What is the process between the second and third step? I don’t get how step 3 has 10^2 power.
Answers
ANSWER
Base raised to logarithm rule
EXPLANATION
Between the second and third steps, a property of logarithms was applied, the base raised to logarithm rule. This property states that when the base of the logarithm is raised to the logarithmic expression, the result is the argument,
[tex]a^{\log_a(x)}=x[/tex]In this case, we can see that it only says "log", so we can assume that the base of this logarithm is 10. To get from step 2 to step 3, we have to raise the base (10) to each side of the equation,
[tex]10^{\log(\frac{x+2}{x+1})}=10^2[/tex]And then, by the property stated above, we have the third line of this solution,
[tex]\frac{x+2}{x+1}=10^2[/tex]In the picture, the equation is inverted, but since there is an equal sign it is equivalent.
Related Questions
Find the greatest common factor of the following function 15x3+9x2-30x
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ok
[tex]undefined[/tex]4(1.8h-2) I need help please.
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To simplify the expression, you need to apply the distributive property as shown above
You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 12-sided die and one 12-sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, what are the random variables?
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As per given by the question,
There are given that, two 12-sided die and rolling together.
Now,
If there are two 12-sided die, and rolling together,
Then the total oucomes of the both die is,
[tex]12\times12=144[/tex]Now,
Plot the points and determine the slope of the line containing them. Graph the line.
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We were given the following details:
[tex]\begin{gathered} (x_1,y_1)=(-2,-4) \\ (x_2,y_2)=(7,-4) \end{gathered}[/tex]We will proceed to graph these points, we have:
The slope is given by:
[tex]\begin{gathered} slope(m)=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ slope(m)=\frac{-4-(-4)}{7-(-2)} \\ slope(m)=\frac{0}{9}=0 \\ slope(m)=0 \\ \\ \therefore slope(m)=0 \end{gathered}[/tex]Hence, the slope (m) = 0
The diagram shows two parallel lines A & B cut by a transversal line .what is the value of x
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Vontae, this is the solution:
Angle that measures 52 degrees is congruent to the third angle adjacent to angle X.
Therefore,
X = 180 - 52 -48
X = 180 - 100
X = 80
The correct answer is 80 degrees
Find the inverse function of g(x) = 1 /x − 2
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we have teh function
[tex]g(x)=\frac{1}{x}-2[/tex]step 1
Let
y=g(x)
[tex]y=\frac{1}{x}-2[/tex]step 2
Exchange the variables
x for y and y for x
[tex]x=\frac{1}{y}-2[/tex]step 3
Isolate the variable y
[tex]\begin{gathered} \frac{1}{y}=x+2 \\ y=\frac{1}{(x+2)} \end{gathered}[/tex]step 4
[tex]g^{(-1)}(x)=\frac{1}{x+2}[/tex]Debbie has already taken 2 pages of notes on her own, and she will take 1 page during each hour of class. In all, how many hours will Debbie have to spend in class before she will have a total of 16 pages of notes in her notebook?
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Based on the given information, we can define the following expression
[tex]y=2+1x[/tex]Where x represents hours and y represents pages.
For 16 pages, we have
[tex]\begin{gathered} 16=2+x \\ 16-2=x \\ x=14 \end{gathered}[/tex]Debbie will have to spend 14 hours to have 16 pages of notes.Write 3 and 2 fifths as an improper fraction and as a mixed number. b. 16 : a. C. 13 d. 17.2 Please select the best answer from the choices provided|| A B С D
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Given the fraction 3 and 2 fifths,
[tex]2\text{fifths}=\frac{2}{5}[/tex]Converting 3 and 2/5 to mixed fraction,
Mixed fraction is the combination of a whole number and a proper fractiion.
A proper fraction is the fraction with the numerator smaller than the denominator.
Therefore,
[tex]\begin{gathered} 3\text{ and}\frac{\text{ 2}}{5}\text{ to mixed fraction will be,} \\ 3+\frac{2}{5}=3\frac{2}{5} \end{gathered}[/tex]Hence, 3 and 2/5 to mixed fraction is,
[tex]=3\frac{2}{5}[/tex]Let us now convert 3 2/5 to improper fraction,
[tex]\begin{gathered} 3\frac{2}{5}=\frac{(3\times5)+2}{5} \\ =\frac{15+2}{5}=\frac{17}{5} \end{gathered}[/tex]Hence, 3 2/5 to improper fraction is 17/5.
Option D is correct answer.
Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0 ≤ < 2.)
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Given a complex number z:
[tex]z=a+bi[/tex]We can write this number in trigonometric form, using:
[tex]\begin{gathered} z=r(\cos\theta+i\sin\theta) \\ . \\ a=r\cos\theta \\ . \\ b=r\sin\theta \\ . \\ r=\sqrt{a^2+b^2} \end{gathered}[/tex]In this case, we are given:
[tex]z=-8+2i[/tex]We need to find r and θ. We know:
· a = -8
· b = 2
Thus:
[tex]r=\sqrt{(-8)^2+2^2}=\sqrt{64+4}=\sqrt{68}=2\sqrt{17}[/tex]And now, we can find θ:
[tex]-8=2\sqrt{17}\cos\theta[/tex]And solve:
[tex]\begin{gathered} \cos\theta=-\frac{8}{2\sqrt{17}} \\ . \\ \theta=\cos^{-1}(-\frac{4\sqrt{17}}{17})\approx2.89661 \end{gathered}[/tex]Now we can write the number in trigonometric form:
[tex]z=2\sqrt{17}(\cos(2.9)+i\sin(2.9))[/tex]If the frequency of a sine function is 2, what is the period?
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A sine function in the form:
[tex]y=A\sin(B(x+C))+D[/tex]has its period equal to 2/B, and its frequency equal to the reciprocal of that.
Simply put, the period and the frequency are reciprocals of each other.
So, it the frequency is equal to 2, then the period is equal to 1/2.
A rectangle is 1.2 in wide and 6.1 in tall.If it is enlarged to a width of 7.2 in, thenhow tall will it be?
Answers
Answer:
The rectangle is 36.6 in tall;
[tex]l_2=36.6\text{ in}[/tex]Explanation:
Given that a rectangle is 1.2 in wide and 6.1 in tall.
[tex]\begin{gathered} w_1=1.2\text{ in} \\ l_1=6.1\text{ in} \end{gathered}[/tex]If it was then enlarged to a width of 7.2 in, then the length l would be;
[tex]w_2=7.2[/tex]Since they would be similar shapes, then we can write;
[tex]\begin{gathered} \frac{w_2}{w_1}=\frac{l_2}{l_1} \\ l_2=\frac{l_1\times w_2}{w_1} \\ \text{substituting the given values;} \\ l_2=\frac{6.1\times7.2}{1.2} \\ l_2=36.6\text{ in} \end{gathered}[/tex]Therefore, the rectangle is 36.6 in tall;
[tex]l_2=36.6\text{ in}[/tex]
consider the following system of equations mad up of line 1 and 2. which of the following statements are ture
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the options that apply are:
option #1. because 0+5*2=10
option #2. Because -2*-5-2*3=4 and -5+5*3=10
Option#4 because -2*-10-2*8=4
Which is the best buy?3-kilogram bag of lollipops for $10.505-kilogram bag of lollipops for $18.672-kilogram bag of lollipops for $9.224-kilogram bag of lollipops for $12.64
Answers
Given
3-kilogram bag of lollipops for $10.50
5-kilogram bag of lollipops for $18.67
2-kilogram bag of lollipops for $9.22
4-kilogram bag of lollipops for $12.64
Required
we need to find which among these is the best buy.
Explanation
For 3-kilogram bag for $10.50
[tex]\text{ cost of 1 kg bag=}\frac{10.50}{3}=3.5[/tex]For 5-kilogram bag of lollipops for $18.67
[tex]\text{ cost of 1 Kg bag=}\frac{18.67}{5}=3.73[/tex]for 2-kilogram bag of lollipops for $9.22
[tex]\text{ cost of 1 Kg bag=}\frac{9.22}{2}=4.61[/tex]for 4-kilogram bag of lollipops for $12.64
[tex]\text{ cost of 1 Kg bag =}\frac{12.64}{4}=3.16[/tex]Here the minimum cost per kg is for 4-kilogram bag of lollipops for $12.64. So it is the best buy.
What is the greatest common factor of 63, 84, and 105?
Answers
Answer:
Explanation:
The factors of 63 are: 1, 3, 7, 9, 21, 63
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 1
A cylinder popcorn tin had lid with a circumference of approximately 25.12 inches which expression can be used to describe the relationship between circumference and the diameter of the popcorn tin lid.
Answers
Answer:
The last choice: 25. 12 / pi
Explanation:
The relationship b
Segment the resultat reflecting acrostine Select all of the correct statements about the unchanged properties of segment AB and segment A'B! Band 8 have the same coordinates Segment AB and Segment AB' have the same lengths
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Take into account that when a line or a segment is reflected across a reference axis or line, the length of the line or segment remains the same.
Furthermore, only points on the reference axis or life of reflection have the same coordinates after the reflection (then, the image of point B, which is B' has different coordinates).
Hence, the only valid statement about the segment A'B' is:
Segment AB and segment A'B' have the same length
15 POINTS PLEASE ANWSER ASAP
Answers
Answer:
Congruent
Step-by-step explanation:
Angle 3 and angle 7 are congruent because of congruent angles. But more specifically they are both corresponding.
A single die is rolled. Find the probability of rolling an oddnumber or a number less than 6.
Answers
Given
A single die is rolled.
To find the probability of rolling an odd number or a number less than 6.
Explanation:
It is given that,
A single die is rolled.
Then, the sample space is,
[tex]\begin{gathered} S=\lbrace1,2,3,4,5,6\rbrace \\ n(S)=6 \end{gathered}[/tex]Let A be the event of getting an odd number.
Then,
[tex]\begin{gathered} A=\lbrace1,3,5\rbrace \\ n(A)=3 \end{gathered}[/tex]Let B be the event of getting a number less than 6.
Then,
[tex]\begin{gathered} B=\lbrace1,2,3,4,5\rbrace \\ n(B)=5 \end{gathered}[/tex]Also,
[tex]\begin{gathered} A\cap B=\lbrace1,3,5\rbrace \\ n(A\cap B)=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{n(A\cap B)}{n(S)} \\ =\frac{3}{6}+\frac{5}{6}-\frac{3}{6} \\ =\frac{3+5-3}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Hence, the answer is 5/6.
The probability of rolling an odd number or a number that is less than 6 is 5/12
Probability is the likelihood of the occurrence of an event and is the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The sample space or possible outcomes when rolling a die is S = {1, 2, 3, 4, 5, 6}
We can say, n(S) = 6
Consider X as an event of getting an odd number
X = {1, 3, 5}
n (X) = 3
So P (X) = n(X)/ n(S)
By substituting the values,
P(X) = 3/6 = 1/2
Consider Y as an event of getting a number less than 6
Y = {1, 2, 3, 4, 5}
n (Y) = 5
So P (Y) = n(Y)/ n(S)
Substituting the values
P(Y) = 5/6
The probability of rolling an odd number or a number less than 6 = 1/2 × 5/6 = 5/12
Hence, the probability of rolling an odd number or a number less than 6 is 5/12.
Learn more about the probability of dice:
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the volume of the cone.Radius: 5 m, Height: 5 mnd to the nearest whole number.Volume[ ? ] m³
Answers
EXPLANATION
The volume of the cone is given as;
[tex]V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\times5^2\times5=\frac{125}{3}\pi\approx131m^3[/tex]Answer: 131 cubic meteres
one of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest
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The angles of ABC from smallest to largest: 52.83°, 57.53°, 69.64°
Explanation:Given:
AC = 18in, AB = 20 in, BC = 17 in
To find:
the angles of ABC from smallest to largest
To determine the angles, we will apply cosine rules:
[tex]a^2\text{ = b}^2\text{ + c}^2\text{ - 2bcCosA}[/tex][tex]\begin{gathered} c\text{ = side opposite angle C}=\text{ AB} \\ c\text{ = 20} \\ b\text{ = side opposite angle B = AC} \\ b\text{ = 18} \\ a\text{ = side oppsite angle A = BC} \\ a\text{ = 17} \end{gathered}[/tex][tex]\begin{gathered} 17^2\text{ = 18}^2\text{ + 20}^2-\text{ 2\lparen18\rparen\lparen20\rparen cos A} \\ \\ 289\text{ = 724 -720cosA} \\ \\ -435\text{ = -720cosA} \\ \\ cosA\text{ = }\frac{-435}{-720}\text{ = 0.6042} \\ \\ A\text{ = cos}^{-1}(0.6042) \\ \\ A=\text{ 52.83\degree} \end{gathered}[/tex][tex]\begin{gathered} To\text{ get B, we will use the formula:} \\ b^2\text{ = a}^2\text{ + c}^2\text{ - 2acCosB} \\ \\ 18^2\text{ = 17}^2\text{ + 20}^2\text{ - 2\lparen17\rparen\lparen20\rparen cosB} \\ \\ 324\text{ = 689 -680cosB} \\ \\ -365\text{ = -680cosB} \\ \\ cosB\text{ = }\frac{-365}{-680}=\text{ 0.5368} \\ \\ B\text{ = cos}^{-1}(0.5368) \\ \\ B=\text{ 57.53\degree} \end{gathered}[/tex][tex]\begin{gathered} To\text{ get C, wewill apply sum of angles in a triangle:} \\ A+\text{ B}+\text{ C}=\text{ 180\degree} \\ \\ 52.83°\text{ + 57.53\degree +}C=\text{ 180} \\ \\ 110.36\text{ + C = 180} \\ \\ C\text{ = 180 - 110.36} \\ \\ C=\text{ 69.64\degree} \end{gathered}[/tex]The angles of ABC from smallest to largest: 52.83°, 57.53°, 69.64°
Malaysia hits a softball straight up at a speed of 120 ft / sec. Her bat contacts the ball at a height of 3 ft above the ground. This scenario can be modeled by the function f(x) = -16x^2 + 120x +3, where x represents the time elapsed (in seconds) since the ball was hit and f(x) represents the ball's height (in feet) a. What do the x intercepts represent in this scenario? b. When does the ball reach its maximum height? (What feature is being requested in this question?) a. x coordinate of vertex b. у coordinate of vertex C. x coordinate of roots d. y coordinate of roots c. Justify your answer to #b.d. What is the value of 3 in the context of the question?
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a. x intercepts represent the time that the ball was at 0 feet.
b. answer is a. x coordinate of vertex
c. Since it is time you need, it is the x coordinate of vertex (maximum height)
Solve for x ...........
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We are given an equation
2(4x - 9) = 14
To solve for x
Firstly, we need to open the parenthesis
2 *4x - 2*9 = 14
8x - 18 = 14
Collect the like terms
8x = 18 + 14
8x = 32
Divide both sides by 8
8x/8 = 32 / 8
x = 32/8
x = 4
The answer is 4
HURRY!! select ALL the correct answers
Which operations involving complex numbers have solutions represented by point A on the graph?
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We have to find the solutions represented by point A on graph.
point A is represented (1 , 5i)
1. (1 - 4i) - (2 + i)
= 1 - 4i - 2 - i
= -1 - 5i
This option is not correct because it does not as same point as A.
2. -1(1 - 4i) + (2 + i)
= -1 + 4i + 2 + i
= 1 + 5i
This solution is same as point A so this option is correct.
3. (-1 + 4i) - (2 + i)
= -1 + 4i - 2 - i
= -3 + 3i
This option is not correct because it does not as same point as A.
4. (-1 + 4i) + (2 + i)
= -1 + 4i + 2 + i
= 1 + 5i
This solution is same as point A so this option is correct.
Therefore options 2 and 4 are correct.
Learn more about the solutions and graph here:
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Question 3 of 10 * - 3 is a factor of P(x) =*? – 73? + 158-9 O A. True O B. False
Answers
Given,
The expression is,
[tex]P(x)=x^3-7x^2+15x-9[/tex]If x- 3 is the factor of the given polynomial function, then on substituting the value of x = 3 in the polynomial function, it become zero.
Thus subsituting the value of x in the polynomial,
[tex]\begin{gathered} P(3)=3^3-7\times3^2+15\times3-9 \\ =27-7\times9+45-9 \\ =27+45-63-9 \\ =72-72 \\ =0 \end{gathered}[/tex]Here, the obtained value of polynomial is 0.
Hence, x-3 is a factor of the given polynomial.
Thus, option A(true) is correct.
Find the equation of the line that has a y-intercept of 1 and is perpendicular to the graph of the line 2x + y = 4.y = -2x + 1y = 2 + 1y = -x + 1y=x+1
Answers
We have the equation
2x+y = 4
We need to find the slope so we rewrite the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept
2x+y-2x = -2x+4
y = -2x +4
The slope is -2
Perpendicular lines have slopes that multiply to -1
-2 * m = -1
m = 1/2
The slope of a line that is perpendicular is 1/2
Using slope intercept form
y = mx+b and a slope of 1/2 and the y intercept of 1
y = 1/2x + 1
Find the mean, median, mode, and range of this data: 47, 56, 57, 63, 89, 44, 56. If the answer is not a whole number, round to the nearest tenth.
Answers
The data given are 47, 56, 57, 63, 89, 44, 56
To calculate the mean:
The mean of the data can be defined as
[tex]undefined[/tex]List the side lengths of △TUV in order from smallest to largest.
Answers
The sum of angles in a triangle is 180°
From the given angles given, if we are to determine the sizes of the angles from least to the highest, we will simply add the angles together and then equate to 180°
Solution
[tex](P+60)+(44P)+(P+74)=180[/tex][tex]\begin{gathered} 2P+44P+134=180 \\ 46P=180-134 \\ 46P=46 \\ P=\frac{46}{46} \\ P=1 \end{gathered}[/tex]The next step will be to find the values of each angle
[tex][tex][tex]Since we have the values of each angle of the triangles, we can list out the sides of the triangles from smallest to largest
we will have
The smallest to be UV
The bigger will be UT
The biggest will be TV
Thus, the order is
[tex]UVWhich side lengths represent the side of a right triangle
Answers
ANSWER
B) 7, 24, 25
EXPLANATION
The sides of a right triangle always satisfy the Pythagorean Theorem,
[tex]c^2=a^2+b^2[/tex]Where a and b are the legs, and c is the hypotenuse - which is the longest side.
Thus, to answer this question, we have to see for what set of lengths the sum of the squares of the shortest ones is equal to the square of the longest one.
• For 2, 3, 5,
[tex]\begin{gathered} 5^2=2^2+3^2 \\ 25=4+9 \\ 25=13\rightarrow FALSE \end{gathered}[/tex]So, this set does not represent a right triangle.
• For 7, 24, 25,
[tex]\begin{gathered} 25^2=7^2+24^2 \\ 625=49+576 \\ 625=625\rightarrow TRUE \end{gathered}[/tex]So, this set does represent a right triangle.
• For 7, 23, 25,
[tex]\begin{gathered} 25^2=7^2+23^2 \\ 625=578\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
• For 12, 16, 21,
[tex]\begin{gathered} 21^2=12^2+16^2 \\ 441=400\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
Hence, the side lengths that represent the lengths of the sides of a right triangle are 7, 24, 25.
twice a number increased by 7 is 35 . find the number
Answers
Hello there. To solve this question, we'll have to remember how to translate a statement to a mathematical equation and then solve the equation for a number.
Twice a number increased by 7 is 35. We want to find that number.
In this case, say this number is n.
Twice this number is the same as multiplying this number by 2, hence
[tex]2n[/tex]Now increasing it by 7 is the same as adding 7 to the expression, therefore
[tex]2n+7[/tex]And this must be equal to 35
[tex]2n+7=35[/tex]Now we have to solve this equation for n.
Subtract 7 on both sides of the equation
[tex]2n=28[/tex]Divide both sides of the equation by a factor of 2
[tex]n=14[/tex]This is the number we're looking for.
the points (-9,-9)and (-6,a)fall on a line with a slope of 6.what is the value of a
Answers
Answer:
a=9
Explanation:
Given that the slope of the points below is 6:
• (x1,y1) = (-9,-9)
,• (x2,y2) = (-6,a)
Substitute the points into the slope formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This gives:
[tex]\begin{gathered} 6=\frac{a-(-9)}{-6-(-9)} \\ 6=\frac{a+9}{-6+9} \\ 6=\frac{a+9}{3} \\ \text{Cross multiply} \\ a+9=6\times3 \\ a+9=18 \\ a=18-9 \\ a=9 \end{gathered}[/tex]The value of a is 9.