator and vice versa) So that it's exponent become positive.

=> [tex]\frac{4y^6z^8}{5x^9}[/tex]

Answer: D) [tex]\frac{4y^6z^8}{5x^9}[/tex]

Step-by-step explanation:

(4/5)x^-9y^6z^8 = [tex]\frac{4x^{-9}y^6z^8}{5}[/tex]

Any negative exponent can be taken to the other side of the fraction to be positive.  Thus,

[tex]\frac{4x^{-9}y^6z^8}{5}[/tex] = [tex]\frac{4y^6z^8}{5x^9}[/tex]

Hope it helps <3

Answer:

Step-by-step explanation:I think the answer is 12?