Let A and B be sets, where:

A = {3, 6, 8}

B = {0, 2, 4, 5, 9}

The result of the expression 3(x + 2)² - 4 is equivalent to 44.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the equation as -

(x + 2) = 4

We have to find the result of -

3(x + 2)² = 4

It is given that -

(x + 2) = 4

So, we can write -

3 x 4 x 4 = 4

48 - 4

44

Therefore, the result of the expression 3(x + 2)² - 4 is equivalent to 44.

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{Question in english -

If (x+2)=4 what is the result of 3(x+2)^2=4}

Considering the context of the question and the percentage analysis, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%.

A percentage is a number or ratio indicated as a fraction of 100. To get the percentage of any number, such number will be divided by the number of the whole and multiplied by 100. Hence, the percentage means, a part per hundred

In this case, Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $220. Now the cost is $305

Hike in price = 305 - 220 = 85

Hike % = 85/220 * 100% = 38.64%

When the extra charge is $50 for extra baggage, the total price = is $355

Hike in price = 355 - 220 = 135

Hike % = 135/220 *100% = 61.36%

Hence, in this case, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%

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The perimeter of the figure, is represented by the expression, 14x + 16.

The perimeter of a figure is the total length of the outer boundaries of the figure. It is the sum of all the sides of the figure.

The perimeter is used to determine the size of a figure and can be calculated by adding the lengths of all the sides together.

Therefore:

Perimeter of the figure = 4(2x - 1) + 2(3x + 10)

To simplify the expression 4(2x - 1) + 2(3x + 10), we can distribute the constants (4 and 2) to the expressions inside the parentheses.

First, we'll simplify 4(2x - 1) using the distributive property:

4(2x - 1) = 4(2x) + 4(-1) = 8x - 4

Next, we'll simplify 2(3x + 10) using the distributive property:

2(3x + 10) = 2(3x) + 2(10) = 6x + 20

Now we can add the two simplified expressions together:

8x - 4 + 6x + 20 = 14x + 16

So, the simplified form of 4(2x - 1) + 2(3x + 10) is 14x + 16.

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Answer: Your answer is 1/3(b-21), aka the first answer slot

Step-by-step explanation: If we factor 1/3b-7, the common factor is 1/3. by this knowledge, we put 1/3(b-7/1/3), and 7/1/3 = 7x3 which is 21. So we simplify and get the answer
1/3(b-21)

The statement that is true is D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25

To convert between pounds and kilograms, we use the conversion factor of 1 pound = 2.2 kilograms. This means that 1 pound is equal to 2.2 kilograms, and 2 pounds is equal to 4.4 kilograms, and so on.

In this case, we are given that there is 25 pounds of dog food in a bag, and we want to convert this to kilograms. To do this, we can multiply 25 pounds by the conversion factor of 1 pound = 2.2 kilograms.

25 pounds * (1 kilogram / 2.2 pounds) = 25/2.2 = 11.3636363636 kg.

So, there is approximately 11.36 kilograms of dog food in the bag.

The other options are incorrect. In option A, 1/2.2= 55/22 which is not equal to 25 pounds and the same case in option C. In option B the calculation is not correct as well because 1/2.2 = 25/11.36 doesn't make sense.

Therefore, the only true statement is D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25

Using the given information, the value of the number is 12

From the question, we are to determine the value of the number.

From the given information, we have that
"7 more than twice a number is 5 less than three times the same number"

Let the number be x

7 more than twice a number means

2x + 7

5 less than three times the number is

3x - 5

Thus,

The equation becomes

2x + 7 = 3x - 5

Now, solve for x

2x + 7 = 3x - 5

7 + 5 = 3x - 2x

12 = x

x = 12

Hence, the value of the number is 12

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The equation of a line is 3y+2x+59.

When we have given one point and slope we can write the equation as

y-y1=m(x-x1)

here x1=-11,y1=-13,m=-2/3

y+11=-2/3(x+13)

=3y+2x+59

The equation becomes =3y+2x+59.

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Answer: Lena walks 63 miles in 10 days.

Step-by-step explanation:

To find out how many miles Lena walks in 10 days, you need to add up all the distances she walks each day.

From the information provided, it seems that the distances walked each day are:

23 miles, 11 miles, 10 miles, 19 miles and the remaining days is not given.

So, to find the total miles Lena walks in 10 days, you would add up the distances walked each day:

23 + 11 + 10 + 19 = 63 miles

So, Lena walks 63 miles in 10 days.

The total miles in 10 days will bed 14 miles. The closest option is OD, which is 19 miles.

To find the total distance Lena walks in 10 days, we need to add up all the distances on the line plot:

Starting from day 1, we can count the distances and add them up:

On day 1, Lena walks 1 mile

On day 2, Lena walks 2 miles

On day 3, Lena walks 1 mile

On day 4, Lena walks 1 mile

On day 5, Lena walks 2 miles

On day 6, Lena walks 1 mile

On day 7, Lena walks 2 miles

On day 8, Lena walks 1 mile

On day 9, Lena walks 1 mile

On day 10, Lena walks 2 miles

Adding up all these distances, we get:

1 + 2 + 1 + 1 + 2 + 1 + 2 + 1 + 1 + 2 = 14

Therefore, Lena walks a total of 14 miles in 10 days.

Thus, the closest option is OD, which is 19 miles.

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The area of this circle is 12.5 yd²

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

The area of the circle is the product of the pie and the square of the radius.

The area of the circle = πr²

We are given that floor of a round hut has a diameter of 4 yards.

r = 2 d

Then we know that

Area = πr²

Substitute the values r = 2

π = 3.14

Area = 3.14(2)²

Area = 3.14 × 4

Area = 12.5663706 yd²

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Therefore , as a result, the answer to the given function problem is that the  f(x) = y  = - |x-4 | represents the given points.

Mathematics encompasses a wide range of topics, including the study of numbers and their variations, equations and related structures, as well as the limits and potential uses of geometry. A "useful" is the connection between several inputs that together produce a particular output. A functional is an output-input relationship where each input yields a single, easily recognisable output. Every technique has both a territory, often known as a domain, and a city .

Here,

Given : (6,1)  and (-6,-5)

We need to choose which of the four potential functions corresponds to the graph; we have such a graph & four possible functions.

From putting the points in the below function f(x) , we get it represents the given points.

As a result, the essential task would be:

=>  y  = - |x-4 |

=> f(x) = y  = - |x-4 |

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Answer:

[tex]tan(A)=\frac{5}{12}[/tex]

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

The TAN function can be expressed as [tex]tan(x)=\frac{Opp}{Adj}[/tex].

The side opposite to angle A is 15

The side adjacent to angle A is 36.

Therefore

[tex]tan(A)=\frac{15}{36}[/tex]

We can simplify the fraction.

Factor 3 out of 15.

[tex]\frac{3(5)}{36}[/tex]

Factor 3 out of 36.

[tex]\frac{3(5)}{3(12)}[/tex]

Cancel the common factor of 3.

[tex]\frac{5}{12}[/tex]

Answer:

tan(A)=\frac{5}{12}tan(A)=

12

5

\frac{5}{12}

12

5

Step-by-step explanation:

The TAN function can be expressed as tan(x)=\frac{Opp}{Adj}tan(x)=

Adj

Opp

.

The side opposite to angle A is 15

The side adjacent to angle A is 36.

Therefore

tan(A)=\frac{15}{36}tan(A)=

36

15

We can simplify the fraction.

Factor 3 out of 15.

\frac{3(5)}{36}

36

3(5)

Factor 3 out of 36.

\frac{3(5)}{3(12)}

3(12)

3(5)

Cancel the common factor of 3.

\frac{5}{12}

12

5

The output when the input is 8 is 36 and the input when the output is 42 is 206

You should be aware that input involves materials used in producing a particular thing while the output is the yielding result of the production.

(The input)  n*5 - 4 = (The output)

When the input is 8,

8 * 5 -4

= 40 - 4

= 36

When the output is 42.

(The input)  n× 5 - 4

(The input) 42× 5 -4

(The input) = 206

The input was 206.

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Complete question:

Here is a number machine.

input

-5*3 output

a) Work out the output when the input is 8

b) Work out the input when the output is 42

Answer: Let's call the number of hours Deborah drives "d" and the number of hours Cornell drives "c".

We know that:

c = 3d (because Cornell drives 3 times the hours that Deborah does)

and

c + d = 8 (because they drive for a total of 8 hours)

We can use the first equation to substitute the value of c in the second equation:

3d + d = 8

4d = 8

d = 2

So Deborah drives 2 hours.

Now we can use the first equation to find the number of hours Cornell drives:

c = 3d

c = 3(2) = 6

So Cornell drives 6 hours.

Step-by-step explanation:

Answer:The most general form of a polynomial function of degree n that has real coefficients is:

f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0

where a_n, a_{n-1}, ..., a_1, a_0 are real numbers, and a_n is not equal to zero.

The number of distinct roots of a polynomial function of degree n can be determined using the fundamental theorem of algebra, which states that a polynomial function of degree n has exactly n roots, counting multiplicities. This means that a polynomial function of degree n can have n distinct roots, n-1 distinct roots, or any integer value in between, depending on the multiplicities of the roots.

Using the factor theorem, it is possible to determine the number of distinct roots of a polynomial function by factoring it into its irreducible factors. If the polynomial function is fully factored, the number of distinct roots is equal to the number of irreducible factors.

However, the nature of the roots (real or complex) and constraints imposed by the discriminant are also important to consider. The discriminant of a polynomial function is the value of the expression b^2-4ac, where a, b, and c are the coefficients of the polynomial function in the form f(x) = ax^2+bx+c. The discriminant determines the nature of the roots of the polynomial function. If the discriminant is positive, the roots are real and distinct. If the discriminant is zero, the roots are real and repeated. If the discriminant is negative, the roots are complex and non-real.

So, the most general form of a polynomial function of degree n that has real coefficients, can be determined by the form of the polynomial, the number of distinct roots by the fundamental theorem of algebra, by factoring the polynomial into its irreducible factors and the nature of the roots is determined by the discriminant.

Step-by-step explanation:

Answer: To find the perimeter of a triangle, we need to add the length of all three sides of the triangle.

To find the length of each side, we can use the distance formula which is the square root of (x2-x1)^2 + (y2-y1)^2.

The distance between point A (9,-2) and point B (5,1) is: √((9-5)^2 + (-2-1)^2) = √16 + 9 = √25 = 5.

The distance between point B (5,1) and point C (9,-3) is: √((9-5)^2 + (-3-1)^2) = √16 + 16 = √32 = 5.66.

The distance between point C (9,-3) and point A (9,-2) is: √((9-9)^2 + (-3- -2)^2) = √1 + 1 = √2 = 1.41

The perimeter is the sum of the length of all three sides:

Perimeter = 5 + 5.66 + 1.41 = 12.07

Round the answer to two decimal places, the perimeter of the triangle is 12.07.

Step-by-step explanation:

Answer:

To find out how many batches of cookies the factory made, we need to divide the total amount of flour used (7 1/2 bags) by the amount of flour used per batch (3 3/4 bags).

We can start by converting 7 1/2 bags of flour to a mixed number: 7 1/2 bags = 7 + 1/2 = 7.5 bags

Next, we can convert 3 3/4 bags of flour to a mixed number: 3 3/4 = 3 + 3/4 = 3.75 bags

Then, we can divide the total amount of flour used by the amount of flour used per batch:

7.5 bags / 3.75 bags/batch = 2 batches

Therefore, the factory made 2 batches of cookies yesterday

Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -4x + 20

Step-by-step explanation:

The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).

To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.

Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:

y - y1 = m(x - x1)

Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:

y - 4 = -1/2(x + 6)

Which can be written as:

y = -1/2x + 4

So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -1/2x + 4

Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.

Answer:

Step-by-step explanation:

.

The best way for Anthony to plan his garden is to create a rectangular plot. He can use the side of the barn as one side of the rectangle, and then measure out the other three sides. The total length of the three sides will be 176 feet. He can divide this into two sides that are 88 feet long and two sides that are 44 feet long. This will give him a rectangular plot that is 176 square feet.

Once Anthony has the dimensions of the plot, he can build a fence around it to protect it from rabbits. He can use a variety of materials such as wood, wire, or plastic mesh to build the fence. The fence should be at least four feet tall and buried at least six inches deep to be effective. If he chooses to use wire, he should use thick, galvanized wire to make sure that the rabbits cannot chew through it.

Once the fence is in place, Anthony can begin planting his garden. He should also consider adding a layer of mulch or straw around the outside of the fence to discourage the rabbits from digging underneath it. With the right planning and protection, Anthony should be able to enjoy a successful garden.

The survey methods that would result in a valid random sample of the community include:

Option E. All of the above is correct.

Simple random sampling involves selecting a random sample of participants from a larger population using a random number generator or a random sampling software. This method ensures that every member of the population has an equal chance of being selected.

Stratified random sampling involves dividing the population into smaller groups or strata based on certain characteristics, such as age, gender, income, etc. A random sample is then selected from each stratum. This method is useful when the population is heterogeneous and you want to ensure that the sample is representative of the entire population.

Systematic sampling involves selecting participants at regular intervals from a list of the population. This method is useful when the population is ordered, such as a list of customers.

Cluster sampling involves selecting a random sample of clusters or groups from the population, and then sampling individuals within those clusters. This method is useful when the population is geographically dispersed or it's difficult to obtain a complete list of the population. So Lily can use any of these survey methods to come up with a sample of the community.

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Options for this question include:

Answer:

In order to find when the two trains will meet up, we can use the concept of relative speed. The relative speed of two trains is the sum of their individual speeds.

In this case, the relative speed is 30 + 50 = 80km/h

Since we know that the distance between London and Bristol is 100km, we can divide the distance by the relative speed to find the time it takes for the two trains to meet up:

100km / 80km/h = 1.25 hours

So, the two trains will meet up in 1.25 hours

Answer:

1 hour 15 minutes

Step-by-step explanation:

Relative Speed

If the two objects are moving in the opposite direction at different speeds, relative speed is the sum of their two speeds:

Using the formula:

[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]

Therefore:

[tex]t=\dfrac{d}{v_1+v_2}[/tex]

where:

Given:

Substitute the given values into the formula to find the time at which the two trains meet:

[tex]\implies t=\dfrac{100}{30+50}=\dfrac{100}{80}=1.25\; \sf hours=1\; hour\;15\;mins[/tex]

Therefore, the two trains meet at 1 hour 15 minutes.

Answer:

You could convert 21/2 to a whole number by multiplying it by 2 and then dividing by 2, so 21/2 = 21/2 = 10.5, then dividing the total by the number of people that is 10.5 / 7 = 1.5 glasses/person.

Answer:

Step-by-step explanation:

Let x be the amount invested in the 6% account.

Since he invested twice as much in the lower-yielding account, the amount invested in the 10% account is 2x.

We know that the annual interest is $3080 dollars, and the interest is calculated on the invested amount at each rate.

The interest in the 6% account is (6/100) * x = 3/50 * x

The interest in the 10% account is (10/100) * 2x = 1/10 * 2x

The total annual interest is 3/50x + 1/102x = 3/50x + 1/5x = (3+1)/5x = 4/5x

Therefore, we can write the equation:

4/5*x = 3080

To find x, we can divide both sides by 4/5:

x = 3080*5/4

x = $2310

So, the man invested $2310 in the 6% account and $2310*2 = $4620 in the 10% account.

The number of tiles in figure 70 and figure 93 are 142 and 188.

Figure 2 = 6

Figure 3 = 8

The common difference = 8 - 6

= 2

figure 2 = a + (n - 1)d

Where,

a = first term

figure 2 = a + (n - 1)d

6 = a + (2 - 1)2

6 = a + (1)2

6 = a + 2

6 - 2 = a

a = 4

Figure 70 = a + (n -1)d

= 4 + (70-1)2

= 4 + (69)2

= 4 + 138

Figure 70 = 142

Figure 93 = a + (n -1)d

= 4 + (93 - 1)2

= 4 + (92)2

= 4 + 184

Figure 93 = 188

Therefore, figure 70 and 93 have 142 and 188 tiles respectively.

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Dalton's Atomic Theory (1804)

From his experiments and observations, as well as the work of peers of his time, Dalton proposed a new theory of the atom. This later became known as Dalton's atomic theory. The general tenets of this theory were as follows:

According to Dalton’s atomic theory, all matter, whether an element, a compound, or a mixture is composed of small particles called atoms.

Dalton based his theory on two laws: the law of conservation of mass and the law of constant composition.

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After 10 years, the investment compounded periodically will be worth $ 132. 53 more than the investment compounded annually.

The worth of the investment compounded annually would be:

= investment principal x  ( 1 + Annual interest ) ^ number of years

= 9, 000 x ( 1 + 5 %) ¹⁰

= $ 14, 660.05

The worth of the periodically compounded interest investment would be:

= 9, 000 x ( 1 + 5 % / 4 ) ¹⁰ ˣ ⁴

= $ 14, 792. 58

The difference is :

= 14, 792. 58 - 14, 660. 05

= $ 132. 53

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= 4a + 4b

Answer:

[tex] \sf \: 4a + 4b [/tex]

Step-by-step explanation:

Given expression,

→ 4(a + b)

Let's simplify the expression,

→ 4(a + b)

→ 4(a) + 4(b)

→ (4 × a) + (4 × b)

→ 4a + 4b

Hence, the answer is 4a + 4b.

Answer:

False

Step-by-step explanation:

False.  That is how a decimal is converted to a percent.  

A percent is converted to a decimal by  taking the percent and dividing by 100%

For example:

56% is converted to a decimal by dividing by 100%

56%/100%  The percents cancel out and when you divide by 100, you move the decimal two places to the left.  .65

Answer:

C) -24

Step-by-step explanation:

We have two functions here:

[tex]f(x) = x^{2} + 4[/tex]

and

[tex]g(x) = 2x + 1[/tex]

Now, both of these functions will be multiplied together after they are figured out (since they are next to each other), and they will have -2 replace x. For function f, we get:

[tex]-2^{2} + 4[/tex]

For function g, we get:

[tex]2 * -2 + 1[/tex]

Simplifying these two gives us:

[tex](4 + 4) * (1 - 4)[/tex]

Simplifying further gives us:

[tex]8 * -3 = -24[/tex]

So, the value of f(-2)g(-2) is C) -24.

Hope this helped!

Answer:

B)  -24

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+4\\g(x)=2x+1\end{cases}[/tex]

To find f(-2)g(-2), substitute x = -2 into both functions and multiply them:

[tex]\begin{aligned}\implies f(-2)g(-2)&=\left((-2)^2+4\right)\left(2(-2)+1\right)\\&=\left(4+4\right)\left(-4+1\right)\\&=8 \cdot -3\\&=-24\end{aligned}[/tex]

The probability of a measure less than 78 pounds is given as follows:

0.9452 = 94.52%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 70, \sigma = 5[/tex]

The probability of a weight less than 78 pounds is the p-value of Z when X = 70, hence:

Z = (78 - 70)/5

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

The mean and the standard deviation of the distribution are given as follows:

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Answer: Cannot be determined from graph

Step-by-step explanation:

The oil and coolant will be changed together after 15000 miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a car manual recommends changing the oil every 5000 miles and inspecting the engine coolant system every 15,000 miles.

The change for both together for the first time will be after 15000 miles.

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