Given the functions:
[tex]\begin{gathered} f(x)=x^2-7 \\ g(x)=x^2+3x+7 \end{gathered}[/tex]We will find: f(x) • g(x)
So, we will find the product of the functions
We will use the distributive property to get the result of the multiplications
So,
[tex]\begin{gathered} f\mleft(x\mright)•g\mleft(x\mright)=(x^2-7)\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^2\cdot(x^2+3x+7)-7\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3+7x^2-7x^2-21x-49 \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49 \end{gathered}[/tex]so, the answer will be:
[tex]f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49[/tex]what's the difference between two whole number 1/2 percent of 36 and 30% of 10
Here, we proceed step by step, to obtain our answer,
[tex]\frac{1}{2}[/tex] % of 36 can be written as ,
0.5 % of 36 , which means,
100 % refers to 36, then
0.5 % refers to what, thus, by cross multiplication we get,
0.5 % of 36 = [tex]\frac{0.5 X 36}{100}[/tex] = 0.18 ___(1), which can be expressed in whole numbers as 0.
Now, 30 % of 10 means,
100 % refers to 10, then
30 % refers to what, thus, by cross multiplication we get,
30 % of 10 = [tex]\frac{30 X 10}{100}[/tex] = 3 __(2)
From equations (1) and (2),
the whole numbers that we obtain are 0 and 3, respectively,
Thus the difference between these two whole numbers is,
= 3 - 0 = 3.
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Use the multiplication method to solve the following systems of equations. c + 3t = 7 and 3c – 2t = –12
5x – 4z = 15 and –3x + 2z = 21
–4m + 3n = 50 and 2m + n = 10
2p – 4q = 18 and –3p + 5q = 22
3a + 4b = 51 and 2a + 3b = 37
After solving the system of equations we get the values as:
c=-2 and t=3x= -57 and z=-75m=-2 and n=14p=-89 and q=-49a=5 and b=9Given the equations are as follows, we need to solve them using multiplication method:
c+3t=7 and 3c-2t=-12take c+3t=7
rearrange the terms.
c = 7-3t
substitute c value in other equation.
3(7-3t)-2t=-12
21-9t-2t=-12
21-11t=-12
-11t = -12-21
-11t=-33
t=33/11
t=3
now substitute t value in c = 7-3t
c = 7-3(3)
c=7-9
c=-2
hence t and c values are 3 and -2.
5x – 4z = 15 and –3x + 2z = 21take 5x – 4z = 15
5x = 15+4z
x=15+4z/5
substitute x value in other equation.
-3(15+4z/5)+2z=21
-45-12z+10z=105
-45-2z=105
-2z=105+45
z=-75
substitute z value in x=15+4z/5
x=15+4(-75)/5
x=-57
hence x and z values are -57 and -75.
–4m + 3n = 50 and 2m + n = 10consider, -4m+3n=50
3n = 50+4m
n=50+4m/3
substitute n value in other equation.
2m+n=10
2m+50+4m/3 = 10
6m+50+4m=30
10m=30-50
10m=-20
m=-2
substitute m value in n=50+4m/3
n = 50+4(-2)/3
n = 50-8/3
n = 42/3
n = 14
hence m and n values are -2 and 14.
2p – 4q = 18 and –3p + 5q = 22consider 2p - 4q = 18
2p = 18+4q
p = 9+2q
substitute p value in other equation.
-3p+5q=22
-3(9+2q)+5q=22
-27-6q+5q=22
-27-q=22
-q = 22+27
q = -49
now p = 9+2q
p = 9+2(-49)
p = 9-98
p=-89
hence p and q values are -89 and -49.
3a + 4b = 51 and 2a + 3b = 37consider 3a + 4b = 51
3a = 51-4b
a=51-4b/3
substitute a value in other equation.
2(51-4b/3)+3b=37
102-8b+9b=111
102+b=111
b=111-102
b=9
now, a=51-4(9)/3
a = 51-36/3
a = 15/3
a = 5
hence a and b value are 5 and 9.
Therefore, we solved the required system of equations.
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(1.2 x 10^7)(2.2 x 10^-3)
The value of the expression is:
2.64 x 10² or 26400
Step - by - Step Explanation
From the question;
(1.2 x 10⁷ )(2.2 x 10⁻³)
To sim plify the expression above, we will multiply the decimal part and then apply indices to the exponent.
That is;
[tex]1.2\times2.2\times10^{7-3}[/tex][tex]=2.64\times10^2[/tex]Or
=26400
37. The average height of American adult males is 177 cm, with a standard deviation of 7.4 cm. Meanwhile, the average height of Indian males is 165 cm, with a standard deviation of 6.7 cm. Which is taller relative to his nationality, a 173-cm American man or a 150-cm Indian man? The American man The Indian man
ANSWER
The American man
EXPLANATION
To find the man that is taller relative to his nationality, we have to find the z-score of both men. The z-score represents how far away from the mean that a data value is.
To find the z-score, apply the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = data value; μ = mean; σ = standard deviation
For the American man, the z-score is:
[tex]\begin{gathered} z=\frac{173-177}{7.4} \\ z=\frac{-4}{7.4} \\ z=-0.541 \end{gathered}[/tex]For the Indian man, the z-score is:
[tex]\begin{gathered} z=\frac{150-165}{6.7} \\ z=\frac{-15}{6.7} \\ z=-2.239 \end{gathered}[/tex]We see that the American man has a height with a z-score higher than that of the Indian man.
This means that the American man is taller than the Indian man relative to their nationalities.
The sales tax on a table saw is $12.41. a. What is the purchase price of the table saw (before tax) if the sales tax rate is 7.3%? b. Find the total price of the table saw. a. The purchase price is $
We know that the tax rate is 7.3% and it corresponds to $12.41. We want to find the total price of the table saw without taxes, it is to say the 100%. We have the following equivalence:
100% ⇔ ??
7.3% ⇔ $12.41
If we divide both parts of the equivalence we will have the same result:
[tex]\frac{100}{7.3}=\frac{?\text{?}}{12.41}[/tex]Multiplying both parts of the equation by 12.41:
[tex]\begin{gathered} \frac{100}{7.3}=\frac{?\text{?}}{12.41} \\ \downarrow \\ \frac{100}{7.3}\cdot12.41=?\text{?} \end{gathered}[/tex]Now, we can find the total price of the table saw without taxes:
[tex]\begin{gathered} \frac{100}{7.3}\cdot12.41=170 \\ \text{??}=170 \end{gathered}[/tex]Answer A. the purchase price is 170
BThe total price of the table saw (it is to say, including taxes, $12.41), is
170 + 12.41 = 182.41
Answer B. the total price is 182.41
Use the Quotient Rule to find the derivative of the function.f(x) = x/(x − 6)f'(x)=
ANSWER
[tex]\frac{-6}{(x-6)^2}[/tex]EXPLANATION
We want to find the derivative of the function:
[tex]f(x)=\frac{x}{x-6}[/tex]The quotient rule states that:
[tex]f^{\prime}(x)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]where u = the numerator of the function
v = the denominator of the function
From the function, we have that:
[tex]\begin{gathered} u=x \\ v=x-6 \end{gathered}[/tex]Now, we have to differentiate both u and v:
[tex]\begin{gathered} \frac{du}{dx}=1 \\ \frac{dv}{dx}=1 \end{gathered}[/tex]Therefore, the derivative of the function is:
[tex]\begin{gathered} f^{\prime}(x)=\frac{(x-6)(1)-(x)(1)}{(x-6)^2} \\ f^{\prime}(x)=\frac{x-6-x}{(x-6)^2} \\ f^{\prime}(x)=\frac{-6}{(x-6)^2} \end{gathered}[/tex]A pancake recipe asked for one and 2/3 times as much milk as flower if two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Let x be the quantity of flour used
Let y be the quantity of milk used
A pancake recipe asked for one and 2/3 times as much milk as flour:
[tex]y=1\frac{2}{3}x[/tex]If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Find x when y=2 1/2:
[tex]2\frac{1}{2}=1\frac{2}{3}x[/tex]Write the quantities as fractions;
[tex]\begin{gathered} 2+\frac{1}{2}=(1+\frac{2}{3})x \\ \\ \frac{4}{2}+\frac{1}{2}=(\frac{3}{3}+\frac{2}{3})x \\ \\ \frac{5}{2}=\frac{5}{3}x \end{gathered}[/tex]Solve x:
[tex]x=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{15}{10}[/tex]Write the answer as a mixed number:
[tex]\frac{15}{10}=\frac{10}{10}+\frac{5}{10}=1+\frac{5}{10}=1+\frac{1}{2}=1\frac{1}{2}[/tex]Then, for 2 1/2 cups of milk would be needed 1 1/2 cups of flourAnswer: 1 1/2Comment on the similarities and differences for the graph of every polynomial function.
There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.
See examples below:
However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.
some animals on farms eat hay to get energy. A cow can eat 24 pounds of hay each day Write and evaluate an expression to find how many pounds a group of 12 cows can eat in two weeks. will send image
1 day a cow can eat = 24 pounds
1 day 12 cows can eat = 24 x 12
2 weeks = 14 days
therefore:
12 cows can eat in two weeks = 24 x 12 x 14 or 12 ( 24x14 )
answer: A. 12(24x14)
(3x² − 5x + 7) and (2x² + x − 2).
By using polynomial rule we can get 6x^4-7x^3+3x^2+17x-14
What is polynomial rule?
All exponent in the algebraic expressions must be non-negative integer in order for the algebraic expressions to be a polynomial.
A polynomial is defined as per an expression which is the composed of variables, constants and exponents, that are combined using the mathematical operations are such as addition, subtraction, multiplication and division.
Sol- (3x^2-5x+7).(2x^2+x-2)
(3x^2-2x^2+3x^2.x-3x^2.2)-5x.2x^2-5x.x+5x.2+7.2x^2+7.x-14
{polynomial multiplication rule}
=6x^4+3x^2-6x^2-10x^3-5x^2+1x+14x^2+7x-14
{Plus or minus with the same x coefficient}
We are get=
6x^4-7x^3+3x^2+17x-14
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How do you determine 1 and 2/5 - 6/10 =
[tex]\frac{4}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]
2. Rewrite the fractions with a common denominator.A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:
[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]
3. Take all the rewritten fractions and rewrite the operation.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5}[/tex]4. Solve.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]
5. Express your result.[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].
[tex]\frac{4}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]
2. Rewrite the fractions with a common denominator.A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:
[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]
3. Take all the rewritten fractions and rewrite the operation.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5}[/tex]4. Solve.[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]
5. Express your result.[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].
A rectangular garden has a walkway around it. The area of the garden is 2(4.5x +1.5). Thecombined area of the garden and the walkway is 3.5(8x + 4). Find the area of the walkway aroundthe garden as the sum of two terms.The area of the walkway around the garden is(Simplify your answer. Use integers or decimals for any numbers in the expression.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
DataL
garden area = 2(4.5x +1.5)
garden + walkway area = 3.5(8x + 4)
walkway area = ?
Step 02:
walkway area:
walkway area = 3.5(8x + 4) - 2(4.5x +1.5)
= 28x + 14 - 9x - 3
= 19x + 11
The answer is:
The area of the walkway around the garden is 19x + 11
A solid plastic cube has sides of length 0.5 cm. Its mass is m g. Write a formula for its density in grams per cubic centimetres
The density of the cube is equal to ρ = m / L³.
What is the density of a plastic cube?
The density of the plastic cube (ρ), in grams per cubic centimeter, is equal to the mass of the cube (m), in grams, divide to the volume of the cube. The volume is equal to the cube of the side length (L), in centimeters. Then, the density of the plastic cube is:
ρ = m / L³
By using the definition of density, the density of the element is equal to ρ = m / L³.
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Find the probability that a randomly chosen point is the figure lies in the shaded region. Give all answers in fraction and percent forms.help with number 5 or all of them if u can pls
NUMBER 5:
INFORMATION:
We have a trapeze and, we need to find the probability that a randomly chosen point is the figure lies in the shaded region
STEP BY STEP EXPLANATION:
To find the probability, we must divide the area of the shaded region by the total area of the trapeze
[tex]\text{ Probability}=\frac{Shaded\text{ area}}{Total\text{ area}}[/tex]- Total area:
To calculate the total area, we must use the formula for the area of a trapeze
[tex]A_{trapeze}=\frac{(b_1+b_2)h}{2}[/tex]Where, b1 and b2 are the bases and h is the height
Then, analyzing the trapeze we can see that b1 = 20, b2 = 14 and h = 12
[tex]A_{total}=A_{trapeze}=\frac{(20+14)12}{2}=204[/tex]So, the total area is 204 square units
- Shaded area:
To find the shaded area, we must subtract the no shaded area from the total area.
We can see that the no shaded area is a rectangle with width = 14 and height = 12
Now, using the formula for the area of a rectangle
[tex]A_{rectangle}=\text{ width}\times\text{ height}=14\times12=168[/tex]Then, subtracting the area of the rectangle from the total area
[tex]A_{\text{ no shaded}}=204-168=36[/tex]So, the no shaded are is 36 square units.
Finally, the probability would be
[tex]\begin{gathered} \text{ Probability}=\frac{36}{204} \\ \text{ Simplifying,} \\ \frac{3}{17}\approx17.65\text{ \%} \end{gathered}[/tex]ANSWER:
the probability that a randomly chosen point is the figure lies in the shaded region is
[tex]\frac{3}{17}\approx17.65\text{ \%}[/tex]The r value of -0.89 suggests that the independent variable ________, the dependent _________
We have that a correlation coefficient shows us how related is the dependent variable to the behavior of the independent variable.
MagnitudA correlation coefficient of ±1 means that the dependent variable moves as the independent variables moves too.
0 means that the dependent variable can move or not no matter how the independent variable changes.
As ±0.89 is near to ±1, we can say that in this case dependent and independent variable are related.
SignWhen the coeffitcient of correlation is negative it means that if the independent variable goes up, the dependent goes down, and visceversa.
In this case, while one decreases the other increases.
Answer: as the independent value increases, the dependent value decreases.
Question 2 Multiple Choice Worth 2 points)(08.07 LC)Two friends are reading books. Jimmy reads a book with 21,356 words. His friend Bob reads a book with one-and-a-half times as many words. Which expressionrepresents the number of words Bob reads?O 21,356 x 2O 21,356 x6 x 1nents1adesO 21,356 xO 21.356 x112Question 3 Multiple Choice Worth 2 points)(08.07 LC)Question 1 (Answered)OVIOUS QuestionNexd Quest
The number of words of the book Jimmy reads os 21,356, and the number of words of the book Bob reads is one-and-a-half times (that is, 1.5x) as many words, so to find the number of words Bob reads, we just need to multiply the number of words of Jimmy's book by the factor of 1.5:
[tex]21356\cdot1.5=32034[/tex]If ¼ gallon of paint covers 1/12 of a wall, then how many quarters of paint are needed for the entire wall?
We know that
1 quarter gallon of paint ⇄ 1/12 wall
?? ⇄ 1 wall
Now we just divide both sides of the equivalence
[tex]\begin{gathered} \frac{1}{?}=\frac{\frac{1}{12}}{1} \\ \frac{1}{?}=\frac{1}{12} \end{gathered}[/tex]We clear the equation in order to find the unkown value
[tex]\begin{gathered} \frac{1\cdot12}{1}=\text{?} \\ 12=\text{?} \end{gathered}[/tex]Then, we need 12 quarters of paintWould you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain.
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
As given in the question,
Interest rate = 5%
Types of account = Saving account
Pays the interest in two forms :
Compounded semiannually and Compounded daily
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
Reason :
Frequency of interest given on compounded daily is much higher and increase the amount much faster as compare to compounded semiannually.
When interest compounded daily generate 365 compounding periods a year, where as compounded semiannually generates two times in a year.
Therefore, saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
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triangle QRS is shown below using the information given determine the measure of r
个HS: Math II North Carolina High School Math II [M] (Prescripti8. Which statement is true?O OIf two figures are congruent, then they have the same shape but nOIf two figures are congruent, then they are similar.OIf two figures are similar, then they are congruent.OIf two figures are similar, then corresponding sides must be congru
For two triangles to be similar, it is enough if two angles of one triangle are equal to two angles of the other triangle.
If two figures are congruent, the corresponding sides must be equal and also the corresponding sides.
Therefore, the answer is:
If two figures are congruent, then they are similar
An unsharpened, round pencil is in the shape of a right circular cylinder. For one such pencil, the radius is 4.6 mm and the length is 167.7 mm. Find the volume of the pencil. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
The volume of the cylindrical pencil to the nearest whole number is 11149cubic millimeters
What is a cylinder?A cylinder is a 3-D shape consisting of two circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
The volume of a cylinder is πr^2h
r is the radius, h is the height or length of the cylinder
putting the values of r and h in the formula and π=3.142
V= 3.142×4.6×4.6×167.7
there the volume of the cylindrical pencil is 11149cubic millimeters ( nearest whole number)
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A teacher determines the linear equation y=12x + 40 best models the number of points a student should earn on a test, y, if the student studies for x hours. Which statement is true
Given the equation:
y = 12x + 40
Where x represents the number of hours and y represents the number of points the student should earn.
To find the correct statement substitute the number of hours and points given for x and y respectively. If the left hand side of the equation equals the right hand side then the statement is the true.
We have:
1. A student who studies for 3 hours should earn about 76 points.
x = 3
y = 76
Substitute 3 for x and 76 for y.
y = 12x + 40
76 = 12(3) + 40
76 = 36 + 40
76 = 76
This statement is true.
2.
Write a value that will make the relation not represent a function
Given:
There are given that the data for x and y are in the form of a table.
Explanation:
According to the concept of function:
The function is not defined when the value of x will be repeated.
That means if the input value is repeated again and again then the given relation will not function.
In the given relation, we can put 7 into the input box.
Final answer:
Hence, the value is 7.
Function g is defined as g(x)=f (1/2x) what is the graph of g?
Answer:
D.
Explanation
We know that g(x) = f(1/2x)
Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).
It means that f(-2) = 0 and f(2) = 0
Then, g(-4) = 0 and g(4) = 0 because
[tex]\begin{gathered} g(x)=f(\frac{1}{2}x_{}) \\ g(-4)=f(\frac{1}{2}\cdot-4)=f(-2)=0 \\ g(4)=g(\frac{1}{2}\cdot4)=f(2)=0 \end{gathered}[/tex]Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.
Write the inequality stamens in a describing the numbers (-∞,-5)
The numbers are given to be:
[tex](-\infty,-5)[/tex]This is written in Interval notation.
In "Interval Notation" we just write the beginning and ending numbers of the interval, and use:
a) [ ] a square bracket when we want to include the end value, or
b) ( ) a round bracket when we don't.
Because the interval given uses round brackets, the inequality will contain all real numbers between negative infinity and -5, but not including negative infinity and -5.
Therefore, the inequality will be:
[tex]-\inftyWhich subsets of numbers does belong to?
Natural numbers are just counting numbers. It doesn't include a negative number. Integers include both positive and negative whole numbers. rational numbers are fractions that can be expressed as two integers. We can have - 8/1 = - 8
Finally, real numbers is any positive or negative number. It includes integers and rational numbers. Therefore, the subset that contains - 8 would be
real, rational and integer numbers
Find the most important variable in the problem. A bag of marbles is full with 20 marbles, 12 of which are yellow. How many are not yellow? A. the total number of marbles B. the number of yellow marbles C. the number of marbles that are not yellow
Since there are 20 marbles and 12 of them are yellow; the marbles that are not yellow is not the same number as the marbles, and neither the number of Yellow marbles because they are yellow. So the answer is C.
I need help with my math
Answer:
The fourth choice: y+3 = 1(x+2); y= x-1
Explanation:
The point slope form of a linear equation is
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point on the line and m is the slope.
Now we first calculate the slope.
[tex]m=\frac{3-(-3)}{4-(-2)}=\frac{6}{6}=1[/tex]therefore, we have
[tex]y-y_0=1(x-x_0)[/tex]Now we use (x0, y0) = (-2, -3) and get
[tex]y-(-3)_{}=1(x-(-2))[/tex][tex]\boxed{y+3=1\mleft(x+2\mright)}[/tex]which is our equation in point-slope form.
Now, we convert the equation above into the slope-intercept form.
Subtracting 3 from both sides gives
[tex]y+3-3=x+2-3[/tex][tex]\boxed{y=x-1}[/tex]which is the equation in slope-intercept form.
Hence, the answer to the question is
[tex]y+3=1(x+2);y=x-1[/tex]which is the fourth option.
Which of the following could be an example of a function with a domain (-0,) and a range (-0,2)? Check all that apply. A. V= - (0.25)* - 2 - B. v= -(3)*-2 O c. v= -(3)*+2 1 v= - (0.25)*+2 D.
It is desired that the domain and range of the function should, respectively, be
[tex]\begin{gathered} \text{Domain}=(-\infty,\infty) \\ \text{Range}=(-\infty,2) \end{gathered}[/tex]Observe the given choices of function.
It is evident that all the functions are exponential functions, so their domain must be the set of all real numbers,
[tex](-\infty,\infty)[/tex]Now, we have to check the range of each of the 4 given functions.
Option A:
The function is given as,
[tex]y=-(0.25)^x-2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(0.25)^x\rightarrow0\Rightarrow-(0.25)^x-2\rightarrow-2\Rightarrow y\rightarrow-2 \\ x\rightarrow-\infty\Rightarrow-(0.25)^x\rightarrow-\infty\Rightarrow-(0.25)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,-2)[/tex]Since this does not match with the desired range. This is not a correct choice.
Option B:
The function is given as,
[tex]y=-(3)^x-2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(3)^x\rightarrow-\infty\Rightarrow-(3)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \\ x\rightarrow-\infty\Rightarrow-(3)^x\rightarrow0\Rightarrow-(3)^x-2\rightarrow-2\Rightarrow y\rightarrow-2 \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,-2)[/tex]Since this does not match with the desired range. This is not a correct choice.
Option C:
The function is given as,
[tex]y=-(3)^x+2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(3)^x\rightarrow-\infty\Rightarrow-(3)^x+2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \\ x\rightarrow-\infty\Rightarrow-(3)^x\rightarrow0\Rightarrow-(3)^x+2\rightarrow2\Rightarrow y\rightarrow2 \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,2)[/tex]Since this exactly matches with the desired range. This is a correct choice.
Option D:
The function is given as,
[tex]y=-(0.25)^x+2[/tex]Consider the following,
[tex]\begin{gathered} x\rightarrow\infty\Rightarrow-(0.25)^x\rightarrow0\Rightarrow-(0.25)^x+2\rightarrow2\Rightarrow y\rightarrow2 \\ x\rightarrow-\infty\Rightarrow-(0.25)^x\rightarrow-\infty\Rightarrow-(0.25)^x-2\rightarrow-\infty\Rightarrow y\rightarrow-\infty \end{gathered}[/tex]Thus, we see that the range of the function is,
[tex]\text{Range}=(-\infty,2)[/tex]Since this exactly matches with the desired range. This is also a correct choice.
Thus, the we see that the functions in option C and D possess the desired domain and range.
Therefore, option C and option D are t
a line intersects the points (2,2) and (-1, 20).What is the slope of the line in simplest form?m = _
Given: The points a line intersects as shown below
[tex]\begin{gathered} Point1:(2,2) \\ Point2:(-1,20) \end{gathered}[/tex]To Determine: The slope of the line in its simplest form
Solution
The formula for finding the slope of two points is as shown below
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Let us apply the formula to the given points
[tex]\begin{gathered} Points1(x_1,y_1)=(2,2) \\ Point2(x_2,y_2)=(-1,20) \\ slope=\frac{20-2}{-1-2} \\ slope=\frac{18}{-3} \\ slope=-6 \end{gathered}[/tex]Hence, the slope of the line in simplest form is -6