I need help with this question how is dividing with an area model simlar to multiplaying with an area model differnt

The equation of the quadratic function is x² + x - 6

Note that functions are equations, laws or expressions showing the relationship between two variables.

These variables are;

From the information given, we have that;

x = 2 and  = -3 are the roots

Then,

(x -2)(x + 3)

expand the bracket, we get;

x² + 3x - 2x - 6

collect the like terms, we have;

x² + x - 6

Hence, the equation is x² + x - 6 = 0

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The value of (f - g)(-1) is 5.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -5x³ - 8x² - 4x + 3

g(x) = 3x³ - 2x² - 8x - 4

Now,

(f - g)(x)

= f(x) - g(x)

= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)

= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4

= -8x³ - 6x² + 4x + 7

Now,

(f - g) (-1)

Substitute x = -1.

= -8(-1)³ - 6(-1)² + 4(-1) + 7

= -8 x -1 - 6 - 4 + 7

= 8 - 6 - 4 + 7

= 8 - 10 + 7

= 15 - 10

= 5

Thus,

(f - g)(-1) = 5

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To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.

The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.

To solve mathematically, we can use the mode formula:

mode = value with the highest frequency

In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.

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The roots of the quadratic equation are -

{x} = 4 ± i(√2/2)

The  general form of a quadratic equation is -

y = f(x) = ax² + bx + c

Given is the quadratic equation as -

f(x) = x² - 8x + 17

We can write the roots of the equation as -

x = {- b ± √(b² - 4ac)}/2a

x = {8 ± √(64 - 68)}/2

x = {8 ± i√2}/2

x = 4 ± i(√2/2)

Therefore, the roots of the quadratic equation are -

{x} = 4 ± i(√2/2).

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The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.

Perimeter of the triangle is equal to

= 9x + 6

First side of the triangle = 5x

Second side of the triangle = 3x - 7

Let 'n' be the third side of the triangle

perimeter of the triangle = 9x + 6

⇒ 5x + 3x - 7 + n = 9x + 6

⇒ n + 8x - 7 = 9x + 6

⇒ n = 9x -8x + 6 + 7

⇒ n = x + 13

Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.

The above question is incomplete , the complete question is :

A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?

a. x + 13       b. x − 1            c. 8x − 7         d. 17x − 1

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On a coordinate plane, locations of the points (2 , -1) and (2 , 1) related by reflection across the x-axis.

It is given that the locations of the two points are (2 , -1) and (2 , 1).

We have to find the relation between two points.

From the given points (2 , -1) and (2 , 1), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.

If a figure is reflected across the y-axis, then we change the sign of y-coordinate and the x-coordinates remain same,

So, it is reflection across the x-axis.

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Answer: £122.45

Step-by-step explanation: 7.90*15.5

Answer: 109?

Step-by-step explanation:

If 5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar, We will be having 7 grams of sugar for one ounce of mango and 6 1/4 grams of sugar for one ounce of pineapple.

The problem states that we have 5 1/2 ounces of mango with 17 1/2 grams of sugar, and 4 ounces of pineapple with 25 grams of sugar. We are asked to determine the grams of sugar per ounce for each type of food. To determine the grams of sugar per ounce for each type of food, we can use the following calculations:

For mango: 5 1/2 ounces is equivalent to 11/2 + 1/2 = 2 ounces + 1 ounce/2, so we have 17 1/2 grams of sugar in 2 1/2 ounces of mango. To find the grams of sugar per ounce, we can divide 17 1/2 by 2 1/2, which gives us 7 grams of sugar per ounce of mango.

For pineapple: 4 ounces of pineapple has 25 grams of sugar. To find the grams of sugar per ounce, we can divide 25 by 4, which gives us 6 1/4 grams of sugar per ounce of pineapple.

Therefore, the grams of sugar per ounce for mango and pineapple are 7 and 6 1/4, respectively.

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Complete question is:

5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar. Determine the grams of sugar for ounce for each type of food​.

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'

Here we have

f(x) = - 6x + 14  and g(x) = - 2ˣ + 6  

The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows

=> - 6x + 14 =  - 2ˣ + 6    

=> - 6x + 8 = - 2ˣ    

=> - 6x + 8 = - 2ˣ

=> - 6x + 2ˣ = - 8          

By using the trial and error method

At x = 2

=> - 6(2) + 2² = -8

=> - 12 + 4 = -8

Therefore,

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

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The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.

An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).

A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."

Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).

In the given question,

The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).

S'(t) = 112

Therefore, when S'(t) = 112, t = 3.5.

This means that the rocket reaches its maximum height at t = 3.5 seconds.

Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.

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Answer:

7 and 7x

Step-by-step explanation:

We distributing these factors are the only that can make sense

First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:

[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]

The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].

The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:

[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]

The volume of the cone is about [tex]226.08 in^{3}[/tex].

Subtract 226.08 from 452.16 and you get 226.08.

The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].

The percentage increase of the gas would be 2.5%.

We can calculate the value of the percentage increase by the following formula,

percentage increase = (final value - initial value) / initial value × 100%

As per the given question, we have

initial value = $2.81 , and final value = $2.88

Substitute the values in the above formula, and we get

percentage increase= (2.88 - 2.81 ) / 2.81 × 100%

percentage increase = (0.07) / 2.81× 100%

percentage increase = 0.0249 × 100%

Apply the multiplication operation, and we get

percentage increase = 2.49%

Thus, the percentage increase of an item would be 2.5%.

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Answer:

Step-by-step explanation:

4 = d

5=1/5

3 the first one is 4x1/12 and 2x3/12

The dimensions are 5 units each

The area of the rectangle is 25 units

It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.

They are also described as expressions with mathematical operations.

From the information given, we have that;

x² - 5x + 3x - 15

To solve the quadratic equation, let us use the factorization method

Group the values in pairs

(x² - 5x) + (3x - 15)

factor the terms

x(x -5) +3(x - 5)

Then, x + 3 = 0

x = -3

And x - 5 = 0

x =5

But area of a rectangle is;

= Length× width

= 5 × 5

= 25 square units

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Answer:

Step-by-step explanation:

7/x^-8 = 7x^8

Answer: B

Step-by-step explanation:

if r is close to 1 (or -1) it means the relationship is strong, -0.2041 is really close to 0 so the data is most likely scattered and the association is weak

Answer:

Strong

Step-by-step explanation:

edge 2023

The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)

A graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:

y = ax^2 + bx + c,

where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.

A graph of a linear equation is a straight line. A general form of a linear equation is given by:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In this problem, the ordered-pairs will be the point in which they intersect with each other.

Looking carefully at the graph, the ordered pair will be at points

A = (-2, 7)

B = (2, -1)

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Answer:

The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.

Step-by-step explanation:

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

Let's call the total area of the common space "A". Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm, which means that one foot on the plan represents 4 cm in real life. So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3. And the area of the social area on the plan is (2A/3) / 4.

Area of the social area on the plan is (2A/3) / 4.

Here,

Let the total area of the common space "A".

Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm

So,

One foot on the plan represents 4 cm in real life.

So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3.

Thus the area of the social area on the plan is (2A/3) / 4.

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The correct statements are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

One leg of an isosceles triangle is 6√2 feet.

As, we know isosceles triangle two of its sides equal in length then the other side can be  6√2 feet.

Now, using Pythagoras theorem

H² = P² + B²

H² = (6√2)² + (6√2)²

H² = 72 + 72

H² = 144

H= 12 units

The statements that applies here are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

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Answer:

The answer is B and D

Step-by-step explanation:

I took the test.

let me know if you would like an explanation down in the comments!

D. The length is 18 inches and the width is 9 inch

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that the scale factor of the gardener is 1:15.

The dimensions of his drawing are 6 inches long by 3 inches wide.

Therefore the original dimensions are 6*15= 90 inches.

3*15= 45 inches.

The scale of his partner is 1:5.

So, we have to divide the original dimensions by 5.

The dimensions of the scale drawing are 90/5= 18 inches long

45/5=9 inches wide.

Therefore length is 18 inches and the width is 9 inches.

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Answer:

Any line except a vertical line represents a linear function.

Step-by-step explanation:

Any "diagonal" line is a linear function. Even a horizontal line represents a linear function. Only a vertical line does NOT represent a linear function.

The percentage increase in the population of the town is 12%.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Increase in population =  90,000 - 80,000  = 10,000

          Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%

Hence the percentage increase in the population of the town is 12%.

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Answer:

it will be £960

Step-by-step explanation:

first £800×20/100

simplify £8×20

£160= VAT

Total cost=VAT+ normal cost

£160+£800

=£960

The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2

The equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.

Another common form of the equation of a line is the slope-intercept form, which is represented as:

y = mx + b

where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

In this problem, we need to write the table of values and the find the slope of the line.

3x - 2y = 6

rewriting this equation;

2y = 3x - 6

y = 3x/2 - 3

when y = 0

0 = 3x/2 - 3

3x/2 = 3

3x = 2 * 3

3x = 6

x = 2

when x = 0

y = 3(0)/2 - 3

y = 0 - 3

y = -3

The slope of the line can be calculated using the two points from above.

slope (m) = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 0 - 2

m = 3/2

The slope is 3/2

The graph of the equation is attached below

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Answer:

1. SAS

2. Not congruent

Step-by-step explanation:

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

The solution is,

1. SAS

2. AAS

3. SAS

4. Not congruent.

Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.

here, we have,

we know that,

To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.

Meaning of congruent:

In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.

Two triangles are congruent:

In the case of triangles two factors should be considered:

1) Lengths of each side are equal.

2) Angles are equal.

This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.

now, we have,

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

Hence, 1. SAS

2. AAS

3. SAS

4. Not congruent.

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