Which is a solution to the following system of inequalities?

A. (6,6)
B. (7,8)
C. (8,7)
D. (9,7)

Equivalent expressions are expressions that have the same value, and can be used interchangeably.

The result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

The expression is given as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex]

Rewrite the expression as:

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})[/tex]

Evaluate the roots

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})[/tex]

Open the brackets

[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})[/tex]

The above expression cannot be further simplified.

Hence, the result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]

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The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

We have to determine, the sum of the given expression.

According to the question,

Expression; [tex]2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})[/tex]

To determine the sum of the given expression following all the steps given below.

Rewrite the expression term in the form of their cubes,

[tex]\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex]

Hence, The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].

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Answer:

105°.

Step-by-step explanation:

1) to calculate m(∠ABC): m(∠ABC)=180-m(∠BAC)-m(∠(ACB)=180-90-65=25°;

2) note, m(∠ABC)=m∠(ABD)=25°, then it is possible

3) to calculate m(∠BAD): m(∠BAD)=180-m(∠ABD)-m(∠ADB)=180-25-50=105°.

Answer:

(100-12) - 3

Step-by-step explanation:

we dont know what the cost of the shirts are so that one should be it.

Answer:

1000x or 1000 thousand times greater

Step-by-step explanation:

every decimal to the left is 10x greater than the one right of it.

Answer:

[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]

Step-by-step explanation:

[tex]4w^2+9w=-2[/tex]

[tex]4w^2+9w+2=0[/tex]

[tex]w^2+9w+8=0[/tex]

[tex](w+1)(w+8)=0[/tex]

[tex](4w+1)(w+2)=0[/tex]

[tex]w_1=-\frac{1}{4},w_2=-2}[/tex]

[tex] =( \frac{1}{2} \times 10.4 \times 16.9) {ft}^{2} \\ = (5.2 \times 16.9) {ft}^{2} \\ = 87.88 {ft}^{2} [/tex]

Answer:

The area of the triangle is 87.88 square feet.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

x = 7

Step-by-step explanation:

you can create a proportion:

PT / ST =  PQ / RQ

36 / 30 = (5x+13) / (6x-2)

cross-multiply:

36(6x-2) = 30(5x+13)

distribute:

216x - 72 = 150x + 390

216x = 150x + 462

66x = 462

x = 7

The value of x for the given triangle sides is x = 7.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.

Given that the side PQ = 5x + 13 and the QR is 6x- 2. The value of x will be calculated by the concept of similarity.

PT / ST =  PQ / RQ

36 / 30 = (5x+13) / (6x-2)

Cross-multiply the equations,

36(6x-2) = 30(5x+13)

Distribute:

216x - 72 = 150x + 390

216x = 150x + 462

66x = 462

x = 7

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Answer:

Cost of each share is [tex]6Rs[/tex]

Step-by-step explanation:

Let the cost be [tex]5x,7x,4x[/tex]

We have

[tex]5x+7x+4x=96\\\\16x=96\\\\x=6[/tex]

Cost of each share is [tex]6Rs[/tex]

Answer:

6, 60, 0.6, 600 are the answers

the questions all use the same digits but that the powers of 10 are different between the dividends and divisors for some

Step-by-step explanation:

Answer:

$0.73

Step-by-step explanation:

Let's say an orange costs O dollars and a grapefuit costs G dollars.

We add G dollars for each grapefuit and O dollars for each orange, so, for example, 12 grapefuit = G added 12 times = 12 *G = 12G

a.

6G = 10O

12G + 24O = 12

6 grapefuit = 6G = 10 oranges = 10O

b.

6G = 10O

12G + 24O = 12

We can solve this using substitution. First, we can solve the first equation for G. After that, we can plug that into the second to find O and go from there.

6G = 10O

divide both sides by 6 to remove the coefficient for G

G = (10/6)O

plug that into the second equation

12*(10/6)O + 24O = 12

20O + 24O = 12

44O = 12

divide both sides by 44 to solve for O

O=12/44 = 6/22

6G = 10O

6G = 60/22

divide both sides by 6 to solve for G

10/22 = G

c.

These solutions mean that an orange (O) costs 6/22 dollars and a grapefuit (G) costs 10/22, so 1O + 1G = 16/22 dollars ≈ $0.73. Note that O and G are kept as fractions because they are not exact dollar amounts, e.g. 0.27 repreating

Answer:

Step-by-step explanation:

Since B is the right angle, AC is the opposite side - hypotenuse.

Use Pythagorean and find the missing side, AB:

There is no info given to link the triangles ABC and XYZ and hence can't provide solution to any dimension of XYZ.

If the scale factor was given as k, then XZ would be:

Answer:

LCM(57624, 416745) = 23,337,720 or  LCM = 23337720

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 57624 is:

2 x 2 x 2 x 3 x 7 x 7 x 7 x 7  =>  23 x 31 x 74

Prime Factorization of 416745 is:

3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7  =>  35 x 51 x 73

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 3, 3, 3, 3, 3, 5, 7, 7, 7, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7 x 7 = 23337720

In exponential form:

LCM = 23 x 35 x 51 x 74 = 23337720

LCM = 23337720

Therefore,

LCM(57624, 416745) = 23,337,720

Answer:

(71.10-57)/3=amount of gigabytes, 14.10/3=4 gigabytes allowed

Step-by-step explanation:

$71.10-$57=$14.10, the amount of money that Jonathan can spend on gigabytes. Then, determine how many times 3 can go into 14.10: 4 times. Jonathan can use four gigabytes and keep his bill under $71.10 a month.

Step-by-step explanation:

Simply divide the percent by 100 and multiply by the number. For example, 48.9 /100 x 264 = 129.096 or 0.489 x 264 = 129.096

Rounded to nearest hundredth

= 129.10

Answer:129.10

Step-by-step explanation:

Simply, the equation for the percentage value of a number is:

x*(z%/100%)=y

where x is your initial value, z is your percentage value, and y is the resultant value

for this question, the equations gives us as follows

264*(48.9%/100%)=129.096=129.10

Answer:

Step-by-step explanation:

5

+

1

=

3

+

7

5x+1=3x+7

Solve

1

Subtract  

1

1

from both sides of the equation

5

+

1

=

3

+

7

5x+1=3x+7

5

+

1

−

1

=

3

+

7

−

1

5x+1{\color{#c92786}{-1}}=3x+7{\color{#c92786}{-1}}

2

Simplify

Subtract the numbers

Subtract the numbers

5

=

3

+

6

5x=3x+6

3

Subtract  

3

3x

from both sides of the equation

5

=

3

+

6

5x=3x+6

5

−

3

=

3

+

6

−

3

5x{\color{#c92786}{-3x}}=3x+6{\color{#c92786}{-3x}}

4

Simplify

Combine like terms

Combine like terms

2

=

6

2x=6

5

Divide both sides of the equation by the same term

2

=

6

2x=6

2

2

=

6

2

\frac{2x}{{\color{#c92786}{2}}}=\frac{6}{{\color{#c92786}{2}}}

6

Simplify

Cancel terms that are in both the numerator and denominator

Solution

=

3

Answer:

1) the baseball will take approx 0.514 seconds to move 18 meters.

35/1 = 18/x

x = 0.514s

2)  the car's average speed is 60 km per hour.

870/14.5 = x/1

x = 60h

Answer:

He earn approximately $2.14 everyday

Step-by-step explanation:

hope this helps :3

Answer:

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{8+3}{12}[/tex] = [tex]\frac{11}{12}[/tex] ≈ 1

The correct answer is the last one (C)

Step-by-step explanation:The second way of approximating a square root is to use a calculator. Most calculators have a radical sign on them. To find the square root of a number, we enter the radical sign, then the value and press enter. This will give us a decimal approximation of the square root.

[tex]m \cdot n = \sqrt{m^2 -n^2}\\\\\text{When m =5 and n =3,}\\\\\\5\cdot 3 = \sqrt{5^2 -3^2} =\sqrt{25 -9} = \sqrt{16} = 4[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming:}[/tex]

[tex]\mathbf{m\times n = \sqrt{(m^2 - n^2)}}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{\rightarrow 5\times 3 = \sqrt{(5^2 - 3^2)}}[/tex]

[tex]\mathbf{\rightarrow 15 = \sqrt{(5\times5 - 3\times3)}}[/tex]

[tex]\mathbf{\rightarrow 15 = \sqrt{(25 - 9)}}[/tex]

[tex]\mathbf{\rightarrow 15 = \sqrt{16}}[/tex]

[tex]\mathbf{15\neq4}[/tex]

[tex]\huge\textbf{Thus, this answer should be:}[/tex]

[tex]\huge\boxed{\boxed{\textsf{This statement is most likely: \boxed{\textsf{FALSE}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

$31.68

Step-by-step explanation:

Multiply each by the correct number

almond= 1.4*9.15= 12.81

cashews= 10.75* 0.8= 8.6

Peanuts= 3.95 * 2.6= 10.27

Add them all up

12.81+8.6+10.27

you’ll get 31.68

Answer:

The answer is t^-1 (r)=120r/120-r

i hope this is right sry if im wrong have a good day :)

The inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).

According to the question

Janine is building a circuit that contains two lightbulbs in parallel.

One of the lightbulbs has a resistance of 120 ohms.

R = 120ohms

r = resistance of the second lightbulb

t = total resistance in the circuit  

[tex]t = \frac{120r}{r+120}[/tex]

Now,

The inverse of Janine's equation in which we will make r independent

[tex]t = \frac{120r}{r+120}[/tex]

[tex]t(r+120) = 120r[/tex]

[tex]tr + 120t = 120r[/tex]

[tex]120t = 120r - tr[/tex]

[tex]120t = r(120-t)[/tex]

[tex]r = \frac{120t}{120-t}[/tex]

Hence, the inverse of Janine's equation is [tex]r = \frac{120t}{120-t}[/tex] .

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Answer:

  y = x³ +2x² +x -1

Step-by-step explanation:

The attachment shows the four points we can read from the graph and the cubic regression function that fits them.

  y = x³ +2x² +x -1

_____

Additional comment

It is useful to become familiar with the regression function capability of your graphing calculator or spreadsheet. Free or inexpensive apps are available for tablet or phone, and on the web.

Answer:

$3.74

Step-by-step explanation:

Proportions:

6 pounds ⇔ $22.44

1 pound ⇔ $ C

C = 22.44*1/6

C = $3.74

Answer:

[tex]\frac{\frac{1}{4}}{1}=\frac{\frac{5}{6}}{x}[/tex]

Step-by-step explanation:

Per = 1

[tex]\frac{1}{4}[/tex]

So, if we were to solve:

[tex]\frac{1}{4}=\frac{5}{6x}[/tex]

[tex]\frac{1}{4}\cdot \:6x=1\cdot \:5[/tex]

[tex]\frac{3}{2}x=5[/tex]

[tex]\frac{3}{2}x\cdot \:2=5\cdot \:2[/tex]

[tex]3x=10[/tex]

[tex]\frac{3x}{3}=\frac{10}{3}[/tex]

[tex]x=\frac{10}{3}[/tex]

Troy can make [tex]\frac{10}{3}[/tex] dozen of cupcakes.

Answer:

135%

Step-by-step explanation:

Answer:

Option B

176

Step-by-step explanation:

take 11 to the next side of the equation making the division multiplication getting us 16×11=176

Answer:

x=12

Step-by-step explanation:

4x-6+2x=18

2x-6=18

2x=24

x=12

Answer:

the asnwer is (2,3)

Step-by-step explanation:

Answer:

parallelogram is the answer

Answer:

Step-by-step explanation:

The quadrilateral is a parallelogram ( more precisely is the rhombus )