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Nadusha1986 [10]
3 years ago
15

A line passes through the origin and has a slope of 2/3​

Mathematics
1 answer:
Shalnov [3]3 years ago
5 0

Answer:

y=2/3x

Step-by-step explanation:

the origin is the point (0,0) and the given slope is 2/3

the equation for slope-intercept form is y=mx+b, where m is the slope and b is the y intercept

the slope is given, meanwhile, the y intercept is the point where the line passes through the y axis, and the x value is 0.

In this question, we actually have the y intercept given, which is (0,0)

we can put it all together then:

y=2/3x+0

or

y=2/3x

Hope this helps :)

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Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12
Inessa05 [86]

Answer:

The solution of the equations are -6 and 1

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- We want to find the solution of the equation (x + 2) (x + 3) = 12

- <em>At first lets use the Foil method to multiply the two brackets</em>

 (x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)

 (x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term

 (x + 2) (x + 3) = x² + 5x + 6

∵ (x + 2) (x + 3) = 12

∴ x² + 5x + 6 = 12

- Subtract 12 from both sides

∴ x² + 5x - 6 = 0

- <em>Factorize the left hand side</em>

∵ x² = (x)(x)

∵ -6 = 6 × -1

∵ 6x + -1x = 5x

∴ (x + 6)(x - 1) = 0

- <em>Lets use the zero product property </em>

∵ (x + 6)(x - 1) = 0

∴ x + 6 = 0 ⇒ <em>OR</em> ⇒ x - 1 = 0

∵ x + 6 = 0

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6 0
3 years ago
Read 2 more answers
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard devi
Tanya [424]

Answer:

Confidence Interval = (23.776, 24.224)

Step-by-step explanation:

Restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average.

⇒ Mean = 24 ounces.

Standard Deviation = 0.8

Number of bottles used for sample = 49

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Confidence level = 95%

Corresponding z value with 95% confidence level = 1.96

Now, confidence interval is given by the following expression :

Mean \pm z^*\times \frac{\sigma}{\sqrt{n}}\\\\=24\pm1.96\times \frac{0.8}{\sqrt{49}}\\\\=24\pm 0.224

Hence, Confidence Interval = (23.776, 24.224)

6 0
3 years ago
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