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1 year ago

Calculate AC to 1 decimal place ?

Mathematics

1 answer:

AlladinOne [14]1 year ago

8 0

Step-by-step explanation:

first we need to find the length of CD, so that we can use Pythagoras to find AC.

to get CD we use again Pythagoras. there is a smaller right-angled triangle on top of the BCD rectangle.

so, AD = 11 = 4 + 7

7 = the vertical leg of the upper right-angled triangle.

the horizontal leg is congruent to CD and is

sqrt(16² - 7²) = sqrt(256 - 49) = sqrt(207).

AC² = sqrt(207)² + 11² = 207 + 121 = 328

AC = sqrt(328) = 18.11077028... cm ≈ 18.1 cm

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How fast should the ant walk to go around the rectangle in 4 minutes?

vekshin1

Question:

How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches

Answer:

The ant should walk 14 inches per minute

Solution:

Given that,

Dimensions of rectangle are 12 inches and 16 inches

Find the perimeter of rectangle

Perimeter = 2(length + width)

Perimeter = 2(12 + 16)

Perimeter = 2(28) = 56

Thus perimeter of rectangle is 56 inches

Time taken = 4 minutes

We have to find the speed at which ant covers 56 inches in 4 minutes

The speed is given by formula:

$speed = \frac{distance}{time}$

$speed = \frac{56}{4} = 14$

Thus the ant should walk 14 inches per minute

4 0

2 years ago

Lines x and y intersect to make two pairs of vertical angles, q, s and r, t. Fill in the blank space in the given proof to prove

bonufazy [111]

Answer:

C) Subtraction property of equality.

Step-by-step explanation:

Given that, two lines $x$ and $y$ intersect to make pairs of vertical angles:

$\angle q, \angle s$ and $\angle r, \angle t$ .

Kindly refer to the attached image for details of the given angles and lines.

Proof that $\angle q\cong \angle s$ :

$\begin{center}\begin{tabular}{ c c}Statements & Reasons \\ m\angle q+m\angle r=180^\circ & \angle q\ and\ \angle r\ are\ supplementary \\ m\angle r+m\angle s=180^\circ & \angle r\ and\ \angle s\ are\ supplementary \\ \angle q+\angle r=\angle q+\angle r & Algebraic substitution \\ m\angle q = m\angle s & Subtraction property of equality\end{tabular}\end{center}$

Here, subtraction property of equality is used in the last step shown in the above.

As per the Subtraction property of equality, when some value is subtracted from both the sides of the equality, equality remains the same.

5 0

3 years ago

Which equation represents the circle described? the radius is 2 units. the center is the same as the center of a circle whose eq

zaharov [31]

The equation of the circle x² +y² – 8x – 6y + 21 = 0 is equal to the equation (x + 4)² + (y − 3)² = 2². Then the correct option is C.

<h3>What is a circle?</h3>

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

The equation of the circle is given as

x² + y² – 8x – 6y + 21 = 0

The equation can be written as

x² – 8x + 16 + y² – 6y + 9 = 4

(x + 4)² + (y − 3)² = 2²

Then the center of the circle is at (-9, 6) and the radius of the circle is 10 units.

More about the circle link is given below.

brainly.com/question/11833983

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2 years ago

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7 0

2 years ago

How to do this question

slava [35]

Answer:

Length of the shorter diagonal is 8.68 cm.

Step-by-step explanation:

Length of the side AB = 11 cm

Length of side BC = 5 cm

Angle between these sides, m∠ABC = 50°

By cosine rule in ΔABC,

AC² = AB² + BC² - 2AB.BC.cos B

AC² = (11)² + 5² - 2(11)(5)cos50°

AC² = 121 + 25 - 70.71

AC = √(75.29)

AC = 8.68 cm

By the property of parallelogram,

m∠B + m∠C = 180° [Interior consecutive angles]

50° + m∠C = 180°

m∠C = 130°

Similarly, In ΔBCD,

BD² = BC² + CD² - 2BC.CD.cos130°

BD² = (5)² + (11)² - 2(5)(11)cos130°

BD² = 25 + 121 + 70.71

BD² = 216.71

BD = 14.72 cm

Therefore, length of the shorter diagonal will be 14.72 cm.

7 0

2 years ago