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erma4kov [3.2K]
2 years ago
15

What is the solution of the quadratic equation. Equation: 2x + 7x - 5= 10

Mathematics
1 answer:
Slav-nsk [51]2 years ago
4 0

Step-by-step explanation:

2x+7x-5=10

2x+7x= 10+5= 15

2x ×9=15

2x =15-9=5

x=5/2=2.5

<h3>hope it helped</h3>
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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40
malfutka [58]
PART A

The given equation is

h(t) = - 16 {t}^{2} + 40t + 4

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4

We add and subtract

- 16(- \frac{5}{4} )^{2}

to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4

We again factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4

This implies that,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4

The quadratic trinomial above is a perfect square.

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4

This finally simplifies to,

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29

The vertex of this function is

V( \frac{5}{4} ,29)

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

29

PART B

When the ball hits the ground,

h(t) = 0

This implies that,

- 16 ( t- \frac{5}{4}) ^{2} +29 = 0

We add -29 to both sides to get,

- 16 ( t- \frac{5}{4}) ^{2} = - 29

This implies that,

( t- \frac{5}{4}) ^{2} = \frac{29}{16}

t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }

t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}

t = \frac{ 5 + \sqrt{29} }{4} = 2.60

or

t = \frac{ 5 - \sqrt{29} }{4} = - 0.10

Since time cannot be negative, we discard the negative value and pick,

t = 2.60s
8 0
3 years ago
We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental
mr Goodwill [35]

Answer:

1.1-2.02\frac{4.9}{\sqrt{50}}=-0.30    

1.1+2.02\frac{4.9}{\sqrt{50}}=2.50    

So on this case the 90% confidence interval would be given by (-0.30;2.50)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=1.1 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=51 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=51-1=50

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,50)".And we see that t_{\alpha/2}=2.02

Now we have everything in order to replace into formula (1):

1.1-2.02\frac{4.9}{\sqrt{50}}=-0.30    

1.1+2.02\frac{4.9}{\sqrt{50}}=2.50    

So on this case the 90% confidence interval would be given by (-0.30;2.50)    

8 0
3 years ago
Which of the following describes the end behavior of y = -x^2+bx+c as x approaches either positive or negative infinity?
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The end behavior model of y is -x^2.
As x approaches either positive or neg infinity, -x^2 will always be negative.
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Answer:

A,C,D

Step-by-step explanation:

Snap

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7 0
3 years ago
Read 2 more answers
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