The value of x is 10.04 using log properties.
What is the log in math?The power to which a number must be increased in order to obtain another number is known as a logarithm. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship. The logarithmic function logₐN = x is created from the exponential function [tex]a^{x}[/tex] = N. For instance, since ten raised to the power of two equals 100, the base ten logarithms of 100 is 2: log 100 = 2.
logₐ xy = logₐ x + logₐ y (product property)
logₐ x/y = logₐ x - logₐ y (quotient property)
logₐ [tex]x^{y}[/tex] = ylogₐ x (power property)
log2x = 3
2x = e³
x = e³/2
= 10.04
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what is the density of a 10g box measuring 10 cm by 5 cm by 5 cm
Answer:1 g/cm^3
Step-by-step explanation:
what is its base of the parallelogram is72 meters²
The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
g(x)= x^2+3h(x)= 4x-3Find (g-h) (1)
Given:-
[tex]g(x)=x^2+3,h(x)=4x-3[/tex]To find:-
[tex](g-h)(1)[/tex]At first we find the value of (g-h)(x), so we get,
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =x^2+3-(4x-3) \\ =x^2+3-4x+3 \\ =x^2-4x+6 \end{gathered}[/tex]So the value of,
[tex](g-h)(x)=x^2-4x+6[/tex]So the value of (g-h)(1) is,
[tex]\begin{gathered} (g-h)(x)=x^2-4x+6 \\ (g-h)(1)=1^2-4\times1+6 \\ (g-h)(1)=1-4+6 \\ (g-h)(1)=7-4 \\ (g-h)(1)=3 \end{gathered}[/tex]So the required value is,
[tex](g-h)(1)=3[/tex]Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities:≤12−3<−23+1
Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.
The intersection (common) of the shaded regions, which are both below the two lines, is region D.
Translate this phrase into an algebraic expression.Six less than the product of 13 and Mai's heightUse the variable m to represent Mai's height.
If m is the Mai's height you can write for the given description:
13m - 6
The previous expression means six less than the product of 13 and Mai's height.
May I please get help with this. I have tried multiple times but still could not get the correct or at least accurate answers
step 1
Find out the value of y
we have that
y+75=180 degrees ------> by same side ineterior angle
solve on a map. 1 inch equals 14.7 miles. if two cities are 3.5 inches apart on the map, how far are they actually apart? (round to a decimal)
On a map. 1 inch equals 14.7 miles
1 inch = 14.7 miles
Two cities are 3.5 inches apart on the map
Distance between two cities = 3.5 inches
[tex]\begin{gathered} \text{ 1 inch = 14.7 miles} \\ \text{ Then for 3.5 inches in miles : Multiply 3.5}\times14.7\text{ } \\ 3.5\text{ inches=3.5}\times14.7\text{ miles} \\ 3.5\text{ inches=}51.45\text{ miles} \end{gathered}[/tex]So, the distance between two cities is 51.45 miles
Answer : 51.45 miles
Write the sentence as an equation. 136 is equal to 194 times b Type a slash (/) if you want to use a division sign.
Given the sentence 136 is equal to 194 times b, we are to write this statement as an equation.
Let us take it one after the other.
For 194 times b, this can be written as;
= 194 * b
= 194b .
Since 136 is equal to the exxpression, the final equation will be gotten by simply equationf 136 to 194b as shown;
136 = 194b
You can then re-arrange
194b = 136
Hence the reuired equation is 194b = 136
I need some help. Could someone explain it to me?
Problem
We have the following table given:
x y
0 2
1 6
4 -9
8 8
Solution
We know that the domain correspond to the value of x in the relationship and then the correct answer for this case would be:
2
0
Jusrt 2,9 are the values in the domain of the function
True or False-Choose "A" for true or "B" for false.40. The inverse property of addition states that a number added to its reciprocal equals one.41. The associative properties state that the way in which numbers are grouped does notaffect the answer.42. The identity property of addition states that zero added to any number equals thenumber.43. The distributive property is the shortened name for the distributive property ofmultiplication over addition.44. The commutative property of addition states that two numbers can be added in anyorder and the sum will be the same.45. is the multiplicative inverse of35346. One is the identity element for addition.
Given
Statements
Find
Correctness of statements
Explanation
40) False (sum of number and its opposite is 0)
41)True
42) True
43) True
44) True
45) True
46) False (One is Identity Element for multiplication)
Final Answer
40) False
41)True
42) True
43) True
44) True
45) True
46) False
How many ones are between 1 and 1,000,000 (inclusive)?
There are 600,001 ones are between 1 and 1,000,000.
By using the below process we can find the number of ones between 1 and 1,000,000.
The number of times a digit 2 to 9 digit appears in numbers 1 to [tex]10^n = n(10^(^n^-^1^))[/tex].
The number of times the digit 1 appears in numbers in numbers 1 to [tex]10^n = n(10^(^n^-^1^)) + 1[/tex]
Therefore, the number of times a digit 1 appears in numbers 1 to 1,000,000 [tex]= 6(10^(^6^-^1^)) + 1\\= 6(10^5) + 1\\= 600,000 + 1\\= 600,001[/tex]
Therefore, there are 600,001 ones are between 1 and 1,000,000.
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Identity two angles that are marked congruent to each other on the diagram below.(Diagram is not to scale.)Mthth& congruent toSub Arwwer
Congruency in this context is a term that describes a pair of angles as being identical.
In our shape, we have a parallelogram and
Hi, can you help me to solve thisexercise, please!!For cach polynomial, LIST all POSSIBLE RATIONAL ROOTS•Find all factors of the leading coefficient andconstant value of polynonnal.•ANY RATIONAL ROOTS =‡ (Constant Factor over Leading Coefficient Factor)6x^3+7x^2-3x-1
1) We can do this by listing all the factors of -1, and the leading coefficient 6. So, we can write them as a ratio this way:
[tex]\frac{p}{q}=\pm\frac{1}{1,\:2,\:3,\:6}[/tex]Note that p stands for the constant and q the factors of that leading coefficient
2) Now, let's test them by plugging them into the polynomial. If it is a rational root it must yield zero:
[tex]\begin{gathered} 6x^3+7x^2-3x+1=0 \\ 6(\pm1)^3+7(\pm1)^2-3(\pm1)+1=0 \\ 71\ne0,5\ne0 \\ \frac{1}{2},-\frac{1}{2} \\ 6(\pm\frac{1}{2})^3+7(\pm\frac{1}{2})^2-3(\pm\frac{1}{2})+1=0 \\ 2\ne0,\frac{7}{2}\ne0 \\ \\ 6(\pm\frac{1}{3})^3+7(\pm\frac{1}{3})^2-3(\pm\frac{1}{3})+1=0 \\ 1\ne0,\frac{23}{9}\ne0 \\ \frac{1}{6},-\frac{1}{6} \\ 6(\frac{1}{6})^3+7(\frac{1}{6})^2-3(\frac{1}{6})+1=0 \\ \frac{13}{18}\ne0,-\frac{5}{3}\ne0 \end{gathered}[/tex]3) So the possible roots are:
[tex]\pm1,\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6}[/tex]But there are no actual rational roots.
Graphed the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation
To dilated the figure by a scale factor 3 and center origin
Multiply the coordinates of each point by 3
The image of the point (x, y) is (3x, 3y)
The zookeeper records how many scoops of peanuts she feeds the elephant for several days . Tuesday 21 Wednesday 19 5/8.
Explanation:
We want to know the difference between the amount of scoops she fed the elephant on Wednesday and on Tuesday:
[tex]21-19\frac{5}{8}[/tex]We can write the second number as an improper fraction:
[tex]21-(19\cdot\frac{8}{8}+\frac{5}{8})=21-(\frac{152}{8}+\frac{5}{8})=21-\frac{157}{8}[/tex]And now substract the two numbers:
[tex]\begin{gathered} 21-\frac{157}{8}=\frac{21\cdot8}{8}-\frac{157}{8} \\ 21-\frac{157}{8}=\frac{168}{8}-\frac{157}{8} \\ 21-\frac{157}{8}=\frac{168-157}{8}=\frac{11}{8} \end{gathered}[/tex]Answer:
She fed the elephant 11/8 scoops of peanuts more on Tuesday than on Wednesday
the marketing department of a company has determined that the profit for selling x units of a product is appropriated by function f(x)= 15× -600
You have the following function for the profit for selling x units of a product:
f(x) = 15x - 600
in order to determine the profit for 15,600 units, replace x = 15,600 into the previous function and simplify:
f(15,600) = 15(15,600) - 600 = 233,400
Hence, the profit for 15,600 units is $233,400
there are 3 members on a hockey team (including all goalie) at the end of a hockey game each member if the team shakes hands with each member of the opposing team. how many handshakes occur?
Hi I need help with this
Knowledge CheckUse the distributive property to remove the parentheses.--7(-5w+x-3)X 5
The distributive property states that:
[tex]k\cdot\left(a+b+c\right?=k\cdot a+k\cdot b+k\cdot c.[/tex]In this problem, we have the expression:
[tex]-7\cdot(-5w+x-3)=(-7)\cdot(-5w+x-3).[/tex]Comparing this expression with the general expression of the distributive property, we identify:
• k = (-7),
,• a = -5w,
,• b = x,
,• c = -3.
Using the general expression for the distributive property with these values, we have:
[tex]\left(-7\right)\cdot(-5w)+\left(-7\right)\cdot x+\left(-7\right)\cdot(-3).[/tex]Simplifying the last expression, we get:
[tex]35w-7x+21.[/tex]AnswerApplying the distributive property to eliminate the parenthesis we get:
[tex]35w-7x+21[/tex](A) The lines have different slopes and intersect at one point?(B) The lines have the same slope and y intercept.?(C) The lines are parallel and do not intersect.?(D) The lines have the same slope and y-intercept.?(E) Infinitely many solutions.?(F) They are the same line.? (G) No Solution ? (H) One solution.?
Recall that if two lines have the same slop then these two lines are parallel to each other.
the y-intercept is an x-coordinate of the point where the line intersects at the y-axis.
Consider graph 1.
The line intersects at one point and has different slopes, hence this has one solution.
(A) and (H) is true for graph 1.
Consider graph 2.
The lines have the same slope, therefore parallel but there is no y-intercept point.
This have infinitely many solutions.
They are also the same line.
(E) and (F) is true for this graph 2.
Consider graph 3.
The lines have the same slope and they are parallel.
It gives B) is correct
They do not intersect since parallel does not intersect each other.
It gives C) is correct
There is no solution since they do not intersect.
It gives G) is correct.
These lines have intercepted at -1 and -4.
It gives D) is correct
B), D), C), G), D) are correct for graph 3.
Results:
Options Graph
A) 1
B) 3
C) 3
D) 3
E) 2
F) 2
G) 3
H) 1
help meeeeeeeeee pleaseee !!!!!
The values of the functions are determined as:
a. (f + g)(x) = 3x² + 2x
b. (f - g)(x) = -3x² + 2x
c. (f * g)(x) = 6x³
d. (f/g)(x) = 2/3x
How to Determine the Value of a Given Function?To evaluate a given function, substitute the equation for each of the functions given in the expression that needs to be evaluated.
Thus, we are given the following functions as shown above:
f(x) = 2x
g(x) = 3x²
a. To find the value of the function (f + g)(x), add the equations for the functions f(x) and g(x) together:
(f + g)(x) = 2x + 3x²
(f + g)(x) = 3x² + 2x
b. To find the value of the function (f - g)(x), find the difference of the equations of the functions f(x) and g(x):
(f - g)(x) = 2x - 3x²
(f - g)(x) = -3x² + 2x
c. To find the value of the function (f * g)(x), multiply the equations of the functions f(x) and g(x) together:
(f * g)(x) = 2x * 3x²
(f * g)(x) = 6x³
d. To find the value of the function (f/g)(x), find the quotient of the equations of the functions f(x) and g(x):
(f/g)(x) = 2x/3x²
(f/g)(x) = 2/3x.
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help me pleaseeeeeeeee
Answer:
x = -2
Step-by-step explanation:
f(x) = y
f(x) represents the y-axis
f(x) = -3 or y = -3 or y = (0, -3)
When y = -3, x = -2
x = -2
I hope this helps!
Use U-Subscription to solve the following polynomial. Compare the imaginary roots to the code breaker guide. Hi this is a project and this is one of the questions, I have the guide so ignore the code piece part.
We will substitute the variable x with the variable u using the following relation:
[tex]u=x^2[/tex]Then, we can convert the polynomial as:
[tex]4x^4+2x^2-12=4u^2+2u-12[/tex]We can use the quadratic equation to calculate the roots of u:
[tex]\begin{gathered} u=\frac{-2\pm\sqrt[]{2^2-4\cdot4\cdot(-12)}}{2\cdot4} \\ u=\frac{-2\pm\sqrt[]{4+192}}{8} \\ u=\frac{-2\pm\sqrt[]{196}}{8} \\ u=\frac{-2\pm14}{8} \\ u_1=\frac{-2-14}{8}=-\frac{16}{8}=-2 \\ u_2=\frac{-2+14}{8}=\frac{12}{8}=1.5 \end{gathered}[/tex]We have the root for u: u = -2 and u = 1.5.
As u = x², we have two roots of x for each root of u.
For u = -2, we will have two imaginary roots for x:
[tex]\begin{gathered} u=-2 \\ x^2=-2 \\ x=\pm\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\cdot\sqrt[]{-1} \\ x=\pm\sqrt[]{2}i \end{gathered}[/tex]For u = 1.5, we will have two real roots:
[tex]\begin{gathered} u=1.5 \\ x^2=1.5 \\ x=\pm\sqrt[]{1.5} \end{gathered}[/tex]Then, for x, we have two imaginary roots: x = -√2i and x = √2i, and two real roots: x = -√1.5 and x = √1.5.
Answer:
Let u = x²
Equation using u: 4u² + 2u - 12
Solve for u: u = -2 and u = 1.5
Solve for x: x = -√2i, x = √2i, x = -√1.5 and x = √1.5
Imaginary roots: x = -√2i and x = √2i
Real roots: x = -√1.5 and x = √1.5
A manufacturer pays its assembly line workers $11.06 per hour. In addition, workers receive a piece of work rate of $0.34 per unit produced. Write a linear equation for the hourly wages W in terms of the number of units x produced per hour. Linear equation: W = _______ What is the hourly wage for Mike, who produces 17 units in one hour? Mike’s wage = _________
Let's assume the following variables.
x = number of units produced
It is stated in the problem that for every unit produced, there is an additional wage of $0.34. Hence, on top of $11.06 per hour wage, there will be an additional of $0.34x per hour. In equation, we have wage per hour:
[tex]W=11.06+0.34x[/tex]If Mike was able to produce 17 units, our x here is 17. Let's plug this value to the formula.
[tex]W=11.06+0.34(17)[/tex]Then, solve.
[tex]\begin{gathered} W=11.06+5.78 \\ W=16.84 \end{gathered}[/tex]Therefore, Mike's hourly wage is $16.84.
Ex) The function f(x) is shown on the graph. Plot two points on this grid to create the graph of the line that would represent f(x) - 2.
ANSWER and EXPLANATION
We have the graph of the function f(x) given.
We want to find 2 points that will represent f(x) - 2.
This (f(x) - 2) is a transformation of the function f(x).
It is called a vertical translation. It means that the function moves on the y axis.
It is generally represented as:
f(x) + b
Comparing the required translation with the general form, we can conclude that there is a -2 shift on the y axis.
Therefore, to find two points for the new function, we have to simply pick two points from the given graph and subtract 2 from their y coordinates.
Let the two points be:
(0, 1) and (-4, 4)
Therefore, the two points will be:
(0, 1) => (0, 1 - 2) = (0, -1)
(-4, 4) => (-4, 4 - 2) = (-4, 2)
Plotting them:
The green line is the line of the new function.
On a particular college campus, 22% of the students belong to a fraternity or sorority. If 56 college students are randomly chosen:a. What is the probability that 16 are members of a fraternity or sorority?Round to at least three decimal places.Incorrectb. What is the mean of this distribution? Round to at least one decimal.Incorrectc. What is the standard deviation of this distribution? Round to at least one decimal
Explanation
Part A
From the question,
[tex]\begin{gathered} p=\frac{22}{100};q=1-\frac{22}{100} \\ p=0.22;q=0.78 \\ Also,n\text{ =56} \end{gathered}[/tex]Using the binomial probability distribution formula;
[tex]undefined[/tex]Which statement best reflects the solution(s) of the equation? X/ x-1 - 1/ x-2 = 2x-5/x^2-3x+2 There is only one solution: x=4. The solution x=1 is an extraneous solution. There are two solutions: x=2 and x=3. There is only one solution: x=3. The solution x=2 is an extraneous solution. There is only one solution: x=3. The solution x=1 is an extraneous solution.
The best reflects solution of the equation is, There is only one solution: x = 3. The solution x = 2 is an extraneous solution.
What is extraneous solution?
An extraneous solution is a root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.
We are given the following equation,
(x / x - 1) - (1 / x - 2) = (2x - 5)/(x^2 - 3x + 2)
Solving the given equation we have,
(x^2 - 3x + 1) / (x^2 - 3x + 2) = (2x - 5) / (x^2 - 3x + 2)
x^2 - 3x + 1 = 2x - 5
x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x - 3) - 2(x - 3) = 0
(x - 3)(x - 2) = 0
(x - 3) = 0, (x - 2) = 0
x = 3, x = 2
At x = 2 the denominator of the equation will be 0. So solution of the equation is not valid at x = 2.
Therefore, x = 3 is the only one solution. The solution x = 2 is an extraneous solution.
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Find g(x), where g(x) is the translation 4 units left of f(x)=|x|.
The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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PLS HELP WILL ASAP WILL GIVE BRAINLIST
Answer:
if the bottom side is 4n + 15, then n=8
n times 5 is 40
40+7=47
Explain why m<1>m<3.which statement below can be made, according to the corollary to the Triangle Exterior Angle Theorem?
In the given image you have that m∠1 is lower than angle m∠3 becasue it is clear that angle ∠1 is an angle greater than 90° and angle ∠3 is lower than 90°. Then m∠1 > m∠3.
Now, in order to determine which of the given statements is true for the given figure, you take into account that the exterioir angle theorem stablishes that the measure of an exterior angle of the triangle is greater that any of the measure of the remote interioir angles of the triangle.
Thus, you can notice that the measure of the external angle ∠1 is greater than the measure either angle ∠4 or angle ∠2.
Hence, following statement is true:
m∠1 > m∠4 and m∠1 > m∠2