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maria [59]
3 years ago
9

The slope from 2 points

Mathematics
2 answers:
Eddi Din [679]3 years ago
8 0
The slope would be 2/3!
bearhunter [10]3 years ago
6 0
Y2-Y1/X2-X1
Slope = 2/3
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A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(
alekssr [168]

Answer:

\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right) or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1

Set f'(x) equal to 8/7 and solve for x:

\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}

Therefore, f(x) will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into f(x) to get the y-coordinate:

\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

5 0
2 years ago
Standard Form: 3x+4y=−16
Gnesinka [82]

Answer:

i know the answer

Step-by-step explanation:

8 0
2 years ago
Sally is buying new school supplies. She used a 15% off coupon on a set of markers that was originally $3.00. She also bought so
fenix001 [56]
The original price of the paper was $3.50

I hope this helps! let me know if you need help with anything else! I'd be happy to help you in anyway I can! :)
6 0
3 years ago
To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil
Debora [2.8K]

Answer:

statistic value t= 5.43

p-value: < 0.00001.

Step-by-step explanation:

Hello!

To obtain information over the corrosion-resistance properties of a certain type of steel conduit a random sample of 45 specimens was taken and buried for two years.

The study variable is:

X: Max. penetration of a steel conduit.

The data of the sample

n= 45

sample mean X[bar]= 53.4

sample standard deviation S= 4.2

The conduits are manufactured to have a true average penetration of at most 50 mills, symbolically: μ ≤ 50

The hypothesis is:

H₀: μ ≤ 50

H₁: μ > 50

α: 0.05

To choose the corresponding statistic to use to study the population mean, the variable must have a normal distribution. There is no available information to check this, so I'll just assume that the variable has a normal distribution and, since the population variance is unknown and the sample is small, the statistic to use is a Student t.

Under the null hypothesis, the critical region and the p-value are one-tailed.

Critical value:

t_{n-1; 1-\alpha } = t_{44; 0.95} = 1.68

Rejection rule:

Reject the null hypothesis when t ≥ 1.68

t= \frac{53.4 - 50}{\frac{4.2}{\sqrt{45} } }

t= 5.43

The calculated value is greater than the critical value, thedecision is to rject the null hypothesis.

p-value:

P(t ≥ 5.43) = 1 - P(t < 5.43) = < 0.00001.

The p-value is less than α so the decision is to reject the null hypothesis.

Since the null hypothesis was rejected, then the population average of the penetration of the conduits specimens is greater than 50 mils. It is not recommendable to use these conduits.

I hope it helps!

4 0
3 years ago
Can someone please give me the (Answers) to this? ... please ...<br><br> I need help….
bezimeni [28]

Answer:

see explanation

Step-by-step explanation:

2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord.

6

BE × ED = AE × CE , that is

10 × 3x = 12(2x + 1) ← distribute parenthesis by 12

30x = 24x + 12 ( subtract 24x from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

then

ED = 3X = 3(2) = 6

7

RJ × JP = SJ × JQ , that is

6 × 3x = 4(4x + 1) ← distribute parenthesis by 4

18x = 16x + 4 ( subtract 16x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

then

RP = RJ + JP = 6 + 3x = 6 + 3(2) = 6 + 6 = 12

6 0
1 year ago
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