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3 years ago

4. How much sugar is needed to make 3 cup cakes?

Mathematics

1 answer:

amid [387]3 years ago

6 0

Answer:

A. $\frac{1}{2}$ Cups

Step-by-step explanation:

Firstly, we need to know that the recipe makes 12 cupcakes. This means that we need only a quarter of the required ingredients.

A normal batch has 2 cups of sugar

$2*\frac{1}{4} =\frac{2}{4} =\frac{1}{2}$

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Arrange in ascending order :

Musya8 [376]

Answer: 1/4, 4/7, 5/8

Step-by-step explanation: There are three ways:

1. <u>Convert each to a decimal: </u>

1/4 = 0.25

4/7 = 0.571

5/8 = 0.625

2. <u>Convert to a common denominator:</u>

It looks like we can multiply each by a whole number that will result in a denominator of 56:

1/4 *(14/14) = 14/56

4/7*(7/7) = 35/56

5/8 *(8/8) = 32/56

Now they can be directly compared to get the answer.

3. <u>Estimate the values. </u>

5/8 is clearly larger than 1/4. 4/7 is somewhere in between. Therefore, 1/4, 4/7, 5/8

8 0

2 years ago

Read 2 more answers

A given line has the equation 10x + 2y = −2.

worty [1.4K]

The equation is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2

Divide both sides by two

y = -5x -1

The slope-intercept form is $\boxed{ \ y = mx + c \ }$ , with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:

$\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }$

10x + 2y = −2 ⇒ a = 10, b = 2

$\boxed{m = - \frac{10}{2} \rightarrow m = -5}$

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same $\boxed{ \ m_1 = m_2 \ }$ . So $\boxed{m_1 = m_2 = -5}.$

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

$\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }$

Given that

m = -5
(x₁, y₁) = (0, 12)

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form $\boxed{ \ y = mx + c \ }$

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

$\boxed{Standard \ form: ax + by = c, with \ a > 0}$

$\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}$

$\boxed{Slope-intercept \ form: y = mx + k}$

<h3>Learn more </h3>

A similar problem brainly.com/question/10704388
Investigate the relationship between two lines brainly.com/question/3238013
Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant