For the given equation 6e^4x = 14, the value of x is [tex]x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
How to Find x's Value?Getting x alone on one side of the equation and everything else on the other side will be the first step towards solving for x. The golden rule of algebra states that everything done to one side of an equation must also be done to the other.
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
For the given equation,
6e^4x = 14
[tex]x = ln \frac{3^{3/4} * \sqrt[4]{7} }{3}\\ \\x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
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Are 1/2 and 9/3 integers, rationals or irrational numbers
The number 1/2 is a rational number and the number 9/3 is an integer rational number.
What is a rational number?They are referred to as rational numbers if the value of a numerical expression terminates, in which case they are a rational number, and as irrational numbers if the value of the expression does not terminate.
The numbers are given below.
1/2 and 9/3
The fraction numbers are converted into decimal numbers. Then we have
1/2 = 0.5
9/3 = 3
The number 1/2 is a rational number and the number 9/3 is an integer rational number.
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slope (-5,6),(-10,10)
The Slope is [tex]\frac{4}{-5}[/tex].
What is a Slope?A line's slope is defined as the ratio of the change in y-coordinate to the change in x-coordinate.Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.A line's slope provides information on the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.m = change in y/change in x = Δy/Δx
= (y2 – y1)/(x2 – x1)
Where “m” is the slope of a line.
As a result, using the formula above, we can quickly determine the slope of a line connecting two points.
Given points are (-5,6),(-10,10).
⇒ m = Δy / Δx
= [tex]\frac{10 - 6}{-10 - (-5)}[/tex]
= [tex]\frac{4}{-5}[/tex]
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Question 8
-
Evaluate the expression if g = 2, r = 3, and t = 11.
g + 6t
Answer:
68
Step-by-step explanation:
2+6(11)
2+66
68
Hope this helps!
need for find the Value of x
Since these angles are a pair of exterior alternate angles, then they are supplementary and add up to 180°
[tex](3x + 2) + (2x + 23) = 180 \\ 3x + 2 + 2x + 23 = 180 \\ 5x = 180 - 23 - 2 \\ 5x = 180 - 25 \\ 5x = 155 \\ x = \frac{155}{5} = 31[/tex]
The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle.
The side of the equilateral triangle is 14inches.
Let the side of the square be denoted as x inches
The formula for the perimeter of equilateral triangle is
[tex]P_{t}[/tex] = 3a where a is the side of the triangle.
The formula for the perimeter of the square is
[tex]P_{s}[/tex] = 4x where x is the side of the square
We have been given that,
[tex]P_{t} = 10 + P_{s}[/tex] (1)
and a = 6 + x inches (2)
Equation (1) can be written as
3a = 10 + 4x
From equation (2) ,
3( 6+x) = 10 + 4x
18 + 3x = 10 + 4x
x = 8
Substituting the value of x in equation (2) we get
a = 6+8
a = 14 inches
Hence the side of the triangle is 14 inches.
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FUNDRAISING The sophomore class is making blakets for the local animal shelter. The cost to make the blakets can be modeled by 0. 2x^2 + 7.2x + 78 where represents the number of blankets. Find how many blankets the sophomore class can make if they have $663 to spend on supplies.
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
How to illustrate the information?It should be noted that from the information, tje sophomore class is making blakets for the local animal shelter and the cost to make the blakets can be modeled by 0.2x² + 7.2x + 78.
Therefore, the number of blankets the sophomore class can make if they have $663 to spend on supplies will be illustrated as:
C = 0.2x² + 7.2x + 78.
0.2x² + 7.2x + 78 = 663
0.2x² + 7.2x = 663 - 78
0.2x² + 7.2x - 585 = 0
Using almighty formula, it should be noted that x will be 69.
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
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PlS ANSWER QUESTION IN THE PICTURE. IT IS REFLECTIONS IN IXL. *40 Points
Using translation concepts, the image of the kite after the reflection over the line y = x is given on the graph at the end of the answer.
What are transformations on the graph of a function?Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.
Examples of transformations are as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The rule for a reflection over the line y = x is given by:
(x,y) -> (y,x).
The vertices of the kite are given as follows:
S(-6,5), R(-5,6), P(-5,4), Q(1,5).
After the reflection, the vertices of the image are given as follows:
S'(5,-6), R'(6,-5), P'(4,-5), Q'(5,1).
The image of the kite after the reflection over the line y = x is given on the graph at the end of the answer, with the vertices labeled.
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A manufacturer must test that his bolts are 4.00cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 81 randomly selected bolts off the assembly line, he calculates the sample mean to be 3.97cm. He knows that the population standard deviation is 0.14cm. Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
Step 1 of 4: State the null and alternative hypotheses for the test.
Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 4: Compute the critical value. Round your answer to two decimal places.
Step 4 of 4: Draw a conclusion and interpret the decision.
Using the z-distribution, it is found that since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.
What are the hypothesis tested?At the null hypothesis, it is tested if the machine is calibrated correctly, that is, the mean is of 4 cm, hence:
[tex]H_0: \mu = 4[/tex]
At the alternative hypothesis, it is tested if the machine is not calibrated correctly, that is, the mean is different of 4 cm, hence:
[tex]H_1: \mu \neq 4[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are given as follows:
[tex]\overline{x} = 3.97, \mu = 4, \sigma = 0.14, n = 81[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.97 - 4}{\frac{0.14}{\sqrt{81}}}[/tex]
z = -1.93.
What is the critical value and what is the conclusion?We have a two-tailed test, as we are testing if the mean is different of a value, with a significance value of 0.01, hence, using a z-distribution calculator, the critical value is given by:
|z| = 2.575 -> z < -2.575 or z > 2.575.
Hence:
Since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.
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Riemann stock rose $7 Monday, dropped $8 Tuesday, and rose $2 Wednesday. What was the net change in price of the stock?
The net change in price of the stock is $1
How to determine the net change in price of the stock?The given parameters are
Monday = $7 rise
Tuesday = $8 drop
Wednesday = $2 rise
The net change in price of the stock is calculated as
Net change = Monday + Tuesday + Wednesday
Where
Rise = +
Drop = -
So, we have
Net change = 7 - 8 + 2
Evaluate
Net change = 1
Hence, the net change in price of the stock is $1
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the graph of g(x) is the result of translating the graph of f(x)=3^x six units to the right.what is the equation of g(x)?
•g(x)=3^^x-6
•g(x)=3^x^+6
•g(x)=3^x-6
•g(x)=3^x+6
Answer:
[tex]3^{x-6}[/tex]
I cannot make out from the answer choices which correspond to this, the formatting is all gone but this is the answer. Choose the correct option from the original question which has formatting.
See graph for visual proof
Step-by-step explanation:
Translation of a graph on the x-axis by a units means moving the graph left or right by a units
When you translate a function f(x) by a units to the right, the translated function becomes f(x - a)
Original function is f(x) = 3ˣ
When you translate the graph by 6 units to the right, the translated graph is [tex]g(x) = f(x-6) = 3^{x-6}[/tex]
Two numbers have a sum of 29. If one number is p, express the other number in terms of p.
The answer is
Answer:
29-p
Step-by-step explanation:
The answer is "29-p" because if the sum is 29 and we know that one number is p, then the remainder would be "29-p".
Hope this helped! :)
Select the equation that most accurately depicts the word problem.
The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.
68 = 9(L + 2)
68 = 2L + 2(9)
68 = 2(L - 9)
68 = 9L + 2
68 = 2/L + 2/9
68 = L/2 + 2(9)
Determine the following estimate without using a calculator. Then use a calculator to perform the computation
necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer?
If a person who works 40 hours per week earns $71,600 per year, estimate that person's hourly wage by rounding the
annual income to the nearest ten thousand. Use the estimate that there are 50 weeks in a year.
Answer:
estimate: $35.00 per houractual: $34.42 per hourwithin 2%, quite reasonableStep-by-step explanation:
You want to use rounding and approximation to compute the hourly wage of a person working 40 hours per week and making $71,600 per year. You also want a reasonableness check compared to the actual answer.
EstimateRounding the $71,600 salary to the nearest $10,000, it becomes $70,000. Considering 50 weeks per year and 40 hours per week, the number of hours in a year is approximated by 40×50 = 2000. Then the hourly wage is approximately ...
$70,000/(2000 h) = $35/h . . . . estimated wage
CheckIf we assume exactly 52 weeks in a year, there are 40×52 = 2080 working hours in a year. That means the hourly wage is actually ...
$71,600/(2080 h) ≈ $34.42 . . . . actual hourly wage
The difference of the estimate from the actual value is ...
$34.42 -35.00 = -$0.58
That is the actual value is between 1% and 2% lower than the estimate, a quite reasonable error. (Often anything within 10% is a reasonable estimate.)
__
Additional comment
Often, when doing estimates, you want to estimate the error in your estimating process. Here, there are two contributors.
Rounding 71,600 down to 70,000 reduces the value by a factor of 700/716, or 175/179. That means the error will be about 4 parts in 180 (an estimate), or 1 part in 45, about 2.2% (low).
Rounding 52 weeks per year down to 50 increases the value by a factor of 52/50 = 1.04, causing the estimated value to be about 4% high. These two errors are in opposite directions, so the net effect is an estimated error of about 4% -2.2% = 1.8% (high).
The error estimate has errors of its own, but this gets you in the ballpark of approximate error in the estimated value.
A year of 365 days is 52 weeks plus one day, so can be 2088 working hours. Using this value for hours reduces the hourly wage to about $34.29.
If a toy animal 5 inches tall. How tall is an actual animal?
Answer:
Step-by-step explanation:
Because in your previous question the scale factor was 1:30 you would simply multiple 5 by 30 to get 150 inches
Solve the following system of equations for all three variables.
5x + 7y + 2z = -7
9x + 7y + 2z = 5
2x - 7y5z = -2
X=
y =
z =
Answer:
X= -7/5 - 7y/5 - 2z/5
X= 5/9 - 7y/9 - 2z/9
X= -1 + 7y^5z/2
Y= -1 - 5x/7 - 2z/7
Y= 5/7 - 9x/7 - 2z/7
Y= (square root symbol is the line--->) ^5 |4802z^4(x+1)/7z
Z= -7/2 - 5x/2 - 7y/2
Z= 5/2 - 9x/2 - 7y/2
Z= 2/7y^5 + 2x/7y^5
Step-by-step explanation:
I hope this makes sense.
Identify a pattern in this list of numbers
3,4,6,9,13,18
Answer: Add 1, then add 2, then add 3, then add 4, then add 5!
How do I solve this problem?
Answer:you need to show the options at the bottom
Step-by-step explanation:
may I please get help
Answer:
X = .35 (80.99)
Step-by-step explanation:
To find the new amount of something after a discount is applied, you would need to take the discount and turn it into a decimal, if it hadn't been already. Then, you multiply it by the initial amount to get your answer.
Hope this helps! :)
133,358 rounded to the hundred
Answer:
133,400
Step-by-step explanation:
Answer:
133.36?
Step-by-step explanation:
What is the slope of the line that passes through the points (6, -5) and (-6, -5)? What is the simplest form
The slope of the line for which the line passes through the points (6, -5) and (-6, -5) is zero .
The slope of a line is outlined because the amendment in y coordinate with relation to the amendment in x coordinate of that line. net amendment in y coordinate is Δy, whereas net amendment within the x coordinate is Δx. The slope of a line will be calculated victimisation 2 points lying on the line. Given the coordinates of the 2 points, we will apply the slope of line formula m = y₂ - y₁ / x₂ - x₁ where (x₁ , y₁) are the coordinate of the first point and (x₂ , y₂) are the coordinate of the second point .We have given two points (6, -5) and (-6, -5) .
Using slope formula , we get
m = - 5 - (-5) / - 6 - 6
m = - 5 + 5 / -12
m = 0 / 12
m = 0
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The quotient 250÷5/8 tells about how far a sloth may move in one hour. How far can a sloth go in 90 minutes?
According to the given statement;
a sloth go 600 units in 90 minutes
Define Fraction?A fraction is used to denote a piece or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
According to the given values;
A sloth may move in one hour = 250÷5/8.
let us simplify 250÷5/8 first.
Division sign can be convert into multiplication sign and flip the right side fraction 5/8 to 8/5.
250×8/5
Dividing 250 by 5, we get
= 50 × 8
Multiplying 50 and 8, we get
= 400.
So, we could say, a sloth may move in one hour = 400 units.
We need to find distance covered in 90 minutes.
Let us convert 90 minutes into hours.
60 minute = 1 hour.
1 minute = 1/60 th of an hour.
and 90 minutes = 90 * 1/60 = 90/60 = 9/6 = 1.5 hours.
a Sloth may move in one hour = 400 units.
Therefore, in 1.5 hours Sloth can move = 1.5 × 400 = 600 units.
So, a sloth go 600 units in 90 minutes
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The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8000.
Find the cost function C when x energy drinks are manufactured.
Write the five smallest integers that are greater than the number -3.1
What is −30y − 15 if y is 7? (I NEED THIS ASAP)
A: −225
B: −195
C: −52
D: −36
Answer:
-225
Step-by-step explanation:
-30(7)-15
-210-15
-225
Solve the system.
5x+y=4
x+6y=9.5
Can I please get some help on my math
Answer:
28
Step-by-step explanation:
[tex]4(3)^{2}+2(-5)-(-2)=36-10+2= 28[/tex]
Hope this helps
Concept Check
Find the federal income tax withheld each week using the Weekly Payroll tables on pages 8-11.
Dan Caine, a welder, is married, claims 2 allowances, and earns $390.50 per week.
1.
Using proportions, it is found that the federal income tax withheld each week is given by $24.69.
What is the missing information?The rates for a married person are given as follows:
Between $51.00 and $195.00 is of 0% plus 10% of excess over $51.00Between $195.00 and $645.00 is of 14.40 plus 15% of the excess over 195.00.Between $645.00 and $1,482.00 is of 81.90 plus 25% of excess over 645.00.Additionally, we have that:
Each weekly allowance is of $63.46.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Removing the allowances, the taxable amount is:
390.50 - 2 x 63.46 = $263.58.
Hence, applying the rates, the withheld amount is given by:
14.40 + 0.15(263.58 - 195) = $29.69.
The federal income tax withheld each week is given by $24.69.
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the area of a square photo is 9 square inches. how long is each of the photo?
The square picture whose area is 9 square is 3 inch long.
Square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of rectangle.
Area of Square is the total number of unit squares forming a square is referred to as the square's area. In other terms, it is described as the area that the square occupies.
It is given that,
The area of a square = 9 square inches
We need to find,
The side length of the given square
Also, we know that,
Area of square = [tex]a^{2}[/tex]
Putting values in the formula
We get,
9 = [tex]a^{2}[/tex]
a = [tex]\sqrt{9}[/tex]
a = 3 inch
Hence, the side length of the given square picture whose area is 9 square inches is 3 inch
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7(4a-3)-3a{8-2a(1+2a)}
if its solve then we can do it like above
Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow. On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
1. In simplest form, what is the ratio of blue paint to yellow paint in the mixture? (2 points)
2. On days 1 and 2 how much blue paint did Marc use? How much yellow paint? (2 points)
3. How many cans of each type of paint does Marc have left for day 3? (3 points)
4. Day 3's mixture must use the same simplified ratio of blue to yellow as the other two days. What is the greatest number of cans of blue and yellow paint Marc can mix on day 3? Assume he mixes only whole cans of paint. (3 points) HELP
Answer: 1. 7:10
2. 10 blue cans
15 yellow cans.
3. 4 cans of blue paint.
5 cans of yellow paint.
4. 2 blue cans and 3 yellow cans.
Step-by-step explanation:
1. 14 blue paint cans/20 yellow paint cans=
14/20=
7/10 ==> 7:10
2. 4+6 blue cans=10 blue cans
6+9 yellow cans=15 yellow cans.
3. 14-10=4 cans of blue paint.
20-15=5 cans of yellow paint.
4. 10 blue cans/15 yellow cans=
10/15=
2/3 ==> 2:3 ==> 2 blue cans and 3 yellow cans.
Answer:
Step-by-step explanation:
Answer: 1. 7:10
2. 10 blue cans
15 yellow cans.
3. 4 cans of blue paint.
5 cans of yellow paint.
4. 2 blue cans and 3 yellow cans.
Step-by-step explanation:
1. 14 blue paint cans/20 yellow paint cans=
14/20=
7/10 ==> 7:10
2. 4+6 blue cans=10 blue cans
6+9 yellow cans=15 yellow cans.
3. 14-10=4 cans of blue paint.
20-15=5 cans of yellow paint.
4. 10 blue cans/15 yellow cans=
10/15=
2/3 ==> 2:3 ==> 2 blue cans and 3 yellow cans.
