Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 2}{log \\7}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a +log_c b = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_7{2}[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_7{2}[/tex] = [tex]\frac{log \ 2}{log \ 7}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log \\2}{log \\7}[/tex]
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Describe and correct the error made in solving the equation.
The error is due to different bases of logarithmic value on both sides.
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x = expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]In the question,
the error is due to different bases on both the sides.
correct solution is:
[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\log_2x=log_33^4\\log_2x=4log_33\\log_2x=4\\x=16[/tex]
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The complete question is :
Describe and correct the error made in solving the equation.
[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\x=9^2\\x=81[/tex]
a diver starts at 5 m and changes -16 m?
The depth that the driver is will be -11 meters
How to illustrate the information?From the information, it was stated that diver starts at 5 m and changes -16 m.
Therefore, it should be noted that the depth that he is will be:
= Starting position + Change
= 5 + -16
= -11
Therefore. the depth that he is will be -11 meters.
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A diver starts at 5 m and changes -16 m. What depth is he now?
Gil traveled 4. 5 miles and continues at a speed of 62. 5 miles per hour. Andy has traveled 29. 5 miles per hour and continues at a speed of 50 miles per hour. If the cars continue at the same speed, how many hours will it take for andy and gill to travel the same number of miles
If Gil traveled 4. 5 miles and continues at a speed of 62.5 miles per hour and Andy has traveled 29.5 miles and continues at a speed of 50 miles per hour, then the number of hours it will take for Andy and Gill to travel the same number of miles is equal to 2.
The number of hours it will take for Andy and Gill to travel the same number of miles can be determined by using an algebraic expression.
An algebraic expression to find the number of hours can be given as,
4.5 + 62.5(x) = 29.5 + 50(x)
Here, x is equal to the number of hours.
Solving to find the value of x,
62.5x - 50x = 29.5 - 4.5
12.5x = 25
x = 25 ÷ 12.5
x = 2
Hence, the number of hours it will take for Andy and Gill to travel the same number of miles is calculated to be 2.
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g = x - c solve for x
A certain missing number will result in the expression 20x +24 when using the distributive property. what number must be multiplied by (5x +6) to result in the expression 20x+24
If a certain missing number will result in the expression 20x +24 when using the distributive property, then the number that must be multiplied by (5x + 6 ) to result in the expression 20x + 24 is 4.
The distributive property is a property of multiplication, according to which if two or more values that are added together are multiplied by a number, then the result will be the same if each of these values is multiplied separately with that number and then the products are added together.
Considering y to be the number that must be multiplied by (5x + 6),
y (5x + 6) = y(5x) + y(6)
As the expression is,
20x + 24
y(5x) = 20x and y(6) = 24
6y = 24
y = 24 ÷ 6
y = 4
This can be confirmed as follows,
y(5x) = 20x
Putting y = 4 in this equation,
4(5x) = 20x
Hence the number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is calculated to be 4.
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Solve each equation by factoring. Check your answers.
x²+9 x+20=0
The factors of equation are -4 and -5.
Rewriting the equation -
x² + 9x + 20 = 0
ax² + bx + c = 0
The mentioned equation will be factorized using the given two rules -
1. sum of the factors will be equal to numeral in middle expression b (9x in this case)
2. product of factors will be equal to product of a and c (20 in this case)
Using above rules, the appropriate factors should be 5 and 4.
Representing the factors in mentioned equation -
x² + 4x + 5x + 20 = 0
Taking common factors
x(x + 4) +5(x + 4) = 0
(x + 4) (x + 5) = 0
x = -4, -5
Hence, the two factors of given equation are -4 and -5.
To check the answer, we will keep each value of x in the equation -
When x = -4
x² + 9x + 20 = 0
(-4)² + 9(-4) + 20 = 0
16 -36 + 20 = 0
36 - 36 = 0
0 = 0
When x = -5
x² + 9x + 20 = 0
(-5)² + 9(-5) + 20 = 0
25 - 45 + 20 = 0
45 - 45 = 0
0 = 0
As both Left Hand Side and Right Hand Side of the equation are same for both values of x, the factors are correct.
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PLS HELP
SHOW WORK
ALSO WRITE THE SOLUTION AND EQUATION
Answer:
P = 3.75x - 7
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle
P = 1.5x - 3 + 1.5x - 3 + 0.75x - 1 ← collect like terms
= 3.75x - 7
solve for x
c=2[tex]\pi[/tex]r
angle a and angle B are supplementary angles. if M angle a equals 2X +27 and M angle B equals 5X -1 then find the measure of angle a 
The value of the angle A is; ∠A = 74°.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two angles are termed supplements of one another. In other words, because unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.Supplementary angles are classified into two types.supplementary angles adjacentNon-adjacent supplementary anglesFrom the stated question;
∠A = 2X +27 and ∠B = 5X -1.
From the property of supplementary angles;
∠A + ∠B = 180
Put the values;
2X +27 + 5X -1 = 180
On simplification;
7X = 154
X = 22
Put the value of X in ∠A = 2X +27.
∠A = 2 x 22 + 27
∠A = 74°.
Therefore, the measure of the angle A is ∠A = 74°.
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Determine the slope. (0, -6) & (-2, 8) Responses
ABCD is a rectangle that represents a park
The lines show all the paths in the park
The circular path is in the center of the rectangle and has a diameter of 15m
calculate the shortest distance from A to C across the park using only the lines shown
image is attached below
Answer:
Hence,required shortest distance =102.89m
The shortest distance from A to C is 102.89 m.
What is Perimeter?Perimeter refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
Using Pythagoras theorem
AC² = 50²+80²
AC² =8900
AC =√8900
AC = 94.33
So, the distance removing the diameter
= 94.33-15
= 79.33
Now, Circumference of semicircle = πr
= 23.56 m
So, the possible distances
A - B - C = 50 +80= 130
A-C = 23.56 + 79.33= 102.89
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What is the value of ax? - 5xV + 512 for x=-6 and J/ = 22
Two expressions with equal sign is called as Equation, The value of - 5xV + 512 for x=-6 and J/ = 22 is 1172.
What is Equation?Two expressions with equal sign is called as Equation.
- 5xV + 512 for x=-6 and J/ = 22
Plug in values of x and V in above expression.
-5(-6)22+512
negative into negative is positive.
=660+512
=1172
There The value of expression - 5xV + 512 is 1172.
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What are the coordinates of the point P that lies along the directed
segment from L(-6, 5) to M (4, -6) and partitions the segment in
the ratio of 1 to 3?
The coordinates of point P are ( -3.5, 2.25).
Given points L( -6, 5) and M( 4, - 6). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 1 to 3.
The coordinates of the point that divides a line segment internally in the ratio m:n are given as follows:
[ (mx₂ + nx₁ ) / (m + n) , (my₂ + ny₁ ) / (m + n) ]
Now, m : n = 1 : 3
( x₁, y₁ ) = L( - 6 , 5 )
( x₂, y₂ ) = M( 4, - 6 )
Therefore,
P( x, y) = [ ( 1 × 4 + 3 × -6 ) / 4 , ( 1 × - 6 + 3 × 5) / 4 ]
P( x, y) = [ ( 4 - 18 ) / 4 , ( - 6 + 15) / 4 ]
P( x, y ) = [ -14/4 , 9/4 ]
P( x, y) = ( - 7/2 , 9/4 )
P( x, y) = ( - 3.5, 2.25 )
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E and f are supplementary. If m e = (9x-38) and m f = (2x+42) find m f
Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.
What is the numerical measure of angle F?Supplementary angles are angles that sum up to 180 degrees.
Given the data in the question;
E and f are supplementaryMeasure of angle E = ( 9x - 38 )°Measure of angle F = ( 2x + 42 )°Numerical measure of angle F = ?Since E and F are supplementary, it means they sum up to 180 degrees.
Measure of angle E + Measure of angle F = 180°
Plug in the given values and solve for x
( 9x - 38 ) + ( 2x + 42 ) = 180
9x + 2x - 38 + 42 = 180
11x + 4 = 180
11x = 180 - 4
11x = 176
Divide both sides by 11
11x = 176
11x/11 = 176/11
x = 16
Now, the numerical measure of angle F will be;
Measure of angle F = ( 2x + 42 )
Measure of angle F = 2( 16 ) + 42
Measure of angle F = 32 + 42
Measure of angle F = 74°
Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.
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Convert them please
Answer:
a) 1.999 moles He
b) 0.50 moles Cu
Step-by-step explanation:
Step-by-step explanation:
1 km = 1000 m = 0.621371 miles
so,
786.3 m = 0.7863 km (simply divide by 1000).
40 km/h = 40×0.621371 mph (as the reference of 1 hour stays the same).
= 24.8548 mph
always consider the direction of the conversion rate : are you going from a smaller to a larger unit, or from a larger to a smaller unit ?
if we would have said
1 m = 0.001 km
then we would have converted 786.3 m by multiplying it by 0.001 (also getting 0.7863 km as result, of course).
but because we defined it the other way around, we had to divide by 1000. it is clear that this is the same operation, yes ?
in the same way, if we would have said
1 mile = 1.60934 km
then we would have converted 40 km to miles by dividing 40 by 1.60934. again getting the same result, of course.
Evaluate: 50% of 3,000= ?
Answer:
1500
Step-by-step explanation:
imagine 30 / 5 = 15 then add the two zero's after
Answer:
50% of 3,000 is 1500
Step-by-step explanation:
hope this helps!
On Earth with a gravitational acceleration \text{g} , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
Equation that models the potential energy of a 2 kg skateboard that is sliding down a ramp is :
U = 2gh
What is Gravitational acceleration ?Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .
What is Potential Energy ?Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
mass = 2kg
as, U = mgh
therefore, U = 2gh
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The complete question is :
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
what is the common denominator of 3/20 and 9/40 ?
Answer:
The answer is 40.
Step-by-step explanation:
Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).
Tanya bought 8.05 yards of fleece fabric to make costumes for a school play. She needs 1.25 yards of
fabric for each costume. How many costumes can Tanya make with the fabric she bought ( long division )
Answer: 6 costumes
Step-by-step explanation: 8.05 divided by 1.25 would be 6.44, but how can you make 6.44 costumes? The most costumes Tanya can make are 6 costumes for the school play.
Mariana and her children went into a movie theater and she bought $51.25 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She bought a total of 13 candies and pretzels altogether. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mariana bought. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
you could use multiplication or addition,
Answer:
Step-by-step explanation:
James has 23 cans, but the people gets 15 cans, What cans left?
A 13
B 8
C 10
D 7
Answer:
B
Step-by-step explanation:
23-15=8
Which of the following is a rational number?
A. [tex]\sqrt{10}[/tex]
B.[tex]\sqrt{100}[/tex]
C.[tex]\sqrt{1000}[/tex]
D.[tex]\sqrt{100000}[/tex]
Can you please explain your answer I want to understand it
The rational numbers are √10, √1000 and √100000 . Options A, C and D
What is a rational number?A rational number can be defined as a number that can be expressed as a fraction.
It also has the numerator and denominators as integers and expressed in decimal forms.
Given the values;
√10√100√1000√100000√10 = 3. 162
√100 = 10
√1000 = 31. 6
√100000 = 316. 22
Thus, the rational numbers are √10, √1000 and √100000 . Options A, C and D
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please help please im giving so much
Answer:
D
Step-by-step explanation:
The highest number that divides exactly into two or more numbers. 3 and 9 cannot be divided by anything greater than 3.
Answer: i think its D.
Step-by-step explanation:
If the distance from P to R is three units what is the distance from Q to S explain your reasoning
The scaling factor is 2: 1, the distance between Q and S is 3 units.
A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the original dimensions are known, the scaling factor may be determined.
When describing a shape, you must define the amount to which it has been enlarged.
AC = 6
It signifies that the 6/3 = 2:1 scale factor has been preserved.
As a result, the total dimension of PQRS is half of ABCD.
So,
QS = 1/2 (BD)
Because BD = 6, (can be counted by graph grid)
So,
QS = 1/2 (5) = 3
Hence "Because the scale factor is 2: 1, the distance between Q and S is 3 units."
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Which function family does the graphed function belong to? !!!!!70 POINTS!!!!!!
Answer:
Y=x³ is the parent graph I don't know if that helps.
Answer:
Cubic
Step-by-step explanation:
Six friends each use a $2-off coupons to buy themselves a movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?
The price of one movie ticket without the coupon is $9.
arithmetic operations
Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.
...
There are 7 arithmetic operators in Python :
Addition.
Subtraction.
Multiplication.
Division.
Modulus.
Exponentiation.
Floor division.
since they spend a total of $42.
so the price of one movie ticket without the coupon is
⇒ (42+12)/6
⇒54/6
⇒ 9
so the price of one movie ticket will be $9.
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If AABC = ADEF, AB = 8, BC = 19, AC=14, EF = 4x-1, and DE=y-6, find the values of
x and y.
When given triangles are given then the value of x and y is 5 and 14 respectively.
When BC is similar to EF.
19= 4x-1
19+1=4x
20=4x
x=5
When DE is similar to AB
y-6 =8
y=8+6
y=14
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.
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A=7x
2
−3x+10
B=−4x
2
+6x−4
A-B=A−B=
Answer:
3/4
Step-by-step explanation:
7x +4x = - 3x+10+6x-4
11x=-3x+6x+10-4
11x=3x+6
11x-3x=6
8x=6
X=3/4
can someone help me with this
Answer:
this is a little much if you broke it down into single questions I would be happy to help
Step-by-step explanation:
Answer:
The answer is below!!
Step-by-step explanation:
I. Fill in each step of the problem-solving process to solve this problem.
Cadence went to the amusement park and paid $14.25 for a souvenir refill cup. Refills cost $1.25 each. If Cadence spent a total of $23, how many refills did she get? ~
Step 1: What is the unknown?
The number of refills is the unknown.Step 2: What is the key information that can be used to solve the problem?
Let x be the number of refills.Step 3: What is a strategy (equation) that can be used to solve the problem?
Equation: 14.25 + 1.25x = 23Step 4: What is the solution to the problem?
↓
[tex]\sf 14.25+1.25x=23[/tex]
[tex]\sf 14.25\cdot \:100+1.25x\cdot \:100=23\cdot \:100[/tex]
[tex]\sf 1425+125x=2300[/tex]
[tex]\sf 1425+125x-1425=2300-1425[/tex]
[tex]\sf 125x=875[/tex]
[tex]\sf \cfrac{125x}{125}=\cfrac{875}{125}[/tex]
[tex]\boxed{\sf x=7}[/tex]
Step 5: Check your answer.
To check your answer, plug x = 7 in the given term
[tex]\sf 14.25+1.25(7)=23[/tex]
[tex]\sf 14.25+8.75=23[/tex]
[tex]\sf 23=23[/tex]
→ → → →
II. Solve each problem. Show your work.
Jordan’s bill for car repairs was $500. The cost for parts was $240 and the mechanic charged $65 per hour. How many hours did it take the mechanic to repair Jordan’s car?
Let the number of hours = x
[tex]\sf 65x+240=500[/tex]
[tex]\sf 65x=260[/tex]
[tex]\sf x=4[/tex]
Therefore, it took the mechanic 4 hours to repair Jordan’s car!
→ → → →
2. Marcus made 6 baskets in his first basketball game. In each of the next 4 games, he made the same number of baskets. If he made a total of 34 baskets , how many baskets did he make in each of the 4 games?
Let x = baskets Marcus made in each of the 4 games
[tex]\sf 4x+6=34[/tex]
[tex]\sf 4x=34-6[/tex]
[tex]\sf \cfrac{4x}{4}=\cfrac{28}{4}[/tex]
[tex]\sf x=7[/tex]
Therefore, Marcus made 7 baskets in each of the 4 games!
And we're done!
________________________
Hope this helps!
Have a great day!
MN¯has an endpoint at M(–2, –2) and an endpoint at N(7, –5).
What is the length of MN to the nearest tenth?
The length of the segment MN is 9.5 units
How to determine the length of the segment MN?The endpoints of the line segment MN are given as
M = (-2, -2)
N = (7, -5)
The length of the segment MN is calculated as:
MN = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the known values in the above equation
So, we have
MN = √(-2 - 7)^2 + (-2 + 5)^2
Evaluate the sum and the difference
So, we have
MN = √-9^2 + 3^2
Evaluate the exponents
So, we have
MN = √81 + 9
Evaluate the sum
So, we have
MN = √90
Evaluate the exponents
So, we have
MN = 9.5
Hence, the length of the segment MN is 9.5 units
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