given line ac with line ab=2x-4, bc=4x and ac=2x+12 find ac

Answer:

The answer to your question is: 3.7 hours

Step-by-step explanation:

Kam can make 72 cookies/ 3 hours

Madison can make 120 cookies/4 hours

Time to make 200 cookies together = ?

First, calculate the number of cookies make per hour

Kam            72 ---------------- 3

                   x   ----------------  1 hour

  x = 72/3 = 24 cookies/h

Madison

             120 -------------   4 hours

               x ---------------      1 hour

x = 120 / 4 = 30 cookies

Now we write and equation where "t" will be time

         24t + 30t = 200      and solve it

         54t = 200

        t = 200/54

        t = 3.7 hours

The time taken by both of them will be 3.7 hours.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The given problem can be solved as follows,

The number of cookies made by Kam in 1 hour = 72/3 = 24.

The number of cookies made by Madison in 1 hour = 120/4 = 30.

The total number of cookies made by them in one hour = 30 + 24 = 54.

The time taken to make 200 cookies is the ratio of 200 and 54 as given below,

Time taken by both to make 200 cookies = 200/54 = 3.7 hours.

Hence, Kam and Madison would take 3.7 hours to make the cookies together.

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Answer:

This is cluster sampling.

Step-by-step explanation:

American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.

This is a type of cluster sampling.

This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.

Answer:

The answer to your question is:

a) ∠FGH = 34°

b) ∠HGI = 34°

c) ∠FGI = 68°

Step-by-step explanation:

We know that GH bisects ∠FGI

a) Find ∠FGH

∠ FGH = 5x - 6

∠ HGI = 6x -14

                      ∠ FGH = ∠ HGI

                     5x - 6   =  6x - 14

                    5x - 6x = -14 + 6

                          -1x = - 8

                            x = 8

∠ FGH = 5(8) - 6

            = 40 - 6

            = 34°          

b) m∠HGI = 6(8) -14

                = 48 - 14

                =  34°          

c) m∠FHI =  ∠ FGH + ∠ HGI

                = 34 + 34

               = 68°    

−2x + 3y + 5z = −21

−4z = 20

6x − 3y = 0

do -4z=20 first

divide both sides by -4 to get z by itself

-4z/-4=20/-4

z=-5

Use z=-5 into −2x + 3y + 5z = −21

-2x+3y+5(-5)=-21

-2x+3y-25=-21

move -25 to the other side

sign changes from -25 to +25

-2x+3y-25+25=-21+25

-2x+3y=4

6x-3y=0

find x by eliminating y

Add the equations together

-2x+6x+3y+(-3y)=4+0

-2x+6x+3y-3y=4

4x=4

Divide by 4 for both sides

4x/4=4/4

x=1

Use x=1 into 6x − 3y = 0

6(1)-3y=0

6-3y=0

Move 6 to the other side

6-6-3y=0-6

-3y=-6

Divide both sides by -3

-3y/-3=-6/-3

y=2

Answer:

(1, 2, -5)

Answer:

55 children's tickets

Step-by-step explanation:

Let the number of adult tickets sold  = a

Let the number of children tickets sold = c

As per the statement "The adult tickets were sold four times as many as children's tickets".the equation will be

a = 4c ----- (1)

As per second statement "the prices of the tickets for adults and children are $10 and $5 respectively."

The total price of the adult tickets = 10a

the total price of the children tickets = 5c

total tickets were sold for = $2,475

So the equation will be

10a + 5c = 2,475 ------(2)

Now substitute the the value of a from equation (1) to equation (2).

10(4c) + 5c = 2,475

40c + 5 c = 2,475

45c = 2,475

c = [tex]\frac{2475}{45}[/tex]

c = 55

The number of children's tickets 55.

Final answer:

To find the number of children's tickets sold in a spaghetti dinner event with given total sales and ticket prices, set up and solve the relevant equations step by step.

Explanation:

Given:

Total ticket sales for a spaghetti dinner = $2475

Adult ticket price = $10

Children's ticket price = $5

Number of adult tickets sold = 4 times the number of children's tickets sold

To find: Number of children's tickets sold

Step-by-Step Solution:

Let the number of children's tickets sold be x

Number of adult tickets sold = 4x

Write the equation: 5x + 10(4x) = 2475

Solve for x to find the number of children's tickets sold

x = 55

Answer:

  1)  60°, 75°, 120°, 105°

  2)  101.5 m

Step-by-step explanation:

1) The sum of ratio units is 4+5+8+7 = 24, which corresponds to the sum of angles, 360°. Then each ratio unit must stand for 360°/24 = 15°. Multiplying the given ratio units by 15° gives the angle measures:

__

2) The similarity statement and the scale factor mean ...

  MJ : TQ = 4 : 7

  7·MJ = 4·TQ . . . . . . . . . "cross multiply"

  TQ = 7/4×MJ = 7/4(58 m) . . . . . divide by 4, substitute the value of MJ

  TQ = 101.5 m

Answer:

5x - y = 27

Step-by-step explanation:

Slope is the direction of line and it is calculated as,

[tex]Slope = \frac{y-y_{1}}{x-x_{1}} [/tex]

where (x₁, y₁) is any two points on the line.

Here, we have given that

Slope = 5  and (x₁, y₁) = (5, -2)

∴  [tex]5 = \frac{y-(-2)}{x-5} [/tex]

⇒ 5(x - 5) = y + 2

⇒ 5x - 25 = y + 2

⇒ 5x - y = 27

Hence, the equation of a line is: 5x - y = 27

Answer:

Han used a convenience nonrandom sampling approach

Step-by-step explanation:

The convenience nonrandom sampling approach consists in collecting a sample just because it is convenient. This means that the subjects are easy to select.

Han did precisely this, he went to the teacher's lounge and surveyed the faculty present there. He did not put any further effort like, for example, wait for more teachers to have a larger sample or make sure the ratio between female and male teachers was the same.

Answer:

q.1 quarter mile

q.2 half mile

:)

addition!

Step-by-step explanation:

Answer:

C. y = 115 000(1.05)^x

Step-by-step explanation:

The formula for the amount accrued on an investment earning compound interest is

[tex]A = P(1 + r)^{t}[/tex]

where

P = the amount of money invested (the principal)

r = the interest rate per period expressed as a decimal fraction

t = the number of periods

In this problem,  

P = $115 000

r =  5 % = 0.05

By 2010, Luca's house will have increased in value for three years. Its value will be  

[tex]A = 115000(1 + 0.05)^{3}\\\text{The correct formula for the value of his home x years after 2010 is}\\ y = 115000(1.05)^{x}[/tex]

Answer:

C: y = 115,000(1.05)x

Step-by-step explanation:

(havn’t actually did any math, but this is just process of elemination.)

{I’m just looking at the end of these, because the start is all the same}

if the number with the (perenthese) is below 1, it is a decreas, and the problem says it’s increasing by 5%. (1.5) Is equal to 50% increase so that means your answer would be (1.05) Because anything times 1 is the larger number, but when u add that 0.5, it’s raising the number up by 5%.

Analyzing the data, the following values were

Mean = 21.84

Median = 15.8=

Standard deviation = 18.97

Coefficient of skewness = 0.955

a. To find the mean, median, and standard deviation, you can use the following formulas:

Mean = sum of all values / number of values

Median = middle value when the values are arranged in ascending order

Standard deviation = square root of [(sum of squared differences from the mean) / (number of values - 1)]

Mean = (4.2 + 6.3 + 7.5 + ... + 83.6) / 15 = 21.84

Median = 15.8 (the 8th value when arranged in ascending order)

Standard deviation = √([(4.2 - 21.84)² + (6.3 - 21.84)² + ... + (83.6 - 21.84)²] / 14) = 18.97

b. To find the coefficient of skewness using Pearson's method, you can use the following formula:

Coefficient of skewness = (3 * (mean - median)) / standard deviation

Coefficient of skewness = (3 * (21.84 - 15.8)) / 18.97 = 0.955

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Answer: 20 times

Step-by-step explanation:

1 hour = 60 minutes.

Duration of the song = 3 minutes each time = 3minutes/time

So, the number of times the song can be played in an hour=

= 60minutes÷3minutes/time = 20 times

So, you can play that song in an hour for 20 times.

Answer: 20 times

[tex]\textit{\textbf{Spymore}}[/tex]  

Final answer:

A 3-minute song can play 20 times in an hour by simply dividing the 60 minutes in an hour by the length of the song, which is 3 minutes.

Explanation:

A 3-minute song can play 20 times in an hour. Here's a step-by-step breakdown of the math:

Understand that there are 60 minutes in an hour.

Divide the total minutes in an hour (60) by the length of the song (3 minutes).

The result is the number of times the song can be played in one hour, which is 20 times.

The question seems to diverge from the provided information about the collection of songs with varying lengths. However, for the direct question asked, we do not need those details.

Answer:

See explanation

Step-by-step explanation:

Each ounce of fruit will supply

Each ounce of nuts will supply

Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.

Then x ounces of fruit will supply

and y ounces of nuts will supply

Every package must provide

A. You get the system of three inequalities

[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]

B. See attached diagram

[tex]\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}[/tex]

Three inequalities were formulated: 1x + 1y ≥ 7 for protein, 2x + y ≥ 11 for carbohydrates and x + y ≤ 10 for fat, with x being fruit and y being nuts. These needs to be graphed to find a feasible region that meets all conditions. A table summarizing the needed unit amount per ounce for protein, carbohydrates, and fats for both fruits and nuts was also provided.

To solve your question, first, let's express the given conditions as inequalities:

Graphing

these inequalities would result in a feasible region that should fulfill all conditions.

The following table summarizes this:

Fruit

Nuts

Requirements per package

Protein1 unit per ounce1 unit per ounceAt least 7 unitsCarbohydrates2 units per ounce1 unit per ounceAt least 11 unitsFat1 unit per ounce1 unit per ounceNo more than 10 units

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Answer:

so, the figure here is a cylinder with a semi sphere on the top, we know the height of whole structure, and the radius of the semi sphere, which is the same as the radius of the cylinder (you can see it because the radius of the semisphere is constant, and you can thin on it as half a sphere over a cylinder).

First, the cylinder will be the structure without the semi sphere, so his height will be te total height minus the radius of the semi sphere, which is 0.9μm.

so now we know the height and the radius of the cylinder, the surface or the sides of it is 2*3.14*r*h = 2*3.14*0.9μm*0.1μm = 0.5662[tex]μm^{2}[/tex].

The surface area of the cylindrical part of the microvillus is calculated by multiplying pi (3.14) with the diameter (0.1μm) and height (1.0μm) to yield a result of 0.314μm².

To calculate the surface area of the cylindrical 'sides' of the microvillus, which we can consider to be a cylinder without its top and bottom parts, the formula used is: π * diameter * height. In this case, the diameter of the microvillus is 0.1μm (which is the diameter of the hemispherical top) and the height is 1.0μm.

Substitute these values into the formula:

Surface area = π * diameter * height = 3.14 * 0.1μm * 1.0μm = 0.314μm².

Thus, the surface area of the cylindrical part of the microvillus is 0.314 micrometers squared.

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Answer:

Actual Perimeter = 100 km

        Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

                1 mm = 5 km

               5 mm = 5 × 5 km

                          = 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

                                 = 4 × 25

                                = 100 km

                                        = 25 × 25

                                        = 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

the answer is b)  5/3    1/3

                           x       y

Answer:

896 apples

Step-by-step explanation:

We need to order this data to solve the problem. "X" will be the total number of apples he collected.

"He gave the first guard half of his apples and 1 apple more". Mathematically:

[tex]Guard 1 = \frac{X}{2}+1\\[/tex]

"To the second guard, he gave half his remaining apples and 1 more". Mathematically:

[tex]Guard2 = \frac{X}{4}+1[/tex]

"He did the same to each of the remaining five guards". Mathematically:

[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":

[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Solving this equation results in X = 896 apples.

Answer:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Step-by-step explanation:

We will have a partial funcion to define an expression for the monthly phone charge, because we have a condition that changes the monthly cost.

For months under 130 minutes, there will not be any additional charge other that tha base monthly cost, so the expression for the months under 130 minutes will be the monthly fee.

For months over 130 we will have the same information than above, but we have to add a fee for every minute over 130 minutes. To find the amaunt of minutes over 30 minutes we will just subtract 130 to the amount of minutes used: (m-130). Then we will multiply that number times the cos of each minute over 130 minutes: 9*(m-130). Finally we will add the basic phone fee: 15.99 + (0.09*(m-130)).

Now we set the conditions and use the correct notation for a partial function and we get:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Answer:

1st car is 6mph 2nd car is 100mph

Step-by-step explanation:

ans to first car is in the question

and just subtract total travelled distance of car 1 after 2.5 hours. then subtrct it from the total distance and with the remaining distance solve for speed of other car which is distance over time.

The speed of the slower car is 52 mph, and the speed of the faster car is 52 mph + 6 mph, which equals 58 mph. This was calculated using the relationship between speed, distance, and time.

Let's denote the speed of the slower car as v miles per hour (mph), which means the faster car will have a speed of (v + 6) mph. Since they are travelling in opposite directions, their speeds add up when determining how far apart they will be over a period of time.

Combined speed = v + (v + 6) = 2v + 6 mph

After 2.5 hours, they are 275 miles apart. Using the formula for distance, which is Distance = Speed ×Time, we have:

Distance = (2v + 6) × 2.5

275 miles = (2v + 6) × 2.5

Solving for v, we divide both sides by 2.5:

110 = 2v + 6

Now, subtract 6 from both sides:

104 = 2v

Finally, divide by 2 to find the speed of the slower car:

v = 52 mph

Therefore, the speed of the slower car is 52 mph, and the faster car is 52 mph + 6 mph, which equals 58 mph.

Explanation:

All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.

The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.

The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.

Answer:

The function input is -20 when the output is 25

Step-by-step explanation:

we have

[tex]y=-75-5x[/tex]

where

y is the dependent variable or output

x is the independent variable or input

If the output is 25

then

y=25

substitute

[tex]25=-75-5x[/tex]

Solve for the function input is the same that solve for x

Isolate the variable x

Adds 5x both sides

[tex]25+5x=-75-5x+5x[/tex]

[tex]25+5x=-75[/tex]

subtract 25 both sides

[tex]25+5x-25=-75-25[/tex]

[tex]5x=-100[/tex]

Divide by 5 both sides

[tex]x=-20[/tex]

therefore

The function input is -20 when the output is 25

Final answer:

To find the function input when the output is 25, solve the given equation 25 = -75 - 5x to find x = -20.

Explanation:

When the function's output is 25, the equation is 25 = -75 - 5x. To find the function input when the output is 25, solve for x:

25 = -75 - 5x
100 = -5x
x = -20

Therefore, the function input when the output is 25 is -20.

Answer:

The same amount of applesauce, nuts, flour, and raisins is used.

Step-by-step explanation:

Have you ever heard of the question, "which weighs more, a pound of steel, or a pound of feathers?" And then everyone is shocked when they weigh the same, even though they both were said to weigh a pound?

This question is like that.

One cup of each is used, so they are all a cup, which means an equal amount of all of them were used.

Answer:

It will take them 3.43 hours.

Step-by-step explanation:

Let T denote the total cookies that need to be cocked. Observe that:

Then, by 1) and 2), if they work together would we able to make

[tex]\frac{T}{6}+\frac{T}{8}=\frac{8T+6T}{48}=\frac{14}{48}T=\frac{7}{24}T[/tex]

cookies per hour.

Therefore, in order to finish the T cookies they will need [tex]\frac{24}{7}\approx3.43 hours[/tex]

Answer:13

Step-by-step explanation: Six down to zero. Then zero up to seven.

Answer: B

Because you can eliminate the ones that don’t have an inequality symbol so that leaves you with B and D and the 20 should be on the right by itself since that is the constant we are given and it’s not altered in the question

The algebraic expression for the given problem is:

Speed of airplane = 2x + 20

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) used to represent a quantity or a mathematical relationship between quantities.

" An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour"

The algebraic expression for the given problem is:

Speed of airplane = 2x + 20

Where x is the speed of the car in miles per hour.

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Answer:

  y = 8x + 3

Step-by-step explanation:

The slope-intercept form of the equation of a line is ...

  y = mx + b

Putting 8 where m is, and 3 where b is, we get ...

  y = 8x + 3

_____

Yes, it's really that simple.

The equation of the line with a slope of 8 and a y-intercept of 3 is y = 8x + 3. This is found by substituting the given values into the slope-intercept formula, which is y = mx + b.

In Mathematics, the slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept of the line. So, for the question, since the given slope, m = 8, and the y-intercept, b = 3, you can substitute these values into the formula to get the equation of the line. This results in the equation y = 8x + 3.

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Answer:

The answer to your question is: $ 3.92 / kg

Step-by-step explanation:

Data

Lean ground beef cost = $1.78

price of 1 kg = ?

Equivalence  1 kg = 2.2 lbs

Process (rule of three)

                                 $1.78  -------------------   1 pounds

                                    x      -------------------    2.2 pounds

                       x = 2.2(1.78) / 1 = $ 3.92 / kg

Answer:

9 (option D)

Step-by-step explanation:

Hi Dlynjen! How are you?

Well, as maybe you know a quadratic function is a polynomial of degree 2, that is, the highest exponent in the variable is 2 (formula: y = ax^2 + bx + c). The graph of a quadratic function is a parabola (it has a U-shape).

The vertex of a parabola is the highest or lowest point of the curve (depending on whether the U opens up or down). In this case the parabola opens up because the exercise mentions the vertex is the point (x = 0, y = 1) and then for the other values of “x” (1, 2, 3, etc.) the values of “y” are higher (1, 4, 9, etc.), that's why the vertex is the lowest point in this case.

The exercise asks you to calculate the slope (or average rate of change) of the curve between x = 5 and x = 6, all you know so far is that as the curve opens up it is assumed that the slope will be positive but to calculate the slope must apply the following formula:

M = (y2 - y1) / (x2 -x1)

But we only know x1 = 5, x2 = 6, y1 = 16 (value of the table that corresponds to x1 = 5) and we must first know how much y2 is worth (for x2 = 6). For this we must know what is the quadratic function (formula) that gives rise to our parable.

If we analyze the table, we see that for each value of “x”, the value of “y” is equal to the square of (x-1), that is, if we take x = 3 as an example, the value of Y = (3 -1) ^ 2 = (2) ^ 2 = 4. And so with all the values. Having obtained this formula we can now calculate the value of “y” for x2 = 6:

Y2 = (6-1) ^ 2 = (5) ^ 2 = 25

Finally, we calculate the average exchange rate with the previous formula, knowing x1 = 5, x2 = 6, y1 = 16 and y2 = 25:

m = (y2 - y1) / (x2 -x1)  

m = (25-16) / (6-1)  

m = (9) / (1)  

m = 9

I hope I've been helpful!

Regards!