1)The square shown has a perimeter of 32 units. The square is rotated about line k. 

What shape is created by the rotation and what is the approximate circumference of the base?
Circumference of a circle: C = 2πr
a cone with a base circumference of about 25 units
a cone with a base circumference of about 50 units
a cylinder with a circumference of about 25 units
a cylinder with a circumference of about 50 units

2) The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm.

What shape is created by the rotation and what is the approximate circumference of the base?  

Circumference of a circle: C = 2πr
a cylinder with a circumference of about 63 mm
a cylinder with a circumference of about 126 mm
a cone with a base circumference of about 63 mm
a cone with a base circumference of about 126 mm

An angle of elevation of 58 degrees with the ground means that the angle started at the x-axis and terminates on the first quadrant region through a counter clockwise direction. Imagining a triangle, the string of the kite becomes the hypotenuse, the angle 58 degrees is the angle between the hypotenuse and the ground, and the height of the kite is the side opposite to the angle.

Therefore, we can calculate for the height of the kite using the sin function:

sin θ = opposite side / hypotenuse

sin 58 = opposite side / 50 m

opposite side = 50 m * sin 58

opposite side = 42.4 m

Therefore the kite is about 42.4 m above the ground.

Answer:  The measure of the fourth angle of the given quadrilateral is 50°.

Step-by-step explanation:  Given that a quadrilateral has three angles that measure 90° , 100° and 120°.

We are to find the measure of the fourth angle of the quadrilateral.

Let x° be the measure of the fourth angle of the quadrilateral.

We know that

The sum of the measures of the four angles of a quadrilateral is 360°.

So, for the given quadrilateral, we have

[tex]90^\circ+100^\circ+120^\circ+x^\circ=360^\circ\\\\\Rightarrow 310^\circ+x^\circ=360^\circ\\\\\Rightarrow x^\circ=360^\circ-310^\circ\\\\\Rightarrow x^\circ=50^\circ.[/tex]

Thus, the measure of the fourth angle of the given quadrilateral is 50°.

Answer:

1: The GCF of 96x2 and 88x is:    Answer: 8x

2: Each term written as a product, where one factor is the GCF, is:     Answer: 8x(12x)+8x(11)

3: The factored form of the expression is:      Answer: 8x(12x+11)

Step-by-step explanation:

You're explanation is the answers hope I helped !!!! Good luck!!!!!

he 2 kites are identical

CD is the same as WX

 so it would be x +0

 answer is A

Answer:

A,B,D

Step-by-step explanation:

6 * (4+2)^2 -3^2 =

6 * 6^2 -3^2 =

6* 36-9 =

216-9=

207

Answer is C. 207

The solution of the given quadratic equation will be ( -5, 0 ).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Given equation is:-

x²  =   -5x

x²  +   5x  =  0

x  (  x + 5 ) = 0

x  =  0   and   x  =  -5

Therefore the solution of the given quadratic equation will be ( -5, 0 ).

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The solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex] can be calculated after modifying the quadratic equation and rewriting it to [tex]x^{2} + 5x + 3 = 0[/tex], and then this can be calculated using the quadratic formula. The solutions are x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex]and x =[tex]\frac{{-5 - \sqrt{13}}}{2}[/tex] .

To find the solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex], let's first rewrite it in the standard form:

[tex]\[x^2 + 5x + 3 = 0\][/tex]

Now, we can use the quadratic formula to find the solutions:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

Where a = 1,,b = 5, and c=3.

[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot 3}}}}{{2 \cdot 1}}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 12}}}}{2}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{13}}}{2}\][/tex]

So, the solutions are:

x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex] and [x = [tex]\frac{{-5 - \sqrt{13}}}{2}[/tex]

Final answer:

The odds of dealing yourself a blackjack in a single deck game of blackjack, by drawing an ace and a face card or 10 in either order, is 128 out of 2652, which simplifies to approximately 1 in 20.7.

Explanation:

In the game of blackjack, to determine the odds of dealing yourself a blackjack (ace plus a face card or 10), we need to calculate the probability of drawing an ace and then a ten-value card, or vice versa, from a single deck. A standard deck of cards has 52 cards, with 4 aces and 16 ten-valued cards (10, J, Q, K across four suits). The probability of drawing an ace first is 4 out of 52, and then a ten-value card is 16 out of 51. Alternatively, the probability of drawing a ten-value card first is 16 out of 52, and then an ace is 4 out of 51.

The total probability is the sum of both probabilities:

We then add these two probabilities together to find the total probability of dealing a blackjack from a single deck.

The total probability is (4/52) * (16/51) + (16/52) * (4/51) which simplifies to (64/2652) + (64/2652), or 2 * (64/2652), which simplifies further to (128/2652). Therefore, the odds of dealing a blackjack are 128 out of 2652, or approximately 1 in 20.7 when simplified.

The simpliest way is to use the AAS Postulate.

AAS Postulate: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

From the diagram you have:

1. one pair of angles with measure 40°;

2. one pair of angles with measure 60°;

3. the non-included side of one triangle is congruent to the non-included side of another triangle (their lengths are 10).

Answer: correct choice is D (AAS)

Answer:

AAS postulate :)

Step-by-step explanation:

9c + 32/5=f this is the answer

i think

Final answer:

The expressions provided are different forms of similar linear expressions, which could potentially describe the measure of angle RST if related algebraically or geometrically. The expression for m∠ RST is 6x - 9

Explanation:

Calculating the measure of angle RST involves understanding that the angles around a point add up to 360°, and the angles on a straight line add up to 180°. Based on the provided expressions, we are likely looking for the expression that adheres to these geometric rules.

The expressions given are: 3x – 9, 6x – 18, 1.5x – 4.5, and 6x – 9. To determine which one correctly represents the measure of angle RST, we would need some context from the problem or a diagram. However, assuming a relationship between the expressions and angle RST using linear or angular sums, we can observe that the expressions 3x – 9 and 6x – 18 are equivalent (by factoring out a 2 from the second expression), and similarly, 1.5x – 4.5 is equivalent to 3x – 9 upon multiplying by 2. The expression 6x – 9 could also be related if RST formed a linear pair with another given angle.

To estimate the gravitational constant (G), we apply Newton's law of universal gravitation, using the provided values of the force of gravity between Earth and Mars, the masses of both planets and their distance apart. The calculation yields an estimated G value of approximately 6.67 × 10⁻¹¹ N·m²/kg², which aligns with the known gravitational constant.

To estimate the gravitational constant (G), we can use Newton's law of universal gravitation, which states that the force of gravity (F) between two masses (m₁ and m₂) is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers:

F = G * (m₁*m₂) / r²

Given that:

We can rearrange the formula to solve for G:

G = F * r² / (m₁ * m₂)

Plugging in the values:

G = (64.32 × 10¹⁴ N) * (2 × 1011 m)² / (6 × 10²⁴ kg * 6.4 × 10²³ kg)

G ≈ 6.67 × 10⁻¹¹ N·m²/kg²

This value is approximately equal to the known gravitational constant, solidifying our understanding of gravitational forces and confirming the validity of our calculations.