Solve the following quadratic equations
\(x { }^{2} - x - 42\)
\(x {}^{2} + x - 6\)
\(r {}^{2} - 25\)

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

To solve these equations equate them to zero, that is

x² - x - 42 = 0

Consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (- 1)

The factors are - 7 and + 6, since

- 7 × 6 = - 42 and - 7 + 6 = - 1 , thus

(x - 7)(x + 6) = 0

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 6 = 0 ⇒ x = - 6

Solutions are x = - 6, x = 7

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

x² + x - 6 = 0 ← in standard form

(x + 3)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Solutions are x = - 3, x = 2

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

x² - 25 = 0 ( add 25 to both sides )

x² = 25 ( take the square root of both sides )

x = ± \(\sqrt{25}\) = ± 5

Solutions are x = - 5, x = 5


Related Questions

what is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?

Answers

The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is  \(\\& =0.175823334\end{aligned}\)

A probability simple definition is what?

The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.

A probability may it be negative?

Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.

The number of choosing  cards out of 52 is = ⁵²C₃

Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃

Probability of choosing 5 hearts =  ¹³C₃ × ³⁹C₄ /  ⁵²C₃

\(\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}\)

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In a class of students, the following data table summarizes how many students play
an instrument or a sport. What is the probability that a student chosen randomly
from the class plays a sport?
Plays a sport
Does not play a sport
Plays an instrument Does not play an instrument
3
8
10
9

Answers

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Point d is the center of the inscribed circle of abc. which step can you use to draw the inscribed circle of abc? a. draw arcs of equal lengths intersecting , , and in two points each. b. draw the perpendicular bisectors of , , and that pass through point d. c. label a point e on and draw a line joining e with d. d. draw a line through d that is perpendicular to one of the sides, , , or . e. draw one arc each on and , and find their point of intersection.

Answers

The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.

Steps to draw an Inscribed Circle:

a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.

b. draw a line perpendicular to one side of the triangle that passes through its center.

c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.

As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

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help please... and thank you :)​

help please... and thank you :)

Answers

Answer:

The answer is 1

Step-by-step explanation:

Any number to the power of 0 is 1

Answer:

1 is the answer.

Step-by-step explanation:

This is the answer because when you place a number to the 0th power then they are equal to 1. This applies to all numbers and variables.

The scatter plot and line of best fit below show the length of 12 people's femur (the long leg bone in the thigh) and their height in centimeters. What is the meaning of the y-value on the line when x=40? 0 x y 0 Height (centimeters) Femur Length (centimeters)
a. The height of an actual person with a femur length of 158.4 centimeters is 40 centimeters.
b. An expected height of 158.4 centimeters when the femur has a length of 40 centimeters.
c. The height of an actual person with a femur length of 40 centimeters is 158.4 centimeters.
d. An expected height of 40 centimeters when the femur has a length of 158.4 centimeters.

Answers

The y-value on the line when x=40 is An expected height of 40 centimeters the femur has a length of 158.4 centimeters. d.

Based on the given information, the scatter plot and line of best fit depict the relationship between femur length and height.

The y-value on the line represents the predicted or expected height when the femur length is given.

x = 40 (referring to the femur length of 40 centimeters), the meaning of the y-value on the line is the predicted or expected height.

The line of best fit provides an estimation of the relationship between femur length and height based on the observed data.

It allows us to make predictions about the height for a given femur length within the range of the data.

Without additional context or specific statistical information, we cannot determine the exact value of the y-coordinate at x = 40 without referring to the graph or the equation of the line.

The scatter plot and line of best fit show the association between femur length and height based on the provided data.

When the femur length is known, the y-value on the line reflects the anticipated or forecast height.

When x = 40 (the length of the femur in centimetres), the y-value on the line represents the expected or forecast height.

Based on the observed data, the line of best fit estimates the association between femur length and height.

It enables us to forecast the height for a specific femur length within the constraints of the data.

We cannot precisely establish the value of the y-coordinate at x = 40 without additional context or particular statistical data.

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May i have some help please ^^ im not really good at this stuff
Samra's guardians invested money for her into a 529 College Savings Plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 400(1.02)x. What is the meaning of the y-intercept in the context of the problem?

The initial value of the investment is $400.
The principal amount put into the savings plan is $1.02.
The percent rate of change is 400%.
The average rate of change that is occurring is 1.02.

Answers

The y-intercept is the initial value of the investment is $400.

What is the y-intercept?

If an investment is compounded annually, it means that both the initial amount invested and the interest that is accrued increases in value once a year. The equation that is used to determine the future value of the investment that earns a compound interest is an exponential function.

The form of the exponential function is:

FV = P (1 + r)^nm

Where:

FV = Future valueP = Present valueR = interest ratem = number of compoundingN = number of years

The y-intercept of an exponential function is the point where the graph touches the y-axis. It is the point where the value of x is zero. The y-intercept is the initial value of the investment. The initial value of the investment is $400.

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Luke climbed from an elevation of 23,201 ft up to the summit of k2 which is at 28,251 ft. How many ft did Luke climb?


I need to explain the variable

write an equation

and solve it

Answers

The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft

How to find the feet climbed?

The number of feet that Luke climbed, can be found by the formula:

Number of feet climbed = Summit of K2 - Luke's starting elevation

Summit of K 2 = 28, 251 ft

Luke's starting elevations = 23, 201 ft

Elevation climbed by Luke was therefore:

= 28, 251 - 23, 201

= 5, 050 ft

In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.

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1. five friends go to the movie theater together. (a) if there are 5 seats open in a row, how many ways can the friends choose seats? (b) if there are 7 seats open in a row, how many ways can the friends choose seats? (note that two seats will remain empty.) (c) repeat part (b), but where two of the friends are required to sit next to each other. (d) repeat part (b), but where two of the friends are required to not sit next to each other.

Answers

he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

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For each of the following statements below, decide whether the statement is True or False. (i) The solution set to the equation x² + x² + x² = 1 is a subspace of R³. (No answer given) ♦ [2 marks] (ii) Suppose V is a subspace of R2 and V contains the vector (1,0). Then V contains the entire 1-axis. (No answer given) [2 marks] (iii) Recall that P(7) denotes the space of polynomials in x with degree less than or equal 7. Consider the function L : P(7) → P(7), defined on each polynomial p by L(p) = p', the first derivative of p. The image of this function is a vector space of dimension 7. (No answer given) [2marks] (iv) The solution set to the equation 5. x3 + 4 ⋅ x2 + 5 ⋅ x₁ = 0 is a subspace of R³. (No answer given) [2marks] (v) The set of all vectors in the space R5 whose first entry equals zero, forms a 4-dimensional vector space. (No answer given) [2marks]

Answers

(i) False.

(ii) True

(iii) False.

(iv) True.

(v) False.

(i) False. The equation x² + x² + x² = 1 simplifies to 3x² = 1, which is a quadratic equation. The solution set of this equation is not a subspace of R³ because it does not satisfy the subspace properties. Specifically, it does not contain the zero vector (0, 0, 0) and it is not closed under scalar multiplication.

(ii) True. If V is a subspace of R² and it contains the vector (1, 0), then it must also contain all linear combinations of that vector. The entire 1-axis corresponds to the set of vectors of the form (0, t), where t is a real number. We can express (0, t) as a linear combination of vectors in V by taking t times the vector (1, 0), which is in V. Therefore, V contains the entire 1-axis.

(iii) False. The dimension of the image of the function L : P(7) → P(7), defined as L(p) = p', where p' is the first derivative of p, is not necessarily 7. Taking the derivative of a polynomial reduces its degree by 1, so the image of L will consist of polynomials of degree at most 6. Therefore, the dimension of the image will be at most 7, but it could be less depending on the specific polynomials in P(7) and their derivatives.

(iv) True. The solution set to the equation 5x³ + 4x² + 5x₁ = 0 is a subspace of R³. This equation represents a homogeneous linear equation, and the solution set always forms a subspace. It contains the zero vector (0, 0, 0), and it is closed under vector addition and scalar multiplication.

(v) False. The set of all vectors in the space R⁵ whose first entry equals zero forms a 3-dimensional vector space, not a 4-dimensional vector space. The vectors in this set can be expressed as (0, x₂, x₃, x₄, x₅), where x₂, x₃, x₄, and x₅ can take any real values. The dimension of this vector space is the number of linearly independent vectors that span the space, which in this case is 3.

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2 triángulos congruentes son semejantes

Answers

Answer:

Spanish

Teorema: “ Si dos triángulos tienen sus dos ángulos correspondientes congruentes, entonces el tercero también será congruente y los triángulos son semejantes”. Teorema: “ Dos triángulos son semejantes si tienen un ángulo congruente comprendido entre lados proporcionales”.

English

Theorem: "If two triangles have their two corresponding angles congruent, then the third will also be congruent and the triangles are similar." Theorem: "Two triangles are similar if they have a congruent angle between proportional sides."

Step-by-step explanation:

x/5 - 74 = 26

what is x​

Answers

Step-by-step explanation:

x/5 - 74 = 26

x/5 = 26 + 74

x/5 = 100

x = 100 x 5

x = 500

I need help with someone explaining how to find the range of this! This course didn’t explain anything!

I need help with someone explaining how to find the range of this! This course didnt explain anything!

Answers

Answer:

\((-infinity,3)\), D

Step-by-step explanation:

3 if x is greater than or equal to 1 is nothing. That leaves us with \(h(x)=2x+1\) if x<1. If you substitute in 1 for x, you get 3, but of course that isn't possible, so the range is \((-infinity,3)\), which is D.

x/3-4=7
whats the answer i cant figure this out?

Answers

I think x is 33

that's your answer

I believe x is 33 I hope this helps

For brainily please help

For brainily please help

Answers

Answer:

Yes, these create an isosceles triangle, where two sides are equivalent

solve -1/3x > 5 I don't understand ​

Answers

Answer:

x = 15

Step-by-step explanation:\

Multiply both sides of the equation by 3

3 x 1/3 x X = 3 x 5

Simplify both sides of the equation.

Simplify 3 x 1/3 x X.

1 x X = 3 x 5

Multiply x by 1.

x = 3 x 5

Multiply 3 by 5.

and you get x = 15

Hope it helps!


What is the value of tan O?

Answers

Answer:

In trigonometry, the value of tan 0 is 0. The word 'Trigonometry' is derived from the Greek word and the subject is developed to solve geometric problems involving triangles. It is used to measure the sides of a triangle.

Answer:

→ 0 (zero)

Step-by-step explanation:

The value of tan 0 is 0.

The selling price of a gas cooker is 450.00 if a customer allowed a discount of 20% calculate the discount amount paid by the customer​

Answers

Answer:

the customer pays 4500 for the gas cooker

please answer the question hurry up get 25 point ​

please answer the question hurry up get 25 point

Answers

Answer:

\(x = - 1.\)

Step-by-step explanation:

\( {2}^{x} = \frac{1}{2} \\ {2}^{x} = {2}^{ - 1} \\ x = - 1.\)

♨Rage♨

Step-by-step explanation:

Hey there!

Given;

\( {2}^{x} = \frac{1}{2} \)

We know that (1/2) can be written as 2^-1. So, it will be;

\( {2}^{x} = {2}^{ - 1} \)

Looking on both sides we find that both have same base. So,

x = -1

(Note: While solving the exponential equation you must make base same by simplifying them and then equate the power)

Hope it helps...

Find the distance between points.

Find the distance between points.

Answers

Answer:

4 Units

Step-by-step explanation:

Here, The distance between two points is 4 units

-TheUnknownScientist

A square coaster measures 4 inches on each side. Use a formula to find the perimeter of the coaster in inches.

Answers

Answer:

16

Step-by-step explanation:

Formula: 4(a)

Plug it in: 4(4)

Answer: 16

Jim builds a robot that travels no more than 10 feet per minute. Graph the inequality showing the relationship between the distance traveled and the time elapsed.
Is it possible for the robot to travel 27 feet in 3 minutes?

Answers

Answer:

no robot can travel 27 feet in 3 minutes

Step-by-step explanation:

It rains three times during the first week of summer vacation.
Compute the total amount if it rains 2.05 inches, 0.29 inches, and 3 inches.

Answers

The total amount of rainfall during the first week of summer vacation is 5.34 inches.

To compute the total amount of rainfall during the first week of summer vacation, we need to add up the amounts of rainfall on each day.

Given that it rains three times during the week, the amounts of rainfall on those days are 2.05 inches, 0.29 inches, and 3 inches, respectively.

To find the total amount of rainfall, we add these amounts together:

Total amount of rainfall = 2.05 inches + 0.29 inches + 3 inches

= 5.34 inches

Therefore, the total amount of rainfall during the first week of summer vacation is 5.34 inches.

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The following statements may or may not be true. For a true statement, write a proof. For a false statement, write a disproof. i. (6pts) If L₁ is a decidable language (a language in R) and L2 is a regular language, then L₁ L₂ is regular. (Write your proof or disproof here)

Answers

The statement is false. I will provide a disproof.

To disprove the statement, we need to find a counterexample where L₁ is a decidable language and L₂ is a regular language, but their concatenation L₁L₂ is not regular.

Consider L₁ as the decidable language consisting of all strings over the alphabet {a} that have an even number of 'a's. L₁ can be decided by counting the number of 'a's in a string and accepting if the count is even.

Now consider L₂ as the regular language consisting of all strings over the alphabet {a} that have an odd number of 'a's. L₂ can be described by the regular expression "a(aa)*".

The concatenation of L₁ and L₂, L₁L₂, would consist of strings that have an even number of 'a's followed by strings that have an odd number of 'a's. The resulting language L₁L₂ would contain strings with an odd number of 'a's, which is not a regular language.

Therefore, we have shown a counterexample where L₁ is a decidable language and L₂ is a regular language, but L₁L₂ is not regular. This disproves the given statement.

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If dy/dt=f(t)g(y), the equilibrium solutions can be obtained by finding the solutions to f(t)=0

Answers

The statement "If dy/dt=f(t)g(y), the equilibrium solutions can be obtained by finding the solutions to f(t)=0" is not entirely correct.

In a differential equation of the form dy/dt = f(t)g(y), the equilibrium solutions are the constant solutions where dy/dt = 0. These occur when g(y) = 0.

To find the equilibrium solutions, we need to solve g(y) = 0. Once we have found these solutions, we can determine their stability by analyzing the sign of f(t) near these equilibrium values. If f(t) is positive near an equilibrium value, the solution is unstable (i.e., solutions near the equilibrium will move away from it). If f(t) is negative near an equilibrium value, the solution is stable (i.e., solutions near the equilibrium will move towards it).

So, while f(t) = 0 may be useful in some cases for finding equilibrium values, it is not the correct approach for finding all equilibrium solutions in a differential equation of the form dy/dt = f(t)g(y). The equilibrium solutions are found by solving g(y) = 0.

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Amir arranged 9 photos on a bulletin board. He put the photos in rows. Each row contains the same number of photos. How many photos could be in each row? (Giving Brainliest)

Options:
a. 1, 6 or 9 photos
b. 1, 3 or 9 photos
c. 1, 2 or 9 photos
d. 1, 3 or 6 photos

Answers

Answer:

I select b, 1,3, or 9 photos as my answer.

Which number(s) below belong to the solution set of the equation? Check all that apply.x+10 = 40

Answers

Answer:

the answer is 30

did it on apex

Step-by-step explanation:

The sum of two numbers is 99 and the difference is 13. Use a system of two equations and two variables to solve and find the two
numbers.

Answers

Answer:

56 and 43

Step-by-step explanation:

(x+13)+x = 99

2x+13 = 99

2x = 99-13

2x = 86

x = 86/2

x = 43

Smaller number = 43

Larger number is 56

Check

56-43 = 13

56+43 = 99

Answer:

The two numbers are 43 and 56.

Step-by-step explanation:

Represent the numbers by x and y.

Then, according to the given information,

x + y = 99 and x - y = 13

Rewrite these two equations in a column:

x + y = 99

x -  y = 13

Solve this system of linear equations through elimination by addition/subtraction:

x + y = 99

x -  y = 13

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

2x = 112, so that x = 56

Next, find y by substituting 56 for x in either of the two equations:

56 - y = 13

This reduces to 43 - y = 0, or y = 43

The two numbers are 43 and 56.

Check:  Is the difference between 56 and 43 equal to 13?  YES

Is the sum of the numbers 56 and 43 equal to 99?  YES

Jerome is a photographer. He earns $125 per hour

Jerome is a photographer. He earns $125 per hour

Answers

The graph of the data from the table is added as an attachment

Creating a graph of the data from the table.

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

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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Jerome is a photographer. He earns $125 per hour

i thought of a number. four times the number increased by 30 equals 70 decreased by the number. what was my number?

Answers

Answer:

number is 8

Step-by-step explanation:

let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30

70 decreased by the number means subtracting n fro 70 , 70 - n

then

4n + 30 = 70 - n ( add n to both sides )

5n + 30 = 70 ( subtract 30 from both sides )

5n = 40 ( divide both sides by 5 )

n = 8

What is the rate of change of the function?
-2
-1/2
1/2
2

What is the rate of change of the function?-2-1/21/22

Answers

Answer:

-2/1

Step-by-step explanation:

Answer:

-2/1

Step-by-step explanation:

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