find the least common multiple of x^2-25 and x-5

Answers

Answer 1

To find the least common multiple of x^2-25 and x-5, we need to factor both expressions first.

x^2-25 can be factored as (x+5)(x-5)

x-5 is already factored.

Now, we can find the least common multiple by taking the product of the highest powers of each factor.

The highest power of (x+5) is 1, and the highest power of (x-5) is 2. Therefore, the least common multiple is:

(x+5)(x-5)^2

which can also be written as:

(x-5)(x^2-10x+25)

Answer 2

Answer: The least common multiple is (x−5) (x−5)

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Related Questions

The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?

Answers

The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

Identifying the graph of the function g(x)?

From the question, we have the following parameters that can be used in our computation:

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

Answers

The transformation in the function y = -1/3f(x + 4) - 5 is described below

Describing the transformation in the function

From the question, we have the following parameters that can be used in our computation:

y = f(x)

The transformed function g(x) is given as

y = -1/3f(x + 4) - 5

The sequence of transformation on the transformed function is as follows

Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 units

Answers

Answer:

20 : 4 : 15

Step-by-step explanation:

1 : 0.2 : 0.75

1 : 2/10 : 75/100

1 : 20/100 : 75/100

(×100)

100 : 20 : 75

(÷5)

20 : 4 : 15

The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking

Answers

The volume of the prism is V = 4000 cm³

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the prism be h = 10 cm

Let the width of the prism be w = 20 cm

Let the length of the prism be l = 20 cm

So , the base area of prism = l x w

Base area = 400 cm²

Now , the volume of the prism is V = 400 x 10

V = 4000 cm³

Hence , the volume of prism is V = 4000 cm³

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Which equation can be used to solve for x

Answers

Answer:

(a) 7(x +3.5x) = 56

Step-by-step explanation:

You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.

Daily run

The morning run is given as x.

The evening run is 3.5 times as long, so is 3.5x

The total mileage each day is (x +3.5x).

Weekly total

In 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:

7(x +3.5x) = 56

Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.

What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?

Answers

The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

What is a circle?

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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Part A: Is it possible to make a triangle that is both equilateral triangle and a right triangle? Explain

Part B: Is it possible to draw a triangle with side lengths of 15, 15 and 20? Explain.

Answers

Answer:

A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.

B. Yes, it is possible. By the Triangle Inequality Theorem:

15 + 15 > 20, and 20 + 15 > 15

PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT

Answers

p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

What is an arithmetic series?

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle.

questions 1)

m

question 2)

m

question 3)

m

Answers

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

How to solve

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining sides c and ∠B and ∠C

Using the Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c = 4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

Answers

Answer:

2600This is a probability conversion problem.

pleaseeee help me!!

mathematics the pic below

Answers

Answer:

15, 18, 21, 24, 27, 30 ( +3)

7, 14, 28, 56, 112, 224, 448 ( x 2)

77, 70, 63, 56, 49, 42, 35 ( - 7)

20, 31, 42, 53, 64, 75, 86, 97 (+11)

22, 35, 48, 61, 74, 87 (+13)

Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5

Answers

The calculated area of the triangle B is 1.8 square units

What is the area of triangle B

From the question, we have the following parameters that can be used in our computation:

Triangle A and B

Where

Area of A = 1/2 base * height

Sp, we have

Area of A = 1/2 * 2 * 5

Next, we have

Area of B = Area of A * Scale factor^2

Using the above as a guide, we have the following:

Area of B = 1/2 * 2 * 5 * (3/5)^2

Evaluate

Area of B = 1.8

Answers

Roger and Trish can complete 11/30 of the math homework in 1 hour if they work together.

What is an expression?

An expression is a sentence that has at least two numbers/variables and at least one math operation.

According to the given information:

Let the total amount of work in the math homework is 1.

In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work.

If they work together for 1 hour, then the total amount of homework they can finish is the sum of the parts each of them can finish in one hour:

1/6 + 1/5 = 5/30 + 6/30 = 11/30

So together they can finish 11/30 of the homework in one hour.

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A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

C(t)=18(0.91)t

Answers

The initial temperature of the soda is 18 degrees Celsius.

Its temperature after 20 minutes is 2.73 degrees Celsius.

What is an exponential function?

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.

When time, t = 0, the initial value can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]

C(0) = 18(1)

C(0) = 18 degrees Celsius.

When time, t = 0 = 20, the temperature can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]

C(20) = 2.73 degrees Celsius.

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Complete Question:

A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

[tex]C(t)=18(0.91)^{t}[/tex]

Find the initial temperature of the soda and its temperature after 20 minutes?

The area of a rectangular shaped rug is 81 square feet. If the rug is 9 ft long, what is ire perimeter?

Answers

The perimeter of the rug is 36ft

What is perimeter?

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

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Which statement concerning the equation x² - 1 = x is true?

1. Its discriminant is 0, so it has no solution.

2. Its discriminant is 5, so it has two real solutions.

3. Its discriminant is 0, so it has one real solution.

4. Its discriminant is -3, so it has two complex solutions.

Answers

The statement "Its discriminant is 5, so it has two real solutions" is not true for the equation x² - 1 = x.

The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, the equation can be rewritten as x² - x - 1 = 0, so a = 1, b = -1, and c = -1. Therefore, the discriminant is (-1)² - 4(1)(-1) = 5.

Since the discriminant is positive, the equation has two real solutions. However, this statement does not apply to the given equation because it is not in standard quadratic form.

To solve the equation x² - 1 = x, we can rearrange it as x² - x - 1 = 0 and then use the quadratic formula to find its solutions. The quadratic formula is x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values a = 1, b = -1, and c = -1, we get x = (1 ± sqrt(5)) / 2. Therefore, the equation has two real solutions, which are x = (1 + sqrt(5)) / 2 and x = (1 - sqrt(5)) / 2.

Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.

The acts in a talent competition consist of 10 instrumentalists, 12 singers, and 8 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?

Answers

Answer:

P=4/15

Step-by-step explanation:

P(dancer first) = 8/30=4/15

the perimeter of a triangle is 53 inches. the length of the one side is 15 inches the other two sides are congruent find the lengths

Answers

53 - 15 is 38 then divide that by 2 which would mean both the angles are 19

whats the probility that she selects a non-mathamatical major, given that she choosees randomly from only sophmores From mrs. Burke's math class

Answers

The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.

What is the probability?

Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.

Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.

The number of Sophomores in Mathematics Majors = 16

The number of Sophomores in Non-Mathematics Majors = 17

The total number of Sophomores in Mrs. Burke's Mathematics Class = 33

The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)

Mrs. Burke's Mathematics Class

Academic Year Mathematics Majors Non-Mathematics Majors Total

Freshmen 19 18 37

Sophomores 16 17 33

Juniors 11 15 26

Seniors 12 13 25

Total 58 63 121

Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.

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Question Completion:

Mrs. Burke's Mathematics Class

Academic Year Mathematics Majors Non-Mathematics Majors

Freshmen 19 18

Sophomores 16 17

Juniors 11 15

Seniors 12 13

What is the area of one of the bases,b, of the prism b=_in2

Answers

Answer: 6

Step-by-step explanation:

Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².

Answer:

Step-by-step explanation:

B= area of the triangle 1+area of triangle 2

(1/2*3*1)+(1/2*2*1)

=1.5+1

=2.5

Anna wants to borrow $15,000 to buy a used sail boat. After looking at her financial situation, she realizes that she can only afford monthly payments of $300. The bank is offering financing at 6.1%. For how long will Anna need to finance the boat to stay within her monthly payment?

Answers

Answer:

47 months

Step-by-step explanation:

find 6.1% of 15k then divide that by 300

6.1% = 915

15,000 - 915 = 14085

14085 divided by 300 is 46.95 then rounded is 47

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 169 cm and a standard deviation of 2.2 cm. For shipment, 10 steel rods are bundled together.

Answer the following rounding to three decimals where appropriate.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm.

P(M > 168.58) = ???

Answers

The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

How to calculate the probability

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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100 POINTS!!!

Question:

Answers

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65 for KW 3 calculation are 16,23,30,37,114,121,128, just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is 15+2x=15+2*0=15

output x=1 is 15+2x=15+2*1=17

output x=2 is 15+2x=15+2*2=19

output x=3 is 15+2x=15+2*3=21

output x=4 is 15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is 60+2x=60+2*1=61

output x=2 is 60+2x=60+2*2=63

output x=3 is 60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is 16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is 16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65 for KW 3 calculation are 16,23,30,37,114,121,128, just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is 15+2x=15+2*0=15

output x=1 is 15+2x=15+2*1=17

output x=2 is 15+2x=15+2*2=19

output x=3 is 15+2x=15+2*3=21

output x=4 is 15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is 60+2x=60+2*1=61

output x=2 is 60+2x=60+2*2=63

output x=3 is 60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is 16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is 16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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Directions - Answer the questions based on the following scenario and graph.
Jim and Cassie are both saving money each week in order to buy an awesome Bulls snapback hat (and leave the price stickers on it, of course). The hat costs $27.

Answers

Jim's rate of savings (slope): 3

Cassie's rate of savings (slope): 3

Jim's y intercept: 3

Cassie's y intercept: 12

Jim's Savings Equation: y = 3x + 3

Cassie's Savings Equation: y = 3x + 12

Number of weeks it will take to Cassie to save $27: 5

Number of weeks it will take to Jim to save $27: 8

Yes, Jim and Cassie's rates parallel.

Cassie will be able to buy the hat first.

We know that the slope intercept form of a straight line is,

y = mx + c, where m is the slope of the line and c is the y intercept.

For the straight line for Cassie:

The line passing through the points (0, 12) and (1, 15).

So the slope = (15 - 12)/(1 - 0) = 3

The y intercept is = 12.

Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.

For the straight line for Jim:

The line passing through the points (0, 3) and (1, 6).

So the slope = (6 - 3)/(1 - 0) = 3

The y intercept is = 3

Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.

Since the slope of both are equal so the rates of both are parallel.

Substituting the value y = 27 in equation (i) and (ii) we get,

equation (i): 3x + 12 =27

3x = 27 - 12

3x = 15

x = 15/3

x = 5

So Cassie needs 5 weeks to save $27.

Equation (ii): 3x + 3 = 27

3x = 27 - 3

3x = 24

x = 24/3

x = 8

So Jim needs 8 weeks to save $27.

Hence Cassie will be able to buy the hat first.

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The question is incomplete. The complete question will be -

(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24

Answers

1. Pour la première question, si le garçon peut courir une distance de 10 mètres pendant que la voiture en parcourt 0, alors le garçon peut courir la même distance que la voiture en un temps infini, ce qui signifie qu'il peut courir pendant que la voiture parcourt 66 mètres. Par conséquent, la réponse est (A) 0.

2. Pour la deuxième question, nous pouvons utiliser la formule suivante:

Nombre total d'uniformes produits = nombre d'ouvriers x nombre d'uniformes produits par ouvrier

Soit n le nombre d'ouvriers dans l'équipe. Avant l'augmentation de 20%, chaque ouvrier produisait en moyenne 1000 / n uniformes par semaine. Après l'augmentation, chaque ouvrier produit en moyenne (1000 / n) x 1.2 + 50 uniformes par semaine. Par conséquent, nous avons l'équation suivante:

n x [(1000 / n) x 1.2 + 50] = 1200

Simplifiant l'expression, nous obtenons:

1200 = 1200 + 50n / n

50n = 0

Par conséquent, la réponse est (A) 4, ce qui implique qu'il y avait seulement 4 ouvriers dans l'équipe. Cependant, cette réponse est peu plausible, car il est peu probable qu'une équipe de seulement 4 ouvriers puisse produire 1000 uniformes par semaine avant l'augmentation de 20%.

multiply 9/11 x 44/81

Answers

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 15 square feet use 3.14 for pi

Answers

The distance from which the sprinkler can spread water is 4.37 feet

How to determine the value

To determine the value, we need to know the area of the circle.

The formula for the area of a circle is expressed as;

A = πr²

Given that the parameters are;

A is the area of the circler is the radius of the circle

Substitute the values, we have;

15 = 3.14r²

Divide both sides by the coefficient, we get;

r² = 4. 77

find the square root of both sides, we get;

r = 2. 19 feet

But note that the formula for diameter is given as;

Diameter = 2radius

Diameter = 2(2.19)

multiply the values

Diameter = 4.37 feet

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PLS HELP ASAP
I AM SO CONFUSED WID THIS!
The numbers 1-20 are written on pieces of paper and put in a box. Two pieces of paper are randomly selected and not replaced.

a) Are the events dependent or independent? _________

b) What is the probability of selecting a number less than 6 both times? ________

Answers

the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

how to find probability ?

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5

z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2

PLease help

Answers

Let's analyze each equation and the mistakes made by Daniel:

1. 25x^2 - 16 = 9

Daniel's mistake: He took the square root of each term separately, which is not correct.

Explanation: When we take the square root of an equation, we must take the square root of both sides of the equation, not just each term separately.

Correct solution:
25x^2 - 16 = 9
25x^2 = 25
x^2 = 1
x = ±1

Therefore, the correct solutions are x = 1 and x = -1.

2. z^3 - 2 = 6

Daniel's mistake: He correctly found the cube root of 8, but forgot to consider the negative cube root as well.

Explanation: When we take the cube root of an equation, we must consider both the positive and negative cube roots, since a cube can have both a positive and negative cube root.

Correct solution:
z^3 - 2 = 6
z^3 = 8
z = ∛8
z = 2 or -2

Therefore, the correct solutions are z = 2 and z = -2.

Use the estimated angle to find the distance of the life-raft from the lighthouse.

Answers

The correct angle of elevation for the lighthouse's top is roughly 1.91°.

How to find the distance of the lift-raft from the lighthouse?

Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.

The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".

a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.

[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]

putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.

[tex]tan3 = \frac{20}{d}[/tex]

[tex]d = \frac{20}{tan3}[/tex]

d = 354.14 (rounded to 2 decimal points

The life raft is therefore roughly 354.14 meters away from the lighthouse.

Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.

[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]

solving for [tex]\alpha[/tex] we get,

[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]

Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.

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