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taurus
1 month ago
8

A square rotated about its center by 360º maps onto itself at: a) 1 B) 2 C) 3 D) 4 different angles of rotation. You can reflect

a square onto itself across A) 2 B) 4 C) 8 D) 16 different lines of reflection.
Mathematics
2 answers:
PIT_PIT [12.4K]1 month ago
4 0

Answer: A square that undergoes rotation around its center by 360º aligns with itself at D) 4 distinct angles during the process. Furthermore, a square can be reflected onto itself over B) 4 various lines.

Explanatory breakdown:

A square is a geometric shape characterized by equal-length sides and right angles ( 90^{\circ} ).

Thus, it is capable of being rotated around its center by 360^{\circ}.

It reverts to its original outline at 4 unique rotation angles ( at every 90^{\circ} angle).

The square can also be reflected onto itself across 4 lines (2 through the non-parallel sides and 2 through the corners).

zzz [12.3K]1 month ago
3 0

Answer:

For plato, both blank one and two is four.

:)

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Triangle abc above is isosceles with an=ac and bc=48. The ratio of de to de is 5:7 . What is the length of dc
PIT_PIT [12445]

Answer:

The diagram displaying triangle ABC and the relevant statement along with the answer options is attached.

According to this, the answer is: The length of DC is 28.

Explanation:

From the diagram and the data that segment AB equals segment AC, you comprehend that angles B and C of the isosceles triangle ABC are congruent.

Triangles BED and CFD possess two sets of congruent angles (angle B is congruent to angle D, and angles BED and DFC are congruent), indicating that triangles BED and CFD are similar.

This similarity leads to the proportional relationship:

  • DE / DF = DB / DC

Given that the ratio of DE to DF is 5:7, we have:

  • 5/7 = DB / DC

Also, it is stated that segment BC is 48.

From the figure:

  • BC = DB + DC = 48.

This results in two equations:

  • 5/7 = DB / DC

  • DB + DC = 48.

Now, we define DC = x, which implies DB = 48 - x, leading to the equation:

  • 5 / 7 = (48 - x) / x

Solve this:

  • 5x = 7 (48 - x)... [multiplication property: multiply by x and 7]

  • 5x = 336 - 7x... [distributive property]

  • 12x = 336... [addition property: add 7x to both sides]

  • x = 336 / 12... [division property: divide by 12]

  • x = 28... [simplification]

Therefore, the length of segment x = DC = 28.

6 0
1 month ago
On a coordinate plane, 2 lines are shown. Line P Q has points (negative 8, 2) and (4, 2). Line M N has points (8, 6) and (8, neg
Svet_ta [12734]

Response:

PQ's slope is 0

MN's slope equals infinity

The lines PQ and MN are perpendicular to one another

Detailed explanation:

For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:

y1 - y2/x1-x2\\\\For \ line \ PQ\\slope = 2 - 2/-8-4 = 0\\\\For \ line \ MN \\slope = 6 - (-8)/8-8 = 1/0 = infinity\\\\

If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis

If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis

Moreover, it is established that X and Y are perpendicular to each other.

As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis

With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.

Therefore, lines PQ and MN are indeed perpendicular.

4 0
1 month ago
Read 2 more answers
What is the answer? The glee club has 120 cupcakes to sell. they have decided to arrange the cupcakes in the shape of a rectangl
PIT_PIT [12445]
<span>Determine the configuration of columns and rows for the rectangular arrangement of 120 cupcakes.
=> There must be an even number of rows and an odd number of columns.
=> 120 = 2 x 2 x 2 x 15
=> 120 = 8 x 15
=> 120 = 120
Consequently, the glee club should organize the cupcakes in 8 rows and 15 columns.
This totals up to 120 cupcakes altogether.

</span>



8 0
1 month ago
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
Svet_ta [12734]

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

6 0
1 month ago
Which is the solution of the quadratic equation (4y – 3)2 = 72? y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction a
Inessa [12570]

Answer:

y = \frac{3 + 6\sqrt{2} }{4} y y = \frac{3 - 6\sqrt{2} }{4}

y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction

Explicación paso a paso:

La ecuación cuadrática que tenemos es (4y - 3)² = 72

Debemos encontrar el valor de y.

Ahora, 4y - 3 = ± 6√2

⇒ 4y = 3 ± 6√2

⇒ y = \frac{3 + 6\sqrt{2} }{4} y y = \frac{3 - 6\sqrt{2} }{4}

Por lo tanto, las soluciones son y = StartFraction 3 + 6 StartRoot 2 EndRoot Over 4 EndFraction y y = StartFraction 3 menos 6 StartRoot 2 EndRoot Over 4 EndFraction (Respuesta)

6 0
1 month ago
Read 2 more answers
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