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2 years ago

Which would be the best method to use to solve the following equations? Explain your reasoning.

Mathematics

1 answer:

o-na [289]2 years ago

7 0

A. square root property

$3x^2-192=0\\x^2-66=0\\x^2=66\\x= -\sqrt{66} or \sqrt{66}$

it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format

B. factorising

$x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3$

i just felt like this was easier to factorise than the other 2 options left

C. Completing the square

$x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7$

same reason personal preference

D- Quadratic

$x^2-17x-7=0\\x=\frac{-(-17)+\sqrt{(-17)^2-4(1)(-7)} }{2(1)} \\x=\frac{-(-17)-\sqrt{(-17)^2-4(1)(-7)} }{2(1)}\\x=17.4\\x=-0.402$

the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal

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statuscvo [17]

Answer: The required ratio would be 3 miles : 4 minutes.

Step-by-step explanation:

Since we have given that

Speed of a cheetah = 45 miles per hour

So, it means

Distance = 45 miles

Time = 1 hour = 60 minutes

So, the ratio of the distance it travels to the time it takes would be

Distance : Time

$45\ miles:60\ minutes\\\\=3\ miles :4\ minutes$

Hence, the required ratio would be 3 miles : 4 minutes.

3 0

2 years ago

What kinds of regular polygons can be used for regular tesselations

Ahat [919]

To tessellate a surface using a regular polygon, the interior angle must be a sub-multiple (i.e. factor) of 360 degrees to cover completely the surface.

For a regular three-sided polygon, the interior angle is (180-360/3)=60 °
Since 6*60=360, so a regular three-sided polygon (equilateral triangle) tessellates.
For a regular four-sided polygon, the interior angle is (180-360/4)=90 °
Since 4*90=360, so a regular four-sided polygon (square) tessellates.
For a regular five-sided polygon, the interior angle is (180-360/5)=108 °
Since 360/108=3.33... (not an integer), so a regular five-sided polygon (pentagon) does NOT tessellate.
For a regular six-sided polygon, the interior angle is (180-360/6)=120 °
Since 3*120=360, so a regular six-sided polygon (hexagon) tessellates.

5 0

3 years ago

Read 2 more answers

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1000 voters in th

garri49 [273]

Answer:

$z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945$

$p_v =P(Z>1.945)=0.0259$

If we compare the p value obtained with the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 2% of significance the proportion of residents who favored annexation is not significantly higher than 0.39.

Step-by-step explanation:

1) Data given and notation

n=1000 represent the random sample taken

$\hat p=0.42$ estimated proportion of residents who favored annexation

$p_o=0.39$ is the value that we want to test

$\alpha=0.02$ represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is higher than 0.39:

Null hypothesis: $p\leq 0.39$

Alternative hypothesis: $p > 0.39$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.02$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(Z>1.945)=0.0259$

4 0

3 years ago

Simple 3c-9d+7c+5d<br> Please help me

timama [110]

I believe 10c-4d would be your answer

4 0

2 years ago

Eli is following this recipe to bake bread rolls. He uses 600ml of water. How much of the others ingredients does he use? 600g f

RoseWind [281]

Answer:

720 grams of flour.

10.8 grams of salt.

14.4 grams of yeast

36 ml of oil.

Step-by-step explanation:

The recipe is:

600g flour

9g salt

12g yeast

30ml oil

500ml water

Now we use 600ml of water.

We can take the quotient between the amount of water we use and the amount of water in the recipe, this is:

600ml/500ml = 1.2

Then the ratio between the quantities we need to use and the quantities un the recipe should be always 1.2

Or the quantities that Eli needs to use will be 1.2 times the ones shown in the recipe.

Then she needs to use:

1.2*600g flour = 720 grams of flour.

1.2*9g salt = 10.8 grams of salt.

1.2*12g yeast = 14.4 grams of yeast

1.2*30ml oil = 36 ml of oil.

7 0

3 years ago