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2 years ago

F(x)=4x^2+2x-6.find the range of function f(x).

Mathematics

1 answer:

Triss [41]2 years ago

4 0

Answer:

y ≥ 6.25

Step-by-step explanation:

f(x)=4x²+2x-6

positive (4) leading coefficient, curve is left up and right up

x coordinate of vertex: x = - b/2a = - 2/2*4 = - 1/4 (-0.25)

y = 4*(-1/4)² + 2*(-1/4) - 6 = -6 1/4 (-6.25) ... extreme

range: y ≥ - 6.25 [-6.25,∞)

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AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A

Snowcat [4.5K]

Answer:

The area of APC is 70m². The area of triangle PMC is 35m².

Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

$\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}$ .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

$\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}$ ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

$\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}$ .....(3)

The area of triangle APM is 35m².

$\text{Area of }\triangle APM=\frac{x}{4}$

$35=\frac{x}{4}$

$x=140$

Therefore the area of triangle ABC is 140m².

Using equation (2).

$\text{Area of }\triangle APC=\frac{x}{2}$

$\text{Area of }\triangle APC=\frac{140}{2}$

$\text{Area of }\triangle APC=70$

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

$\triangle BPC=\triangle BPM+\triangle PMC$

$70=35+\triangle PMC$

$35=\triangle PMC$

Therefore the area of triangle PMC is 35m².

8 0

3 years ago

a math teacher claims that she has developed a review course that increases the score of students on the math portion of a colle

madam [21]

Answer:

$H_0: \mu\leq514\\\\H_1: \mu>514$

B. Z=2.255. P=0.01207.

C. Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. P(z>0.94)=0.1736

Step-by-step explanation:

<em>A. state the null and alternative hypotheses.</em>

The null hypothesis states that the review course has no effect, so the scores are still the same. The alternative hypothesis states that the review course increase the score.

$H_0: \mu\leq514\\\\H_1: \mu>514$

B. test the hypothesis at the a=.10 level of confidence. is a mean math score of 520 significantly higher than 514? find the test statistic, find P-value. is the sample statistic significantly higher?

The test statistic Z can be calculated as

$Z=\frac{M-\mu}{s/\sqrt{N}} =\frac{520-514}{119/\sqrt{2000}}=\frac{6}{2.661}=2.255$

The P-value of z=2.255 is P=0.01207.

The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

Then we can conclude that the score of 520 is significantly higher than 514, in this case, specially because the big sample size.

C. do you think that a mean math score of 520 vs 514 will affect the decision of a school admissions adminstrator? in other words does the increase in the score have any practical significance?

Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. test the hypothesis at the a=.10 level of confidence with n=350 students. assume that the sample mean is still 520 and the sample standard deviation is still 119. is a sample mean of 520 significantly more than 514? find test statistic, find p value, is the sample mean statisically significantly higher? what do you conclude about the impact of large samples on the p-value?

In this case, the z-value is

$Z=\frac{520-514}{s/\sqrt{n}} =\frac{6}{119/\sqrt{350}} =\frac{6}{6.36} =0.94\\\\P(z>0.94)=0.1736>\alpha$

In this case, the P-value is greater than the significance level, so there is no evidence that the review course is increasing the scores.

The sample size gives robustness to the results of the sample. A large sample is more representative of the population than a smaller sample. A little difference, as 520 from 514, but in a big sample leads to a more strong evidence of a change in the mean score.

Large samples give more extreme values of z, so P-values that are smaller and therefore tend to be smaller than the significance level.

8 0

2 years ago

Solve the equation: 10y-7=27

mrs_skeptik [129]

Answer:

10y=27+7

10y=34

y=34/10

y=3.4

Step-by-step explanation:

Firstly 7 is added to 27

Then adding 7 and 27

Dividing 34 by 10

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3 years ago

A couple finds that they are experiencing debt problems and decide to find a credit counseling agency. What are three (3) things

Serggg [28]

Answer:

This is an odd question...

The couple should find out the following:

1.) is the agency legitimate?

2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score

3.) Will they charge me to review my current credit reports?

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2 years ago

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Blababa [14]

Answer:

59.06, I'm right I promise.

Step-by-step explanation:

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3 years ago

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