Which of the following is the equation c^(4d+1)=7a-b written in logarithmic form?
Answers
We have the expression:
[tex]c^{(4d+1)}=7a-b[/tex]We can apply logarithm to both sides. We would use it in order to get "4d+1". Then, we would apply logarithm with base c. This is beacuse of the definition of logarithm:
[tex]\log _c(x)=y\Leftrightarrow c^y=x[/tex]If we apply this to our expression, we get:
[tex]\begin{gathered} c^{(4d+1)}=7a-b \\ \log _c(c^{(4d+1)})=\log _c(7a-b) \\ 4d+1=\log _c(7a-b) \end{gathered}[/tex]If we rearrange both sides, we get the expression in Option B (we have to switch the sides):
[tex]\begin{gathered} 4d+1=\log _c(7a-b) \\ \log _c(7a-b)=4d+1 \end{gathered}[/tex]Answer: Option B
Related Questions
Use the table of values for f and g below to find the indicated compositions.f(g(8))=Answerg(f(5))=Answerf(f(4))=Answerg(g(2))=Answer
Answers
Starting from the first question, we want:
[tex]f(g(8))[/tex]Let's start from the inside part:
[tex]g(8)[/tex]Since the inside of "g" is 8, this means we need to check for the row with x = 8, thay is, "8" in the column "x". Finding this row, we check the value in this row and column "g", which is "4".
This means that:
[tex]g(8)=4[/tex]Now, we can substitute this back in:
[tex]f(g(8))=f(4)[/tex]And we can do similarly. We check the row which has "4" in the "x" column and see the corresponding value in column "f". We can see that it is also "4", so, the answer for the first is:
[tex]f(g(8))=f(4)=4[/tex]Lastly, for the second, we do the same thing, the inside part is:
[tex]f(5)[/tex]So, we got to line x = 5 and check column "f". It is 0, so:
[tex]\begin{gathered} f(5)=0 \\ g(f(5))=g(0)_{} \end{gathered}[/tex]Now, we check row x = 0 and column "g" to find "9", so:
[tex]g(0)=9[/tex]Thus, the answer for the second is:
[tex]g(f(5))=g(0)=9[/tex]repeat the following procedure for the four given numbers. multiply the number by 2. add 10 to the product. divide the sum by 2. subtract 5 from the quotient. the first number is 2, the 2nd number is 4, the 3rd number is 8,the 4th number is 10
Answers
Lets start with the first case (the number is 2). Then, we get
Now, for the second case (the number is 4), the result is
Now, for 3rd case ( the number is 8), we have
And for 4th case (the number is 10) we get
a) As we can note, the result is always the same number we started with.
Then, if we represent the first number by n, the result is n.
b) Let n be the given number, then, we can write:
-Multiply the number by 2:
[tex]2n[/tex]-Add 10 to the product:
[tex]2n+10[/tex]- Divide the sum by 2:
[tex]\frac{2n+10}{2}[/tex]but this is equal to
[tex]\frac{2n+10}{2}=\frac{2n}{2}+\frac{10}{2}=n+5[/tex]- Substract 5 from the quotient:
[tex]\frac{2n+10}{2}-5[/tex]but (from our last result) this is equal to
[tex]n+5-5=n[/tex]which is our first number n. Thats why the answer in all cases is the same number we started with.
is a projectile is launched from a height of 5 m with an intial velocity of 25 meters per second, how many seconds will it take the projectile to hit the ground
Answers
In this problem we know that the initial velocity in the horizontal axis is 25, however the initial velocity in the y axis will be o so we can use this equation:
[tex]y=y_0+v_it+\frac{1}{2}at^2[/tex]So to find the time the object get the grownd we can replace the initial high for 5 miter, the final one for 0 and the aceleration by -9.8 (gravity) so:
[tex]0=5+0(t)+\frac{1}{2}(-9.8)t^2[/tex]and we solve for t so:
[tex]\begin{gathered} 9.8t^2=5\cdot2 \\ t^2=\frac{10}{9.8} \\ t\approx\sqrt[]{1} \\ t\approx1 \end{gathered}[/tex]So the projectil takes one secon to hit the grownd
A football team played A games last year. They lost B of those games. What was their winning percentage
Answers
Answer:
(A - B)/A x 100%
Explanation:
If they played A games last year and lost B of those games, they win the rest of the games, so they win A - B games.
Then, the percentage is calculated as the number of games that they win over the total number of games multiplied by 100, so the winning percentage is
(A - B)/A x 100%
Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.tan4(4x)
Answers
Solution
[tex]\begin{gathered} \tan^2(4x)=\frac{1-\cos(8x)}{1+\cos(8x)} \\ \\ \Rightarrow\tan^4(4x)=\frac{1-2\cos(8x)+\cos^2(8x)}{1+2\cos(8x)+\cos^2(8x)} \\ \\ \text{ since }\cos^2(8x)=\frac{1+\cos(16x)}{2} \\ \\ \Rightarrow\tan^4(4x)=\frac{1-2\cos(8x)+\frac{1+\cos(16x)}{2}}{1+2\cos(8x)+\frac{1+\cos(16x)}{2}} \\ \\ \Rightarrow\tan^4(4x)=\frac{2-4\cos(8x)+1+\cos(16x)}{2+4\cos(8x)+1+\cos(16x)} \\ \\ \Rightarrow\tan^4(4x)=\frac{3-4\cos(8x)+\cos(16x)}{3+4\cos(8x)+\cos(16x)} \end{gathered}[/tex]The answer is:
[tex]\frac{3-4\cos(8x)+\cos(16x)}{3+4\cos(8x)+\cos(16x)}[/tex]what is 12 times 12?
Answers
Answer:
144
Step-by-step explanation:
Answer: 12x12=144.
I hope this helps!!!!!!!!!!!!!!!!!!!!!!!!!!
Describe the transformations: F(x) = - 3(x +1)^2 + 5 What is the Parent Function: Opens UP or DOWN:Stretch or Shrink: Vertical Movement Up or Down, how many units:Horizontal Movement Left or Right, how many units:
Answers
You have the following transformation:
[tex]F(x)=-3(x+1)^2+5[/tex]The previous function if a parabola. the Parent Function of any parabola is:
[tex]y=x^2[/tex]All others parabolas can be obtained by applying transformation to the Parent Function.
If you expand the parenthesis of F(x), you obtain:
[tex]\begin{gathered} F(x)=-3(x^2+2x+1)+5=-3x^2-6x-3+5 \\ F(x)=-3x^2-6x+2 \end{gathered}[/tex]The dominant term, that is, the term with the variable x powered to 2, has a negative coefficient, it demands that the parabola open DOWN.
The coefficient of the dominant term is -3, then I-3I = 3 > 1. It means that the function stretches away from the x-axis.
The function streches way from x-axis by a factor of 3 units.
Vertical movement Up with 5 units. This is becasue the constant of the function, 5, which means the vertical translation of the Pater Function, if the constant is positive the translation is upward, if the translation is negative, it is downward.
Horizontal translation Left with 1 untit. The horizontal trasnlation is given by the constant term inside the quadratic parenthesis, in this case is + 1, whichi represents a translation of the graph to the left.
create a linear equation in the slope-intercept form that contains points (2,8) and (6,-4)
Answers
the two points are,
A(2,8)
B (6,-4)
the equation of the line in the slope intercept form is,
[tex]y-8=\frac{-4-8}{6-2}(x-2)[/tex][tex]\begin{gathered} y-8=\frac{-12}{4}(x-2) \\ y-8=-3x+6 \\ y=-3x+14 \end{gathered}[/tex]thus, the equation of the line is
y = -3x + 14
2. A shop owner raises the price of a $150 pair of shoes by 40%. After a few weeks,because of falling sales, the owner reduces the price of the shoes by 40%. Acustomer then says that the shoes are back at the original price.d. By what percent should the shoes be decreased in order to have the priceback at $150?Kk
Answers
Answer:
Explanations:
Given the following parameters;
Original price of shoe = $150
If the price is increased by 40%, the new price will be expressed as:
[tex]\begin{gathered} New\text{ price}=\$150+(0.40\times\$150) \\ New\text{ price}=\$150+\$60 \\ New\text{ price}=\$210 \end{gathered}[/tex]If the the owner reduces the price of the shoes by 40% due to falling price, hence;
[tex]\begin{gathered} New\text{ price}=210-(0.4\times210) \\ New\text{ price}=210-84 \\ New\text{ price}=\$126 \end{gathered}[/tex]Find the GCF of 24m^4n and 16m^2n.
Answers
Answer:
[tex]8m^2n[/tex]Step-by-step explanation:
To find the GCF (greatest common factor), we have to find the prime factors of each number. Then, we have to find similar factors.
In this exercise, we have:
24m⁴n = 2 * 2 * 2 * 3 * m * m * m * m * n
16m²n = 2 * 2 * 2 * 2 * m * m * n
The GCF will be 2 * 2 * 2 * m * m * n
So, The GCF is 8m²n.
hey! I need help/answers to 20 questions. Heres the first question Find the volume of a pyramid with a square base, where the side length of the base is 10.9 m and the height of the pyramid is 4.7 m. Round your answer to the nearest tenth of a cubic meter.
Answers
Answer:
The Volume of the pyramid is;
[tex]186.1\text{ }m^3[/tex]Explanation:
Given the pyramid with a square base and dimensions;
[tex]\begin{gathered} l=10.9m \\ h=\text{4}.7m \end{gathered}[/tex]Recall that the volume of a pyramid can be calculated using the formula;
[tex]V=\frac{l\times l\times h}{3}[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{10.9\times10.9\times4.7}{3} \\ V=186.1m^3 \end{gathered}[/tex]Therefore, the Volume of the pyramid is;
[tex]186.1\text{ }m^3[/tex]Find the slope and y-intercept of the line.y = -3,000 + 30x
Answers
The given equation is
[tex]y=-3,000+30x[/tex]It's important to know that this is a linear equation, and it's written in the form
[tex]y=mx+b[/tex]Where m is the slope, and b is the y-intercept.
That means we only need to look for these values and that's it!
According to the given equation, we have
[tex]m=30,b=-3,000[/tex]Therefore, the slope is 30, and the y-intercept is at (0, -3000).equation allows the nurse to use theratio and proportion method todetermine how many tablets the patientrequires?O 100 mg/50 mg x 1 tabletO 50 mg/100 mg x 1 tablet50 mg/1 tablet = 100 mg/ x tablets
Answers
SOLUTION
From the question, the patient needs 100 mg but the drug is available in 50 mg tablets.
We can see that 100 is twice of 50, so using 50 mg tablets should be twice that to make it 100 mg
If the number of tablets is given as x, so the requirement will be calculated as
[tex]x\text{ tablets = }\frac{1\text{ tablet }}{50\text{ mg}}\times100\text{ mg/1 tablet }[/tex]Hence the last option is the correct answer
Solve the equation by factoring. Separate multiple answers with a comma.
Answers
x = -4, 0, 6
Explanations:The given equation is:
[tex]x^3-24x=2x^2[/tex]The equation can be re-written as:
[tex]x^3-2x^2\text{ - 24x = 0}[/tex][tex]\begin{gathered} x(x^2\text{ - 2x - 24) = 0} \\ x\lbrack x^2\text{ - 6x + 4x - 24\rbrack = 0} \\ x\lbrack x(x-6)\text{ + 4(x - 6)\rbrack = 0} \\ x\text{ (x - 6) (x + 4) = 0} \\ x\text{ = 0} \\ x\text{ - 6 = 0} \\ x\text{ = 6} \\ x\text{ + 4 = 0} \\ x\text{ = -4} \end{gathered}[/tex]x = -4, 0, 6
The table below represents the data collected at a sandwich shop for the last six months withrespect to the type of bread people ordered (sourdough or wheat) and whether or not theygot cheese on their sandwich.With cheeseWithout cheeseSourdough800425Wheat1200700What is the P(cheese | wheat)? Show all work to receive full credit. You can place your workin this box or attach it in the box on the final question.
Answers
Given:
The table represents the data collected at a sandwich shop for the last six months with respect to the type of bread
We will find P(cheese | wheat)
We will use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Let A represents cheese, and B represents wheat
From the table:
[tex]\begin{gathered} A\cap B=1200 \\ B=1200+700=1900 \end{gathered}[/tex]So, the probability will be as follows;
[tex]P\left(cheese|wheat\right)=\frac{1200}{1900}=\frac{12}{19}[/tex]So, the answer will be:
P(cheese | wheat) = 12/19 = 0.63
A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
Answers
A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
we have that
The area covered by grass is equal to the area of a rectangular yard minus the area of the square flower garden
so
A=(22)(19)-(10.5)^2
A=307.75 ft2an airplane is flying at an altitude of 5000 ft in starseed sitting at a rate of 150 ft per minute what we'd altitude of the plane after 10 minutes
Answers
Problem
An airplane is flying at an altitude of 5000 ft in starseed sitting at a rate of 150 ft per minute what we'd altitude of the plane after 10 minutes
Solution
For this case we can define the following notation:
y= altitude
x= time in minutes
We can find the altitude at any time with the following formula:
y = 5000 - 150 x
And we can find the value for the altitude at x=10 we got:
y = 5000 -150(10) =3500 ft
Circle O has a center at (2,-2) and a diameter of 8 units. Identify which point lies on Circle O. O A. (0,1) O B. (6,-2) O C. (2, 2) O D. (-3,-2)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
circle
center (2,-2)
diameter = 8
point on the circle = ?
Step 02:
equation of a circle
(x - a)² + (y - b)² = r²
r = d / 2 = 8 / 2 = 4
(x - 2)² + ( y - (-2))² = 4²
(x - 2)² + ( y + 2)² = 16
Step 03:
We must verify the points with the equation.
A. If (0 , 1)
(x - 2)² + ( y + 2)² = 16
( 0 - 2)² + ( 1 + 2)² = 16
4 + 9 = 16
15 < 16 the point is inside of the circle
B. If ( 6, -2)
(x - 2)² + ( y + 2)² = 16
(6 - 2)² + ( -2 + 2)² = 16
16 = 16 the point is on the circle
The answer is:
B. (6 , -2)
Solve this quadratic equation and explains the steps to help you solve it . Also which two specific methods help you to solve it: Is it quadratic formula, Factoring, Square Root Property or Completing square. And explains.
Answers
Recall that the quadratic formula states that, the solutions to the quadratic equation
[tex]ax^2+bx+c=0[/tex]are
[tex]\frac{-b\pm\sqrt{(-b)^2-4ac}}{2a}.[/tex]Now, in the given equation, a=-1 ,b=-6, and c= 8. Therefore, the solutions to the equation are:
[tex]x=\frac{6\pm\sqrt{36+32}}{-2}.[/tex]Simplifying the above result, we get:
[tex]x=-3\pm(-1)\sqrt{17}.[/tex]Answer:
[tex]\begin{gathered} x_1=-3+\sqrt{17,} \\ x_2=-3-\sqrt{17}. \end{gathered}[/tex]Kobe is 2.07 metres tall.
Marcus is 1.79 metres tall.
Stephen is taller than Marcus by half the difference between Kobe's height and
Marcus's height.
How tall, in metres, is Stephen?
Answers
The height of Stephen is = 1.79 + 0.14 = 1.93 meters
What is unitary method ?In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple. How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used.
CalculationStep: 1
The height of Kobe is 2.07 meters
The height of Marcus is 1.79 meters
The difference between Kobe's height and Marcus's height = 2.07 - 1.79 meters
And its half is = 1/2 * 0.28 = 0.14 meters
Stephen is taller than Marcus by half the difference between Kobe's height and Marcus's height
The height of Stephen is = 1.79 + 0.14 = 1.93 meters
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Simply the expression. (Cos x) (sec x)-(sin^2 x)
Answers
[tex]Cos^{2}x[/tex] is the solution for the expression [tex](Cosx)(secx) - sin^{2}x[/tex]
The given expression is:
[tex](Cosx)(secx) - sin^{2}x[/tex]
Recall form Pythagorean Identity that;
[tex]secx = \frac{1}{cosx}[/tex]
We apply this property to obtain;
[tex](cosx)(\frac{1}{cosx}) - sin^{2}x[/tex]
By simplifying we get that;
[tex]1 - sin^{2}x[/tex]
Recall from the Pythagorean, we identity that;
[tex]1 - sin^{2}x = cos^{2}x[/tex]
Hence the answer is [tex]cos^{2}x[/tex] is the solution for the expression [tex](Cosx)(secx) - sin^{2}x[/tex]
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I really need help. volume of this figure using 3.14 without rounding.
Answers
We get that the volume of the figure is the volume for the rectangular prism and the cylinder with radius 4
[tex]\begin{gathered} V=16\cdot11\cdot11+3.14\cdot4^2\cdot9 \\ =1936+452.16 \\ =2388.16 \end{gathered}[/tex]Drag each label to the correct location on the image. Are these functions even, odd , or neither?
Answers
We know that if a function is even then the graph of the function is symmetrical about y-axis.
Look at the first function, it is symmetrical about y-axis, henve it is even,
if a function is odd then the graph of the function is symmetrical about origin
Look at the second function, it is symmetrical about origin, henve it is odd,
And the third function is neither symmetrical about y-axis nor symmetrical about origin and so it neither odd nor even.
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
Adu pick one pen from a box,
containing one blue pen, 2 red
pens and 3 green pens without.
looking into the box. What is the
probability of picking
(1) Blue Pen
if Red pen
( Green pen
(iv) green or blue pen
Red or green pen
Answers
The probability of picking Blue pen, Red pen and Green pen out of the box at random will be 1/6, 1/3 and 1/2 respectively.
As per the question statement, we are supposed to find the probability of picking Blue pen, Red pen and Green pen out of the box at random.
It is given that the box contains one blue pen, 2 red pens and 3 green pens.
Total pen = 6
Probability of Blue pen = 1/6
Probability of Red pen = 2/6 = 1/3
Probability of Green pen = 3/6 = 1/2
Hence, the probability of picking Blue pen, Red pen and Green pen out of the box at random will be 1/6, 1/3 and 1/2 respectively.
Probability: The chance of happening or not happening of any event is its probability. It is the ratio of favorable outcome and the total number of event.To learn more about probability and similar concept, click on the link given below:
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Show that when -9p2 + 4p + 1970 = 0, Total Revenue is at its maximum.Find the price and quantity which maximise Total Revenue.
Answers
Step 1
Write the demand function equation
[tex]Q=-9p^2+4p\text{ + 1970}[/tex]Step 2:
To find the price and quantity which maximize the revenue
You will find the derivative of Q with respect to price
[tex]\begin{gathered} \frac{dQ}{dp}\text{ = -18p + 4} \\ -18p\text{ + 4 = 0} \\ 18p\text{ = 4} \\ p\text{ = }\frac{4}{18}\text{ = }\frac{2}{9} \end{gathered}[/tex]Step 3:
Find the quantity demand by substituting p = 2/9
[tex]\begin{gathered} Q\text{ = -9 }\times\text{ (}\frac{2}{9})^2\text{ + 4 }\times\text{ }\frac{2}{9}\text{ + 1970} \\ =\text{ -0.44 + 0.888 + 1970} \\ =\text{ 1970.444} \\ =\text{ 1970} \end{gathered}[/tex]Final answer
The price which maximizes the total revenue is p = 2/9
The quantity is Q = 1970
Only need help with finding the mean and standard deviation.
Answers
Given
Probability distribution table
Find
Mean and standard deviation
Explanation
mean for probability distribution is given by
[tex]mean=\sum_^xP(x)[/tex]so , mean
[tex]\begin{gathered} 0+0.25+0.54+0.36+0.64 \\ 1.79 \end{gathered}[/tex]standaed deviation
[tex]\begin{gathered} \sum_^x^2P(x) \\ 0+0.25+1.08+1.08+2.56 \\ 4.97 \end{gathered}[/tex]Final Answer
mean = 1.79
standard deviation = 4.97
A cone-shaped pile of sawdust has a base diameter of 30 feet, and is 10 feet tall. Find the volume of the pile. Round your answer to the nearest tenth if necessary.
Answers
The formula for calculating the volume of a cone (pile) is expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]r is the radius
h is the height of the cone (pile)
Given
Base diameter = 30 feet
radius = diameter/2
radius = 30/2
radius = 15 feet
height = 10feet
Required
Volume of the pile
To get the volume, you will substitute the given data into the formula as shown;
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\pi(15)^2(10) \\ V\text{ = }\frac{1}{3}\pi(225)(10) \\ V=\frac{1}{3}(3.14)(2250) \end{gathered}[/tex]Evaluate the final expression;
[tex]\begin{gathered} V\text{ =}\frac{7065}{3} \\ V\text{ = }2355ft^3 \end{gathered}[/tex]Hence the volume of the pile is 2355ft^3
list 6 different types of geometric principles represented in the picture.
Answers
We need to list 6 geometric principles represented in the picture.
We can see the vertices of something that looks like leaves, arranged in a spiral.
Those vertices form angles. Also, the leaves seem to be tridimensional, so they have a surface area and a volume.
Also, notice that leaves equidistant from the center of the spiral seem to be congruent.
Therefore, we can list the following types of geometric principles:
• vertices
,• spiral
,• angles
,• surface area
,• volume
,• equidistance
,• congruent
PLEASE HELP I’M IN MIDDLE SCHOOL AND I CANT FIND THE ANSWERS. ITS ALSO DUE IN A FEW HOURS.
Answers
To form a triangle the three angles must follow the inequality principle that says: The sum of any two sides must always be greater than the length of the third side. With this in mind let's check the angles.
For the first item we have:
[tex]\begin{gathered} 70+90>20\rightarrow160>20 \\ 70+20>90\rightarrow90>90 \\ 20+90>70\rightarrow110>90 \end{gathered}[/tex]Since the second inequality is invalid the angles don't form a triangle.
For the second item we have:
[tex]\begin{gathered} 55+45>75\rightarrow100>75 \\ 55+75>45\rightarrow130>45 \\ 45+75>55\rightarrow120>55 \end{gathered}[/tex]Since all the inequations are valid then the angles form a triangle. Since all the angles are smaller than 90 degrees, then this is an acute triangle.
For the third item we have:
[tex]\begin{gathered} 27+27>126\rightarrow54>126 \\ 27+126>27\rightarrow153>27 \end{gathered}[/tex]Since the second inequation is invalid, then the angles don't form a triangle.
For the fourth item we have:
[tex]\begin{gathered} 38+87>55\rightarrow125>55 \\ 38+55>87\rightarrow93>87 \\ 55+87>38\rightarrow142>38 \end{gathered}[/tex]Since all the inequalities are valid, then the angles form a triangle. All of its angles are smaller than 90 degrees, therefore this triangle is an acute triangle.
If AABC – ADEF, which angle corresponds with angle A in the following image?Side16deee3ce67551e9dd974313e76f08f2 webm 10Blank 1:
Answers
Answer:
Angle D corresponds to angle A
Explanations:
Since △ABC ≅ △DEF;
It means both triangles have corresponding sides and angles.
To make it obvious which angle in △DEF corresponds to angle A in △ABC, let us redraw △DEF to look like △ABC
Obviously from the diagrams I drew above,