Evaluate log2 10 using the change of base formula. Round your answer to the nearest thousandth.
Answers
Take into account the following property:
[tex]\log _ab=\frac{\log b}{\log a}[/tex]Then, for the given expression you have:
[tex]\log _210=\frac{\log10}{\log2}=\frac{1}{\log }\approx3.322[/tex]Hence, the answer is approximately 3.322
Related Questions
Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Answers
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
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1x + 2y = 7 and y = -2x + 3
Answers
Answer:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
Solve the system of equations:
1x + 2y = 7
y = –2x + 3
Substitute y = –2x + 3 for y in the first equation:
1x + 2y = 7
1x + 2(–2x + 3) = 7
Substract 6 from both sides:
–3x + 6 = 7
–3x + 6 – 6 = 7 – 6
–3x = 1
Divide:
–3x/–3 = 1/–3
x = –1/3
Substitute –1/3 for x in the second equation:
y = –2x + 3
y = –2(–1/3) + 3
y = 11/3
Solution:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
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Write the equation in slope intercept form:2x+y=2
Answers
Answer:
y = - 2x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + y = 2 ( subtract 2x from both sides )
y = - 2x + 2 ← in slope- intercept form
Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
Answers
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
Answers
The area of a pool from the given situation is 816 ft².
Given that, the dimensions of plot is 50 ft and 40 ft.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, area of a plot = Length × Width
= 50 × 40
= 2000 ft²
Area of a pool = Area of a plot - Area of a grass
= 2000 - 1184
= 816 ft²
Therefore, the area of a pool from the given situation is 816 ft².
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Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope -1.
Answers
The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.
Hence,
y - y₁ = m(x - x₁)
where
m = slopey₁ and x₁ are the coordinates of the point.Therefore,
m = slope = -1
using (-12, 15)
Hence,
y - 15 = - 1(x - (-12))
Therefore,
y - 15 = - 1(x + 12)
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Determine a series of transformations that would map Figure I onto Figure J
and its not just rotate the figure 90 degrees clockwise, you have the do TWO translations
Answers
3 × 90 thus equals 280 degrees.
The figure moves onto the following quadrant of the graph with each 90 degree rotation. In order to shift Figure I to the location of Figure J, you must move the three figure quadrants in a clockwise direction. 3 × 90 thus equals 280 degrees. Only one transformation is needed.
Which transformation corresponds to turning a figure 90 degrees counterclockwise?
The coordinate transformation (x, y) (y, x) is equivalent to a rotation of the origin 90 degrees counterclockwise. The coordinate transformation (x, y) (x, y) is comparable to a 180 degree counterclockwise rotation of the origin.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, making y negative.
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Find the slope between these two points:
(3, 0), (-11, -15)
Answers
Answer:
3/4 or 0.75
Step-by-step explanation:
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step? Original Equation: 5.x2 + (10x2 + 10) = 3x? First Step: 15x2 + 10 = 3.2 commutative property of multiplication commutative property of addition multiplication property of equality
Answers
The original equation is:
5 x^2 + (10 x^2 + 10) = 3 x^2 - 5
The first step the person did was:
15 x^2 + 10 = 3 x^2 - 5
so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.
Please check if there is an option that states such among your options.
On the freeway it is unsafe to drive too slowly or two quick the safest driving speeds on the freeway near Allentown worst scientifically determined to be between the minimum and maximum speed in miles per hour according to the equation X -55 in value equals 4.2 which equation can be used to determine the maximum safe driving speed
Answers
Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.
As given in the question,
Given equation :
|x – 55| = 4.2
To determine the maximum and minimum speed in miles per hour from the given equation we have,
x-55 = 4.2 or x-55 =-4.2
Add 55 both the side of the equation,
x-55 +55 =4.2+55 or x-55+55 = -4.2 +55
x =59.2 or x = 50.8
Maximum speed is 59.2 determine by equation x-55 = 4.2
Minimum speed is 50.8 determine by equation x-55 = -4.2
Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to
x -55 =4.2.
The complete question is:
On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?
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Round 1.9541 to the nearest tenth
Answers
Answer:
2
Step-by-step explanation:
1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2
ASAP DUE TODAY!!
Please include answers AND an explanation. Giving branliest <3
Answers
(1) The graph is attached with the answer below.
(2)The equation of the line is y = x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The points are ( 3, 0 ) and ( 0, 3). The slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 3 - 0 ) ( 0 - 3 )
Slope = 1
Calculate the y-intercept,
y = mx + c
3 = 0 + c
c = 3
The equation of the line will be:-
y = x + 3
Therefore, the graph is attached with the answer below the equation of the line is y = x + 3.
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O is the center of the regular decagon below. Find its perimeter. Round to the nearest
tenth if necessary.
16
Answers
Answer:
Step-by-step explanation:
The perimeter of the given polygon rounded to the nearest tenth is; 24.7
What is the perimeter of the Polygon?
The given polygon as we can see has 10 sides.
Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.
Thus, the other two angles will be; (180 - 36)/2 = 72° each
Using sine rule, we can find the length of a side of the polygon as;
x/sin 36 = 4/sin 72
x = (4 * sin 36)/sin 72
x = 2.472
Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7
the temperature at sunrise is 48°F . each hour the temperature rises 6°F write an equation that models the temperature y in degrees Fahrenheit after x hours. what is the graph of the equation.
Answers
EXPLANATION
Let's see the facts:
Temperature at sunrise = 48 °F
Rate = 6°F/h
The equation is given by the following expression:
Let's call "x" to the number of hours elapsed
y = 48 + 6x
The graph is given by the following representation:
matthew is thinking about applying for a credit card with a low interest rate. the loan application asks how much he owes on his mortgage and on his existing credit cards matthew used his calculator to figure out these two numbers and they are 2.4e5 and 1.25e4. how much money does matthew owe?(a) $232,500(b) $240,000(c) $252,500(d) $265,000
Answers
so:
[tex]240000+12500=252000[/tex]Answer:
(c) $252,500
The sizes of two matrices A and B are given. Find the sizes of the product AB and BA, whenever these products exist.A=3*2, B=2*3
Answers
Let's begin by identifying key information given to us:
A is a 3 x 2 matrix
B is a 2 x 3 matrix
AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix
Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist
Please help! Super confused!
Enter the inverse function of f(x) = -9x - 10.
Answers
Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Step-by-step explanation:
[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
I haven’t came across one of these questions so not sure how to solve
Answers
m∠F = 140º
1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:
[tex]\begin{gathered} S_i=180(n-2) \\ S_i=180(4-2) \\ S_i=180(2) \\ S_i=360 \end{gathered}[/tex]Note that "n" refers to the number of sides:
Notice also that angle H is a right angle since this is not an Isosceles Trapezoid
So we can write out the following
9x +14x +4x + 90 = 360º
27x = 360 -90
27x = 270
x =10
Alternatively, angles between parallel lines are supplementary
2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:
m∠F = 14x
m∠F = 140º
Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of d days that have passed. A. Write an equation for the situation.B. Find the a amount of money he began with.C. How much money does Marty have after 9 days?
Answers
Given:
Amount Marty spent per day = $3
Number of days = 14
Remaining amount = $68
Since the amount left depends on the number
#5 Pam a nurse made $93 in 6 hours determine an equation that represents how much she gets paid per hour #6 using your equation from problem 5 how much would a modern if she work for 15 hours?#7 using your equation from problem 6 how much would Pam earn if she work for 3 1/2 hours?
Answers
Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below
[tex]\begin{gathered} \text{ amount she earned per hr=}\frac{93}{6}=15.5 \\ The\text{ equation that can represent how much she earned per hour is} \\ \text{amount earned per hour = 15.5x} \\ x=\text{ hours worked} \\ \text{amount earned per hour}=15.5(1)=15.5\text{ dollars} \end{gathered}[/tex][tex]\begin{gathered} \text{amount she earned in 15 hrs=}15.5x \\ \text{amount she earned in 15 hrs}=15.5\times15=232.5dollars \end{gathered}[/tex][tex]\begin{gathered} \text{amount earned in 3}\frac{1}{2}\text{hrs}=15.5x \\ \text{amount earned in 3}\frac{1}{2}\text{hrs=15.5}\times\frac{7}{2}=\frac{108.5}{2}=54.25dollars \end{gathered}[/tex]Negative t divide by four equal’s negative three pie?
Answers
Answer:
Step-by-step explanation:
yes it does
Which rule explains why these triangles are congruent?
Answers
Answer:
SAS Congruence Rule
A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.
Answer: SAS (side side angle postulate.)
Step-by-step explanation:
can be used to prove triangles congruent.
sides and the corresponding angle of the other, then the triangles are congruent.
Please help gotta get my grade up ASAP this was due the 11th and it’s the 23rd now, super behind!!
Find f(7) if f(x) = 6x + 10. Enter DNE if the value does not exist.
f(7) =
Answers
Answer: f(7) = 52
Step-by-step explanation:
x = 7, so you would substitute x for 7
f(7) = 6(7) + 10
f(7) = 42 + 10
f(7) = 52
Hope this helps!
Which of the following equations represents a proportional relationship? Select all that apply. A 5 5 = 11 11 B 3 6 = 6 3 C 2x 12 = 3x 18 D 8 15 = 4 30 E 4 6 = 10 15 F 4x 18 = x 18
Answers
The equations that represent proportional relationships are:
A. 2x/12 = 3x/18
C. 4/6 = 10/15
E. 5/5 = 11/11
How to Determine a Proportional Relationship Equation?To determine if an equation represents a proportional relationship, ensure each side of the equation gives the same value when simplified. If they do not have the same value, then the equation does not represent a proportional relationship.
A. 2x/12 = x/6
3x/18 = x/6
Therefore, 2x/12 = 3x/18 represents a proportional relationship.
B. 3/6 = 1/2
6/3 = 2
Therefore, 3/6 = 6/3 does not represent a proportional relationship.
C. 4/6 = 2/3
10/15 = 2/3
Therefore, 4/6 = 10/15 represents a proportional relationship.
D. 4x/18 = 2x/9
x/18 = x/18
Therefore, 4x/18 = x/18 does not represent a proportional relationship.
E. 5/5 = 1
11/11 = 1
Therefore, 5/5 = 11/11 represents a proportional relationship.
F. 8/15 = 8/15
4/30 = 2/15
Therefore, 8/15/2/15 does not represent a proportional relationship.
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Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
Answers
The property demonstrated by:
a(b+c)=(a.b)+(a.c)
Is the Distributive property
Which property is demonstrated below?Here we have the next expression:
a*(b + c) = (a*b) + (a*c)
So we have the product between a and the sum of b and c, is equal to the sum between the products of a and b, and a and c, so we "distributed" the product.
This property is called the "Distributive property".
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Can someone please answer this!
Answers
Considering the situation described, it is found that:
a) The numeric values of the piecewise function are as follows:
W(30) = $300.W(40) = $400.W(47) = $505.W(52) = $580.b) The new piece-wise function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38.c) The new piece-wise function is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the rule is one for times up to 40 hours, and another for times greater than 40 hours, hence the numeric values are given as follows:
W(30) = 10 x 30 = $300.W(40) = 10 x 40 = $400.W(47) = 15 x (47 - 40) + 400 = $505.W(52) = 15 x (52 - 40) + 400 = $580.For item b, the new reference is of 38 hours, hence the function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38. (the earnings for the first 38 hours are of 38 x 10 = $380).For item c, the new hourly wage is of 12 hours, hence the rule is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. (pay and half = 12 x 1.5 = 18, wage for the first 40 hours of 40 x 12 = 480).More can be learned about piecewise functions at brainly.com/question/19358926
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In the diagram below, segment PB is a tangent. IF AC = 18 and PA = 6, find PB.
Answers
Explanation
we have a secant and a tangent
To solve the question, we will apply the intersecting secant and tangent theorem
So, for the question
we have
[tex]\begin{gathered} PB^2=PA(PA+AC) \\ \\ PB^2=6(6+18) \\ \\ PB^2=6(24) \\ \\ PB=144 \\ \\ PB=12 \end{gathered}[/tex]Therefore, the value of PB is 12
aMathWhich of the following shows the solution and graph to the inequality2x + 1 s 15?
Answers
Answer:
[tex]\text{ Option }\Rightarrow\text{ D}[/tex]Explanation: We need to find the answer to the inequality
[tex]2x+1\leq15[/tex]Solution:
[tex]\begin{gathered} 2x+1\leq15 \\ 2x\leq15-1 \\ \therefore\Rightarrow \\ 2x\leq14\rightarrow2x\leq\frac{14}{2} \\ x\leq7 \end{gathered}[/tex]Graph:
The solution as found through solving inequality and demonstrated in the graph is
[tex]\text{ is Option D}[/tex]Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answers
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
Determine the distance between the points (−4, −7) and (−8, −13).
Answers
Answer:
2[tex]\sqrt{23}[/tex]
Step-by-step explanation:
The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.
To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:
[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:
x1 = -4, y1 = -7 (coordinates of the first point)
x2 = -8, y2 = -13 (coordinates of the second point)
Now, we substitute these values into the distance formula:
[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.
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