I need to know if this is a False conjecture

6x - 9y = 111

Vikentia [17]

The answer to this question is x=8; y= -7

3 0

2 years ago

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Helppppppppp pleaseeee Someoneeeee pleaseeee I neeed

Stella [2.4K]

Answer:

The minimum value of f(x) is 2

Step-by-step explanation:

To find the minimum value of the function f(x), you should find the value of x which has the minimum value of y, so we will use the differentiation to find it

Differentiate f(x) with respect to x and equate it by 0 to find x, then substitute the value of x in f(x) to find the minimum value of f(x)

∵ f(x) = 2x² - 4x + 4

→ Find f'(x)

∵ f'(x) = 2(2) $x^{2-1}$ - 4(1) $x^{1-1}$ + 0

∴ f'(x) = 4x - 4

→ Equate f'(x) by 0

∵ f'(x) = 0

∴ 4x - 4 = 0

→ Add 4 to both sides

∵ 4x - 4 + 4 = 0 + 4

∴ 4x = 4

→ Divide both sides by 4

∴ x = 1

→ The minimum value is f(1)

∵ f(1) = 2(1)² - 4(1) + 4

∴ f(1) = 2 - 4 + 4

∴ f(1) = 2

∴ The minimum value of f(x) is 2

7 0

2 years ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

jarptica [38.1K]

We are given

△ABC, m∠A=60° m∠C=45°, AB=8

Firstly, we will find all angles and sides

Calculation of angle B:

we know that sum of all angles is 180

m∠A+ m∠B+m∠C=180

we can plug values

60°+ m∠B+45°=180

m∠B=75°

Calculation of BC:

we can use law of sines

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

now, we can plug values

$\frac{8}{sin(45)}=\frac{BC}{sin(60)}$

$BC=\frac{8}{sin(45)} \times sin(60)$

$BC=9.798$

Calculation of AC:

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

now, we can plug values

$\frac{8}{sin(45)}=\frac{AC}{sin(75)}$

$AC=\frac{8}{sin(45)} \times sin(75)$

$AC=10.928$

Perimeter:

$p=AB+BC+AC$

we can plug values

$p=10.928+8+9.798$

$p=28.726$

Area:

we can use formula

$A=\frac{1}{2}AB \times AC \times sin(A)$

now, we can plug values

$A=\frac{1}{2}8 \times 10.928 \times sin(60)$

$A=37.85570$ ...............Answer

6 0

3 years ago

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Someone help please!

UNO [17]

If we imagine it in our head, we can see that the width (base) is 2 and the height is 9
the area is 1/2bh or 1/2*2=9 square units
it is rotated around x axis
meaning we have a sideways cone that is 2 hight and radius is 9
Vcone=1/3(hpir^2)
h=2
r=9
V=(1/3)(2)(3.141592)(9^2)
V=(2/3)(3.141592)(81)
V=(54)(3.141592)
V=169.6459
round
V=169.6 cubic units

base is 2 units
height is 9 units
area is 9 square units
it's a cone (sideways)
it has a volume of 169.6 cubic units

3 0

3 years ago

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Five balls are chosen from a bag of eight blue balls, six red balls, and five green balls. How many of these five-ball selection

Harlamova29_29 [7]

Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.

The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the <em>combination formula</em> is used to solve this question. If the order was important, then the permutation formula would be used.

<h3>What is the combination formula?</h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:

$C_{6,5} = \frac{6!}{1!5!} = 6$

Hence six of these five-ball selections contain exactly five red balls.

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1

4 0

1 year ago