To solve the logarithmic equation with different bases, one must recognize the importance of base conversion and utilize logarithmic properties to guide conversion or comparison, not just directly equate the logarithmic arguments, which was a misunderstanding.
Explanation:To solve the equation log_4(x + 3) = log_2(2 + x), we need a system that represents this equation effectively by considering logarithmic properties and base conversion.
Steps for Solving the Equation
Recognize that both sides of the equation are logarithms, which implies their arguments must be equal if their outputs are equal. Thus, it means x + 3 = 2 + x.
This simplification does not directly solve our original equation due to the different bases of the logarithms. We utilize the property that allows us to convert between bases: log_a(b) = log_c(b) / log_c(a), specifically focusing on changing base 4 logarithm to base 2.
We apply this to convert log_4(x + 3) to a base 2 logarithm, yielding a new equation: log_2(x + 3)/log_2(4) = log_2(2 + x).
Since log_2(4) = 2, the equation simplifies to 0.5 * log_2(x + 3) = log_2(2 + x).
This step reveals that the initial transformation inadvertently simplified through a direct comparison, which doesn't correctly express the conversion between bases or the nature of the original problem.
To correctly translate the given logarithmic equation into a system of equations, acknowledge that the original task was misunderstood in Step 1, as it did not account for the different log bases and their properties.
Instead, consider equations that capture the essence of converting bases or applying logarithmic identities to derive a solution.
A more accurate representation would involve recognizing the base conversion and understanding that without a direct means of converting or equating the logarithms due to their different bases and the variables involved, it does not straightforwardly lead to a solvable system without further information or manipulation that squarely addresses the base disparity.
1.
A train car can hold 1500 pounds of cargo that occupies 138 cubic feet of space. A computer
desk weighs 50 pounds and occupies a space of 4 cubic feet. A single drawer file cabinet weighs
30 pounds and occupies a space of 3 cubic feet. Which system of equations can be used to find
the total number of computer desks, d, and single drawer file cabinets, c, that can be carried in
the train car?
a. 4d + 3c = 138
50d + 30c = 1500
C. 50d + 30c = 138
30d + 3c = 138
b. 50d + 30c = 1500
50+ 4d = 1500
d. 4d + 3c = 138
30 + 3c = 1500
Answer:
A
Step-by-step explanation:
Let d be the total number of computer desks and c be the total number eof single drawer file cabinets.
1. A computer desk weighs 50 pounds, then d computer desks weigh 50d pounds. A single drawer file cabinet weighs 30 pounds, then c cabinets weigh 30c pounds. In total, a train car can hold 1500 pounds of cargo, so
50d+30c=1500
2. A computer desk occupies a space of 4 cubic feet, then d computer desks occupy 4d cubic feet. A single drawer file cabinet occupies a space of 3 cubic feet, then c cabinets occupy 3c cubic feet. In total, a train car can hold 138 cubic feet of space, so
4d+3c=138.
Thus, we get a system of two equations:
[tex]\left \{ {{50d+30c=1500} \atop {4d+3c=138}} \right.[/tex]
What is the value of n in the equation –1/2(2n + 4) + 6 = –9 + 4(2n + 1)?
Answer:
n = 1Step-by-step explanation:
[tex]-\dfrac{1}{2}(2n-4)+6=-9+4(2n+1)\qquad\text{use the distributive property}\\\\\left(-\dfrac{1}{2}\right)(2n)+\left(-\dfrac{1}{2}\right)(-4)+6=-9+(4)(2n)+(4)(1)\\\\-n-2+6=-9+8n+4\qquad\text{combine like terms}\\\\-n+(-2+6)=8n+(-9+4)\\\\-n+4=8n-5\qquad\text{subtract 4 from both sides}\\\\-n=8n-9\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-9n=-9\qquad\text{divide both sides by (-9)}\\\\n=1[/tex]
6. When solving an equation like 2x + 10 = 2(x + 5), and, when simplified, you get x = x, 10 = 10, or 0 = 0, what is the solution for X
no solution
any real number
10
zero
HELP PLS THANK U
Answer:
any real number
Step-by-step explanation:
Answer when simplified gives 0 = 0
This indicates that any real value of x is a solution.
Usually because the equations on both sides are equal.
That is 2x + 10 = 2x + 10 leading to 0 = 0
BRAINLIEST Help please I need this fast
Answer:
x=20
Step-by-step explanation:
Since this is a right angle, it is equal to 90 degrees
x + 3x+10 = 90
Combine like terms
4x+10 = 90
Subtract 10 from each side
4x+10-10 =90-10
4x=80
Divide by 4
4x/4=80/4
x = 20
what’s the lateral area of the cone?
Which numbers belong to the solution set of the ineqaulity? 5x<55
Answer:
x<11
Step-by-step explanation:
To solve this inequality, we must isolate the x. To do that, we divide both sides by 5. This gives us x<11. So all numbers less than eleven belong to the solution set of the inequality.
Answer:
All number less than 11.
Step-by-step explanation:
5x < 55
We just isolate x by dividing both sides by 5:
5x / 5 < 55/5
x < 11.
A function g(x) is defined as shown.
2 + 3x, 0 < x < 4
Q(x) = 0.5x + 10, 4 AKB
| 16, KEB
What is the value of g(4)?
10
12
14
16
Answer:
g(4) = 12
Step-by-step explanation:
We need to find the value the function g(x) when x = 4, that is;
g(4)
In the first definition of the function, the value of x is strictly less than 4. Consequently, we shall use the second definition of the function to evaluate g(4)
In the second definition, g(x) is given as;
Q(x) = 0.5x + 10
plug in x = 4 and simplify;
Q(4) = 0.5(4) + 10
Q(4) = 12
You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1,000 square feet. The fertilizer comes in 50-pound bags. How many bags of fertilizer will you need to complete the job?
Answer: 10 bags
Step-by-step explanation:
First we must calculate the field area. Assuming it is a rectangle then its area equals the product of its length times its width
[tex]A =360*160\\\\A = 57600 ft^2[/tex]
You use 8 pounds of fertilizer per 1,000 square feet
So the amount of fertilizer you should use is:
[tex]57,600 ft^2 * \frac{8\ pounds}{1,000\ ft^2} = 460.8\ pounds[/tex]
As the fertilizer comes in bags of 50 pound then you need
[tex]460.8\ pounds * \frac{1\ bag}{50\ pounds} = 9.2\ bags[/tex]
Since you can not buy 9.2 bags then we round up to the next whole number.
Finally you need 10 bags of fertilizer
Eggs are purchased at rs.120per dozen and are sold out at rs.130per dozen.find profit or loss
Answer:
= 10 rs
Step-by-step explanation:
C.P. - 120
S.P. - 130
cp < sp
120 < 130
so , profit = sp - cp
= 130-120
= 10 rs.
hope it helps !
To find the profit for selling eggs, subtract the cost price from the selling price, resulting in a profit of Rs. 10 per dozen.
Explanation:To calculate the profit or loss from buying and selling eggs, we need to follow a series of steps. First, we find the cost of buying the eggs, which is Rs. 120 per dozen. Then, we find the revenue from selling the eggs, which is Rs. 130 per dozen. The difference between these two amounts will give us the profit or loss made on each dozen of eggs sold.
The calculation is as follows:
Selling Price (SP) per dozen = Rs. 130
Cost Price (CP) per dozen = Rs. 120
Profit per dozen = SP - CP
Profit per dozen = Rs. 130 - Rs. 120 = Rs. 10
Therefore, for each dozen of eggs sold, there's a profit of Rs. 10.
Which equation is equivalent to?
For this case we must find an equation equivalent to:
[tex]\sqrt {x ^ 2 + 81} = x + 10[/tex]
We square both sides of the equation to eliminate the root:
[tex]x ^ 2 + 81 = (x + 10) ^ 2[/tex]
We have by definition that:
[tex](a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2[/tex]
So, rewriting the right side of the equation we have:
[tex]x ^ 2 + 81 = x ^ 2 + 2 * 10 * x + 10 ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x + 100[/tex]
ANswer:
Option D
Sophie purchased 8 candles at a total cost of $32. The red candles cost $3 each and the silver candles cost $7 each. The equations and graph below can be used to determine the number of each type of candle Sophie purchased, where x represents the number of red candles and y represents the number of silver candles.
A. 7 red candles, 1 silver candle
B. 6 red candles, 2 silver candles
C. 2 red candles, 6 silver candles
D. 3 red candles, 5 silver candles
Answer:
A. 7 red candles, 1 silver candle
Step-by-step explanation:
6 red candles * $3 each = $18
2 silver candles * $7 each = $14
$18 + $14 = $32 (the total cost)
Answer:
B. 6 red candles, 2 silver candle
Step-by-step explanation:
What is the value of y?
у+ 30°
А. 100
ОВ. 55
Ос. 85°
D. 110°
Answer:
B y=55
Step-by-step explanation:
The sum of the angles of a triangle a 180 degrees
40 + y + (y+30) = 180
Combine like terms
70 + 2y = 180
Subtract 70 from each side
70-70 +2y = 180-70
2y = 110
Divide by 2
2y/2 = 110/2
y = 55
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = x − y = x − y = 3x − 3 y = 3x − 7
Given line: y =3x - 7
Slope-intercept form is y = mx + b where m is slope and b is the y intercept
To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)
the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]
This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]
This is the current formula you found:
[tex]y=\frac{-1}{3} x + b[/tex]
To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b
-1 = [tex]\frac{-1}{3}[/tex](2) + b
-1 = [tex]\frac{-2}{3}[/tex] + b
[tex]\frac{-1}{3}[/tex] = b
That means that the equation perpendicular to y = 3x - 7 is...
y = [tex]\frac{-1}{3} x - \frac{1}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y =3x - 7
Step-by-step explanation:
What is the answer to the question
Answer:
From top to bottom:
3
7
6
12
Step-by-step explanation:
You just simply add the number in the top row and the number in the column together.
2 + 1 = 3
4 + 3 = 7
2 + 4 = 6
6 + 6 = 12
Determining angle side relationships What are the angle measures in trainable ABC?
Answer:
m∠A=90°, m∠B=60°, m∠C=30°
Step-by-step explanation:
step 1
Verify if the triangle ABC is a right triangle
Applying the Pythagoras theorem
[tex]12^{2}=6^{2}+(6\sqrt{3})^{2}[/tex]
[tex]144=144[/tex] ----> is true
therefore
Is a right triangle
m∠A=90°
Find the measure of angle C
sin(C)=AB/BC
substitute
sin(C)=6/12=1/2
so
m∠C=30°
Find the measure of angle B
we know that
m∠C+m∠B=90°------> by complementary angles
so
m∠B=90°-30°=60°
What is the length of h in the following composite figure? All angles are right angles.
5 m
4 m
3 m
2 m
The length of h in the given composite figure will be 4, i.e. option B.
What is composite figure?Composite geometric figures are made from two or more geometric figures.
We have,
A composite figure,
Now,
From the figure -- (dash) marked lines are equal , and all dashed marked lines are equal to 1.
Now,
h of the given composite figure consists of two dashed marked lines and 2m.
i.e.
h = 1 + 1 + 2
So,
h = 4 m
So,
The length of h is 4m.
Hence, we can say that the length of h in the given composite figure will be 4, i.e. option B.
To know more about composite figure click here
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Can someone help me out with this question??
Answer:
6 units²
Step-by-step explanation:
The area (A) of a triangle is
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 3 and h = 4, hence
A = 0.5 × 3 × 4 = 0.5 × 12 = 6
henry recorded the number of miles he biked each day for a week. his miles were 25, 40, 35, 25, 40, 60 and 75. what is the standard deviation of the miles henry biked to the nearest tenth
Answer:
17.1
Step-by-step explanation:
The standard deviation of the miles Henry hiked is 17.1
The standard deviation of the miles henry biked to the nearest tenth will be 17.08.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.
The standard deviation is given as,
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
Henry recorded the number of miles he biked each day for a week. The data is given below.
25, 40, 35, 25, 40, 60, 75
Then the mean of the data is given as,
μ = (25 + 40 + 35 + 25 + 40 + 60 + 75) / 7
μ = 300/7
μ = 42.857
Then the standard deviation is given as,
[tex]\sigma = \sqrt{\dfrac{(25 - 42.857)^2 + (40- 42.857)^2 + ......+(75- 42.857)^2}{7}}[/tex]
Simplify the equation, then we have
σ = √(2042.857 / 7)
σ = √291.837
σ = 17.08
More about the standard deviation link is given below.
https://brainly.com/question/12402189
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A line has a slope of and a y-intercept of –2.
What is the x-intercept of the line?
Answer:The equation of the line that has a slope of -1/2 and a y-intercept of -2 is: y=-1/2x-2. All you really have to do here is replace m with -1/2, which is the slope you gave, and replace b with -2, the y-intercept you gave, in the equation y=mx+b.
If this helped, please mark me brainliest, thank you and if you need more help, feel free to message me .
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
edge
×=25 but how to get it?
The angle at B is 1/2 the angle at O
Angle B = 54
B +C = 54 + 29 = 83
Angle A + B + C = O
A + 54 + 29 = 108
A = 108 - 83
A = 25
X = 25
which lists the fractions 2/3 , 5/6 , 7/12 from least to greatest
Ans.
7/12 , 2/3 , 5/6
Why:
If we give all the fractions the same denominator then the fractions are, 8/12 , 10/12 , 7/12. We then can easily see what is the order. Once ordered correctly, just simplifiy.
Answer:
7/12 , 2/3 , 5/6
Step-by-step explanation:
Firstly, give them a common denominator.
What do 3,6 and 12 all have in common? 12
So what we do to the bottom, we do to the top.
Multiply the 2/3 by 4 (3x4=12) to make 8/12.
Multiply the 5/6 by 2 (2x6=12) to make 10/12
7/12 already has 12 as the denominator.
Now order them.
7/12 , 8/12, 10/12.
Change them back to the original sums.
7/12 , 2/3 , 5/6
What is the product?
(x2+3y+7) [yy+1)
Theo has $5 more than denise and denise has $11 more than rudy . Together , they have $45. How much money does denise have?
the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to. what is the round trip distance in miles from city 1 to city 3
Answer:
The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.
Step-by-step explanation:
It is given that the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to.
[tex]\begin{bmatrix}0 & 5 & 15\\ 5 & 0 & 35\\ 15 & 35 &0 \end{bmatrix}[/tex]
Here first element of first row represents the distance in miles from city 1 to city 1.
[tex]C_1\Rightarrow C_1=0[/tex]
Second element of first row represents the distance in miles from city 1 to city 2.
[tex]C_1\Rightarrow C_2=5[/tex]
Third element of first row represents the distance in miles from city 1 to city 3.
[tex]C_1\Rightarrow C_3=15[/tex]
The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.
You have 15 milliliters of a drink that contains 15% milk. How many millimeters of a drink containing 63% milk needs to be added in order to have a final drink that is 45% milk?
Answer:
4 ml of the 63% milk drink
Step-by-step explanation:
Multiplying 15 ml by 0.15 results in 2.25 ml, the amount of whole milk in the drink. Let m represent the number of ml of a drink that is 63% milk.
The final amount of milk drink that is to be 45% milk will be 15 ml + m, and the amount of whole milk contained in this drink will be 0.45(15 + m).
Then:
0.15(15 ml) + 0.63(m) = 0.45(15 + m), where m is to be in milliliters.
2.25 + 0.63m = 6.75 + 0.45m
First: consolidate the m terms on the left. 0.63m less 0.45m yields 18 m; then we have:
2.25 + 18m = 6.75, or
18 m = 4.50, or m = 4 ml.
In conclusion: adding 4 ml of that 63% milk drink to the initial 15 ml of 15% milk will result in (15 ml + 4 ml) of a 45% milk drink.
what is the linear function of y-8= 1/2 (x-4)
Answer:
y= 1/2 x +6
Step-by-step explanation:
y-8= 1/2 (x-4)
y-8= 1/2 *x - 1/2*4
y= 1/2 *x - 1/2*4 +8
y= 1/2 *x - 2 +8
y= 1/2 *x +6
Need help don’t understand
Answer:
2 real solutions
Step-by-step explanation:
To determine the nature of the solutions use the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real solutions
• If b² - 4ac = 0 the 2 real and equal solutions
• If b² - 4ac < 0 then no real solutions
Given
x² + 9x + 20 = 0 ← in standard form
with a = 1, b = 9, c = 20, then
b² - 4ac
= 9² - (4 × 1 × 20 ) = 81 - 80 = 1
Since b² - 4ac > 0 then there are 2 real solutions
The amount of money left in Alma’s bank account is expressed by the linear equation y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account
If we are given the equation y = -27x + 577 and that
x = weeks
y = money left in account
Then you must replace 145 (the money) for y and solve for x (the weeks)
145 = -27x + 577
145 - 577 = -27x + 577 - 577
-432 = -27x
-432/-27 = -27x/-27
16 = x
This means that after 16 weeks Alma will have $145 left in her account
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
b
Step-by-step explanation:
What’s the measure of angle S?
a. 50°
b. 60°
c. 100°
d. 30°
Answer:
D
Step-by-step explanation:
If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle.
So
[tex]85-25=60[/tex]
[tex]\frac{60}{2}=30[/tex]
1/5(x-2)=20 PLZZZZZZZZ HELPPPPP
Answer:
x=102
Step-by-step explanation:
[tex]\frac{1}{5}[/tex](x-2)=20 (multiply both sides by 5)
x-2=100 (move the -2 to the right)
x=100+2 (add)
x=102
hope this helps :)
Step-by-step explanation:
1/5(x-2) =20
multiply both sides by 5
=> (x-2) = 100
make x the subject of the formula...
x = 100 + 2
x = 102