Explanation:
f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:
[tex]\begin{gathered} f(x)=\ln (x+3)=0 \\ x+3=1 \\ x=1-3 \\ x=-2 \end{gathered}[/tex]For greater values, the function is positive and for less values the function is negative.
Answers:
(1) x = -2
(2) x < -2. In interval notation x:(-∞, -2)
(3) x ≥ -2. In interval notation x:[-2, ∞)
23.What is the missing piece of information required to provethese triangles congruent?a) QYQYb) NYPYC) ZN 2 Pd) QY is the perpendicular bisector
In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.
The missing information, that can also be seen in the picture, is that we have a shared side that is QY.
If we applied the reflexive property, we know that:
[tex]QY\cong QY[/tex]and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.
Answer: QY = QY (Option A).
(2-5). (6.0)Find the midpoint
Let:
(x1,y1)=(2,-5)
(x2,y2)=(6,0)
The midpoint is given by:
[tex]\begin{gathered} xm=\frac{x1+x2}{2} \\ xm=\frac{2+6}{2} \\ xm=\frac{8}{2}=4 \\ ym=\frac{-5+0}{2}=-\frac{5}{2}=-2.5 \end{gathered}[/tex]Therefore the midpoint is:
M = (4 , -5/2) or M = (4, -2.5)
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week.
The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,
W = W(n) = Pb'
Here P = 106 and b = 1.04
Hence the required formula is,
⇒ W = 106 × 1.04ⁿ
Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
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The question seems to be incomplete the correct question would be
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.
What is the area of this triangle?
Pls help :(
If I take a 45 min. break at 2:15pm what time do I come back?
The break time is 2:15 pm.
The time interval for break is 45 min.
Determine the time at which interval ends.
[tex]\begin{gathered} 2\colon15+00.45=2\colon60 \\ =3\colon00 \end{gathered}[/tex]So break ends (individual come back) at 3:00.
Graph the linear equation.
x=-2/12/12
X=
Use the graphing tool to graph the linear equation.
Click to
enlarge
graph
3
10
8
6
2
d
4
6
8
40
The graph of (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis, while the graphs of (-3, 2), (-3, -2) and (3, -2) are located 3 units to the left of the y-axis and 2 units below the x-axis, 3 units to the right of the y-axis, and 3 units to the bottom of the x-axis, respectively.
What is linear equations?The ordinate of the point is the distance from the x-axis that it is placed at, and the abscissa of the point is the distance from the y-axis that it is located at. An algebraic equation of the type known as a linear equation.
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110,169 is larger than 110,72
110,169 is larger than 110,72
This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.
110,169 is larger than 110,72
This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.
What is the polar form of the equation? What type of polar curve is this?
The curve is given to be:
[tex]x^2+y^2+12y=0[/tex]We can rewrite the equation in the form:
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]Using the Completing the Square method, we have the equation to be:
[tex]\frac{\left(x-0\right)^2}{6^2}+\frac{\left(y-\left(-6\right)\right)^2}{6^2}=1[/tex]Therefore, the ellipse's center is (0, -6).
Kia rides her bicycle at 20 miles per hour. Which equation represents the situation? Leth represent the hours traveled. Let d represent the distance traveled. Od 2012 Oh= 200 Od 20 h O h = 20 -
Velocity= 20 miles/hour
Can someone help me out??
The correct option for the missing sides of given triangles is-
Part 1: x = 30Part 2: x = 21Part 3: x = 49Part 4: x = 22What is termed as the similar triangles?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size.For the given question,
The dimension of the two triangles are given with the missing sides.
Part 1: In the given rectangles;
5/3 = x/18
x = 30
Part 2: In the given rectangles;
9/x = 3/7
x = 21
Part 3: In the given triangles;
x/63 = 7/9
x = 49
Part 4: In the given triangles;
16/x = 8/11
x = 22
Thus, the missing sides of the given shapes are found.
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f (x+2) - 3o vertical shiftvertical stretchhorizontal reflectionhorizontal shiftvertical compressionhorizontal stretchhorizontal compressionvertical reflection
ANSWER:
[tex]\begin{gathered} (5x+3)\cdot(x+4) \\ x=-\frac{3}{5}\text{ and }x=-4 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]5x^2+23x+12[/tex]we factor and calculate the roots like this:
[tex]\begin{gathered} (5x+3)\cdot(x+4) \\ (5x+3)=0\rightarrow x=-\frac{3}{5} \\ (x+4)=0\rightarrow x=-4 \end{gathered}[/tex]Therefore the factored form would be
[tex](5x+3)\cdot(x+4)[/tex]And the roots of the functions are - 3/5 and -4
Write this trinomial in factored form. 5a² - 30 - 14
replace x with a for this exercise
we use this formula to factor
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a=5, b=-3 and c=-14
[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]we have two roots
[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]and
[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]so the simplified equation is
[tex](x-2)(x+\frac{7}{5})[/tex]now replace x for a
[tex](a-2)(a+\frac{7}{5})[/tex]what is 3 in the 9th power equal
3 in the 9th power means that you have to make 3 to the power of 9.
[tex]3^9=3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3=19,683[/tex]The answer is 19,683.
which of the following are like terms3y^5, 2x^53y^5, 2y^56y^2, 2 z3y^4, 4x^3
In this case the answer is very simple.
3y^5, 2y^5 are like terms.
Because the variables and their exponents are the same.
what is the line that passes through points(-6,-10)(-2,-10)
The line passes through the points, (-6,-10) and (-2,-10)
We know equation of the line passing through points (x',y') and (x'',y'') is given by:
[tex]y-y^{\prime}=\frac{y^{\prime}^{\prime^{}}-y^{\prime}}{x^{\prime}^{\prime}-x^{\prime}}(x-x^{\prime})[/tex]So the equation of the line is:
[tex]\begin{gathered} y-(-10)=\frac{-10-(-10)}{-2-(-6)_{}}(x-(-6)) \\ \Rightarrow y+10=0 \\ \Rightarrow y=-10 \end{gathered}[/tex]The equation of the line is y=-10
A team won 5 and lost 2 of their first 7 games. The team continued to win at this rate and won w games in the 28-game season. Which of the following proportions could be used to determine w? 2. 7 28 B 2 5 28 5 7 28 D U NICT 28
Answer:
C. 5/7 = w/28
Explanation:
We're told from the question, the team won 5 and lost 2 of their first 7 games and later continued to win at this rate and won w games in the 28-game season.
Since w represents the number of games won in a 28-game season, in order to create a proportion to determine the value of w, we have to consider the number of games won (which was 5) in 1st 7 games.
So the proportion can then be written as;
[tex]\frac{5}{7}=\frac{w}{28}[/tex]Solve 3 (4x - 7) * 7x - 10 0 12x - 7 12x - 21 12x + 21
Answer:
12x-21
Explanation:
Given the expression
3 (4x-7)
On expanding using distributive law;
3(4x-7)
3(4x) - 3(7)
12x - 21
Hence the result required is 12x-21
In the figure below, m2 = 49. Find mx 1.
By definition, a Right angle is an angle that measures 90 degrees.
Complementary angles are those angles that add up to 90 degrees.
For this case, you can identify that the angle 1 and the angle 2 are Complementary angles, because when you add them, you get 90 degrees (a Right angle).
Knowing the above, you can set up the following equation:
[tex]m\angle1+m\angle2=90\degree[/tex]Since you know that:
[tex]m\angle2=49\degree[/tex]You can substitute this value into the equation and the solve for the angle 1 in order to find its measure. You get that this is:
[tex]\begin{gathered} m\angle1+49\degree=90\degree \\ m\angle1=90\degree-49\degree \\ m\angle1=41\degree \end{gathered}[/tex]The answer is:
[tex]m\angle1=41\degree[/tex]I need a little understanding on a one page math assignment
a person who weighs 145 pounds on Earth would weigh 47.2 pounds on Mercury. How much would a person weigh on Mercury if they weigh 135 pounds on Earth?
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
Weight of person on Earth = 145pounds
145 = mg
Weight of person on Mercury = 47.2pounds
47.2 = ma
145/47.2 = mg/ma
145/47.2 = g/a
a = 47.2g/145 .....1.
If weight of person on earth = 135pounds
135 = mg
m = 135/g .......2.
Then, Weight of person on Mercury = ma
using the above values of a and m we we get
= (135/g)x (47.2g/145 )
= 135 x 47.2 / 145
= 43.94 pounds
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
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Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =
For finding y, we can replace the value of x in any equations.
Solution (-3,2)
Plot graphs
what is the answer to 65y=12
In this case, we have a equation with one unknown value (y)
all you have to do is to isolate y
Let's see
65 y=12
[tex]\begin{gathered} 65y=12 \\ \text{divide each side by }65 \\ \\ \frac{65y}{65}=\frac{12}{65} \\ \\ y=\frac{12}{65} \\ \end{gathered}[/tex]so the solution is y=12/65
I really hope it helps
The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =
For part c) and e), Is the assumption of normal necessary? NoYes
Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(22, 1.45).
b) The distribution is: ∑x ~ N(902, 59.55).
c) P( ¯x > 19.8214) = 0.9332 = 93.32%.
d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.
e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.
f) Q1 for the x¯distribution = 21 points a game.
g) P( ∑x > 829.0774) = 0.8888 = 88.88%.
Assumption of normality is not necessary, as the sample sizes are greater than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.For a single game, the mean and the standard deviation of the number of points scored are given as follows:
[tex]\mu = 22, \sigma = 9.3[/tex]
For the average of 41 games, the standard error is:
[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]
Hence the distribution is: x¯ ~ N(22, 1.45).
For the sum of the 41 games, the mean and the standard error are given as follows:
41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].Hence the distribution is: ∑x ~ N(902, 59.55).
In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (19.8214 - 22)/1.45
Z = -1.5
Z = -1.5 has a p-value of 0.0668.
1 - 0.0668 = 0.9332 = 93.32%.
The 60th percentile for the distribution is X when Z = 0.253, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
0.253 = (X - 22)/1.45
X - 22 = 0.253 x 1.45
X = 22.37.
For item e, the probability is the p-value of Z when X = 23.2262 subtracted by the p-value of Z when X = 20.6214, hence:
X = 23.2262:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (23.2262 - 22)/1.45
Z = 0.85
Z = 0.85 has a p-value of 0.8023.
X = 20.6214:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (20.6214 - 22)/1.45
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
0.8023 - 0.1711 = 0.6312 = 63.12%.
The first quartile for the distribution is X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 22)/1.45
X - 22 = -0.675 x 1.45
X = 21.
For item g, the probability is one subtracted by the p-value of Z when X = 829.0774, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (829.0774 - 902)/59.55
Z = -1.22
Z = -1.22 has a p-value of 0.1112.
1 - 0.1112 = 0.8888 = 88.88%.
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Kareem ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
Answer:
A
Step-by-step explanation:
Patrick is buying a new car. He can choose the body style, color and engine type. If there are 54 ways he can select a car, with there body styles and two engine choices , his many colors are available
Given:
Total Number of ways = 54
Number of body styles = 3
Number of engine choices = 2
Let's find the number of colors available.
To find the number of colors available, we have:
Number of ways = Number of body styles x Number of engine choices x Number of colors
54 = 3 x 2 x c
Where c represent the available number of colors.
Let's find c.
54 = 3 x 2 x c
54 = 6c
Divide both sides by 6:
[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]Therefore, there are 9 colors available to select from.
ANSWER:
9
Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit
In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:
[tex]GF=HE[/tex]Substituting we get:
[tex]z+10=2z[/tex]Now, we solve for "z". First, we subtract "z" from both sides:
[tex]\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}[/tex]Therefore, the value of "z" is 10.
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answer:
2/3
Step-by-step explanation:
y = xk
6 = 72K Solve for k Divide both sides by 72
[tex]\frac{1}{12}[/tex] = k
y = xk
y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]
y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4
y = 2/3
What’s the correct answer answer asap for brainlist
The sentence in B uses the underlined word incorrectly. The kirt was clever in concocting a story about hossatye zot in trouble.
What is adjective ?An adjective is a word that generally modifies or describes a noun or noun phrase. Its semantic role is to alter the information provided by the noun.Here the word,
Ingenious means smart and clever, whereas ingenuous means innocent and naïve. The clever villain in your favorite comic book series may devise devious plots, while the clever heroine is completely unaware.Despite the fact that the adjective ingenious is more closely related to the noun engine than to the word genius, a genius is more likely to have ingenious ideas. Ingenious invention of a self-cleaning house. So is calculating the math required to launch a rocket to the moon.So here option B is vocabulary incorrect .
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What is the unit digit of 8433165483 x 946621539 x 5514381138
The value of the unit digit 8433165483 x 946621539 x 5514381138 will be6.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
For getting a number, we will first multiply each digit by its position and then;
8433165483 x 946621539 x 5514381138
Which is;
3 x 9 x 8
= 27 x 8 = 216
Therefore, the unit digit number will be 6.
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In the equation Q = 45e1.031a quantity Q is changing over time t.(a) What is the quantity at timet = 0?(b) Is the quantity increasing or decreasing over time?(c) What is the percent per unit time continuous growth or decay rate?
(a) The equation is given as Q=45e^1.03t
where e=2.718
Taking t=0 the equation will be :
[tex]Q=45e^{1.03\ast0}[/tex]This will give;
[tex]Q=45\ast2.718^0[/tex]Q=45