Hello! I need some assistance with this homework question for precalculus, please?HW Q20
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According to the logarithm definition:
[tex]\log_bc=a\Leftrightarrow b^a=c[/tex]In this question:
[tex]\begin{gathered} 3.6=6^x \\ which\text{ }is\text{ }the\text{ }same\text{ }as \\ 6^x=3.6 \end{gathered}[/tex]Then, comparing with the definitionm:
a = x
b = 6
c = 3.6
And, transforming to the log form:
[tex]\begin{gathered} \begin{equation*} \log_bc=a \end{equation*} \\ \log_6(3.6)=x \end{gathered}[/tex]Answer:
[tex]\operatorname{\log}_{6}(3.6)= x[/tex]Related Questions
Jessica made the addition model below of the expression (-5]+(-2)+3
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Let's see what are the steps Jessica made:
First step : - 5
This means that the arrow should be on the left, over - 5
Second step: + (-2)
Let's recall that:
Two like signs make a positive sign, two unlike signs make a negative sign.
Therefore + (
Gabe says the rectangle will be reduced.Gabi says the rectangle will be enlarged
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Gabi says the reectangle will be enlarged
Explanation:Rectangle BCDE dilation will give B'C'D'E'
A scale factor of 3/2 = 1.5
if scale factor is >1, it is an enlarement
if scale factor is <1, it is a reduction
Scale factor is greater than 1 here.
Hence, Gabi says the rectangle will be enlarged
solve the system by substitution. y= -2x + 18 y= -4x
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Substitute -4x for y in equation y = -2x + 18 to obtain the value of x.
[tex]\begin{gathered} -4x=-2x+18 \\ -4x+2x=18 \\ x=\frac{18}{-2} \\ =-9 \end{gathered}[/tex]Substitute -9 for x in the equation y = -4x to obtain the value of y.
[tex]\begin{gathered} y=-4\cdot(-9) \\ =36 \end{gathered}[/tex]Thus solution of system of equation is (-9,36).
A spinner has the colors red, orange, yellow, andgreen on it. Maria spins it 10 times, and it lands ongreen 4 times. What is the experimentalprobability of spinning a green?ABC21
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The probability is the likelihood or chance that an event will occur:
[tex]P=\frac{expected}{total\text{ outcome}}[/tex]And given:
Total number of spin = 10 times
Number of times it lands on green = 4
So, the probability of spinning a green is:
[tex]P(spinning\text{ a green\rparen=}\frac{4}{10}=\frac{2}{5}[/tex]Answer: A.
Find the slope from the table: (Hint: Look at the units for your answer choices!)
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Since we have a linear relationship between these variables, we can find the slope of these linear relationship using any combination of two points from the table. We can select the points:
x1 = 0, y1 = 50
x2 = 2, y2 = 40
(We can also can get x1 = 0, y1 = 50, and x2 = 4, y2 = 30, and we can get the same result).
The formula for the slope in a linear relationship is as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And then, using the previous values (without using units):
[tex]m=\frac{40-50}{2-0}\Rightarrow m=\frac{-10}{2}\Rightarrow m=-5[/tex]Therefore, the slope for this linear relationship is negative (as far as time passes the water level is less and less), and the value for this is m = -5 ft per hr.
a rectangle is 11 and 1/3 by 7 what is its area
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79 1/3 u²
1) Considering that we have a Mixed Number, let's turn that into an improper fraction to make our calculations easier.
Keep the denominator and multiply by the whole number and add to the numerator:
[tex]11\frac{1}{3}=\frac{3\times11+1}{3}=\frac{34}{3}[/tex]2) So now we can plug those dimensions into the Area of a rectangle:
[tex]S=b\times h\Rightarrow S=\frac{34}{3}\times7\Rightarrow S=\frac{238}{3}[/tex]Turning that into a Mixed Number we can write, dividing 238 by 3
Note that the quotient will be the whole number, the remainder the numerator, and the divisor the denominator.
Hence, the answer is 79 1/3 u²
2. The cost of tuition at Johnson Community College is$160 per credit hour. Each student also has to pay$50 in fees. Model the cost, c, for x credit hourstakenA) C(x)=SOXB) C(x)=160%C) C(x)=110%D) C(x)=160x450(MGSE9-12.N.O.2) Descriptive Modeling3 Which of the following is the graph of413- 2x 28
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Cost per credit hour = $160
Number of credit hours = x
fixed fee = $50
The cost will be the sum of the fixed fee cost (50) and the product of the number of credit hours (x) and the cost per hour (160)
C(x) = 160x + 50
Okay I think so I can send it in the
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ANSWER
[tex]\begin{gathered} a)320ft^ \\ b)320ft \end{gathered}[/tex]ANSWER
The area of the shaded rectangle is;
[tex]\begin{gathered} (6-2)\times80 \\ l=(6-2)=4 \\ b=80 \\ A=L\times B \\ A=4\times80 \\ =320ft \end{gathered}[/tex]b) To estimate the change in the train's position on the time interval [2,6]. The constant velocity as measured at the midpoint of the interval equals;
[tex]\begin{gathered} \frac{2+6}{2}=\frac{8}{2} \\ =4 \end{gathered}[/tex]Hence, the midpoint of the interval is 4 sec.
From the graph, at t= 4 sec, the velocity is 80ft/sec.
During the interval [2,6] which is 4sec.
The change in position of the train is;
[tex]\begin{gathered} \Delta s=velocity\times time \\ =80\times4 \\ =320ft \end{gathered}[/tex]in the fifth grade elected elementary school there are four fifths is many students who did not wear glasses as those who do wear glasses if they're only 60 students to wear glasses how many students are in the 5th grade
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Let be "x" the total number of students in the 5th grade.
Let be "n" the number of students who do not wear glasses and "g" the number of students do that wear glasses.
Based on the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}n=\frac{4}{5}g \\ \\ g=60\end{cases}[/tex]Subsitute the value of "g" into the first equation:
[tex]n=\frac{4}{5}(60)[/tex]Evaluating, you get that "n" is:
[tex]\begin{gathered} n=\frac{240}{5} \\ \\ n=48 \end{gathered}[/tex]Then, "x" will be the sum obtained by adding "n" and "g". This is:
[tex]\begin{gathered} x=48+60 \\ x=108 \end{gathered}[/tex]The answer is: 108 students.
6/7 - 3/4 subtract fraction with unlike denominators
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Substraction of fractions:
[tex]\frac{a}{b}-\frac{d}{e}=\frac{a\cdot e-b\cdot d}{b\cdot e}[/tex]For the given substraction:
[tex]\frac{6}{7}-\frac{3}{4}=\frac{6\cdot4-7\cdot3}{7\cdot4}=\frac{24-21}{28}=\frac{3}{28}[/tex]Then the result of the given substraction is 3/28
Y’all what is -13/11 as a decimal help
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we have
-13/11
-13/11=1.1818181818...
Its a repeating decimal
so
the answer is
The third option
Hello, May I please get some assistance with this homework question? I posted an image below. Parts A and B are already completed. Q2 (Part C.)
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SOLUTION
The given functions are
[tex]f(x)=4x+3,g(x)=x^2[/tex]Recall the rule of composite function
[tex]f\circ g=f(g(x))[/tex]a. f o g
This can be rewritten as
[tex]f\circ g=f(g(x))[/tex]Substitute the value of g(x) into the expression
This gievs
[tex]f(g(x))=f(x^2)[/tex]Substitute x² for x into the expression
[tex]f(x^2)=4x^2+3[/tex]Therefore fog is
[tex]4x^2+3[/tex]The domain of fog is all real numbers
Following the same procedure it follows
b.
[tex]\begin{gathered} \text{gof}=g(f(x)) \\ =g(4x+3) \\ =(4x+3)^2 \end{gathered}[/tex]The domain of gof is all real numbers
c. fof
[tex]\begin{gathered} f\circ f=f(f(x)) \\ =f(4x+3) \\ =4(4x+3)+3 \\ =16x+12+3 \\ =16x+15 \end{gathered}[/tex]The domain of fof is all real numbers
d. gog
[tex]\begin{gathered} g\circ g=g(g(x)) \\ =g(x^2) \\ =(x^2)^2 \\ =x^4 \end{gathered}[/tex]The domain of gog is all real numbers
Simplify.secx sinhUse algebra and the fundamental trigonometric identities.Your answer should be a number or use a single trigonometric function.sinocosatancotsecocscХ?
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We need to simplify the given trigonometric equation
[tex]\sec x\sin x[/tex]The function secant is defined as
[tex]\sec x=\frac{1}{\cos x}[/tex]Substitute it on the trigonometric equation above, we get
[tex]\sec x\sin x=\frac{1}{\cos x}\sin x[/tex]Or
[tex]\sec x\sin x=\frac{\sin x}{\cos x}[/tex]The trigonometric expression sin x/cos x is basically the tangent function, hence
[tex]\sec x\sin x=\tan x[/tex]Answer: tan x
Match each operation with the correct conclusion we can draw when testing diagonals in a quadrilateral, please.
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To answer the questions, we need to review the properties of the diagonals of a quadrilaterals.
For parallelograms, the diagonals bisect each other.
If the parallelogram is a rectangle, then the diagonals are also congruent.
If the parallelogram is a rhombus, on the other hand, then the diagonals are perpendicular. It means that they form right angles at their intersection.
If the quadrilateral is a square, then its diagonals bisect each other, are congruent and are perpendicular as well because a square is a parallelogram, a rectangle, and a rhombus all at the same time.
If the quadrilateral, on the other hand, is a trapezoid, there is only a special relationship between the diagonals if it is an isosceles trapezoid (i.e. it has two congruent non-parallel sides)--the diagonals are congruent.
If the quadrilateral is a kite, then the diagonals do not bisect each other, but are perpendicular.
Let's go back to the questions.
The first one tests if the midpoints are the same. This means that the diagonals bisect each other because both of them pass through the same midpoint. Then, it is a parallelogram.
The second one tests if the slopes of the diagonals are negative reciprocals which means that they are perpendicular to one another. This is the case for either a rhombus or a kite.
The third one tests the distance of the diagonals and if they are congruent. This is for an isosceles trapezoid.
If you're testing the slope, midpoint, and distance, then you're testing if the quadrilateral is a square.
The next one does not test diagonals but rather the sides. If only 2 of the sides are parallel, the nit is a trapezoid by definition.
Finally, if none of the tests hold true, then we simply have an irregular quadrilateral.
Topic: Interpret phrases that imply an inequality Rewrite the given "Word sentence" as a "math sentence" Each math sentence will use one of the following symbols: >, <, <, >. Use "x" in place --- --of the number.Word Sentence Example: I am thinking of a number that is greater than 13. 1. I am thinking of a number that is at least 13. 2. I am thinking of a number that is no fewer than 13. 3. I am thinking of a number that does not exceed 13. 4. I am thinking of a number that is at most 13. 5. I am thinking of a number that is no more than 13. 6. I am thinking of a number that is fewer than 13. 7. I am thinking of a number that is not above 13. 8. I am thinking of a number that is less than 13. 9. I am thinking of a number that is not under 13. 10. I am thinking of a number that is not greater than 13.
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Given
Interpret phrases that imply an inequality Rewrite the given "Word sentence" as a "math sentence"
Procedure
1. I am thinking of a number that is at least 13
[tex]x\ge13[/tex]2. I am thinking of a number that is no fewer than 13.
[tex]x\ge13[/tex]3. I am thinking of a number that does not exceed 13
[tex]x\leq13[/tex]4. I am thinking of a number that is at most 13.
[tex]x\leq13[/tex]5. I am thinking of a number that is no more than 13.
[tex]x\leq13[/tex]6. I am thinking of a number that is fewer than 13.
[tex]x<13[/tex]7. I am thinking of a number that is not above 13.
[tex]x\leq13[/tex]8. I am thinking of a number that is less than 13.
[tex]x<13[/tex]9. I am thinking of a number that is not under 13
[tex]x\ge13[/tex]10. I am thinking of a number that is not greater than 13.
[tex]x\leq13[/tex]15. If g(x) = -f(x + 3), how does g(x) compare to f(x)?
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Explanation:
f(x+3) is a translation 3 units to the left, because x + 3 = 0 → x = -3.
Then -f(x) is a reflection where x stays the same and the y-values change:
[tex](x,y)\rightarrow(x,-y)[/tex]Which is a reflection over the x-axis.
Answer:
(A) Vertical reflection about the x-axis, horizontal translation 3 units left.
what would the answer be and what step do i have to take to find true answer
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Given:
There are given the equation:
[tex](1-3x)^{\frac{1}{2}}-1=x[/tex]Explanation:
According to the question:
We need to find the value of x.
So,
From the given equation:
[tex](1-3x)^{\frac{1}{2}}-1=x[/tex]Then,
Add 1 to both sides of the equation:
So
[tex]\begin{gathered} (1-3x)^{\frac{1}{2}}-1=x \\ (1-3x)^{\frac{1}{2}}=x+1 \end{gathered}[/tex]Then,
Square both sides of the above equation:
[tex]\begin{gathered} (1-3x)^{\frac{1}{2}}=x+1 \\ (1-3x)=(x+1)^2 \\ (1-3x)=x^2+2x+1 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 1-3x-x^2-2x-1=0 \\ -x^2-5x=0 \\ -x(x+5)=0 \\ x(x+5)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} x(x+5)=0 \\ x=0,x=-5 \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
For the polynomial below, what is the coefficient of the term with the power of 3? x + x4 +6X +5
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In the algebraic term, there are a number and a variable, the number is called the coefficient of the variable
EX: 2x is an algebraic term, where 2 is the coefficient of x
In the given polynomial
[tex]x^3+\frac{1}{3}x^4+6x+5[/tex]There are 4 algebraic terms
[tex]\begin{gathered} x^3 \\ \frac{1}{3}x^4 \\ 6x \\ 5 \end{gathered}[/tex]The coefficient of each term in the number before the variable
If there is no number that means the coefficient is 1
Since there is no number before x^3, then
Its coefficient is 1
The answer is D
Which definition best describes a median?Required to answer. Single choice. A line segment from a vertex of the triangles to the opposite side that divides an angle into two congruent adjacent angles. A line segment from a vertex of the triangles to the midpoint of the opposite side.A line segment from any vertex perpendicular to the line containing the opposite side of a triangle.A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint).
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The median is line drawn from a vertex of triangle and falls upon the opposite side of vertex. The point where median intersects the opposite side divide the side in two equal parts.
In triangle AOC median from vertex O is drawn which divide the opposite side is two equal parts as AC = BC.
Thus correct option is,
A line segment from a vertex of the triangles to the midpoint of the opposite side.
What is the mean of the data set?12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18A.14.00B.14.75C.13.50D.15.75
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SOLUTION:
We want to find the mean of the data set;
[tex]12,17,16,10,20,13,14,14,12,12,19,18[/tex]how do I interpret the slope in terms rise over run
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Given:
Slope of the line = 1
Let's interpret the slope in terms of rise and run.
Apply the slope formula:
[tex]slope=\frac{rise}{run}[/tex]The slope of a line can be said to be the rise divided by the run.
Here, since the slope of the line is 1, we have:
[tex]slope=\frac{rise}{run}=\frac{change\text{ in y}}{change\text{ in x}}=\frac{1}{1}[/tex]This means that the graph rises 1 unit for each 1 unit of run.
ANSWER:
The graph rises 1 unit for each 1 unit of run.
Solve for t in the formula above to obtain a formula expressing t as a function of V.V= 14.5 – 1.3t t=
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Answer
t = 11.15 - 0.769V
Explanation
We are asked to make t the subject of formula
V = 14.5 - 1.3t
1.3t = 14.5 - V
Divide through by 1.3
[tex]\begin{gathered} \frac{1.3t}{1.3}=\frac{14.5}{1.3}-\frac{V}{1.3} \\ t=11.15-0.769V \end{gathered}[/tex]t = 11.15 - 0.769V
Hope this Helps!!!
Convert each geometric sequence into an exponential function. 4, 20, 100, 500,….
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Answer:
[tex]\text{ a}_n=4\cdot(5)^n[/tex]Explanation:
here, we want to convert the given geometric sequence into an exponential function
We have the exponential function generally as:
[tex]y=ab^x[/tex]with respect to the geometric sequence, it will be in the form:
[tex]\text{ y = ar}^n[/tex]where a is the first term ,r is the common ration and n is the term number
Looking at the given arrangement, 4 is the first term
Now, we can get the common ratio by dividing subsequent terms
Mathematically, we have that as:
[tex]\frac{100}{20}\text{ = }\frac{500}{100}\text{ = }\frac{20}{4}\text{ = 5}[/tex]So, we have the first term as 4 and the common ratio as 5
Thus, we have the exponential function as:
[tex]\text{ a}_n=4\cdot(5)^n[/tex]where n is the term number
Complete the table to order the objects from farthest away to closest tosea level.
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The elevations of the objects are given both positive and negative.
We need the absolute value of the distances. Then, we can arrange farther and closest.
Let's get the absolute value of the distances. Shown below >>>
• Scuba Diver = |-75| = ,75
,• Light in a Lighthouse = |137| = ,137
,• Shark = |-48| = ,48
,• Fish = |-6| = ,6
,• Top of weather buoy = |10| = ,10
,• Submarine = |-182| = ,182
The sea level is "0".
Thus,
Farthest to Closest >>>
Submarine, Light in a LightHouse, Scuba Diver, Shark, Top of weather buoy, Fish
Question 2011. Find f (2) + g (-2) using the following equation (type in a number onlyinclude a negative sign if needed.)f(x) = 6x + 7 andg(x) = 2 - 4
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the original price of a Bluetooth speaker was $125,but after a discount it now costs 81.25 what was the percent of change of the discount
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Explanation:
The percent change formula is:
[tex]\frac{\text{ end value - start value}}{\text{ start value}}\times100[/tex]The start value is 125 and the end value is 81.25:
[tex]\frac{125-81.25}{125}\times100=-35[/tex]It's negative because the end value is less, since it's a discount.
Answer:
The discount was 35%
1. Write a compound inequality problem to represent the domain2. Write the domain in the interval notation3. Write a compound inequality to represent the range
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Get the domain of the graph
[tex]\begin{gathered} The\: domain\: of\: a\: function\: is\: the\: set\: of\: input\: or\: argument\: values\: for\: which\: the\: function\: is\: real\: and\: defined \\ \mathrm{The\: function\: has\: no\: undefined\: points\: nor\: domain\: constraints.\: \: Therefore,\: \: the\: domain\: is} \\ -\infty\: Hence, the compound inequality to represent the domain is:[tex]-\infty\:STEP 2: Write the domain in interval notation.
[tex]\begin{gathered} \text{The compound inequality is written as: }-\infty\: Hence, the domain in interval notation is written as:[tex](-\infty,\infty)[/tex]STEP 3: Write a compound inequality to represent the range
[tex]\begin{gathered} The\text{ range of a function is:} \\ \mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined} \end{gathered}[/tex]Hence, the compound inequality of the range is written as:
suppose that the function g is defined, for all real numbers, as follows in the picture. find g(-2), g(0), and g(5)
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We have to evaluate the piecewise defined function
[tex]g(x)=\mleft\{\begin{aligned}-2\text{ }if\text{ x<-2} \\ (x-1)^2-2\text{ if -2}\leq x\leq2 \\ -\frac{1}{2}x+2\text{ if x>2}\end{aligned}\mright.[/tex]to evaluate this type of function we have to be careful to choose the right relation for the number we are evaluating.
Let's do the first one
[tex]g(-2)[/tex]Since the -2 lies in the second interval of the function we have to choose the second relation in the function, then
[tex]\begin{gathered} g(-2)=(-2-1)^2-2 \\ =(-3)^2-2 \\ =9-2 \\ =7 \end{gathered}[/tex]therefore g(-2)=7.
To evaluate g(0) we notice that x=0 also lies in the second interval of the piecewise function. Then
[tex]\begin{gathered} g(0)=(0-1)^2-2 \\ =(-1)^2-2 \\ =1-2 \\ =-1 \end{gathered}[/tex]therefore g(0)=-1.
Finally, to evaluate g(5) we notice that x=5 lies in the third interval of the function, then
[tex]\begin{gathered} g(5)=-\frac{1}{2}(5)+2 \\ =-\frac{5}{2}+2 \\ =-\frac{1}{2} \end{gathered}[/tex]Therefore g(5)=-1/2.
7. Leah took a total of 4 quizzes over the course of 2 weeks. How many weeks of school will Leah have to attend this quarter before she will have taken a total of 6 quizzes? *Just type the NUMBER - no label!* *
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4 quizzes per 2 weeks = 2 quizzes per week
Leah took a total of 4 quizzes , so she only needs to take two more quizzes . that means she will have to attend one more week since 2 quizzes are given each week.
Answer:
Leah must attend 3 weeks of school this quarter for her to take a total of 6 quizzes.
Write and solve the inequality6 times a number is greater than 4 times the number minus 2.
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We have to find the value of a number, let's call it x
What we know...
We know 6 times a number (6x),
is greater than 4 times the number minus 2 (4x - 2)
Therefore
6x > 4x - 2
Solving the inequality...
6x - 4x > -2 [Substracting 4x both sides]
2x > -2 [6x - 4x = 2x]
x > -2/2 [Divinding by 2 both sides}
x > - 1 [ -2/2 = -1 ]
Answer: The number that satisfies the condition must be greater than -1: x >-1