Given that log5 21 =m and log9 75= n show that log5 7 = 1÷2n-1(2mn-m-2)
Answer: To show that log5 7 = 1/(2n-1)(2mn-m-2), we'll start by using logarithmic properties and the given information.
First, let's express log9 75 in terms of the base 5 logarithm, using the change of base formula:
log9 75 = log5 75 / log5 9
Next, let's simplify the expression inside the logarithm by breaking down 75 and 9 into their prime factors:
log5 (3^2 * 5^2) / log5 (3^2)
Now, using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:
log5 (3^2) + log5 (5^2) - log5 (3^2)
Simplifying further, we have:
2 log5 3 + 2 log5 5 - 2 log5 3
The 2 log5 3 and -2 log5 3 terms cancel each other out, leaving:
2 log5 5
Now, let's substitute the value of m from the given information (log5 21 = m) into the expression:
2 log5 5 = 2 (log5 (5^2)) = 2(2 log5 5) = 4 log5 5 = 4m
Now, let's substitute the value of n from the given information (log9 75 = n) into the expression:
4m = 4(log5 5) = 4(1/2 log5 (5^2)) = 4(1/2 log5 25) = 4(1/2 log5 (5^2 * 5^2))
Using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:
4(1/2 (log5 5^2 + log5 5^2)) = 4(1/2 (2 log5 5 + 2 log5 5)) = 4(1/2 (4 log5 5))
Simplifying further, we have:
4(1/2) (4 log5 5) = 4(2 log5 5) = 8 log5 5 = 8n
Finally, substituting the values of m and n into the expression:
log5 7 = 1/(2n-1)(2mn-m-2) = 1/(2(8) - 1)(2(4m) - m - 2) = 1/(16 - 1)(8m - m - 2) = 1/15(7m - 2)
Therefore, we have shown that log5 7 = 1/(2n-1)(2mn-m-2) = 1/15(7m - 2), using the given values of log5 21 = m and log9 75 = n.
a sphere has a diameter of 9 and find the volume in terms of Pi and volume to the nearest tenth
Answer:
V = 381.7 or 121π
Step-by-step explanation:
V=4/3πr³
Radius is half the diameter so, 9/2 = 4.5
r=4.5
V = 4/3π(4.5)³
V=4/3π(91.125)
V = 381.7 or 121π
18 ft 5in - 15 ft 6 in
7 in.
12 in.
6 in.
What is the surface area of this rectangular prism?
The surface area of the rectangular prism is 396 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
7 in by 12 in by 6 in
The surface area of the rectangular prism is calculated as
Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)
Evaluate
Area = 396
Hence, the area is 396 square inches
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I’ll give brainliest pls help me my future is in risk rn.
Both containers hold the same amount of water.
Given are two solid figures, we need to compare which of them holds more water,
The container one has a base dimension of 3 ft × 180 in with height 90 in. and the second container has base dimension of 3 ft × 180 in with height 90 in.
To compare which container holds more water, we can calculate the volume of each container.
For consistency, let's convert all measurements to a single unit.
1 foot is equal to 12 inches, so the base dimensions of both containers can be expressed as
3 ft × (180 in + 3 ft × 12 in/ft) = 3 ft × 216 in
= 648 in × 648 in.
The volume of a container is calculated by multiplying the base area by the height.
Therefore, the volume of each container can be determined as follows:
Container 1:
Volume = Base area × Height
Volume = (648 in × 648 in) × 90 in
Container 2:
Volume = Base area × Height
Volume = (648 in × 648 in) × 90 in
Since the base dimensions and the height are identical for both containers, their volumes will also be the same.
Therefore, both containers hold the same amount of water.
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Find the arc length of the curve below on the given interval.
x=(y^4/4)+(1/8y^2) for 2<=y<=3
Answer:
[tex]\frac{4685}{288}[/tex]
Step-by-step explanation:
The explanation is attached below.
A firm has an unlevered cost of capital of 10 percent, a cost of debt of 9 percent, and a tax rate of 34 percent. If it desires a cost of equity of 14 percent, what must its target debt/equity ratio be
The required target debt/equity ratio is 0.5 or 1:2.
To calculate the target debt/equity ratio,
Use the following formula,
⇒ Target D/E Ratio = (Target Equity / Target Debt)
First, we need to calculate the weights of equity and debt in the firm's capital structure.
We can use the following formula,
Weight of Equity = Equity / (Equity + Debt)
Weight of Debt = Debt / (Equity + Debt)
Since the firm is unlevered,
its capital structure consists only of equity.
Therefore,
The weight of equity is 1 and the weight of debt is 0.
Now we can use the weighted average cost of capital (WACC) formula to find the firm's current cost of equity.
The WACC formula is as follows,
WACC = (Weight of Equity Cost of Equity)
+ (Weight of Debt Cost of Debt x (1 - Tax Rate))
Substituting the given values, we get:
⇒ 10% = (1 Cost of Equity) + (0 9% x (1 - 34%))
Solving for Cost of Equity, we get:
Cost of Equity = 10% - (0 9% (1 - 34%))
Cost of Equity = 10%
Since the firm desires a cost of equity of 14%,
we can set up an equation to solve for the target debt/equity ratio:
⇒ 14% = (1 / (1 + Target D/E Ratio)) 10% + ((Target D/E Ratio) / (1 + Target D/E Ratio)) 9% x (1 - 34%)
Simplifying the equation, we get:
⇒ 14% = 10% / (1 + Target D/E Ratio) + 0.0594 x Target D/E Ratio
Multiplying both sides by (1 + Target D/E Ratio), we get:
⇒ 0.14 + 0.14 Target D/E Ratio = 0.1 + 0.0594 Target D/E Ratio
Subtracting 0.0594 x Target D/E Ratio from both sides, we get:
⇒ 0.08 x Target D/E Ratio = 0.04
Dividing both sides by 0.08, we get:
⇒ Target D/E Ratio = 0.5
Therefore, the firm's target debt/equity ratio is 0.5 or 1:2.
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The graph show the probability distribution of a
random variable.
What is the value of P(2 < X <5)?
O 0.30
O 0.35
O 0.40
O 0.45
0.3
0.25
0.2
0.15
0.1
0.05
1
Probability Distribution
2
3 4
S.
9.
N
B
The solution is : the value of P(2≤X≤5) is 0.50.
Here, we have,
given that,
The graph show the probability distribution of a random variable.
we know that,
The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.
so, we have,
P(2≤X≤5)
=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)
= 0.2+ 0.1 +0.05+0.15
= 0.50
Hence, The solution is : the value of P(2≤X≤5) is 0.50.
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Can someone help me find the plume of these shapes, then round the answer to the nearest whole number please?
The volume for each cone in this problem is given as follows:
11) V = 94 in³.
12) V = 367 ft³.
13) V = 1005 in³.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
For item 11, the dimensions are r = 3 in and h = 10 in, hence the volume is given as follows:
V = π x 3² x 10/3
V = 94 in³.
For item 12, the dimensions are r = 5 ft and h = 14 ft, hence the volume is given as follows:
V = π x 5² x 14/3
V = 367 ft³.
For item 13, the dimensions are r = 8 in(half the diameter) and h = 15 in, hence the volume is given as follows:
V = π x 8² x 15/3
V = 1005 in³.
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subtract the following measurements 450l 890ml from8700l 750ml
The solution of expression after subtraction is,
⇒ 8249 L 860 ml
We have to given that;
Subtract measurements 450l 890ml from 8700l 750ml
Now, WE can simplify as,
⇒ L ml
8700 750
- 450 890
---------------------------
8249 860
Therefore, After subtraction we get;
⇒ 8249 L 860 ml
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PLEASE ANSWER BOTH QUESTIONS!
The correct statement regarding the transformation is given as follows:
Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.
The true statements about the dilation are given as follows:
Dilating a line segment can change the length.Dilating a polygon can change the area.What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:
k = 0.5.
The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.
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What is the mode of the data represented in this line plot?
Enter your answer in the box.
5 - xx
6 - xxxx
7 - xxx
8 - xxxxxx
9 - xx
10 - xxxx
11 - xx
The mode of the data represented in this line plot will be 8.
Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.
The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.
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Find the line parallel to y = 7x+2
that includes the point (3, -1).
Answer:
? = 7
Step-by-step explanation:
The equation of the line parallel to another line will have the same slope. The given line y = 7x + 2 has a slope of 7.
To find the equation of the line that passes through the point (3, -1) and is parallel to the given line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
So, the equation of the line parallel to y = 7x + 2 and passing through the point (3, -1) is:
y - (-1) = 7(x - 3)
Simplifying this, we get:
y = 7x - 21 - 1
y = 7x - 22
So, the equation of the line is y = 7x - 22.
Given the form of the equation y + 1 = ?(x -3). We then know the answer is y + 1 = 7 (x - 3)
The line's equation is :
↬ y + 1 = 7(x - 3)Solution:
If two lines are parallel then their slopes are equal.
The slope of [tex]\sf{y=7x+2}[/tex] is 7, so the slope of the line parallel to it is 7.
Now, we should plug the slope and the point into the point slope equation. See, we're even given a hint :
Remember : y - y₁ = m(x - x₁).
This hint tells us the point slope equation.
Wherem = slope(x₁, y₁) is a point on the lineSo I plugin :
[tex]\bf{y-(-1)=7(x-3)}[/tex]
Simplify.
[tex]\bf{y+1=7(x-3)}[/tex]
This is it, we don't have to simplify all the way to slope intercept.
Hence, the equation is y + 1 = 7(x - 3)Please help me :(
What is the measure of p in the following diagram?
PS: Its in a Chapter 11 Go math book! Maybe... can you help me pls?
The measure of p in the diagram is,
m∠P = 45°
We have to given that;
PM is perpendicular to MO.
Now, If m ∠P = m∠2
then it's an isosceles triangle.
And, m ∠M = 90°, therefore it's an isosceles right triangle.
We know that,
the sum of measures of angles in a triangle is equal 180°.
Therefore we have the equation:
m∠P + m∠2 + m∠M = 180°
Substitute m∠M = 90° and m∠P = m∠2 = x:
x + x + 90° = 180°
substract 90° from both sides
2x = 90°
divide both sides by 2
x = 45°
m∠P = 45°
Thus, The measure of p in the diagram is,
m∠P = 45°
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There are approximately as many boys between 167 and 169 as there are between 169 and 170. True False
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
In statistics, understanding and interpreting data is an essential skill. One way to interpret data is by analyzing the distribution of values within a certain range.
To determine whether the statement is true or false, we need to analyze the distribution of boy's heights between the two ranges. Assuming the heights of boys are normally distributed, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of boys within each range.
The empirical rule states that in a normal distribution:
68% of the values fall within one standard deviation of the mean
95% of the values fall within two standard deviations of the mean
99.7% of the values fall within three standard deviations of the mean
We can use this rule to estimate the percentage of boys within each range as follows:
Between 167 and 169: This range is one standard deviation below the mean. Therefore, approximately 68% of boys' heights fall within this range.
Between 169 and 170: This range is between one and two standard deviations below the mean. Therefore, approximately 27% of boys' heights fall within this range.
Based on this analysis, we can see that there are not approximately as many boys between 167 and 169 as there are between 169 and 170. In fact, there are significantly more boys between 167 and 169 than there are between 169 and 170.
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
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What is the central idea of Sowells speech Morality vs Sanctimoniousness
Thomas Sowell's speech "Morality vs. Sanctimoniousness" addresses the distinction between genuine moral actions and the outward appearance of moral superiority.
What is the central idea ?The keynote of his speech is to prioritize practical and fruitful measures over merely appearing sensible or righteous. According to Sowell, it is crucial to solve prevalent social problems with pragmatic, yet effective solutions instead of adopting self-righteous attitudes that lack meaningful outcomes.
Essentially, he opines that authentic ethical principles should be anchored in consideration for others' welfare and empirical evidence rather than being fueled by personal moral validation or pretentiousness.
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There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people didn't use any facilities?
8 people didn't use any of the gym pool or track facilities.
The number of people use any facilities need to subtract the total number of people who used at least one facility from the total number of people in the sport centre.
The total number of people who used at least one facility by adding the number of people who used each facility and subtracting the number of people who used two facilities and three facilities:
Total = Gym + Pool + Track - (Gym and Pool) - (Pool and Track) - (Gym and Track) + (Gym and Pool and Track)
Total = 77 + 62 + 65 - 27 - 23 - 31 + 4
Total = 127
The number of people who didn't use any facilities is:
135 - 127 = 8
8 people didn't use any of the gym, pool or track facilities.
The number of individuals who did not utilise any facilities must be subtracted from the total number of individuals who utilised at least one facility.
The total number of individuals who utilised at least one facility is calculated by adding the individuals who utilised each facility and deducting the individuals who utilised two and three facilities:
Total = Fitness Centre + Pool + Track - Fitness Centre and Pool - Fitness Centre and Track - Fitness Centre and Pool and Track
Total = 77 + 62 + 65 - 27 - 23 - 31 + 4
Total = 134-127
= 8
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- Darrell Morris has a family plan. The HMO annual premium is $12,240. The employer pays 90% of the cost.
a) How much is Darrell's annual contribution? b) How much is his semimonthly deduction?
Answer:The employer pays .90 * 12240 = $ 11016. The emplyee pays .10 *12240 = $ 1224 = annual contribution. Contribution rate = (100% - 90%) = 10%.
Step-by-step explanation:
Answer:
a) $1,224
b) $51
Step-by-step explanation:
a) To calculate Darrell's annual contribution, we need to determine the portion he pays out of the total premium.
Given that the employer pays 90% of the cost, Darrell is responsible for the remaining 10%.
Annual contribution = Total premium × 10%
= $12,240 × 0.10
= $1,224
Therefore, Darrell's annual contribution is $1,224.
b) To find Darrell's semimonthly deduction, we divide his annual contribution by the number of semimonthly periods in a year.
Number of semimonthly periods in a year = 12 (months) × 2 (semimonthly periods per month) = 24
Semimonthly deduction = Annual contribution / Number of semimonthly periods
= $1,224 / 24
= $51
Therefore, Darrell's semimonthly deduction is $51.
Hope this helps!
Which of the following is a difference of perfect squares?
A). x^2+4
B). 9x^2-100
C). x^2-18
D). 4x^2+36
If 3² + 4² = c², then c equals
Answer:
The answer is 5
Step-by-step explanation:
c²=3²+4²
c²=9+16
c²=25
[tex] \sqrt{ {c}^{2} } = \sqrt{25} [/tex]
c=5
The value of c is :
↬ c = 5, c = -5
Solution:
First off, we should square the numbers:
[tex]\sf{3^2+4^2=c^2}[/tex]
[tex]\sf{9+16=c^2}[/tex]
[tex]\sf{25=c^2}[/tex]
Now I square-root each side :
[tex]\sf{5=c}[/tex]
[tex]\sf{-5=c}[/tex]
This means that :
[tex]\sf{c=5,\:c=-5}[/tex]
How did this happen? We should know that once we take the square root of a number, we end up with two solutions that are opposites of each other. This phenomenon is explained below.
When we square 5, we get 25. When we square -5, we also get 25.
So then, when taking the square root of 25, we get both 5 and -5. And now, we know why.
Hence, c = 5 and c = -5.50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
Polygon D is similar to polygon ABCD.
Function
�
gg can be thought of as a scaled version of
�
(
�
)
=
�
2
f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f represents the equation y equals x squared. A parabola labeled g passes through the point negative 1, 4, through the origin, and through the point 1, 4.
Write the equation for
�
(
�
)
g(x)g, left parenthesis, x, right parenthesis.
The equation for g (x) is,
⇒ g(x) = x² -3
Since, The function is,
⇒ f (x) = x²
when x = 0, f(x) = 0
hence it has vertex at (0,0)
Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),
Then, g(x) must be shifted along y axis.
So, We get;
g(x)= x²+c
when x = - 1, g(x)= 4
4 = (-1)² + c
4 = 1 + c
c = 3
Thus, The equation for g (x) is,
g(x) = x² -3
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Kevin got the following scores on his math tests this semester.
85, 94, 98, 88, 85, 92, 97, 81
What is his mean score so far?
ANSWERED
What score will Kevin need to get on his next test to raise his mean score to exactly 91?
Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
To find out what score Kevin will need to get on his next test to raise his mean score to exactly 91, we can use the formula for the mean:
mean = (sum of all scores) / (number of scores)
We know the current mean score is:
mean = (85 + 94 + 98 + 88 + 85 + 92 + 97 + 81) / 8
= 89.5
To raise the mean to 91, we can set up the equation:
(85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x) / 9 = 91
where x is the score Kevin needs to get on his next test.
Multiplying both sides of the equation by 9, we get:
85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x = 819
Simplifying, we get:
710 + x = 819
Subtracting 710 from both sides, we get:
x = 109
Therefore, Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
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Sam is training for a 5
km run. While training he runs for 6
minutes, then rests for 2
minutes, runs for 6
minutes, rests for 2
minutes, etc., until he finishes the 5
km. It takes him 26
minutes in total (with the rest periods) to finish the 5
km rum. If Sam runs at a constant speed (when he is not resting), what is this speed in kilometers per hour? (Recall there are 60
minutes in 1
hour.)
Answer:
15 km/h
Step-by-step explanation:
How many intervals of running and resting are needed to run and rest for 26 minutes?
Running is in parentheses, resting is not.
Each time he runs (6 minutes) and rests (2 minutes), he takes 8 minutes.
Three times this cycle is 24 minutes. He needs 2 more minutes of running to have a total of 26 minutes.
(6) + 2 + (6) + 2 + (6) + 2 + (2)
Add all the numbers in parentheses which are the times of running.
6 + 6 + 6 + 2 = 20
He ran for 20 minutes and rested for 6 minutes.
He ran 5 km in 20 minutes (of running).
speed = distance/time
speed = [5 km / (20 minutes)] × (60 minutes)/(1 hour)
speed = 15 km/h
Answer: 15 km/h
(PLEASE SHOW WORK EXPLAIN YOUR ANSWER!!!!)
After a party,Brad had leftover pizza. Brad had  1/2 of a cheese pizza . 3/4 of sausage pizza and 2/6 of a pepperoni pizza? How much leftover pizza did Brad have?
Part A: How much leftover pizza did Brad have?
Part B: Steve had 2/3 of a pizza how much more does bread have the Steven?
Part A:
To find out how much leftover pizza Brad had, we need to add up the fractions of each type of pizza:
1/2 cheese pizza + 3/4 sausage pizza + 2/6 pepperoni pizza
We can simplify the fractions by finding a common denominator:
1/2 = 3/6
3/4 = 4.5/6
2/6 = 2/6
Now, we can add the fractions:
3/6 + 4.5/6 + 2/6 = 9.5/6
This means Brad had 9.5/6 of a pizza leftover.
Part B:
Steve had 2/3 of a pizza. To compare this to Brad's leftover pizza, we need to convert Brad's leftover pizza to a fraction with the same denominator as 2/3:
9.5/6 = 9/6 + 0.5/6 = 3/2 + 1/12 = 19/12
Now we can compare:
19/12 - 2/3 = 38/12 - 8/12 = 30/12 = 2.5
This means Brad has 2.5 more pizzas than Steve.
Leigh designs and conducts a computer simulation with 30 trials and uses the data from the stimulation to create the relative frequency bar graph shown. The graph shows the relative frequency of the number of spins needed for a spinner divided into 6 equal sections labeled A through F on each letter at least once
The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%
How to explain the probabilityExperimental probability is a type of probability that is based on actual observations or experiments.
In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.
In this case, experimental probability = number of times the event occurred / total number of trials
Experimental probability = 0.1 + 0.35 + 0.3 / 1
= 0.75 / 1
= 75%
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Maurice ran 110 meters in 20.9 seconds. Yolanda ran 110 meters in 20.0 seconds. Who had the fastest time, Maurice or Yolanda?
A.Yolanda
B.Maurice
apex
Answer: I believe the answer is Yolanda.
Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.
HELP PLEASE DUE IN 10 MIN
The correct statement regarding the measure of variability used to represent the data is given as follows:
The IQR of 10 is the most accurate to use, as the data is skewed.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.
The charity received 18 donations, hence the quartiles are given as follows:
First quartile: 0.25 x 18 = 4.5th element = median of 10 and 15 = 12.5.Third quartile: 0.75 x 18 = 13.5th element = median of 20 and 25 = 22.5.Hence the IQR is given as follows:
IQR = 22.5 - 12.5
IQR = 10.
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Find the value of the unknown variable. -c/6 = -4
The value of the unknown c in the algebraic fraction equation is equal to -24
How to solve the algebraic fraction equationTo solve the simple algebraic fraction equation, we cross multiply to eliminate the fractions, then simplify by solving for the unknown
Given the algebraic equation:
-c/6 = 4
(-c/6) × 6 = 4 × 6
-c = 4 × 6
-c = 24
multiply both sides by -1
-1 × -c = -1 × 24
c = -24
Therefore, the value of the unknown c in the algebraic fraction equation is equal to -24
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Estimate then find the product 34•12
Answer:
I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408
Step-by-step explanation: