All categories

2 years ago

Write y=x^2-4x-1 in vertex form

Mathematics

1 answer:

Dvinal [7]2 years ago

7 0

Answer: y= (x+2)² − 5

Step-by-step explanation:

The way I got this answer is by completing the square. The first step though, when looking at this equation, is to see if we can factor it. The way to check is to look at the coefficient for x² which is 1, and the constant, in this case -1. If we multiply those together, we get −. Now we look at the middle term, 4x. We need to find any numbers that multiply to equal − 1x² and add to 4x. There aren't any, which means it is not factorable.

Hope I helped

You might be interested in

Can you help me find each measure?

madam [21]

Answer:

Step-by-step explanation:

1. the measure for HJ you can already see, start from h and draw a line to J. The measure shows 63 degrees.

2. start at F and draw a line to G first. the measure shows 65 degrees. Now continue the line from where you stopped at G, to H. There's no measure but you can see it is in a semicircle. A semicircle is 180 degrees andthe other two angles are 63 and 65.

So...

180=63+65+GH

subtract to get GH

180-63-65= 52

so the measure GH is 52 degrees. The full measure you are trying to find is FGH thought. So ad the 65 and the 52.

FGH =117 degrees.

3. The meaure is CDE. CD as you can see is a right angles, so 90 degrees. But there is no measure for DE. If you look to the angle vertical from DE which is BA. It measures 40 degrees. DE and BA are vertical so they are congruent. If DE equals 40 and CD equals 90, put them together and you get 130.

CDE= 130 degrees

4. Next measure is BCD. We already know CD is a 90 degree angle but BC is blank. You can see the measure BCD is in a semi circle. A semicircle equals 180, CD equals 90, and BA equals 40

so...

180= 90+40+BC

so subtract

180-90-40= 50

BC =50

so add BC=50 and CD=90. SO, BCD is 140 degrees.

5.The angle LMN is next. MN is 30 but LM is blank. LMN is in a semi circle.

A semicircle is 180 degrees.

so...

180=105+30+LM

subtract

180-105-30=45

LM = 45

Add LM=45 and MN=30

LMN is 75 degrees.

6.The last angle is LNP

If you look at it MP is a semi circle, so 180 degrees. And LM is 45 from our last question. so 180 +45=225

LNP=225

hope this helps

4 0

3 years ago

The burges are moving across the country .Mr burges leaves 3 hours before mrs.burges. If he averages 50 mph and she averages 70

kirill [66]

10.5 hours

let t be time then distance travelled by both is

Mr Burges ⇔ d = 50t ( distance = speed × time )

Mrs Burges ⇒ d = 70(t - 3)

At the point of overtaking both will have travelled the same distance

equating their distance and solving for t

70(t - 3) = 50t

70t - 210 = 50t ( subtract 50t from both sides )

20t - 210 = 0 ( add 210 to both sides )

20t = 210 ( divide both sides by 20 )

t = 10.5 hours

4 0

3 years ago

Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow

Pavel [41]

Answer:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

Step-by-step explanation:

Data given and notation

$\bar X_{1}=104$ represent the mean for the sample 1

$\bar X_{2}=106$ represent the mean for the sample 2

$\sigma_{1} =8.4$ represent the population standard deviation for the sample 1

$\sigma_{2}=7.6$ represent the population standard deviation for the sample 2

$n_{1}=80$ sample size for the group 1

$n_{2}=70$ sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0: $\mu_{1}-\mu_{2} =0$

H1: $\mu_{1} -\mu_{2} \neq 0$

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

7 0

2 years ago

In our solar system, 6 of our 8 planets have moons. What percentage of the planets have moons?

bija089 [108]

75% of our planets have moons

8 0

3 years ago

Read 2 more answers

How many steps do we take from 0 to -13???

Rus_ich [418]

Answer:

Step-by-step explanation:

because thats how u get to 13

6 0

2 years ago