Use the conversion factor 4 quarts / 1 gallon to convert 5.25 gallons to quarts

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.

In rectangle ABCD, the value of x, given that the lengths of the diagonals BD and AC are expressed as 10x + 8 and 9x + 20 respectively, is 12.

In a rectangle, the diagonals are equal in length. This gives us the following equation,

10x + 8 = 9x + 20, where BD and AC represent the lengths of the diagonals respectively.

To solve this for x, we subtract 9x from both sides, which gives: x + 8 = 20. Then, subtracting 8 from both sides of the equation gives: x = 20 - 8 = 12.

So, the value of x that suits this rectangle is 12.

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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

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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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.

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.

The simplest form of 34 / 710 is 17 / 355.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given that the expression 34 / 710.

Now to write the above expression in simple form, we divide the numerator and denominator by 2

34 / 710 = 34/ 2 ÷ 710 / 2

34 / 710 = 17 / 355

Now the above expression is not easily divisible by any number.

Therefore, The simplest form of 34 / 710 is 17 / 355.

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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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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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Answer:

93 and 110 upper fourth

Step-by-step explanation:

Q3 is at 93 and the max number is at 110 so the upper fourth should fall between 93 and 110, the middle half of the responses  will fall between 70 and 93 and the lower fourth of the responses will fall between 40 and 70

30-24 = 6

6/2 = 3

24 + 3 = 27

 median width = 27

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

A circle is defined as all co-planar points equidistant from a given point

A line segment is a piece of a line that has two endpoints.

It is a part of a line with one end point and proceeds on in one direction.

A line refers to collection of line along a straight path proceeding in opposite directions with no endpoints.

Level: Middle school

Subject: Geometry

Topic: Shapes and terms in geometry