1. Refer to the equation 2x − 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph the line.

Answer:

B

Step-by-step explanation:

Remember that slope=rise/run. You can find the right graph with the slope of 2/3 very easily by counting, upward 2 and rightward 3.

The number of bags he can make without having any cookies left over is 4 bags.

48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

64 = 1, 2, 4, 8, 16, 32 and 64

100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The highest common factor of 48, 64 and 100 is 4

Therefore, the number of bags he can make without having any cookies left over is 4 bags

Each bag has:

chocolates cookies = 48/4

= 12 each

Vanilla cookies = 64/4

= 16 each

Raisin cookies = 100/4

= 25 each

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Diego can make 12 bags without having any cookies left over, ensuring each bag contains an equal number of each flavor.

To determine how many bags Diego can make without having any cookies left over, we need to find the greatest common divisor (GCD) of the quantities of each type of cookie.

Step 1:

Find the GCD of the quantities of each type of cookie:

GCD(48, 64, 100) = 4

Step 2:

Calculate the number of bags Diego can make:

Each bag will contain 4 cookies of each flavor, as determined by the GCD.

For chocolate chip cookies: 48 cookies ÷ 4 cookies/bag = 12 bags

For vanilla cookies: 64 cookies ÷ 4 cookies/bag = 16 bags

For raisin cookies: 100 cookies ÷ 4 cookies/bag = 25 bags

Step 3:

Determine the minimum number of bags Diego can make without any cookies left over:

The minimum number of bags is determined by the smallest number of bags he can make for any type of cookie, which is 12 bags for chocolate chip cookies.

Therefore, Diego can make 12 bags without having any cookies left over.

Answer:

A=lw is a formula for the area. L is length, W is width.

The distance from Indiana to Louisville is 1.37 inches on map.

Step-by-step explanation:

Distance from texas to milwaukee = 1000 miles

Distance on map = 13.7 inches

Distance from indiana to louisville = 100 miles

Distance on map = x

Using proportion;

Distance from texas to milwaukee: distance on map :: Distance from indiana to louisville : Distance on map

[tex]1000:13.7::100:x[/tex]

Product of mean = Product of extreme

[tex]100*13.7=1000*x\\1370=1000x\\1000x=1370[/tex]

Dividing both sides by 1000;

[tex]\frac{1000x}{1000}=\frac{1370}{1000}\\x=1.37\ inches[/tex]

The distance from Indiana to Louisville is 1.37 inches on map.

Keywords: Ratio, proportion, distance

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Answer:

Filled table below

Step-by-step explanation:

There are three columns to fill out according to the requirements of the question:

The observed time will be taken from the given table (or scattered points in the graph)

The predicted time will be computed from the equation of the best fit line

The residual will be the difference between both  

For x=4.0, the time spent exercising is 4.5 hours

If we use the line, we have

[tex]y=-0.4x+7.02= -0.4(4.0)+7.02=5.42[/tex]

The residual is 5.42-4.5=0.92

For x=5.0, the time spent exercising is 6.5 hours

If we predict with the line, we have

[tex]y=-0.4x+7.02= -0.4(5.0)+7.02=5.02[/tex]

The residual is 5.02-6.5=-1.48

The values will be shown in the table below

Answer:

n=-2

Step-by-step explanation:

-6n-2n=16

-8n=16

n=16/-8

n=-2

Answer:

A. (x , y) = ( 1,  4) is the SOLUTION of the given system of equations.

Step-by-step explanation:

Here, the given set of equations is:

2 y + 5x = 13  ....... (1)

2y - 3x = 5    ...... (2)

Now, to solve this question by SUBSTITUTION:

From (1), we get:

2 y + 5x = 13   ⇒   2 y = 13 - 5 x

or, [tex]y = \frac{13 - 5x}{2}[/tex]

Put this value of y in (2) . We get

[tex]2y - 3x = 5  \implies 2\times\frac{(13-5x)}{2}  - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x  = -8\\\implies x = 1[/tex]

Now, x = 1, put this value of x  in (1),

2 y + 5x = 13     ⇒ 2y + 5(1) = 13

or, 2 y = 13- 5 = 8

or, y = 8 / 2  = 4,   ⇒ y = 4

Hence, x  = 1, y = 4 is the SOLUTION of the given system of equations.

Answer:

The answer is A

Step-by-step explanation:

y = mx + c

m = 1/2

(2,-3)

y = (1/2)x + c

-3 = (1/2)(2) + c

c = -4

y = (1/2)x - 4

Option 3

The solution for given expression is [tex]\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}[/tex]

Given that we have to divide,

[tex]\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}[/tex]   ---- (A)

Let us first factorize each term and then solve the sum

Using [tex]a^2 - b^2 = (a + b)(a - b)[/tex]

[tex]x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)[/tex]  ----- (1)

[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex]   ----- (2)

[tex]x^2 + 5x + 4 = (x+1)(x + 4)[/tex]   ---- (3)

[tex]x^2 -2x - 8 = (x-4)(x + 2)[/tex]   ---- (4)

Now substituting (1), (2), (3), (4) in (A) we get,

[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}[/tex]

To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.

[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \times \frac{(x - 4)(x + 2)}{(x + 1)(x + 4)}[/tex]

On cancelling terms we get,

[tex]= \frac{(x -4)(x-4)}{(x + 3)(x + 1)}[/tex]

Thus option 3 is correct

Answer:

There are 80 birds in the flock of cardinals.

Step-by-step explanation:

Given,

Number of seagulls in a flock = 20

Total number of birds of new flock = 100

To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.

Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock

Number of birds in cardinal = [tex]100-80=20[/tex]

Hence there are 80 birds in the flock of cardinals.

Answer:

x = 0.6 and x = -1.75

Step-by-step explanation:

80x2+92x−84=0

Use quadratic formula

x = (−b ±√(b2−4ac))/√2a

x = (-92 ± √(35344)) / 160

x = 95/160 and x = -280 / 160

x = 0.6 and x = -1.75

Answer:

y = 2

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32, thus

y = [tex]\frac{32}{x^2}[/tex] ← equation of variation

When x = 4, then

y = [tex]\frac{32}{4^2}[/tex] = [tex]\frac{32}{16}[/tex] = 2

Answer:

6 large, 12 medium and 18 small

Step-by-step explanation:

Lets call small pizzas s, medium pizzas m and large pizzas l, with its respective prices $10, $15 and $40.

As they sell as many small as medium and large combined we can say that:

s = m + l [eq 1]

Also, as the number of medium is twice the larges we can say that:

m = 2l [eq 2]

Finally, as the get $600 we know that every amount sold multiplied by its price, and summing all together must bring $600:

10s + 15m + 40l = 600 [eq 3]

Lets replace s by its value in eq 1:

10s + 15m + 40l = 10 (m+l) 15m + 40l = 10m +10l + 15m + 40l = 600

25m + 50l = 600

Now we can replace m by its value in eq 2:

25m + 50l = 25 (2l) + 50 l = 50l + 50l = 100l = 600

100l = 600

Now divide both sides by 100:

l = 6

So, 6 large pizzas were sold.

Replace l=6 in eq 2:

m = 6*2

m = 12

12 medium pizzas were sold.

Finally, replace l=6 and m=12 in eq 1

s = m + l = 12 + 6 = 18

And 18 small pizzas were sold.

Lets verify our results in eq. 3:

10*(18) + 15*(12) + 40*(6) = 600

180 + 180 + 240 = 600

360 + 240 = 600 ---> Verified!

The ratios of the number of people to the number of rollercoaster cars are proportional because all the given ratios simplify to 6:1.

To determine if the ratios of the number of people to the number of rollercoaster cars are in a proportional relationship, we must see if the ratios are equivalent. If we look at the provided ratios, 18:3, 30:5, 36:6, and 48:8, we see that when simplified all become 6:1. This indicates that the relationship is indeed proportional because the same ratio is maintained throughout all given pairs.

D) 12 cm is the right answer

Step-by-step explanation:

Given

[tex]Radius\ of\ sphere = r_s = 6\ cm\\Height\ of\ cone = h = 6 cm\\[/tex]

As the volumes of cone and sphere are same

[tex]V_s = V_c\\\frac{4\pi {r_s}^3}{3} = \frac{\pi {r_c}^2h}{3}[/tex]

Putting the known values

[tex]\frac{4\pi {6}^3}{3} = \frac{\pi {r_c}^2*(6)}{3}[/tex]

Dividing both sides by pi

[tex]\frac{4\pi {(6)}^3}{3\pi } = \frac{\pi {r_c}^2*(6)}{3\pi }\\\frac{4*{(6)}^3}{3} = \frac{{r_c}^2*(6)}{3}[/tex]

Multiplying both sides by 3

[tex]4*(6)^3 = 6{r_c}^2\\{r_c}^2 = \frac{4*(6)^3}{6}\\{r_c}^2 = 4 * 6^2\\{r_c}^2 = 144[/tex]

Taking Square root on both sides

[tex]\sqrt{{r_c}^2}=\sqrt{144}\\r_c = 12\ cm[/tex]

Hence,

D) 12 cm is the right answer

Keywords: Volumes, areas

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Two expressions connected with equal sign is called equation. a=1/3b is the value for equation 12ab=4.

Two expressions connected with equal sign is called equation.

Given 12ab=4

We need to solve for a

12ab=4

Divide both sides by 12b

a=4/12b

a=1/3b

So  a=1/3b is the value of a for equation 12ab=4

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Answer:

a=-2 and b=-2

Step-by-step explanation:

So I just used Elimination I made the top part the same as b then I just subtract and did some other stuff,hope the pic helps

Answer:

Your answer is C. ( - infinity , 2]

Step-by-step explanation:

Because it is, and I found the answer right next to an image I was searching up. Coincidences, am I right?

The range is: B. {12, 4, -6}

Step-by-step explanation:

Given

12x + 6y = 24

Here x is the input and y is the output

So,

Replacing y with f(x)

[tex]12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}[/tex]

Domain =  {-4, 0, 5},

We will put the elements of domain, one by one, to find range

[tex]f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6[/tex]

Hence,

The range is: B. {12, 4, -6}

Keywords: Range, Domain, functions

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{12, 4, -6}

Step-by-step explanation:

The relation is given by the equation as 12x + 6y = 24 ........... (1)

Now, the domain of this function is {-4, 0, 5}

We have to find the range of this function corresponding to the given domain.

Now, for x = - 4,  

12(-4) + 6y = 24 {From equation (1)}

⇒ 6y = 72

⇒ y = 12

Now, for x = 0,  

12(0) + 6y = 24 {From equation (1)}

⇒ 6y = 24

⇒ y = 4  

Now, for x = 5,  

12(5) + 6y = 24 {From equation (1)}

⇒ 6y = -36

⇒ y = -6

Hence, the range for the relation is {12, 4, -6} (Answer)

1. 8/64=1/8

2. 5/16

3. 33/84

4. 15/45=3/9=1/3

Answer:

1. 8/64=1/8

2. 5/16

3. 33/84

4. 15/45=3/9=1/3

Step-by-step explanation:

Answer:

The answer is 34

To solve this, percentage calculations were used. The geologist visited 6 volcanoes in California, which is 15% of 40, and the remaining 34 in Alaska.

The question requires us to calculate the number of volcanoes the geologist visited in California and Alaska. The total number of volcanoes visited is 40, and 15% are in California. To find the number of volcanoes in each state, we employ basic percentage calculations.

First, to find the number of volcanoes in California, we multiply the total number by 15% (or 0.15):
Number of volcanoes in California = 40 * 0.15 = 6.

To find the number of volcanoes in Alaska, we subtract the number of volcanoes in California from the total:
Number of volcanoes in Alaska = 40 - 6 = 34.

Therefore, the geologist visits 6 volcanoes in California and 34 volcanoes in Alaska.

Answer:     edmentum 100%

f(x) − g(x)  = 2.5e-0.04x − (1.2 + 0.2x)

= 2.5e-0.04x − 1.2 − 0.2x

Step-by-step explanation:

The algebraic expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

Given that the functions from part A are :

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

To find the expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term.

Step 1: Given two functions

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

Step 2: find f(x) - g(x),  subtract each term:

[tex]f(x) - g(x) = (2.5e^{(-0.04x)}) - (1.2 + 0.2x)[/tex]

Simplifying further, combine like terms:

[tex]f(x) - g(x) = 2.5e^{(-0.04x) }- 1.2 - 0.2x[/tex]

Therefore, the algebraic expression resulting from f(x) - g(x) is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

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Answer:

3.45

Step-by-step explanation:

if you look at the picture all the steps are provided

GOOD LUCK!!

Answer: Radius

Step-by-step explanation: The radius of a circle is a segment that joins the center of the circle to a point on the circle.

The minute hand on a clock would start in the center and go outwards towards a certain number. However, the minute hand would not go the full length across the clock so it's not the diameter.

The circumference of a circle which is another way of saying the perimeter of the circle is the distance around the circle so it would not be the circumference.

This means that the minute hand would represent the radius of a clock.

The 5 inch length of the minute hand on the clock is actually a radius, not a diameter or circumference. This radius is the distance from the center of the clock face to the tip of the minute hand. The diameter, which would be twice the length of the radius, would be 10 inches, and the circumference of the circle formed by the minute hand's movement would be approximately 31.4 inches.

In this case, the 5 inches refers to the radius of the circle that is created by the minute hand of the clock as it moves around the clock face. This radius is the distance from the center of the clock face to the tip of the minute hand. In general, in any circular motion, the length of the revolving component, like a clock hand, from the center to its tip is called the radius of the circle.

The diameter is simply twice the radius, and in this case if the radius is 5 inches, the diameter would be 10 inches. The circumference of a circle is calculated by the formula 2πr (2 times the value of pi times the radius), hence, in this instance, it would be 10π inches or approximately 31.4 inches.

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Answer:

Part a) [tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) [tex]V(3)=18.75\pi\ in^3[/tex]  (see the explanation)

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of cylinder

h is the height of the cylinder

we have that

[tex]B=\pi r^{2}[/tex]

Part a) Write the function, V(h), that represents the volume of the cylinder

we have

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]B=\pi (2.5)^{2}[/tex]

[tex]B=6.25\pi\ in^2[/tex]

The volume is

[tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) Find V(3) and tell what it represents

V(3) represent the volume of the cylinder with a height of 3 inches

so

For h=3 in

substitute

[tex]V(3)=6.25\pi(3)\ in^3[/tex]

[tex]V(3)=18.75\pi\ in^3[/tex]

Final answer:

The function for the volume of the cylinder with diameter 5 inches is V(h) = π * (2.5 inches)² * h. To find V(3), we calculate the volume with height 3 inches, which represents the physical volume of the cylinder at that height.

Explanation:

To find the volume of the cylinder, V(h), we must use the formula V = πr²h, where r is the radius of the base, and h is the height of the cylinder.

Part A: Given that the diameter is 5 inches, the radius is half of the diameter, so r = 5 / 2 = 2.5 inches. Thus, the function representing the volume is V(h) = π * (2.5 inches)² * h.

Part B: To find V(3), we substitute h with 3 inches into the function: V(3) = π * (2.5 inches)² * 3 inches. This gives us the volume of the cylinder when the height is 3 inches.

M=4/5 y - intercept of -2

y= mx+b - slope formula

slope is also m

b is the y-intercept

answer:

y= 4/5x-2

Answer:

y = [tex]\frac{4}{5}[/tex] x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{4}{5}[/tex] and c = - 2

y = [tex]\frac{4}{5}[/tex] x - 2 ← equation of line

Answer:

f=10

Step-by-step explanation:

Answer:

B 35%

Step-by-step explanation:

35/100 reduces to .35. To turn this into a percent, multiply it by 100 and add a percent sign. .35 * 100 = 35. 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares is 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares.

= 35/100 x 100

= 35%

Thus,

The percentage of shaded squares is 35%

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They sold 25 packets, containing 7 pencils each. So, they sold a total of

[tex]25\cdot 7=175[/tex]

pencils. This means that

[tex]319-175=144[/tex]

pencils were not sold.

Answer:

i believe it is the 2nd one

Step-by-step explanation:

I think the answer is B because the line is a congruent to the line segment.