Mathematics College

ACTIVITY 3: Solve the following equations.

Answers

Answer 1

The value of x in each expressions are:

1) 6

2) 1

3) -3

4) -21

5) -4

We have,

The expressions are:

[tex]3^x = 9^3[/tex]

And,

9³ = (3²)³ = [tex]3^6[/tex]

So,

[tex]3^x = 3^6[/tex]

And,

x = 6

[tex]4^{x + 1}[/tex] = 16

16 = 4²

So,

x + 1 = 2

x = 2 - 1

x = 1

[tex](1/3)^x[/tex] = 27

27 = 3³

So,

[tex]3^{-1x}[/tex] = 3³

-x = 3

x = -3

[tex]5^{3x}[/tex] = [tex]25^{x - 1}[/tex] =

[tex]5^{3x}[/tex] = [tex]5^{2x - 21}[/tex]

3x = 2x - 21

3x - 2x = -21

x = -21

[tex]2^{-x}[/tex] = 16

16 = [tex]2^4[/tex]

So,

-x = 4

x = -4

Thus,

The value of x in each expression are:

1) 6

2) 1

3) -3

4) -21

5) -4

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Related Questions

f ( x ) = 12 ( 7 ) x using base e

Answers

The answer is 473m in my perspective

In its second year of operation, a local Internet provider’s profits were $170,500. If this amount was 576% of the company’s first-year profits, find the first- year profits (to the nearest hundred dollars).

Answers

Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

What is a proportion?

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500 ÷ 5.76)

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please help for this question

Answers

Translating the shape S by the vector ( -1 , - 3 ) would lead to S ' with vertices of ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

How to translate the figure ?

Given that the translation vector is negative, this means that you would have to subtract the corresponding values of the vector from the x and y coordinates of each vertex.

The vertices of the new shape S' would be :

Vertex 1: (2 , 1 ) + ( -1, -3 ) = ( 2 - 1 , 1 - 3 ) = ( 1, -2 )

Vertex 2: ( 2, 2 ) + ( -1, -3 ) = ( 2 - 1, 2 - 3 ) = ( 1, - 1 )

Vertex 3: ( 4, 1 ) + (-1 , -3 ) = ( 4 - 1 , 1 - 3) = (3 , -2)

Vertex 4: ( 4, 4 ) + (- 1, -3 ) = (4 - 1, 4 - 3 ) = (3 , 1 )

In conclusion, the translated vertices would be ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

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Maggie spent $16 on rock climbing. This included a $6 charge for climbing shoes and a $2.50 charge per hour she climbed. If h represents the number of hours she climbed for, write an equation that can be solved to find the number of hours she spent rock climbing.

Answers

Answer:

16 = 6+2.5h

Step-by-step explanation:

The total cost is 16 dollars. She spends 6 dollars for shoes and 2.50 per hour.

16 = 6+2.5h

To solve, subtract 6 from each side

16-6 = 6+2.5h-6

10 = 2.5h

Divide each side by 2.5

10/2.5 = 2.5h/2.5

4 =h

She can climb for 4 hours.

Is AB perpendicular to CD? Explain? pls yall fwm on the answer

Answers

Answer: No

Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.

40% of the fish are carp and 60% of the fish are bass. What’s the probability that the next three fish I catch are all carp?

Answers

Answer:

0.064 or 6.4%

----------------------------

The probability of catching a carp is 40% since 40% of the fish are carp.

We assume the fish is replaced each time so the probability of three carps is:

P = 0.4³ = 0.064 or 6.4%

Can someone help me please

Chapter 13/14. The Civil War. Watch the Hari Jones TED talk. Then, answer the following questions in 7-10 sentences. Then, respond to two different classmates' posts by asking a question or challenging their assertions (respectfully). Try to make sure everyone has a response to their post. Finally, respond to the question or assertion your classmate(s) replied to you. Responses are meant to acknowledge what the other student has communicated, and either expand on their ideas, or push back on them, then offer positive feedback. Consider using the following template: "Hi _____. I was interested in ______ about your post because _______. Also/However, ______. I think ______ because _____. Do you think/feel _____/? I feel _____. "

In serving in the military, what contributions did African Americans make to the Union war effort?

What kinds of discrimination did they face? What kind of heroism did they exhibit, and when?

Write a reaction to Dr/ Jones' TED talk. What did you know/not know? What surprised/amazed/angered/made you proud/saddened/made you happy?

Answers

Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?

How did African Americans contribute?

Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.

Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.

Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.

Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.

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Help pleaseee

Expand the logarithm as much as possible

logy^10

Answers

The expanded form of log y^10 is either 10 log y or 10 ln y

Expanding the logarithm

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

Answers

The simplified expression for the perimeter of the rectangle is 10x-30

What is perimeter of a rectangle?

The perimeter of a shape is the addition of all the sides of the shape. If l is the length and w is the width, then the perimeter of a rectangle can be expressed as ;

p = 2(l+w)

The length is 3x-8 and the breadth is 2x-7

therefore the perimeter = 2( l+w)

= 2( 3x-8+2x-7)

= 2( 5x-15)

= 10x-30

therefore, the simplified expression for the perimeter of the rectangle is 10x-30

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A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Which statements about this situation are true?

Answers

The 99% confidence interval of the population mean is (352.32, 371.68).

To find the 99% confidence interval of the population mean, we need to use the following formula:

CI = x; ± zα/2 * (σ/√n)

where:

x' = sample mean (362)

zα/2 = z-score for 99% confidence level (2.576)

σ = population standard deviation (29.6)

n = sample size (40)

Substituting the values, we get:

CI = 362 ± 2.576 * (29.6/√40)

CI = 362 ± 9.68

This means that if we take many random samples of 40 hours from the population, we can be 99% confident that the true population mean of the number of customers per hour falls between 352.32 and 371.68.

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Complete question is:

Please help me this is so hard and i really dont get this. if you help me with both parts ill give you 60 points

Answers

1) We can rewrite the function in vertex form to find the time when the ball hits the ground. To do this, we need to complete the square.

h(t) = -5t^2 + 40t

h(t) = -5(t^2 - 8t)

h(t) = -5(t^2 - 8t + 16) + 80 (adding and subtracting 16 inside the parentheses to complete the square)

h(t) = -5(t - 4)^2 + 80 (factoring and simplifying)

So, the function in vertex form is h(t) = -5(t - 4)^2 + 80.

2) To find when the ball hits the ground, we need to find when h(t) = 0, since h(t) represents the height of the ball above the ground.

0 = -5(t - 4)^2 + 80 (substituting h(t) = 0)

5(t - 4)^2 = 80

(t - 4)^2 = 16

t - 4 = ±4

t = 4 ± 4

So, the ball hits the ground at t = 0 or t = 8 seconds after launch. However, we can discard the t = 0 solution because that represents the time when the ball is launched, and we are looking for when it hits the ground. Therefore, the ball hits the ground at t = 8 seconds after launch.

The graph of f(x) = a × [tex]b^x[/tex] passes through (2,54) and (5,16).

What is the value of b?

Answers

The value of b when the graph of function f(x) = a*bˣ passes through (2,54) and (5,16), is given by, b = 2/3.

Given the function of the graph is,

f(x) = a*bˣ

It is given that the graph of the function passes through the points with coordinates (2, 54) and (5, 16). So this points must satisfy the given function.

Substituting the point (2, 54) in the given function we get,

f(2) = 54

a*b² = 54 ..................... (i)

Substituting the point (5, 16) in the given function we get,

f(5) = 16

a*b⁵ = 16 ..................... (ii)

So dividing equation (ii) by equation (i) we get,

(a*b⁵)/(a*b²) = 16/54

b³ = 8/27

b³ = (2/3)³

b = 2/3

Hence the value of b is 2/3.

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I have part (a) answered, I just need part (b) if anyone could help with that please?

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(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.

What is range?

Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.

According to given information:

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.

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5.
Andre is playing a new card game. This game uses 4 sets of cards:
green, blue, yellow, and red. Each set has 15 cards numbered from
1 to 15. Select all of the actions that have more than 4 possible
outcomes. 7.SP.8, 7.SP.8b
0
selecting a blue card less than 5
selecting a red card greater than 13
selecting a yellow 12 card
selecting an 8 or 9 card of any color
selecting an even-numbered green card greater than 4
selecting a yellow card greater than 4²
selecting a blue card that is a multiple of 3

Answers

The actions that have more than 4 possible outcomes are:

- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)

- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)

- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)

Therefore, only three of the given actions have more than 4 possible outcomes.

Someone please help!! (20 POINTS!)

Answers

Answer: C

Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1

Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.

Answers

Based on the given information that ∠4 ≅ ∠14, we can conclude that lines a and b are parallel by the converse of the corresponding angles theorem. This theorem states that if two lines are intersected by a transversal and corresponding angles are congruent, then the lines are parallel. Therefore, we can conclude that line a is parallel to line b.

However, we cannot conclude that any other lines are parallel based on the given information.

Calculate the area of a circle 4ft ,2in,18ft,5.2in,7.3in,14cm,9m,3m,9.2cm,7m,5m,6m

Answers

Answer:

Step-by-step explanation:

It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.

Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.

Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost?

Answers

The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).

To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.

Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.

Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.

Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).

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A yoga studio sells monthly memberships. The function f(x) = −x^2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.
x = 6, x = 44; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produces a maximum profit.

Answers

The zeros of the quadratic profit function are explained as:

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

How to find the zeros of a quadratic function?

The quadratic function is given as:

f(x) = −x² + 50x − 264

The general form of expression of a quadratic function is:

f(x) = ax² + bx + c

The quadratic formula to find the zeros is:

x = [-b ± √(b² - 4ac)]/2a

Thus, we have the zeros as:

x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)

x = 6 and x = 44

This represents number of monthly memberships where no profit is made.

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A vehicle use 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can 2 3 the vehicle travel per gallon of gasoline?

Answers

If a vehicle uses 2 gallons of gasoline to travel 18¹/₂ miles, at this rate, the vehicle can travel 9¹/₄ miles per gallon of gasoline.

What is the rate?

The rate refers to the average speed of the vehicle.

The rate also describes the unit rate or the rate expressed as a percentage or in terms of speed.

The number of gallons of gasoline used to travel 18¹/₂ miles = 2 gallons

The total distance traveled using two gallons of gasoline = 18¹/₂ miles

The average distance traveled per gallon of gasoline = 9¹/₄ miles (18¹/₂ ÷ 2)

Thus, on the average, the vehicle can travel 9¹/₄ miles miles per gallon of gasoline.

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Correct Question:

A vehicle uses 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?

Evaluate each expression using the values given in the table.

Answers

Answer:

a) f(g(1)) = f(0) = 5

b) f(g(2)) = f(-3) = 8

c) g(f(2)) = g(3) = -8

d) g(f(3)) = g(2) = -3

e) g(g(1)) = g(0) = 2

f) f(f(3)) = f(2) = 3

how large a sample should be taken if the population mean is to be estimated with 98 percent confidence to within $100? The population has a standard deviation of $800.

Answers

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

Understanding Population Estimate

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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Suppose that the function h is defined as follows.

Answers

For the given function h(x) the points can be plotted on,

(-1,-1)(0,0)(1,1)(2,2)

The given function h(x) is having four conditions and each condition can be clearly discussed below:

Given that for the first condition, the x-axis is ranging from -1 [tex]\leq[/tex] x < 0, the y-axis point is present exactly at -1. Similarly, for the second condition, the x-axis is ranging from 0 [tex]\leq[/tex] x < 1, and the y-axis point is present at 0. For the third condition, the x-axis is ranging from 1 [tex]\leq[/tex] x < 2, and the y-axis point is at 1.Finally, for the fourth condition, the x-axis is ranging from 2 [tex]\leq[/tex] x < 3, and the y-axis point is at 2.

From, the above analysis we plotted the graph and attaching below.

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20x^2-7x-6=0 by factoring

Answers

Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

4x=3

X=3/4

100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.

Answers

The quotient of functions f(x) and g(x) is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

How to obtain the quotient function?

The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:

(f/g)(x) = f(x)/g(x)

The functions for this problem are given as follows:

f(x) = x² + 7x + 12.g(x) = x² - 9.

The functions can be factored as follows:

f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.

The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

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What is the least common dominator of 4/13 and 4/5?

Answers

Answer:

52 is the least common dominator

Answer:

52/65

Step-by-step explanation:

The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple

The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.

The simple method for common computing denominators (not least at all) is to multiply all denominators.

In a sample of 1000 adults, 150 said they are very confident in the nutritional information on restaurant menus. for us adults are selected at random without replacement.

Find the probability that none of the four adults are very confident in the nutritional information on the restaurant menus.

Answers

The probability that none of the four adults is very confident in the nutritional information on the restaurant menus is 0.208 or approximately 20.8%.

Ready to approach this issue by utilizing the hypergeometric conveyance, since we are examining without substitution from a limited populace of two sorts (those who are exceptionally sure and those who are not exceptionally sure).

Let X be the number of grown-ups in a sample of 4 who are not exceptionally sure about the wholesome data on eatery menus.

At that point, X takes after a hypergeometric dissemination with parameters N = 1000, n = 4, and K = 850 (since 850 grown-ups are not exceptionally certain).

The likelihood that none of the 4 grown-ups are exceptionally certain can be communicated as:

P(X = 4) = (K select 4) / (N select 4)

where (K select 4) speaks to the number of ways to select 4 grown-ups from the population of 850 who are not exceptionally sure,

and (N select 4) speaks to the entire number of ways to select 4 grown-ups from the populace of 1000.

Utilizing the equation for binomial coefficients, ready to disentangle this expression as:

P(X = 4) = [(850*849*848*847) / (4*3*2*1)] / [(1000*999*998*997) / (4*3*2*1)]

= 0.208

Hence, the likelihood that none of the four grown-ups are exceptionally certain within the wholesome data on eatery menus is 0.208 or approximately 20.8%.

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Help with solving This graph

Answers

Answer:

r=4

center: (-2,4)

Step-by-step explanation:

The equation of a circle is:

(x-h)²+(y-k)²=r²

(h,k) would be the center of the circle and r would be length of the radius

To find r, we simply take the square root of 16, which would be 4

And the center is given in the equation

Which is equivalent to 234 2/5

Answers

234 2/5 is equivalent to 1172/5.

234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.

To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.

The result becomes the new numerator, and the denominator stays the same.

In this case, we have:

234 2/5 = (234 x 5 + 2) / 5

= 1172/5

Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.

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what’s the numbers that correspond to the corret number of solutions

Answers

The number of solutions for the given system of linear equations is: Infinitely many solutions.

Calculating the number of solutions

To determine the number of solutions for the given system of linear equations:

3x - y = 4

6x - 2y = 8

We can use the algebraic method of solving the system of equations by substitution or elimination.

Let's use the algebraic method to determine the number of solutions:

3x - y = 4 (1)

6x - 2y = 8 (2)

We can simplify equation (2) by dividing both sides by 2:

3x - y = 4 (1)

3x - y = 4 (2')

Equations (1) and (2') are equivalent, which means that they represent the same line.

Therefore, the two equations represent the same line, and we have infinitely many solutions.