A classroom will be assembled so that the desks fit within an area that is 8 m by 12 m. The desks will be surrounded by a border that will be the same width on all sides of the rectangular room, to
allow for walking space. The area of the border will equal 20% of the area of the space that the desks
occupy. What is the width of the border, to the nearest hundredth of a meter?

Answer:

D. 22+(4×5)÷2

Step-by-step explanation:

Four 5 pound weight=(4×5)

Barbell weighed 22 pounds

={(4×5)+22}

Paulina lifted it with both arms

Both arms=2

{(4*5)+22}/2

It can be rewritten as

22+(4*5)÷2

Answer:

$5.96

Step-by-step explanation:

To find 12% of 49.65 you multiply 49.65*0.12 (decimal equivalent of 12%) = 5.958. Since it's money, you need to round to the nearest cent.

Answer:

So since the formula for perimeter is 2(w+h)

200 = 2(w+h)

that means that

100 = w+h

100 = 36+x

x=

64 UNITS

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

Given expression is, y = (x + 3)² + (x + 4)²

By solving this expression,

y = x² + 6x + 9 + x² + 8x + 16

y = 2x² + 14x + 25

y = (2x² + 14x) + 25

y = 2(x² + 7x) + 25

y = 2[x² + 2(3.5x) + (3.5)² - (3.5)²] + 25

y = 2[x² + 2(3.5x) + (3.5)²] - 2(3.5)² + 25

y = 2(x + 3.5)² - 24.5 + 25

y = 2(x + 3.5)² + 0.5

[tex]y=(x+\frac{7}{2})^2+\frac{1}{2}[/tex]

Therefore, Option (2) will be the vertex form.

Answer: The speed of the current is 3.5 km/h.

Step-by-step explanation:

When they move in the river, the speed of the canoe is:

Sc is the speed of the canoe and Sr is the speed of the current.

Sc + Sr (when they move in the same direction as the current)

Sc - Sr (when they move in the opposite direction as the current)

So we have that in one hour, they moved 2km and then they returned other 2km.

Now, using the relation:

Velocity*time = distance

we can write 1hour = T1 + T2 such that:

(Sc + Sr)*T1 = 2km

(Sc - Sr)*T2 = 2km

T1 + T2 = 1hour -------> T2 = 1h - T1

Sc = 6km/h.

So we can write this as two equations:

(6km/h + Sr)*T1 = 2km

(6km/h - Sr)*(1h - T1) = 2km.

Now, the first step will be isolate one of the variables in one equation, we can get:

T1 = 2km/(6km/h + Sr)

and replace it in the second equation:

(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.

Now we solve this for Sr, i will ignore the units, so it is easier to read the math.

(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2

(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)

6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0

-Sr^2 + 36 -12 -12 = 0

-Sr^2 + 12 = 0

Sr = √12 = 3.5km/h

(where we take the positive value of the square root)

The speed of the current is 3.5 km/h

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:

(6 - a)(t₁) = 2 km

t₁ = 2 / (6 - a)      (1)

(6 + a)(t₂) = 2 km

t₂ = 2 / (6 + a)   (2)

t₁ + t₂ = 1 hour

[2 / (6 - a)] + [2 / (6 + a)] = 1

12 + 2a + 12 - 2a = 36 - a²

a² - 12 = 0

a = 3.5 km/h

The speed of the current is 3.5 km/h

Find out more at: https://brainly.com/question/22610586

Answer:

100°

Step-by-step explanation:

From the image attached, line BC and line CD are tangents to circle A. Also, AB and AD are the radius of the circle. The tangent theorem states that the angle between a tangent and the radius is 90°. Therefore:

∠ABC and ∠ADC = 90°.

Given triangle ABC:

∠ABC + ∠BCA + ∠CAB = 180°

∠CAB = 180 - ∠ABC - ∠BCA = 180 - 90 - 40 = 50

∠CAB = 50°

From the two tangent theorem, tangents that meet at the same point have the same length. This means BC = CD, ∠ACD = ∠BCA, ∠CAB = ∠CAD.

arc BD = ∠CAB + ∠CAD = 50 + 50

arc BD = 100°

Answer:

D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expand first

-24+6x=14x

-6x on both sides

-24=8x

/x on both sides

X=-3

Answer: [tex]x=-3[/tex]

Step-by-step explanation:

You want to apply the distributive property. Or, you could just divide by 6 on both sides. Ill just apply the distributive property:

[tex]14x = -24 +6x[/tex]

Now subtract 6x from both sides to get:

[tex]8x = -24[/tex]

Divide both sides by 8 to get x = -3

Answer:

14 lines shape symmetry

Answer: Garden = 36 ft², Path = 64 ft²

Step-by-step explanation:

Path is 3 ft wide ON EACH SIDE of the garden

Garden + 2(Path) = 10 ft   --> Garden = 6 ft wide.

Since the garden is a square, Area = 6² = 36

Garden + 2(Path) = 10 ft

Since the Garden + Path form a square, Area = 10² = 100

Area of Garden + Area of Path = Total Area

         36             + Area of Path =      100

                              Area of Path =      64

Answer:

b

Step-by-step explanation:

Answer:

B comet

Step-by-step explanation:

Orbit of a Comet. Comets go around the Sun in a highly elliptical orbit. They can spend hundreds and thousands of years out in the depths of the solar system before they return to Sun at their perihelion. Like all orbiting bodies, comets follow Kepler's Laws - the closer they are to the Sun, the faster they move.

Please BRAINLIEST!

Answer:

C

Step-by-step explanation:

x4(x4-5)+5(x4-5)

=x8-5x4+5x4-25

x8-25

Answer:

Step-by-step explanation:

The vertices (-2, -3) and (-2, 4) are on the same vertical line and are separated by 4 - (-3), or 7, units.  The vertices (-2, 4) and (5, 4) are on the same horizontal line (y = 4) and separated horizontally by 5 - (-2), or 7, units.  If you can picture this in your mind, you'll see a 45-45-90 isosceles triangle with leg lengths 7 (there are two such legs).

The next thing to do is to calculate the length of the hypotenuse of this triangle.  Using the Pythagorean Theorem, we get:

d = √(7² + 7²) = 7√2 ft.

The perimeter of this triangle is thus 7 ft by 7 ft by 7√2 ft, or approximately 23.9 feet, or 7.97 yd

and ...

The area of the triangular shape is A = (1/2)(base)(height), which here is

A = (1/2)(7)(7) = 49/2 ft^2, or 16.4 yd^2

Answer:

First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

First system: 3x-2y=3; 6x-4y=1

From the first equation: y = (3x - 3)/2

Using this value of y in the second equation:

6x - 6x + 6 = 1

6 = 1 -> System has no solution

Second system: 3x-5y=8; 5x-3y=2

From the first equation: x = (8 + 5y)/3

Using this value of x in the second equation:

5*(8 + 5y) - 9y = 6

40 + 25y - 9y = 6

16y = -34 -> y = -2.125

x = (8 - 5*2.125)/3 = -0.875

This system has one solution

Third system: 3x-2y=8; 4x-3y=1

 From the first equation: x = (8 + 2y)/3

Using this value of x in the second equation:

4*(8 + 2y) - 9y = 3

32 + 8y - 9y = 6

y = 26

x = (8 + 2*26)/3 = 20

This system has one solution

Fourth system: 3x-6y=3; 2x-4y=2

  From the first equation: x = 1 + 2y

Using this value of x in the second equation:

2*(1 + 2y) - 4y = 2

2 + 4y - 4y = 2

2 = 2

This system has infinite solutions

Fifth system: 3x-4y=2; 6x-8y=1

  From the first equation: x = (2 + 4y)/3

Using this value of x in the second equation:

2*(2 + 4y) - 8y = 1

4 + 8y - 8y = 2

4 = 2

This system has no solution

Answer:

4

Step-by-step explanation:

The 25ft by 20ft court needs to be covered.

First consider half of the court, meaning 25ft by 10ft.

To cover 25ft by 10ft you can easily place two 13ft by 10ft covers next to each other = 26 ft by 10ft

There is a 1ft overlap, but that seems reasonably acceptable.

If you do the same for the other half, then you will have covered the entire court from the rain.

So in total you need 4 plastic 13ft by 10ft covers, to cover the 25ft by 20ft cord from the rain.

This indicates that the officials will need at least 2 covers of 13ft by 10 ft to cover the court

Data;

Assuming the court is a rectangle from its given dimensions, we can proceed by dividing the dimension of the court by the dimension of the cover

[tex]25ft by 20 ft / 13ft by 10 ft = 2[/tex]

This would give us a value approximately 2.

This indicates that the officials will need at least 2 covers of 13ft by 10 ft to cover the court.

Learn more on area of a rectangle here;

https://brainly.com/question/25292087

Answer:

Step-by-step explanation:

Use the possibility diagram to calculate the probability that the product of the two numbers is

A prime number

Sample Space: 64

Prime Number:8

Probability: 8/64 = 1/8

Not a perfect square

Sample Space:64

Not a perfect square:56

Probability: 56/64 = 7/8

A multiple of 5  

Sample Space:64

A multiple of 5: 16

Probability: 16/64 = 1/4

Less than or equal to 21  

Sample Space:64

Less than or equal to 21:24

Probability: 24/64 = 6/16 = 3/8

Divisible by 4 or 6

Sample Space:64

Divisible by 4 or 6:32

Probability: 32/64 = 1/2

Answer:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume. There are also many other reasons listed below:

Possible reasons:

Please mark Brainliest if correct.

Sorry if it is not correct.

Answer:

Step-by-step explanation:

You didn't give your options, but it doesn't matter. We'll find all the possibilities and then you can pick it from your list.

When I teach this in Algebra 2, I call it the "the c over d thing" and all my students know EXACTLY to what I am referring. "c" is the constant and "d" is the leading coefficient. The combination of c/d give you the possibilities of roots for the polynomial. There are no real roots that a polynomial can have other than the possibilities we find when we do the c/d thing.

Our c is a 20.  All the factors of 20 are as follows (notice that we have both the positive and negative factors):

20: ±1, ±2, ±4, ±5, ±10, ±20

Our d is a 3.  All the factors of 3 are as follows (again, both the + and the -):

3: ±1, ±3 and that's it for 3.

c/d is as follows. Make sure you put ever c over every d!!!:

c/d: ±[tex]\frac{1}{1}[/tex], ±[tex]\frac{2}{1}[/tex], ±[tex]\frac{4}{1}[/tex], ±[tex]\frac{5}{1}[/tex], ±[tex]\frac{10}{1}[/tex], ±[tex]\frac{20}{1}[/tex], ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex], ±[tex]\frac{5}{3}[/tex], ±[tex]\frac{10}{3}[/tex], ±[tex]\frac{20}{3}[/tex]

Those are all the possibilities for your roots for that polynomial. As long as the roots are real (and they won't always all be real!), there are no roots but these.

Answer:

its D on edge

Step-by-step explanation:

Answer:

A

x= 3/x

Step-by-step explanation:

5kx + 6 = 7kx

collect like term

5kx - 7kx = -6

-2kx = -6

minus cancel out

=> 2kx = 6

divide bothside by 2k

=> x = 6/2k

=> x = 3/k

Answer:

Step-by-step explanation:

its A just trust :)

Answer:

Step-by-step explanation:

You can observe the figure in the image attached.

Notice that angle AOE is 90°, that is, it's a right angle. (The little red square indicates its perpendicularity).

Now, the adjacent and congruent angle to AOE is angle EOC, because they are on a straight angle, they are supplementary angles and also adjacent angles.

Answer:

a = 2

Step-by-step explanation:

We can use cross products to solve

8         a

----- = -------

28        7

8*7 = 28*a

Divide each side by 28

56/28 = 28a/28

2 =a

Answer:

2

Step-by-step explanation:

Given:  

    8         a

 ------- = ------   Find the value of a that makes this equation true.  

   28        7

  Cross multiplying, we get 28a  =  56, and so a works out to 2.

Check:  Does 8/28 = 2/7?  Yes.

Answer:

Step-by-step explanation:

We assume that the table represents the complete definitions of the functions of interest.

An x-intercept is a point where the y-value is 0. Only f(x) includes such a point: (-3, 0).

A y-intercept is a point where the x-value is 0. x=0 is not part of the domain of any of these functions, so there are no y-intercepts.

The maximum values of these functions are ...

so h(x) has the greatest maximum value.

The range of each function is the list of its table values. No two functions have the same range.

The domain of each function is the set of x-values for which it is defined. All of these functions have the same domain. That is, they are all defined for all of the x-values listed.

Of the descriptors offered, the two that apply are ...

Answer:

A and E

Step-by-step explanation:

Answer:

v = 7i + 2j

w= - 4i + j

10v = 10(7i + 2j) = 70i + 20j

3w= 3(- 4i + j) = -12i + 3j

10v + 3w

= 70i -12i + 20j +3j

= 58i + 23j

Hope this helps.

Answer:

its 65

Step-by-step explanation:

The measure of ∠JKL = 3 x 20 + 5 = 65 degrees.

We have three lines extending from point K such that one line extends to point J, another to point M, and the other to point L.

We have to determine the degree measure of ∠JKL .

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

According to the question, we have -

Measure of ∠JKL = 3x + 5

Measure of ∠JKM = 45 degrees

Measure of ∠MKL = x degrees

Refer to the image attached for more clarity. It can be seen from the image that -

∠JKL = ∠JKM + ∠MKL

3x + 5 = 45 + x

3x - x = 45 - 5

2x = 40

x = 20

Therefore, the measure of ∠JKL = 3 x 20 + 5 = 65 degrees.

To solve more questions on Angle measurements, visit the link below -

https://brainly.com/question/17107683

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Answer: 2x -5

Step-by-step explanation:

Hi, to answer this question we have to write equations with the information given:

John=x

We have to multiply by 2 the number of marbles that John has (x), and subtract 5.  

Max = 2x -5

Feel free to ask for more if needed or if you did not understand something.  

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

Answer:

The inverse of a function may not always be a function!

The original function must be a one-to-one function to guarantee that its inverse will also be a function.

Answer:

Step-by-step explanation:

A parallelogram is a quadrilateral with four sides.

Given parallelogram ABCD, to prove that opposite sides of the parallelogram are congruent.

Join D to B, the diagonal of the parallelogram which is also a traversal.

So that;

    <ABD = <BDC (alternate angle property)

    <BAC = <ACD (alternate angle property)

Also, diagonals;

      /AC/ = /BD/ (reflexive property)

Then;

      ΔABD = ΔCBD (Angle-Side-Angle, ASA, property)

Thus;

     /AB/ ≅ /CD/ (corresponding sides of congruent triangles are congruent)

    /BC/ ≅ /AD/  (corresponding sides of congruent triangles are congruent)

Therefore, the opposite sides of the parallelogram ABCD are congruent.

Answer:

x^2(x-4) + 3(x-4)

(x^2 + 3)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

First find all the sides of the triangle:

Total parts: 4+5+7 =  16

cm per part = 64/16 = 32/8  =4cm

therefore, all measures: 16cm, 20cm, 28cm.

Answer:

since you have not specified the height, I will use any no.

= 0.16

Step-by-step explanation:

perimeter is the distance round

add the ratios; 4+7+5=16

Ratio 16= Perimeter 64cm

R.16=64cm, find all the ratios

start with ratio 4

R.16=64cm

R.4×64cm÷16=16 cm

R.5×64÷16= 20 cm

R.7×64÷16=28 cm

A=1/2× b×h

1/2×16×20= A= 160cm2

2 dp, divide

0.16

Answer: no , the correct answer is 3x+2

Step-by-step explanation:

Remove parentheses.

x−1+2x+3

Collect like terms.

(x+2x)+(−1+3)

Simplify.

3x+2