Simplify each expression. y¹/₂ . y³/₁₀

Answer:

y = -2

Step-by-step explanation:

Given equation:

[tex]3(-4y-5)=8y+25[/tex]

Distribute:

[tex]\implies 3 \cdot -4y - 3 \cdot 5=8y+25[/tex]

[tex]\implies -12y - 15=8y+25[/tex]

Add 15 to both sides:

[tex]\implies -12y - 15+15=8y+25+15[/tex]

[tex]\implies -12y =8y+40[/tex]

Subtract 8y from both sides:

[tex]\implies -12y-8y =8y+40-8y[/tex]

[tex]\implies -20y =40[/tex]

Divide both sides by -20:

[tex]\implies \dfrac{-20y}{-20} =\dfrac{40}{-20}[/tex]

[tex]\implies y =-2[/tex]

Now we have to,

→ solve for the required value of y.

Let's solve the problem,

→ 3(-4y - 5) = 8y + 25

→ -12y - 15 = 8y + 25

→ -12y - 8y = 25 + 15

→ -20y = 40

→ y = -40/20

→ [ y = -2 ]

Hence, the value of y is -2.

We will get  lne¹⁰ itself after simplifying the given expression lne¹⁰.

So,

Then,

Therefore, we will get  lne¹⁰ itself after simplifying the given expression lne¹⁰.

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Amount $593.84 will be in the account after five years.

According to the question we have been given that the

 amount invested initially = $500

annual interest rate = 0.035

 Time = 5 years.

The formula for the future value is given as

         [tex]FV = a(1 + r)^{t}[/tex]        (1)

where , FV = future value

              a = amount invested initially

               r = annual interest rate

              t = time

putting the required values in equation (1) we get

       [tex]FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}[/tex]

       FV = 500*1.188

       FV = $ 593.84

Thus, $593.84 will be the amount in the account after five years.

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Answer:

It depends on what that number is but -4+29 is equal to 29-4; making the answer to -4+29=5.

Step-by-step explanation:

I think this is one of those trick questions!

I'm going to say the answer is... 90°

because it states within the question that ∠A and ∠B are vertical angles

That is my educated guess. I hope it's helpful!

Pls let me know if my answer is incorrect.

The system of equations are:

25s + 15j = 205

s - j = 5

Where:

s = number of soda bought

j = number of juice bottles bought

In order to determine the number of bottles of soda and juice bought, two sets of equations would need to be formed based on the information provided in the question. The equations would be solved simultaneously.

Grams of sugar in the soda bottle + grams of sugar in the juice bottle = total grams of sugar

difference in the number of bottles bought

25s + 15j = 205

s - j = 5

The methods that can be used to solve the simultaneous equations :

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Answer:

4x - 5 = 131 where x is the first number.

Step-by-step explanation:

Let the first number be x.

Seconder number = 2x + 7.

Third number = x - 12.

So, the equation is :-

x + 2x + 7 + x - 12 = 131

4x - 5 = 131

4x = 136

x = 34

First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.

The factors of equation are 5 and 3.

Rewriting the equation -

x² - 8x + 15 = 0

ax² + bx + c = 0

Factorizing the equation such that -

The suitable factors that can be used for solving the expression are 5 and 3.

x² - 5x - 3x + 15 = 0

x(x - 5) -3 (x - 5) = 0

(x - 5) (x - 3) = 0

(x - 5)= 0

x = 5

(x - 3) = 0

x  = 3

Hence, the two factors of expression are 5 and 3.

To check the factors, we will keep each value of x to see if Left Hand Side is equal to Right Hand Side or not

When x = 5

x² - 8x + 15 = 0

5² - 8×5 + 15 = 0

25 - 40 + 15 = 0

-15 + 15 = 0

0 = 0

When x = 3

x² - 8x + 15 = 0

3² - 8×3 + 15 = 0

9 - 24 + 15 = 0

- 15 + 15 = 0

0 = 0

Since for both factors Left Hand Side is equal to Right Hand Side, thus, 5 and 3 are correct factors of the equation.

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Answer: 8,938 [tex]\frac{8}{9}[/tex] or 8,938.8889 meters per second

Step-by-step explanation:

     To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).

     What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!

     Here is the process you would take to solve your problem:

➜ If we have the units [tex]\frac{hour}{hour}[/tex], they "cancel" out to become one. This way, we make sure we end up with the correct units, [tex]\frac{meters}{second}[/tex].

➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.

[tex]\displaystyle 20,000\; \frac{miles}{hour}*\frac{1 \;hour}{3,600\; seconds} *\frac{1,609\;meters}{1\;mile}=\frac{20,000*1*1,609\;meters}{3,600\;seconds} =\frac{32,180,000\;meters}{3,600\;seconds} = 8,938.89\; \frac{meters}{second}[/tex]

     In other words;

           8,938.89 meters per second

The answer is 127.5146314631

What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.

To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:

To convert integer 87 to octal, follow these steps:

Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent octal number.

87 / 8 = 10 with remainder 7

10 / 8 = 1 with remainder 2

1 / 8 = 0 with remainder 1

Here is the answer to 87 decimal to octal number:

127

For converting decimal fraction 0.65 to octal number, follow these steps:

Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).

Then just write out the integer parts from the results of each multiplication to get equivalent octal number.

0.65 × 8 = 5 + 0.2

0.2 × 8 = 1 + 0.6

0.6 × 8 = 4 + 0.80000000000001

0.80000000000001 × 8 = 6 + 0.40000000000009

0.40000000000009 × 8 = 3 + 0.20000000000073

0.20000000000073 × 8 = 1 + 0.60000000000582

0.60000000000582 × 8 = 4 + 0.80000000004657

0.80000000004657 × 8 = 6 + 0.40000000037253

0.40000000037253 × 8 = 3 + 0.20000000298023

0.20000000298023 × 8 = 1 + 0.60000002384186

Here is the answer to 0.65 decimal to octal number:

0.5146314631

Therefore, decimal number 87.65 converted to octal is equal:127.5146314631

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Answer:

(0, - 9 )

Step-by-step explanation:

x = 2y + 18 → (1)

5x = - 3y - 27 → (2)

substitute x = 2y + 18 into (2)

5(2y + 18) = - 3y - 27

10y + 90 = - 3y - 27 ( add 3y to both sides )

13y + 90 = - 27 ( subtract 90 from both sides )

13y = - 117 ( divide both sides by 13 )

y = - 9

substitute y = - 9 into (1)

x = 2(- 9) + 18 = - 18 + 18 = 0

solution is (0, - 9 )

We get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.

We are given the two functions as:

g (x) = x - 3 and h (x) = x² + 6

Now, we will first find h (1)

h (1) = (1)² + 6

h(1) = 1 + 6

Add them, we get:

h (1) = 7

Now, we will find g (1):

g (1) = 1 - 3

g (1) = - 2

Now we will find the expression  h(1) × g(1):

h(1) × g(1) = 7 × ( - 2 )

h(1) × g(1) = - 14

Therefore, we get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.

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The inverse of the expression y = 5 · (x - 6)² - 5 is x = √[(y + 5) / 5] + 6. (Correct choice: D)

According to the statement we have a function of the form y = f(x) and we need to find its inverse, that is, finding the equation of x in terms of y. This can be done by using algebra properties:

y = 5 · (x - 6)² - 5                          Given

y = 5 · [(x - 6)² - 1]                         Distributive property

y / 5 + 1 = (x - 6)²                          Compatibilities with multiplication and addition / Existence of additive and multiplicative inverses / Associative and modulative properties

x - 6 = √(y / 5 + 1)                         Definition of square root / Symmetric property

x = √(y / 5 + 1) + 6                         Compatibility with addition / Existence of additive inverse / Associative, commutative and modulative properties

x = √[(y + 5) / 5] + 6                      Addition of fractions with different denominators / Result

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

[tex]\mathsf{\dfrac{3x^2 - 5x + 1}{x}}\\\\\mathsf{= \dfrac{3(-2)^2 - 5(-2) + 1}{-2}}\\\\\mathsf{= \dfrac{(3)(4) - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (-10) + 1}{-2}}\\\\\mathsf{= \dfrac{12 + 10 + 1}{-2}}\\\\\mathsf{= \dfrac{22 + 1}{-2}}\\\\\mathsf{= \dfrac{23}{-2}}\\\\\mathsf{-11 \dfrac{1}{2}}\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{-11\dfrac{1}{2}}}}\huge\checkmark[/tex]

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

The inverse function returns the original value for which the output of a function was given.

The value of  f(x) = 10x - 10 is -110.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.

Lett the function be F(x) = 10x - 10

To differentiate with respect to X

F⁻¹(x) = 10

F( f⁻¹(x)) = F(10)

F( f⁻¹(x)) = -10x -10

Substitute the value of X = 10, then we get

F( f⁻¹(x)) = -10(10)-10

simplifying the above equation, we get

F( f⁻¹(x)) = -100-10

F( f⁻¹(x)) = -110

Therefore, the value of (f ⁰ f⁻¹)(d) = -110.

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Answer:

Center: (0,0)

Vertices: (0,-5), (0,5)

Foci: (0,-3) (0,3)

Step-by-step explanation:

Answer:

f(-8)= -7660

Step-by-step explanation:

f(-8)= 3(-8)^2·5(-8)+20

The value of the expression √75 + √125 is 5 (√3 + √5 ).

A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.

A square root is a factor of a number that yields the original number when multiplied by itself.

Consider the expression √75 + √125,

Let's assume x = √75 + √125

Now,

75 = 5 × 15 = 5 × 3 × 5

125 = 5 × 25 = 5 × 5 × 5

Therefore,

x = √75 + √125

x = √ [ 5 × 3 × 5] + √ [ 5 × 5 × 5 ]

x = 5√3 + 5√5

x = 5 × [ √3 + √5 ]

x = 5 × [ 1.73 + 2.24 ]

x = 5 × 3.97

x = 19.85

√75 + √125 = 19.85

Hence, the value of √75 + √125 is equal to 19.85.

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The surface area is the sum of the area of the surfaces. The surface area of the box is 360x^2 - 216x

The formula for calculating the surface area of a box is expressed according to the equation:

Surface area = 2(lw + wh +lh)

Given the following parameters

length = 6x

width = 12x - 9

height = 6x

Substitute

Surface area = 2(6x(12x-9) + (12x-9)(6x) +(6x)(6x))

Expand

Surface area = 2(72x^2-54x) + (72x^2-54x) + 36x^2)

Surface area = 2(180x^2-108x)

Surface area = 360x^2 - 216x

Hence the surface area of the box is 360x^2 - 216x

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The the distance between the school and Nokesville be on the map is 0.7 inches.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

The distance between the school and Target is 4.2 miles and on a map the ratio is 0.5 inches is equal to 3 miles that is :

3 miles = 0.5 inches on map

Now to find the distance between the school and Nokesville be on the map we first find for 1 miles on the map and then multiply it by 4.2 miles :

3 miles = 0.5 inches on map

1  miles = 0.5/3 inches on map

4.2 miles = (0.5/3) x 4.2 inches on map

4.2 miles = 0.7 inches inches on map

Therefore, the the distance between the school and Nokesville be on the map is 0.7 inches.

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An expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.

Given,

Number of credit cards opened at location a = a (t) = 20 + 4t

Number of credit cards opened at location b = b (t) = 25 - t

Hence,

Total amount of credit card:

(a + b) (t) = (20 + 4t) + (25 - t)

(a + b) (t) = 20 + 4t + 25 - t

(a + b) (t) = 45 + 3t

Therefore an expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.

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Answer:

The square of -3 is 9

Step-by-step explanation:

(-3)^2=9

2.

x^2-4y

/2

4^2- (4*-3)

/2

16+12

/2

28/2

14

The inverse of the given equation is  r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.

The car travels a distance of D feet, where D is a function of the speed r miles/hour given by D(r) = (11r + 5)/10

D = (11r + 5)/10

⇒ 10D = 11r +5         (multiply by 10 on both sides)

⇒ 10D - 5 = 11r         (subtracting 5 on both sides)

⇒ (10D - 5)/11 = r      (dividing by 11 on both sides)

Therefore, the inverse of the given equation is r = (10D - 5)/11.

Inverse represents the speed of the car (miles/hour) in terms of the reaction distance D.

The inverse is also a function, which represents the reaction speed of the car in terms of the reaction distance.

Therefore. the inverse of the given equation is  r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.

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the answer for your question is true. I believe.

The given expression , the value of x is 2.

given,

equivalent expression = -3(2x - 4)

                                    = -6x + 12

                                  x  = 2

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

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The cost of each ticket for the ballet is $13.25.

The cost price or simply the cost in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

There are numerous ways to calculate cost pricing, however it all relies on the kind of query we are asking. For instance,

If a selling price and profit are provided, then,

Cost price = Selling price (SP) − profit

If a selling price and loss are provided, then,

Cost price =Selling price + loss

In the given question,

The total amount that Marta paid is $53

=> amount = $53

and total number of tickets = 4

Now, the cost of each ticket = Total amount / number of tickets

                                               = $53 / 4

                                               = $ 13.25

Hence, the cost each ticket for the ballet is $13.25.

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Answer:

(a+b) (a+2ab+b2−3a2b)

Step-by-step explanation:

Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.

If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:

a^-1/2 = 1/a^½

1/a^½ can also be rewritten or expressed as:

1/a^½ = 1/√a

Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:

9^-1/2 = 1/9^½

Rewrite 1/9^½ as 1/√a

1/9^½ = 1/√9

Take the square root of 9

1/√9 = 1/3

This implies that, the value of the expression, 9^-1/2 is 1/3.

In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.

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