Compute the discriminant. Then determine the number and type of solutions of the given solution.
2x2−7x+4=0
What is the discriminant?
Choose the sentence that describes the number and type of solutions of the quadratic equation.
(a) There are two unequal real solutions.
(b) There are two imaginary solutions.
(c) There is one real solution.
(d) There are infinite numbers of real solutions.

Answer:

The answer is 145°

Step-by-step explanation:

Angle 3 and 4 make a right angle (90°) Subtract 55 from 90.

90-55=35

Angle 3 and Angle 1 are vertical angles, hence they have the same measurement.

Angle 1 is 35°

Angle 1 and 2 make a 180° angle. Subtract 35 from 180.

180-35=145

The measurement of angle 2 is 145°

Answer:

Step-by-step explanation:

∠5 + ∠4 = 90 + 55 = 145

∠2 = ∠5 + ∠4 (vertically opposite angles)

∴ ∠2 = 145

Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order.

Mode: The mode is the number that appears most frequently in a set of numbers.

Hi there! Yes, I can certainly show and explain the methods for calculating Mean, Median, and Mode. These are all measures of central tendency, which are used to describe the center of a data set.

Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set. For example, if you have the numbers 2, 4, 6, 8, and 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. For example, if you have the numbers 2, 4, 6, 8, and 10, the median would be 6. If you have the numbers 2, 4, 6, 8, 10, and 12, the median would be (4 + 6) / 2 = 5.

Mode: The mode is the number that appears most frequently in a set of numbers. If there is more than one number that appears the same number of times, there can be more than one mode. For example, if you have the numbers 2, 4, 6, 8, 10, and 10, the mode would be 10 because it appears twice and the other numbers only appear once.

I hope this helps! Let me know if you have any other questions.

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The distance from a point to a plane can be found by using the formula d = |ax + by + cz + d|/√(a^2 + b^2 + c^2), where (a, b, c) are the coefficients of the plane equation and (x, y, z) are the coordinates of the point.

For the first part of the question, the distance from the point (-1, 3, -5) to the plane 4x – 4y + 3z = -2 can be found by plugging in the values into the formula:
d = |(4)(-1) + (-4)(3) + (3)(-5) + (-2)|/√(4^2 + (-4)^2 + 3^2)
d = |-4 - 12 - 15 - 2|/√(16 + 16 + 9)
d = |-33|/√41
d = 33/√41

For the second part of the question, an equation of the plane through the point (-1, -2, 2) and perpendicular to the vector (5, -1, -2) can be found by using the formula ax + by + cz = d, where (a, b, c) are the components of the vector and (x, y, z) are the coordinates of the point. Plugging in the values gives:
(5)(x - (-1)) + (-1)(y - (-2)) + (-2)(z - 2) = 0
5x + 5 - y - 2 - 2z + 4 = 0
5x - y - 2z = -7

Therefore, the equation of the plane is 5x - y - 2z = -7.

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There does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

(a) To show that NG(H) = G, we need to show that every element of G normalizes H. Let g ∈ G, and let h ∈ H. Since H = ker(φ), we know that φ(h) = 1. Now, we need to show that ghg⁻¹ ∈ H. Using the properties of a homomorphism, we can write:

φ(ghg⁻¹) = φ(g)φ(h)φ(g⁻¹) = φ(g)1φ(g⁻¹) = φ(g)φ(g⁻¹) = φ(gg⁻¹) = φ(1) = 1

Therefore, ghg⁻¹ ∈ H, and so g normalizes H. Since this is true for any g ∈ G, we can conclude that NG(H) = G.

(b) Suppose there exists a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}. Since s ∈ ker(φ), we know that φ(s) = 1. However, we also know that rs = sr⁻¹, and so φ(rs) = φ(sr⁻¹). Using the properties of a homomorphism, we can write:

φ(r)φ(s) = φ(s)φ(r⁻¹) = φ(s)φ(r)⁻¹

Since φ(s) = 1, this simplifies to:

φ(r) = φ(r)⁻¹

But this means that φ(r) is its own inverse, and so φ(r)² = 1. However, we also know that rn = 1, and so φ(rn) = 1. Using the properties of a homomorphism, we can write:

φ(rn) = φ(r)ⁿ = (φ(r)²)ⁿ/2 = 1ⁿ/2 = 1

But this means that n/2 must be an integer, which contradicts the fact that n > 2. Therefore, there does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

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Answer:

-4.4166

Step-by-step explanation:

-23/3+(-11/2)+35/4

-24/3-11/2+35/4

use bodmas

addition first then subtract and u find your LCM.

11/2+35/4=57/4 or 14 1/4

LCM=4

-23/3-57/4=-263/12 or -21 11/12.

LCM=12

final answer= -21 11/12.

To prove that C is a field, we need to show that it satisfies the following 11 axioms of a field:

C is closed under addition: For all a, b ∈ C, a + b ∈ C.

C is closed under multiplication: For all a, b ∈ C, ab ∈ C.

C is associative under addition: For all a, b, c ∈ C, (a + b) + c = a + (b + c).

C is associative under multiplication: For all a, b, c ∈ C, (ab)c = a(bc).

C has an additive identity: There exists 0 ∈ C such that for all a ∈ C, a + 0 = a.

C has a multiplicative identity: There exists 1 ∈ C such that for all a ∈ C, a1 = a.

C has additive inverses: For all a ∈ C, there exists b ∈ C such that a + b = 0.

C has multiplicative inverses: For all a ≠ 0 ∈ C, there exists b ∈ C such that ab = 1.

C is commutative under addition: For all a, b ∈ C, a + b = b + a.

C is commutative under multiplication: For all a, b ∈ C, ab = ba.

Multiplication distributes over addition: For all a, b, c ∈ C, a(b + c) = ab + ac.

Proofs of the 11 axioms:

To show that C is closed under addition, we can use the fact that the sum of two complex numbers is also a complex number. That is, for any a, b ∈ C, a + b = (a + bi) + (b + di)i, where i is the imaginary unit. This is clearly a complex number, so C is closed under addition.

To show that C is closed under multiplication, we can use the fact that the product of two complex numbers is also a complex number. That is, for any a, b ∈ C, ab = (a + bi)(b + di) = (ab - bd) + (ad + bc)i, which is also clearly a complex number, so C is closed under multiplication.

To show that C is associative under addition, we can use the associative property of addition for real numbers. That is, for any a, b, c ∈ C, (a + b) + c = a + (b + c).

To show that C is associative under multiplication, we can use the associative property of multiplication for real numbers. That is, for any a, b, c ∈ C, (ab)c = a(bc).

To show that C has an additive identity, we can use the fact that the real number 0 is also a complex number, and that for any a ∈ C, a + 0 = a.

To show that C has a multiplicative identity, we can use the fact that the real number 1 is also a complex number, and that for any a ∈ C, a1 = a.

To show that C has additive inverses, we can use the fact that for any a ∈ C, there exists a complex number -a such that a + (-a) = 0. This is because the real numbers have additive inverses, and the imaginary unit i has an additive inverse -i.

To show that C has multiplicative inverses, we can use the fact that for any a ≠ 0 ∈ C, there exists a complex number 1/a such that a(1/a) =

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Using the angle addition postulate, we found that the measure of the angle, ∠LMN is 135°.

What is the angle addition postulate?

The measure of the angle created by the non-common sides of two adjacent angles is equal to the total of the measures of the two adjacent angles. The angle addition postulate in geometry asserts that if we position two or more angles side by side, with a shared vertex and an arm between each pair of angles, the sum of those angles will be equal to the sum of the resulting angle. Adjacent angles are those two angles that are connected by a common ray. Any pair of neighbouring angles in mathematics can be applied to this postulate.

The figure is given below.

We can solve this using the angle addition postulate.

Given,

m∠FMN = 99°

m∠LMF = 36°

We are asked to find the measure of angle ∠LMN.

According to the angle addition postulate,

m∠FMN + m∠LMF =  m∠LMN

99 + 36 = m∠LMN

m∠LMN = 135°

Therefore using the angle addition postulate, we found that the measure of the angle, ∠LMN is 135°.

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Yes, Tanner has enough spray paint for his arrow.

What is an Area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.

Given : paint available in can = 12 ft²

We know that the arrow is comprised of a triangle and a rectangle.

So, the area of given arrow = area of rectangle + area of triangle

Now, area of triangle = 1/2 ×base × height

                                    = 1/2 × 3 × (6 - 5 1/3)

                                    = 3/2 × ( 6 - 16/3)

                                    = 3/2 × ( 18-16)/3

                                    = 3/2 × 2/3

                                    = 1 ft²

Similarly, area of rectangle =  length × breadth

                                             = 5 1/3 × 2

                                             = 16/3 × 2

                                             = 32/3 ft²

Hence, area of arrow = area of triangle +area of rectangle

                                    = 1 + 32/3

                                    = 35/3 ft²

                                    = 11.67 ft²

So, he has sufficient paint to cover the arrow.

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Answer:

n ≤ 6.5

Step-by-step explanation:

43.5 + n ≤ 50

43.5 + n - 43.5 ≤ 50 - 43.5

n ≤ 6.5

$120,000

The formula for an exponential function passing through the points (-2,--) and (2, 75) is: y = 75 * 2x + 2. To answer the question about the house valued at $120,000, the value of the house is not related to an exponential function. Therefore, the answer is that the value of the house is $120,000.

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The requried rate of change of the function f[x] on the interval -5 ≤ x ≤ 0 is F(x)' = -11/5.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
From the graph we have,
F(-5) = 1 and F(0) = -10

So the rate of change is given as,
F(x)' = F(0) - F(-5) / 0 + 5
F(x)' = -10 - 1 / 5
F(x)' = -11/5

Thus, the requried rate of change of the function f[x] on the interval -5 ≤ x ≤ 0 is F(x)' = -11/5.

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The error that occurred is called a transposition error.

A transposition error is when two digits are reversed or transposed in an accounting transaction. In this case, the debit that was supposed to be made to the Purchaser account was instead debited to the Accounts Payable account.

To correct this error, we need to make a journal entry that reverses the incorrect entry and then make the correct entry. The journal entry to reverse the incorrect entry would be:

Debit: Accounts Payable $5,000
Credit: Purchaser $5,000

This entry reverses the incorrect debit to Accounts Payable and the incorrect credit to Purchaser.

Next, we need to make the correct entry, which is:

Debit: Purchaser $5,000
Credit: Accounts Payable $5,000

This entry correctly debits the Purchaser account and credits the Accounts Payable account.

After these two journal entries are made, the accounts will be correctly balanced and the error will be corrected.

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complete question

A P^(5),000 debit to be made to the Purchaser account was debited to Accounts payabhe instead. which type of error is found here?

As we proved that there exists a δ > 0 such that the function f(x) > 0 for all x ∈ (p − δ, p + δ).

To prove this, we will use the definition of continuity of a function. According to this definition, for a function to be continuous at a point p, the limit of the function as x approaches p must be equal to the value of the function at p.

In this case, we know that f(p) is greater than 0. So, if we can find a δ such that for all x within δ units of p, f(x) is also greater than 0, then we can show that f is continuous at p.

Let's begin by assuming that there is no such δ, i.e., for any δ > 0, there exists an x within δ units of p such that f(x) is less than or equal to 0. This means that we can find a sequence of points xn that approach p such that f(xn) is less than or equal to 0 for all n.

Since f is continuous, we know that lim xn → p f(xn) = f(p) (by the definition of continuity). But we also know that f(p) is greater than 0, so lim xn → p f(xn) cannot be less than or equal to 0. This is a contradiction, which means our assumption that there is no δ such that f(x) is greater than 0 for all x within δ units of p must be false.

Therefore, there must exist a δ > 0 such that f(x) is greater than 0 for all x within δ units of p, which proves our original statement.

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Complete Question:

Let f : (a, b) → R be continuous such that for some p ∈ (a, b), f(p) > 0. Show that there exists a δ > 0 such that f(x) > 0 for all x ∈ (p − δ, p + δ).

Answer:

reads 64 pages in one hour

Step-by-step explanation:

For simplicities' sake, we'll convert 1/4 of an hour into 15 minutes (60 minutes x 1/4 = 15 mins)

Since we have a ratio, of 16 pages to 15 mins, we can create the ratio by making a fraction of 16/15. Since we want to get to 1 hour, to find how many pages she read in an hour, we can multiply the top and bottom (to equalize) by 4 (because 4 x 15 = 60).

16•4/15•4

64/60

Because of this, we can see that the ratio is now 64 pages to 60 mins or one hour. Therefore, she reads 64 pages in one hour.

If you liked this answer, please mark brainliest!

Answer:

64

Step-by-step explanation:

To do this problem you have to figure out Michelle's hourly rate for reading pages. We are given that she will read 16 pages in 1/4 of an hour. This means that in 15 minutes (60 minutes in an hour / 4 for the 1/4 an hour) she will read 16 pages. We only have 15 minutes though and need 60 minutes so 60/15 gives us 4. This means that we will need 4, 15 minute periods to get to a hour. So 4*15minutes = 60 minutes or one hour and 16pages*4 = 64 pages. So in one hour she will read 64 pages.

A faster way to do this is to just multiply both sides by the recripical.

16 pages = 1/4 hour

*4/1              *4/1

64 pages = 4/4 hour

64 pages = 1 hour

Training a regression network with squared error loss requires two steps: the forward pass and the backward pass.

Forward Pass:

Backward Pass:

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The total number of hours Eric worked is 7 3/4 hours.

What is addition in mathematics?

Addition is one of the four basic arithmetic operations in mathematics, along with subtraction, multiplication, and division. Addition is the process of combining two or more quantities or numbers to find their sum, or total. The symbol used to represent addition is the plus sign (+).

For example, if we want to find the sum of 3 and 4, we would write:

3 + 4 = 7

The number 3 and the number 4 are called addends, and the result of the addition operation is called the sum. Addition can involve whole numbers, fractions, decimals, and even negative numbers.

Addition has many applications in mathematics, science, and everyday life. It is used to calculate simple arithmetic problems, such as adding up the cost of items in a shopping cart, as well as more complex calculations, such as adding up the values in a data set or solving equations in algebra.

To find the total number of hours Eric worked in the neighborhood garden, we need to add the number of hours he worked on Monday and Wednesday.

Eric worked 3 1/2 hours on Monday, which can also be written as 7/2 hours.

Eric worked 4 1/4 hours on Wednesday, which can also be written as 17/4 hours.

To add these two amounts, we need to find a common denominator. The smallest number that both 2 and 4 divide into is 4. So we can convert 7/2 to 14/4 by multiplying the numerator and denominator by 2:

7/2 = 14/4

Now we can add the two fractions:

14/4 + 17/4 = 31/4

This is the total number of hours Eric worked in the neighborhood garden, in fraction form. To write it as a mixed number, we can divide the numerator by the denominator:

31 ÷ 4 = 7 with a remainder of 3

So the total number of hours Eric worked is 7 3/4 hours.

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Answer:

See explanation

Step-by-step explanation:

50 is 5*10, so multiply 3 by 5 also to get 5 and 15/50. First answer is 15

5 and 15/50 is also equal to 4 and 65/50. second answer is 65

carry the numerator on the second line to get 30 for the third answer.

finally, subtract 3 from 4 to get 1, and subtract 30 from 65 to get 35/50.

last two answers are 1, and 35.

Answer:

The range stays 48°

Step-by-step explanation:

The range is the difference between the highest and lowest values in the data set. Before adding 80.2°, the highest temperature is 105° and the lowest temperature is 57°, so the range is 105° - 57° = 48°.

After adding 80.2°, the highest temperature becomes 105° + 80.2° = 185.2° and the lowest temperature becomes 57° + 80.2° = 137.2°. So the new range is 185.2° - 137.2° = 48°.

Therefore, the range stays the same at 48°. The answer is: The range stays 48°.

Answer:

The range stays 48°

Step-by-step explanation:

The solution to the system of equations is (x, y) = (-2, 8).15)Unfortunately, the question is incomplete, and I cannot provide an answer without knowing the complete question.

The two given equations are as follows:2x + y = 2x = (1/2)y + 6To solve the above system of equations, we will use the substitution method. First, we will substitute the value of x from the second equation to the first equation.2(1/2)y + 6 + y = 22.5y + 6 = 2Subtracting 6 from both sides, we get:2.5y = -4Dividing both sides by 2.5, we get:y = -4/2.5y = -8/5Substituting the value of y in the second equation to get the value of x:x = (1/2)(-8/5) + 6Multiplying and simplifying:x = -4/5 + 30/5x = 26/514)The given system of equations is:x + y = 6-2x + y = -3We will use the elimination method to solve the system of equations. Adding both the equations, we get:2y = 32y = 16y = 8Substituting the value of y in any of the equations to get the value of x:x + 8 = 6x = 6 - 8x = -2Therefore, the solution to the system of equations is (x, y) = (-2, 8).15)Unfortunately, the question is incomplete, and I cannot provide an answer without knowing the complete question.

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When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.

What is a polygon ?

A polygon is a two-dimensional closed shape made up of line segments. It has three or more straight sides and angles. Some common examples of polygons are triangles, rectangles, squares, pentagons, hexagons, and octagons.

The properties of a polygon, such as the number of sides, angles, and vertices, depend on its type and shape.

The condition that will not create a gap or an overlap at a vertex of polygons is "The sum of the measures of the angles is equal to 360°."

When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.

This condition is also known as the angle sum property of polygons, and it states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

Therefore, When the sum of the angles is exactly 360 degrees, there is no overlap or gap at the vertex.

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Answer:

The answer is B

Step-by-step explanation:

To solve this, we need to combine like terms.
(9c-8d) + (2c-6) + (-d+3)
9c + 2c - 8d - d - 6 + 3
11c - 8d - d - 6 + 3
11c - 9d - 6 + 3
11c - 9d - 3

If there are 240 students in the sixth-grade class then Naomi received 336 votes.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Bridgette and Naomi ran for sixth-grade class president.

In the election, every sixth-grade student voted for either Bridgette or Naomi.

Bridgette received 5 votes for every 7 votes Naomi received.

the first figure represents 5:7 ratio in the story.

Since Bridgette received 5 votes for every 7 votes Naomi received, Bridgette received 5/7 of the total votes and Naomi received 2/7 of the total votes.

We know that the total number of votes cast is equal to the total number of students in the class, which is 240.

Therefore, we can set up the equation:

5/7(x) + 2/7(x) = 240

Simplifying the equation, we get:

(5x + 2x)/7 = 240

7x/7 = 240

x = 240 × 7/5

x = 336

Therefore, If there are 240 students in the sixth-grade class then Naomi received 336 votes.

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The simplified trigonometric expression is sin(a).

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given trigonometric expression is,

=> [tex]\frac{sec(a)}{cot(a)+tan(a)}[/tex]

We know that [tex]cot(a)=\frac{cos(a)}{sin(a)}[/tex] and [tex]tan(a)=\frac{sin(a)}{cos(a)}[/tex] and [tex]sec(a)=\frac{1}{cos(a)}[/tex]

Then,

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos(a)}{sin(a)}+\frac{sin(a)}{cos(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos^2a+sin^2a}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{1}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{1}{cos(a)}\times\frac{sin(a)cos(a)}{1}[/tex]

=> sin a

Hence the simplified trigonometric expression is sin(a).

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The solution to 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.

Inequality is the unequal distribution of opportunities, resources, or rights among people or groups. It can be found in wealth, income, health, education, access to services and resources, and legal rights. Inequality is a social phenomenon that affects people differently depending on race, gender, age, or background. Inequality can be a result of unequal access to resources, differences in power dynamics, or the unequal distribution of resources among people or groups. It can lead to disparities in health, education, and economic outcomes for those who experience it. Inequality can be addressed through policies that promote equity and inclusion, such as targeted education initiatives and access to employment opportunities.

The reason this is happening is because when solving inequalities, we must isolate the variable on one side of the inequality sign. In this case, we can do this by adding 162 to both sides of the inequality. This will move the -21 to the other side and the result is a>-162.

In order to ensure that the solution is correct, it is important to check the answer by substituting a value larger than -162 into the inequality. If the value satisfies the inequality, then the solution is correct.

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The sοlutiοn tο 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.

Inequality is the unequal distributiοn οf οppοrtunities, resοurces, οr rights amοng peοple οr grοups. It can be fοund in wealth, incοme, health, educatiοn, access tο services and resοurces, and legal rights. Inequality is a sοcial phenοmenοn that affects peοple differently depending οn race, gender, age, οr backgrοund. Inequality can be a result οf unequal access tο resοurces, differences in pοwer dynamics, οr the unequal distributiοn οf resοurces amοng peοple οr grοups. It can lead tο disparities in health, educatiοn, and ecοnοmic οutcοmes fοr thοse whο experience it. Inequality can be addressed thrοugh pοlicies that prοmοte equity and inclusiοn, such as targeted educatiοn initiatives and access tο emplοyment οppοrtunities.

The reasοn this is happening is because when sοlving inequalities, we must isοlate the variable οn οne side οf the inequality sign. In this case, we can dο this by adding 162 tο bοth sides οf the inequality. This will mοve the -21 tο the οther side and the result is a>-162.

In οrder tο ensure that the sοlutiοn is cοrrect, it is impοrtant tο check the answer by substituting a value larger than -162 intο the inequality. If the value satisfies the inequality, then the sοlutiοn is cοrrect.

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Complete question:

What is the solution to 3/4a>-16?

a>-21 1/3

a<-21 1/3

a>21 1/3

a<21 1/3

The approximate area of the school is 22857 kilometer square.

The approximate area of the school can be found by multiplying the fraction of space covered by the STEM Innovation Academy building by the total area of the space.

In this case, the fraction of space covered is (4)/(7) and the total area of the space is 40,000 square kilometres.

To find the approximate area of the school, we can multiply these two values together:

(4)/(7) * 40,000 = 22,857.14

Therefore, the approximate area of the STEM Innovation Academy building is 22,857.14 square kilometres.

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Given vectors are v1 = |2| v2 = |3| v3 = |1| |2| |1| |h| |-4| |-4| |4| Let's consider the vectors are linearly dependent. If they are linearly dependent, then the rank of the matrix will be less than 3. So, Values of the parameter h are |2| 3 1 |2| 1 h |-4| |-4| 4

For the matrix to have a rank of less than 3, it must satisfy the following condition : |2| 3 1 |2| 1 h |-4| |-4| 4It can be rewritten as follows: |2| 3 1 |2| 1 h |-4| |-4| 4It can be simplified as follows: |2| 3 1 |2| 1 h |-4| |-4| 4. The matrix can be reduced to the following form: |2| 3 1 |2| 1 h |-4| |-4| 4, By subtracting R1 from R2, we get: |-1| 0 |h-1| |-6| |-h| |-4| |-4| 4The determinant of this matrix is: -4h + 4 + 8h = 4h + 4

Now, let's evaluate the matrix's rank. We can observe that the matrix's second row is equal to twice the matrix's first row. So, the rank of the matrix is 2.Since the rank of the matrix is 2, the given vectors are linearly dependent if h = -1.

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Answer:

8x^2-4x-15

Step-by-step explanation:

To find the sum of the functions, we add them together:

f(x) + g(x) = (5x + 4) + (3x² - 9)

Simplifying, we get:

f(x) + g(x) = 3x² + 9x - 5

Therefore, the sum of the functions is 3x² + 9x - 5, which is option D.

The domain of a relation is the set of all the first elements of the ordered pairs in the relation, and the range of a relation is the set of all the second elements of the ordered pairs in the relation.

So, for the given relation {(5,0),(8,4),(5,2),(-2,4)}, the domain would be {5, 8, -2} and the range would be {0, 4, 2}.

To find the domain, we simply take the first element of each ordered pair and put them in a set. Similarly, to find the range, we take the second element of each ordered pair and put them in a set.

Therefore, the domain of the relation is {5, 8, -2} and the range of the relation is {0, 4,2}.

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The two linear equations with infinitely many solutions and a y-intercept of -2 are y = x - 2 and y - x = -2.

We can use the y-intercept (-2) and another point on the line to calculate the slope. Since we are looking for infinitely many solutions, we can choose any point. Let's choose the point (0, 1):

slope = (y2 - y1) / (x2 - x1) = (-2 - 1) / (0 - 1) = -3

Now we know that the slope of one of the lines is -3. We can use this information to find the equation of the line. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Let's use the point (0, -2):

y - (-2) = -3(x - 0)y + 2 = -3xy = -3x - 2y = -3(0) - 2 = -2y = mx - 2y = -3x - 2y = x - 2y - x = -2

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