h(x) = 3x - 5
g(x) = x² - x
Find (h · g)(x)

Slope can be described as rise/ run, change in the dependent variables relative to the change in the independent variables and Δy / Δx.

The slope of a line is a number that describes both the direction and the steepness of the line.

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, slopes can be described as follows:

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Answer:

91678 milliliters

Step-by-step explanation:

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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:

(a+b) (a+2ab+b2−3a2b)

Step-by-step explanation:

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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It will take 10.3 years for the account to contain $3000.

The formula to be used is given as follows :

              A(t) = a ( 1 + r )^t      (1)

where,  A(t) = future value

               a = principal amount or amount initially deposited.

               r = annual interest rate

               t = time

According to the question we have been given that

            a = $2000

            r = 0.04

            A(t) = $3000

putting the required values in equation (1) we get

          3000 = 2000(1+0.04)^t

          1.5 = (1.04)^t

Taking log both sides we get

    log(1.5) = t log(1.04)

       0.176 = t *0.017

       t = 10.3 years.

Thus it takes 10.3 years for the account to contain $3000.

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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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log₅(-25) is undefined

Since the logarithmic function y = logₐ(x)  is the inverse  of the exponential function,

As the base is positive so x must also be positive

The logarithm of the real base of negative numbers is undefined.

Hence, log₅(-25) is undefined

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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 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 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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According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.

A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.

A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).

A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.

                                                                                           ___

A segment is named by its two endpoints, for example, AB.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).

according to this definition, EA EB EC ED are rays, and ED, and BE are Line

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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.

Answer:

y = 22.5x

Step-by-step explanation:

Using the scale 1:22.5

then the actual length is y = 22.5x

Answer:

Center: (0,0)

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

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

Step-by-step explanation:

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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Step-by-step explanation:

her ratio is therefore 25/10, which can be also written as 5/2, because ratios are just a special form of fractions.

to find how many labels she can type in 1 hour, we need to find the rehashing between 10 minutes and 1 hour.

1 hour = 60 minutes.

60 minutes = 6 × 10 minutes.

so, to find the equivalent ratio based on 1 hour, we need to multiply the denominator (bottom part) by 6.

and to keep the ratio value we need to multiply the numerator (top part) by the same number :

25/10 × 6/6 = 150/60

and since the ratio is always telling us how many labels can be typed per unit of time, we see,

she can type 150 labels in 1 hour (60 minutes)

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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[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]

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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The length of the countertop on the blueprint is 5 cm.

For the given question;

The length of kitchen countertop = 8.75 feet.

The scale used in blueprint is 1 centimeter = 1.75 feet.

Thus, use the unitary method.

1.75 feet -----> 1 cm.

Divide both side by 1.75.

1 feet ------>1/1.75 cm

Multiply both side by 8.75.

8.75 feet ---> 8.75/1.75 cm

8.75 feet ------> 5 cm.

Therefore, the the length of a countertop for the blueprint is found as 5 cm.

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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: 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

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:

Step-by-step explanation:

Draw a line in the middle of the compass slightly slanted like this /with an on top of the line indicating 2 congruent angles being created.

Using the properties of logarithm the value of the expression is  [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

According to the question we have been given the expression as

                        =  [tex]log_{4} 48 - \frac{1}{2}log_{4} 9[/tex]

The properties of logarithm that we are going to use are :

         [tex]log(\frac{x}{y} ) = logx - logy[/tex]  and   [tex]log_{a} a = 1[/tex]

Also we can see that the base are same so we can use the property of logarithm in the given equation and we know that √2304 = 48. Thus replacing 48 by √2304.

Now solving this step by step using the properties of logarithm we get

                       [tex]=log_{4} \sqrt{2304} - \frac{1}{2} log_{4} 9 \\=\frac{1}{2} log_{4} 2304 - \frac{1}{2} log_{4} 9\\= \frac{1}{2} [log_{4} 2304 - log_{4} 9]\\= \frac{1}{2} [log_{4} (2304/9)]\\= \frac{1}{2} log_{4} 256\\= \frac{1}{2} log_{4} (4^{4} )\\= 2 * log_{4} 4\\= 2*1\\= 2[/tex]

Hence using the properties of logarithm the value of the expression is                        

             [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]

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Answer:

The square of -3 is 9

Step-by-step explanation:

(-3)^2=9

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.

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:

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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