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If x, y, and z are positive integers such that 6xyz+30xy+21xz+2yz+105x+10y+7z=812, find x+y+z.

Answer:

Step-by-step explanation:

Given

[tex]z(14x -2y)=7[/tex]

Required;

Solve for x, when

[tex]z(14x -2y)=7[/tex]

Divide both sides by z

[tex]\frac{z(14x -2y)}{z} = \frac{7}{z}[/tex]

[tex]14x -2y = \frac{7}{z}[/tex]

Add 2y to both sides

[tex]14x -2y + 2y= \frac{7}{z} + 2y[/tex]

[tex]14x = \frac{7}{z} + 2y[/tex]

Divide both sides by 14

[tex]\frac{14x}{14} = \frac{1}{14}(\frac{7}{z} + 2y)[/tex]

[tex]x = \frac{1}{14}(\frac{7}{z} + 2y)[/tex]

The above expression is the value of x when [tex]z\neq 0[/tex]

To solve for when z = 0, we simply substitute 0 for z

[tex]x = \frac{1}{14}(\frac{7}{z} + 2y)[/tex]

[tex]x = \frac{1}{14}(\frac{7}{0} + 2y)[/tex]

0 cant't divide any number; hence, from the above expression we conclude that

[tex]x = \ u\ n\ d\ e \ f\ i \ n\ e\ d[/tex]

or

x doesn't have a solution

Answer:

Step-by-step explanation:

1) ∠AED = ∠ BEC

2) ∠AEB = ∠DEC

3) ∠DEC = ∠AEB

4) ∠CEB = ∠AED

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

√81 = 9

So, √83 will be closest to 9

Answer:

x=8in

Step-by-step explanation:

Let the unknown side=xin

Hypotenuse^2=opposite^2+adjacent^2

Hyp=17in

Opp=xin

Adj=15in

Hyp^2=opp^2+adj^2

17^2=x^2+15^2

17^2-15^2=x^2

289-225=x^2

64=x^2

x=√64

x=8in

Answer:

16

Step-by-step explanation:

Triangle area = (1/2)*b*h

Base = b = 4

Height = h = 8

Area = (1/2) * 4 * 8 =  16

The area of the polygon shown in the figure is 16 unit square.

A polygon is a closed figure made up of three or more line segments connected end to end.

Triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle = 1/2 x b x h

WE can see from the given figure;

The Base = b = 4

The Height = h = 8

The Area of figure = (1/2) * 4 * 8

The Area of figure =  16

Hence, the area of the polygon shown in the figure is 16 unit square.

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Answer:

[tex]x=-28[/tex]

Step-by-step explanation:

[tex]x+5=-23\\x=-23-5\\x=-28[/tex]

Answer:

x = -28

Step-by-step explanation:

x-(-5) = -23

Subtracting a negative is adding

x+5 = -23

Subtract 5 from each side

x+5-5 = -23-5

x = -28

Answer:

1/4

Step-by-step explanation:

# of black marbles/ total # of marbles

3/(3+4+5)

3/12

1/4

Answer:

1/4

Step-by-step explanation:

3 black marbles, 4 white marbles and 5 striped marbles. = 12 marbles

P(black) = number of black / total

             =3/12

               =1/4

Answer: 12/35

Step-by-step explanation:

Whenever two numbers are separated by multiplication sign, the numerators will multiply one another, same also applies to the denomintor.

2/5 x 6/7 = (2x6) / (5x7) = 12 / 35

The  simplest form of the given mixed number is 12 / 35.

It is required to convert the mixed number into simplest form.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

Whenever two numbers are separated by multiplication sign, the numerator will multiply with numerators same also applies to the denominator with denominator.

2/5 x 6/7  

2 multiply with 6 and 5 multiply with 7 we get,

= (2x6) / (5x7)

= 12 / 35

Therefore, the  simplest form of the given mixed number is 12 / 35.

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Answer:

Use the quadratic formula

x = [-b  +- sqr root (b^2 - 4*a*c)] / 2a

x = [-3 +- sqr root (9 - 4*1*-7)] / 2

x = (-3 +- sqr root (37) / 2

x1 = 1.5414

x2 =  -4.5414

Step-by-step explanation:

Answer:

I just took the test here's the answer

Step-by-step explanation:

Answer:

3.√

4.√

Step-by-step explanation:

similar rectangles have proportional sides so compare corresponding sides to check

1. 169/1.3 = 49/0.7 → 130 ≠70 no

2. 18.55/5.3 = 10.5/3.5 → 3.5 ≠ 3 no

3. 120/24 = 60/12 → 5 = 5 yes

4. 189/2.1 = 81/0.9 → 90 = 90 yes

Answer:

The required number of outcomes is 4 and the last option is correct.

Important information:

From the given tree diagram, it is clear that the total number of outcomes is 6.

The numbers greater than 1 on the spinner are 2 and 3.

The outcomes that result in a number greater than 1 on the spinner are:

heads, 2

heads, 3

tails, 2

tails, 3

Therefore, the required number of outcomes is 4 and the last option is correct.

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Answer:

Question 4. Option C,

Question 5. Option A

Step-by-step explanation:

Question 4.

Take a look at the procedure below;

[tex]34 / 5 = x / 6,\\34 * 6 = 5 * x,\\204 = 5 * x,\\\\x = 40.80\\\\Conclusion - Option C[/tex]

To solve this problem, you could have to cross - multiply, and through simple algebra, isolate x.

Question 5.

If Becky charges an amount per hour per baby, to determine the total amount she would earn, multiply the number of hours by the number of babies taken care of, and multiply that amount by the cost she demands per hour per baby;

[tex]Children = 3,\\Hours = 5,\\Amount Charged = 7,\\\\Profit = 3 * 5 * 7 = 105 Dollars,\\\\Conclusion - Option A[/tex]

Answer:

[tex]x=1/2[/tex]

Step-by-step explanation:

[tex]27 = 3^{4x+1}[/tex]

[tex]3^3 = 3^{4x+1}[/tex]

[tex]3=4x+1[/tex]

[tex]2=4x[/tex]

[tex]2/4=x[/tex]

The value of x in the given equation is 1/2

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is an equation, [tex]27 = 3^{4x+1}[/tex]

Solving for x,

3³ = [tex]3^{4x+1}[/tex]

Therefore,

3 = 4x+1

4x = 2

x = 2/4

x = 1/2

Hence, the value of x in the given equation is 1/2

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Answer:

d) √2/2

Step-by-step explanation:

cos∠E= 5/5√2= 1/√2=√2/2

Correct option is d)√2/2

Answer:

[tex]5(x - 2)(x+ 2)(x^2 + 4)[/tex]

Step-by-step explanation:

The expression given is:

[tex]5x^4 - 80\\\\5(x^4 - 16)\\\\5(x^4 - 2^4)\\\\5((x^2)^2 - (2^2)^2)\\\\[/tex]

Difference of two squares:

[tex]5(x^2 - 2^2)(x^2 + 2^2)\\\\5(x - 2)(x + 2)(x^2 + 2^2)\\\\5(x - 2)(x+ 2)(x^2 + 4)[/tex]

The factorized form of the given equation is [tex]5(x-2)(x+2)(x-2)(x+2)[/tex] and this can be determined by using the factorization method.

Given :

[tex]f(x) = 5x^4-80[/tex]

The following steps can be used in order to determine the factors of the given function:

Step 1 - Write the given function.

[tex]f(x) = 5x^4-80[/tex]

Step 2 - Take out 5 as common in the above function.

[tex]f(x) = 5(x^4-16)[/tex]

Step 3 - Now, try to factorize the above function.

[tex]f(x) = 5(x^4-2^4)\\f(x) = 5(x-2)(x+2)(x-2)(x-2)[/tex]

From the above steps, it can be concluded that the correct option is B).

For more information, refer to the link given below:

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2563[tex]\pi[/tex]

Step-by-step explanation:

Answer: its C

Step-by-step explanation:

Answer: Number 3 is the correct answer.

Step-by-step explanation:

Answer:

x=100

Step-by-step explanation:

Because they are vertical angles, AEG=FEB

You can see that FED+DEB=FEB

Therefore, 80+20=FEB=100

Since FEB=100 and FEB=AEG

AEG=100

Answer:

100°

Step-by-step explanation:

In this question, vertical angles are key. If you didn't know, vertical angles are basically opposites of each other. A pair of vertical angles are equal.

ACE = 20°

FED = 80°

FED and CEG are vertical angles (+the 20 from ACE), so your answer is 100°

hope this helps, brainliest is appreciated.

Answer:

Area = 25cm²

Step-by-step explanation:

Given

Length of a square = 4.89cm

Required

Estimate the area of the square

The question says that the length of the side of the square be approximated to 1 significant figure.

When 4.89cm is approximated, it gives 5cm.

At this point, the area of the square can be estimated.

Area = Length * Length

Area = 5cm * 5cm

Area = 25cm²

Hence, the estimated area of the square is 25cm²

Answer:

12

Step-by-step explanation:

We just plug in 8 for x and 3 for y which gives us 1/2 * 8 * 3 = 12.

Answer:

12

Step-by-step explanation:

1/2(8)(3)

4(3)

12

Answer:

The error was in step 3

Step-by-step explanation:

The first two steps are correct, the property of addition of internal angles of a triangle that equal [tex]180^o[/tex] is properly used, Also the addition of supplemental angles to total  [tex]180^o[/tex] is also properly used.

In step 3. there is an error. Notice how it should have been done:

[tex]\angle m+\angle n +\angle o=180^o\\\angle o + \angle p = 180^o\\then:\\\angle m+\angle n +\angle o=180^o=\angle o+\angle p\\\angle m+\angle n +\angle o=\angle o+\angle p[/tex]

Answer:

Your answer is mean absolute deviation.

Step-by-step explanation:

Answer:

62○

Step-by-step explanation:

To find the angle all you have to do is subtract 118○ from 180○ to get 62○. Because 180○ is a straight line! :)

Answer:

X = 62

Step-by-step explanation

To start we make x go next to 118 so they make a supplementary angle. We add x and 118 to make 180.

118 + X = 180, OR 180 - 118 = x

X = 62

Answer:

x < 5.1

Step-by-step explanation:

Let's define:

Using Law of Sines we can find x, as follows:

10/sin(95°) = 8/sin(α)

sin(α) = sin(95°)*8/10

α = arcsin(0.8) = 53.13°

β = 180° - 95° - 53.13° = 31.87°

x/sin(β) = 10/sin(95°)

x = 10/sin(95°)*sin(31.87°)

x = 5.3

On the other hand, we know that the addition of the two shorter sides of a triangle must be greater than the long side of the triangle. Therefore:

8 + 5.3 > 3x - 2

Solving:

8 + 5.3 + 2 > 3x  

15.3/3 > x

5.1 > x

or

x < 5.1

The value of x from the given inequality is x < 5.1

Inequality expressions are expressions that are not equal to each other

Given the following variables;

Using the sine law to determine the value of x

10/sin(95°) = 8/sin(α)

sin(α) = sin(95°)*8/10

α = arcsin(0.8) = 53.13°

β = 180° - 95° - 53.13° = 31.87°

x/sin(β) = 10/sin(95°)

x = 10/sin(95°)*sin(31.87°)

x = 5.3

Also, using the rule that states that the addition of the two shorter sides of a triangle must be greater than the long side of the triangle. Hence;

8 + 5.3 > 3x - 2

8 + 5.3 + 2 > 3x  

15.3/3 > x

5.1 > x

x < 5.1

Hence the value of x from the given inequality is x < 5.1

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Answer:

[tex]Initial- Velocity = 0\\Final- velocity = 25m/s\\Time = 6.0\\Acceleration = \frac{Final-velocity-initial-velocity}{time} \\Acceleration = \frac{25-0}{6} \\Acceleration = \frac{25}{6} \\Acceleration = 4.167[/tex]

Step-by-step explanation:

Answer: 1018 sq. mm.

Step-by-step explanation:

Area = πr^2

= π x 18^2

= 324π

The required area of a circle is 1018 millimeters² with a diameter of 36 millimeters.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

As per the question, we have

The diameter of the circle = 36 millimeters

The radius of the circle = diameter/2

The radius of the circle = 36/2 = 18 millimeters

The area of the circle = πr²

The area of the circle = π × 18²

The area of the circle = 3.14 × 324

The area of the circle = 1018

Thus, the required area of a circle is 1018 millimeters² with a diameter of 36 millimeters.

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Answer:

x=2

Step-by-step explanation:

5x - 6(x + 1) + 8 = 0

Distribute

5x -6x-6+8 =0

Combine like terms

-x+2 = 0

Add x to each side

-x+2+x = 0+x

2 =x

Answer:

a) 67.4°

b) 5.0 ft

Step-by-step explanation:

Now we have to use the trigonometric ratios to obtain the angle between the ladder and the level ground. Remember that the problem is a right angled triangle problem.

Let the hypotenuse of the triangle (length of the ladder) be c = 13 ft

Let the distance between the ladder and the ground be a

Let the height from the ground to the top of the ladder be b =12 ft

From;

Sinθ= opposite/hypotenuse

Sinθ= 12/13

Sinθ= 0.9231

θ=Sin^-1(0.9231)

θ= 67.4°

b) distance between the ladder and the foot of the building is obtained from

Cosθ= adjacent/hypotenuse

Adjacent= unknown

Hypotenuse= 13ft

θ= 67.4°

Cos(67.4°) = adjacent/13

Adjacent= cos (67.4°) ×13

Adjacent= 5.0 ft

Answer:

a. x ≈ 67°(nearest degree)

b. distance = 5. 1 ft (nearest tenth)

Step-by-step explanation:

A 13 ft ladder is placed on level ground leans against the side of a house . The ladder reaches a point that is 12 ft up the side of the house. The illustration forms a right angle triangle.

a. The right angle triangle formed has it opposite sides as 12 ft and it hypotenuse side as 13 ft. The angle formed between the ladder and the floor can be solved using sine ratio. Therefore,

let

x = angle

sin x = opposite/hypotenuse

sin x = 12/13

sin x = 0.92307692307

x = sin ⁻¹ 0.92307692307

x = 67.3801350509

x ≈ 67°(nearest degree)

b.  If the same 13 ft ladder is placed against the building using the same angle formed .

The distance between the the foot of the ladder and the foot of the building is the adjacent side of the triangle. Therefore, using the angle formed.

cos 67° = adjacent/hypotenuse

cos 67° = adjacent/13

cross multiply

adjacent = 13 cos 67°

adjacent = 13 × 0.39073112848

adjacent = 5.07950467036

distance = 5. 1 ft(nearest tenth)

Answer: C) f ≥ 35s - 200

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

She needs 35 frames (f) per second (s) ( we have to multiply the number of frames by the number of seconds) f ≥ 35s

She has already 200 frames (since we already have, we can subtract that to the needed frames per second)

f ≥35s -200  

Feel free to ask for more if needed or if you did not understand something.