Given the functions:
[tex]\begin{gathered} g(x)=x^2-64 \\ h(x)=\sqrt[]{8x+512} \end{gathered}[/tex]1. (h/g)(x)
[tex](\frac{h}{g})(x)=\frac{h(x)}{g(x)},\text{ g(x)}\ne0[/tex]We substitute the functions and solve:
[tex](\frac{h}{g})(x)=\frac{\sqrt[]{8x+512}}{x^2-64}[/tex]Factor the common term 8:
[tex]=\frac{\sqrt[]{8(x+64)}}{x^2-64}[/tex]And we have:
[tex]\begin{gathered} x^2-64\ne0 \\ x^2-64+64\ne0+64 \\ x^2\ne64 \\ x\ne8\text{ and x}\ne-8 \end{gathered}[/tex]Create an example of a difference of
polynomials and explain how to simplify
your expression.
(9x² + 8x) - (2x²+ 3x) = 7x² + 5x .
By simplifying we get x( 7x + 5) .
What is polynomial ?Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.The variables and exponents of polynomials do not change when they are subtracted. Only their coefficients are subject to change. This ensures that the difference has variables and exponents that are already classified as polynomials. As a result, the difference is always a polynomial.Consider two polynomials,
(9x² + 8x) and (2x² + 3x)
The difference of polynomials is,
(9x² + 8x) - (2x²+ 3x)
9x² + 8x - 2x²+ 3x
= 7x² + 8x - 3x
= 7x² + 5x
Simplifying we get ,
taking x common,
= x( 7x + 5) .
To learn more about polynomials refer to :
https://brainly.com/question/7693326
#SPJ13
determine the inverse function of f(x) = x² + x - 6, x> - 1/2, if it exists. Then, state its domain and range.
Since the domain is restricted to one side of the axis of symmetry of the full graph of f(x), an inverse does exist.
Letting [tex]f(x)=y[/tex],
[tex]x=y^2 +y-6\\\\x=\left(y+\frac{1}{2} \right)^2 -\frac{25}{4}\\\\x+\frac{25}{4}=\left(y+\frac{1}{2} \right)^2[/tex]
Since the domain is restricted to the right hand side of the axis of symmetry, and since the range of the inverse is the same as the domain of the original function, we take the positive square root.
[tex]\sqrt{x+\frac{25}{4}}=y+\frac{1}{2}\\\\y=f^{-1}(x)=\sqrt{x+\frac{25}{4}}-\frac{1}{2}[/tex]
The domain of the inverse is the range of the original function, which is [tex]\left[-\frac{25}{4}, \infty \right)[/tex].
The range of the inverse is the domain of the original function, which is [tex]\left[-\frac{1}{2}, \infty)[/tex],
0.18 times 7 Show the work to get the answer pls
1.26
1) We can calculate that by writing out this algorithm:
We proceed normally as if we had two whole numbers. Multiplying 7 by each number.
Note that since there are two decimal places in the factor 0.18 we count two decimal places from the left to the right in the product.
2) Thus the answer is 1.26
A science class is going on a field trip to a museum. The school hires vans to take the students to the museum. Each van can hold a maximum 11 people including
passengers and driver
If there are a total of 30 students going on the field trip, which inequality represents the number of vans, V. that will be needed?
Answer: 3 Vans are needed.
Step-by-step explanation:
There are 30 students so already you need 3 vans, if you only have 2 vans, you will be leaving behind 10 students so regardless you need a 3rd van. with 3 vans you can hold 33 people. 30 students+ 3 drivers=33 people.
The inequality that represents the number of vans for the given case is V ≤ 30/11.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
Suppose the number of vans be V.
The number of students for each van is 11.
And, the total number of students is 30.
Now, the inequality for the number of vans can be written as,
11V ≤ 30
⇒ V ≤ 30/11
Hence, the inequality for the number of vans is given as V ≤ 30/11.
To know more about linear inequality click on,
https://brainly.com/question/11897796
#SPJ2
Match the equivalent fractions
5
13
Please help with this question
Answer:
A is correct. √11 and √14 are both between 3 and 4.
does anyone mind helping me?
For the given expression √25 = ∛125. As, 5 is equal to 5.
What is termed as the square root and cube root?Square root: To discover the square root of such a number, look for a number that, when multiplied by itself, yields the original number.For the given question;
Square root of 25 i.e, √25
To identify the square root of 25, determine the number because when multiplied by itself yields 25. The square root of 25 is thus 5.
Cube root: To locate the cube root of a number, look for a number so when multiplied on its own twice yields the original number. In other words.To find the cube root of 125, determine the number that when multiplied on its own twice yields 125.
The cube root of 125 is thus 5, because 5×5×5 = 125.
The radical sign with such a small three (named the index) above and on the left is the symbol for cube root.
Thus, both the values are equal.
√25 = ∛125.
To know more about the square root and cube root, here
https://brainly.com/question/720102
#SPJ13
A country's population in 1993 was 204 million.In 2000 it was 208 million. Estimatethe population in 2015 using the exponentialgrowth formula. Round your answer to thenearest million.burP = AektEnter the correct answer.DONE?DOO
Here, we want to use the exponential growth formula to estimate the 2015 population
In order to use the exponential growth formula, we have to get some of the needed points like the growth rate or constant represented by K
At any point in time, A represents the initial popultaion, which is the population in 1993, given as 204 million
P represents the population at that point in time
k is what we want to calculate
t is the difference in the number of years
Thus, for between 1993 and 2015, we have ;
[tex]undefined[/tex]What is the mass of 2 litre of water
Answer: 2 kg
Step-by-step explanation:
How do I solve this, and how do I know if I need to add or subtract at the beginning
Let's solve the system of equations using elimination:
4x + 5y = 14
-4x -2y = -8
First, we need to get rid of one variable.
Sometimes we multiply them by some factors to have the same number on one variable, but in this case, we can subtract the x variable
4x +5y =14
-4x-2y = -8
----------------------
4x-4x =0, 5y -2y = 3y and 14-8=6
------------------------------
0+3y = 6
Solve the equation for y
Divide by 3 into both sides
3y/3 = 6/3
y = 2
Then, replace this variable on one equation, whichever you want:
4x + 5y = 14
4x +5(2) = 14
4x +10 = 14
and solve the equation for x
4x +10 = 14
Subtract 10 on both sides
4x +10-10 = 14-10
4x = 4
Divide by 4 into both sides
4x/4 = 4/4
x = 1
You can replace both variables to confirm the results:
4x +5y =14
4(1) +5(2) = 14
4 +10 = 14
14 = 14
---------------------------------
-4x -2y = -8
-4(1) -2(2) = -8
-4-4 = -8
-8 = -8
The result is correct, so my ordered pair is (x,y) = (1,2)
Solve for b, then solve for each angle in the triangle
We know that the sum of the interior angles of a triangle equals 180, then,in this case we have the following equation:
[tex]b+2b+(b+16)=180[/tex]then, solving for b, we get:
[tex]\begin{gathered} b+2b+(b+16)=180 \\ \Rightarrow4b+16=180 \\ \Rightarrow4b=180-16=164 \\ \Rightarrow b=\frac{164}{4}=41 \\ b=41 \end{gathered}[/tex]now that we have that b = 41, we can find the measure of each angle:
[tex]\begin{gathered} b=41 \\ 2b=2(41)=82 \\ b+16=41+16=57 \end{gathered}[/tex]
The Organic Produce Stand sells bundles of tomatoes ($8) and bunches of green beans ($5). If
yesterday's total sales were $464 and people bought 3 times as many tomato bundles as green bean
bunches, how many bundles of tomatoes were sold?
Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5
What is selling price or sale?
In mathematics, the term selling price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called selling price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.
According to the question, the organic producer sells bundle of tomatoes as the selling price of $8 and the bunches of green beans as $5.
Total sales amount is: $464
In this, people bought three times more tomatoes as green bean bunches.
Let us assume tomatoes be 'x' and green beans be 'y'
3x + y = $464
x + y = $13
⇒ 2x = 451
⇒ x = 225.5 dollars
Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5 dollars
To learn more about the selling or sales price from the given link:
brainly.com/question/1078746
#SPJ9
all you need is in the photo put only the answer Don't do step by step please answer fast pleaseeeeegkg
Substitute the values of the constant in the equation to obtain the value of x.
[tex]undefined[/tex]What's 9 + 10? ______________________________________________________
Answer:
Hmm, that's a tough one. I think it's 19. I'm not sure though.
Answer:
19
Step-by-step explanation:
Sherry has 40% as much money as Anna. Anna has $80?
Sherry has $112.
bo
Answer: Sherry has $112
Define a variable, set up an inequality, and solve. Only algebraic solutions are accepted. “Mikayla has three savings accounts that she distributes her money into each paycheck. If she wishes to put at least $80 into each account this paycheck, how much money must she make?”
Solution:
Note that Mikayla has three savings accounts that she distributes her money into each paycheck. Now, let us denote by x the money in the accounts, thus if she wishes to put at least $80 into each account this paycheck, this means that the total amount of money must be greater than or equal to 3(80). This is equivalent to say:
[tex]3(80)\leq x[/tex]this is equivalent to:
[tex]240\leq x\text{ }[/tex]so that, we can conclude that the correct answer is:
[tex]x\ge240[/tex]
Compute the complement rate where the trade discount rate is 15%.
The Complement rate where Trade discount rate is 15% = 100 - 15 = 85%.
Thanks
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Kali will have to work a minimum of 10 hours and a maximum of 22 hours to earn between 200 and 400. The inequality representing the solution will be 9 ≤ 15.75x ≤ 22.
In the question, it is stated that Kali earns $15.75 and a flat fee 0f 50. She wants to maintain her earnings between 200 and 400. Potential earning will be 'x'. The equation representing the earnings is 200 ≤ 15.75x + 50 ≤ 400. We will have to solve the inequality and find out the value for x.
=> 200 ≤ 15.75x + 50 ≤ 400
Subtracting 50 from the equation,
=> 150 ≤ 15.75x ≤ 350
Dividing the equation by 15.75
=> 9.52 ≤ x ≤ 22.22
So, here x lies between 9.52 and 22.22. After rounding off we get range 10 and 22.
Hence, the solution for the inequality is 9.52 ≤ x ≤ 22.22
To know more about Inequalities, Click here:
brainly.com/question/20383699
#SPJ1
Determine the average rate of change for 3x²-3x+1 over the interval [-5, 5].
Answer: The average rate of change is −3.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−5 , b=5, f(x)=3x2−3x+1.
(f(b)-f(a))/(b-a)= (1-3(5)+3(5)^2-(1-3(-5)+3(-5)^2)) / (5-(-5)) = -3
I dint know the answers to this and its SUPER important I get it right.
A. The corresponding angles of triangles are coungrent (YES)
B. The triangles have the same shape (YES)
C. The triangles have the same size (YES)
D. The corresponding sides of the triangles are congruent (YES)
find a solution of the quadratic equation.6x squared + 7x + 2 =0
Given the equation:
[tex]6x^2+7x+2=0[/tex]We will use the following rule to find the solution to the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the given equation: a = 6, b = 7, c = 2
So,
[tex]\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4\cdot6\cdot2}}{2\cdot6}=\frac{-7\pm\sqrt[]{1}}{12}=\frac{-7\pm1}{12} \\ x=\frac{-7-1}{12}=-\frac{8}{12}=-\frac{2}{3} \\ or,x=\frac{-7+1}{12}=-\frac{6}{12}=-\frac{1}{2} \end{gathered}[/tex]So, the answer will be option B) x = -1/2, -2/3
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
The required value of t is (-∞, -6) U (4, ∞).
What is a linear inequality and how is it solved?
Expressions with linear inequalities compare any two values using inequality symbols like "<" and ">." The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Polynomial inequality, rational inequality, and absolute value inequality are the several types of inequalities that exist in mathematics.
First, create an equation for the inequality. The given equation must be solved for one or more values. Represent all of the values that you found on the number line now. On the number line, use open circles to symbolize the excluded values. the interval, then. To determine whether the values satisfy the inequality equation, substitute any random value from the interval into the inequality equation. The solutions of the given inequality equation are intervals that fulfil the inequality equation.
Given, the linear inequalities are t + 1 < -5 and t + 1 > 5
Solving the first inequality, t + 1 < -5 ⇒ t < -5 -1 ⇒ t < -6
Again, solving second inequality, t + 1 > 5 ⇒ t > 5 - 1 ⇒ t > 4
Combining the solution of both the inequalities, we have;
the value of t can take any value in (-∞, -6) U (4, ∞).
Therefore, the required value of t is (-∞, -6) U (4, ∞).
To learn more about solution of linear inequalities, tap on the link below:
https://brainly.com/question/21819032
#SPJ13
The ____?____ of “ sets A and B, “ denoted by ____?____ , is the set of elements that belong to “ A or B “ or “both A or B. “
We will have the following:
*The "Union" of sets A and B, denoted by A U B is the set of elements that belong to A or B, or both A or B.
[Option A]
which candy is better to buy $4.12 for 4 bars of 7.14 for 7 bars?
4 candy bars for 4.12=1.03
7 candy bars for 7.14=1.02
so 7 candy bars for 7.14
Answer: The one for 7 candy bars for $7.14.
Step-by-step explanation:
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (-8, 1)?
Oy-8 -2(x-1)
Oy-1=2(2-8)
Oy-1=2(x+8)
Oy-8=2(x+1)
The slope of 2 and passes through the point (-8,1) : y-1 = 2(x+8)
what is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The standard equation of a line in point slope form is expressed as;
so ,
y-y0 = m(x-x0)
m is the slope
(x0, y0) is the point
Given
Slope m = 5 (assumed value)
Point (-8,1)
Substitute the given data's into the formula
y -1 = 5(x-(-8))
y-1 = 5(x+8)
Hence the required equation is y-1 = 5(x+8)
to know more about the slope , click here :
https://brainly.com/question/28871317
#SPJ13
GEOMETRY! PLEASE HELLPPP
Answer: It would be Figure L
Step-by-step explanation:
It is supposed to be reflected off the y-axis and the only shape in that same box across is Figure L. So there, have a nice and blessed day!
Answer:
Figure L
Explanation:
It's reflected across the y-axis. The y-axis is a vertical line
Question 6 is the target pls helo
Answer:
80°Step-by-step explanation:
the angles in a triangle add up to 180
2x + 3x + 4x = 180
(combine like terms)
9x = 180
(divide both sides by 9 to find out what x is)
x = 20
so now we know
(2x)° = 40°
(3x)° = 60°
(4x)° = 80°
What is the measure of the largest angle in the triangle shown above?
80°If x
2 = 25 , where x ε z then x =
The value of the quadratic equation given as x^2 = 25 is 5
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to solve the quadratic equation?The quadratic equation is given as
x2 = 25
Rewrite the equation properly
So, we have
x^2 = 25
Take the square roots of both sides
x = 5
Hence, the solution of the equation is 5
Read more about quadratic equations at
brainly.com/question/1214333
#SPJ1
Fluff and Fold charges $2.25 for each load of laundry. Draw the graph of the proportional relationship between the two quantities, where x is the number of loads of laundry and y is the total cost
The graph of the proportional relationship between the two quantities is attached below.
It is given that the company Fluff and Fold charges $2.25 for each load of laundry.We are also given that "x" is the number of loads of laundry and "y" is the total cost.From the above data, we see that the cost will be as high as the number of loads."y" is directly proportional to "x".To remove the proportionality and make it an equation, we need a constant that represents the cost of a single load.y = 2.25xWe can easily plot this equation on the graph.The graph is attached below.To learn more about equations, visit :
https://brainly.com/question/10413253
#SPJ1
Determine which set of side measurements could be used to form a triangle. 12, 23, 7 10, 7, 2 8, 3, 11 5, 11, 8
Based on the triangle inequality theorem, the set of side measurements that could be used to form a triangle is: D. 5, 11, 8.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that three set of side measurements, a, b, and c would form a triangle if a + b > c, that is, the sum of any of two sides should be greater than the third side.
The set of side of measurements 5, 11, 8 will form a triangle because:
5 + 11 > 8 ⇒ 16 > 8
5 + 8 > 11 ⇒ 13 > 11
8 + 11 > 5 ⇒ 19 > 8
The other set of side of measurements do not conform to this criterion set by the triangle inequality theorem, therefore, the only set of side measurements that will form a triangle is: D. 5, 11, 8.
Learn more about the triangle inequality theorem on:
https://brainly.com/question/309896
#SPJ1
Answer:
D.
5, 11, 8
Step-by-step explanation: