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3 years ago

One solution of the equation x2 + 5x + 4 is -4. What is the other solution?

Mathematics

1 answer:

Oliga [24]3 years ago

7 0

Answer:

Step-by-step explanation:

$x^2+5x+4=0\\\\x^2+x+4x+4=0\\\\x(x+1)+4(x+1)=0\\\\(x+1)(x+4)=0\iff x+1=0\ \vee\ x+4=0\\\\x=-1\ \vee\ x=-4$

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Underline all the ordered pairs (x,y) that are solutions to the equation y=2x+1.

Romashka [77]

Answer:

Step-by-step explanation:

We have the following function:

$y = 2x+1$ .

We are going to check if each ordered pair is a solution.

(3,7)

If when $x = 3, y = 7$ , it is a solution.

$y = 2x + 1 = 2(3) + 1 = 7$

This ordered pair is a solution.

(7,3)

If when $x = 7, y = 3$ , it is a solution.

$y = 2x + 1 = 2(7) + 1 = 15$

This ordered pair is not a solution.

(-1,14)

If when $x = -1, y = 14$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is not a solution.

(0,1)

If when $x = 0, y = 1$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is a solution.

(12,25)

If when $x = 12, y = 25$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is a solution.

(5,11)

If when $x = 5, y = 11$ , it is a solution.

$y = 2x + 1 = 2(5) + 1 = 11$

This ordered pair is a solution.

(0,12)

If when $x = 0, y = 12$ , it is a solution.

$y = 2x + 1 = 2(0) + 1 = 1$

This ordered pair is not a solution.

(1,8)

If when $x = 1, y = 8$ , it is a solution.

$y = 2x + 1 = 2(1) + 1 = 3$

This ordered pair is not a solution.

(12,0)

If when $x = 12, y = 0$ , it is a solution.

$y = 2x + 1 = 2(12) + 1 = 25$

This ordered pair is not a solution.

(-1,-1)

If when $x = -1, y = -1$ , it is a solution.

$y = 2x + 1 = 2(-1) + 1 = -1$

This ordered pair is a solution.

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2 years ago

What is the area of triangle ABC to the nearest tenth of a square meter?

Andrej [43]

we are given with an isosceles triangle with two congruent sides equal to 70 inches and an angle of 36 degrees in between the sides. We are asked for the area of the triangle. The formula is A = 0.5 * ab sin theta where a and b are the sides. The area is equal to 1440. 07 in2.

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3 years ago

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 22 kg. What perce

LenKa [72]

Answer:

14.28% of individual adult females have weights between 75 kg and 83 kg.

92.82% of the sample means are between 75 kg and 83 kg.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

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.

In this problem, we have that:

Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 22 kg. This means that $\mu = 79, \sigma = 22$ .

What percentage of individual adult females have weights between 75 kg and 83 kg?

This percentage is the pvalue of Z when $X = 83$ subtracted by the pvalue of Z when $X = 75$ . So:

X = 83

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

$Z = \frac{83 - 79}{22}$

$Z = 0.18$

$Z = 0.18$ has a pvalue of 0.5714.

X = 75

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

$Z = \frac{75- 79}{22}$

$Z = -0.18$

$Z = -0.18$ has a pvalue of 0.4286.

This means that 0.5714-0.4286 = 0.1428 = 14.28% of individual adult females have weights between 75 kg and 83 kg.

If samples of 100 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 75 kg and 83 kg?

Now we use the Central Limit THeorem, when $n = 100$ . So $s = \frac{22}{\sqrt{100}} = 2.2.$

X = 83

$Z = \frac{X - \mu}{s}$

$Z = \frac{83 - 79}{2.2}$

$Z = 1.8$

$Z = 1.8$ has a pvalue of 0.9641.

X = 75

$Z = \frac{X - \mu}{s}$

$Z = \frac{75-79}{2.2}$

$Z = -1.8$

$Z = -1.8$ has a pvalue of 0.0359.

This means that 0.9641-0.0359 = 0.9282 = 92.82% of the sample means are between 75 kg and 83 kg.

8 0

3 years ago

A bicycle wheel with diameter 16 inches rides over a screw in the street. the screw is on level ground before it punctures the b

weqwewe [10]

The height of the screw = 16 inches.

<h3>How do you determine the number of revolutions in a circle?</h3>

The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.

Given that,

Diameter of a bicycle = 16 inches

The distance the bike moves (forward) after the screw punctures the tire = 56π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16π inches

Therefore,

$\frac{56\pi }{16\pi }$ = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A cos(Bx - C) + D

Where

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2π/B

Bx = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The mid line = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

Hence, After the bike moves forward another 56π inches the height of the screw = 16 inches.

To learn more about number of revolution from the given link:

brainly.com/question/17266654

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8 0

1 year ago

Graph line with slope 1/3 passing through the point (-2,-2)

Oxana [17]

Answer:

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Step-by-step explanation:

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2 years ago

One solution of the equation x2 + 5x + 4 is -4. What is the other solution?​

One solution of the equation x2 + 5x + 4 is -4. What is the other solution?