Rewrite to give an equation without logarithm. Do not solve for X. Solve the equation select the correct choice below and if necessary fill in the answer back to complete your choice
Answers
Given:
[tex]log_2(2x+9)=2[/tex]Required:
We need to solve the given equation.
Explanation:
Consider the formula.
[tex]log_a(b)=x\Rightarrow a^x=b.[/tex]The given equation can be written as follows.
[tex]2^2=2x+9[/tex][tex]4=2x+9[/tex]Solve for x.
[tex]4=2x+9[/tex]Subtract 9 from both sides of the equation.
[tex]4-9=2x+9-9[/tex][tex]-5=2x[/tex]Divide both sides by 2.
[tex]-\frac{5}{2}=\frac{2x}{2}[/tex][tex]-\frac{5}{2}=x[/tex]Final answer:
Rewrite the given equation without logrithmic.
[tex]4=2x+9[/tex]The solution for x.
[tex]x=-\frac{5}{2}[/tex]Related Questions
Write an expression for the measure of the given angle
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Solution:
Remember that the angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference. According to this, we can deduce the following expression for the measure of the given angle:
[tex]m\angle UXY=\frac{arc\text{ }UZW}{2}[/tex]Diego is trying to write the expression 2 + 1 - in a way that makes it easier tocalculate. He says, “I can switch the order of 1 and and write 2+- 1 then I canget an equivalent expression that's easier to compute.Do you agree with Diego's reasoning? Why or why not?
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While switching the order during adding or substraction,
Find the X-intercept and Y-Intercept of the line. Write your answer as exact values. do not write your answer as order pairs
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The equation of the line is given as,
[tex]8x-5y=14[/tex]The intercepts are the points at which the curve intersects the coordinate axes.
The x-intercept of the line will be the value of 'y' at which the x-coordinate becomes zero. This can be calculated as follows,
[tex]\begin{gathered} 8x-5(0)=14 \\ 8x=14 \\ x=\frac{7}{4} \\ x=1.75 \end{gathered}[/tex]Similarly, the y-intercept is the point at which the line intersects the y-axis. This can be calculated as,
[tex]\begin{gathered} 8(0)-5y=14 \\ -5y=14 \\ y=\frac{-14}{5} \\ y=-2.8 \end{gathered}[/tex]Thus, the x-intercept and y-intercept are obtained as,
[tex]\begin{gathered} \text{ x-intercept}=1.75 \\ \text{ y-intercept}=-2.8 \end{gathered}[/tex]Which graph fits this line? O y= 2x + 1 O A O D. B. x / X E. # Oc. *
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Answer: Option A
Given the above equation
y = 2x + 1
Firstly, we need to find the y and x - intercepts
To find y - intercept, make x = 0
y = 2(0) + 1
y = 0 + 1
y = 1
To find x - intercept, put y = 0
0 = 2x + 1
Collect the like terms
0 - 1 = 2x
-1 = 2x
Divide both sides by 2
2x = -1
2x/2 = -1/2
x = -1/2
Therefore, x = -1/2 and y = 1
(-1/2, 1)
Step 2: Graph the point
The triangle ABC shown on the coordinate plane below,is dilated from the origin by scale factor= 1/2. what is the location of triangle A'B'C'?
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Explanation:
With a dialation about the origin of a scale factor of 1/2 every point of the dialated figure is now one half of the points from the original figure:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]We have this points:
• A: (3, 4)
,• B: (-7, 2)
,• C: (2, 2)
The new coordinates of these points will be:
Answer:
• A': (1.5, 2)
,• B': (-3.5, 1)
,• C': (1, 1)
O GEOMETRY Perimeter involving rectangles and circles A rectangular paperboard measuring 20 in long and 13 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.) Explanation +0 13 in 20 in Check 0 in X in² 5 in³ 3/5 ? Nikida E: 6 C E E 121
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The perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
It is given to us that the measurement of rectangular paperboard are -
Length = 20in
Width = 13in
A semicircle is cut out of it.
We have to find out the perimeter of the paperboard that remains after the semicircle is removed.
Now, according to the given figure,
Radius of the semi circle = 1/2 (Width of the paperboard) ---- (1)
Let us say the radius of the semi circle is "[tex]r[/tex]".
So, from equation (1),
[tex]r = \frac{13}{2}\\ = > r = 6.5[/tex] in ---- (2)
Now, Perimeter of the paperboard that remains after the semicircle is removed =
Bottom length + Left width + Top length + Right circumference of the semicircle
= 20 + 13 + 20 + ([tex]\pi r^{2}[/tex]) [Circumference of semicircle = [tex]\pi r^{2}[/tex]]
= 53 + [[tex]\pi (6.5)^{2}[/tex]] [From equation (2), we have [tex]r = 6.5[/tex] in]
= 53 + 132.66
= 185.66 in
Thus, the perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
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I need help finding point slope form
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We were given two points to find the equation of the line, these are (4,3) and (5,5).
We need to find the point-slope form, which can be writen as follow:
[tex]y-y_1=m\cdot(x-x_1)_{}[/tex]Where (y1,x1) is one point on the line and "m" is the slope of the line. We first need to find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (y1,x1) and (x2,y2) are the two known points. We can find the slope by applying the two points given to us:
[tex]m=\frac{5-3}{5-4}=2[/tex]We can know write the expression of the line:
[tex]y-5=2\cdot(x-5)[/tex]Jessica and her father are comparing their ages. At the current time, Jessica's father is 24 years older than her l. Three years from now, Jessica father will be five times her age at the pointQUICK PLEASE
Answers
Current ages
Jessica's age = x
Jessica's father = x + 24
In 3 years time, there ages will be:
Jessica's age = x+ 3
Jessica's father = x + 24 + 3 = x + 27
But Jessica's father will be 5 times her age
Hence;
x + 27 = 5(x+3)
Open the parenthesis
x + 27 = 5x + 15
collect like term
5x - x = 27 - 15
4x = 12
Divide both-side of the equation by 4
x = 3
In the current time;
Jessica is 3 years old
Jessica's father is x + 24 = 3 + 24 = 27 years old
I know the first part but having trouble on the second part
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Take into account that the standard deviation of a probability distribution table is given by:
[tex]\sigma=\sqrt[\placeholder{⬚}]{\Sigma\left(x-\mu\right)^2P\left(x\right)}[/tex]where x is each element of the first column of the table, μ is the mean and P(x) is the corresponding values of P(x) for each value of x in the second column.
By replacing the values of the table you obtain:
[tex]\begin{gathered} \sigma=\sqrt[\placeholder{⬚}]{\left(0-3.79\right)^2\lparen0.04)+\left(1-3.79\right)^2\left(0.23\right)+\left(3-3.79\right)^2\left(0.35\right)+\left(6-3.79\right)^2\left(0.15\right)+\left(7-3.79\right)^2\left(0.23\right)} \\ \sigma=\sqrt[\placeholder{⬚}]{5.6859} \\ \sigma\approx2.38 \end{gathered}[/tex]Hence, the standard deviation of the given data is approximately 2.38
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
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A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
In this problem we have
p=kr
step 1
Find the value of k
k=p/r
we have the ordered pair (4,6)
substitute
k=6/4
k=1.5
therefore
the proportional equation is
p=1.5rInstructions: For the following real-world problem, solve using any method. Use what you've learned to determine which method would be best. Put your answer in the context of the problem and determine the appropriate final answer. A sprinkler is set to water the backyard flower bed. The stream of water and where it hits the ground at the end of the stream can be modeled by the quadratic equation -22 + 14x + 61 = 0 where x is the distance in feet from the sprinkler. What are the two solutions in exact form? 2 x V X or What are the rounded values (to two decimal places)? Which of these answers makes sense in context to be the value of the number of products? x =
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Given the next quadratic equation:
[tex]-x^2+14x+61=0[/tex]we can use the quadratic formula to solve it, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-14\pm\sqrt[]{14^2-4\cdot(-1)\cdot61}}{2\cdot(-1)} \\ x_{1,2}=\frac{-14\pm\sqrt[]{196+244}}{-2} \\ x_{1,2}=\frac{-14\pm\sqrt[]{440}}{-2} \\ x_1=\frac{-14+\sqrt[]{440}}{-2}=\frac{-14}{-2}-\frac{\sqrt[]{440}}{2}=7-\sqrt[]{110} \\ x_2=\frac{-14-\sqrt[]{440}}{-2}=\frac{-14}{-2}+\frac{\sqrt[]{440}}{2}=7+\sqrt[]{110} \end{gathered}[/tex]The rounded values (two decimal places) are:
[tex]\begin{gathered} x_1=7-10.49=-3.49 \\ x_2=7+10.49=17.49 \end{gathered}[/tex]Since x is the distance, in ft, from the sprinkler, it cannot be negative, then the answer which makes sense in the context of this problem is 17.49 ft
What is the average value of -2/5, 7/10, 1/2, -1/5
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The average of numbers is equal to sum of values to number of values.
Determine the average value of observations.
[tex]\begin{gathered} a=\frac{-\frac{2}{5}+\frac{7}{10}+\frac{1}{2}-\frac{1}{5}}{4} \\ =\frac{\frac{-4+7+5-2}{10}}{4} \\ =\frac{\frac{6}{10}}{4} \\ =\frac{3}{20} \end{gathered}[/tex]So average value of the numbers is 3/20.
complete the table using y=5x+9 (x)-1,0,1,2,3(y)
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To complete the table, plug each given x value into the equation. Then,
[tex]\begin{gathered} \text{ If x = -1} \\ y=5x+9 \\ y=5(-1)+9 \\ y=-5+9 \\ y=4 \\ \text{ So, you have the point} \\ (-1,4) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 0} \\ y=5x+9 \\ y=5(0)+9 \\ y=0+9 \\ y=9 \\ \text{ So, you have the point} \\ (0,9) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 1} \\ y=5x+9 \\ y=5(1)+9 \\ y=5+9 \\ y=14 \\ \text{ So, you have the point} \\ (1,14) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 2} \\ y=5x+9 \\ y=5(2)+9 \\ y=10+9 \\ y=19 \\ \text{ So, you have the point} \\ (2,19) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 3} \\ y=5x+9 \\ y=5(3)+9 \\ y=15+9 \\ y=24 \\ \text{ So, you have the point} \\ (3,24) \end{gathered}[/tex]Therefore, you would get the table
Enter the equation of the circle with the given center and radius. Center: (7,0); radius: 3 The equation is
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Given data:
The given coordinate of centre of the circle is (7,0).
The given radius of the circle is r=(3)^(1/2).
The equation of the circle is,
[tex]\begin{gathered} (x-7)^2+(y-0)^2=(\sqrt[]{3})^2 \\ (x-7)^2+y^2=3 \end{gathered}[/tex]Thus, the equation of the circle is (x-7)^2 +y^2 =3.
Please help me I don’t know how to solve this :(
Answers
You have already found the slope, which is 2
m =( y2-y1)/(x2-x1)
= (9200-9000)/(225-125)
= 200/100
= 2
The question tells us that it is a linear function
y = mx +b is the slope intercept form of a linear function
m is the slope and b is the initial value
c(n) = mn+b
c(n) = 2n+b
Using one of the points in the table we can find b
(125,9000)
9000 = 2(125) +b
9000 = 250+b
9000-250 = b
8750 = b
The initial value is 8750
This is also the estimate of c(0) because the initial value is when n=0
We can write the equation
c(n) = fixed cost + unit cost * number of units
The fixed cost is the initial value
the unit cost is the slope or m
c(n) = 8750 + 2n
Graph g(x)= 2|x-2|-3 and the parent function f(x)=|x|. Describe the transformations that occurred from f(x) to g(x). Then, describe the domain and range.
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The first thing to do is to graph both equations, as follows:
It is possible to check from the equations that there is no restriction for the value of x in both equations, and from the graph, we see that for each value of x, there is always a value of Y well defined. For this reason, we are able to conclude that the domain of both equations is all the real numbers.
Now, for the range of each, we can see that the values of Y for both are restricted to real numbers higher than the minimum value. For equation g(x), the range is the real numbers higher or equal to -3, while for f(x) the range is the real numbers higher or equal to 0.
15 Points and branliest for all three!
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According to SAS Congruence Theorem and the reflexive property of congruence, it can be proved that ΔSPQ ≅ ΔTPQ.
It is given to us that -
PQ bisects ∠SPT
SP ≅ TP
We have to prove that ΔSPQ ≅ ΔTPQ
Now, as PQ bisects ∠SPT,
∠SPQ = ∠TPQ
Also, according to the Reflexive Property of Congruence, PQ is a common side of both triangles - ΔSPQ and ΔTPQ.
Thus, according to SAS Congruence Theorem,
"If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent."
Therefore, according to SAS Congruence Theorem, we have proved that ΔSPQ ≅ ΔTPQ.
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Two buses leave town 1404 kilometers apart at the same time and travel toward each other. one bus travels 12 km/h faster than the other. if they meet in 6 hours, what is the rate of each bus?rate of faster bus: km/hrate of slower bus: km/h
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Let rate of faster bus be x km/h and rate of slower bus be y km /hr.
The relation between rate of slower and faster bus is,
[tex]x=y+12[/tex]Two bus are travelling in opposite direction so relative speed is,
[tex]x+y[/tex]Two buses meet in 6 hours so,
[tex]\begin{gathered} (x+y)\cdot6=1404 \\ x+y=234 \end{gathered}[/tex]Substitute y + 12 for x in the equation to obtain the value of y.
[tex]\begin{gathered} y+12+y=234 \\ 2y=234-12 \\ y=\frac{222}{2} \\ =111 \end{gathered}[/tex]Determine the value of x.
[tex]\begin{gathered} x=111+12 \\ =123 \end{gathered}[/tex]So answer is,
Rate of faster bus is 123 km/hr
Rate of slower bus is 111 km/hr.
f(x) = 2x^3+4x^2+2x+1g(x) = x^3 –x^2+7x+9Find (f+g)(x):
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Let's rewrite the functions:
[tex]\begin{gathered} f(x)=2x^3+4x^2+2x+1 \\ g(x)=x^3-x^2+7x+9 \end{gathered}[/tex]To get (f+g)(x), we just add them together:
[tex](f+g)(x)=f(x)+g(x)=2x^3+4x^2+2x+1+x^3-x^2+7x+9[/tex]We can simplify be pairing the terms with the same order:
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x)=2x^3+x^3+4x^2-x^2+2x+7x+1+9= \\ =(2+1)x^3+(4-1)x^2+(2+7)x+10=3x^3+3x^2+9x+10 \end{gathered}[/tex]So:
[tex](f+g)(x)=3x^3+3x^2+9x+10[/tex]What is the smallest figure in geometry?
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By definition, a point is the smallest figure in geometry.
Solve and graph on a number line x - 2 > -5 and x - 2 < 4
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ANSWER
Interval notation: (-3, 6)
Inequality form: -3 < x < 6
Number Line Graph:
EXPLANATION
[tex]\begin{gathered} x\text{ - 2 > - 5 OR x - 2 < 4} \\ x\text{ > - 5 + 2 OR x < 4 + 2} \\ x\text{ > -3 OR x < 6} \\ \end{gathered}[/tex]Hence, -3 < x < 6
In a dog race of 9 equally talented runners, what is the probability that Dasher, Dancer, and Prancer will finish first,second, and third, respectively?21/907201/3628801/5041/3
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Combinations and Variations of Elements
Let's suppose we have two dogs only, A and B. They can only finish in two possible orders: AB or BA.
If we add a third dog, let's say C, the combinations (better-called variations here) are now ABC, ACB, BAC, BCA, CAB, and CBA, a total of 6 variations.
Note that we added a 3rd element and the variations changed from 2 to 6, that is, the number was multiplied by 3.
If we add a fourth dog, the total number of possible variations is 6*4 = 24
Following this very same pattern, for 9 dogs, there will be a total of
9*8*7*6*5*4*3*2 = 362880 variations.
Out of these possibilities, we are trying to find the probability that the first three places are occupied by three specific dogs, and the other 6 positions can be filled up with a random variation that will give us
6*5*4*3*2 = 720 variations.
Thus the required probability is:
[tex]\begin{gathered} p=\frac{720}{362880} \\ \text{Simplifying the result, we get:} \\ p=\frac{1}{504} \end{gathered}[/tex]Kristy is paid semimonthly. The net amount of each paycheck is$750.50. What is her net annual income?a. $18,012b. $4,503c. $19,513d. $9,006
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SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define semimonthly
A semimonthly payroll is paid twice in a month.
STEP 2: Calculate the net annual income
[tex]\begin{gathered} Net\text{ annual income means the total money received in a year.} \\ \text{If net amount of each paycheck is \$750.50 and it is a semimonthly payment, then;} \\ \text{monthly payment=\$750.50}\times2=\text{\$}1501 \\ \\ There\text{ are 12 months in a year,} \\ \text{If Kristy earns in month, then the amount earned in a year is:} \\ 12\times\text{\$1501=\$18,012} \end{gathered}[/tex]Hence, her net annual income will be $18,012
OPTION a
Can you help me find the discriminant of this quadratic question aswell as the number and type of solutions?Problem: 2x^2+2=-5x
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Given the quadratic equation:
[tex]2x²+2=-5x[/tex]we can write it like this:
[tex]2x²+5x+2=0[/tex]the discriminant is the expression b²-4ac. In this case, a = 2, b = 5 and c = 2, then, the discriminant is:
[tex]b²-4ac=(5)²-4(2)(2)=25-16=9[/tex]notice that the discriminant is 9 > 0, therefore, the quadratic function has two real solutions
1.) Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return? ASW
Answers
Let's begin by listing out the information given to us:
Principal (p) = $20,000
Interest rate (r) = 5.2% = 0.052
Number of compounding (n) = 2 (semi annually)
Time (t) = 3 years
The total return is calculated as shown below:
A = p(1 + r/n)^nt
A = 20000(1 + 0.052/2)^2*3 = 20000(1 + 0.026)^6
A = 20000(1.1665) = 23,330
A = $23,330
Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quaters, and 3 dollars. How much money does he have in total
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He has 1999 cents that is equal to 20 dollars approximately as per money conversion theory that defines "The ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another."
What is money?Any tangible object or verifiable record that is commonly accepted as payment for goods and services as well as the repayment of debts, such as taxes, in a specific nation or socioeconomic setting is referred to as money.
Here,
Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quarters, and 3 dollars.
1 Penny=1 cent
1 Nickel=5 cents
1 Dime=10 cents
1 Quarter=25 cents
1 dollar=100 cents
by this,
54 pennies=54*1=54 cents
80 nickels=80*5=400 cents
22 dimes=22*10=220 cents
41 quarters=41*25=1025 cents
3 dollars=3*100=300 cents
The total money he has=54+400+220+1025+300
=1999 cents
100 cents make to 1 dollar.
so 1999 cents will make to 19.99 dollars.
According to the money conversion theory, which states that "the ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another," he has 1999 cents, which is approximately equal to $20.
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write in slope intercept form and identity the slope and y intercept. a. x/3 + y/2 = 1b. 4x -3y + 2 =0c. x - y = 5(x - y)
Answers
Consider that the slope-intercept form of the straight line with slope (m) and y-intercept (c) is given by,
[tex]y=mx+c[/tex]a.
Modify the given equation as,
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=1 \\ \frac{y}{2}=-\frac{x}{3}+1 \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=-\frac{2}{3}x+2[/tex]b.
Modify the given equation as,
[tex]\begin{gathered} 4x-3y+2=0 \\ 3y=4x+2 \\ y=\frac{4}{3}x+\frac{2}{3} \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=\frac{4}{3}x+\frac{2}{3}[/tex]c.
Modify the given equation as,
[tex]\begin{gathered} x-y=5(x-y) \\ x-y=5x-5y \\ 5y-y=5x-x \\ 4y=4x \\ y=x \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=x[/tex]what digit is in the
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SOLUTION
Given the question in the image, the following are steps to solve the question.
Step 1: Write out the given function to be plotted on the graph.
[tex]x=6[/tex]Step 2: Plot the function on the graph. Please note that x=6 means that the line on the graph will pass through the point where x-axis is equal to 6. This can be better explained on the graph below.
The red line passing through x-axis at point 6 indicates x=6.
can you help me solve this
Answers
17% of 800 is what number?
Answers
We want to obtain ;
[tex]17\text{ \% of 800}[/tex]That number would be
[tex]\begin{gathered} \frac{17}{100}\times800=\text{ }\frac{17\times800}{100} \\ =136 \end{gathered}[/tex]Therefore, 17% of 800 is 136.