8. Expand (2a – 3b + 4c)2
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Nowww it’s imp

Given:

In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].

To find:

The length of the hypotenuse.

Solution:

It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the given triangle,

[tex]\sin A=\dfrac{a}{c}[/tex]

Substituting the given values, we get

[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]

By cross multiplication, we get

[tex]1\times c=4\times 2[/tex]

[tex]c=8[/tex]

Therefore, the length of the hypotenuse is 8 units.

Answer:

Step-by-step explanation:

A y = -3.6x + 12.8

The line of best fit is,

⇒ y = - 3.6x + 12.8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, Given that;

⇒ y = ax + b.

And, the best fitting line has values of a = - 3.6 and b = 12.8.

Hence, All you need do is put that into the general equation and try different values for it.

So you have y = - 3.6 x + 12.8

Now Let's run a couple of numbers.

The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.

y = - 3.6(1) + 12.8

y = 9.2

Which is not a bad result for x = 1

You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.

C

-0.998 = -3.6(1) + 12.8

This answer cannot work. We've already shown that x =1 will leave us close to 9  not -998

So, C is incorrect.

B

y = 12.8x - 3.6

Let x = 1

y = 12.8(1) - 3.6

y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5

y= 12.8*5 - 3.6

y = 64 - 3.6 which is no where's near - 5.

So B is wrong.

A

y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.

x = 3. y should come to somewhere near 2.

y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.

It is not close enough to 2 to be acceptable.

Thus, The correct option is,

⇒ y = - 3.6x + 12.8

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Answer:

o ye}x+3 and 3x –y> 2 system of linear inequalities is represented by the graph.

PLEASE LET ME KNOW IF ¡ AM WRONG!

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =≤

Greater than and equal = ≥

We have,

We see that,

When we graph,

y ≥ (1/3)x + 3 and 3x - y  > 2 we get the graph shown.

y ≥ (1/3)x + 3

This inequality is positive on the y-axis.

3x - y  > 2

3x > 2 + y

This inequality is positive on the x-axis.

Thus,

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

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Explanation:

P(T = 1) is the notation that means "The probability of getting exactly one tail". The table shows 3/8 in the bottom row, under the "1" in the top row. So that's why P(T = 1) = 3/8

Or it might make more sense to say P(one tail) = 3/8 so we don't have too many equal signs going on.

Answer:

use 0-9 to fill in blanks

Step-by-step explanation:

Step-by-step explanation:

As a ream or

500

sheets of paper weigh

4.818

pounds

One sheet of paper weighs

4.818

500

=

0.009636

pounds.

It is apparent that pound is too big a unit for a sheet of paper.

As each pound has

16

ounces, one can say

one sheet of paper weighs

0.009636

×

16

=

0.154176

ounces.

If ounce is too big, as we have

1

pound equal to

28.34952

grams

one sheet of paper weighs

0.154176

×

28.34952

≈

4.371

grams

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[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The measures of [tex]x[/tex] and [tex]y[/tex].

[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\: 210°\:and\:\:y\:=\: -30°}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

An exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

[tex] 40° = 70° + y[/tex]

[tex]➪ \: y= 40° - 70°[/tex]

[tex]➪ \: y = - 30°[/tex]

Also,

[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]

[tex]y[/tex] + [tex]x[/tex] = [tex]180°[/tex]

[tex]➪ \: -30° + x= 180°[/tex]

[tex]➪ \:x = 180° + 30°[/tex]

[tex]➪ \:x = 210°[/tex]

[tex]\sf\purple{Therefore,\:the\:measures \:of\:the\:unknown\:angles\:are\:"x=210°"\:and\:"y=-30°.}[/tex]

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]

[tex]HOLA!![/tex]

Answer:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=e^{\frac{1}{3} } }}[/tex]

Explanation:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]

For this we have to take into account:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{x^{n} }{n!} =e^{x} }}[/tex]

Using the properties of factorials and exponents we have:

          [tex]n!=(n-1)n![/tex]  Also.    [tex]\frac{n^{x} }{ n^{y} }=n^{x-y}[/tex]  

We replace:

[tex]{\boxed{ \sum_{n=1}^{\infty}\ \frac{1}{3^{n-1}.(n-1)! } }}[/tex]

Shape it:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} }}[/tex]

Finally:

[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} =e^{\frac{1}{3} } }}[/tex]

Answer: 3×4=12

Step-by-step explanation:

Brackets: X=1 , so 1+3=4 and 3+4=12

9514 1404 393

Answer:

  y = 21/x

Step-by-step explanation:

The inverse variation relation means ...

  y = k/x

For the given values, we can determine the constant k:

  3 = k/7

  3×7 = k = 21

Then the function is ...

  y = 21/x

Answer:

2.04 miles per hour

Step-by-step explanation:

Given

Noel

[tex]n_1 =6miles[/tex]

[tex]r_1 = 2mph[/tex]

Casey

[tex]c_1 = 8miles[/tex]

[tex]r_2 =1mph[/tex]

Required

The rate at which the distance increases

Their movement forms a right triangle and the distance between them is the hypotenuse.

At [tex]n_1 =6miles[/tex] and [tex]c_1 = 8miles[/tex]

The distance between them is:

[tex]d_1 = \sqrt{n_1^2 + c_1^2}[/tex]

[tex]d_1 = \sqrt{6^2 + 8^2}[/tex]

[tex]d_1 = \sqrt{100}[/tex]

[tex]d_1 = 10miles[/tex]

After 1 hour, their new position is:

New = Old + Rate * Time

[tex]n_2 = n_1 + r_1 * 1[/tex]

[tex]n_2 = 6 + 2 * 1 = 8[/tex]

And:

[tex]c_2 = c_1 + r_2 * 1[/tex]

[tex]c_2 = 8 + 1 * 1 = 9[/tex]

So, the distance between them is now:

[tex]d_2 = \sqrt{n_2^2 + c_2^2}[/tex]

[tex]d_2 = \sqrt{8^2 + 9^2}[/tex]

[tex]d_2 = \sqrt{145}[/tex]

[tex]d_2 = 12.04[/tex]

The rate of change is:

[tex]\triangle d = d_2 -d_1[/tex]

[tex]\triangle d = 12.04 -10[/tex]

[tex]\triangle d = 2.04[/tex]

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

Discrete data are those which can take up only specific values. Discrete data values may include the number of children in a particular school, the number of visitors received per day. All this values are specific and cannot just take up any number one f values within an interval. Continous data on the other hand can take up any number of data values between an interval. Continous data types are usually height temperature, length(distance data). There can be infinite number of possible data within interval values.

Answer:

216 yd³

Step-by-step explanation:

Volume of a rectangular prism

= product of the three orthogonal sides

= 6yd * 6yd * 6yd

= 216 yd³

Answer:

216

Step-by-step explanation:

:)

9514 1404 393

Answer:

  x = 2

Step-by-step explanation:

Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.

  (3x +24)° = 30°

  3x = 6 . . . . . . . . . divide by °, subtract 24

  x = 2 . . . . . . . . . . divide by 3

__

Additional comment

What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)

Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.

Answer:

2/7

Step-by-step explanation:

While

9514 1404 393

Answer:

  the end of the whole number and the beginning of the fraction

Step-by-step explanation:

The word "and" means the whole part and the fractional part should be considered together as having a value equal to their sum. It signifies the separation between the whole-number part and the fractional part.

__

It has the same meaning as when used in a decimal mixed number:

1.2 = "one and two tenths"

[tex]w - (14) < 8 \\ = w < 8 + 14 \\ \\ w = < 22[/tex]

Step by Step Explanation:

#CarryOnLearning

Answer:

72

72

96

120

Step-by-step explanation:

The arcs are in the ratio:

3 : 3 : 4 : 5

Add all numbers in the ratio:

3 + 3 + 4 + 5 = 15

In the ratio, the sum of all numbers is 15.

In the real circle, the sum of the measures of all the arcs is 360.

360/15 = 24

Multiply all numbers in the ratio by 24.

72 : 72 : 96 : 120

Answer:

72

72

96

120

Answer:

x+120°+20°=180°[ sum of interior angle of triangle]

x+140°=180°

x=40°

then,

x+y= 180°[being straight line]

40°+y= 180°

y=140°

Answer:

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Step-by-step explanation:

Tem.Before    Tem.After       diff.      

103.7                   102.6            1.1

103.7                   102.7             1

100.7                     98.8             1.9

102.7                    103.5            -0.8

100.7                      99.4             1.3

102.4                      101.41           (Mean)

1.4                             1.9              0.9       Std. Dev.

n =  6

df  =  6  -  1  =  5

CI we propose to be 95 %

Then  α  = 5 %  α = 0.05    

The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever

Hypothesis test

Null Hypothesis                      H₀         μd  = 0

Alternative Hypothesis          Hₐ         μd > 0

(NOTE:)   μd (average) = Temp Before  -  Temp. after

Therefore if   μd >  0   means that there is a statistical difference between values before ( bigger ) and after  or that the aspirin will reduce a child´s fever

To find t(c)  from t-student table  df = 5  and α = 0.05

t(c)  =  2.015

To compute  t(s)

t(s)  =  μd/ sd/√n      t(s)  =  0.98/ 0.9/√6

t(s)  =  2.66

Comparing  t(s) and  t(c)

t(s) > t(c)    

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

1. 3

29-9=19

13+9=22

22-19=3

I don't know number 2, sorry.

Answer:

Here we know that:

[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } }[/tex]

Where V is the speed, C = 3*10^8 m/s

We want to solve:

[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]

We can just isolate V from the above equation, so we will get:

[tex]\frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]

[tex]\frac{1}{\sqrt{1 - \frac{V}{C} } } = 2[/tex]

[tex]1 = 2\sqrt{1 - \frac{V}{C} }[/tex]

[tex](1/2)^2 = 1 - \frac{V}{C}[/tex]

[tex]V = (1 - (1/4))*C = (3/4)*C = (3/4)*3*10^8 m/s = (9/4)*10^8 m/s[/tex]

That is the velocity such that the effective mass is twice the rest mass.

Answer:

10 miles

Step-by-step explanation:

10 miles= 16093.44km

44880ft=13.679424km

15560yards= 14.228064

Answer:

10

Step-by-step explanat

ion:  

Step-by-step explanation:

ejdjbd x bxbx k wbu y DJ UK j HK JM dz

nb

Answer:

Step-by-step explanation:

Add all of the Maintenance costs up, divide by 80. (the number of costs).

Excel formula =SUM(F2:F81)  364151.00/80 = 4551.8875 Rounded to 4552 is your answer.

Answer: [tex]\frac{3}{5} x+10[/tex]

Step-by-step explanation:

three-fifths of a number means multiply three-fifths by a variable [tex]\frac{3}{5} x[/tex]

increased by 10 means addition +10

together it is [tex]\frac{3}{5}x +10[/tex]

Answer:

Slope = 3

intercept = 2

y = 3x + 2

angle y = 70

angle x = 110

Step-by-step explanation:

49 dollars

Step-by-step explanation:

14 times 3 is 42 and 3.50 times 2 is 7, so 42 plus 7 is 49.

Total cost with 2 snacks = $35

Total cost with x  snacks = 28+3.50x

Given :

Carson is going to see a movie and is taking his 2 kids. Movie ticket costs $14 and snacks cost $3.50.

Explanation :

Carson buys 2 snacks . we need to find the total cost that Carson have to pay where he buy 2 snacks.

Total cost = cost of ticket (2 kids) + cost of 2 snacks

[tex]Total \; cost = 14(2) + 2(3.50)=35[/tex]

Total cost with 2 snacks = $35

Total cost with x snacks = cost of ticket (2 kids) + cost of x snacks

[tex]Total \; cost = 14(2) + 3.50(x)\\Total \; cost = 28+3.50x[/tex]

Total cost with x  snacks = 28+3.50x

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