What are the new coordinates of the point (-3, 7) after it has been rotated 90° counterclockwise about the origin?

The length of piece of wire for square = 230 inches

The length of piece of wire for circle = 130 inches.

The given length of  wire = 360 inches

Now let it cuts into lengths r' and r

Therefore,

⇒ r' + r = 360   ...(i)

Now let with length r' square is formed

Therefore,

Area of square = r'xr'

                         = (r')²

And with length of r circle is formed,

Area of circle = π r²

According to the question

Both area are same,

⇒ (r')² =  π r²

Taking square root both sides,

⇒ r' = √π r    ......(ii)

Now from (i) and (ii);

⇒ √π r + r = 360

⇒ r(1 + √π) = 360

⇒      2.77 r = 360

⇒              r = 129.96 ≈ 130 in

Then r' = 360 - 130

            = 230

Hence length are 130 inches and 230 inches.

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Answer:  The slope of the tangent line at the point (3, 2) is [tex]\dfrac[4}{9}.[/tex]

Step-by-step explanation:  We are given to find the slope of the line tangent to the following curve at the point (3, 2).

[tex]3y^2-2x^2=6-2xy~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the derivative of a function at any given point is equal to the slope of the tangent at that point.

Now, differentiating both sides of equation (i) with respect to x, we have

[tex]\dfrac{d}{dx}(3y^2-2x^2)=\dfrac{d}{dx}(6-2xy)\\\\\\\Rightarrow 6y\dfrac{dy}{dx}-4x=0-2\left(y+x\dfrac{dy}{dx}\right)\\\\\\\Rightarrow 2x\dfrac{dy}{dx}+6y\dfrac{dy}{dx}=4x-2y\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4x-2y}{2x+6y}\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{2x-y}{x+3y}.[/tex]

So, at the point (3, 2), we get

[tex]\dfrac{dy}{dx}=\dfrac{2\times3-2}{3+3\times2}=\dfrac{6-2}{3+6}=\dfrac{4}{9}.[/tex]

Thus, the slope of the tangent line at the point (3, 2) is [tex]\dfrac{4}{9}.[/tex]

The slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]) and it can be evaluated by differentiating the given equation of curve.

Given :

To determine the slope of the tangent, differentiation of the given equation of curve is carried out.

Differentiating equation (1) with respect to x.

[tex]\dfrac{d}{dx}(3y^2-2x^2) = \dfrac{d}{dx}(6-2xy)[/tex]

[tex]6y \dfrac{dy}{dx}-4x = 0-2y-2x\dfrac{dy}{dx}[/tex]

Now, further simplification of the above equation gives:

[tex]\dfrac{dy}{dx}(6y+2x)=4x-2y[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x-2y}{6y+2x}[/tex]

Now, at point (3,2) the slope of the tangent will be:

[tex]m = \dfrac{4\times 3-2\times 2}{6\times 2+2\times3}[/tex]

[tex]m = \dfrac{5}{18}[/tex]

So, the slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]).

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Actually the real answer is:

-1.

A coordinate plane is a graphical image that shows two number lines. These number lines have a y-axis and x-axis. The y-axis is the vertical number line and the x-axis is the horizontal number line.

The perimeter of the rectangle is 26.8 units

We would be applying Pythagoras Theorem to find the length and breadth of the rectangle.

Pythagoras Theorem states that:

c² = a² + b²

Note that c = The length or breadth of the rectangle

We have 4 units and 8 units.

a = 4 units

b = 8 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 4² + 8²

c² = 80

c = √ 80

c = 8.9 units

Applying this to the lower part,

We have 4 units and 2 units.

a = 2 units

b = 4 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 2² + 4²

c² = 20

c = √20

c = 4.5 units

Formula = 2L + 2B

Where

L = Length = 8.9 units

B = Breadth = 4.5 units

Hence:

8.9 x 2 + 4.5 x2 = 26.8 units

Therefore, the perimeter of the rectangle is 26.8 units

Option C is the correct answer

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Final answer:

To find two consecutive odd integers whose squares sum to 2594, a quadratic equation is set up and solved, revealing that the integers are 35 and 37.

Explanation:

To solve for two consecutive odd integers whose squares sum to 2594, we can set up equations based on the characteristics of odd integers. Let the smaller integer be n, then the next consecutive odd integer would be n + 2.

The equation based on the sum of the squares of the two numbers is then:

n2 + (n + 2)2 = 2594

Solving this equation:

Solving the quadratic equation we find that n = 35 and n + 2 = 37. Hence, the two consecutive odd integers are 35 and 37.

30-24 = 6

6/2 = 3

24 + 3 = 27

 median width = 27

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

From the graph the inequality intersect lines at (-2, 0) and (0, 5).

The graph is shaded below the line.

So, inequality y ≤ [tex]\frac{5}{2}[/tex] x+5.

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

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The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right triangle.

According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.

Height² + Base² = Hypotenuse²

If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.

The distance formula will be used to determine the length of the sides.

PQ² =  ( 3 - 0)² + (2-1)²

PQ² = 10

PQ = √10

RQ² =  ( 5 - 3)² + (-4-2)²

RQ² = 40

RQ = √40

RP² =  ( 5 - 0)² + (-4-1)²

RQ² =  25 + 36

RQ² =  61

Applying the Pythagoras's Theorem,

61 ≠ 40 + 10

Therefore, it is not a right angled triangle.

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That would be 32, 16 and 34.

I can confirm that Option C is correct, just finished the assignment.

Answer:

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]  

Step-by-step explanation:

To find : Which equation is an identity?    

Solution :

Option a - [tex]11- (2v + 3) = -2v - 8[/tex]          

If we open the parenthesis,

[tex]11- 2v -3 = -2v - 8[/tex]    

[tex]-2v+8\neq -2v - 8[/tex]    

No identity applied.

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]          

If we apply distributive property, [tex]a(b+c)=ab+ac[/tex]

[tex]5w + 8 - w = 6w - 2w+8[/tex]    

[tex]4w+8= 4w+8[/tex]    

Distributive identity is applied.

Option c - [tex]7m - 2 = 8m + 4 - m[/tex]          

Solve by subtracting in RHS

[tex]7m - 2 \neq 7m + 4[/tex]    

No identity applied.

Option d- [tex]8y + 9 = 8y - 3[/tex]          

This is not possible as [tex]8y + 9 \neq 8y - 3[/tex]

No identity applied.          

Therefore, Option b is correct.

equation = g(x) = 2x-2

 when g(-3) replace x with -3

 so you get g(-3) = 2(-3)-2

2*-3 = -6-2 = -8

g(-3) = -8

Answer:

"Billy's age in 8 years", this refers to a future age, which implies adding 8 years to the present age. The expression would be:

[tex]B+8[/tex]

"In 8 years Billy will be 21 years", this expression, using the first one too, would be:

[tex]B+8=21[/tex]

How old is Billy now?

The answer to this question is the solution of the second equation:

[tex]B+8=21\\B=21-8=13[/tex]

Billy is 13 years old now.

A problem for the expression [tex]A-6=10[/tex] could be:

Six years ago Adam was 10 years old.

The six years in the past refers subtracting, and the age back then is the result of that difference.

Answer:  The ratio of the volumes of two pyramids is 27 : 1331.

Step-by-step explanation:  Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.

We are to find the ratio of the volumes of two pyramids.

Let a units and b units be the lengths of the edges of the two pyramids.

The, according to the given information, we have

[tex]a:b=3:11.[/tex]

We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.

Therefore, the ratio of the volumes of two pyramids will be

[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]

Thus, the ratio of the volumes of two pyramids is 27 : 1331.

Answer:

Point B will be 6

Step-by-step explanation:

We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.

To find the middle between two points we have to add the two numbers and divide them by 2:

We would have:

(A+C)/2

We substitute the values of A and C:

B = (-24+36)/2

B = 12/2

B = 6.

We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.

The Answer Is B.2-1/3

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The expression −2/3(3-1/2)(-1) is equivalent to -5/3.

To simplify the expression −2/3(3-1/2)(-1), we can start by simplifying the expressions within the parentheses.

3-1/2 = 6/2 - 1/2 = 5/2

Next, we can multiply the expression −2/3(5/2)(-1).

−2/3(5/2)(-1) = -2/3 * 5/2 * -1 = -10/6 = -5/3

Therefore, the expression is equivalent to -5/3.

Final answer:

Since no candidate won an absolute majority in the Texas Democratic Primary for governor, a runoff election is necessitated between Candidate X and Candidate Y, the top two vote-getters, to ensure the nominee is chosen by a majority.

Explanation:

In the scenario where Candidate X wins 45% of the vote, Candidate Y receives 30%, and Candidate Z wins 25% in the Texas Democratic Primary for governor, no candidate has achieved an absolute majority, as required by Texas law to win the primary outright. An absolute majority means that a candidate must have more than 50% of the votes, specifically fifty percent plus one vote. Since this did not happen, a runoff election is triggered.

The runoff will take place between the two candidates who received the most votes, which in this case, would be Candidate X and Candidate Y. This runoff ensures that the final nominee for governor from the Democratic Party will have the support of a majority of its voters, reflecting a more democratic outcome. The system prevents a candidate from winning the primary nomination with only a plurality of the vote, which could be less representative of the party's voters as a whole.