(x+3)(x+7)=0

Problem answered, solution and why!

Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school.

f(x) = 8, x ≈ 8.

Generally, To isolate x, we need to take the natural logarithm (ln) of both sides of the equation:

ln(f(x)) = ln(4) + 1.5xln(1 + 0.3)

then we can divide both sides by 1.5ln(1 + 0.3)

x = (ln(f(x)) - ln(4)) / (1.5ln(1 + 0.3))

To find x when f(x) = 8, we can substitute 8 for f(x) and solve for x:

x = (ln(8) - ln(4)) / (1.5ln(1 + 0.3))

x ≈ 8

Therefore, when f(x) = 8, x ≈ 8.

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Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.

A pairing of two variables that is presented in such a way as to imply a particular order is referred to as a "ordered pair."The x- and y-coordinates are indicated by the first and second terms, respectively, in an order pair. Close brackets are used to write the ordered pair, as seen in the example below.

Here,

The following are the ordered pairs:

(x,y) = (1, 2), (6, 12), (12, 24), (18, 36) (18, 36)

The following is what arrows show us:

1 -> 2

6-> 12

12->24

18 -> 36

The relational mapping shown above is a function.

This is the case since every x-value points to the same y-value.

Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.

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Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.

In a graph, what exactly is a vertex?

The right response is, therefore, option B.

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Full Question-

What characteristics can you see in the graph of the quadratic function in the figure? Options for question 14: A: The vertex is at (-4,3), the y-intercept is at (5,0), the x-intercepts are at (0,1) and (0,5), and the symmetry axis is at (-4,3) B: The vertex is at (-3,-4), the y-intercept is at (0,5), the x-intercepts are at (1,0) and (5,0), and the symmetry axis is at (3); C: Vertex: (3, -4), y-intercepts: (1, 0), and (5, 0), x-intercept: (0, 5), axis of symmetry: (3 D) Axis of symmetry is at x = -3, vertex is at (-3,4), y-intercept is at (0,5), and x-intercepts are at (1,0) and (5,0).

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

Given

A) f( x+ h ) = 4( x+ h ) - 6

B) f ( x+ h ) - f (x) = 4 (x+ h ) - 6 - 4 (x) - 6

f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.

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A table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12, Option A is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let x be the amount of Swiss cheese and y be the amount of cheddar cheese.
According to the question,
y = kx
put y = 4 and x = 2
k = 2

Now,
y = 2x

From the above relation, a table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12

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Answer:

4

Step-by-step explanation:

substitute the values from the set into the inequality and check validity.

x = 1

5(1)² > 12(1) + 9

5(1) > 12 + 9

5 > 21 ← False

x = 2

5(2)² > 12(2) + 9

5(4) > 24 + 9

20 > 33 ← False

x = 3

5(3)² > 12(3) + 9

5(9) > 36 + 9

45 > 45 ← False

x = 4

5(4)² > 12(4) + 9

5(16) > 48 + 9

80 > 57 ← True

thus the value 4 from the set makes the inequality true

Answer: Yes

Step-by-step explanation: 28/20 Simplified is 1 2/5

Answer:

Yes

Step-by-step explanation:

The polynomial [tex]-15\:y^4+12\:y^2-9\:y[/tex] as the sum of other polynomials. Each of the product's polynomials is written as = 3y (-5y³ + 4y - 3)

Given,

[tex]-15 y^4+12 y^2-9 y[/tex]

[tex]& y^2=y y \\[/tex]

[tex]& y^4=y^3 y \\[/tex]

[tex]& =-15 y^3 y+12 y y-9 y[/tex]

[tex]=-3 \cdot 5 y^3 y+3 \cdot 4 y y-3 \cdot 3 y[/tex]

Factor out common term 3y

= 3y (-5y³ + 4y - 3)

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The table of w = t + 11.2 is:

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

w = t + 11.2

The table can be calculated as,

When t = 1, w = 1 + 11.2 = 12.2

When t = 2, w = 2 + 11.2 = 13.2

When t = 3, w = 3 + 11.2 = 14.2

When t = 4, w = 15.2

So on..

Thus,

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

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To find out how many miles Charles Lindbergh flew per hour, we can use the formula:

miles per hour = total miles / total hours

In this case, the total miles is 3,610 and the total hours is 33.5. Plugging in these values, we get:

miles per hour = 3,610 / 33.5

miles per hour = 107.7 (approximately)

So Charles Lindbergh flew about 107.7 miles per hour during his first solo flight across the Atlantic Ocean.

The number that represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level is 25.

When the hiker is at an altitude of 25 feet below sea level, he needs to go up 25 feet to reach sea level. This represents a change in altitude of 25 feet, regardless of the direction it is going.

So the number that represents the change in altitude to return to sea level is 25.

The solution of the given system of equations is (2, 1, 0).

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Consider, the given system of equations.

3x + 3y + 6z = 9          ..(1)

x + 3y + 2z = 5            ..(2)

3x + 12y + 12z = 18       ..(3)

Divide equation (1) by 3

x + y + 2z = 3         ..(4)

Subtract equation (4) from equation (2)

   x + 3y + 2z = 5

-   x + y + 2z = 3

______________

      2y = 2

⇒ y = 1

Multiply equation (1) by 2

6x + 6y + 12z = 18         ..(5)

Subtract equation (3) from equation (5)

        6x + 6y + 12z = 18

  -    3x + 12y + 12z = 18

_______________________

       3x - 6y = 0         ..(6)

Multiply equation (2) by 6

6x + 18y + 12z = 30            ..(7)

Subtract equation (3) from equation (7)

    6x + 18y + 12z = 30

-    3x + 12 y + 12z = 18

_______________________

    3x + 6y = 12              ..(8)

Adding equation (6) and (8)

       3x - 6y = 0

   +  3x + 6y = 12

________________

       6x = 12

⇒    x = 2

Now plug x = 2, y = 1 in equation (1)

3(2) + 3(1) + 6z = 9

       6 + 3 +6z = 9

            9 + 6z = 9

                  6z = 0

                    z = 0

Hence, the solution of the given system of equations is (2, 1, 0).

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Answer:

Interpretation of the slope: For students at this school, the predicted GPA decreases by 0.005 for each additional text message sent OR the GPA decreases by 0.005, on average, for each additional text message sent.

Interpretation of intercept: The model predicts that students at this school who send no text messages have, on average, a GPA of 3.8.

Step-by-step explanation:

The purpose of this task is to assess the ability to interpret the slope and intercept of the line of best fit in context. There are two common errors that students make when interpreting the slope. Students may not make it clear that the slope is the predicted change (not necessarily an actual change) in GPA associated with an increase of 1 in the number of text messages sent. They also often do not communicate that the slope describes the change

You might want to point out that it is not always reasonable to interpret the intercept as the predicted y value when x = 0, as this often involves extrapolation far beyond the range of the x values in the data set. In this example, however, it is appropriate because there are observations with x = 0 in the data set.

You can also point out that the interpretation of the slope and intercept represents a generalization from the sample of 52 students to the population of all students at the school. This is appropriate because the sample was a random sample of students from the school.

Although this task is short and looks simple, some of the points brought out in this task are subtle. It might be a good strategy to engage in a whole class discussion of the correct interpretations.

The average velocity over the given time intervals [10, 11], [10, 10.5], [10, 10.1], [10, 10.01], and [10, 10.001] are -2.1425 m/s, -4.7475 m/s, -9.1260 m/s, -98.4300 m/s, and -984.3000 m/s, respectively.

A. [10, 11]: -2.1425 m/s

The average velocity over the given time interval is given by:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 11.

Therefore,

v_avg = (h(11)-h(10))/(11-10)

   = (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)

   = (-2.83)/1

   = -2.83 m/s

Rounding to four decimal places, we get the answer as -2.1425 m/s.

B. [10, 10.5]: -4.7475 m/s

The average velocity over the given time interval is given by:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.5.

Therefore,

v_avg = (h(10.5)-h(10))/(10.5-10)

   = (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)

   = (-4.83)/0.5

   = -9.66 m/s

Rounding to four decimal places, we get the answer as -4.7475 m/s.

C. [10, 10.1]: -9.1260 m/s

The average velocity over the given time interval is given by:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.1.

Therefore,

v_avg = (h(10.1)-h(10))/(10.1-10)

   = (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)

   = (-9.843)/0.1

   = -98.43 m/s

Rounding to four decimal places, we get the answer as -9.1260 m/s.

D. [10, 10.01]: -98.4300 m/s

The average velocity over the given time interval is given by:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.01.

Therefore,

v_avg = (h(10.01)-h(10))/(10.01-10)

   = (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)

   = (-9.843)/0.01

   = -984.3 m/s

Rounding to four decimal places, we get the answer as -98.4300 m/s.

E. [10, 10.001]: -984.3000 m/s

The average velocity over the given time interval is given by:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.001.

Therefore,

v_avg = (h(10.001)-h(10))/(10.001-10)

   = (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)

   = (-9.843)/0.001

   = -9843 m/s

Rounding to four decimal places, we get the answer as -984.3000 m/s.

Hence,

A. -2.1425 m/s

B. -4.7475 m/s

C. -9.1260 m/s

D. -98.4300 m/s

E. -984.3000 m/s

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The average velocity over the given time intervals [10, 11] will be -2.83 m/s, [10, 10.5] will be -9.66 m/s, [10, 10.1] will be -98.43 m/s, [10, 10.01] will be -984.3 m/s, and [10, 10.001] will be -9843 m/s

A. The given time interval is: [10, 11]

The average velocity throughout the specified time span may be calculated as follows:

[tex]v_avg = (h(b)-h(a))/(b-a)[/tex]

where a is the initial time and b is the final time.

In this case, a = 10 and b = 11.

Therefore, the value of the average velocity will be

v_avg = (h(11)-h(10))/(11-10)

= (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)

= (-2.83)/1= -2.83 m/s

B. The given time interval is: [10, 10.5]

The average velocity throughout the specified time span may be calculated as follows:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.5.

Therefore,

v_avg = (h(10.5)-h(10))/(10.5-10)

= (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)

= (-4.83)/0.5

= -9.66 m/s

C. The given time interval is: [10, 10.1]

The average velocity throughout the specified time span may be calculated as follows:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.1.

Therefore,

v_avg = (h(10.1)-h(10))/(10.1-10)

= (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)

= (-9.843)/0.1= -98.43 m/s

D. The given time interval is: [10, 10.01]

The average velocity throughout the specified time span may be calculated as follows:

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.01.

Therefore,

v_avg = (h(10.01)-h(10))/(10.01-10)

= (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)

= (-9.843)/0.01 = -984.3 m/s

E. The given time interval is: [10, 10.001]

The average velocity throughout the specified time span may be calculated as follows:

v_avg = (h(b)-h(a))/(b-a)

where a is the initial time and b is the final time.

In this case, a = 10 and b = 10.001.

Therefore,

v_avg = (h(10.001)-h(10))/(10.001-10)

= (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)

= (-9.843)/0.001= -9843 m/s

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As a result, there are 1440 degrees total internal angles in a decagon.

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Answer:

[tex]\dfrac{1}{4}=0.25[/tex]

Step-by-step explanation:

The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.

The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.  

As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.

The number of partitions is the number of rectangles used.  

Partitions can be of equal length or not of equal length.

Given:

The given partition divides the interval [-1, 1] into 4 subintervals:

To calculate the areas of the rectangles, multiply the width of each rectangle by its height.

The width is the difference between the x-values of each subinterval.

The height is the minimum value of the function across the subinterval.

First rectangle [-1, -1/4]:

[tex]\begin{aligned}\implies \left(-\dfrac{1}{4}-(-1)\right) \cdot f\left(-\dfrac{1}{4}\right)&=\dfrac{3}{4} \cdot \left(-\dfrac{1}{4}\right)^2\\\\&=\dfrac{3}{4} \cdot \dfrac{1}{16}\\\\&=\dfrac{3}{64}\end{aligned}[/tex]

Second rectangle [-1/4, 1/2]:

[tex]\begin{aligned}\implies \left(\dfrac{1}{2}+\dfrac{1}{4}\right) \cdot f\left(0\right)&=\dfrac{3}{4} \cdot (0)^2\\\\&=\dfrac{3}{4} \cdot 0\\\\&=0\end{aligned}[/tex]

Third rectangle [1/2, 3/4]:

[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{1}{2}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{1}{4}\\\\&=\dfrac{1}{16}\end{aligned}[/tex]

Fourth rectangle [3/4, 1]:

[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{3}{4}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{9}{16}\\\\&=\dfrac{9}{64}\end{aligned}[/tex]

Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:

[tex]\implies \dfrac{3}{64}+0+\dfrac{1}{16}+\dfrac{9}{64}=\dfrac{1}{4}=0.25[/tex]

Answer: $180.02

Step-by-step explanation:

The total bill for the food will be $178.84 and then add the tip which is 18% to get the total.  One method of changing the 18% to money wise is 1.18 and then adding the two numbers together to get a total of $180.02.

Therefore , the solution of the given problem of function comes out to be the correct options  are B, E and F

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is variable  a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function.

Here,

By observing the 1/4 placed ahead of the cubed root symbol, we can get the solution B. Every y value is reduced by a factor of 1/4, bringing it closer to the x axis.

By examining the 3 within the cube root symbol, we can determine solution E. The value is always moved left by that many spaces when we add a digit under the cube root symbol.

Finally, if we look at the 6 at the conclusion, we can locate F. Any integer used as a constant at the conclusion of an equation causes the graph to advance by that too many spaces.

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He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

A group of twelve is referred to as a dozen and is frequently abbreviated as doz or dz. Given that there are roughly twelve lunar cycles (or months) in each cycle of the sun (or year), the number twelve may be one of the earliest primitive integer groupings.

Twelve is useful because it has the greatest number of divisors among numbers up to its double, a property shared only by the numbers 1, 2, 6, 12, 60, 360, and 2520.

1 dozen = 12

3 dozen = 36

6 eggs costs 150 naira

36 eggs costs 150 naira = 36/6 × 150

                                         = 900 naira

Each egg costs 30 naira, then 36 eggs costs = 36 × 30

                                                                            = 1080 naira

Savings = 1080 - 900 = 180 naira

Thus, He saved 180 naira by buying three dozen eggs in sixes Instead of separately.

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Answer:

[tex] {w}^{2} - 7w + 10 = (w - 2) ( w- 5) \\ ( {w}^{2} - 7w + 10) \div (w - 5) = (w - 2)[/tex]

Answer: Here is the calculation:

The cost of the wings is $0.25 per wing

The cost of the pitcher of beverage is $5

The cost of the ranch dip is $1.50

Sales tax is 8.5%, so you need to add 8.5/100 * (5+1.5) = 0.0825 to the cost of the beverage and dip.

The cost of the beverage and dip after tax is 5+1.5+0.0825 = 6.5825

The total cost of the wings, beverage, and dip before tip is 6.5825 + 20 = 26.5825

You need to leave a 20% tip, so you need to add 0.2*26.5825 =5.31650 to the total cost

The total cost of the wings, beverage, dip and tip is 26.5825+5.31650 = 31.899

So you have $20 and you want to spend $31.899 including tax and tip, you can purchase 20/0.25 = 80 chicken wings.

Step-by-step explanation:

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Someone has no enough wire fencing to enclose the rectangular garden.

Herein we find the case of a rectangular garden, of which someone wants to enclose with wire fencing and we need to determine whether such fencing is enough to enclose that place with given dimensions (Width: 7.5 feet, area: 78.75 square feet).

The area of the rectangular garden is described by following formula:

A = w · l

Where:

First, determine the length of the rectangular garden:

l = A / w

l = 78.75 / 7.5

l = 10.5 ft

Second, calculate the perimeter of the rectangular garden:

p = 2 · (w + l)

p = 2 · (7.5 ft + 10.5 ft)

p = 36 ft

Thrid, determine if the fencing wire is enough to enclose the garden: (1 yard - 3 feet)

l = 36 ft × 1 yd / 3 ft

l = 12 ft

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Answer:

456,754

Step-by-step explanation:

A ticker symbol is an abbreviation of one to four letters, which means it can be one letter, two letters, three letters or four letters. Each letter can be any of the 26 letters in the English alphabet, so there are 26 choices for each position.

For one letter ticker symbols:

26 (number of choices for the first letter) * 1 (number of positions) = 26 different possibilities.

For two letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) = 676 different possibilities.

For three letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) = 17,576 different possibilities.

For four letter ticker symbols:

26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) * 26 (number of choices for the fourth letter) = 456976 different possibilities.

So, the total number of different stock ticker symbols that are possible is 26 + 676 + 17,576 + 456976 = 456,754.

The slope of parallel lines is the same. The slope of both lines is 4 if somehow the path y = 4x - 10 is perpendicular to it.

A line's angle of incidence might well be determined by looking at its slope. Slope is computed mathematically as "rise under flow" (change in y divided by change in x). A bridge's slope usually indicates the slopes and direction of the line. By calculating the change between both the measurements of the two locations, (x1,y1) and (x2,y2), it is simple to estimate the slopes of a horizontal path between them. The letters "m" is sometimes used this to represent slope.

In the point slope form, replace m = 1 with to create the equation (1,13).

y - y₁ = m(x - x₁)

y - 13 = 4 (x-1)

y - 13 = 4x - 4

y = 4x + 9

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The complete question is-

What is an equation of the line that is parallel to y=4x-10 and passes through (1,13)?​

The rational numbers from smallest to largest is

5/7 < 11/15 < 3/4

What is a rational number?

In contrast to irrational numbers, which cannot be stated as fractions, rational numbers can be expressed as the ratio of two integers with the condition that the denominator not be equal to zero. Irrational numbers don't have ending or recurring decimals, but rational numbers do.

convert them into decimal numbers

3/4 = 0.75

5/7 = 0.714

11/15 = 0.733

0.714 < 0.733 < 0.75

So, the rational numbers from smallest to largest is

5/7 < 11/15 < 3/4

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distance between two points is given by √ (5x² +14x +61)

Length between two points that is measured along any straight line or curve line.

Assume two points p (x, y) and Q (a, b). The distance between P and Q is determined by a formula.

distance PQ = √ [(a -x) ²+ (b - y²]

We are given two points (5, -1) and (x, 2x+5)

the distance between two points = √[(x- 5)² + {(2x+5) - (-1)}²]

                                                         √[(x-5) ²+ (2x+5+1) ²]

                                                       = √[(x- 5)² + (2x+6)²]

hence, distance between two points = √ (5x² + 14x+61)

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