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3 years ago

Two regular pentagons have areas of 20 mm² and x² - x mm². What values of x make the pentagons congruent?

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

8 0

<u>Answer</u>

5 and -4

<u>Explanation</u>

If the two triangle are congruent then they have the same area.

20 = x² - x

x² - x - 20 = 0

x² - x + (1/2)² = 20 + (1/2)²

(x - 1/2)² = 20.25

x - 1/2 = √20.25

x - 1/2 = 4.5 or x - 1/2 = - 4.5

x = 4 1/2 + 1/2 x = -4 1/2 + 1/2

= 5 = -4

The values of x are 5 and -4.

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What is the equation of the line that passes through the point (-1, -2) and is parallel to the line with equation -3x+y=4

Ivanshal [37]

Y = 3x + 1
Parallel lines have the same slope so the slope would be 3. Take the given equation and add the 3x to the other side. Using the given point. -2 (y point) = 3(-1(x point)) + b. Solve for b by adding the 3 over. b = 1 which is your y intercept.

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3 years ago

A buyer went to the market to buy strawberries. He purchased 120 randomly selected strawberries from a vendor who claimed that n

mafiozo [28]

Answer:

$z=\frac{0.333 -0.25}{\sqrt{\frac{0.25(1-0.25)}{120}}}=2.10$

$p_v =P(z>2.10)=0.018$

At 5% of significance we can conclude that the true proportion of strawberries damage is higher than 0.25

Step-by-step explanation:

Data given and notation

n=120 represent the random sample taken

X=40 represent the number of strawberries damaged

$\hat p=\frac{40}{120}=0.333$ estimated proportion of strawberries damaged

$p_o=0.25$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that no more than 25% of his total harvest of strawberries was damaged.:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.333 -0.25}{\sqrt{\frac{0.25(1-0.25)}{120}}}=2.10$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.10)=0.018$

At 5% of significance we can conclude that the true proportion of strawberries damage is higher than 0.25

6 0

3 years ago

This table shows values that represent an exponential function. What is the average rate of change for this function for the int

Pepsi [2]

Answer:

$\boxed{12}$

Step-by-step explanation:

When x = 3, y = 13

When x = 5, y = 37

Subtract both y-values to find the change:

37 - 13 = 24

Average of the change:

$\frac{24}{2}$ = 12

6 0

3 years ago

In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest

ryzh [129]

Answer:

B = 61°

A = 29°

a = 10

Step-by-step explanation:

We are given;

c = 16, b = 14

Since we are told that C is a right angle, it means that C = 90°

Thus using sine rule, we have;

c/sin C = b/sin B

16/sin 90 = 14/sin B

16/1 = 14/sin B

sin B = 14/16

sin B = 0.875

B = sin^(-1) 0.875

B ≈ 61°

Now, since C is a right angle, it means that c will be the hypotenuse of the triangle.

Thus, from pythagoras theorem, If the other side of the triangle is a, then;

a² + b² = c²

a² + 14² = 16²

a² = 16² - 14²

a² = 256 - 156

a² = 100

a = √100

a = 10

Since we know B and C, we can find A because sum of angles in a triangle is 180°.

Thus;

A = 180 - (B + C)

A = 180 - (61 + 90)

A = 29°

4 0

3 years ago

(8.5-2x)(11-2x)(x) what is the approximate value of x that would allow you to construct an

Wittaler [7]

The largest volume possible from one piece of paper for open-top box is 64.296 cubic unit.

<h3>What is meant by the term maxima?</h3>

The maxima point on the curve will be the highest point within the given range, and the minima point will be the lowest point just on curve.
Extrema is the product of maxima and minima.

For the given question dimensions of open-top box;

The volume is given by the equation;

V = (8.5-2x)(11-2x)(x)

Simplifying the equation;

V = x(4x² - 39x + 93.5)

Differentiate the equation with respect to x using the product rule.

dV/dx = x(8x -39) + (4x² - 39x + 93.5)

dV/dx = 8x² - 39x + 4x² - 39x + 93.5

dV/dx = 12x² - 72x + 93.5

Put the Derivative equals zero to get the critical point.

12x² - 72x + 93.5 = 0.

Solve using quadratic formula to get the values.

x = 4.1 and x = 1.9

Put each value of x in the volume to get the maximum volume;

V(4.1) = 4.1(4(4.1)² - 39(4.1) + 93.5)

V(4.1) = 3.44 cubic unit.

V(1.9) = 1.9(4(1.9)² - 39(1.9) + 93.5)

V(1.9) = 64.296 cubic unit. (largest volume)

Thus, the largest/maximum volume possible from one piece of paper for open-top box is 64.296 cubic unit.

To know more about the maxima, here

brainly.com/question/17184631

#SPJ1

4 0

1 year ago