The length of a rectangle is 5 yd longer than its width.
If the perimeter of the rectangle is 70 yd, find its length and width

The height of the building after using proportion is  110.5 ft.

What is proportion ?

The main conceptual underpinnings on which proportion is described are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers. For grasping the myriad concepts in science and mathematics, the ratio and proportion are crucial constructing elements. With the right amount of proportion, a variety of problems in daily life, such as those encountered in the kitchen or in business when processing transactions, can be resolved. It facilitates comparison by establishing a relationship between two or more quantities.

Here House height = 13ft

Shadow of the house height = 20 ft

Shadow of the building height = 170ft

Noe using proportion ,

=> [tex]\frac{House height}{shadow of the house} = \frac{building height}{shadow of the building}[/tex]

=> [tex]\frac{13}{20} = \frac{x}{170}[/tex]

=> x=[tex]\frac{13*170}{20}[/tex] =110.5 ft.

Hence the height of the building is 110.5 ft tall.

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The number of ways that a nine question true false quiz can be answered is; 512 ways

We are given;

Number of questions = 9

Options for each answer = 2 (True of false)

The power set is defined as the number of subsets of a set of n elements which is expressed as 2ⁿ

There are 2 ways to answer question 1 and as such it means that there are 2 ways to answer question 2.

For question 2; 2² = 4 ways

For question 3; 2³ = 8 ways

For question 4; 2⁴ = 16 ways

For question 5; 2⁵ = 32 ways

For question 6; 2⁶ = 64 ways

For question 7; 2⁷ = 128 ways

For question 8; 2⁸ = 256 ways

For question 9; 2⁹ = 512 ways

Thus we we conclude that, there are 512 ways to answer 9 true-false tests.

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The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV

we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for  quadrant 2 and 3). Since we know cos² a + sin² a = 1

for α, cos² α + sin² α = 1

=> cos² α = 1 - sin² α

=> cos² α = 1 - 4/25

=> cos α = √21/25

same for β, cos² β + sin² β = 1

=> sin² β = 1 -cos² β

=> sin² β = 1 -1/9

= 8/9

=2√2/3

substituting the known values in the above formula for cos (α+β)

=>cos α cos β - sin α sin β

=√21/25 *1/3- 2/5*2√2/3

=√21/25- 4√2/15

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Answer:

d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]

Step-by-step explanation:

The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!

Have a lovely day!

The set of values for Rents lesser than $700. So, rent 700 <y<0

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444 students will climb the rock wall.

Given, that A class has 484848 students, one group of 242424 students chooses to play volleyball.

Then the teacher divides the remaining students into as many groups of 555 as possible to shoot baskets.

After that, the remaining students (not on a volleyball or basketball team) climb the rock wall.

Now, we are asked that the students who climb the rock wall

So, from a class of 484848 students if One group of 242424 students is made to play volleyball then there will be 242424 students remaining.

Now, to divide 242424 students into groups of 555 students,

we need to divide 242424 by 555, then we get

242424/555 = 436.8

Now there will be 436 groups of 555 students who will shoot basket and remaining 444 students who will climb the rock wall.

Hence, 444 students will climb the rock wall.

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The value of x is 10.6 which is equivalent to 11.

In the given triangle

the triangle is divided into two triangles which are both right angled

However in the bigger triangle

we would use the Pythagoras Theorem

( y + 6 )² = x² + 100 ---------- equation 1

In the smaller triangle;

x² = y² + 64 --------------equation 2

Thus substituting the value of x in equation 1

Thus the equation becomes

( y + 6 )² = y² + 64 + 100

y² + 36 + 12x = y² + 164

Cancelling y² on both sides we will get

36 + 12x = 164

12x = 164 - 36

this implies 12 x = 128

x = [tex]\frac{128}{12}[/tex]

x = 10.6 ≈ 11

Thus the required value of x is 10.6 or 11

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Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

The least possible sum wen the integers, a and b, have a product of 20 is 9.

From the information given, two integers, a and b, have a product of 20. It should be noted that the values that an give a product of 20 will be:

1 × 20 = 20

2 × 10 = 20

4 × 5 = 20

Therefore, the sum of the factors will be:

1 + 20 = 21

2 + 10 = 12

4 + 5 = 9

The least possible sum is 9.

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Answer:

4 to 7 percent.

Step-by-step explanation:

We use the traditional oil-to-vinegar ratio: three parts oil to one part vinegar/acid, but this ratio can vary depending on your choice of vinegar/acid and personal taste. The less acidic the vinegar/acid, the less oil you need. It's all about balance!

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

∠ B + 72° + 36° = 180°

∠ B + 108° = 180° ( subtract 108° from both sides )

∠ B = 72°

Then

∠ B = ∠ C = 72°

this means the 2 base angles in Δ ABC are congruent , then the triangle is isosceles with the 2 legs being congruent , that is

AB = AC

The rate at which length of shadow of person changing is 3 ft /sec.

H = Height of streetlight; 16 ft

h = Height of man; 6 ft

x = Length of man's shadow.

s = Distance from streetlight to man.

Using the similarities of the triangles.

H/h = (s + x)/x

Hx = h(s + x)

Differentiate with respect to 't' on both sides.

H(dx/dt) = h(ds/dt + dx/dt)

Put the values.

16(dx/dt) = 6(5 + dx/dt)

16(dx/dt) = 30 + 5dx/dt

10dx/dt = 30

dx/dt = 3 ft /sec

Thus, the rate at which length of shadow of person changing is 3 ft /sec.

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Answer:

3/5

Step-by-step explanation:

Given problem,

→ (1/10) + (1/2)

Let's solve the problem,

→ (1/10) + (1/2)

→ (1/10) + (5/10)

→ 6/10

→ 3/5 {simplest form}

Thus, answer is 3/5.

a. Timothy is correct regarding the dilation, considering the vertices of each triangle.

b. The two triangles are similar, as they have congruent angle measures.

A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.

The effects of a dilation are given as follows:

The vertices of each triangle in this problem are given as follows:

The scale factor is obtained by the division of any of the equivalent factors, hence:

k = 4.5/3 = 1.5.

Confirming that Timothy's statement regarding the scale factor of the dilation is correct.

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The length of the rectangular area is 800 yards and width is 800 yards

The perimeter of the rectangular area = 3200 yards

The perimeter of the rectangle = 2 (l + w)

Then the equation will be

2(l + w) = 3200

l + w = 3200 / 2

l + w = 1600 yards

w = 1600 - l

The area of the rectangular area = l × w

= l(1600 - l)

Since the area is maximizing the the rate of change of area will be zero

l × w = 0

1600 - 2l = 0

2l = 1600

l = 1600/2

l = 800 yards

Then

w = 1600 - l

Substitute the value of l in the equation

w = 1600 - 800

w = 800 yards

Hence, the length of the rectangular area is 800 yards and width is 800 yards

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Answer:

Range:  [tex]\text{y} \ge 0[/tex]

Domain: [tex]\text{x} \ge 0[/tex]

Both involve "greater than or equal to 0".

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

Explanation:

The domain is the set of allowed inputs (x). The smallest input allowed in this case is x = 0, as it corresponds to the left-most point (0,0) on the blue graph. There is no largest x value since it stretches forever to the right.

Either x = 0 or x > 0 which condenses to [tex]\text{x} \ge 0[/tex] and this is the domain as an inequality.

--------

The range will have us look at the possible y values or possible outputs. We have y = 0 as the smallest output possible, which corresponds to the lowest point (0,0).

There is no largest y value since the blue graph goes forever upward.

Either y = 0 or y > 0 to give us the range of [tex]\text{y} \ge 0[/tex]

Answer:

I believe the answer is number 2, which is 20 degrees.

Step-by-step explanation:

When I plugged that number in for x for both of them I got the numbers 81 and 99. Added them together ad they made 180 degrees. Which makes them supplementary.

well, we know WXYZ is a kite, so is a quadrilateral, namely it has 4 sides, and it has two congruent angles, so

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 94+94+112+\measuredangle ZYW=360\implies \implies \measuredangle ZYW=60[/tex]

Check the picture below.

Answer:

32.2222

Step-by-step explanation:

Answer: 32.22 degrees Celsius.

Answer:

it is 18 mile

Step-by-step explanation:

12mile = 60 min

x = 90 min

we cris cross the equation and

we found x=18 mile

Answer:

Yes.

Step-by-step explanation:

To decide if these triangles are similar, we need to check 2 criteria. The first is that the angles are all the same as their corresponding angles on the other triangle, which is true. The second is to check if the sides are all in the same proportional relationship. To do this, we need to put 40/50, 40/50, and 16/20 to see if they simplify to the same fraction (which is the proportion.) 40/50 and 40/50 simplify to the same fraction, 4/5. 16/20 also simplifies to 4/5, so the sides are all in the same proportion, which means the shapes are similar.

The two trains will pass each other after 7 hours.

Both trains need to cover a distance of 525 miles before they cross each other.

We know, d = s × t

where d ⇒ total distance travelled

s ⇒ speed of the train

t ⇒ time taken for both trains to meet

For train A,

s = 30 miles per hour

Distance covered by train A in t hours = 30 × t

For train B,

s = 45 miles per hour

Distance covered by train B in t hours = 45 × t

As the total distance is 525 miles,

30t + 45t = 525

75t = 525

t = 7 hours

Hence, the trains will pass each other after 7 hours.

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The correct statement regarding the proportional relationship c = 0.8w is given as follows:

The equation c = 0.8w is correctly represented by the graph.

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:

y = kx.

In this problem, the equation is given as follows:

c = 0.8w.

In which:

For a input of 2, the output is given as follows:

c = 0.8 x 2 = 1.6.

Hence point (1,0.8) is in the graph, along with point (2,1.6).

The statements are given as follows:

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Answer:

3/2x

Step-by-step explanation:

The image of (-1,7) after a reflection over the line y = x is (7, -1).

What is a line of reflection?

When reflecting a figure in a line or a point, the image and preimage coincide. A reflection converts each point in a figure from a point to an image via a set line. The reflection line is the name given to the fixed line.

Here, we have

Image : (-1.7)

Now,

Reflect over the line y = x:

When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.

Thus, the point (-1,7) maps to the point (7,-1) when reflected over y=x.

Hence, The image of (-1,7) after a reflection over the line y = x is (7, -1).

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(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.

Domain of the tangent function be, R - {(2n+1)π/2}

Range of the tangent function be, R

Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.

So, the restricted domain be (-π/2 , π/2).

In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.

So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

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Answer:

3

Step-by-step explanation:

45*64=2880

48*60=2880

Answer:

x-intercept(s): (−5,0)

y-intercept(s): (0,−5)

Explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Im also in K12 so Ez Good Luck

Hope this helped!

Answer:

13

Step-by-step explanation:

-3-10, or 10+3 is equal to 13

Answer:

13

Step-by-step explanation:

-3+13=10

Answer:10.3

Step-by-step explanation:

16(5h-29)=360

80h-464=360

80h-464+464=360+464

80h/80=824/80

h=10.3

The answers are as follows -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given are the following relations -

3y = x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

We can write -

x = 3y

as

y = (1/3)x

m = 1/3

Relation 3y=x represents direct variation.

For the relation - {(2,6),(3,9),(5,15)}, we can write -

We can write it as -

y = 3x

Relation {(2,6),(3,9),(5,15)} represents direct variation.

For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.

Therefore -

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