use the functions f (×) and g (×) to complete the comparison statements using <,>,or =.F(x)= -×-5
Answers
First Question:
f(3) = (-3)-5 (Replacing x in the equation)
f(3) = -8 (Operating integers)
From the table we see that g(3) = 8, therefore, f(3)< g(3)
Second Question:
The slope of f is the coefficient of x in the equation, so, the slope of f is -1.
Using the slope formula for g(x) with points (0,2) and (3,8) we find that:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]The slope of g is 2.
Therefore, the slope of f is less (<) than the slope of g
Third Question:
The y-intercept of f is the value next to the term -x, so, it is equal to -5
The y-intercept of g can be found with the point (0,2), when x=0, y is equal to 2, then the y-intercept is 2.
Therefore, the y-intercept of f is less(<) than the y-intercept of g.
Related Questions
2. Here is a riddle: “I am thinking of two numbers that add up to 5.678. The difference between them is 9.876. What are the two numbers?”•Name any pair of numbers whose sum is 5.678. •Name any pair of numbers whose difference is 9.876.•The riddle can be represented with two equations. Write the equations.•Solve the riddle. Explain your reasoning.( You do not need to name a variable for each number in the first part)
Answers
• You know that the sum of the two numbers must be:
[tex]5.678[/tex]In order to find any pair of numbers whose sum is that number shown above, you can subtract 1 from it:
[tex]5.678-1=4.678[/tex]Now you can set up that:
[tex]1+4.678=5.678[/tex]• To find any pair of numbers whose difference is:
[tex]9.876[/tex]You can add 2 to it:
[tex]9.876+2=11.876[/tex]Then, you can set up that:
[tex]11.876-2=9.876[/tex]• Let be "x" and "y" the numbers that add up to 5.678. and whose difference is 9.876.
Then, you can set up these equations:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• To solve the riddle, you can follow these steps:
- Set up a System of equations using the equations found in the previous part:
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ \end{gathered}[/tex]- Apply the Elimination Method by adding both equations and solving for "x":
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ ------------ \\ 2x=15.554 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{15.554}{2} \\ \\ x=7.777 \end{gathered}[/tex]- Substitute the value of "x" into one of the original equations and solve for "y":
[tex]\begin{gathered} (7.777)+y=5.678 \\ \\ y=5.678-7.777 \\ \\ y=-2.099 \end{gathered}[/tex]Therefore, the answers are:
• Any pair of numbers whose sum is 5.678:
[tex]1\text{ and }4.678[/tex]• Any pair of numbers whose difference is 9.876:
[tex]11.876\text{ and }2[/tex]• Equations that represents the riddle:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• Solution of the riddle:
[tex]\begin{gathered} x=7.777 \\ y=-2.099 \end{gathered}[/tex]
f(x) = 2x + 4 and g(x) = -8f(x). = What equation shows the correct rule for the function g? O g(x) = -4x O g(x) = -4x + 4 = g(x) = -8x - 32 O g(x) = -4x - 32 – -
Answers
The given functions are
[tex]\begin{gathered} f(x)=\frac{1}{2}x+4 \\ g(x)=-8f(x) \end{gathered}[/tex]Multiply f by -8 to get g
[tex]\begin{gathered} g(x)=-8(\frac{1}{2}x+4) \\ g(x)=-8(\frac{1}{2}x)+(-8)(4) \\ g(x)=-4x+(-32) \\ g(x)=-4x-32 \end{gathered}[/tex]The correct answer is D
Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form. M= -2, point ( 2,1 )Y=
Answers
The equation of a line in slope-intercept form is;
[tex]y=mx+b[/tex]For the given information, that is the slope and a point on the line, we now have;
[tex]\begin{gathered} (x,y)=(2,1) \\ m=-2 \\ y=mx+b\text{ now becomes;} \\ 1=-2(2)+b \\ 1=-4+b \\ \text{Add 4 to both sides} \\ 1+4=-4+4+b \\ 5=b \\ \text{Now that we have }\det er\min ed\text{ the value of b,} \\ We\text{ can substitute for m and b as follows; } \\ y=mx+b\text{ becomes;} \\ y=-2x+5 \end{gathered}[/tex]ANSWER:
The equation of the line therefore is;
[tex]y=-2x+5[/tex]Answer:
y = -2x + 5
Step-by-step explanation:
Pre-SolvingWe are given that a line contains the point (2,1) and a slope (m) of -2.
We want to write the equation of this line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of the line, we can plug that value into the equation.
Replace m with -2.
y = -2x + b
Now, we need to solve for b.
As the line passes through (2,1), we can use those values to help solve for b.
Substitute 2 as x and 1 as y.
1 = -2(2) + b
Multiply.
1 = -4 + b
Add 4 to both sides.
5 = b
Substitute 5 as b.
y = -2x + 5
Interpret Linear Function Coefficients (From Graph)
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Remember that the equation of the line in slope-intercept form is equal to
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
In this context
we have
C=mt+b
step 1
Find out the slope
we need two points
looking at the graph
we take (0,100) and (1,150)
so
m=(150-100)/(1-0)
m=50 --------> that means $50 per month (monthly fee to remain a member)
the y-intercept is the value of y when the value of x is zero
in this context, the y-intercept is the cost C when the value of t is zero
b=100 ------> that means a one-time fee to join
substitute
C=50t+100and the slope is $50 per month (monthly fee to remain a member)a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion
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If two fractions are in proportion, their inverse ratio are also in proportion.
Proportion:
Proportion means an equation in which two ratios are set equal to each other.
Given,
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion.
Here we need to fill the blank with the correct answer.
According to Invertendo Property,
For the four numbers a, b, c, d,
Consider if a : b = c : d, then b : a = d : c; which means
if two ratios are equal, then their inverse ratios are also equal.
It can be written as,
If a : b :: c : d then b : a :: d : c.
Then it can be written as,
=> a : b :: c : d
⟹ a/b= c/d
When take the inverse, then we get,
⟹ b/a= d/c
Which implies the following,
⟹ b : a :: d : c
Therefore, the answer is inverse ratio.
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Solve the system by substitution. 9y = x - 4x + y = -35 Submit Answer
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Let:
[tex]\begin{gathered} 9y=x\text{ (1)} \\ -4x+y=-35\text{ (2)} \end{gathered}[/tex]Replace (1) into (2):
[tex]\begin{gathered} -4(9y)+y=-35 \\ -36y+y=-35 \\ -35y=-35 \\ y=1 \\ \text{ Replace y into (1)} \\ x=9(1) \\ x=9 \end{gathered}[/tex]hi how do i solvle this word problem?An office building worth $1 million when completed in 2010 is being depreciated linearly over 40 years. What was the book value of the building in 2012? What will it be in 2025? (Assume the scrap value is $0.)2012 $ 2025 $
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Answer:
2012: $950,000
2025: $625,000
Explanation:
Since the scrap value is $0, the amount depreciated each year is equal to the initial worth of the building divided by the number of years, so
[tex]\frac{1,000,000}{40}=25,000[/tex]It means that each year the worth of the building decreases by $25,000
Then, 2012 is 2 years after 2010, so the book value of the building in 2012 is:
$1,000,000 - 2($25,000) = $950,000
In the same way, 2025 is 15 years after 2010, so the book value is
$1,000,000 - 15($25,000) = $625,000
Therefore, the answers are
2012: $950,000
2025: $625,000
use the diagrams to answer the following questions Number 8
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In a cyclic quadrilateral opposite sides add up to 180:
Therefore:
[tex]\begin{gathered} x+82=180 \\ solve_{\text{ }}for_{\text{ }}x: \\ x=180-82 \\ x=98^{\circ} \end{gathered}[/tex]Answer:
∠x = 98
Which inequality represents all values of x for which the product below is defined?A.x 0B.x 6C.x -3D.x 6
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Solution
Step 1:
Write the expression:
[tex]\sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}}[/tex]Step 2:
[tex]\begin{gathered} Apply\text{ the rule below:} \\ \sqrt{a}\text{ . }\sqrt{b}\text{ = }\sqrt{ab} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ \sqrt{(x-6)(x+3)} \\ \\ For\text{ the function to be defined} \\ (x\text{ - 6\rparen\lparen x + 3\rparen }\ge\text{ 0} \end{gathered}[/tex]Step 4:
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:6\:[/tex]Final answer
[tex]\begin{gathered} Option\text{ D } \\ x\text{ }\ge\text{ 6} \end{gathered}[/tex]Which graph was created using a table of values calculated from the equation y=(2/5)^x+1
Answers
Usually, an important point to verify the graph is the point:
[tex](0,f(0))[/tex]It's when the function touches the y-graph, then, let's evaluate the function at x = 0
[tex]\begin{gathered} y=\left(\frac{2}{5}\right)^{x+1}\text{ , \lparen x =0\rparen} \\ \\ y=\left(\frac{2}{5}\right)^{0+1} \\ \\ y=\left(\frac{2}{5}\right)^1 \\ \\ y=\frac{2}{5}=0.4 \end{gathered}[/tex]Therefore the point should be
[tex](0,0.4)[/tex]Therefore any graph that does not include that point is not correct!
We can also eliminate all graph that shows a crescent curve, but, in fact, only the point we calculated can eliminate all graphs and gives us the correct answer:
Find the slope vx and the distance Ay for this pair of coordinates. (-2,-4) (3,-1) Change in y Change in x
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The slope and the distance of two points (a,b), (c,d) is given by
[tex]\begin{gathered} m\text{ = }\frac{d-b}{c-a} \\ d=\sqrt[]{\mleft(c-a\mright)^2+(d-b)^2} \end{gathered}[/tex]Replacing our original points, we have
[tex]\begin{gathered} m=\frac{-1-(-4)}{3-(-2)}=\frac{-1+4}{3+2} \\ m=\frac{3}{5} \\ d=\sqrt[]{(3-\mleft(-2)\mright)^2+(-1}-(-4))^2 \\ d=\sqrt[]{5^2+3^2} \\ d=5.83 \end{gathered}[/tex]5EColumn AColumn B1. eTriangle GAFa. Right, Scalene2.Triangle BECb. Obtuse, Isoscelesa3.bTriangle BFGObtuse, Scalene4.d. Equiangular, Equilateralc сTriangle CFEe. Right, Isoscelesf. Acute, Isosceles
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Triangle GAF is an
[tex]\begin{gathered} Isosceles\text{ triangle as 2 sides are equal and acute angles as all } \\ \text{the angles is less than 90 degre}e \end{gathered}[/tex]Triangle BEC is a
[tex]\begin{gathered} Isosceles\text{ triangle as 2 sides are the same.} \\ it^{}\text{ is an obtuse triangle } \end{gathered}[/tex]Triangle BFG is an
[tex]\begin{gathered} \text{Equilateral triangle as all sides are equal. } \\ Equilateral\text{ triangle are equiangular as all the angles are equal} \end{gathered}[/tex]Triangle CFE is
[tex]\begin{gathered} \text{Right angle triangle .} \\ A\text{ right angle triangle has one angle equal to 90 degre}e. \\ \text{The triangle is also scalene as all the sides are different} \end{gathered}[/tex]A math teacher said that 18 out of 25 students passed the test. What percent of the students did NOT pass the test?can you please show me the work for this?
Answers
Given:
A math teacher said that 18 out of 25 students passed the test.
So,
Total number of students = 25 student
Number of students who passed the test = 18
Number of students who did not pass the test = 25 - 18 = 7
So, the percent of the students who did NOT pass the test =
[tex]\frac{7}{25}\times100=28\%[/tex]So, the answer will be 28%
Jakayla is thinking of a number. The number includes the digits 3,7 and 8 and rounds to 700 when rounding to the nearest hundred. what number could Jakayla be thinking of?
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According to given data we have numbers 3,7,8
So the possible numbers starting from 7 are 738 and 783.
But the nearest to 700 is 738.
So Jakayla is thinking about 738
Simplify -7(-5+3x)-4x
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Solution:
Given:
[tex]-7(-5+3x)-4x[/tex]Expanding the bracket,
[tex]\begin{gathered} -7(-5+3x)-4x \\ (-7)(-5)+(-7)(3x)-4x \\ 35-21x-4x \end{gathered}[/tex]Simplifying further,
[tex]35-21x-4x=35-25x[/tex]Therefore, the solution is;
[tex]-7(-5+3x)-4x=35-25x[/tex]if x-1/x = 20, then x =
Answers
Given
[tex]\frac{x-1}{x}=20[/tex]Solution
[tex]\begin{gathered} \frac{x-1}{x}=\frac{20}{1} \\ \text{cross multiply} \\ 1(x-1)=20(x)_{} \\ we\text{ have} \\ x-1=20x \\ \text{collect the like terms} \\ -1=20x-x \\ -1=19x \\ \text{rewrite} \\ 19x=-1 \\ \text{Divide both sides by 19} \\ \frac{19x}{19}=-\frac{1}{19} \\ \\ x=-\frac{1}{19} \end{gathered}[/tex]The final answer
[tex]x=-\frac{1}{19}[/tex]I am confused on my geometry test review and need help.
Answers
4/3 = ? /12
Multiply both-side of the equation by 12
4/3 x12 = ?
48 / 3 = ?
16 = ?
WX = 16
The price to mail a letter at the post office is $0.51 for the first ounce, and $0.20 for each additional ounce. Stephanie paid $1.31 to mail her letter. How much did the letter weigh?A. 7 ounces B.6 ouncesC.4 ounces D.5 ounces
Answers
The cost of sending mail is given as $0.51 for the first ounce and then every ounce after that costs $0.20.
For each letter, the cost would be expressed as;
[tex]\begin{gathered} C=0.51+0.20x \\ \text{Where x is the weight in ounces} \\ \text{For Stephanie's letter,} \\ 1.31=0.51+0.20x \\ \text{Subtract 0.51 from both sides} \\ 1.31-0.51=0.51-0.51+0.20x \\ 0.8=0.20x \\ \text{Divide both sides by 0.20} \\ \frac{0.8}{0.2}=x \\ 4=x \\ \text{Note that she paid \$0.51 for the first ounce} \\ \text{This means she paid for 1 ounce plus another 4 ounces} \\ \text{Stephanie's letter weighs 5 ounces} \end{gathered}[/tex]Therefore, Stephanie's letter weighs 5 ounces.
The correct answer is option D
)) Rick has decided to examine his checking account statements. The account balance was $2,010 last month, and 50% less this month. What is the account balance this month?
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The account balance this month is $4020
Let the account balance this month = x
From the question, we have
The account balance was $2,010 last month.
∴x* 50%= $2,010
⇒x* 50/100= $2,010
⇒x* 1/2= $2,010
⇒x = $4020
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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I need answers fast
What else would need to be congruent to show that ASTU = AJKL by SAS?
7
R
Glven:
STK
ZSE
S
A. TU. KL
B. TU = JL
C. SU - KL
D. SU JL
Answers
Given:
[tex]STU\cong JKL[/tex]Therefore by the SAS theorem::
[tex]\begin{gathered} ST\cong JK \\ \angle S\cong\angle J \\ SU\cong JL \end{gathered}[/tex]Answer: D.
2) Coefficient of u^2v^2 in expansion of (2u - 3v)^4
Answers
Answer
Step-by-step Explanation
In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.
The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.
mean is 95.3standard deviation is 15.4 finf the probability that a randomly selected adult IQ is greater than 119.8
Answers
we are asked to determine the probability that a variable x is greater than 119.8. To do that we will assume a normal distribution of probability and use the following relationship:
[tex]P(x>119.8)=1-P(x\le119.8)[/tex]To determine the probability that x is smaller than 119.8 we need first to find the z-score of the data set using the following formula:
[tex]z=\frac{x-\bar{x}}{\sigma}[/tex]Where
[tex]\begin{gathered} \bar{x}\colon\operatorname{mean} \\ \sigma\colon\text{ standard deviation} \end{gathered}[/tex]replacing we get:
[tex]z=\frac{119.8-95.3}{15.4}=1.59[/tex]Now we use this value to look into the chart for probabilities, we get 0.94408. This is the probability that x is smaller than 119.8. Replacing in the initial relationship we get:
[tex]P(x>119.8)=1-0.94408=0.056[/tex]Therefore, the probability is 5.6%.
The key concepts used to convert units between different systems of measurement are shown without the final twosteps.1. Identify the units of measure to be converted,2. Write conversion factors,3. Cancel units.4.5.Which two steps will complete the list correctly?4. Divide the original measurement by the conversion factors.5. Check for reasonableness,4. Multiply the original measure by the conversion factors.5. Simplify the answer.4. Multiply the original measure by the conversion factors.5. Check for reasonableness,4. Divide the original measure by the conversion factors.
Answers
Here, we want to select from the options, the two best statements that completes the steps
The two steps are;
Multiply the origi
Line t is graphed in the xy-plane. Line t does not have a y-intercept. Which of the following equations couldrepresent a line parallel to line t?
Answers
when a graph doesn't have a y intercept it means that its y value is zero.
The constants in the equations are all intercepts. The only equation whose y is zero and has no constant ( intercept ) is x = 2
Thus, the solution to the question is x = 2 ( because y=o at this point and it has no constant )
If 8 people share 21 muffins, how many does each person get?
Answers
ANSWER
[tex]\frac{21}{8}or\text{ 2}\frac{\frac{5}{}}{8}[/tex]EXPLANATION
The total number of muffins is 21.
To find out how many muffins each person will receive, you have to divide the total number of muffins by the number of people it is to be shared with;
[tex]\begin{gathered} x=\frac{21}{8} \\ =2.625 \end{gathered}[/tex]Each person will receive 2.625 muffins
Solve the inequality -2d < 5
Answers
Answer:
d> -5/2
Step-by-step explanation:
-2d<5
divide both sides by -2
d>-5/2
Answer:
d > - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
- 2d < 5
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
d > [tex]\frac{5}{2}[/tex] or d > 2.5
Two angles are complementary to each other. One angle measures 23°, and the other angle measures (6x − 20)°. Determine the value of x.
Answers
Answer:
15.5
Step-by-step explanation:
23-20=3
6x-3=90
3-90=93
93÷6=15.5
Answer:
14.5
Step-by-step explanation:
i got it right on the test
Can you please help me out with a question
Answers
Step 1: Write out the formula
By the intersecting secant theorem (interior),
[tex]z=\frac{x+y}{2}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]x=40^0,y=52^0,z=m<1[/tex]Therefore,
[tex]m<1=\frac{40^0+52^0}{2}=\frac{92^0}{2}=46^0[/tex]Hence, m<1 = 46 degrees
Consider the following polynomial function.f(x) = (x+4)²(x - 2)5(x - 1)Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(s).AnswerCorrectSelect the number of x-intercept(s) at which f crosses the axis.
Answers
Given the function:
[tex]f\mleft(x\mright)=(x+4)^2\left(x-2\right)^5(x-1\rparen[/tex]The x-intercept iswhen y =0, so:
[tex]\begin{gathered} x+4=0 \\ x+4-4=0-4 \\ x=-4 \\ \end{gathered}[/tex]And
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]And
[tex]\begin{gathered} x-1=0 \\ x-1+1=0+1 \\ x=1 \end{gathered}[/tex]Therefore, the x-intercepts are:
(-4, 0), (2, 0) and (1, 0)
Answer:
(-4, 0), (2, 0) and (1, 0)
In your own words describe an exponential function. Are there restrictions on the domain why or why not? Are exponential and logarithmic function inverse. why or why not?(this is all one question, from the same page i just am on my laptop so cant provide picture)
Answers
Answer:
An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series, and examples.
An example of an exponential formula is given below as
[tex]y=ab^x[/tex]The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, for x > 1, the value of y = fn(x) increases for increasing values of (n).
Are there restrictions on the domain why or why not?
For any exponential function, f(x) = ab^x, the domain is the set of all real numbers. For any exponential function, f(x) = ab^x, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Hence,
The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take.
Are exponential and logarithmic function inverse. why or why not?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = logx base a is defined to be equivalent to the exponential equation x = a^y
Hence,
Exponential functions and logarithmic functions are inverses of each other