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1 year ago

The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?

Mathematics

1 answer:

Alinara [238K]1 year ago

8 0

Answer:

Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

Step-by-step explanation:

The answer is the first one because the slope is technically $\frac{2}{1}$

Up 2 over 1

Since the slope is positive, the graph goes to the right.

(0, -6) is the y intercept because it intersects the y - axis.

Then you draw those two points and connect them.

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The side length, s, of a cube is 4x2 3. if v = s3, what is the volume of the cube?

Veseljchak [2.6K]

Answer:

The Volume of the cube is

$(64x^{6}+144x^{4}+108x^{2}+27)$

Step-by-step explanation:

we know that

The volume of a cube is equal to

$V=s^{3}$

where

s is the length side of the cube

In this problem we have

$s=(4x^{2} +3)$

Substitute

$V=(4x^{2} +3)^{3}$

Remember that

$(4x^{2} +3)^{3}=(4x^{2} +3)^{2}(4x^{2} +3)$

$(4x^{2} +3)^{2}(4x^{2} +3)=[16x^{4}+24x^{2} +9]( 4x^{2} +3)$

$=64x^{6}+48x^{4}+96x^{4}+72x^{2}+36x^{2}+27$

Combine like terms

$=64x^{6}+144x^{4}+108x^{2}+27$

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1 year ago

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Harriet is cultivating a strain of bacteria in a petri dish. Currently, she has 103 bacteria in the dish. The bacteria divide ev

SVEN [57.7K]

Based on the conditions given above, the number of bacteria at any time t (in hours) is calculated by the equation,
at = (a1)(2^t/2)

where a1 is the initial number of bacteria and at is the number at any time t. Substituting the givens,
a6 = (103)(2^6/2) = 824

Thus, there are 824 bacteria after 6 hours.

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1 year ago

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Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The tab

IceJOKER [234]

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

$\frac{5}{6} = \frac{10}{x}$ - Express the ratios using fractions; use x to show the missing value

$5x = 60$ - Cross multiply to find the value of x

$x = 60 / 5$ - Solve the equation to find x

$x = 12$ - The number of losing is 12 if there are 10 winning spaces

2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.

$\frac{5}{6} = \frac{x}{18}$

$6x = 90$

$x = 90 / 6$

$x =15$ - The number of winning spaces is 15 if there are 18 losing spaces

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1 year ago

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charle [14.2K]

If they sold 10 hammers and each hammer sells together with a package of nails for $12, that would be $120 total. Now subtract that from $950.50 and you get $830.50. Divide that by the remaining packages of nails sold (110 because you already sold 10 together with the hammers) and you get $7.55. Each package of nails sold for $7.55. Hope that helps!

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1 year ago

Expand (2x-3y)^4 using Pascal's Triangle. Show work

deff fn [24]

(2x+3y)⁴
1) let 2x = a and 3y = b

(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle

0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1

0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:

(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):

2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)

16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴

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1 year ago