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bogdanovich [222]
3 years ago
11

The product of two consecutive positive integers is 29 more than their sum. Find the integers

Mathematics
1 answer:
Rina8888 [55]3 years ago
7 0
The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5    then: (x+1)=-5+1=-4  This is not the solution.
x₂=(1+11)/2=6    then: (x+1)=6+1=7    This solution is right.

Answer: the numbers would be 6 and 7. 
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Find an equation of variation where y varies directly as x and y = 7 when x = 0.5 .
Alisiya [41]

Answer:

y = 14x

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in 7 as y and 0.5 as x, and solve for k:

y = kx

7 = k(0.5)

14 = k

Plug this into the equation:

y = kx

y = 14x

So, the equation of variation is y = 14x

4 0
3 years ago
What do the factors (x+2)(-8x+70)in the factored form represent?
Tasya [4]

Answer:

-2(x+2)(4x-35)

Step-by-step explanation:

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3 years ago
If the distribution is really (5.43,0.54)
defon

Answer:

0.7486 = 74.86% observations would be less than 5.79

Step-by-step explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

N(mean, standard deviation)

Which means that:

\mu = 5.43, \sigma = 0.54

What proportion of observations would be less than 5.79?

This is the pvalue of Z when X = 5.79. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.79 - 5.43}{0.54}

Z = 0.67

Z = 0.67 has a pvalue of 0.7486

0.7486 = 74.86% observations would be less than 5.79

7 0
3 years ago
From a hot air balloon that is between his house and parade, john measures the angle of depression to his house of 35 and to the
igomit [66]

4500 feet

Step-by-step explanation:

We can begin by finding x using the tangent rule;

The tangent of the angle = the length of the opposite side / the length of the adjacent side

Tan 35 = 3500 / x

X = 3500 / tan 35

X  = 3500 / 0.7

X = 5000

Now that we have x we can calculate the value of ? using the same tangent rule;

Tan 42 = ? / 5000

? =  tan42 * 5000

? = 0.9 * 5000

? = 4500

Learn More:

For more on trigonometry check out;

brainly.com/question/12710176

brainly.com/question/11275089

#LearnWithBrainly

4 0
3 years ago
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maw [93]
The most simple form (I'm defining the parabola to be an upwards-opening one) would be y=(x-1) ^{2} +3
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