By factor theorem and limits, it is found that the end behavior of g(x) is that it goes to negative infinity.
The values of x and g(x) are
x –4 –1 0 1 5 8 12
g(x) 0 –3 –1 –2 0 3 0
We need to find the end behavior of g(x).
What is Factor theorem?The Factor Theorem states that a function with leading coefficient a and zeros x1,x2,x3...xn is defined by:
g(x)=(x-x1)(x-x2)(x-x3)..(x-xn)
By definition of factor theorem,
g(x)=a(x-(-4))(x-12)
g(x)=a(x+4)(x-12)
g(x)=a(x2-8x-48)
The end behavior is the limit of g(x) as x goes to infinity, thus:
lim[tex]lim \lim_{x \to \infty} g(x)= \lim_{x \to \infty} ax^{2} =a*\infty[/tex]
Since the leading coefficient a is negative:
a*infinity= - infinity
Thus the end behaviour of g(x) it goes to negative infinity.
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25,952,938 rounded to hundred thousands place
Answer:
26,000,000
Step-by-step explanation:
I had that question before
Answer:
26,000,000
Step-by-step explanation:
9 is the hundred thousand digit starting from behind .
So, you start rounding up from 9.
j^² - 5k for j = -4 and k = -1
Answer:
21
Step-by-step explanation:
Hello!
Substitute the values of j and k and evaluate.
Evaluate[tex]j^2 - 5k[/tex][tex](-4)^2 - 5(-1)[/tex][tex]16 + 5[/tex][tex]21\\[/tex]The evaluated value is 21.
For the women age 18-24 in hanes2, the average height was about 64.3 inches; the sd was about 2.6 inches. using the normal curve, estimate the percentage of women with heights
Z = 0.65 for a height of 66 inches.
What is Normal Probability Distribution?The most common continuous probability distribution is the Normal (or Gaussian) distribution. As the curve approaches zero on either side of the mean, the function calculates the likelihood that an event will fall between any two real number limits. The area beneath the normal curve is always one.To find Normal Probability Distribution:
The z-score formula can be used to solve normal distribution problems.The z-score of a measure X in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:[tex]Z=\frac{X-\mu}{\sigma}[/tex]The Z-score indicates how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value associated with this z-score. This p-value represents the probability that the measure's value is less than X, or the percentile of X. Subtracting 1 from the p-value yields the probability that the measure's value is greater than X.The average height was approximately 64.3 inches, with a standard deviation of approximately 2.6 inches.It means: [tex]\mu=64.3, \sigma=2.6[/tex]66 inches :
The z-score for a 66-inch height is:[tex]\begin{aligned}&Z=\frac{X-\mu}{\sigma} \\&Z=\frac{66-64.3}{2.6} \\&Z=0.65\end{aligned}[/tex]Therefore, Z = 0.65 for a height of 66 inches.
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The complete question is given below:
For the women aged 18-24 in HANES2, the average height was about 64.3 inches; the SD was about 2.6 inches. Express each height in standard units. (Decimal form; two places after decimal.) 66 inches:
Show that the point (1,-1,2) is common to the lines which join (6,-7,0) to (16,-19,-4) and (0,3,-6) to (2,-5,10).
Answer:
The given point satisfies both equations of a line, hence is common to the two lines.
Step-by-step explanation:
Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.
Equation of a lineThe equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:
(x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)
For the first pair of points, the equation of the line is ...
(x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)
(x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1
For the second pair of points, the equation of the line is ...
(x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)
x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2
Point on the line?If the given point is on each of these lines, then it will satisfy each of the equations.
Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4 ⇒ -5/10 = -6/12 = -2/4 . . . true
The given point is on Line 1.
Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16 ⇒ 1/2 = 4/8 = 8/16 . . . true
The given point is on Line 2.
The given point is common to both lines.
__
Alternate solution
For points A and B and parameter p, we can write the parameterized equation of each line as ...
(x, y, z) = A +p(B -A)
Using parameters t and s for the two lines, we get ...
Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)
Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)
A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...
6 +10t = 2s-7 -12t = 3 -8s-4t = -6 +16sBy any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...
(6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)
The common point to the two lines is (1, -1, 2).
Grandma has one cup of sugar. How many dozen cookies will she be able to make?
The slope of a plot of the natural log of the vapor pressure of a substance versus 1/t is ________.
The slope of a plot of the natural log of the vapor pressure of a substance versus 1/t is - e.
What is slope?
slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").[tex]l_{n} P = \frac{- Delta H_{vol} }{R} ( 1 T ) + C[/tex]
Yy = mx + c
[tex]m = \frac{- Delta H_{vol} }{R}[/tex]
m = slope
Ans = - e
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Which is an expression of degree 4 which has a leading coefficient of 9 and a
quadratic term with coefficient of 10.
3
A. 9x² + 2x³ + 10x²
B. 10x + 2x³ + 9x²
C. 10x² + 9x + 4
2
D. 4 + 9x + 10x
Answer:
None of those answers contain a polynomial of degree 4. None have a leading coefficient of 9.
Step-by-step explanation:
The degree of such a polynomial is equal to the highest exponent on x.
The leading coefficient is the coefficient for the highest exponent of x.
x^4 - 5x^2 + 6 = 0
solve using quadratic formula
At Zoe's Beading Boutique, 15 out of the 20 beads on clearance are plastic. What percentage
of beads on clearance are plastic?
Write your answer using a percent sign (%).
Submit
+
Work it out
Answer:
75%
Step-by-step explanation:
15 over 20 is equal to 3/4 and 3/4 is 75%
Please help me due in less than an hour
Answers to Question 6: m∠1 = 92, m∠2 = 88
The sum of a linear pair's angles is 180°, so we will set up an equation to solve.
(x + 67) + (3x + 13) = 180
4x + 80 = 180
4x = 100
x = 25
-
(x + 67) ➜ (25 + 67) ➜ 92
(3x + 13) ➜ (3(25) + 13) ➜ 88
Answer to Question 7: m∠2 = 56
Vertical angles are congruent, or equal, so we can set up an equation to solve.
(5x + 16) = (4x + 24)
x = 8
-
(5x + 16) ➜ (5(8) + 16) ➜ 56
(4x + 24) ➜ (4(8) + 24) ➜ 56
Kent has a collection of pennies and nickels with a value of $1.98. thenumber of pennies he has is five less than twice of nicleks. how many of each coin does kent have?
No. of pennies and nickels are 53 and 29 respectively
Let the number of pennies be x
Let the number of nickels be y
Value of pennies = $0.01x
Value of nickels = $0.05y
It is given that value of pennies and nickels = $1.98
Therefore the equation will be,
0.01x + 0.05y = 1.98
x + 5y = 198------(1)
Also, the number of pennies is five less than twice of nickels
x = 2y - 5
2y - x = 5 -------(2)
Adding equations (1) and (2) we get,
(x + 5y) + (2y - x) = 203
7y = 203
y = 29
Substituting the value of y in equation (1) we get,
x = 53
Therefore, the no. of pennies is 53 and the no. of nickels is 29
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If
Δ
C
A
T
≅
Δ
D
O
G
, which statement must be true?
Answer:
Answer: mark me brainlest
Step-by-step explanation:
Answer is A.
Determine whether or not the function is one-to-one, and if it is, determine its inverse function
Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.
What is a horizontal line test?It is simple to establish whether the inverse of a function is also a function using the horizontal line test.
Because it fails the vertical line test, a function's inverse might not actually be a function.
Graph of the line
f\left( x \right) = - x + 2
f(x)=−x+2.
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Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day workec second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to after how many days, d, Danae would make the same amount of money regardless of the job she choose
Answer: 120d + 1,500 = 110d + 2,500
Step-by-step explanation:
Answer:
$1,500 + 120d = $2,500 + 110d
Step-by-step explanation:
Just in case you want the solution as well:
10d = 1000
d = 100
N (-5,2) Q (1,-5)
What is the length of QN
The length between the two points is 9.2 units.
Given points are:
Q(1,₋5)
P(₋5,2)
Let the two points be denoted as
Q(1,₋5) as (x₁,y₁)
P(₋5,2) as (x₂,y₂)
Distance between two points is calculated as:
d = √(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²
d = √(₋5 ₋ 1)² ₊ (2 ₋ (₋5))²
d = √(₋6)² ₊ (7)²
d = √36 ₊ 49
d = √85
d = 9.2
Hence the length of QN is 9.2 units.
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I need this asap pleasee!
Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
HELP ME QUICK PLEASE!!
Manny took home a couple of his friends after soccer practice. He originally had 4 gallons of gas in his car. He used 1.05 gallons of gas to take one friend home and three tenths gallon to take the other friend home. How much gas did he have left in his car after taking both friends home?
A: 1.04 gallons
B: 2.95 gallons
C: 3.70 gallons
D: 2.65 gallons
D) 2.65 gallons of gas left in his car after taking both friends home when 1.05 gallons of gas is used to take one friend home and three tenths gallon to take the other friend home.
Manny used 1.05 + 0.3 = 1.35 gallons of gas to take his friends home.
Since he originally had 4 gallons of gas, he had 4 - 1.35 = 2.65 gallons of gas left in his car after taking both friends home.
So the answer is D.
Here is the solution in more detail:
Manny started with 4 gallons of gas.
He used 1.05 gallons of gas to take one friend home.
He used 0.3 gallons of gas to take the other friend home.
The total amount of gas he used was 1.05 + 0.3 = 1.35 gallons.
Therefore, he had 4 - 1.35 = 2.65 gallons of gas left in his car.
I hope this helps! Let me know if you have any other questions.
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What is it asking for??
I need help with this asap, I don’t know how to solve it
I just think this way if it is wrong sry but at least I try
Problem 12 how do u do this
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's set up some equations based on the information given:
You purchased a desk for 60% of the original price, p[tex]\hookrightarrow \text{60 percent of p} = \frac{60}{100} *p=0.6p[/tex]
The price that you paid is $32 less than your paid is:[tex]\hookrightarrow \text{'32 less than p'} = p-32[/tex]
Therefore:
[tex]\hookrightarrow \text{You paid '0.6p' or 'p - 32'}[/tex]
[tex]\hookrightarrow \text{The equation is } '0.6p = p-32'[/tex]
[tex]0.6p=p-32\\p-0.6p=32\\0.4p=32\\p = 80[/tex]
Answer:
Equation: 0.6p = p - 32Original Price of desk: $80Hope that helps!
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1. Determine whether each relation is a function.
((3, 2), (1,2), (4,3), (6, -2)}
domain = { 3,1,4,6} and range = { 2, 2 , 3 ,-2} are each relation is a function.
Describe domain.
The term "domain," which is specific to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of knowledge or a governing region.Describe Range?
Range is the difference between the largest and lowest values in a dataset in statistics and mathematics. One indicator of data dispersion is the range.
function = ((3, 2), (1,2), (4,3), (6, -2)}
domain = { 3,1,4,6}
range = { 2, 2 , 3 ,-2}
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PLEASE SHOW WORK
Simplify the expression
3/2(4f-10)
Answer:
6f-15
Step-by-step explanation:
First distribute 3/2.
3/2(4) =6
3/2(-10) =15
So, the answer should be 6f-15.
Let me know if you do not understand or need further explanation :)
the ratio of wins to losses to ties for yan's soccer team at was 3:2:1. if the team played 18 games, how many games did they win? Show your work.
Answer:
9
Step-by-step explanation:
Let the ratio's unit be x. We have:
3x:2x:x. We add these up to get 6x. 6x=18, so x=3. 3*3 (since the wins is 3 in the ratio 3:2:1) is 9, so there's your answer! We can double check because 3*2 = 6 losses, and 3*1 = 3 draws, and 9:6:3=3:2:1, and 9+6+3=18!
You put $1,000 into a savings account that pays 7% in annual interest. how much money will you have after 7 years if the account pays only simple interest?
The total amount in the bank account after 7 years will be $1490
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. The principal amount in simple interest is constant.
The formula for simple interest = (P*R*T)/100
where P = principal amount
R = rate of interest
T = time in years
As per the question,
P = 1000
R = 7%
T = 7 Years
Simple interest will be = (1000*7*7)/100 = $490
The amount of money in the savings account at the end of 7 years will be $1000 + $490 = $1490
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coefficients, and constants
g+12 +9g
The variable in the expression is g.
The coefficient of g is 10.
The constant term is 12.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
g + 12 + 9g
Add the like terms.
10g + 12
Now,
The variable in the expression is g.
The coefficient of g is 10.
The constant term is 12.
Thus,
The coefficient is 10.
The constant is 12.
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Which choice is a term in this expression? 3x − 7(x + 4)
The term in the given expression is -3x − 7(x + 4) (A) -3x.
What exactly do we mean by expressions?A finite combination of symbols that is well-formed according to context-dependent rules is referred to as an expression or mathematical expression.A mathematical expression is a phrase that has at least two numbers or variables, at least one mathematical operation, and at least one mathematical operation.Addition, subtraction, multiplication, and division are all considered math operations.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).Term:
Terms are expression parts that are separated by + or - signs.Because it is separated from the rest of the expression by a - sign, -3x is a term.Therefore, the term in the given expression is (A) -3x.
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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)
How can the graph rule y=2x+1 be used to predict the result for an input (x-Value) of 7
The value of y for the given input x=7 is 15.
The given function is y=2x+1.
We need to graph the given function.
How to graph the given function?Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, need some skill and some mathematical concepts to understand.
Now,
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0, 1)
Plot the points (0, 1) and (1, 3)
The value of y for x=7 is y=2(7)+1=15
Therefore, the value of y for the given input x=7 is 15.
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2/14 in simplist form
Answer: 1/7 or 0.142857
Step-by-step explanation:
Answer:
1/7 :)
Step-by-step explanation:
Miguel is asked to solve the problem below and wants to convert the values to the same form. Which form would you encourage Miguel to choose?
Group of answer choices
Since 5/6 is a terminating decimal, Miguel should convert 5/6 to a decimal and multiply the decimals.
Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.
Since 5/6 is a repeating decimal, Miguel should convert the fraction 5/6 to a decimal and multiply decimals.
Please Help Me!
The correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now the given mixed fraction is,
-0.6(5/6)
Now since 5/6 is a repeating decimal,
Therefore converting 0.6 into fraction, we get
0.6 = 6/10
Therefore, -0.6(5/6) = -(6/10)*(5/6)
Rearranging we get,
-0.6(5/6) = -(6/6)*(5/10)
⇒ -0.6(5/6) = -1*(5/10)
or, -0.6(5/6) = -(5/10)
simplifying 5/10 we get,
-0.6(5/6) = -(1/2)
Thus, the correcting answer is - Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.
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rewrite (156 + 243) using factoring
Answer:
399
Step-by-step explanation:
Factor the polynomial, and that will give you 399.
Using factor (156 + 243), can be rewritten as 3.(52+81).
What is factor?Factor is a number that devides any other number and does not leave any remainder.
The given term is,
(156 + 243)
The factor of 156 = 2×2×3×13
The factor of 243 = 3×3×3×3×3
The common factor is 3,
So (156 + 243) can be rewritten as,
3(2×2×13+3×3×3×3)= 3.(52+81).
So, the required term is 3.(52+81).
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