-Exponential and Logarithmic Functions- Solve the following, round the answer to the nearest hundredth.
Answer:
x = 1.70
Explanation:
We were given that:
[tex]\begin{gathered} 5^x=15.4 \\ \text{Take the natural logarithm of both sides, we have:} \\ \ln 5^x=\ln 15.4 \\ x\cdot\ln 5=\ln 15.4 \\ \text{Divide both sides by ''ln5'', we have:} \\ x=\frac{\ln 15.4}{\ln 5}=1.699 \\ x=1.699\approx1.70 \\ x=1.70 \\ \\ \therefore x=1.70 \end{gathered}[/tex]Therefore, x = 1.70
simplify the rational expression. 18x3y5 45x5y9
Which choice is equivalent to the expression below?V-81A. 91B. AiC.D. -29E. -9SUBMIT
Given the expression:
[tex]\sqrt[]{-81}[/tex]As we know, there is no square root for the negative numbers
But, using the complex numbers:
[tex]i=\sqrt[]{-1}[/tex]So, the given expression can be written as:
[tex]\sqrt[]{-81}=\sqrt[]{-1}\cdot\sqrt[]{81}=i\cdot9=9i[/tex]So, the answer will be option A) 9i
Find angle a in the taper shown,x = 9.342 inchesy = 6.692 inchesz = 2.952 inches
We need to find angle a in the figure.
We know that:
x = 9.342 inches
y = 6.692 inches
z = 2.952 inches
We can do so by finding the legs in the following triangle:
The adjacent leg is x. And the opposite leg is found by subtracting z from y, and then dividing the result by two (assuming the figure is symmetric):
[tex]\frac{y-z}{2}[/tex]Thus, we have:
[tex]\begin{gathered} \sin a=\frac{\text{ opposite leg}}{\text{ adjacent leg}} \\ \\ \sin a=\frac{\frac{y-z}{2}}{x} \\ \\ \sin a=\frac{\frac{6.692-2.952}{2}}{9.342} \\ \\ \sin a=\frac{1.87}{9.342} \\ \\ a=\arcsin\left(\frac{1.87}{9.342}\right) \\ \\ a\cong11.55\degree \end{gathered}[/tex][tex]5x + 17 = 82[/tex]simplify as much as possible
To answer this question, we can follow the next steps:
1. Subtract 17 to both sides of the equation (we apply here the subtraction property of equality):
[tex]5x+17-17=82-17\Rightarrow5x+0=65\Rightarrow5x=65[/tex]2. To isolate the variable, x, in the equation, we need to divide by 5 to both sides of the equation, as follows:
[tex]\frac{5x}{5}=\frac{65}{5}\Rightarrow\frac{5}{5}=1\Rightarrow x=\frac{65}{5}\Rightarrow x=13[/tex]We can check this result if we substitute this last value into the original equation:
[tex]5x+17=82\Rightarrow5(13)+17=82\Rightarrow65+17=82\Rightarrow82=82[/tex]The result is always TRUE.
Therefore, the value for the unknown value of x is x = 13.
Write all the possible integer values of x.
x > 1 and x ≤ 6
Separate answers with commas.
Step-by-step explanation:
college level ? what teacher puts such a question in on college level ? and you can't answer this ?
that is middle school basics.
what is going on ?
x can have in the defined interval the integer values
2, 3, 4, 5, 6
there, that was all to it ...
A)what height was the basketball thrown from? B)what is the maximum height the basketball went ?C)after how many seconds did the basketball reach its maximum height?D)how many seconds did it take for the basketball to hit the ground ? make sure you look at the exact value in the graph?pleaseeeeeeeeeeeeeeee
We have the following:
The questions can be found thanks to the graph of the statement
A)what height was the basketball thrown from?
The graph starts at the point (0, 6) therefore the basketball was thrown from 6 feet height
B)what is the maximum height the basketball went ?
The highest point of the graph is (2, 10), therefore the maximum height is 10 ft
C)after how many seconds did the basketball reach its maximum height?
The highest point of the graph is (2, 10), therefore the time it reached this height was 2 seconds
D)how many seconds did it take for the basketball to hit the ground ? make sure you look at the exact value in the graph?
The ground would be when the value of y is equal to 0, therefore according to the point (5.162, 0) the time was 5.162 seconds
Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
if the slope of a line and a point on the line are known the equation of the line can be found using the slope intercept form y=mx+b. to do so substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. using the above technique find the equation of the line containing the points (-8,13) and (4,-2).
The general equation of a line is;
[tex]y\text{ = mx + b}[/tex]m is the slope and b is the y-intercept
To find the slope, we use the equation of the slope as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (-8,13)} \\ (x_2,y_2)\text{ = (4,-2)} \\ \\ m\text{ = }\frac{-2-13}{4-(-8)}\text{ = }\frac{-15}{12}\text{ = }\frac{-5}{4} \end{gathered}[/tex]We have the partial equation as;
[tex]\begin{gathered} y\text{ = }\frac{-5}{4}x\text{ + b} \\ \\ \text{Substitute the point (-8,13)} \\ \text{x = -8 and y = 13} \\ \\ 13\text{ = }\frac{-5}{4}(-8)\text{ + b} \\ \\ 13\text{ = 10 + b} \\ b\text{ = 13-10 = 3} \end{gathered}[/tex]We have the complete equation as;
[tex]y\text{ =}\frac{-5}{4}x\text{ + 3}[/tex]T is in seconds and L is the length of the pendulum in centimeters. Find the period of the pendulum of the given lengths. Give your answer to two decimal places using 3.14 for π. Show and explain your work below. a. L = 23 cm b. L = 192 cm
The period of the pendulum in each case is given as follows:
a. L = 23 cm: 0.96 s.
b. L = 192 cm: 2.78 s.
Period of pendulumThe period of a pendulum is defined according to the following equation:
P = 2π sqrt(L/g)
In which the parameters are as follows:
L is the length of the pendulum which we want to find the period.g = 9.8 m/s² is the acceleration of the pendulum due to the gravity.For a length of 23 cm = 0.23m, in item a, considering 3.14 for π, the period is calculated as follows:
P = 6.28 x sqrt(0.23/9.8) = 0.96 s.
In item b, the length is of 192 cm = 1.92 m, as each cm has 100 m, hence the period is given by:
P = 6.28 x sqrt(1.92/9.8) = 2.78 s.
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The Cunninghams are moving across the country. Mr.Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 55 mph and sheaverages 75 mph, how many hours will it take Mrs. Cunningham to catch up to Mr. Cunninham to catch up to mr.cunningham
Solution:
Remember, distance traveled is the rate times the time. (d = rt) Mrs. Cunningham will overtake Mr. Cunningham when they have traveled the same distance.
Mrs. Cunningham's equation will be:
[tex]d=\text{ }75t[/tex]Since he was traveling 3 hours longer, Mr. Cunningham's equation will be:
[tex]d=55(t+3)[/tex]If they travel the same distance, the equations can be set equal to each other:
[tex]\text{ }75t=55(t+3)[/tex]applying the distributive property, this is equivalent to:
[tex]\text{ }75t=55t\text{ +165}[/tex]this is equivalent to:
[tex]75t-55t\text{ = 165}[/tex]this is equivalent to:
[tex]20t\text{ = 165}[/tex]solving for t, we obtain:
[tex]t\text{ =}\frac{165}{20}=8.25[/tex]So that, we can conclude that the correct answer is:
It will take Mrs. Cunningham 8.25 hours to overtake her husband.
what is 40+56 in GCF
The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
[tex]\begin{gathered} 40=2\cdot2\cdot2\cdot5 \\ 56=2\cdot2\cdot2\cdot7 \end{gathered}[/tex]We now multiply the numbers that appear on both.
[tex]\text{GCF}=2\cdot2\cdot2=8[/tex]We now apply the distributive property:
[tex]8\cdot(5+7)[/tex]M/4 + q ; m=2/3 , and q= 1/4
Given the expression:
[tex]\frac{m}{4}+q[/tex]We will find the value of the expression when m=2/3, and q= 1/4
So,
[tex]\begin{gathered} (\frac{2}{3}\div4)+\frac{1}{4} \\ \\ =(\frac{2}{3}\times\frac{1}{4})+\frac{1}{4} \\ \\ =\frac{1}{6}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{5}{12} \end{gathered}[/tex]So, the answer will be: 5/12
Which is 56,900,000 in scientific notation?o 5.69 x 10⁷o 56.9 x 10⁷o 5.69 X 10⁶o 56.9 X 10⁶
Answer:
5.69 x 10⁷
Explanation:
A number is said to be in the scientific notation when it is written as a product of a number between 1 and 10 and a power of 10.
The number 56,900,000 in scientific notation is 5.69 x 10⁷.
The correct choice is A.
Match each expression on the left with its sum on the right. Some answer options on the right will not be used.
To match the expression with the sum, what you have to do is solve each sum.
Remember that to sum/subtract two fractions, both of them should be expressed using the same denominator,
1)
[tex]-\frac{2}{3}+\frac{5}{6}[/tex]The denominators of these fractions are "3" and "6", the least common denominator between both values is 6. To express the first fraction as its equivalent with denominator 6, you have to multiply it by 2:
[tex]-\frac{2\cdot2}{3\cdot2}+\frac{5}{6}=-\frac{4}{6}+\frac{5}{6}[/tex]Now you can proceed to add both fractions:
[tex]-\frac{4}{6}+\frac{5}{6}=\frac{-4+5}{6}=\frac{1}{6}[/tex]The result for this sum is 1/6
2)
[tex]\frac{7}{12}+(-\frac{3}{4})[/tex]First, simplify both symbols, when a plus symbol and a minus symbol and next to each other, the plus sign gets canceled:
[tex]\frac{7}{12}+(-\frac{3}{4})=\frac{7}{12}-\frac{3}{4}[/tex]To subtract both fractions the first step is to express them using the same denominator. The least common denominator between 12 and 4 is 12, to express -3/4 as its equivalent with denominator 12, you have to multiply the fraction by 3:
[tex]\frac{7}{12}-\frac{3\cdot3}{4\cdot3}=\frac{7}{12}-\frac{9}{12}[/tex]Next, subtract both fractions:
[tex]\frac{7}{12}-\frac{9}{12}=\frac{7-9}{12}=-\frac{2}{12}[/tex]The result is no in its simplest form, 2 and 12 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator by 2:
[tex]-\frac{2\div2}{12\div2}=-\frac{1}{6}[/tex]The result for this expression is -1/6
3)
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Same as before, the first step is to express both fractions with the same denominator. the least common denominator for both fractions is 8. To express -1/4 as its equivalent with denominator 8, you have to multiply the fraction by 2
[tex]-\frac{1\cdot2}{4\cdot2}+\frac{3}{8}=-\frac{2}{8}+\frac{3}{8}[/tex]Next, add both fractions:
[tex]-\frac{2}{8}+\frac{3}{8}=\frac{-2+3}{8}=\frac{1}{8}[/tex]The result for this sum is 1/8
So the corresponding matches are:
[tex]\begin{gathered} 1)-\frac{2}{3}+\frac{5}{6}=\frac{1}{6} \\ 2)\frac{7}{12}+(-\frac{3}{4})=-\frac{1}{6} \\ 3)-\frac{1}{4}+\frac{3}{8}=\frac{1}{8} \end{gathered}[/tex]231231312312312312311
Answer: 3456765432345
Step-by-step explanation:
2345676543456
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was5%, and the tax in the second city was 6%. The total hotel tax paid for the two cities was $552.50. How much was the hotel charge in each city before tax?Note that the ALEKS graphing calculator can be used to make computations easier.
SOLUTION
Let us represent the hotel charge with different variables x and y:
Let the hotel charge before tax in the first city be x
Let the hotel charge before tax in the second city be y
Now, let us represent the word problem in equation form:
First, we were told that the charge before tax in the second city is $500 more than the charge before tax in the first city, this can be represented thus:
[tex]y=x+500\ldots\text{.eqn 1}[/tex]Going forward in the question, we were told the tax for the first city (x) is 5%(0.05), and the tax for the second city is 6%(0.06). The total tax from both cities is $552.5, this expression can be written mathematically as:
[tex]0.05x+0.06y=552.5\ldots\ldots\text{eqn 2}[/tex]Now, by solving equation 1 and equation 2 simultaneously, we will obtain the hotel charge in each city before tax. (that is the value of x and y).
[tex]\begin{gathered} y=x+500 \\ 0.05x+0.06y=552.5 \\ \end{gathered}[/tex]Using, the substitution method of solving simultaneous equation, we will solve further:
[tex]\begin{gathered} \text{substitute equation 1 into equation 2} \\ 0.05x+0.06(x+500)=552.5 \\ 0.05x+0.06x+30=552.5 \\ 0.11x+30=552.5 \end{gathered}[/tex][tex]\begin{gathered} 0.11x=552.5-30 \\ 0.11x=522.5 \\ x=\frac{522.5}{0.11} \\ x=4750 \end{gathered}[/tex]The hotel charge before tax in the first city is $4750.
Now, substitute the value of x into equation 1 to get the value of y (hotel charge before tax in the second city)
[tex]\begin{gathered} y=x+500 \\ x=4750 \\ y=4750+500 \\ y=5250 \end{gathered}[/tex]The hotel charge before tax in the second city is $5250.
Which of the following graphs is a polynomial function with intercepts of(-2,0), (1, 0), and (4, 0)711-15 4NO C.O D.
Explanation
We are given the following:
We are required to determine which of the following graphs is a polynomial function with intercepts of
(-2,0), (1, 0), and (4, 0).
This can be achieved by looking for the graph that crosses the x-axis at the points -2, 1 and 4.
Hence, the answer is option C.
The National Oceanic and Atmospheric Administration tracks the amount of oysters harvested from the Chesapeake Bay each year.Years since 1900 2 28 53 67 78 89Oysters (metric tons) 54.2 22.5 7.38 5.28 3.52 2.38Find the exponential regression equation that models this data.Ay=-58(-0.964)OB. y = -58(0.964)Oc.y=58(0.964)*OD.y=58(-0.964)*Reset SelectionPreviouNext
Explanation
We are given the following table:
We are required to determine the exponential regression equation that models the data.
This is achieved thus:
We know that an exponential equation is given as:
[tex]y=ab^x[/tex]Using a graphing calculator, we have:
From the graph, we have:
[tex]\begin{gathered} a=58 \\ b=0.964 \end{gathered}[/tex]Hence, the answer is:
[tex]y=58(0.964)^x[/tex]A linear function has a slope of 11. Interpret this slope with a complete sentence using the words“inputs” and “outputs”. (1 point)As the inputs________,_______
Answer
the inputs increase by 1 and the outputs increase by 11
Step-by-step explanation:
The standard form of a linear function is written as
y = mx + c
where m = slope
Since the slope is 11
y = 11x + c
This implies that the inputs increase by 1 and the outputs increase by 11
Question 6 of 1
For f(x)-3x+1 and g(x)=x²-6, find (f-g)(x).
A. -x²+3x+7
OB.x²-3x-7
O C. 3x²-17
OD. -x²+3x-5
-x² + 3x + 7 is value of function .
What is function in math?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.f(x) = 3x + 1
g(x) = x² - 6
Then,
According to the' question :-
(f - g)(x) = f(x) - g(x)
= 3x + 1 - (x² - 6)
= 3x + 1 - x² + 6
= -x² + 3x + 7
Hence,
Option 1st : -x² + 3x + 7 is Correct.
Learn more about functions
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how many 3×3 cm squares would fit in a 4×6 inch rectangle
Answer:2
Step-by-step explanation:
6 divided by 2 would be 3, which is the length size of the square. The height does not allow to stack, which means you can fit two squares.
4. Ifline m has the equation y = 3x - 1, and line k is perpendicular to m and goes through the point (-4,3), find the equation of line k.
Answer:
The equation of the line k is
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Explanation:
Given that k is perpendicular to line m, defined as:
y = 3x - 1
the slope of k is the negative reciprocal of the slope of line m.
The slope of m is 3
The negative reciprocal of m is -1/3 (this is the slope of k)
Therefore, k is in the form
[tex]y=-\frac{1}{3}x+b[/tex]Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b
[tex]\begin{gathered} 3=-\frac{1}{3}(-4)+b \\ \\ 3=\frac{4}{3}+b \end{gathered}[/tex]Solving for b by subtracting 4/3 from both sides
[tex]\begin{gathered} b=3-\frac{4}{3} \\ \\ =\frac{5}{3} \end{gathered}[/tex]The equation is therefore,
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Multiplying and Dividing Integers 10-16 Name: 1. As a cold front passed through Temple, the temperature changed steadily over 6 hours. Altogether it change -18 degrees. What was the change in temperature each hour for the 6 hours? a.-18 - 6 = -3 degrees b. 18 - 6 = 3 degrees c. 18 + 6 = 24 degrees d. 18 - 6 = 12 degrees 2. Q. Four college roommates rented an apartment together. When they moved out, they were charged $1500 for damages to the carpet and walls. The roommates agreed to equally share the cost. What integer represents how much each person will have to pay?
Given the total change in temperature in 6 hours, it is necessary to divide it by the number of hours
[tex]-\frac{18}{6}=-3[/tex]The change in temperature each hour is -3 degrees
translate the following verbal statement into an algebraic equation and then solve: demetrius paid 9$ for a matinee movie. this is 1$ less than the price in the evening what is the price of the movie at night?use x for your variable equation ________x=______
Answer:
x = price of the movie at night
x = $9 + $1
Explanation:
We need to find the price of the movie at night, so, let's call x the price of the movie at night.
Then, the price of the matinee movie $9 is $1 less than the price in the evening. Therefore, we can write the following equation:
9 = x - 1
Solving for x, we get:
x = 9 + 1
Can u please help me solve? I'm reviewing for finals.
Given:
Consider the given graph as a reference of the solution.
To find:
[tex]-3(u\cdot v)[/tex]Explanation:
By analyzing the graph, we can define the coordinate of vector u and v:
[tex]\[\begin{align} & \vec{u}=(-8,-9)-(0,0)=(-8,-9) \\ & \vec{v}=(3,7)-(0,0)=(3,7)\end{align}\][/tex]Now, let perform the dot product of two vectors,
[tex]\begin{gathered} u\cdot v=(-8,-9)\cdot(3,7) \\ u\cdot v=(-8)(3)+(-9)(7) \\ u\cdot v=-24-63 \\ u\cdot v=-87 \end{gathered}[/tex]Now, perform the required operation,
[tex]\begin{gathered} -3(u\cdot v) \\ =-3(-87) \\ =261 \end{gathered}[/tex]Final answer:
Hence, the required solution is:
[tex]-3(u\cdot v)=261[/tex]The sum of two numbers is 40. If 2 is added to the larger number, theresult is equal to twice the smaller number. What are the two numbers?
We have 2 numbers. We can call them x and y, being x the smaller one.
The sum of this two numbers is 40, so we can write:
[tex]x+y=40[/tex]We know that if 2 is added to the larger number (that we name as y), the result is twice the smaller number, that would be 2x. Then, we can express this as:
[tex]y+2=2x[/tex]We can express y in function of x from the second equation and then replace it in the first equation to solve for x:
[tex]y+2=2x\Rightarrow y=2x-2[/tex][tex]\begin{gathered} x+y=40 \\ x+(2x-2)=40 \\ 3x-2=40 \\ 3x=40+2 \\ 3x=42 \\ x=\frac{42}{3} \\ x=14 \end{gathered}[/tex]Now, we can calculate y as:
[tex]\begin{gathered} y=2x-2 \\ y=2(14)-2 \\ y=28-2 \\ y=26 \end{gathered}[/tex]Answer: the two numbers are 14 and 26.
numbers in order from greatest to least 1/5 0.12 0.17
1/5 = 0.2
the order is:
1/5
0.17
0.12
Explain if the triangles are similar using SAS-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)
We have two triangles GBL and XYL.
From the picture we notice that the GL=39 and BL=34. We also notice that XL=30 and YL=27.
The SAS theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
This means that we need that:
[tex]\frac{GL}{XL}=\frac{BL}{YL}[/tex]and that the angle between them is the same.
It is clear that the angle L is the same for both triangles, hence we only need to proof tha the sides are congruent, but in this case:
[tex]\frac{39}{30}\ne\frac{34}{27}[/tex]since the sides are not proportional, we conclude that triangles are not congruent.
Find the interest and future value of a deposit of $12,000 at 5.5% simple interest for 10 years.
Given:
Principal - $12,000
Annual Interest Rate = 5.5% or 0.055 in decimal form
Time in years = 10 years
Find: simple interest and future value
Solution:
The formula for getting the simple interest is:
[tex]Interest=Principal\times Rate\times Time[/tex]Let's replace the variables in the formula with their corresponding numerical value.
[tex]Interest=12,000\times0.055\times10[/tex][tex]Interest=6,600[/tex]The interest after 10 years is $6, 600.
So, if the interest is 6,600, the future value of the money is:
[tex]FV=Principal+Interest[/tex][tex]FV=12,000+6,600[/tex][tex]FV=18,600[/tex]The future value of the deposited money after 10 years is $18, 600.