Find the value of x.
x
x = [?]

Answer:

C.  74°

Step-by-step explanation:

Cosine Rule (for finding angles)

[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

Given:

Substitute these values into the formula:

[tex]\implies \sf \cos(\theta)=\dfrac{5^2+11^2-(\sqrt{115})^2}{2(5)(11)}[/tex]

[tex]\implies \sf \cos(\theta)=\dfrac{25+121-115}{110}[/tex]

[tex]\implies \sf \cos(\theta)=\dfrac{31}{110}[/tex]

[tex]\implies \sf \theta=\cos^{-1}\left(\dfrac{31}{110}\right)[/tex]

[tex]\implies \sf \theta=74^{\circ} \quad (nearest\:degree)[/tex]

The system of equations has the solution:

x = 111/42

y = 27/14

z = -15/6

We start with 3 linear equations:

2x+y-z=8

x+4y+z=7

-3x+2y-3z=21

To solve this, first we need to isolate one of the variables. I will isolate x on the second one:

x = 7 - 4y - z

Now we can replace that in the other two:

2*( 7 - 4y - z) + y - z = 8

-3*(7 - 4y - z) + 2y - 3z = 21

Now we need to isolate other variable, let's isolate y on the above one:

14 - 8y - 2z + y - z = 8

-7y - 3z = 8 - 14 = -6

z = (-6 + 7y)/-3 = 2 - (7/3)*y

Now we replace this on the last equation:

-21 + 12y -3z + 2y - 3z = 21

14y - 6z = 42

14y - 6*(2 - (7/3)*y) = 42

14y - 12 + 14y = 42

28y = 42 + 12 = 54

y = 54/28 = 27/14

Now that we know the value of y, we can find the value of z:

z = 2 - (7/3)*y = 2 - (7/3)*27/14 = 2 - 27/6 = -15/6

And the value of x:

x = 7 - 4y - z = 7 - 4*(27/14) + 15/6 = 7 - 48/7 + 15/6 = 111/42

So the solution is:

x = 111/42

y = 27/14

z = -15/6

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The expression that represents the quotient of seven and four is 7/4

The statement is given as:

quotient of seven and four is 7/4

Quotient means divide

So, the interpretation of the expression is seven divide four i.e. 7/4

Hence, the expression that represents the quotient of seven and four is 7/4

Read more about quotient expressions at:

https://brainly.com/question/7068223

#SPJ1

Answer:

  7.2 cm

Step-by-step explanation:

The height of the trapezium can be found by making use of the area formula with known values filled in.

__

The area of a trapezium is given by ...

  A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height

Using the given values, we have ...

  90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values

  (90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h

The height of the trapezium is 7.2 cm.

I think you meant to say the equation is

y = 2x² - 2x + 3

Differentiate both sides with respect to x :

dy/dx = 4x - 2

At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.

Using the point-slope formula, the equation of the normal line is

y - 0 = -1/10 (x - 3)   ⇒   y = (3 - x)/10

Answer:

Step-by-step explanation:

-2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9

7x^4 - y^3 - 3

Answer:

28x-3y-3

Step-by-step explanation:

(-2x × 4 - 4v × 3 + 4z× 3 + 6) - (-9× × 4 - 3v× 3 + 4

Multiply the monomials

（-8×-4y×3+ 42×3+6)-（-9××4-3y×3+42×3+9

Multiply the monomials

(-8x-12y + 4z × 3 + 6) - (-9x× 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x - 12y + 12z +6) - (-9× × 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x-12y +12z +6) - (-36x -3y × 3+ 4z × 3 + 9)

Multiply the monomials

(-8x-12y + 12z + 6) - (-36x - 9y + 4z × 3 + 9)

8×-12y+122+6-（-36×-9y+122+9

Remove the parentheses for addition or

subtraction

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

Reorder and gather like terms

(-8x + 36x) + (-12y + 9y) + (12z - 12z) + (6 - 9) 3 steps

Collect coefficients of like terms

(-8+36) ××+ (-12 + 9) × y+ (12 - 12) × z+ (6 - 9)

Answer:

Step-by-step explanation:

(a). In set notation:

B. { x | x < 2 }

(b).

( - ∞ , 2 )

(c). See attachment.

For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E,  the ground speed of the plane and its direction is mathematically given as

Generally, the equation for the velocity of the plane is mathematically given as

[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]

Therefore

Vp=530cos45i+530sin45j

Vp= 374.76i+374.76j

For wind speed

Vm=80cos(90+30)i+80sin(90+30)j

Vm=-40i+69.28j

Hence, there resultant is

Vr=Vm +Vp

Vr=374.76i+374.76j + 40i+69.28j

Vr=334.77i+1444.05j

In conclusion, the Ground speed is

[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]

Vg=556.10km/hr

Direction

[tex]Tan \theta=\frac{444.05}{334.77}[/tex]

[tex]\theta=52.99East[/tex]

Read more about Arithmetic

https://brainly.com/question/22568180

#SPJ1

The height of the mountain estimated by two students is 2,467.98 meters.

The height of the mountain is calculated as follows;

tanα = h/( a + b + x)

where;

tan37 = h/(1850 + 740 + x)

tan37 = h/(2590 + x)

h = tan37(2590 + x)

h =1,951.82 +  0.7536x  ---- (1)

tanβ = h/(b + x)

tan60 = h/(740 + x)

h = tan60(740 + x)

h = 1,281.68 + 1.732x ---- (2)

Solve (1) and (2) together

1,951.82 +  0.7536x = 1,281.68 + 1.732x

1,951.82  -  1,281.68 = 1.732x  -  0.7536x

670.14 = 0.9784x

x = 684.93 m

h = 1,281.68 + 1.732x

h = 1,281.68 + 1.732(684.93)

h = 2,467.98 m

Thus, the height of the mountain estimated by two students is 2,467.98 meters.

Learn more about angle of elevation here: https://brainly.com/question/88158

#SPJ1

Answer:

D

Step-by-step explanation:

with this functional definition y can never have a negative value.

so, A and C are automatically out.

and then find some core points (like x = 0 and y = 0).

for x = 0 we get y = 3. ok, that fits to both B and D.

for y = 0 x must be 3.

and that leaves only D as right answer.

Answer:

the answer is a on my test

Step-by-step explanation:

Answer:

Interest= 15,000

Maturity Value=40,000

Step-by-step explanation:

Simple Interest

V= (principal) * (rate) * (# of periods)

=(25,000)*(0.12)*(5)

=15,000

Maturity Value

V= P*(1+rt)

=25,000*(1+(.12)(5))First, converting R percent to r a decimal

r = R/100 = 12%/100 = 0.12 per year.

Solving our equation:

V = 25000(1 + (0.12 × 5)) = 40000

V = 40,000.00

hope it will help you

thank u

Using proportions, it is found that the correct amount to administer of CC would be of:

A. 0.5.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 500 mg are equivalent to one cc. How many cc are equivalent to 250 mg? Hence the rule of three is given by:

500 mg - 1 cc

250 mg - x cc

Applying cross multiplication:

500x = 250

c = 0.5.

Hence option A is correct.

More can be learned about proportions at https://brainly.com/question/14398287

#SPJ1

Answer:

6.25 gm left

Step-by-step explanation:

Find the number of half lives in 26.3 years

   26.3 / 5.26 = 5 half lives

(1/2)  ^5   = 1/32 nd  of the original will be left

   1/32 * 200g = 6.25 gm left

Answer:

THE ANSWER IS A CORRECT ME IF I WRONG

Answer:

1, 4, 5, 6

Step-by-step explanation:

to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).

you can also double check by plugging both into a calculator and see if they equal the same number.

Answer:

Divide 12 by -6

Answer:

Solution: Here, the given equations are,

[tex]: \implies8x+5y=2...(i)\:and\:y-2=0...(ii)[/tex]

From equation,(ii); y-2=0

[tex] \therefore \: y = 2.........(iii)[/tex]

Substituting the value of y from equation (iii) to equation (i),we get

[tex]: \implies{8x + 5y = 2}[/tex]

[tex]: \implies{8x + 5(2) = 2}[/tex]

[tex]: \implies{8x = 2 - 10}[/tex]

[tex]: \implies{8x = - 8}[/tex]

[tex]: \implies{x = - 1}[/tex]

[tex] \therefore \: x = - 1[/tex]

Thus, x= -1 and y= 2 is the solution.

8x+5y=2...(i) y-2=0...(ii)

8(-1)+5(2)=2 2-2=0

2=2(True) 0=0(True)

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]

Answer:

A. 41 (12 - 2)

Step-by-step explanation:

If the club decided to charge $12 for a hat, but reduced the price by $2, the reduced price of the hat is (12 - 2). The amount of money earned is based upon the price of the hat multiplied by the number of hats sold. Therefore, the answer is 41 (12 - 2).

Hope this helped :)

Answer:

( we know that square of perimeter is 4L now,4L=6c-4(c-5),4L=6c-4c+20,4L=2c+20,then L=(c+10)/2

The side of a given square is c/2+5. Therefore, option C is the correct answer.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, the perimeter of a square is 6c-4(c-5).

We know that, the perimeter of a square is 4a, where a is the side.

Now, 4a=6c-4(c-5)

4a=6c-4c+20

4a=2c+20

a=c/2+5

Therefore, option C is the correct answer.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ2

The composition of the transformation is (b) A rotation of 90° and then a translation left 2, up 4.

The transformation rule is given as:

r (90, 0) T(−2,4)

The r(90,0) represents a rotation of 90 degrees.

The other part of the transformation rule can be rewritten as:

T(-2,4) => (x - 2,y + 4)

This means a translation right by 2 units and up by 4 units

Hence, the composition of the transformation is (b)

Read more about transformation at:

https://brainly.com/question/4289712

#SPJ1

Answer: left 2

Step-by-step explanation:

The question requires the computation of loss body fluid. The results show that Don Pedro's loss of body fluid per hour is 54,234ml/hours. See computation below.

This refer to the rate at which a human being loses water on the hour. The formula for this is given as:

The Body weight in lb x percentage rate of dehydration (given in decimal form) x 500.

Hence, Don Pedro's loss of fluid per house is:

82 x 0.6 x 500;

Recall that in the formula, the weight is given in lb. So we convert Pedro's weight to Lb.

1kg = 2.20462Lb

Hence

80kg = 80 * 2.20462 = 176.37

Hence

Pedro's loss of fluid per house =

180.779 x 0.6 x 500

= 54,233.70

≈ 54, 234 ml/h


Learn more about loss of body fluid at:
https://brainly.com/question/2060910
#SPJ1

The total time for the trip is:

T =  3mi*( 3/2x).

Where x is the rate at which she comes home.

Remember the relation:

distance = rate*time.

We know that the distance is 3 miles (done twice).

First, the rate is 2x and then the rate is x, then the time it took the first half is:

t = 3mi/2x

And for the coming back:

t = 3mi/x

Then the total time for the trip is:

T =  3mi/2x +  3mi/x = 3mi( 1/2x + 1/x) = 3mi*( 3/2x).

If you want to learn about rates:

https://brainly.com/question/605631

#SPJ1

Answer:

55 x 224 yards

Step-by-step explanation:

w + w  +  2 * ( 4 + 4w)  = 558     (given)

10 w + 8 =558

w = 55      then L = 4 + 4w = 224 yards

Answer:

(i)  (0, -32)

(ii)  (-4, 0) and (8, 0)

(iii)  x = 2

(iv)  (2, -36)

(v)  (2, -36) minimum

Step-by-step explanation:

Given quadratic equation:

[tex]y=x^2-4x-32[/tex]

Part (i)

The y-intercept is the point at which the curve crosses the y-axis.

To find the y-intercept, substitute x = 0 into the given equation:

[tex]\implies (0)^2-4(0)-32=-32[/tex]

Therefore, the y-intercept is at (0, -32)

Part (ii)

The zeros are the points at which the curve crosses the x-axis.

To find the zeros, substitute y = 0 into the given equation and factor:

[tex]\implies x^2-4x-32=0[/tex]

[tex]\implies x^2-8x+4x-32=0[/tex]

[tex]\implies x(x-8)+4(x-8)=0[/tex]

[tex]\implies (x+4)(x-8)=0[/tex]

Therefore:

[tex](x+4)=0 \implies x=-4[/tex]

[tex](x-8)=0 \implies x=8[/tex]

So the zeros are (-4, 0) and (8, 0)

Part (iii)

The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts.  The axis of symmetry is the x-value of the mid-point of the zeros.

[tex]\sf \implies midpoint=\dfrac{8+(-4)}{2}=2[/tex]

Therefore, the axis of symmetry is:  x = 2

Part (iv)

The vertex is the turning point of the parabola.

If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.  

If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.

The axis of symmetry is the x-value of the vertex.

To find the y-value, substitute x = 2 into the equation:

[tex]\implies (2)^2-4(2)-32=-36[/tex]

Therefore, the vertex is (2, -36)

Part (v)

The optimal value is also known as the vertex.

Therefore, the optimal value is (2, -36).  

As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.

The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:

50% for necessities (housing, food, transportation, utilities) $740

30% for luxuries, savings, vacations, entertainment, etc. $461

20% for Emergency Funds and Retirement $335

A personal budget is the household budget for a single person for a period.

The personal budget shows an estimate of the person's revenue and expenses over the period.

Hourly rate of earnings = $12

Working hours per week = 40 hours

Working hours per month = 160 hours (40 x 4 weeks)

Total monthly earnings = $1,920 ($12 x 160)

Assumed tax rate = 20%

After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)

Rent of apartment = $300

Heating = $40

Water cost = $20

Sewage bill = $10

Food = $300

Transportation = $50

Other costs = $20

Total cost for necessities = $740

Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.

Learn more about personal budgets at https://brainly.com/question/1943261

#SPJ1

The value of k is[tex](3\sqrt{ 10})/2[/tex]

Given:

x-y=k.............(eq i)

2x²+y²-15..............(eq ii)

We would make y the subject formula in eq ii

2x²+y²-15= 0

2x² + y²= 15

y²= 15-2x²

y= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)

Substitute the value of y into eq i

x-([tex]\sqrt{15-2x^2}[/tex]= k

x- ([tex]\sqrt{15} - 2x[/tex]= k

k= [tex](3\sqrt{ 10})/2[/tex]

Read more about simultaneous equations here:

https://brainly.com/question/16863577

#SPJ1

Answer:

Step-by-step explanation: