Which of the following ordered triples is the solution to the system of equations?

2x − y − z = −1

3x + y − z = 2

x + y − 5z = −8

The volume of the cylinder as a function of its radius is V = 2πr^3

The given parameters are

Diameter = Height

This can be represented as

d = h

The radius of a cylinder is calculated as

r = d/2

This means that

d = 2r

Substitute d = 2r in d = h

h = 2r

The volume of a cylinder is

V = πr^2h

Substitute h = 2r in V = πr^2h

V = πr^2(2r)

Evaluate

V = 2πr^3

Hence, the volume of the cylinder as a function of its radius is V = 2πr^3

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Answer:

[tex]27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}[/tex]

Step-by-step explanation:

Rewrite 9 as 3²:

[tex]\implies 9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{(2 \cdot \frac{3}{2})}=3^3[/tex]

Therefore:

[tex]\implies 3^3= 3 \cdot 3 \cdot 3=27[/tex]

---------------------------------------------------------

Rewrite 27 as 3³:

[tex]\implies 27^{\frac{1}{3}}=\left(3^3\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{(3 \cdot \frac{1}{3})}=3^1[/tex]

Therefore:

[tex]\implies 3^1=3[/tex]

---------------------------------------------------------

Rewrite 125 as 5³:

[tex]\implies 125^{\frac{2}{3}}=\left(5^3\right)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 5^{(3 \cdot \frac{2}{3})}=5^2[/tex]

Therefore:

[tex]\implies 5^2=5 \cdot 5=25[/tex]

---------------------------------------------------------

Solution

In order, from smallest to largest:

[tex]27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}[/tex]

Answer:

answer for this question is alternative A (80, 60) & (95,85)

The number 1.092×[tex]10^{1}[/tex] is 15.6 times larger than 7×[tex]10^{-1}[/tex]

Given,

The first number = 1.092×[tex]10^{1}[/tex]  

The second number =7×[tex]10^{-1}[/tex]

Here,

Convert the given numbers to the simplest form

The first number 1.092×[tex]10^{1}[/tex] =1.092×10

=10.92

The second numbers 7×[tex]10^{-1}[/tex]= 7×0.1

=0.7

We know the division is one the basic arithmetic operations in the mathematics. It is the process of the splitting a particular amount or number into equal parts.

To find how many time larger 1.092×[tex]10^{1}[/tex] than 7×[tex]10^{-1}[/tex], we have to divide the first number by second number.

10.92 ÷ 0.7 =15.6

Hence, the number 1.092×[tex]10^{1}[/tex] is 15.6 times larger than 7×[tex]10^{-1}[/tex]

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Answer:

A=2.5×x

10cm=2.5×x

10÷2.5=2.5÷2.5×x

x=4

Answer:

addingadddddddddddddddddd

Answer:

he has $6 left.

Step-by-step explanation:

Answer:

$18.99 for each student

Step-by-step explanation:

First we need to find out how much he spent on each student for the calculators.

We can do that by dividing 84.14, the total, by the number of students, 14:

84.14/14 = 6.01

He spent 6.01 on each student and has 25 for each student, so we can subtract that:

25 - 6.01 = 18.99

Answer:

(0, 1 )

Step-by-step explanation:

2x + 5y = 5 → (1)

- 3x + 7y = 7 → (2)

to eliminate y multiply (1) by 7 and (2) by - 5 , then add the result

14x + 35y = 35 → (3)

15x - 35y = - 35 → (4)

add (3) and (4) term by term to eliminate y

29x + 0 = 0

29x = 0 ⇒ x = 0

substitute x = 0 into (1) and solve for y

2(0) + 5y = 5y

0 + 5y = 5

5y = 5 ( divide both sides by 5 )

y = 1

solution is (0, 1 )

The interval to find the true average tip is  (14.62,13.78).

Average is a number that is calculated by adding quantities together and dividing the total by the number of quantities.

The Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range

Given:

We know that the confidence interval = sample mean ± standard deviation substitute the values in it then confidence interval = 14.2  ±2.5/(35)^1/2

confidence interval = 14.2 ± 2.5/5.91

confidence interval = 14.2 ± 0.42

confidence interval = 14.2 + 0.42 ,

confidence interval = 14.2 - 0.42

confidence interval = (14.62,13.78)

So, an interval to estimate the true average tip is  (14.62,13.78).

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fraction of the volume of the atom taken by nucleus = 1.07*10^-13

Space occupied by the sphere is the volume of sphere.

A straight line passing from side to side through the center of the body especially a circle or sphere is known as diameter.

Volume of sphere = 4/3πr³

Diameter of an Atom = 2.00Â

Diameter of an nucleus = 9.50×10⁻⁵Â

Radius of an Atom = 1.00Â

[tex]\frac{4}{3}\pi r^3=\frac{4}{3}\pi (4.75*10^(-5))^3\\[/tex]

Volume of an Atom = [tex]\frac{4}{3}\pi r^3= \frac{4}{3}\pi 1^3=\frac{4}{3}\pi[/tex]

Volume of nucleus = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi (4.75*10^-5)^3\\=\frac{4}{3} \pi 107.1718*10^-15[/tex]

fraction of the volume of the atom taken by nucleus =

4/3π 107.17*10^-15/ 4/3π =107.17*10^-15 = 1.07 *10^-13

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Answer:

FH = 24

Step-by-step explanation:

HG = 13

FH = 37 - 13

= 24

Answer:

The value of FH is 24.

Step-by-step explanation:

The equation will be,

→ FHG = FH + HG

Then the value of FH will be,

→ 37 = FH + 13

→ FH = 37 - 13

→ [ FH = 24 ]

Hence, the value of FH is 24.

The possible number of flowers you sell is 3 to 25

The given parameters are:

Selling price = $5

Total cost of trip = $75

Bus ride = $15

If you earn enough to cover the total cost of the trip, the maximum numbers (Max) of flowers you sell is

Max = Total cost of trip/Selling price

This gives

Max = 75/5

Max = 25

If you earn enough to cover the bus ride, the minimum numbers (Min) of flowers you sell is

Min = Bus ride/Selling price

This gives

Min = 15/5

Min = 3

Hence, the possible number of flowers you sell is 3 to 25

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The interest rate of the account is 2%

From the question, we are to determine the interest rate of the account

From the compound interest formula, we have that

A = P(1 + r/n)^{nt}

Where A is the amount

P is the principal

r is the rate

n is the number of times compounded

t is the time in years

From the given information,

A = $1,325.71

P = $1,130

n = 6

t = 8 years

Thus,

1325.71 = 1130(1 + r/6)⁶⁽⁸⁾

1325.71 = 1130( 1 + r/6)⁴⁸

1325.71/1130 = ( 1 + r/6)⁴⁸

Take the 48th root of both sides

1.003333 = 1 + r/6

1.003333 - 1 = r/6

0.003333 = r/6

r = 6 × 0.003333

r = 0.019998

r ≈ 0.02

r ≈ 2%

Hence, the interest rate of the account is 2%.

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15 protrusions were counted by her.

Clearly, there are multiple ways to treat verruca. For this type of patient, we would try a prescription for Drysol to apply topically once daily. In many of these patients, the skin is too moist. In our practice, we write a prescription for physical therapy for ultrasound application to the verruca. There is no guarantee with any treatment for verruca. Vitamin A adjunct treatment is often instituted: approx 7500 IU /day for 3 weeks.

Let no. of protrusions be x

3 * x = -4 * (-x) - 15

3x-4x = -15

x = 15

Therefore 15 protrusions were counted by her.

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Answer:

131°

Step-by-step explanation:

Sum of all angles of a quadrilateral = 360°

We can find the unknown angle ∠B, by subtracting the sum of the angles ∠A, ∠C, ∠D from 360°.

∠A + ∠B + ∠C + ∠D = 360

105 + ∠B + 34 + 90  = 360

           ∠B +  229      = 360

                     ∠B       = 360 - 229

                           ∠B = 131°

Answer:

The measure of m<GHE is 49°, the correct option is B.

What is a Quadrilateral?

A quadrilateral is a polygon with four sides.

It is of various types,

Trapezoid, which have one pair of parallel sides,

Parallelogram, it has two pairs of parallel sides,

Rhombus, it has all sides equal,

Rectangle, opposite sides are parallel and equal, and,

Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.

The quadrilateral ABCD is ≅ quadrilateral EFGH

When two figures are congruent then by CPCTC, corresponding parts of congruent figures are congruent.

The measure of the angle

B = m<BCD = 90°

m<BAD = 131°

As the quadrilaterals are congruent,

By CPCTC

∠F = ∠FGH = 90°

m ∠FEH =  131°

The measure of m<GHE has to be determined.

The sum of the measures of all angle so of a quadrilateral is 360 degree.

The ∠F + ∠FGH + ∠FEH + ∠GHE = 360

90 +90+ 131 +∠GHE = 360

∠GHE = 49°

Step-by-step explanation:

Answer:

a. Price needs to decrease by 6 Bozats.

[tex]\sf b. \ \ \sf x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]

Explanation:

Equation: p = 200 - 6x

where:

a.

To sell an additional kilogram of snig that is (x + 1) kilogram of snig.

current price = 200 - 6(x + 1) = 200 - 6x - 6

b.

[tex]\rightarrow p = 200 - 6x[/tex]

[tex]\rightarrow - 6x = p-200[/tex]

[tex]\rightarrow x =\dfrac{ p-200 }{-6}[/tex]

[tex]\rightarrow x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]

Solving a quadratic equation, it is found that the largest possible value of a is of a = 5.

A quadratic equation is modeled by the following rule:

y = ax^2 + bx + c

The solutions of the equations are the values of x for which y = 0.

For this problem, the equation is:

a² - 6a - 9 = b.

b = -9 - a, hence we replace in the equation as follows;

a² - 6a - 9 = -9 - a

a² - 5a = 0.

Traditionally, the solutions are given using Bhaskara's formula, however, since the coefficient c is zero, we can solve the equation by elimination as follows:

a² - 5a = 0.

a(a - 5) = 0.

Then the solutions are:

5 > 0, hence the largest possible value of a is of a = 5.

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The expression is simplified to 6w

Algebraic expressions are expressions made up of terms, variables, factors, coefficients and constants.

They also consist of arithmetic operations such as addition, subtraction, multiplication, division, etc

Given the expression;

-2w+w+7w

Using the BODMAS rule, we have to add

-2w + 8w

6w

Thus, the expression is simplified to 6w

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The radius of 8th sphere is 3/2.

The 8th sphere's center and the hexagon's two opposing ends should form an isosceles triangle. Then put up another triangles between the point of tangency of the 7th and 8th spheres, and the point of tangency between the 7th sphere and 2 of the original spheres on different sides of the hexagon. Each triangle's side length should be expressed in terms of r (the sphere's 8 radius) and h. (the height of the first triangle). The values of h and r may then be determined by setting up two equations for the two triangles using the Pythagorean Theorem.

(1+r)² = [tex]2^{2}[/tex] + [tex]h^{2}[/tex]

(3√2)² =3² + (h+r)²

r= 3/2

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Answer:

y = x + 5

Step-by-step explanation:

Slope: m = (y2-y1)/(x2-x1)

m = (16 - 5)/(9 - 0) = 9/9 = 1

Using m = 1, y = 5, x = 0

then y = mx + b

5 = 1(0) + b

b = 5

so y = x + 5

The required subtraction problem that is represented on the number line is 3 -(-5). Option B is correct.

Given that,
To determine the subtraction problem that is represented on the number line.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
The line marked above the number line from -5 to 3
The subtraction problem would be given as 3 - (-5)

Thus, the required subtraction problem that is represented on the number line is 3 -(-5). Option B is correct.

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Since questions seem to be incomplete,

The given solution is based on the question given below,
Which subtraction problem is represented by the number line?

A: 3-5

B: 3 - (-5)

C: 3-8

D: 3-(-8)

x+12+4x-16= 6x-13

5x-4=6x-13

-4=x-13

x=9

9+12+4(9)-16

21+36-16

57-16= 41

JL=41 units

The value of a is 2.5

As FG is the line and M is the midpoint of the line

  F   ______________·_________________G

                                    M

So by this, we have that

    FG = FM + MG

Where FM = MG as M is the midpoint of the line.

Therefore FG = 2FM

As it is given that FM = 8a + 1 and FG = 42

Now putting the values we have

42 = 2( 8a + 1)

21 = 8a + 1

20 = 8a

a = 2.5

Therefore the value of a is 2.5.

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The number after rounding off to the nearest tenth will be 9.4

In this question, we have been given that Miguel made up an equation in which three times of square of a particular number equals 265. We have to set up the equation according to this.

Taking the number as 'x'. We get the equation according to the condition :

               => 3x² = 265

By solving this equation we get :

               =>  3x² = 265    =>  x² = 88.3

               => x = 9.39

We get x = 9.39. By rounding off x to the nearest tens, we get x = 9.4

Hence, the number to the nearest tenth will be 9.4

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Pattern uses 6233.76 inches² fabric.

Firstly we will convert units in required form. Therefore, converting equivalent of yard² in inches². As per the given information, 1 yard = 3 feet and 1 foot = 12 inches.

As 1 foot = 12 inches, so, 3 feet = 36 inches, which is further equal to 1 yard.

Now, 1 yard² = (36 inches)²

1 yard² = 1296 inches²

Coming back to the problem, we will now calculate inches² from fabric measurement in yard². So, relating the units for conversion.

1 yard² = 1296 inches²

4.81 yard² = 1296 × 4.81

Performing multiplication

Measurement of 4.81 yard² in inches² = 6233.76

Hence, the pattern uses 6233.76 inches² fabric.

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Answer:

267/5 ( or ) 53.2

Step-by-step explanation:

Note : -

□ means 90°

2x - 42 + 3x + 45 + 90 = 360

2x + 3x + 45 - 42 + 90 = 360

5x + 3 + 90 = 360

5x + 93 = 360

5x = 360 - 93

5x = 267

x = 267/5 ( in fraction )

    ( or )

x = 53.2° ( in decimal )