-3x - 7 = -6x + 2 ......................

The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]

To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.

Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]

 Using the formula for the area of a sector:

[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]

Substituting [tex]\(\theta = 90^\circ\):[/tex]

[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]

Simplifying the fraction:

[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]

 So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.

The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.

If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:

y = 2*6 - 4

So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.

https://brainly.com/question/21511618

#SPJ2

Answer:

a,b and c.

Step-by-step explanation:

We have to find the the functions that are their own inverses.

a.t(p)=p

Then the inverse function of given function is

[tex]p=t^{-1}(p)[/tex]

Therefore, the given function is inverse function of itself.

Hence, option a is true.

b.y(j)=[tex]-\frac{1}{j}

Let y(j)=y then we get

[tex]y=-\frac{1}{j}[/tex]

[tex]j=-\frac{1}{y}[/tex]

[tex]j=-\frac{1}{y(j)}[/tex]

[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]

[tex]j=j[/tex]

Hence, the function is inverse of itself.Therefore, option b is true.

c.[tex]w(y)=-\frac{2}{y}[/tex]

Suppose that w(y)=w

Then [tex]w=-\frac{2}{y}[/tex]

[tex]y=-\frac{2}{w}[/tex]

[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]

[tex]w(y)=w[/tex]

[tex]w(y)=-\frac{2}{y}[/tex]

Hence, the function is inverse function of itself.Therefore, option c is true.

d.[tex]d(p)=\frac{1}{x^2}[/tex]

Let d(p)=d

If we replace [tex]\frac{1}{x^2}by p then we get

[tex]d=\frac{1}{x^2}[/tex]

[tex]x^2=\frac{1}{d}[/tex]

[tex]x=\sqrt{\frac{1}{d}}[/tex]

[tex]x=\sqrt{\frac{1}{d(p)}[/tex]

Hence, the function is not self inverse function.Therefore, option d is false.

Answer:
Option A, (x + 2)² + (y - 1) = 9

Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.

From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9

The equation for the given circle is (x + 2)² + (y - 1)² = 9

The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.

The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.

We rewrite the middle term using these two numbers and then group the terms to factor by grouping:

The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.

Answer: 22 ft, 1 s

Step-by-step explanation:

Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft

Step-by-step explanation:  Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]

where:

b is base of a triangle

h is height of a triangle

For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:

hypotenuse² = side² + side²

[tex]12^{2} = s^{2} + x^{2}[/tex]

[tex]x^{2} = 12^{2} - s^{2}[/tex]

[tex]x^{2} = 144 - s^{2}[/tex]

x = [tex]\sqrt{144 - s^{2} }[/tex]

To determine the Area of the right triangle as function of s:

A = [tex]\frac{b.h}{2}[/tex]

A = [tex]\frac{1}{2}[/tex](s.x)

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

Therefore, the area of the right triangle is:

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:

hypotenuse² = side² + side²

h² = 13² + 5²

h² = 169 + 25

h = [tex]\sqrt{194}[/tex]

h = 14

The minimum length the ladder has to have to reach the top is 14 ft.

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

Answer: (5, -9)

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

we have that

the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]

The transformed function has the vertex at point [tex](-3,-2)[/tex]

so

the rule of the translation is equal to

[tex](x,y)------> (x-3,y-2)[/tex]

That means

The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down

therefore

the answer is

the transformed function is [tex]y=\left|x+3\right|-2[/tex]

Root plot for :  y = 3x2+7x+2
Axis of Symmetry (dashed)  {x}={-1.17} 
Vertex at  {x,y} = {-1.17,-2.08}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = {-2.00, 0.00} 
Root 2 at  {x,y} = {-0.33, 0.00} 

Answer:

The answer is A. y = √2x

Step-by-step explanation:

In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.

In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.

Since KF and LM are parallel, KF = LM. Therefore, LM = 10.

Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.

Hence, KN = KL + LM = AN + LM = AN + 10.

Therefore, KN = AN + 10.

Answer:

4 ÷ 5

Step-by-step explanation: becuz i said so

We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.

The formula for the combination is given by

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be

[tex]^{50}C_6[/tex]

Using the above formula, the number of different selections are

[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]

Therefore, 15890700 different selections are possible.