what is an equivalent expression ​

Answer:

[tex]x = 45 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] {3}^{2 log_{3}(x) + log_{3}(5) } = {3}^{ 4log_{3}(15) } [/tex]

[tex] {3}^{ log_{3}( {x}^{2} ) } {3}^{ log_{3}(5) } = {3}^{ log_{3}( {15}^{4} ) } [/tex]

[tex]5 {x}^{2} = {15}^{4} [/tex]

[tex] {x}^{2} = \frac{ {15}^{4} }{5} [/tex]

[tex]x = \frac{ {15}^{2} }{ \sqrt{5} } ( \frac{ \sqrt{5} }{ \sqrt{5} } )[/tex]

[tex]x = \frac{ {15}^{2} \sqrt{5} }{5} = 45 \sqrt{5} [/tex]

Answer: C, {(1, -4), (4, -1)}

Step-by-step explanation: Where the two graphs meet are their solutions, and the points where they meet are {(1, -4),(4,-1)}.

The number of the solutions of the equations are 2 that are (1, 0) and (-3, 4).

The equations are given below.

y = x² + x − 2  ...1

y = – x + 1       ...2

From equations 1 and 2, we have

x² + x − 2 = – x + 1

x² + 2x − 3 = 0

Then the factor of the equation will be

x² + 3x – x − 3 = 0

    (x + 3)(x – 1) = 0

                     x = 1, –3

Then  the value of y will be

At x = 1, we have

y = -1 + 1

y = 0

At x = -3, we have

y = -(-3) + 1

y = 4

Then the number of the solutions of the equations are 2 that are (1, 0) and (-3, 4).

The graph is given below.

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In the given diagram, the length of OQ is 11

From the question, we are to determine the length of OQ

From the given information,

OP = 17

QP = 6

In the diagram, we can observe that

OQ + QP = OP

∴ OQ + 6 = 17

Subtract 6 from both sides

OQ + 6 - 6 = 17 - 6

OQ = 11

Hence, the length of OQ is 11

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[tex]\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11[/tex]

Answer:

Step-by-step explanation:

Comment

There is only 1 number under probability that is greater than or equal to 5. That number is 15

There are 4 possible answers. Only 1 is successful.

Answer: P(y≥5) = 1/4 or 0.25

Answer:

$0.16

Step-by-step explanation:

unit price = price of carton / number of eggs

unit price = $1.92/12

unit price = $0.16

The benefit value of the widget on the books of abc is $8

The given parameters are:

Cost price = $5 cash

Selling price = $8 account

The benefit value of the widget is the same as their selling price on account

Hence, the benefit value of the widget is $8

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Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

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The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40, 10, 30
see picture

Step-by-step explanation:

Based on the calculations on these invertible functions, f⁻¹(f(6.022)) is equal to 6.022 and f⁻¹(-10) + f(-6) is equal to -16.

An invertible function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a function and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property, we have:

f⁻¹(f(6.022)) = 6.022.

From the table, we have:

f⁻¹(-10) = -6

f(-6) = -10

Therefore, f⁻¹(-10) + f(-6) is given by:

f⁻¹(-10) + f(-6) = -6 - 10

f⁻¹(-10) + f(-6) = -16.

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Answer:

(3(3) × 3(4) ) ÷ 3(2)

(9 × 12) ÷ 6

108 ÷ 6

18

Answer:

[tex]n {}^{2} + 3[/tex]

Triangle JKL was rotated 90 degrees about the origin and translated 2 units left to form triangle J"K"L"

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Triangle JKL was rotated 90 degrees about the origin and translated 2 units left to form triangle J"K"L"

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Answer:

Step-by-step explanation:

Answer:

The second statement is true.

Step-by-step explanation:

Draw the corresponding parabola and use it to verify  all statements.

Answer:

The function is negative for all real values of x where

x < –3 and where x > 1.

Step-by-step explanation:

The answer above is correct.

Answer:

70 is the right answer....

Answer:

70 ways

Step-by-step explanation:

8 C 4 =   8 ! / ( 4! * 4!) = 70 ways

The scale factor for triangle ABC to A'B'C' is 2

The complete question is in the attached image

From the attached image, we have the following corresponding sides

AC = 4 cm

A'C' = 8 cm

The scale factor is then calculated as:

Scale factor = A'C'/AC

This gives

Scale factor = 8cm/4cm

Evaluate the quotient

Scale factor = 2

Hence, the scale factor for triangle ABC to A'B'C' is 2

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Answer:

x = 7 y = 4 JKL = 262 degrees

Step-by-step explanation:

According to a circle theorem, sum of the opposite angles in a circle which touch its circumference must equal 180, hence:

7x + 131 = 180

x = 7

According to another theorem, a quadrilateral inside a circle must equal 360 so:

99 + 7(7) + 131 + 11(7) + y = 360

Note: remember to substitute 7 for all values of x

y = 4

The angle subtended by an arc at the centre is twice the angle subtended at the circumference

Following this rule, we can conclude that:

2(7x) or 2(2 x 7) = 2(49) which is 98

Lastly, 360 - 98 = 262

Answer: I dont really understand your questions

Step-by-step explanation: find the solution to your problem

Answer:

20

Step-by-step explanation:

each year each child will get additional age

example 5 children average of the age 20 years old.

after 20 years all of them.will be 20+20=40 years old.

the group of the children not changing but average of the groups will be increase in 20 years.

Answer:

false

Step-by-step explanation:

so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years

a)

We know that a 4-sided polygon's angles add up to 360 degrees

so to find x:

360-(69+118+84)=89 degrees

b)

For a 4-sided polygon we also know that the outside angles add up to 360 degree.

so to find p:

360-(100+62+106)=92 degrees

Hope it helps!

Answer:

D) -12

Step-by-step explanation:

[tex]3(x-4)+(2-x)-x^2[/tex]

Replace X With 5

[tex]3(5-4)+(2)(5)-5^2[/tex]

[tex]=-12[/tex]

I Hope This Helps

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Answer:

Option C is equal to 7^1/3

Answer:

[tex]\frac{x-22}{(x+2)(x-4)}[/tex]

Step-by-step explanation:

multiply the numerator/denominator of the first fraction by (x - 4)

multiply the numerator/denominator of the second fraction by (x + 2)

this ensures that the fractions have a common denominator

[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]

= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator

= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]

=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]

The value of the x will be 25. The force involved vertically to the surface of an object per unit area is pressure.

The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.

The given data in the problem is;

The base of the block of metal is a rectangle of 20 cm by x cm.

The block exerts a force of 1500 newtons on the ground. The pressure on the ground is 3 newtons/cm²

The area of the rectangle;

A = L × B

A=20 × x

[tex]\rm P = \frac{F}{A}\\\\ 3 N / cm^2 = \frac{1500 N}{20 \times x } \\\\ x= 25[/tex]

Hence the value of the x will be 25.

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Answer:

x=3 and y = -3/2

A method for solving a system of linear equations where you add or subtract equations to eliminate a variable. Eliminating one variable by combining two equations with a common term with adding or subtracting.

___________________________________

Let's solve your system by elimination.

4x−2y=15;2x+2y=3

4x−2y=15

2x+2y=3

Add these equations to eliminate y:

6x=18

Then solve 6x=18 for x:

6x=18

6x/6 = 18/6 (Divide both sides by 6)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

4x−2y=15

Substitute3 for x in 4x−2y=15:

(4)(3)−2y=15

−2y+12=15(Simplify both sides of the equation)

−2y+12+−12=15+−12(Add -12 to both sides)

−2y=3

-2y/-2 = 3/-2 (Divide both sides by -2)

y = -3/2

Answer:

x=3 and y = -3/2

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The choice is tangent rule and the distance from the base to the tower is 3. 98 meters

The trigonometric ratio to use is

tan α = opposite side/ adjacent side

This is so because the angle 86° is facing the side of the distance from the top to the base

The choice is tangent rule

adjacent  = x

Angle = 86°

Opposite side = 57

We have

tan 86° = 57/x

14. 300= 57/x

x = 57 ÷ 14.300

x = 3.98meters

Thus, the choice is tangent rule and the distance from the base to the tower is 3. 98 meters

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A graph is a way to represent a lot of data in such a visual format. The graph for the given situation can be drawn as shown below.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The graph for the given situation can be drawn as shown below, where the x-axis represents the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and the y-axis represents the total cost of the rice.

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