Step-by-step explanation:
The derivative of log is
[tex] \frac{d}{dx} ( log_{a}(x) ) = \frac{1}{x \: ln(a) } [/tex]
You can easily derive this using the Change of base rule, and natural log rules
[tex] log_{a}(x) = \frac{ log_{e}(x) }{ log_{e}(a) } = \frac{ ln(x) }{ ln(a) } [/tex]
Next, we differentiate with respect to x.
[tex] \frac{d}{dx} \frac{ ln(x) }{ ln(a) } = \frac{1}{ ln(a) } \times \frac{d}{dx} ln(x) [/tex]
[tex] = \frac{1}{x ln(a) } [/tex]
So back to the topic at hand,.
a=7, so we get
[tex] \frac{1}{x ln(7) } [/tex]
We plug in 0, we would get undefined
Theodore invests a total of $11,000 in two accounts paying 8% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $780.00.
________ was invested at 8% and
______ was invested at 4%.
The amount loaned at the interest rate of 8% is $2,500.
The amount loaned at the interest rate of 4% is $8,500.
What are the linear equations that represent the question?a + b = 11,000 equation 1
0.08a + 0.04b = 780 equation 2
Where:
a = amount loaned at the interest rate of 8%b = = amount loaned at the interest rate of 4%How much was loaned at 8% and 4%?In order to determine how much was loaned at 4%, take the following steps:
Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 2 from equation 3:
0.04b = 100
Divide both sides by 0.04:
b = $2500
Subtract 2,500 from 11,000 :
11,000 - 2,500 = $8,500
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An angle measures 87.6° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
1.2° and 88.8°Step-by-step explanation:
Complementary angles are angles that add up to 90°.
Let's say angle 1 is x, and angle 2 is 87.6 less than x.
We already know that angle 1 + angle 2 = 90, so we can just substitute x now.
We know that complementary angles add up to 90, so one of the angles is 90-x, and the other one is 90-x-87.6.
x = (90 - x) - 87.6
Simplifies to:
x = 2.4-x
Add x to both sides
2x = 2.4
Divide by 2
x = 1.2
To get the other angle, add 87.6 to 1.2
1.2+87.6 = 88.8
So, angle1 = 1.2, and angle2 = 88.8
Let's check our work.
88.8 + 1.2 = 90, so the angles are complementary and have a difference of 87.6
Hope this helps (:
Answer:
1.2°, 88.8°
Step-by-step explanation:
let one angle=x
other angle=y
y=x-87.6
also
x+y=90
x+x-87.6=90
2x=90+87.6=177.6
x=88.8
other angle=88.8-87.6=1.2
the university of detroit mercy is 3/4 miles from dana’s house. Marygrove college is 2/5 miles from her house. what is the difference in the two distances
i need help with the problem PLS help
1) It's best to draw out a picture of a rectangle and label each corner with the coordinates given: Let's say (-5, 2) is point A, (-5, -2 1/3) is point B, (2 1/2, 2) is point C, and (2 1/2, -2 1/3) is point D.
2) That being said, line AB is one side of the rectangle, BC is another, CD is another, and lastly, AD is the fourth side.
3) We can use the distance formula and plug in the coordinates of each line to find how long every side is. Then you just need to solve it.
For example: if I want to find how long side AB is, I would use the point A (-5, 2) and B (2 1/2, 2) and plug them into the distance formula, where (-5, 2) is (x1, x2) and (2 1/2, 2) is (x2, y2) and solve that.
4) Repeat this process with side BC, CD, and AD, and add the results together. This will be your final answer; the perimeter of the rectangle.
If PQRS is a rhombus,which statement must be true? Check all that apply.
Answer: A, B, C, D
Step-by-step explanation:
A. This is true because all rhombi are parallelograms, and diagonals of a parallelogram bisect each other.
B. This is true because the diagonals of a rhombus are perpendicular.
C. This is true because diagonals of a rhombus bisect the angles from which they are drawn,
D. This is true because all sides of a rhombus are congfruent.
E. This is not always true - all rhombi are parallelograms, and adjacent angles of a parallelogram are supplementary, but not always congruent.
F. This is not always true - diagonals of a rhombus are not always congruent.
Find the equation of the line.
Through (-11, -1); perpendicular to y=15.
Answer:
x = - 11
Step-by-step explanation:
y = 15 is a horizontal line parallel to the x- axis
a perpendicular line must therefore be a vertical line parallel to the y- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
the line passes through (- 11, - 1 ) with x- coordinate of - 11 , then
x = - 11 ← equation of perpendicular line
Answer:
x = -11
Step-by-step explanation:
The line y = 15 is a horizontal line to the x-axis passing which passes through x = 0, y = 15
The line perpendicular to y = 15 passing through (-11, -1) is a vertical line where x = -11 for all values of y including -1
So the equation is x = -11
See attached graph
In circle A shown below the measure of angle BAD is 148 degrees If mBC is 102 degrees, what is mCD?
The measure of arc CD from the given figure is 46 degrees
Circle theoremFrom the attached figure, the expression below is true;
arcBC + arcCD = <BAD
Given the following
<BAD = 148 degrees
arcBC = 102 degrees
Substitute
arcCD =148 - arcBC
arcCD = 148 - 102
arcCD = 46 degrees
Hence the measure of arc CD from the given figure is 46 degrees
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Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help.)
Sentence : "I did 60 brush strokes in 1 minute"
The dependent and the independent variable in the relationship y=60x are y and x respectively.
The Independent variables are variables whose value does not depend on any other variable. And it causes the change in other variables.
The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.
Given that you did 60 brush strokes in 1 minute. Therefore, the rate can be written as,
Rate = 60 strokes per minute
Now, the number of stokes in x minutes can be written as,
y = 60x
where y is the number of stokes,
x is the number of minutes
In the above relation, y is the dependent variable because its numerical value depends on time, while x is the independent variable.
Hence, The dependent and the independent variable in the relationship y=60x are y and x respectively.
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Calculate the slope of the line between each pair of coordinates.
a. A: (3, 6) and B: (4, -3)
b. C: (-5, -3) and D: (-3, -7)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Calculate the slope of the line between each pair of co-ordinates
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\LARGE\textsf{Question 1}}[/tex]
The points given are,
[tex]\begin{cases} \bf{(3,6)} \\ \bf{(4,-3) \end{cases}[/tex]
To find the slope [tex]\textbf{M}[/tex] of this line,
we will utilise the [tex]\textbf{Slope Formula}[/tex].
The first thing to do is
to put in the co-ordinates
of the two points given.
[tex]\bf{\dfrac{-3-6}{4-3}}[/tex] | subtract on top and bottom
[tex]\bf{\dfrac{-9}{1}}[/tex] | divide on top and bottom
[tex]\bf{-9}[/tex]
[tex]\LARGE\textsf{Question 2}[/tex]
The points given this time are,
[tex]\begin{cases} \bf{(-5,-3)} \\ \bf{(-3,-7)} \end{cases}}[/tex]
Last time we needed to
put in the co-ordinates.
Similarly, we ought to
put in the co-ordinates
in this problem.
[tex]\bf{\dfrac{-7-(-3)}{-3-(-5)}}[/tex] | simplify
[tex]\bf{\dfrac{-7+3}{-3+5}}[/tex] | add on top and bottom
[tex]\bf{\dfrac{-4}{2}}[/tex] | divide on top and bottom
[tex]\bf{-2}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\begin{cases}\bf{Slope=-9} \\ \bf{Slope=-2} \end{cases}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X<5), n=6, p=0.3
The required probability of success is given by 0.98906500
Assume the random variable X has a binomial distribution with the given probability of obtaining a success.
P(X<5), n=6, p=0.3
In binomial distribution for number trials we are investigating the probability of getting a success remain the same.
n = number of trails,
p = probability of success
x = the number of success
p(x<5) = P(x=0)+ p(x=1) + p(x=2)+p(x=3)+p(x=4)
= [tex]\binom{6}{0}(0.3)^0(1-0.3)^6+\binom{6}{1}(0.3)^1(1-0.3)^5+\binom{6}{2}(0.3)^2(1-0.3)^4+\binom{6}{3}(0.3)^3(1-0.3)^3+\binom{6}{4}(0.3)^4(1-0.3)^2[/tex]
p(x<5) = 0.98906500
Thus the required probability of success is given by 0.98906500
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Find the radius of a circle with diameter 91yd
Answer: 45.5yds
Step-by-step explanation:
- the radius is simply half of the diameter so: 91 / 2= 45.5yd
- so the radius is 45.5yds
hope this helps :)
r= d/2 = 91/2 =45.5yd
Question 16 of 50
Jayden received a bonus check from his work for $6,000. He is going to deposit the money into a bank account that receives 5% compounded annually.
The amount of interest earned after year 5 is:
O $7,657
O $8,421
O $7,300
Does anyone know the solution to the 11th number sum? Thank you!
Answer:
20
Step-by-step explanation:
Correct option is A)
let the number be x.
∴75% of x=15
∴
100
75
×x=15
∴x=15×
3
4
∴x=20
The value of x is 20.
HELP ME!!!!Question 13 of 25
What is the approximate value of tan B?
h
17.46
16
A. 2.29
B. 0.40
C. 0.44
D. 0.92
Answer: A
tan= Opposite ÷ Alternate
tan B= 16 (which is the opposite side of B) ÷ 7 (it's the side beside B, excluding 17.46 as it's the hypotenuse)
Therefore 16÷7 = 2.285714286
= 2.29 (3sf)
Answer:
just choose one
If property taxes (part of the fixed costs) are decreased by $12,000 per year, what effect does this have on the graph of the cost function?
Option D. If property taxes are decreased by $12000, the effect that it would have on the cost function is shifts downward by 12 units.
How to solve for the effect on the graphWe have a function of this type
fx = Ax + B
where A = labor and material
B = fixed cost
We have a graph of this form. g(x) = ax + b - 12, with b and a representing costs in thousands of American currency.
Complete questionA factory has a linear cost function f(x)=ax+b, where b represents fixed costs and a represents the labor and material costs of making one item, both in thousands of dollars. If property taxes (part of the fixed costs) are decreased by $12,000 per year, what effect does this have on the graph of the cost function? a. shifts to the left by 12 units b. shifts to the right by 12 units c. shifts upward by 12 units d. shifts downward by 12 units
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Which system of equations is represented in the graph? On a coordinate plane, a horizontal line is at y = negative 2 and another line goes through (0, negative 3) and (6, 0). y = negative 2. x minus 2 y = 6. y = negative 2. x + 2 y = 3. x = negative 2. 2 x minus y = 3. x = negative 2. 2 x + y = negative 3.
The system of equations that is represented in the graph is:,y = -2.x-2y =6..Option B is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Two lines may be seen on the graph:
y = -2
The lines pass through (-3) and (6, 0). We use the slope-intercept form to get the second line's equation: y=mx+c
m = 0-(-3)/(6-0)
m=3/6
m=1/2
Substitute the values as;
[tex]\rm y = \frac{1}{2}x+c[/tex]
For the point x = 0 and y = -3
[tex]\rm y = \frac{1}{2}x-3[/tex]
The equation can be written as;
x - 2y = 6
The system of equations that is represented in the graph is:,y = -2.x-2y =6..
Hence, option B is correct.
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Whats the correct answer answer asap for brainlist?
Answer:
b elephants and zebras
Step-by-step explanation:
Answer:
Step-by-step explanation:
Comment
I'll give you the answer, but my guess is the question will be deleted because it is in the wrong place.
The answer is B. You might think it is D but those creatures are mostly in North America.
2 In the diagram below of AABC, TV || BC, AT = 5,
TB = 7, and AV = 10.
B
A
What is the length of VC?
1) 3-1/2
2) 7-½-1
3) 14
4) 24
C
4
Answer:
14
Step-by-step explanation:
AT/TB = AV/VC
5/7 = 10/VC
VC = 14
For the given figure length of VC = 14.
In the given figure,
We can see that,
ΔATV and ΔABC are similar triangle,
Since we know that,
Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The '' sign here denotes the resemblance of triangles.
Therefore,
AT/TB = AV/VC
It is given that,
AT = 5
TB = 7
AV = 10
Now put these values we get,
⇒ 5/7 = 10/VC
⇒ VC = 14
Hence,
Length of VC is 14 units.
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F THREE DIAGONALS ARE DRAWN INSIDE A HEXAGON WITH EACH ONE PASSING THROUGH THE CENTER POINT OF THE HEXAGON, HOW MANY TRIANGLES ARE FORMED?
If three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.
Diagonals in a hexagonThere are nine diagonals in a regular hexagon
But for one with three diagonals drawn through the center, six equilateral triangles are formed.
Thus, if three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.
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There are 32 students in the orchestra and twice that number in the band. There are 19 boys and 11 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. The total number of students that are in the orchestra, the band, and the choir is 126.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
There are 32 students in the orchestra and twice that number in the band. Therefore the number of students in the band is:
Number of students in band = 2 (Number of students in Orchestra)
= 2 × 32 = 64
The number of students in the Choir is the sum of the number of boys and girls. Therefore, the number of students in the Choir is,
Number of students in the Choir = 19 + 11 = 30
Total number of students = 32 + 64 + 30 = 126
hence, the total number of students that are in the orchestra, the band, and the choir is 126.
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Question 2(Multiple Choice Worth 5 points)
(01.05 LC)
If x² = 10, what is the value of x?
O ± √ 10
O± √20
+5
+20
Answer:
If you mean:
x² = 10
√x² = √10
x = √10
if you meant:
2x = 10
2x/2 = 10/2
x = 10/2
x = 5
hope this helps
If you mean x^2 then there would be no answer after all, 3^2= 9 and 4^2= 16 so
If you mean 2x then the answer would be 5
Step-by-step explanation:
:0
What are the factors of 32Round the following items to the nearest £1:
Item
Cost
Cost rounded to nearest £1
Notebook
£2.15
£
Pencil Case
£3.80
£
Colouring Pencil
£1.49
£
?
The factors of 32 as required in the task content are; 2, 4, 8, 16, 32.
What are the factors of 32?The factors of the number 32 as required in the task content are numbers whose multiples amount to 32 and are as listed above.
The item prices as given in the task content rounded to the nearest £1 are;
Notebook
£2.15 = £2
Pencil Case
£3.80 = £4
Colouring Pencil
£1.49 = £1
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please can you help me?
Answer:
A) 65
B) 60
Step-by-step explanation:
64.9963 rounds to 65
To the nearest 10 it would round down as the second intiger the 4 is below 5 meaning as a result it rounds down
After rounding the given number 64.9963:
(a) Near 2 decimal places is: 64.70
(b) And the nearest 10 is: 60
When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The given number is:
64.9963
To round off the nearest 2 decimal places:
Since the third digit after the decimal is 6 which is greater than 5.
Add 1 to their previous digit.
Therefore,
After rounding near to 2 decimal places the number becomes:
64.70
To round off the nearest 10:
Since the tense digit is 4 and it is less than 5
Therefore,
The number after rounding off the nearest 10 is:
60.
Hence, after rounding the number:
Near 2 decimal places is: 64.70
And the nearest 10 is: 60
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7. Three vertices of a parallelogram are (0, 0), (−4,0) and (0, 5). Find all 3 possible coordinates for
the fourth vertex to make a rectangle and 2 different parallelograms. Explain or justify your
coordinate choice of how you know the sides are parallel. Find the lengths of each side
mathematically.
a) rectangle coordinate:
b) parallelogram:
c) parallelogram#2:
The given vertices combine with the fourth vertex as follows;
a) Coordinates; (-4, 5)
Lengths of the sides; 4 and 5
b) Coordinates; (4, 5)
Lengths of the sides; 4 and √41
c) Coordinates; (-4, -5)
Lengths of the sides; 5 and √41
How can the vertex coordinates be found?The given vertices are;
(0, 0): The origin
(-4, 0): 4 units to the left of the origin along the abscissa
(0, 5): 5 units above the origin, along the ordinate
a) The point that forms a rectangle is above the point (-4, 0) and to the left of the point (0, 5), which gives;
The coordinates of the point that forms a rectangle is the point (-4, 5)
The lengths of the sides are;
0 - (-4) = 4
5 - 0 = 5
b) The first parallelogram is formed by moving an equal distance of the point (-4, 0) from the origin from the point (0, 5), which gives;
The first parallelogram is formed by the point (4, 5)The lengths of the sides are;
4 - 0 = 4√((5 - 0)^2 + (4 - 0)^2) = √41c) The second parallelogram is formed by the moving an equal distance of the point (0, 5) from the origin from the point (-4, 0), which gives;
The second parallelogram is formed by the point (-4, -5)The lengths of the sides are;
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What number exceeds y by 4 less than x
Answer: y + x - 4
Step-by-step explanation:
We will write an expression for this "number" by looking at the details given.
exceeds y { can become } y +
4 less than x { can become } x - 4
Now we will put the parts together.
y + x - 4
The number that answers this question is:
y + x - 4
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Teachers need to help children to view and describe their world mathematically. Which of the following would NOT be a recommendation?
A. Encourage children to recognize and talk about math in everyday situations.
B. Support children in linking formal math vocabulary, symbols, and procedures to their informal knowledge and experiences.
C. Provide math quizzes to help children learn how to apply their math knowledge.
Encourage children to recognize and talk about math in everyday situations, this statement teacher not recommendation.
What is mathematics?
Quality, structure, space, and change are the subjects of study in mathematics. The study of mathematics involves utilizing symbols and numbers to quantify and analyze the characteristics of quantities and sets.
It is impossible to encourage kids to understand and discuss arithmetic in normal contexts since the subject's solutions are based on numbers and symbols, which makes it inappropriate.
As a result, option (a) is correct.
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Describe the transformations to the graph of y = x² to obtain y = -2 ( x + 5 )²- 3 .
Using translation concepts, the transformations are given as follows:
Reflection over the x-axis.Vertical stretch by a factor of 2.Shift left of 5 units.Shift down by 3 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
y = x².
The translated function is:
y = -2(x + 5)² - 3.
In this problem, we have that:
The function was multiplied by -2, hence it was reflected over the x-axis, as it was multiplied by a negative value, and vertically stretched by a factor of 2.x -> x + 5, hence the function was shifted left 5 units.y -> y - 3, hence the function was shifted down 3 units.More can be learned about translation concepts at https://brainly.com/question/4521517
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Which problem solving strategy would be best to solve this problem?Austin, Texas is two hours ahead of San Diego, California. If the time in Austin is 1:00 P.M., what time is it in San Diego?A.guess, check and reviseB.use a formulaC.work backwardsD.write an equation
Answer:
D. Write an equation
Step-by-step explanation:
x = The time of Sand Diego
t = Current designated time
n = The difference in time
So the equation is x = t+/-n.
You can determine if it would be + or - based of the word problem.
For this word problem the equation is x = 1:00pm - 2hrs
Hope this helps.
how did you find the height? thats what im confused on. A=(1/2)b x (h)
A triangle is a three-edged polygon with three vertices. The height of the triangle can be written as h = (2A)/b.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The complete question is:
Given the equation of the area of a triangle. how did you find the height of the triangle? A=(1/2)b x (h)
(Hint: Solve the equation for h)
Given the equation of the area of the triangle. Therefore, the height of the triangle can be written as,
A=(1/2)b x (h)
2A = b x h
h = (2A)/b
where h is the height of the triangle and b is the length of the base of the triangle.
Hence, the height of the triangle can be written as h = (2A)/b.
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At the beginning of a population study, a city had 370,000 people. Each year since, the population has grown by 6. Let be the number of years since start of the study. Let y be the city's population . Write an exponential function showing the relationship between y and
The exponential function that gives the relationship between y and t is:
[tex]y = 370000(1.06)^t[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 370000, r = 0.06.
Hence the equation is:
[tex]y = A(0)(1 + r)^t[/tex]
[tex]y = 370000(1 + 0.06)^t[/tex]
[tex]y = 370000(1 .06)^t[/tex]
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