Simplify the expression:
8x+1b=c

Answer:

[tex]\dfrac{19}{25}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{4}{10}+\dfrac{6}{10}\right)-\left(\dfrac{4}{10} \times \dfrac{6}{10}\right)[/tex]

[tex]=\left(\dfrac{10}{10}\right)-\left(\dfrac{24}{100} \right)[/tex]

[tex]=\left(\dfrac{100}{100}\right)-\left(\dfrac{24}{100} \right)[/tex]

[tex]=\dfrac{76}{100}[/tex]

[tex]=\dfrac{19}{25}[/tex]

Solution:

Note that:

Simplify the expression:

Simplify the fraction:

19/25 is the difference.

Will recommend to keep in touch with picture as name of angles are based on it!

[tex] \\ [/tex]

So as you can see BA is parallel to DC as the arrow signs are made on it. And the figure has four sides , therefore we get to know that the above picture is of parallelogram.

[tex] \\ [/tex]

[tex] \rm\angle B = \angle D [/tex]

How ?

As we know it's a parallelogram, so there's one property of parallelogram that opposite sides of Angle are equal.

[tex] \\ [/tex]

[tex] \hookrightarrow \sf2x =130 \degree [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x =130 \degree\div 2 \degree [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x = \dfrac{130}{2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x = \dfrac{13 \times 10}{2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x = \dfrac{13 \times\cancel{ 10}}{\cancel2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x = \dfrac{13 \times5}{1} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x =13 \times5[/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow \sf x =65 \degree[/tex]

[tex] \\ [/tex]

Now Let's find value of y.

[tex] \rm \angle DAB =\angle DCB[/tex]

How ?

As we know it's a parallelogram, so there's one property of parallelogram that opposite sides of Angle are equal.

[tex] \\ [/tex]

[tex] \dashrightarrow \rm x = y[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \rm 65 = y[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \bf y = 65 \degree[/tex]

[tex] \\ [/tex]

angles on same line

[tex] \\ [/tex]

At last :-

x = 65°

y = 65°

z = 55°

The values of the unknown x, y and z in the figure are 65°, 35° and 85° respectively.

Data

The sum of angles in a parallelogram is equal to 360°. To solve for all the missing numbers, we have to use some properties of parallelogram.

2x = 130

Reason: Opposite angles in a parallelogram are equal.

let's solve for x

[tex]2x = 130 \\\frac{2x}{2} = \frac{130}{2}\\x = 65^0[/tex]

The value of x is 65°

Let's solve for y

[tex]x+ 130 + y + 2x= 360\\x = 65\\65 + 130 + y + 2(65) = 360\\325 + y = 360\\y = 360 - 325\\y = 35[/tex]

The value of y is 35°

Let's solve for z

[tex]60 + y + z = 180[/tex]

reason: sum of angles on a straight line is equal to 180°

[tex]60 + y + z = 180\\60 + 35 + z = 180\\95 + z = 180\\z = 180 - 95\\z = 85^0[/tex]

The values of the unknown x, y and z in the figure are 65°, 35° and 85° respectively.

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Parabolas are used to represent curved functions

The shortest distance between the parabola and the point is [tex]x = -\frac 1{2}[/tex]

The parabola is given as:

[tex]y=(7x+5)^{1/2}[/tex]

Rewrite as:

[tex]y=\sqrt{7x+5}[/tex]

Let p represent a point on the parabola.

So, we have:

[tex]P(x,\sqrt{7x + 5})[/tex]

Next, calculate the distance between P and the point (3,0) using the following distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

So, we have:

[tex]d = \sqrt{(x- 3)^2 + (\sqrt{7x + 5})^2[/tex]

[tex]d = \sqrt{x^2- 6x + 9 + 7x + 5}[/tex]

Evaluate the like terms

[tex]d = \sqrt{x^2+ x + 14}[/tex]

Square both sides

[tex]d^2 = x^2+ x + 14[/tex]

The shortest distance is then calculated as:

[tex]x = -\frac b{2a}[/tex]

Where:

a = 1, b = 1 and c = 14

So, we have:

[tex]x = -\frac 1{2*1}[/tex]

[tex]x = -\frac 1{2}[/tex]

Hence, the shortest distance between the parabola and the point is [tex]x = -\frac 1{2}[/tex]

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Answer: D

Step-by-step explanation:

By the cosine rule, [tex]BC=\sqrt{10^{2}+14^{2}-2 \cdot 10 \cdot 14 \cdot \cos 70^{\circ}}[/tex]

Now, we can use the law of sines to get that:

[tex]\frac{\sqrt{10^{2}+14^{2}-2\cdot 10 \cdot 14 \cdot \cos 70^{\circ}}}{\sin 70^{\circ}}=\frac{14}{\sin \angle ABC}[/tex]

Meaning that [tex]\sin \angle ABC =\frac{14\sin 70^{\circ}}{\sqrt{10^{2}+14^{2}-2 \cdot 10 \cdot 14 \cdot \cos 70^{\circ}}}[/tex]

And thus [tex]\angle ABC=\sin^{-1} \left(\frac{14\sin 70^{\circ}}{\sqrt{10^{2}+14^{2}-2 \cdot 10 \cdot 14 \cdot \cos 70^{\circ}}} \right) \approx 68.39^{\circ}[/tex]

Answer:

=] - 13

Step-by-step explanation:

=>21+(-34)

=> 21-34

=> -13

Answer:

Tavian is correct.

Step-by-step explanation:

If you solve the systems of equations, y=0 and x=7, so the solution is (7, 0).

Answer:

ABD= ABC - DBC

=140 - 36

=104

Answer:

3 trumpet players

Step-by-step explanation:

t=1 and 3x1=3t

Answer:

a) P(not red) = 37/49

b) P(purple) = 17/49

Step-by-step explanation:

Prob. of not red = (20+17) / (12+20+17) = 37/49

Answer:

27*n

Step-by-step explanation:

A theater has 27 rows with n seats in each row. Which expression shows how many seats are in the entire theater?

27n or 27*n

You got it right.

Ex: A theater has 27 rows with 2 seats in each row.  Which expression shows how many seats are in the entire theater?

27*2 = 54 seats

Hope this helps!

The expression showing the number of seats in the considered entire theater is given by: Option A: [tex]27 \times n[/tex]

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as [tex]a[/tex] and [tex]b[/tex]

Then, their multiplication can be interpreted as:

[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]

For example,

[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]

Now, for the considered situation in the problem's statement, we are specified that:

So, total number of seats = n + n + ... + n (27 times) = [tex]27 \times n[/tex]

Thus, the expression showing the number of seats in the considered entire theater is given by: Option A: [tex]27 \times n[/tex]

Learn more about multiplication here:

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Hello.

Remember, equivalent means equal.

Let's simplify the expression.

First, let's use the Distributive Property, which states

[tex]\hookrightarrow[/tex] [tex]\mathrm{a(b+c)=ab+ac}[/tex]

Use it:

[tex]\hookrightarrow\mathrm{-4+8(7+x)}[/tex]

[tex]\hookrightarrow[/tex] [tex]\mathrm{-4+56+8x}[/tex]

[tex]\hookrightarrow\mathrm{52+8x}[/tex]

Therefore, the answer is

[tex]\mathrm{52+8x}[/tex]

I hope this helps you.

Have a nice day.

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

Answer:

6 ln x + 3 ln y

Step-by-step explanation:

Answer:

In explanation

Step-by-step explanation:

So, let's solve for y in both of these equations

3y + 2x = 8

3y = 2x+8

y = 2/3x+8/3

-3x - 2y = 6

-2y = 3x + 6

y = -3/2x-3

The lines are perpendicular, since their slopes are the negative reciprocal of each other.

Negative reciprocal =>     -1/n

The sum of the equations demonstrates this relationship, with 0x + 0y = 14

or 0 = 14 in which a result like this only occurs when the lines are perpendicular

Your welcome, comment if you have any questions! :D

Answer:

Line BC is parallel to line AD. The system of equations has the sum 0 = 14. Since this is a false equation, the system has no solution, which means the lines will never intersect.

Step-by-step explanation:

Answer:

1. [tex]\frac{3}{17}[/tex] (3/17)

2. [tex]\frac{3}{7}[/tex] (3/7)

3.  [tex]\frac{45}{184}[/tex] (45/184)

Step-by-step explanation:

1. [tex]\frac{\frac{3}{5} }{3\frac{2}{5}}[/tex] = [tex]\frac{\frac{3}{5} }{\frac{17}{5}}[/tex] = [tex]\frac{\frac{3}{1} }{\frac{17}{1}}[/tex]= [tex]\frac{3}{17}[/tex]

2. [tex]\frac{2}{4\frac{2}{3}}[/tex] = [tex]\frac{\frac{2}{1} }{\frac{14}{3}}[/tex]= [tex]\frac{2}{1} /\frac{14}{3}[/tex] = [tex]\frac{2}{1} *\frac{3}{14}[/tex] = [tex]\frac{6}{14}[/tex] = [tex]\frac{3}{7}[/tex]

3. [tex]\frac{\frac{5}{4} }{5\frac{1}{9} }[/tex] = [tex]\frac{\frac{5}{4} }{\frac{46}{9}}[/tex] = [tex]\frac{5}{4}/\frac{46}{9}[/tex] = [tex]\frac{5}{2}/\frac{23}{9}[/tex] = [tex]\frac{5}{2}*\frac{9}{23}[/tex] = [tex]\frac{45}{184}[/tex]

Hope this helps!

The equation of the line passing through (-1, 1) and (0, 10) is y = 9x + 10.

A linear equation is in the form:

y = mx + b

Where m  is the rate of change (slope) and b is the initial value of y.

Given the points (-1, 1) and (0, 10). The equation of the line passing through this point is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x - x_1)\\\\y-1=\frac{10-9}{0-(-1)}(x-(-1))\\ \\y=9x+10[/tex]

The equation of the line passing through (-1, 1) and (0, 10) is y = 9x + 10.

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Answer:

Should be 19.533333 (3 keeps repeating)

Step-by-step explanation:

if you add all the numbers up it equals

293

There are 15 points so you should just have to do 293/15

Answer:

0.38km²

Step-by-step explanation:

A=h and b/2

= 1·0.75/2=

0.375km²

Answer:

80% off

Step-by-step explanation:

(0.15 - 0.75)/0.75 = -0.8 = -80%

Answer:

Simplify the expression:

1x+10y=4+3

Step-by-step explanation:

1 : x+10y=4+3

x+10y=4+3

x+10y=7

x+10y-10y=7-10y

x=7-10y

hope it helps

Answer:

x=7-10y

Step-by-step explanation:

Add the numbers with no variables:

4+3=7

1 and x are the same so the 1 cancels out u get x and since your solving for x you would put x=:

Since you got rid of the would you have to swap the equations around:

x=7-10y

By getting the motion equations for the bugs, we will see that:

a)

b) 150 units.

c) 60 seconds

d) The graph can be seen at the end.

e) Directly proportional.

a) We know that bug P moves 12 units in 4 seconds, then its velocity is:

Vp = 12/4s = 3 units per seg.

And bug N moves -8 units in 8 seconds, then its velocity is:

Vn = -8/4s = -2 units per seg.

Then we have:

b) The distance between the bugs at the time t is:

d = x - y

At 30 segs, that distance is:

d(30s) = (3 units per seg)*30s - (-2 units per seg)*30s = 150 units.

c) Now we need to write:

d = 300 units =  (3 units per seg)*t - (-2 units per seg)*t

300 units = (5 units per seg)*t

(300 units)/(5 units per seg) = t = 60s

The distance between the bugs will be 300 units after 60 seconds.

d) The graph of:

d(t) = (5 units per seg)*t

Can be seen at the end.

e) As the time increases also does the distance, so these two are proportional.

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Answer:

There are 721 columns.

Step-by-step explanation:

6,489 ÷ 9 = 721

Answer:

V = 141.37 cm³

Surface area = 150.80 cm²

Step-by-step explanation:

Answer:

V = 141.37 cm³

Surface area = 150.80 cm²

i. Doubling the radius to 6 cm, while the height remains 5

Step-by-step explanation:

Given that :

Radius, r = 3cm

Height, h = 5cm

Volume, V of right cylinder :

V = πr²h

V = π * 3² * 5

V = 141.37166

V = 141.37 cm³

Surface Area :

2πr(h + r)

2 * π * 3(3 +5)

18.849555(8)

150.79644

= 150.80 cm²

Volume at r = 6 ; h = 5

V = π * 6² * 5

V = 565.48667 cm³

Volume at r = 3 ; h = 15

V = π * 3² * 15

V = 424.11500 cm³

Answer:

See below

Step-by-step explanation:

Part A

The surface area of a cylinder is [tex]SA=2\pi rh+2\pi r^2[/tex] with [tex]r[/tex] being the radius and [tex]h[/tex] being the height:

[tex]SA=2\pi rh+2\pi r^2\\\\SA=2\pi(7)(3)+2\pi(7)^2\\\\SA=2\pi(21)+2\pi(49)\\\\SA=42\pi+98\pi\\\\SA=140\pi[/tex]

Therefore, the surface area of the given cylinder is 140π cm².

Part B

The volume of a cylinder is [tex]V=\pi r^2h[/tex]:

[tex]V=\pi r^2h\\\\V=\pi (7)^2(3)\\\\V=\pi(49)(3)\\\\V=147\pi[/tex]

Therefore, the volume of the given cylinder is 147π cm³.

Part C

The first cylinder would have a volume of [tex]V_1=\pi(14)^2(3)=\pi(196)(3)=588\pi cm^3[/tex]

The second cylinder would have a volume of [tex]V_2=\pi (7)^2(9)=\pi(49)(9)=441\pi cm^3[/tex]

Therefore, the first cylinder with a radius of 14cm and a height of 3cm gives a greater volume of 588π cm³.

Answer: he can have 45 plants

Combine like terms:

-5u + 5u = 0

The you are left with just -8

Answer: -8

Answer:

-8

Step-by-step explanation:

-5u+5u-8=(-5+5)u-8

=(0)u-8

=-8

Answer:

19

Step-by-step explanation:

10 + 9 = 19

because when you add those 2 numbers together you get

19

Answer: False

Step-by-step explanation:

The angles require more than 2 lines to be formed, meaning they cannot be formed by intersecting lines.