An executive hires 3 office workers from 5 applicants.

How many ways can the selection be made ?

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, we have to find the value of x

We have given quadrilateral ABCD here , whose angles are as follows

[ The measure of right angled triangle is 90° ]

We know that,

That is

[tex]\bold{\angle{ A + }}{\bold{\angle{B +}}}{\bold{\angle{C + }}}{\bold{\angle{D + = 360{\degree}}}}[/tex]

Subsitute the required values

[tex]\sf{ ( 6x + 5){\degree} + 80{\degree}+ 90{\degree} + (9x - 10){\degree} = 360{\degree}}[/tex]

[tex]\sf{ 6x + 5 + 170{\degree} + 9x - 10 = 360{\degree}}[/tex]

[tex]\sf{ 15x - 5 = 360{\degree} - 170{\degree}}[/tex]

[tex]\sf{ 15x - 5 = 190 {\degree}}[/tex]

[tex]\sf{ 15x = 190 {\degree} + 5 }[/tex]

[tex]\sf{ 15x = 195 {\degree}}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{ 195}{15}}}[/tex]

[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 195}{15}}}}[/tex]

[tex]\bold{ x = 13 }[/tex]

Hence, The value of x is 13 .

[tex]\bold{\huge{\underline{\red{ Verification }}}}[/tex]

Measure of Angle A

[tex]\sf{ = (6x + 5){\degree}}[/tex]

[tex]\sf{ = (6(13) + 5 ){\degree}}[/tex]

[tex]\sf{ = (78 + 5 ){\degree}}[/tex]

[tex]\sf{ = 83{\degree}}[/tex]

Measure of Angle D

[tex]\sf{ = (9x - 10){\degree}}[/tex]

[tex]\sf{ = (9(13) - 10){\degree}}[/tex]

[tex]\sf{ = (117 - 10 ){\degree}}[/tex]

[tex]\sf{ = 107{\degree}}[/tex]

Now, we know that,

That is,

[tex]\sf{ 83{\degree} + 80{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}[/tex]

[tex]\sf{ 163{\degree}+ 90{\degree} + 107 {\degree} = 360{\degree}}[/tex]

[tex]\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}[/tex]

[tex]\sf{ 253{\degree}+ 107 {\degree} = 360{\degree}}[/tex]

[tex]\bold{ 360{\degree} = 360{\degree}}[/tex]

[tex]\bold{ LHS = RHS }[/tex]

Hence, Proved.

Step-by-step explanation:

5⁴(3406 - 867) + (1.9 x 6)

=625(2539) + 11.4

= 1586875 + 11.4

=1586886.4

Answer:

= 1586886.4

Step-by-step explanation:

5^4 = 5 x 5 x 5 x 5
= 625

625(3406 - 867)
625 x 3406
= 2128750

625 x 867
= 541875

2128750 - 541875
= 1586875

1.9 x 6
= 11.4

1586875 + 11.4
= 1586886.4

Answer:

4 inches squared… but if this is wrong it’s probably because you didn’t specifically say what shape it is

Answer:
1/7(n)-7 < 98

Step-by-step explanation:

Step-by-step explanation:

inequalities follow basically the same rules as equalities (ahem, equations). for creation and calculation.

you just indicate whole areas above or below given lines.

behind every inequality is a "normal" equation that defines the delimiter.

the question already tells us which variables to use.

x = number of hot dogs

y = number of peanuts (I guess, bags of peanuts)

he wants to buy at least 4 snacks.

hmmm.

what would you do, if the question asked us :

he wants to buy 4 snacks.

what did you learn from the previous questions ?

the equation would be

x + y = 4.

but now it asks us about "at least" 4 snacks. so every solution, 4 or more, is valid. not only 4.

so, the inequality is

x + y >= 4

and he has $20 to buy these snacks.

again, with equations we would have said

3x + 2y = 20

remember, a hot dog costs $3, a bag of peanuts costs $2. so, every single hot dog and every single bag of peanuts brings itself into the cost calculation with that amount.

x hot dogs cost $3x. y bags of peanuts cost $2y.

but here, we are now flexible. he can spend $20, but he does not have to fully exceed his budget. he can also spend less.

so, the inequality is

3x + 2y <= 20

together these inequalities now describe the situation that he cannot spend more than $20, but he can spend as little as he wants, as long as he gets at least 4 snacks.

all combinations of x and y values that satisfy these conditions are valid solutions.

the actual solution would be then more complex, as the real life scenario gives us more constraints :

0 <= x <= 6 (because with more than 6 hot dogs alone he would already bust his budget).

0 <= y <= 10 (after buying 10 bags of peanuts the $20 are gone).

that eliminates the negative value solutions that the basic 2 equations would allow.

Answer:

The answer without rounding the numbers to the highest place value is 239074.473 if this was rounded to the nearest whole number it will be 239074

Step-by-step explanation:

3812.99 would be rounded to 3813

62.7 would be rounded to 63

3813*63=240219 <-----Correct answer

hope this helps mark brainliest please :)

two segment drawn from one point outside the circle are equal

[tex]\\ \rm\hookrightarrow 6/x=5/x+3[/tex]

[tex]\\ \rm\hookrightarrow 6(x+3)=5x[/tex]

[tex]\\ \rm\hookrightarrow 6x+6=5x[/tex]

[tex]\\ \rm\hookrightarrow x=-6[/tex]

#2

[tex]\\ \rm\hookrightarrow \dfrac{4}{2x}=\dfrac{5}{x}[/tex]

[tex]\\ \rm\hookrightarrow 4x=10x[/tex]

No solution.

Answer:

the lines are parallel because yes

Answer:

Step-by-step explanation:

The point (7, 0) becomes the point (7, 0) when reflected over the x-axis. That is, its coordinates do not change.

The point (7, 0) lies on the x-axis, so is on the line of reflection. Any point on the line of reflection is invariant--it doesn't move.

__

The transformation for reflection in the x-axis is ...

  (x, y) ⇒ (x, -y)

  (7, 0) ⇒ (7, 0) . . . . . . the opposite of 0 is 0

6 plates with 3 spoons or 9 plates with 2 spoons

Step-by-step explanation:

(i) 240 ÷ 4000 = 0.06

(ii) 760 ÷ 4000 = 0.19

(iii) (20 + 10) ÷ 4000 = 0.0075

I guess this is the answer

i am not sure!!!!

The arc angle LM of the circle is 60 degrees.

The arc angle LM of the circle can be found as follows:

The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Therefore, let's find the central angle that subtend LM in the circle as follows:

central angle = 180 - 120 = 60 degrees(angle on a straight line)

Hence, the central angle is equals to the arc angle.

Therefore,

arc LM = 60 degrees

learn more on angles here: https://brainly.com/question/28626462

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Answer:

6/5

Step by step explanation:

Here we are provided with a equation which is ,

[tex]\longrightarrow 15x + 18y = 270 [/tex]

And we are interested in finding the slope of the line which is perpendicular to the given line. We may rewrite the equation as ,

[tex]\longrightarrow 18y = -15x +270\\ [/tex]

[tex]\longrightarrow y =\dfrac{-15x+270}{18}\\[/tex]

[tex]\longrightarrow y =\dfrac{-15}{18}x +\dfrac{270}{8}\\ [/tex]

[tex]\longrightarrow y =\dfrac{-5}{6}x +\dfrac{135}{4} [/tex]

Recall the slope intercept form of the line which is y = mx + c .On comparing to which we get ,

[tex]\longrightarrow m =\dfrac{-5}{6} [/tex]

Again , recall that product of slopes of two perpendicular lines is -1. So that ,

[tex]\longrightarrow m_{\perp} =-\bigg(\dfrac{1}{m}\bigg)[/tex]

Hence ,

[tex]\longrightarrow\underline{\underline{ m_{\perp}= \dfrac{6}{5}}}[/tex]

And we are done !

The slope of the line perpendicular to the line with the equation 15x + 18y = 270 is 6/5.

The equation of the given line is 15x + 18y = 270. To find the slope of this line, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where 'm' represents the slope.

First, solve for 'y':

18y = -15x + 270

y = (-15/18)x + 270/18

y = (-5/6)x + 15

The slope of the given line is -5/6.

For a line perpendicular to this, the slope will be the negative reciprocal of -5/6. The negative reciprocal of a fraction 'a/b' is -b/a.

So, the slope of a line perpendicular to the given line is:

Slope = -(-6/5) = 6/5

Fully simplified, the slope of the line perpendicular to the line with the equation 15x + 18y = 270 is 6/5.

To know more about slope:

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Answer:

I think that A 60 and B is acute it must de a bigger 90.

Step-by-step explanation:

Answer: 15.75

Step-by-step explanation: 4.5 x 3.5

Answer:

A rational number is defined as a number that can be written as a fraction and a number that terminates.

An irrational number is defined as a number that can't be written as a fraction and a number that has no end.

Step-by-step explanation:

4/7 is irrational because, in decimal form, it is 0.57142857...

Square root of 30 is also irrational because the square root is 5.47722557...

21 divided by square root of 4 is rational because square root of 4 is 2 and 21 divided 2 is 10.5.

pi is irrational because, in decimal form, it is 3.14159265....

-27 is also rational because it terminates

Answer:

4/7 rational, Sq root 30 irrational, 21/Sq root 4 rational, pi irrational, -27 irrational

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

y = a f(x)

If |a| > 1 then a f(x) is f(x) stretched vertically by scale factor of a

If 0 < |a| < 1 then f(x)  is squashed vertically

If a < 0 then f(x)  is also reflected in the x-axis

y = f(ax)

If |a| > 1 then f(ax) is f(x) squashed horizontally by a scale factor of a

If 0 < |a| < 1 then f(x)  is stretched horizontally

If a < 0 then  f(x) is also reflected in the y-axis

g(x) has been squashed vertically by a scale factor of 1/3 (green on the attached diagram) and then reflected in the x-axis (red on the attached diagram)

Therefore, the solution is [tex]g(x) = -\dfrac13f(x)[/tex]

Answer: 17

Step-by-step explanation:

Answer:

=10cm

Step-by-step explanation:

=4times5 divided by 2

But that is only one triangle, the whole area is 40cm*2

Answer:

P   = 6 2/3 ft

Step-by-step explanation:

The formula for the perimeter of a rectangle of length L and width W is

P = 2(L + W).

Here the perimeter is P = 2(1 2/3 + 5/6) = 2(5/2 + 5/6)

                                                                  = 2(15/6 + 5/6) = 2(20/6)

                                                                  = 40/6 = 20/3

                                                              P   = 6 2/3 ft

Answer:

A

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+( y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (5, 1 ) and (x₂, y₂ ) = B (- 3, - 3 )

AB = [tex]\sqrt{(-3-5)^2+(-3-1)^2}[/tex]

     = [tex]\sqrt{(-8)^2+(-4)^2}[/tex]

     = [tex]\sqrt{64+16}[/tex]

     = [tex]\sqrt{80}[/tex]

     = [tex]\sqrt{16(5)}[/tex]

     = [tex]\sqrt{16}[/tex] × [tex]\sqrt{5}[/tex]

     = 4[tex]\sqrt{5}[/tex] → A

Answer:

A

Step-by-step explanation:

x^2-14x+49 factors into (x-7)(x-7) or (x-7)^2

Answer:

Step-by-step explanation:

Answer:

17/18

Step-by-step explanation:

okay this one is a bit different

you have to take the total number that are batwing-shaped (12) and the total number that are made of cotton (12) and then subtract the ones that are both batwing-shaped and made of cotton.

so 12+12-7 which is 17

then you put that over the total (18)

17/18 doesn't simplify