The solution to the Logarithmic Expression Log ₅ 8 given that Log 5 = 1.61 And Log 8 = 2.08 is; 1.29
How to solve logarithmic expressions?Some of the rules of logarithm are as follows;
Rule 1; Log (M*N) = Log M + Log N
Rule 2; Log (M/N) = Log M - Log N
Rule 3; Log (M)ⁿ = nLog(M)
Rule 4; Log 1 = 0
Rule 5; Logₐ a = 1
Now, we are given that Log 5 = 1.61 And Log 8 = 2.08. We want to find Log ₅ 8.
From the rules of logarithm, we can say that;
Logₐ7 = (Log 7)/(Log a)
Thus;
Log ₅ 8 = (Log 8)/(Log 5)
= 2.08/1.61
= 1.29
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Complete question is;
If Log 5 = 1.61 And Log, 8 = 2.08, Then Log ₅ 8 = O 3.25 O 3.35 10 0.47 O 2.69 O 1.29
Write a sequence of rigid motions to take figure CBA to figure MLK
We have the following:
• The first thing is to ,rotate, in the opposite direction of the hands of the clock, in such a way that it is the same.
,• Then make a ,translation, from left to right until it overlaps one on the other
From an elevation of 0.5 m below the surface of the water, a swimmer dives at a rate of 0.25 m/s. What is the depth of the swimmer after 4 minutes?A. -60.5 mB. 60.5 mC. -1.5 mD. 1.5 m
By assuming that the rate is constant and the speed is given by
[tex]\text{speed = }\frac{dis\tan ce}{time}[/tex]we have that
[tex]0.25\frac{m}{s}=\frac{d}{240s}[/tex]because 4 minutes is equal to 240 seconds. Then, the distance is given as
[tex]\begin{gathered} d=(0.25\frac{m}{s})(240s) \\ d=60\text{ m} \end{gathered}[/tex]Therefore, the depth of the swimmer will be 60 meters plus 0.5 meters. Then, the answer is -60.5 meters (option A)
Your credit card charges 16.5% interest on any unpaid balance. If your credit card balance forthe month is $650, how much will you be charged in interest and what will your new balancebe?
Solve for interest
[tex]\begin{gathered} \text{convert the rate first from percentage to decimal} \\ 16.5\%\rightarrow0.165 \\ \\ \text{Then multiply it to the balance to get the interest} \\ \$650\times0.165=\$107.25 \\ \\ \text{Therefore, the interest is \$107.25} \end{gathered}[/tex]Solve for new balance.
[tex]\begin{gathered} \text{Add the interest the the credit card balance to get the new balance.} \\ \$650+\$107.25=\$757.25 \\ \\ \text{Therefore, the new balance will be \$757.25} \end{gathered}[/tex]Convert percent to fraction and simplify if possible 11% =
To convert percent to fraction divide it by 100
Then to change 11% to a fraction divide 11 by 100
[tex]\frac{11}{100}[/tex]Since 11 and 100 can not divide by the same number, then
11% = 11/100 in the simplest form
Determine the discriminant, and then state the nature of the solutions. x^2+4x+7=0The discriminant tells us there is Answer
The discriminant of a quadratic equation is given by:
[tex]\begin{gathered} b^2-4ac \\ \text{with the quadratic equation in the form} \\ ax^2+bx+c=0 \end{gathered}[/tex]•When the calculation of the discriminant gives a negative number, the equation has two complex roots
•when the discriminant is zero, the equation has a root, double root
•when the calculation of the discriminant is a positive number, the equation has two distinct roots.
the given quadratic equation is
[tex]\begin{gathered} x^2+4x+7=0 \\ \text{In this equation, the coefficients will tell us that values for }a,b,\text{ and }c \\ a=1 \\ b=4 \\ c=7 \end{gathered}[/tex]Substitute these values to get the discriminant.
[tex]\begin{gathered} b^2-4ac \\ =(4)^2-4(1)(7) \\ =16-28 \\ =-12 \end{gathered}[/tex]Since the discriminant is negative, we can conclude that there is two complex solutions.
10^4 divided by 10^6 in expanded form, then find out what the answer is with a single power.
The given expression is:
[tex]\frac{10^4}{10^6}[/tex]Exapanding the above expression,
[tex]\frac{10\times10\times10\times10}{10\times10\times10\times10\times10\times10}[/tex](The number of 10s are the same as the power of 10).
Now, cancel out the common terms in the numerator and the denominator of the above expression.
[tex]\frac{1}{10\times10}[/tex]The denominator of the above expression can now be expressed as the power of 10 as,
[tex]\frac{1}{10^2}[/tex]According to the law of exponents,
[tex]\frac{1}{x_{^{^m}}}=x^{-m}[/tex]Hence, we can write
[tex]\frac{1}{10^2}=10^{-2}[/tex]Therefore, 10^4 divided by 10^6 can be expressed as a term with a single power as,
[tex]10^{-2}[/tex]weir the equation of a line for the following problems
The equation of line in slope intercept form is given by:
[tex]y=mx+c[/tex]Where m is the slope and c is the y-intercept
It is given that the slope of the line is 0 and the y-intercept is -3 so it follows:
[tex]m=0,c=-3[/tex]Hence the equation is given by:
[tex]\begin{gathered} y=0x-3 \\ y=-3 \end{gathered}[/tex]Hence y=-3 is the equation of the line ith
f(x)=8x+14 and g(x)=5x-8(f o g)(2)=?
Given the functions:
[tex]\begin{gathered} f(x)=8x+14 \\ g(x)=5x-8 \end{gathered}[/tex]1. You need to substitute the function g(x) into the function f(x), in order to find:
[tex](f\circ g)(x)[/tex]Then:
[tex](f\circ g)(x)=8(5x-8)+14[/tex]2. You need to substitute this value of "x into the function:
[tex]x=2[/tex]And then evaluate, in order to find:
[tex](f\circ g)(2)[/tex]You get:
[tex](f\circ g)(2)=8(5(2)-8)+14[/tex][tex](f\circ g)(2)=8(10-8)+14[/tex][tex](f\circ g)(2)=8(2)+14[/tex][tex](f\circ g)(2)=16+14[/tex][tex](f\circ g)(2)=30[/tex]Hence, the answer is:
[tex](f\circ g)(2)=30[/tex]im using goformative to answer my question and I already did number 7 but the rest show my answer is incorrect so I will appreciate if I can get a help from you, I will paste the image of the work.
To get side QR we can use the the tangent function:
[tex]\begin{gathered} \tan 37=\frac{9}{QR} \\ QR=\frac{9}{\tan37} \\ QR=11.9 \end{gathered}[/tex]Now, to find PR we can use the sine function:
[tex]\begin{gathered} \sin 37=\frac{9}{PR} \\ PR=\frac{9}{\sin 37} \\ PR=15 \end{gathered}[/tex]Finally to find the remaining angle we have to remember that the interior angles of any triangle have to add to 180, then angle P is 53°.
Triangle JKL is graphed below. If triangle JKL is translated 4 units down and 1 unit to the left, what will be the coordinates of L’ ? A. (-3,1) B. (-1,3) C. (1,-3) D. (3,-1)
J = (-2, 4) K = (3, 4) L = (2, 1)
Translated 4 units down
J = (-2, 4 - 4) K = (3, 4 - 4) L = (2, 1 - 4)
J = (-2 , 0) K = (3, 0) L = (2, -3)
Translated 1 unit to the left
J = (-2 -1, 0) K = (3 - 1, 0) L = (2 - 1, -3)
J = (-3. 0) K = (2, 0) L = (1, -3)
Select the expressions that equivalent to 8(4r)
The expression that is equivalent to 8(4r) is 32r.
The given expression is 8(4r)
The given expression is an algebraic expression with constant and variables, here, r is the variable, and 4 and 8 are constant terms.
We need to simplify the expression as much as possible.
In order to simplify it, we need to solve the brackets, when we open the brackets, the terms get multiplied by each other,
So, here we go,
8(4r) = 8* 4r = 32r
This is the simplest form that we can have,
So, 8(4r) = 32r
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Use a composite figure to estimate the area of the figure. the grid has squares with side lengths of 1 cm. Please help.
From the given figure we can see that there is a rectangle with 3 x 4 squares
A semi-circle at the top with about 6 squares
A semi-circle at right with about 4 squares
Then the total number of squares = 12 + 6 + 4 = 22 squares
Since the area of each square is 1 x 1 = 1 cm^2
Then the area of the figure = 22 x 1 = 22 cm^2
The area of the figure is about 22 cm^2
Amount of money in Ivanna's account and the amount of money in Brian's account and write the equation
Given
Starting amount of Ivanna = $180
put per month = $70
Starting amount of Brian = 0
put per month = $100
Find
Amount of money in Ivanna's account
the amount of money in Brian's account
equation to show when the two accounts have the same amount of money
Explanation
Let x be the number of months after today.
so, according to the question ,
Amount of money in Ivanna's account = starting amount + amount per month.
so , 180 + 70x
amount of money in Brian's account = 0 + 100x = 100x
equation to show when the two accounts have same amount of money =
[tex]180+70x=110x[/tex]so ,
[tex]\begin{gathered} 180=110x-70x \\ 180=40x \\ x=4.5 \end{gathered}[/tex]so , in 4.5 months both have same money
Final Answer
Hence ,
Amount of money in Ivanna's account = 180 + 70x
Amount of money in Brian's account = 110x
Equation to show when the two accounts have same amount of money =
[tex]180+70x=110x[/tex]Elena and Diego each wrote equations to represent these diagrasolve it. You can assume that angles that look like right anglesa35°to
∠35 and ∠w are vertical angles, therefore:
[tex]\angle w=35[/tex]Since ∠w and ∠x are supplementary, we can conclude:
[tex]\begin{gathered} \angle w+\angle x=180 \\ 35+x=180 \end{gathered}[/tex]Therefore:
Diego has written the correct equation.
Suppose that the functions g and h are defined as follows.g(x) = x-8h(x) = (x+4)(x+5)(a) Find(-3).h(b) Find all values that are NOT in the domain of8hIf there is more than one value, separate them with commas.
The given functions are
g(x) = x - 8
h(x) = (x + 4)(x + 5)
To find (g/h)x, we would divide g(x) by h(x)
Thus,
g(x)/h(x) = (x - 8)/(x + 4)(x + 5)
To find (g/h)(-3), we would substitute x = - 3 into (x - 8)/(x + 4)(x + 5). Thus, we have
(g/h)(-3) = (- 3 - 8)/(- 3 + 4)(- 3 + 5) = - 11 * 1/2
(g/h)(-3) = - 11/2
All values that are not in the domain are all values of x that does not satisfy the expression. If we put x = - 4 or x = - 5 in the denominator, the denominator would be zero and this makes the expression undefined. these values do not satisfy the g/h
Thus, the values are x = - 4 and x = - 5is
Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (9a^2-4)(9a^2+4) This simplifies to: AnswerThe degree of our simplified answer is: Answer
Given:
[tex](9a^2-4)(9a^2+4)[/tex]The shown represents the difference between the squares
So, the product of the polynomials will be as follows:
[tex]\begin{gathered} (9a^2-4)(9a^2+4) \\ =(9a^2)^2-(4)^2 \\ =81a^4-16 \end{gathered}[/tex]So, the answer will be:
This simplifies to:
[tex]81a^4-16[/tex]The degree of our simplified answer is 4
the letter "t" estimated makes up 10% of a language. a random sample of 700 letters is taken from a book. what is the approximate probability that the random sample of 700 letters will contain 8.9% t's
In this problem, we have a Binomial Probability Distribution
so
n=700
x=700*(8.9/100)=62.3=62
[tex]P(x=62)=\frac{700!}{62!(700-62)!}\cdot0.10^{(62)}\cdot0.90^{(700-62)}[/tex]P(x=62)=0.0313
the aprroximate probability is 3.13%Consider the right triangle shown below that has side lengths of x, y and r units.For each of the following questions, write an expression in terms of θ that answers the question. Enter "theta" for θ.y is how many times as large as r? ____times as large x is how many times as large as r? _____times as large y is how many times as large as x? ___times as large
Determine relation between side of triangle by using trigonometry.
[tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ y=r\sin \theta \end{gathered}[/tex]So y is sin theta times as large as r.
[tex]\begin{gathered} \cos \theta=\frac{x}{r} \\ x=r\cos \theta \end{gathered}[/tex]So x is cos theta times as large as r.
[tex]\begin{gathered} \tan \theta=\frac{y}{x} \\ y=x\tan \theta \end{gathered}[/tex]So y is tan theta times as lasrge as x.
I need help with number 16 can I please get help?
We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.
We break apart the figure as shown below:
First,
Area of Triangle = 0.5 * base * height
Area of Rectangle = base * height
Now, let's find each of the Areas A through D:
Area of A:
To find the base of this triangle, we have to use pythagorean theorem. By which we can write:
[tex]b^2+4^2=6^2[/tex]Where b is the base. let's solve for b:
[tex]\begin{gathered} b^2+16=36 \\ b^2=36-16 \\ b^2=20 \\ b=\sqrt[]{20} \\ b=\sqrt[]{4}\sqrt[]{5} \\ b=2\sqrt[]{5} \end{gathered}[/tex]Area is
[tex]\begin{gathered} 0.5\cdot\text{base}\cdot\text{height} \\ =\frac{1}{2}\cdot2\sqrt[]{5}\cdot4 \\ =4\sqrt[]{5} \end{gathered}[/tex]Area of B:
This is a rectangle with base = 10 and height 4, so the area is:
Area = 4 * 10 = 40
Area of C:
Area of C is exactly same as area of B, base is 10 and height is 4. So,
Area = 4 * 10 = 40
Area of D:
Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ \end{gathered}[/tex]Solving for b:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ b^2+16=20.25 \\ b^2=\frac{17}{4} \\ b=\frac{\sqrt[]{17}}{\sqrt[]{4}} \\ b=\frac{\sqrt[]{17}}{2} \end{gathered}[/tex]Now, area of triangle is:
[tex]A=\frac{1}{2}(\frac{\sqrt[]{17}}{2})(4)=\sqrt[]{17}[/tex]Area of whole figure:
[tex]\begin{gathered} 4\sqrt[]{5}+40+40+\sqrt[]{17} \\ =80+4\sqrt[]{5}+\sqrt[]{17} \end{gathered}[/tex]Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:
[tex]3\times(80+4\sqrt[]{5}+\sqrt[]{17})\approx279.202[/tex]It will cost around:
$279.20
(4, - 1); 3x - 5y = 2How do I get the real answer of this?
Step 1: Identify the question
We have the following equation given:
[tex]3x-5y=2[/tex]And for this case we have the following values for x and y given:
x=4, y=-1
We want to check if the point given (4,-1) is a solution for the equation 3x-5y=2
Step 2: Solve the problem
We just need to replace in the equation given x=4 and y=-1:
[tex]3\cdot4-(5\cdot-1)=12+5=17[/tex]Step 3: Solution to the problem
And we can conclude that the point (4,-1) is not on the line 3x-5y=2
Step 4: Solution
For this case we can see that the point is not a solution of the equation because the solution is not equal to 2
Which car traveled at the slowest rate? a.750 miles in 10 hours b. 800 miles in 12 hours c. 450 miles in 6 hours d.1000 miles in 14 hours e. 1000 miles in 14 hours
The car with the smallest speed (or slowest rate) exists the car with 800 miles in 12 hours.
What is meant by rate of speed?The ratio of the distance traveled and the time it took to travel that distance yields the rate at which cars move (also known as the speed).
To determine each unit rate (number of miles traveled in 1 hour). To determine the unit rate, we will divide the distance by the time.
rate = distance/time
Substitute the values in the above equation, we get
Then, for each car we will the speeds:
a) S = 750 mi/10 h = 75 mi/h
b) S = 800 mi/12 h = 66.66 mi/h
c) S = 450 mi/6 h = 75 mi/h
d) S = 1000 mi/14 h = 71.428 mi/h
Then we can see that the car with the smallest speed (or slowest rate) is the car with 800 miles in 12 hours.
Therefore, the correct answer is option b) 800 miles in 12 hours.
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your pay rate is 7$ per hour how mutch money di you make if you worked 1 hour
$7 per hour
if I work 1 hour i will earn $7
HelpClassify each number below as a rational number or as an irrational number
By definition:
- Rational numbers are those numbers that can be written as simple fractions. A fraction has this form:
[tex]\begin{gathered} \frac{a}{b} \\ \end{gathered}[/tex]Where "a" is the numerator and "b" is the denominator. Both are Integers, and:
[tex]b\ne0[/tex]- Irrational numbers cannot be written as simple fractions.
Then, knowing those definitions, you can identify that:
1. The number:
[tex]-\sqrt[]{25}=-5[/tex]Since -5 is an Integer, it can be written as:
[tex]=\frac{-5}{1}[/tex]Therefore, it is a Rational Number.
2. You can identify that the second number is a Repeating Decimal because the line over the decimal digits indicates that its digits are periodic.
By definition, Repeating Decimals are Rational Numbers.
3. Notice that the next number is:
[tex]-\sqrt[]{10}\approx-3.162278[/tex]Since it cannot be written as a simple fraction, it is not a Rational Number.
4. For the number:
[tex]-\frac{18}{5}[/tex]You can identify that it is a fraction whose numerator and denominator and Integers. Then, it is a Rational Number.
5. Notice that the last number is:
[tex]18\pi[/tex]By definition, π is an Irrational Number.
Therefore, the answer is:
If I work 4weeks on and one week off how many weeks per year
We know that the year has 52 weeks
From 5 weeks, you work 4. So, we can use the rule of three
Number of weeks Weeks of work
5 4
52 x
[tex]\begin{gathered} 5x=4\cdot52 \\ 5x=208 \\ x=\frac{208}{5} \\ x=41.6\text{ w}eeks \\ or\text{ 41 complete w}eeks\text{ } \end{gathered}[/tex]Need!!!!
In the following diagram, A II B
1) Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x.
2) Solve for x, showing all of your work.
Find the measure of angle 6.
The value of x in the intersecting lines is 24.
The value of angle 6 is 79 degrees.
How to find angles in intersecting lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore,
∠6 = 3x + 7(corresponding angles)
Corresponding angles are congruent.
Therefore,
3x + 7 + 4x + 5 = 180(sum of angles on a straight line)
7x + 12 = 180
7x = 168
x = 168 / 7
x = 24
∠6 = 3x + 7 = 3(24) + 7 = 72 + 7 = 79 degrees.
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if the coordinates of r are (4, 7) and the midpoint of RS is (0, 5 ), what are the coordinates of s?
To solve this problem, we recall that the formula for the coordinates of the midpoint between (x₁,y₁), and (x₂,y₂) is:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2}, \\ y=\frac{y_1+y_2}{2}. \end{gathered}[/tex]Substituting the given coordinates for the midpoint and one of the terminal points, we get:
[tex]\begin{gathered} 0=\frac{4+s_x}{2}, \\ 5=\frac{7+s_y}{2}. \end{gathered}[/tex]Solving the above equations for s_x, and s_y, we get:
[tex]\begin{gathered} s_x=0*2-4, \\ s_y=5*2-7. \end{gathered}[/tex]Finally, we get that the coordinates of s are:
[tex](-4,3).[/tex]Answer:
[tex](-4,3).[/tex]902 degrees Celsius round the temperature to the nearest ten
The temperature is 92 degrees celsius. Rounding 92 degrees celsius to the nearest ten will be 90 degrees celsius. The closest ten to 92 is definitely 90.
Therefore,
[tex]92^{\circ}\approx90^{\circ}(To\text{ the nearest tens)}[/tex]Determined whether the graph of the equation is symmetric with respect to the y-axis,the orgin,more than one of these,or none of these. y^2=x^2+20
Solution
For this case we have the following equation:
[tex]y^2=x^2+10[/tex]And on this case we have an hyperbola given by:
[tex]y^2-x^2=10[/tex]Then the correct choice is:
Origin
Solve each proportion and give the answer in simplest form 1. 6:8= n: 12 2. 2/7 = 8/n 3. n/6= 11/3 4. 4:n = 6:9
The first proportion:
[tex]6\colon8=n\colon12[/tex]can be written like this:
[tex]\frac{6}{8}=\frac{n}{12}[/tex]then, we have the following:
[tex]\begin{gathered} \frac{6}{8}=\frac{n}{12} \\ \Rightarrow n=(\frac{6}{8})\cdot12=\frac{72}{8}=9 \\ n=9 \end{gathered}[/tex]For the next proportions, we have the following:
[tex]\begin{gathered} \frac{2}{7}=\frac{8}{n} \\ \Rightarrow n=\frac{8}{\frac{2}{7}}=\frac{8\cdot7}{2}=\frac{56}{2}=23 \end{gathered}[/tex][tex]\begin{gathered} \frac{n}{6}=\frac{11}{3} \\ \Rightarrow n=\frac{11}{3}\cdot6=\frac{66}{3}=22 \end{gathered}[/tex]and finally:
[tex]\begin{gathered} \frac{4}{n}=\frac{6}{9} \\ \Rightarrow n=\frac{4}{\frac{6}{9}}=\frac{4\cdot9}{6}=\frac{36}{6}=6 \end{gathered}[/tex]6. A concert promoter's profit is p(n) = 61n - 5500, where n is the number of tickets sold. Find theprofit for the promoter if he sells 850 tickets. Show your work and explain what your answer means interms of the problem. (5 points)6
Given:prfit p(n)=61n-5500
Find: profit when he sells 850 tickets.
Explanation: n=850
put in the given equation of profit , we get
[tex]\begin{gathered} p(n)=61\times850-5500 \\ =51850-5500 \\ =46350 \end{gathered}[/tex]Final answer: the profit is 46350.