Solve the equation in the image below correct to 2 decimal places. in Logarithm Terms
The solution to the given equation is 5.630.
What is a logarithmic equation?
An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Here, we have
2^(x+1) = 3^(2x-5)
Taking logarithms on both sides, we get
(x+1)log2 = (2x - 5)log3
xlog2 + log2 = 2xlog3 - 5log3
log2 + log3⁵ = 2xlog3 - xlog2
log 2* 243 = x(log6 - log2)
log486 = x(log6/2)
log486 = xlog3
x = log486/log3
x = 5.630
Hence, the solution to the given logarithmic equation is 5.630.
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6:3(3+3)= can anyone answer this
Are the figures congruent?
Yes these triangles are congruent.
What is congruent triangles?
Two triangles live aforesaid to be congruent if all 3 corresponding sides are equal and every one the 3 corresponding angles are equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruousness is’ ≅’.
Main body:
Firstly we need to find the co-ordinates of each point.
M = (-1,5) R= (1,1)
L = (-2,2) S= (-5,-1)
N= (5,3) Q= (2,-2)
to prove these triangles are congruent we need to show that the distance of their sides are equal.
distance formula= [tex]\sqrt{(x1-x2)^2+(y1- y2)^{2}[/tex]
Now in ΔLMN =
ML = [tex]\sqrt{(-1+2)^{2}+(5-2)^{2} }[/tex]
ML= [tex]\sqrt{10}[/tex] units
LN =[tex]\sqrt{(5+2)^{2}+(3-2)^{2} }[/tex]
LN= [tex]\sqrt{50}[/tex] units
MN =[tex]\sqrt{(5+1)^{2}+(3-5)^{2} }[/tex]
MN=[tex]\sqrt{40}[/tex] units
Now in ΔQRS=
RS= [tex]\sqrt{(1+5)^{2}+(1+1)^{2} }[/tex]
RS = [tex]\sqrt{40}[/tex] units
SQ = [tex]\sqrt{(2+5)^{2}+(1-2)^{2} }[/tex]
SQ = [tex]\sqrt{50}[/tex] units
RQ = [tex]\sqrt{(1-2)^{2}+(1+2)^{2} }[/tex]
RQ = [tex]\sqrt{10}[/tex] units.
We can clearly see on side of each triangle is equal to one side of another one.
Hence ΔLMN≅ΔQRS.
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How many 3/16-yard pies can be cut from 3/4 yard of ribbion?
The number of 3 / 16 yards pieces that can be cut from 3 / 4 yard of ribbon is 4.
How to find how many pieces of ribbon that can be cut?The actual length of the ribbon is 3 / 4 yards.
He wants to cut 3 / 16 yards pieces from the actual length of the ribbon.
Therefore, the number of 3 / 16 yard that can be cut from 3 / 4 yard of ribbon can be calculated as follows;
number of pieces of ribbon = 3 / 4 ÷ 3 / 16
number of pieces of ribbon = 3 / 4 × 16 / 3
number of pieces of ribbon = 48 / 12
Therefore,
number of pieces of ribbon = 4 yards
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The polynomial P(x) of degree 4 has
a root of multiplicity 2 at x = 4
• a root of multiplicity 1 at x = 0 and at x = -1
• It goes through the point (5,21)
Find a formula for P(x).
P(x) =
Question Help: Message instructor
Answer:
P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x
Step-by-step explanation:
given a polynomial with roots x = a and x = b , then the factors are
(x - a) and (x - b)
If x = a is of multiplicity 2 then factor is (x - a)²
the polynomial is then the product of the factors
p(x) = a(x - a)(x - b) ← a is a multiplier
give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor
x = 0 has factor (x - 0) , that is x
x = - 1 has factor (x - (- 1)) , that is (x + 1)
the polynomial is then the product of the factors
P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL
= ax(x + 1)(x² - 8x + 16)
= a(x² + x)(x² - 8x + 16) ← distribute
= a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)
= a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)
to find a substitute (5, 21 ) into P(x)
21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))
21 = a(625 - 875 + 200 + 80)
21 = 30a ( divide both sides by 30 )
0.7 = a
then
P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis
P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x
Write as a single fraction in its lowest terms: 3(2x-1)/5 -2 (4x -2)/2
The single fraction in its lowest terms will be;
⇒ - 7(2x - 1)/2
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2
Now,
Solve the fraction as;
The fraction is,
⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2
⇒ 3 (2x - 1)/5 - (4x - 2)
⇒ 3 (2x - 1)/5 - 2 (2x - 1)
⇒ (2x - 1) (3/5 - 2)
⇒ (2x - 1) (3 - 10)/2
⇒ (2x - 1) (- 7/2)
⇒ - 7(2x - 1)/2
Thus, The single fraction in its lowest terms will be;
⇒ - 7(2x - 1)/2
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3.) Johannes sold an order of 3 Strawberry pies
for $12.50 each. She paid her assistant
$1.10 for each Strawberrye pie sold. How much
money did Johannesearn from the pies sold?
Answer:
$34.20
Step-by-step explanation:
Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.
We know that there were 3 pies sold so you must solve the equation below
11.40*3
The answer is $34.20
4x/3 -x=x/15-12/5 x =??????????
What is the y-intercept of this line?
Answer:
The Y intercept of this line is -3.
Step-by-step explanation:
The X intercept of the crossing line is about -1.4.
On finding the Y intercept:
Step 1: look at the vertical black line (Y Axis)
Step 2: Locate where the blue line crosses on this line.
Step 3: graph Y function of the point as your answer.
Hope this helped a bunch!
Have a great day!
- Kit-Kat~
.......................................
Answer:
c is ur answer
I hope it's help◉‿◉
Determine when the function is positive, negative, increasing, or decreasing.
The function is positive and increasing from 0 to 2.5, at negative and decreasing from 0 to -2.5, respectively.
How to find returns to scale?
Returns to scale involves an increase in an output more than when all the inputs increase proportionately.
Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5. this shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.
In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.
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What does the Big Bang Theory explain?
Answer:
The big bang is how astronomers explain the way the universe began. It is the idea that the universe began as just a single point, then expanded and stretched to grow as large as it is right now—and it is still stretching!
Step-by-step explanation:
In 1927, an astronomer named Georges Lemaître had a big idea. He said that a very long time ago, the universe started as just a single point. He said the universe stretched and expanded to get as big as it is now, and that it could keep on stretching The universe is a very big place, and it’s been around for a very long time. Thinking about how it all started is hard to imagine. Some More Information
Just two years later, an astronomer named Edwin Hubble noticed that other galaxies were moving away from us. And that’s not all. The farthest galaxies were moving faster than the ones close to us. This meant that the universe was still expanding, just like Lemaître thought. If things were moving apart, it meant that long ago, everything had been close together.
Everything we can see in our universe today—stars, planets, comets, asteroids—they weren't there at the beginning. Where did they come from?
A Tiny, Hot Beginning
When the universe began, it was just hot, tiny particles mixed with light and energy. It was nothing like what we see now. As everything expanded and took up more space, it cooled down.
The tiny particles grouped together. They formed atoms. Then those atoms grouped together. Over lots of time, atoms came together to form stars and galaxies.
The first stars created bigger atoms and groups of atoms. That led to more stars being born. At the same time, galaxies were crashing and grouping together. As new stars were being born and dying, then things like asteroids, comets, planets, and black holes formed!
Chang will run at least 21 miles this week. So far, he has run 12 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles
What is an InequalityIn Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
To find the number of additional miles he will run, let's set the unknown number equals t
12 + t > 21
t > 21 - 12
t >9
Chang will need to run at least 9 miles
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find the horizontal asymptote
The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].
Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]
Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.
We will calculate limits :
[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]
[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]
Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].
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Find the side length of x. Round your answer to nearest hundredth
For the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).
As given in the question,
Given right angled triangle,
Base of the triangle is equal to 10 units
Perpendicular side of a triangle is equal to 9 units
Side length 'x' is the hypotenuse of the right angled triangle.
Using Pythagoras theorem we get,
(Hypotenuse)² = ( Base)² + ( Perpendicular side)²
⇒ x² = (10)² + (9)²
⇒ x² = 100 + 81
⇒ x² = 181
⇒ x = √181
⇒ x = 13.4536...
⇒ x = 13.45 units ( nearest hundredth)
Therefore, for the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).
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a.
Lesson 2.16 Practice Problems
There are many cylinders with a volume of 1447 cubic inches. The height h(r) in
inches of one of these cylinders is a function of its radius r in inches where h(r) =
b.
What is the height of one of these cylinders if its radius is 2 inches?
What is the height of one of these cylinders if its radius is 3 inches?
What is the height of one of these cylinders if its radius is 6 inches?
144
1) The height of one of these cylinders if its radius is 2 inches is
115.207 inches.
2) The height of one of these cylinders if its radius is 3 inches is
51.203 inches.
3) The height of one of these cylinders if its radius is 6 inches is
12.800 inches.
VOLUME OF CYLINDER = πr²h = 1447 cubic inches1) when radius is 2 inches then:
πr²h = 1447
h = 1447/ (3.14 x 2²) = 115.207 inches
2)when radius is 3 inches then:
πr²h = 1447
h = 1447/ (3.14 x 9²) = 51.202 inches
3) when radius is 6 inches then:
πr²h = 1447
h = 1447/ (3.14 x {36}²) = 12.800 inches
1) The height of one of these cylinders if its radius is 2 inches is
115.207 inches.
2) The height of one of these cylinders if its radius is 3 inches is
51.203 inches.
3) The height of one of these cylinders if its radius is 6 inches is
12.800 inches.
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help me out thanks 10 ponits
Answer:
yes yes ...................
Please help! I will award top rating for the first to help! (the questions are on the image)
It needs to be fully simplified!
Answer:
Step-by-step explanation:
4x(power of 5) divided by x(power of 2)
5y(po7) div by y(po2)
not 100% sure as i havent learnt this before lol
35 lbs of bananas
cost $280. How
much would 42 lbs
cost?
Answer:
$336
Step-by-step explanation:
[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]
The current on the Little River is 8 mph. Tom's
boat goes 15 mph in still water. How far upstream
can Tom's boat go on the Little River in 1.5 hours?
a) 12 miles
b) 25 miles
c) 10.5 miles
d) 34.5 miles
10.5 miles far upstream can Tom's boat go on the Little River in 1.5 hours.
How to calculate the relative velocity ?The relative velocity formula is written as follows. V is equal to
V → = V A B → + V B C →
Where. VAB is the velocity in relation to A and B, VBC is the velocity in relation to B and C, and VAC is the velocity in relation to A and C.
The current on the Little River is 8 mph.
Tom's boat goes 15 mph in still water.
For Upstream
the Velocity of the boat = 15 mph - 8mph
= 7mph
How far upstream
can Tom's boat go on the Little River in 1.5 hours = 7* 1.5 = 10.5 miles
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According to the questions that are asked in the various Government exams that are held across the nation, the boat and stream concept is one of the most frequently covered subjects.
How to calculate Boat and Stream?The four terms that a candidate has to comprehend in order to grasp the notion of streams are listed below.Stream: A river's flowing water is referred to as a stream.Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The boat's upstream speed in this situation is its net speed.Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream. In this instance, the boat's downstream speed is its net speed.Still Water - In this situation, the water is seen as being immobile and has no speed.The main focus of this topic is determining the speed of anything moving through water, whether it is moving with the current or against it.For example : In one hour, a boat goes 13 km/hr in the direction of the stream and 7 km/hr against the direction of the stream. What will be the speed of the boat in still water?Utilizing the formula,Boat speed in still water = 1/2 (downstream speed + upstream speed).
Boat's speed in still water equals 1/2 (13+7) = 1/2 × 20 = 10 km/hr.
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How can I find the scale factor of the two similar triangles and how can I use similarity and scale factor to find the length?
Answer:
i think, x equal 12 and y equal 20
Simon invests $7000 into an account that earns 0.4% simple interest annually.
Which statement best describes the relationship between the number of years Simon has his money invested and the account balance in any year?
1:
The relationship is linear. His account increases each year by a constant value of $280.
2:The relationship is exponential. The ratio of his account balance any year to the previous year is 1.004.
3:The relationship is exponential. The ratio of his account balance any year to the previous year is 0.004.
4:The relationship is linear. His account increases each year by a constant value of $28.
The relationship is linear. His account increases each year by a constant value of $28.
The relationship between the number of years that Simon's money is invested and the account balance can be described as 4:The relationship is linear. His account increases each year by a constant value of $28.
How to find the relationship between variables?The simple interest due to Simon's account every year is:
= Simple interest rate x Amount invested
= 0.4% x 7, 000
= $28
This means that every year, Simon's account would increase by a value of $28.
This represents a linear relationship because in linear relationships, the value of the variables increases by a constant amount each year or period.
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At 12 noon it was discovered that a driver has travelled 3/8 of the distance from Kano to lagos ,while another driver had travelled 3/10 of that distance from lagos,travelling at the same rate .if the two drivers are 390km apart .find the distance from Kano to lagos
The distance from Kano to Lagos is 1200 km
How to determine the distance from Kano to LagosThe problem involves addition of fractions
The fraction required are:
let the distance form kano to Lagos be x
it was discovered that a driver has travelled 3/8 = 3x/8
another driver had travelled 3/10 of that distance = 3x/10
The drivers are still 390 km apart
total distance, x
x = 390 + 3x/8 + 3x/10
x - 3x/8 - 3x/10 = 390
0.325x = 390
x = 390 / 0.325
x = 1200 km
From the driving distance information 1200 km is the distance from Kano to Lagos
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Which symbol correctly compares the fractions below?
2/3 ? 6/9
A. >
B. none of these are correct
C. =
D.
Answer:
C
Step-by-step explanation:
6/9 simplified is 2/3
Hope this helps
A city block is 3 times as long as it is wide. If the distance around the city block is 16.8 kilometers, what is the area of the city block?
The area of the city block is 13.23 kilometers².
How to calculate the area?The city block is 3 times as long as it is wide. In this case, the width can be represented by w. The length will be 3w.
Therefore, perimeter will be:
= 2(length + width)
= 2(3w + w) = 16.8
8w = 16.8
Divide
w = 16.8 / 8
w = 2.1
Length = 3w = 3 × 2.1 = 6.3km
The area will be:
= Length × Width
= 6.3 × 2.1
= 13.23km²
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Answer:
The area of the city block is 13.23 kilometers².
Step-by-step explanation:
For a circle with a radius = 4.3, find the following:
(Use π = 3.14 for all answers. Do not round!)
Circumference =
Area =
Answer: Circumference equals = 27.004
Area equals = 58.0586
We can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.
What is a two - dimensional figure?A two - dimensional figure is a collection of two - dimensional points enclosed by a single dimensional entity. For example, triangle, circle, trapezium etc all represent a two - dimensional figure. The points inside these figures can be expressed as (x, y).Given is that a circle with a radius of 4.3.
We can write the area of the given circle as -
Area = πr²
Area = π x 4.3 x 4.3
Area = 18.49π square units
We can write the circumferance of the given circle as -
circumferance = 2πr
circumferance = 2 x π x 4.3
circumferance = 8.6π units
Therefore, we can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.
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in 2017, a journal reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed in a 24-hour period. The study was done in 2005 and repeated in 2014. The numbers who consumed a sugary beverage such as soda or fruit juice in a day are shown in the accompanying table
The 95% confidence interval for the distribution of the difference of proportions, using the z-distribution, is given as follows:
(0.11, 0.146).
How to find the confidence interval for the difference of proportions?The first step is finding the proportion and standard error for each sample, as follows:
2005: [tex]n = 3486 + 2248 = 5734, p_1 = \frac{3486}{5734} = 0.608, s_1 = \sqrt{\frac{0.608(0.392)}{5734}} = 0.0064[/tex]2014: [tex]n = 2754 + 2980 = 5734, p_2 = \frac{2754}{5734} = 0.48, s_2 = \sqrt{\frac{0.48(0.52)}{5734}} = 0.0066[/tex]For the distribution of differences, the mean and the standard error are given as follows:
p = 0.608 - 0.48 = 0.128.s = sqrt(0.0064² + 0.0066²) = 0.0092.The z-distribution is used as we are working with proportions, hence the bounds of the interval are given as follows:
p ± zs.
The critical value for a 95% confidence interval with the z-distribution is of z = 1.96.
Hence the lower bound of the interval is:
0.128 - 1.96 x 0.0092 = 0.11.
The upper bound of the interval is:
0.128 + 1.96 x 0.0092 = 0.146.
What is the missing information?
The information regarding each sample is given by the image at the end of the answer, and the problem asks for the 95% confidence interval for the differences.
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Show, by shading on the grid, the region defined by all three of the inequalities
x ≤ 5 y ≥ 3 y ≤ x
Answer:
See below
Step-by-step explanation:
The area (triangle) marked 'x' in the diagram below
Select the equations of the line that goes through the point 6,-2 and is perpindicular to the line y+2=-2/5(x-10) .
A. y=-2/5x+2
B. y=5/2x-17
C. 5x-2y=34
D. 2x+5y=2
E. y+2=-2/5(x-6)
F. y+2=5/2(x-6)
y + 2 = 5/2 (x - 6) ; 5x-2y=34 ; y=5/2x-17 is the equations of the line that goes through the point (6,-2) and is perpendicular to the line y+2=-2/5(x-10), Hence the correct options are B, C and F.
What is equation of the line?The standard forms of the equation of a line are:
Slope-intercept form:
y = mx + c
Where m indicates the slope of the line and c is the y-intercept
Intercept form:
x/a + y/b = 1
General form of the equation of the straight line, i.e. Ax+By+C = 0
x/(-C/A) + y/(-C/B) = 1
where a = -C/A and b = – C/B
Normal form:
The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:
x cos α+y sin α = p
Given,
Point = (6,-2) = (x2,y2)
Equation of line = y+2=-2/5(x-10)
General equation of the line = y - y1 = m ( x-x1 )
After comparing we get,
Slope of the given line = -2/5
As we know both the lines are perpendicular to each other so, product of their slopes must be equal to -1.
m1 × m2 = -1
-2/5 × m2 = -1
We get m2 = 5/2
So the equation of the line having slope 5/2 and passing through (6,-2) is:
y - y2 = m2 ( x-x2 )
y -(-2) = 5/2 (x - 6)
y + 2 = 5/2 (x - 6)
Hence, we get equation of the line as y + 2 = 5/2 (x - 6) .
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Divide 647,457 by 325,712,318