Select the correct answer.
If f(x) = 2x²-x-6 and g(x) = x2 - 4, find f(x) + g(x).

The area of the shape ABCD and EFGH are 64cm² and 25cm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

Since the sides of a square are equal. The area of a square is given as;

A = l²

For square ABCD,

one grid square represents 1 square cm

Therefore ,ABCD represents 8 square centimeters.

This means the area of square ABCD is given as;

A = 8²

= 64cm²

For square EFGH,

EFGH has 5 grid squares, therefore the area of the square is given as;

A = 5²

A = 25cm²

therefore the area of squares ABCD and EFGH are 64cm² and 25cm²

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The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

Postulate 2 states that if you have two distinct points, you can uniquely determine a line that passes through both of them. In other words, any two points in space define a line, and there is only one line that can pass through those two points.

This postulate is a fundamental concept in Euclidean geometry, which is the study of geometry based on the work of the ancient Greek mathematician Euclid.

This postulate is often used as a basic assumption or starting point in geometric proofs and constructions. It implies that a line is uniquely defined by just two points, and any additional points on that line can be determined by extending it infinitely in both directions.

It also implies that two distinct points always lie on exactly one line, and no more than one line can pass through them.

Postulate 2 is a fundamental principle in geometry and serves as the basis for many geometric theorems and proofs.

It helps establish the relationship between points and lines in Euclidean space, and it is used to reason about the properties and behavior of lines and points in geometric constructions, proofs, and demonstrations.

therefore, The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

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The maximum volume of the box is approximately 128.0in³.

Since the cardboard has dimensions of 8 inches by 12 inches, the largest possible length and width of the box are both 8 inches (since 8 is the smaller of the two dimensions).

Then we can cut two 8-inch by 8-inch squares from the cardboard to make the top and bottom of the box, and then cut out four 8-inch by 2-inch rectangles from the remaining cardboard to make the sides of the box.

The height of the box will be the same as the width of the 8-inch by 2-inch rectangles, which is 2 inches. Therefore, the maximum volume of the box is:

V = l × w × h = 8 in × 8 in × 2 in = 128 in³

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Answer:

Step-by-step explanation:

point m

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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The area of ​​the triangular pyramid is 787.27 mm²

The volume of a right-angled triangular pyramid  is given by the formula V = 1 3 × B × h, where B is the area of ​​the base of the triangle and h is the height (the distance from the apex to the base).

 To calculate the  area of ​​a triangular pyramid, we need to find the area and base of the four triangles.

First, we find the area of ​​the base of an equilateral triangle. The formula for the area of ​​an equilateral triangle is (sqrt(3)/4)*a², where a is the side length. Substituting a=19, we get:

Area of ​​base = (√(3)/4)*19²

= 207.39 mm²

Then we find the area of ​​one triangular surface. We can use the formula for the area of ​​a triangle, which is (1/2) the height of the base. The base of the triangle is the other side of an equilateral triangle with a length of 19 mm. The height of the triangle is the  height of the diagonal of the pyramid, which is 17 mm. Using the Pythagorean theorem, we can find the length of the height of the triangle:

h = √ (slope² - (1/2 base)²)

= √(17² - (1/219)²)

= 15.27 mm

Thus, the area of ​​one triangular surface is:

Area of ​​triangle = (1/2)1915.27

= 144.97 mm²

Since there are four triangular faces, the total area of ​​the triangular faces is:

Total area of ​​triangular surfaces = 4 × 144.97

= 579.88 mm²

Finally, the  area of ​​the pyramid is the sum of the area of ​​the base and the area of ​​the four triangular sides:

Area = area  of ​​base Total area of ​​triangular surfaces

= 207.39 + 579.88

= 787.27 mm²

Therefore the  area of ​​the triangular pyramid is 787.27 square millimeters.

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The percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio is 55.56%.

Time spent using the internet = 4 hours

Time spent doing chores = 4 hours

The time spent listening to the radio = 10 hours

The total time spent during the week is 4 + 4 + 10 = 18 hours

The percentage of this total time that is spent listening to the radio is:

(10 hours / 18 hours) x 100% =55.56%

This is basic arithmetic operations and is used in calculation of numbers.

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The equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

What is the rate?

In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

The initial population is 2.33 × 10¹.

After one year, the population will be:

P₁ = 2.33 × 10¹ + 0.07 × 2.33 × 10¹

P₁ = 2.33 × 10¹ (1 + 0.07)

After two years, the population will be:

P₂ = P₁ + 0.07 P₁

P₂ = P₁ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)²

After three years, the population will be:

P₃ = P₂ + 0.07 P₂

P₃ = P₂ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)³

And so on, until after six years:

P₆ = 2.33 × 10¹ (1 + 0.07)⁶

Simplifying the expression, we get:

P₆ = 2.33 × 10¹ (1.07)⁶

Therefore, the equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

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It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  [tex]9 \frac{1}{10}[/tex]   to a decimal number:

⇒ [tex]9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}[/tex]

⇒ [tex]\frac{91}{10}[/tex]  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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The magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2[/tex] evaluated using the kinematic equation of motion.

We can use the kinematic equation of motion to determine the acceleration of the car at the given distance:

[tex]s = ut + (1/2)at^2[/tex]

where s=distance traveled, u = initial velocity, a =acceleration, and t =

time taken.

We can rewrite this equation as:

[tex]t = (2s/u)^(1/2)[/tex]

Substituting the given values, we get:

[tex]t = (2(100)/20)^(1/2)[/tex] = 2.236 seconds

Now, we can use the kinematic equation:

v = u + at

where v is the final velocity.

We know the initial velocity u is 20 m/s, and the car's acceleration At=0.5 [tex]m/s^2[/tex]. To find the final velocity, we can use the kinematic equation again:

[tex]s = ut + (1/2)at^2 + vt[/tex]

Rearranging and substituting the given values, we get:

[tex]v = (s - ut - (1/2)at^2) / t[/tex]

v = (100 - (20)(2.236) - (1/2)(0.5)(2.236)^2) / 2.236

v = 27.839 m/s

Now we can evaluate the acceleration using the equation:

a = (v-u) / t

Substituting the given values, we get:

a = (27.839 - 20) / 2.236

a = 3.49[tex]m/s^2[/tex] (rounded to two decimal places)

Therefore, the magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2.[/tex]

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Answer:

g(-5) = 8(-5) - 24 = -40 - 24 = -64

g(5) = 8(5) - 24 = 40 - 24 = 16

y = 8x - 24

8x = y + 24

x = (1/8)(y + 24) = (1/8)y + 3

g^-1(x) = (1/8)x + 3, -64 < x < 16

Answer:

28%

Step-by-step explanation:

Let's assume that there are 2x girls and 3x boys in the school, as given the ratio of girls to boys is 2:3. Therefore, the total number of students in the school is 5x.

According to the problem, 25% of the girls have school dinners. So, the number of girls having school dinners is 0.25*2x = 0.5x.

Similarly, 30% of the boys have school dinners. So, the number of boys having school dinners is 0.3*3x = 0.9x.

Therefore, the total number of students having school dinners is 0.5x + 0.9x = 1.4x.

The percentage of students having school dinners can be found by dividing the total number of students having school dinners by the total number of students in the school and multiplying by 100%.

So, the percentage of students having school dinners is (1.4x/5x) * 100% = 28%.

Hence, the total percentage of students at the school who have school dinners is 28%.

To verify the answer, let's consider a numerical example.

Let's assume there are 200 students in the school, out of which 2/5 (i.e., 40%) are girls and 3/5 (i.e., 60%) are boys.

According to the problem, 25% of the girls have school dinners, which is 0.25 * 2/5 * 200 = 20 students.

Similarly, 30% of the boys have school dinners, which is 0.3 * 3/5 * 200 = 36 students.

Therefore, the total number of students having school dinners is 20 + 36 = 56.

The percentage of students having school dinners is (56/200) * 100% = 28%.

Hence, the answer is verified.

Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:

# Load HardyWeinberg package

library(HardyWeinberg)

# Load Mourant dataset

data(Mourant)

# Extract the genotype counts for the 206th row

counts <- Mourant[206, 2:4]

# Calculate the MLE of M allele frequency

mle <- hw_mle(counts)

# Extract the MLE of M allele frequency

mle_M <- mle$p[2]

Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.

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Answer:

51.1 to nearest tenth of a degree.

Step-by-step explanation:

Sin x = 7/9

x = 51.05756 degrees

Answer:

m = 7√2/2

n = 7√2/2

Step-by-step explanation:

sin45 = m/7

√2/2 = m/7

m = 7√2/2

cos45 = m/7

√2/2 = m/7

m = 7√2/2

A student who does not have a sister has a 2/9 chance of having a brother.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It's a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an occurrence is estimated by dividing the number of possible outcomes by the number of ways the event might occur.

Consider the following events:

"Has a brother"

"Doesn't have a sister," says B.

The probability of occurrence A given event B is written as P(A|B). We can use Bayes' theorem to write:

P(A|B) equals P(B|A) * P(A) / P(B).

where P(B|A) represents the probability of not having a sister given that the student has a brother, P(A) represents the probability of having a brother (equal to the proportion of students who have a brother), and P(B) represents the probability of not having a sister (equal to the proportion of students who do not have a sister).

We can use the table values to fill in the blanks:

P(B|A) = 2 / (5 + 2) = 2/7

P(A) = (5 + 2) / (5 + 2 + 9 + 7) = 7/23

P(B) = (2 + 7) / (5 + 2 + 9 + 7) = 9/23

Plugging these values into the formula, we get:

P(A|B) = (2/7) * (7/23) / (9/23) = 2/9

Therefore, A student who does not have a sister has a 2/9 chance of having a brother.

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Inequality in standard form:

5x² - 40x - 45 ≤ y ≤ x² + 8x + 9 and y ≤ x² - 8x - 9 and y ≥ 5x² + 40x + 45

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal.

To find the inequality that represents the shaded region, we can first simplify each inequality and then combine them using "and" or "or" operators as necessary.

Starting with each inequality:

y ≥ x² + 8x + 9: This is a parabola that opens upwards and has a vertex at (-4,1). The inequality means that all points above or on the parabola are included in the shaded region.

y ≥ x² - 8x - 9: This is a parabola that opens upwards and has a vertex at (4,-1). The inequality means that all points above or on the parabola are included in the shaded region.

y ≤ 5x² - 40x - 45: This is a parabola that opens upwards and has a vertex at (4,-125). The inequality means that all points below or on the parabola are included in the shaded region.

y ≥ 5x² + 40x + 45: This is a parabola that opens upwards and has a vertex at (-4,-125). The inequality means that all points above or on the parabola are included in the shaded region.

Combining the inequalities using "and" or "or" operators:

Since all of the inequalities have "y ≥" or "y ≤" in them, we know that the shaded region is above or below some combination of the parabolas. Specifically, the shaded region is above the first two parabolas and below the second two parabolas. Therefore, we can use "and" to combine the inequalities as follows:

y ≥ x² + 8x + 9 and y ≥ x² - 8x - 9 and y ≤ 5x² - 40x - 45 and y ≤ 5x² + 40x + 45

This gives us the final inequality in standard form:

5x² - 40x - 45 ≤ y ≤ x² + 8x + 9 and y ≤ x² - 8x - 9 and y ≥ 5x² + 40x + 45

Note that we flipped the direction of the inequality for the last term (y ≥ 5x² + 40x + 45) to make it consistent with the other three inequalities.

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Answer:

674

Step-by-step explanation:

Upon answering the query we can say that  As a result, in rectangle  AC is 75 units long.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It is also known as an equiangular quadrilateral since each of its angles is equal. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with a rectangle-like form has equal parallel sides and four 90-degree vertices. Due of this, it is occasionally referred to as a "equirectangular rectangle". Due to its opposing sides' equal and parallel lengths, a rectangle is occasionally referred to as a parallelogram.

The diagonals of a rectangle are of equal length. As a result, we have:

[tex]AC = BD\\3x + 15 = 4x - 5\\15 = x - 5\\x = 20\\[/tex]

Now, we can change the equation for AC to use this value of x:

[tex]AC = 3x + 15\\AC = 3(20) + 15\\AC = 60 + 15\\AC = 75\\[/tex]

As a result, AC is 75 units long.

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The quotient number is 1.

What is Quotient?

When two quantities are divided by one another, the result is a quotient. The number of times a quantity (the divisor) may be divided into a second amount (the dividend) without a remainder is known as the quotient in the division.

In order to express the given data, let's first set up the equation as follows:

(number/8) + 1/2 = 5/8

(x/8) + 1/2 = 5/8

We need to isolate the number as a variable on one side of the equation so that we can solve it.

Let's start by adding the fractions to simplify the left side of the equation:

(x/8) + 4/8 = 5/8

Next, we can combine the fractions further:

x/8 = 1/8

We can multiply both sides of the equation by 8 to find the number as follows:

number = 1

Therefore, the number is 1.

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If the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

Graph is a data structure composed of nodes (vertices) and edges. It is a non-linear data structure that is used to represent relationships between objects, events, or ideas. Graphs are widely used in computer science, mathematics, engineering, and other fields for representing various types of data. Graphs can be used to represent a wide variety of data sets, including networks, social relationships, and even biological systems. Graphs can also be used to identify patterns, trends, and correlations in data.

The graph below shows the relation between time (hours) and distance (km) for a train trip that lasted from 0 to 7 hours.

The line of best fit is a linear line with a positive slope, indicating that the distance travelled increases as the time spent travelling increases. Therefore, it can be estimated that if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be calculated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis, which is approximately 90 km.

In conclusion, if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

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Complete questions as follows-
On the grid below, draw a graph of the relationship between  and  for a trip that lasted from 0to 7 hours.  8Time (hours) If the train was traveling nonstop, how many  would it travel in 5.5 hours?

When both t and d are zero, we can immediately see that c = 0 because the train begins at rest. Additionally, the rate of change is the constant speed, making m = 95. Thus, d = 95t is the necessary relationship.

A graph is a type of data structure that consists of edges and nodes (vertices). It is a non-linear data structure intended to depict connections between things, occasions, or concepts. Graphs are frequently used to represent numerous forms of data in computer science, mathematics, engineering, and other disciplines. A wide range of data sets, including networks, social relationships, and even biological systems, can be represented using graphs. Graphs can also be used to spot trends, correlations, and patterns in data.

The necessary equation should be d = mt +c,

Where the arbitrary real constants m and c are used.

When t = 1, d = 95

so that 95= m+c ---> (1)

Also, when t=2, d = 190,

hence 190 = 2m+c ---> (2)

When the first equation is taken out and the second equation is added back in,

we get 2m+c-m-c = 190-95 or, m = 95.

When this value of m is substituted in the first equation,

we get 95 = 95+c so that c = 95-95 = 0.

Thus, the require3d equation is d = 95t. Since 95*3 = 285 and 95*4= 380, All of the given facts are satisfied by this equation.

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The complete question and graph attached below,

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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According to the given data,the equation y = 0.5x is correctly represented by the graph.

Graphs are visual representations of data or mathematical functions. They are useful tools for displaying and analyzing information in a clear and concise way. Graphs can be used to show trends, patterns, and relationships between different variables.

The statement "The equation y = 0.5x is correctly represented by the graph" is true.

The given equation y = 0.5x represents a proportional relationship between the variables x and y, where y is half of x. This means that as x increases, y increases in proportion to x.

The graph shown is a straight line that passes through the points (0,0) and (9,3), and this line represents the proportional relationship between x and y described by the equation y = 0.5x.

Therefore, the equation y = 0.5x is correctly represented by the graph.

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We have the reasons given as;

<4 + <3 = 180 degrees; supplementary angles

m<1 + m<2 + m<3 = 180; sum of angles in a triangle

m<1 + m<2 = m<4; substitution of equality

Angle n and n are corresponding angles

angle n + <3 are supplementary angles

First, we need to know the following deductions;

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Hence, after finding the solution, Jimmy discovered 16 dimes and 15 nickels. By assuming variables, this problem can be resolved.

In mathematics, a variable is a symbol or letter that designates a value of the variable or amount. Variables are fundamental to many fields of science, technology, and mathematics and are used to formulate and solve equations.

Let's use constants to depict Jimmy's discovery of nickels and dimes.

Let x be the quantity of nickels and y be the quantity of dimes.

We may create the following pair of equations using the data:

Formula 1: x + y = 31 

Equation 2 reads: 0.05x + 0.10y = 2.35, which equals the total worth of the coins at $2.35.

The methods of substitution and elimination can be used to calculate the characteristics of x and y. Substitutions made

Equation 1 might be used to convert this x into units of y: x = 31 - y

In Equation 2, replace x with the following expression: 0.05(31 - y) + 0.10y = 2.35

Simplify the equation and find y as follows: 1.55 - 0.05y + 0.10y = 2.35 0.05y = 0.80 y = 16

Jimmy therefore found 16 pennies.

Equation 1 can be changed to y = 16 to determine the amount of nickels: x + 16 = 31 x = 15

Jimmy therefore discovered 15 nickels.

Jimmy discovered 16 dimes and 15 nickels as a result.

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If all nickels and dimes and came out to a total amount of $2.35. Jimmy found 15 nickels and 16 dimes.

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's assume that Jimmy found x number of nickels and y number of dimes. Then we can write two equations based on the given information:

The total number of coins is 31:

x + y = 31

The total value of the coins is $2.35:

0.05x + 0.10y = 2.35

To solve for x and y, we can use the first equation to solve for x in terms of y:

x = 31 - y

Then we can substitute this expression for x into the second equation:

0.05(31 - y) + 0.10y = 2.35

1.55 - 0.05y + 0.10y = 2.35

0.05y = 0.80

y = 16

So Jimmy found 16 dimes. To find the number of nickels, we can substitute this value of y into either of the two equations we started with. Let's use the first equation:

x + y = 31

x + 16 = 31

x = 15

Therefore, Jimmy found 15 nickels and 16 dimes.

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Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

Answer:

[tex]y =- \frac{3}{10} x + \frac{17}{20}[/tex]

Step-by-step explanation:

We are given the line 6x+20y=17, and we want to write it in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept, hence the name.

As we can see, in slope-intercept form, y is by itself on one side. So, we should solve the equation for y.

To do that, we can start by subtracting 6x from both sides.

6x + 20y = 17

-6x             -6x

_________________

20y = -6x + 17

Now, we should divide both sides by 20 to isolate y.

20y = -6x + 17

÷20   ÷20

_______________

[tex]y=-\frac{6}{20} x + \frac{17}{20}[/tex]

This can be simplified to:

[tex]y =- \frac{3}{10} x + \frac{17}{20}[/tex]

Based on the angle of two-tangent theorem, the value of x in the image is: x ≈ 4.

The angle of two-tangent theorem states that when two tangent lines intersect outside of a circle, the angle that they form has a measure equal to half the positive difference between the measures of the arcs intercepted by the angle.

Applying the theorem, we have:

70 = 1/2[(360 - 27x + 2) - (27x + 2)]

140 = 360 - 27x + 2 - 27x - 2

140 = 360 - 54x

140 - 360 = -54x

-220 = -54x

-220/-54 = x

x ≈ 4

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The first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would choose a salad was 0.64.

The idea of probability is used to calculate the possibility or probability of a specific occurrence.

It is a number between 0 and 1, where 0 indicates that the event is inconceivable and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using fractions, decimals, or percentages.

There is a 0.2 likelihood that any student will choose a salad if their lunch tastes are assumed to be independent of one another's.

If you ask the principal understudy, there is a 0.2 chance that they will answer they prefer a dish of mixed greens. You move on to the next youngster if they don't want a salad.

Because the first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would prefer a salad was (1-0.2) (1-0.2) = 0.64.

Since none of the n-1 understudies who came before them did, the likelihood that the nth understudy would like a platter of mixed greens is only 0.2. 1-0.2n-1 is the likelihood that none of the first n-1 students will choose a salad.

Therefore, in order to identify a student who prefers salad, you must ask an expected number of students the following questions:

E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Even though this is an infinite series, by truncating it after a predetermined amount of words, we can approximate it. Let's imagine we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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Answer:

Step-by-step explanation: