how is the composition of function related to the order of operations

According to question

6 + 4 d = d - 9

4d - d = -9 - 6

3d = - 15

d = -15/3

d = -5

the ratio 6/5 means for every 6 boys there are 5 girls.

Add the ratio: 6+5 = 11

Divide class total by 11: 22/11 = 2

Multiply each ratio number by 2 to find the number of boys and the number of girls:

6 x 2 = 12 boys

5 x 2 = 10 girls.

10 out of the 22 kids are girls.

The probability of picking a girl would be 10/22, which reduces to 5/11

First write the function [tex]y=(x+12)(x-6)[/tex] in standard form [tex]y=ax^2+bx+c:[/tex]

[tex]y=x^2-6x+12x-72,\\\\y=x^2+6x-72.[/tex]

Find the x-coordinate according to the rule

[tex]x_{vertex}=-\dfrac{b}{2a}.[/tex]

Thus,

[tex]x_{vertex}=-\dfrac{6}{2\cdot 1}=-3.[/tex]

Now find the y-coordinate of the vertex substituting x=-3 into the parabola equation:

[tex]y_{vertex}=(-3)^2+6\cdot (-3)-72=9-18-72=-81.[/tex]

Answer: the x-coordinate if the vertex is -3.

The x-coordinate of the parabola’s vertex is 3

from the question, we have the following parameters that can be used in our computation:

y = (x - 6)(x + 12)

When expanded, we have

y = x² - 6x + 12x - 72

So, we have

y = x² + 6x - 72

the x-coordinate of the parabola’s vertex is calculated as

x = -b/2a

So, we have

x = -6/2* 1

Evaluate

x = -3

Hence, the x-coordinate of the parabola’s vertex is 3

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We can write this in expression form as follows:

[tex]\frac{3}{\frac{4}{4} }[/tex]

Notice that we get a 4/4 in the denominator in which case we multiply the two (because they are both denominators:

[tex]\frac{3}{\frac{4}4} } = \frac{3}{16}[/tex]

So, the unit rate is 3/16 lbs/person.

To find the unit rate in pounds per person, divide the total weight of the candy by the number of people. In this case, the unit rate is 3/16 lb per person.

To find the unit rate in pounds per person, we divide the total weight of the candy (3/4 lb) by the number of people (4). This can be represented as 3/4 ÷ 4. To simplify the division, we can multiply the numerator and denominator by 4 to get rid of the fraction. This gives us 3/16 lb per person as the unit rate in pounds per person.

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B. The equation has one solution.

Step 1. Subtract 2 from both sides

3 + x - 2 = -3x

Step 2. Simplify 3 + x - 2 to x + 1

x + 1 = -3x

Step 3. Subtract x from both sides

1 = -3x - x

Step 4. Simplify -3x - x to -4x

1 = -4x

Step 5. Divide both sides by -4

-1/4 = x

Step 6. Switch sides

x = -1/4

The answer is 15. Take 180/12. 12  can only go into 18 1 time with a remainder of 6. bring down the 0 12 goes into 60 5 times for 60.

The solution to the given number division 180 divided by 12 is: 15

When dividing two numbers, we know that the number that will be in the numerator part is called Dividend while the number that will be in the denominator part is called Divisor.

Thus:

180/12

180 is the dividend while 12 is the divisor

Factors of 180 are  1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

Factors of 12 are 1, 2, 3, 4, 6 and 12.

However, 12 is also a factor of 180 and the number that it is multiplied by to get 180 is 15. Thus:

180/12 = 15

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Answer:

Step-by-step explanation:

a = -3

Factor out the common term 3.

Cancel 3.

Subtract a from both sides.

Simplify 1 + 2a - a to 1 + a

Subtract 1 from both sides.

Simplify -2 - 1 to -3

Switch sides.

Answer:

The answer is A

Step-by-step explanation:

The distance of 7,500,000 miles expressed in scientific notation is 7.5 × 10⁶, which corresponds to option A) 7.5 × 10⁶.

The spacecraft travels 7,500,000 miles in one year. To express this distance in scientific notation, we need to convert it into the form of a × 10ⁿ, where a is a number between 1 and 10, and n is an integer.

To find the correct form, we can manipulate the original number. We move the decimal point 6 places to the left (since there are six zeros in the million), which gives us 7.5. Thus we can write 7,500,000 as 7.5 × 10⁶. So, the correct answer is A) 7.5 × 10⁶.

0.0018

Move the decimal place two places to the right.

1.8*10^3

Answer:

The correct answer is A) 1.8 * 10^-3

Step-by-step explanation:

100,000 at round tree, 170,000 at Samson. both would be 270,000

if the terms of a geometric sequence are

[tex]a_{1}[/tex], [tex]a_{2}[/tex], [tex]a_{3}[/tex], [tex]a_{4}[/tex], .....

then the common ratio r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{a_{2} }{a_{1} }[/tex]

Answer:

In a geometric sequence the ratio between consecutive terms is constant.

Step-by-step explanation:

A geometric sequence is that sequence where the ratio between two consecutive terms is constant.

This ratio is called the common ratio.

For example:

Lets take an example :

1,6,36,216,1296,.....

To find the common ration we divide the second term by first term.

[tex]\frac{6}{1} =\frac{216}{36} =6[/tex]

Here, the common ratio is 6.

Write an equation representing what you already know:

x=29.6

x represents fluid ounces. One fluid ounce is 29.6 mL.

You want to find 8 fluid ounces.

8x=8*29.6

x=236.8

Round to the nearest whole number.

x=237

Answer:

A

Step-by-step explanation:

Final answer:

To find the total number of burgers sold by the fast food restaurant, calculate the burgers sold without cheese using the ratio provided and then find the total by adding burgers with cheese and without cheese.

Explanation:

To find out how many burgers the fast food restaurant sold in total, we first need to determine the number of burgers sold without cheese. Since the ratio of burgers sold with cheese to without cheese is 7:3, we can calculate that for every 7 burgers sold with cheese, 3 were sold without cheese. Therefore, 35 burgers with cheese corresponds to 35 / 7 * 3 = 15 burgers without cheese. Hence, the total number of burgers sold is 35 (with cheese) + 15 (without cheese) = 50 burgers.

Yes, if it exists, and reduce our fraction by dividing both numerator and denominator by it. GCF = 11, and get our simplified answer

Answer:no

Step-by-step explanation:

¯\_(ツ)_/¯

7/11 in decimal form = .6363

Answer:

Answer:

Using triangle similarity theorems, GF is 16 cm (fourth option)

Step-by-step explanation:

If points S and T are midpoints of the sides of triangle FGH, the segment ST is parallel to the side GF and the triangles FGH and TSH are similars, and their corresponding sides must be proportionals, then:

GF/ST=FH/TH=GH/SH

TH=6 cm→FT=6 cm, because T is the midpoint of side FH, and:

FH=2 TH = 2 FT =2 (6 cm)→FH=12 cm

GS=4 cm→SH=4 cm, because S is the midpoint of side GH, and:

GH=2 GS = 2 SH =2 (4 cm)→GH=8 cm

ST= 8 cm

Replacing the known values in the proportion:

GF/ST=FH/TH=GH/SH

GF/(8 cm)=(12 cm)/(6 cm)=(8 cm)/(4 cm)

GF/(8 cm)=2=2

GF/(8 cm)=2

Solving for GF: Multiplying both sides of the equation by 8 cm:

(8 cm) [GF/(8 cm)]=(8 cm)(2)

GF=16 cm

If Points S and T are midpoints of the sides of triangle FGH, the measure of the length GF is 16cm. Option D is correct

To get the length of Gf, we will need to use the similarity theorem of a triangle as shown:

HT/TS = HF/Gf

From the diagram, we have the following:

HT = FT = 6cm

ST = 8cm

Substitute the given parameters into the formula to have:

6/8 = 6+6/GF

6/8 = 12/GF

6FG = 96

FG = 96/6

FG = 16cm

Hence the measure of the length GF is 16cm

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y = |x| means that if -∞ < x <∞ Then y will be between 0 < ∞

The answer is that y can never equal a negative number.

With the help of the definition of alternate angle and corresponding angle, the result obtained is The letter 'F' illustrates corresponding angle Fourth option is correct

What is alternate angle and corresponding angle?

At first we need to understood what is angle, parallel lines and transversal Angle When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle. Parallel lines Two lines are said to be parallel if on extending them indefinitely, they will never intersect Transversal is a line that intersects two or more parallel lines Alternate angle The angle formed on the opposite side of transversal  is called alternate angle. Corresponding angles are those angles formed on same side of transversal when a transversal intersect two or more parallel lines

Here,
The letter 'F' illustrates corresponding angle

Fourth option is correct

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i believe the answer is B

Answer:

C: A dilation of magnitude 2 centered at the origin.

(for anyone in the future, this is correct!)

The aerobics class lasted 20 minutes and the yoga class lasted 50 minutes. This was determined by setting up an equation and solving for the duration of each class, given the total time and the information that the yoga class was 30 minutes longer.

The student is trying to find out how long each class was—Nicole attended an aerobics class and a yoga class for a total of 1 hour and 10 minutes, with the yoga class lasting 30 minutes longer than the aerobics class. To find the answer, we can set up an equation. Let the duration of the aerobics class be x minutes. Therefore, the duration of the yoga class would be x + 30 minutes. According to the question, the total time spent in both classes is 70 minutes (1 hour and 10 minutes).

Now, we can write an equation that represents the total time:

x (aerobics class) + x + 30 (yoga class) = 70 minutes

Combining the x terms we get:

2x + 30 = 70

To find x, we subtract 30 from both sides of the equation:

2x = 40

Dividing both sides by 2 gives us:

x = 20

So the aerobics class lasted 20 minutes, and since the yoga class was 30 minutes longer, it lasted 50 minutes.

B Should be your answer!

Answer:

B. [tex]350x+625[/tex].

Step-by-step explanation:

Let x represent number of weeks.

We have been given that Patricia is starting a part-time job that pays her $350 a week. So the amount saved after x weeks would be [tex]350x[/tex].

We are also told that Patricia has saved $625. So total amount saved by Patricia after x weeks would be [tex]350x+625[/tex].

Therefore, the expression [tex]350x+625[/tex] represent Patricia's total savings after x weeks and option B is the correct choice.

The answer is f(x) ≥ 2x^2 + 4x

Hope this helps!

Answer: a) f(x) ≤ -2x^2 + 4x

Step-by-step explanation:

In the graph you can see that the "hands" of the quadratic function go up, this means that the principal constant (the one that multiplicates the square term) is positive:

this is:

for a function f(x) = a*x^2+ b*x + c

if a is positive, the hands will go upside, if a is negative, the hands will go downside.

we also can see that the shaded area is upside the curve, so we are looking for f(x) > something.

Then we can discard the third option because we have f > -2*x^2..

the remaining options are:

a) f(x) ≤ -2x^2 + 4x or f(x) ≥ 2x^2 - 4x

b) f(x) ≥ 2x^2 + 4x

first, you can see that in the second function both terms have the same sign, so there can be only one x-intercept, but in the graph, we can see two x-intercepts, so we can also discard option b.

The remaining option, and the correct one, is option a.

In the magic penny parable, choosing a penny that doubles in value every day leads to a significant amount of money. After 8 days, you would have 256 pennies.

The magic penny parable is a story that demonstrates the power of compound interest. In the story, a person is given the choice between taking a million dollars or a penny that doubles in value every day for 30 days. By choosing the penny, they end up with over 5 million dollars at the end of 30 days.

To determine how much money you would have after 8 days, we can use the formula for compound interest:

Final amount = Initial amount * (1 + interest rate) ^ number of periods

In this case, the initial amount is 1 penny, the interest rate is 100% (as the penny doubles in value), and the number of periods is 8 days.

Using this formula, the calculation would be:

Final amount = 1 penny * (1 + 1)^8 = 1 penny * 2^8 = 1 penny * 256 = 256 pennies.

Therefore, after 8 days, you would have 256 pennies.

To find the number of students in the group, we can use algebra to solve two equations simultaneously.

Let's solve this problem using algebra. Let's say there are x students in the group.

If Mr. Chan gives each student 2 pencils, he will have 10 pencils left. This can be expressed as the equation 2x + 10 = P, where P represents the total number of pencils Mr. Chan bought.

If Mr. Chan gives each student 3 pencils, he will have no pencils left. This can be expressed as the equation 3x = P.

Solving these two equations simultaneously, we can find the value of x, which represents the number of students in the group.

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Multiplicity refers to the exponents of the factors.  For example:

x³(x + 1)(x + 2)²(x² + 1) = 0

x:        has a multiplicity of 3 because its exponent is 3

x + 1:    has a multiplicity of 1 because its exponent is 1:  (x + 1)¹

x + 2:    has a multiplicity of 2 because its exponent is 2

x² + 1:    has a multiplicity of 1 because its exponent is 1: (x² + 1)¹

Hope this helped!

Answer:

$236.38

3.20%

Step-by-step explanation:

Simple interest = PNR/100 where P = Principal = 13132/-

N = 8 months = 8/12 years and r = 2.7%

Hence simple interest = 13132 (8/12)(2.7/100)

= 236.376

= 236.38 dollars

-----------------------------------------------------

2) On the same notation, here PNR/100 = 8546(1)(R)/100=273.47

Solving

R = 273.47(100)/8546 = 3.19999

= 3.20% apprxy.

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20 divided by 1/3 = 6 2/3, therefore Ms Chavez used 6 and two thirds of eggs.

Final answer:

Ms. Chavez will use 6 eggs to make cookies.

Explanation:

Ms. Chavez bought 20 eggs at the market. She will use 30% of these eggs to make cookies.

To find out how many eggs Ms. Chavez will use to make cookies, we can multiply the total number of eggs by the percentage used:

Number of eggs used = 20 × 0.30

Number of eggs used = 6

Therefore, Ms. Chavez will use 6 eggs to make cookies.

0.85=0.85

3/5=0.60

0.15=0.15

7/10=0.70

L-G

0.15, 3/5, 7/10, 0.85

To order the numbers from least to greatest, convert the fractions to decimals and compare. The ascending order is 0.15, 0.6, 0.7, and 0.85.

To order the given numbers from least to greatest, we can convert all the fractions to decimals.

The numbers in ascending order are: 0.15, 0.6, 0.7, 0.85.

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