The width of a rectangle is 2/3 its length. The perimeter of the rectangle is 400 ft. What is the length, in feet, of the rectangle?

Step-by-step explanation:

the positive integer numbers that are divisible by 7 are an arithmetic sequence by always adding 7 :

a1 = 7

a2 = a1 + 7 = 7+7 = 14

a3 = a2 + 7 = a1 + 7 + 7 = 7 + 2×7 = 21

...

an = a1 + (n-1)×7 = 7 + (n-1)×7 = n×7

the sum of an arithmetic sequence is

n/2 × (2a1 + (n - 1)×d)

with a1 being the first term (in our case 7).

d being the common difference from term to term (in our case 7).

how many terms (what is n) do we need to add ?

we need to find n, where the sequence reaches 200.

200 = n×7

n = 200/7 = 28.57142857...

so, with n = 29 we would get a number higher than 200.

so, n=28 gives us the last number divisible by 7 that is smaller than 200 (28×7 = 196).

the sum of all positive integers below 200 that are divisible by 7 is then

28/2 × (2×7 + 27×7) = 14 × 29×7 = 2,842

[tex]5(4x - 4) = 5(3x + 3) \\ \cancel5(4x - 4) = \cancel5(3x + 3) \\ (4x - 4) = (3x + 3) \\ 4x - 3x = 4 + 3 \\ x = 7[/tex]

Put the value of X in equation:-

LHS:-

[tex]5(4x - 4) = 5(4(7) - 4) \\ 5(28 - 4) \\ 5(24) = 120[/tex]

RHS:-

[tex]5(3x + 3) = 5(3(7) + 3) \\ 5(21 + 3) \\ 5(24) = 120[/tex]

LHS= RHS

Hence proved

Answer:

x = 7

Step-by-step explanation:

Divide by 5 on each side :

Add 4 on each side :

Subtract 3x from each side :

Answer:

63 quizzes= 7 weeks

90 quizzes= x weeks

63x = (7)(90)

x= (7)(90)/63

x= 10 weeks

Answer:

[tex]\frac{6}{k-6}[/tex]

Step-by-step explanation:

First, we can factor all of the following equations to turn that weird, huge looking thing into [tex]\frac{(k+6)(k-6)}{(k-6)(k-10)}[/tex] ÷ [tex]\frac{(k-6)^2}{k(k-6)}[/tex] × [tex]\frac{6(k-10)}{k(k + 6)}[/tex]. We know that division is simply multiplication by the reciprocal, so that whole equation will turn into [tex]\frac{(k+6)(k-6)}{(k-6)(k-10)}[/tex] × [tex]\frac{k(k-6)}{(k-6)^2}[/tex] × [tex]\frac{6(k-10)}{k(k+6)}[/tex]. Now we can cancel out some values if they are both in the numerator and denominator, which will turn that still huge looking thing into [tex]\frac{6}{k-6}[/tex] which is our final answer, as it cannot be simplified further.

Hope this helped! :)

Answer:

Step-by-step explanation:

Answer: m<AOB is 60 degrees.

Step-by-step explanation: If BCD is 30 degrees, it intercepts the arc BA, and therefore, any angle that intercepts an arc is half of the arc it intercepts. Thus, AOB is 60 degrees.

Answer:The answer iis 1810.3cm^2

Step-by-step explanation:

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{12 \: cm}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 12 cm. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(12 \: cm)^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(144 \: cm^2)[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(452.16 \: cm^2)[/tex]

[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 1809 \: cm^2}[/tex]

Therefore :-

[tex]\\[/tex]

Learn more about the surface area of the sphere at https://brainly.com/question/28988747

Have a great day! <33

Answer:

The probability of a certain event is 1 or 100%

The probability of an impossible event is 0 or 0%

Answer:

See below ~

Step-by-step explanation:

Answer:

The volume of the cylinder is equal to 70.65 cm³.

General Formulas and Concepts:
Geometry

Volume Formula [Cylinder]: V = πr²h

Step-by-step explanation:

Step 1: Define

Identify given variables from diagram.

r = 3 cm

h = 2.5 cm

Step 2: Find Volume

∴ we found the volume of the cylinder to be 70.65 cm³.

---

Topic: Geometry

Answer:

Step-by-step explanation:

AB = altitude = 2.7 miles

BC =  8.3 miles

[tex]\sf tan \ \theta = \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \theta}\\\\Tan \ \theta = \dfrac{AB}{BC}=\dfrac{2.7}{8.3}\\\\Tan \ \theta = 0.33\\\\\theta = tan^{-1} \ 0.33[/tex]

[tex]\boxed{\theta = 18.3}[/tex]

Answer:

x > 9

The graph is a half-plane. (All the points with their abscissa (their value on the x-axis) greater than 9

Step-by-step explanation:

6 +x > 15

x > 15 - 6

x > 9

Answer:

X>9

Step-by-step explanation:

the other guy has the graph

Answer:

last option (x-2)(x+1)/3

Step-by-step explanation:

(x^2-4)/(x-7) ÷ (3x+6)/(x^2-6x+7)

(x^2-4)/(x-7) * (x^2-6x+7)/(3x+6)

(x+2)(x-2)/(x-7) * (x-7)(x+1)/3(x+2)

(x-2)/1 * (x+1)/3

(x-2)(x+1)/3

The composition of the function and its inverse function is always one. Then the correct option is C.

Suppose that the given function will be

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is a reverse operator, that takes back the effect of 'f'

Suppose that f and g are functions that are inverse of each other.

When f is composed of g or vice versa. Then the composition will be

We know that the composition of the function and its inverse function is always one. Then we get

When f is composed of g or vice versa. Then the composition will be 1.

Thus, the correct option is C.

Learn more about inverse function here:

https://brainly.com/question/19425567

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Answer:

maybe option 2 is the correct answer

Answer:

1 and 3/8 or C

Step-by-step explanation:

the longer pencil is 5 and 2/8 and the length of the shorter pencil is 3 and 7/8

5 2/8 - 3 7/8= 11/8 or 1 and 3/8

I hope this helps!!!

Answer:

▪︎ Domain: all real numbers (x can be any number)

▪︎ Range: y <= 0 (y can never become greater than 0 bc the vertex of this function (highest point) is (0,0))

Answer:

vertex = (4, - 37 )

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 2x² - 16x - 5 ← factor 2 out of the first 2 terms

    = 2(x² - 8x) - 5

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

f(x) = 2(x² + 2(- 4)x + 16 - 16) - 5

    = 2(x - 4)² - 32 - 5

   = 2(x - 4)² - 37 ← in vertex form

with vertex = (4, - 37 )

Answer:

10.533

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

0.04

Step-by-step explanation:

The sensors made by Breaker's have a 4% defect rate

Answer:

I'd say 11 but could also be 30

You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.

Answer:

 Transitive Property of Equality

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the value of x if the perimeter is 20

20 = X + 4X - 6 + X + 8

20 + 6 - 8 = 6X

18 = 6X

x = 18 : 6

x = 3

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

check

20 = 3 + 3 * 4 - 6 + 3 + 8

20 = 20

the answer is good

Answer:

Value of x is 3

Step-by-step explanation:

Given perimeter of figure = 20

x + (x+8) + (4x-6) = 20

x + x + 8 + 4x - 6 = 20

6x + 2 = 20

6x = 20 - 2

6x = 18

x = 18 / 6

x = 3

Answer:

y=-1/3x

Step-by-step explanation:

if it’s going down by one there should be one on top on since it’s going over by 3 it should be 3 on the bottom

Answer:

c. 22

Step-by-step explanation:

Let x = Tata's age and y = Kaka's age.

x - 10 = y

x+3 + y+3 = 40

Now, we can substitute in x - 10 for y.

x + 3 + (x - 10) + 3 = 40

so 2x = 44

x = 22

Therefore, Tata's current age is 22.

1) 7 = 7.0

2) 23 = 23.0

3) 1.562 = 1.6

Answer:

1) round off 7 to the nearest 10 is 10

2) round off 23 to the nearest 10 is 20

3)round off 1.562 to the nearest 10 is1.6

step by step explanation :

any whole number that is 5 and more can be rounded off to 10 e.g 5, 6 ,7 but numbers that are less than 5 can't be rounded off to 10 so it's becomes 0 e.g 4,2,3

example : round off 12 to the nearest ten

the answer is 10

Answer:

2x to the 4th power

Step-by-step explanation:

Hope this helps

Answer:

153.86 in²

Step-by-step explanation:

The area of a circle is:

A = π r²

Radius is just half of the diameter so r = 7.

Substitute 3.14 for π.

Restate the equation:

A = 3.14 x 7² = 3.14 x 49

A = 153.86

Based on the height of the pyramid and the dimensions of the square base, the space that Maria has inside the pop-up net is 1,280 in³.

This can be found as the volume of a pyramid which is:

= (Length x Width x Height) / 3

Solving gives:

= (16 x 16 x 15) / 3

= 3,840 / 3

= 1,280 in³

Find out more on the volume of a pyramid at https://brainly.com/question/3722054.

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65.6

First find the hypotenuse:

(hyp)²=(opp)²+(adj)² theo. of pyth.

(hyp)²=(11)²+(5)² subt.

(hyp)²=121+25 calc.

√(hyp)²=√146

hyp=12.08cm

sinx = 11/12.08

x=sin-¹(11/12.08)

x=65.6°

=========================================================

Explanation:

There are 3 red out of 9 total

The probability of picking red at random is 3/9 = 1/3

If the first marble is not put back, then the chances of picking red again are now 2/8 = 1/4

Notice how I subtracted 1 from the numerator and denominator of 3/9 to get to 2/8. This is because the red count and the total count both go down by 1 each.

Now multiply the fractions mentioned:

(3/9)*(2/8) = (1/3)*(1/4) = (1*1)/(3*4) = 1/12

If you did this trial 12 times, then you should expect to get two reds about once. That's one way to interpret the probability of 1/12.

Side note: 1/12 = 0.0833 = 8.33% approximately