expand the brackets and simplify the equasion
2(z-5)+6z

Answer:

(x - y) = 9

Step-by-step explanation:

**Note: we cannot use similar triangle proportionality, as ΔABC is NOT a right triangle**

Using Pythagoras' Theorem a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle)

Create equations for both smaller interior right triangles using Pythagoras' Theorem:

Larger right triangle

   CD² + x² = 17²

⇒ CD² = 17² - x²

Smaller right triangle

   CD² + y² = 10²

⇒ CD² = 10² - y²

Equate equations:

        CD² = CD²

⇒ 17² - x² = 10² - y²

Given:

AB = 21  and AB = x + y

⇒ x + y = 21

⇒ y = 21 - x

Substitute  y = 21 - x  into  17² - x² = 10² - y²  and solve for x:

⇒ 17² - x² = 10² - (21 - x)²

⇒ 17² - x² = 10² - (441 - 42x + x²)

⇒ 17² - x² = 10² - 441 + 42x - x²

⇒ 289 = 100 - 441 + 42x

⇒ 630 = 42x

⇒ x = 630 ÷ 42

⇒ x = 15

Substitute found value for x into  y = 21 - x and solve for y:

⇒ y = 21 - 15 = 6

Finally, substitute found values for x and y into (x - y):

⇒ x - y = 15 - 6 = 9

Answer:

Step-by-step explanation:

9 is 16.12

11 is 38.36

13 is 9

Answer:

The answer is A because the line is in -2 negative and positive 5

The count of 4-digit personal identification numbers possible if the number cannot contain a zero is given by: Option B: 6561

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex]  ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

For the given case, there are 4 digit locks, each of them can be from {1,2,3,4,5,6,7,8,9}

So each one has 9 options to choose from.

Thus, using the rule of product, we get the total possible personal identification numbers  as: [tex]9 \times 9 \times 9 \times 9= 6561[/tex]

Thus, the count of 4-digit personal identification numbers possible if the number cannot contain a zero is given by: Option B: 6561

Learn more about rule of product here:

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Answer:

I believe the answer is D.) three and three eighteenths

Explanation:

5 3/6 = 33/6

2 1/3 = 7/3 = 14/6

33/6 - 14/6 = 19/6 = 3 1/6 or 3 3/18

I hope I helped! ^-^

Answer:

15

Step-by-step explanation:

Sum of points divided by number of games

Answer:

b) 130

Step-by-step explanation:

The total of the internal angles of any simple hexagon (six sides)  is 720°.

720 = 150+95+105+145+95+x

720= 590 + x

720 - 590 = x

130 = x

Answer:

The other factor is 5x-2

Step-by-step explanation:

Using the factorisation method:

Two numbers that multiply to give -10 and add to give +3:

+5 and -2

[tex]5x^{2} +5x-2x-2[/tex]

[tex]5x(x+1) -2(x+1)[/tex]

[tex](x+1)(5x-2)[/tex]

So the other factor is 5x-2

I'm not sure about the second part of the question but I hope you understood how to deal with the first part.

Answer

74.40

Step-by-step explanation:

circumference= 2πr

so, 12×2×pi= 24π

24π= 75.39822369

=75.40

Answer: 72

Step-by-step explanation:

convert 68% to decimal:

0.68

Multiply by 225

0.68*225

= 153

Subtract:

225-153=
72

Answer:

area = 132 m²

perimeter = 62 m

Step-by-step explanation:

The easiest way to calculate the area of the shape is to work out the area of the entire rectangle, then subtract the area of the 2 small (white) square:

Area of a rectangle = width x length

⇒ area = 10 x 15 = 150 m²

Area of one square = 3 x 3 = 9

Total area = 150 - 9 - 9 = 132 m²

Perimeter = (2 x 10) + 15 + (9 x 3) = 62 m

Answer:

Step-by-step explanation:

Sum of interior angles of a triangle is 180 degrees

Add the angles up

2z-1+z+14+95 = 180

3z+108 = 180

3z = 72

z = 24

Z = 24

Answer:

(147 - 298)/298 x 100

-151/298  × 100

Change ≈ -50.6711%

Step-by-step explanation:

Answer:

102.7

Step-by-step explanation:

your starting number is 147,

your earned number is 298,

to get the percentage, it will be in decimal form

the answer is-

102.72108843537416 %

Now you round to the nearest tenth-

102.7

I hope this helps you-

Step 1: Calculate the change (subtract old value from the new value) ...

Step 2: Divide that change by the old value (you will get a decimal number)

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

The area of the composite figure = 10,874.1 sq. m.

The perimeter of the composite figure = 406.9 m

Perimeter of a rectangle = 2(length + width)

Area of a rectangle = length × width

Perimeter of a circle = 2πr

Area of a circle = πr²

The figure is made up of two semicircles (1 full circle) and a rectangle.

Area of the composite figure = area of circle + area of rectangle

= πr² + length × width

r = 36.5 + 1.2 = 37.7 m

length = 85.0 m

width = 2(36.5) + 2(1.2) = 75.4 m

Substitute

Area of the composite figure = π(37.7)² + 85.0 × 75.4 = 10,874.1 sq. m.

Perimeter of the composite figure = perimeter of circle + 2(length of the rectangle)

= 2πr + 2(L)

Plug in the values

= 2π(37.7) + 2(85.0)

Perimeter of the composite figure = 406.9 m

Learn more about composite figures on:

https://brainly.com/question/391747

Answer:

[tex]\huge\boxed{\sf{Linear}}[/tex]

Step-by-step explanation:

Hello.

This function is linear.

Remember, linear functions look like so:

y=mx+b (where m = slope & b = y-intercept)

Is y=3x+2 linear? Sure!

Compare:

y=mx+b

y=3x+2

They look the same, huh? The only difference is that the first one has variables, and the second one has numbers. ;)

Now, what about the graph?

All linear functions have a graph that looks like a straight line.

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

The equation which correctly shows the Commutative Property of Multiplication is 6 x 7/8 = 7/8 x 6

This is the property which holds when a set of operations are changed but still remain the same value.

Check all that applies:

6 x 7/8 = 7/8 ÷ 6

7/8 ÷ 6

= 8/7 × 6

No

6 x 7/8 = 6 x 7/8

Yes

6 + 7/8 = 7/8 x 6

No

6 x 7/8 = 7/8 x 6

Yes

Therefore, 6 x 7/8 = 7/8 x 6 is the answer because the values were interchanged but still remain the same.

Learn more about cummutative property:

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Answer:

15. 10i√3

16. -1

17. 6

18. √35 - 2√5

     --------------

            3

19. x√35 - 3√7x + 4√5x - 12

20.    9√7

   -   ---------

          14

Step-by-step explanation:

15)

√-300 = √-100 × 3 = 10i√3

16)            5

i^22 = 4√22   =    i²   =   -1

             -20

             ------

                2

17)

(√7 + 1) (√7 - 1)

√7 (√7 + 1) - 1 (√7 + 1)

√49 + √7 - √7 - 1

7 - 1 = 6

18)

√5           √7 - 2          √35 + 2√5                      √35 - 2√5        √35 - 2√5

---------  x  ---------    =    ------------------             =    --------------    =   -----------------

√7 + 2     √7 - 2          √49 - 2√7 + 2√7 - 4           7 - 4                     3

19)

(√7x + 4)(√5x - 3)

√7x (√5x - 3) + 4 (√5x - 3)

√35x² - 3√7x + 4√5x - 12

x√35 - 3√7x + 4√5x - 12

20)

-√81       -9              √7         -9√7       -9√7

-------- = -------   x   -------   =  -------   =    -------

√28       2√7        √7         2√49         14

I hope this helps!

Answer:

Step-by-step explanation:

The maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

The maxima of a parabola is where, it opens down its vertex at the maximum point in a coordinate graph. By equating the derivative of equation of parabola equal to zero, it can be found out.

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain.

A cross-section of the road can be represented on a graph using the function,

[tex]f(x) = (x - 16)(x+ 16),[/tex]

Here, x represents the distance from the center of the road, in feet.

This equation can be written as,

[tex]f(x) = (x - 16)^2[/tex]

Now to find the maximum height, find the derivative of the above function as,

[tex]f(x) = (x - 16)^2\\f'(x) = (x - 16)^2\\f'(x)=2(x-16)(1)\\f'(x)=2(x-16)[/tex]

Equate the above equation to zero as,

[tex]0=2(x-16)\\0=x-16\\x=16[/tex]

Thus, the maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

Learn more about the maxima of parabola here;

https://brainly.com/question/5399857

Answer: READ MY EXPLANATION.

Yes, both of them have 90 degrees And sided triangles.

Step-by-step explanation: Hi m4rra! I'm sorry to say but your account has been reported quite a few times and you may want to start a new account, it has been reported by the following people: maylie186, ionfieldbest, gtchappymuch, and many more. I'm going to repeat what I mean but in less formal words. your account has been reported quite a bit, we are going to need you to delete this account. you may make a new one if you wish. . . sincerely, . The Brainly Team

Answer:

35%

Step-by-step explanation:

7/20 = 0.35

please mark brainliest

Answer:

[tex]18=y[/tex]

Step-by-step explanation:

Assuming that your equation is [tex]1x+1+15=y[/tex], you would first substitute in the 2: [tex](1*2)+1+15=y[/tex]

Next, simplify and combine like terms: [tex]2+16=y[/tex]

Finally, simplify again to get the answer: [tex]18=y[/tex]

Answer: The correct answer is 44.60

Step-by-step explanation:

Let's find the area of the rectangle first, and then add it with the area of the Circle to find the total area of the whole shape.

We know that the area of a Rectangle is L(Length) x W(Width)

So using the given information, 8 x 4 = 32

So the Area of the Rectangle = 32

Now let's find the area of the given circle,

Area of a Circle: πr2                                     Remember ^ = stands for power

The radius is half of the diameter

The diameter of the circle is 4

4/2 = 2 which is our radius, and now let's replace it in the equation.

= 3.14(r)^2

= 3.14(2)^2

= 3.14(4)

= 12.56 or some may have got 12.57

So now we add all areas together to get the total area,

32+12.57 = 44.57

Now rounding off to the nearest tenths, would give us 44.60

So the area of the figure rounded to the nearest tenth is 44.60

Answer:

[tex]44.56[/tex]

Step-by-step explanation:

Rectangle area:

[tex]4 \times 8 = 32[/tex]

2 circles area (full circle, since they are both a half of circle):

[tex] { (\frac{4}{2}) }^{2} \times π = 12.56[/tex]

Total area:

[tex]32 + 12.56 = 44.56[/tex]

Answer:

12:1

………………………………………………

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Answer:

Step-by-step explanation:

The area of a compound figure is the sum of the areas of its parts. The perimeter is the sum of the lengths of all of the edges.

This compound figure is conveniently divided into a semicircle of radius 2.5 and a trapezoid with bases 5 and 7, and height 3.

Semicircle

The area of the semicircle is half the area of a circle with the same radius. It will be ...

  A = 1/2πr²

  A = 1/2π(2.5²) = 3.125π . . . . square units

Trapezoid

The area of the trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5 +7)(3) = 18 . . . . square units

Then the total area of the figure is ...

  3.125π +18 ≈ 27.8 . . . . square units

__

Perimeter

The perimeter will be the sum of the lengths of the straight line segments and the length of the semicircular arc.

Arc

  The arc length is half the circumference of the circle, so is ...

  arc = 1/2(2πr) = πr = 2.5π . . . . units

Diagonal segments

The figure is bounded by two congruent line segments that are each the hypotenuse of a triangle 1 unit wide and 3 units high. The Pythagorean theorem tells us that length is ...

  diagonal length = √(1² +3²) = √10 . . . . units

The two diagonal sides have a total length of 2√10 units.

Horizontal segments

The figure is bounded by two congruent horizontal segments of length 1 unit each, and one horizontal segment of length 5 units. Their total length is ...

  horizontal length = 1 + 1 + 5 = 7 . . . . units

The total perimeter is ...

  perimeter = horizontal length + diagonal length + arc length

  7 +2√10 +2.5π ≈ 21.2 . . . . units