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katen-ka-za [31]

2 years ago

5

Dillion works at the park every third day. Wlliam works at the parkevery fourth day. Francis works at the park every fifth day.

They all worked together on Thursday. The park is open every day. On what day of the week will they all next work together?

1 answer:

Gennadij [26K]2 years ago

5 0

They will work next Thursday.

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What are the coordinates of Point A after the

Flura [38]

Answer:

A' (-3,7)

B' (0,10)

C' (12,10)

D' (-2,-4)

Step-by-step explanation:

A' (-6+3 , 3+4) = (-3,7)

B' (-3+3 , 6+4) = (0,10)

C' (9+3 , 6+4) = (12,10)

D' (-5+3 , -8+4) = (-2,-4)

5 0

2 years ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

2 years ago

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Which angles are acute?

postnew [5]

Answer:

Angles DBA, GFE, and GFH (not an option) are acute.

Step-by-step explanation:

Acute means less than 90 degrees. I hope that this helps! :)

5 0

1 year ago

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Drina wrote the system of linear equations below.

zalisa [80]

Answer:

Option c, A square matrix

Step-by-step explanation:

Given system of linear equations are

$3x-2y=-2\hfill(1)$

$7x+3y=26\hfill(2)$

$-x-11y=46\hfill(3)$

Now to find the type of matrix can be formed by using this system

of equations

From the given system of linear equations we can form a matrix

Let A be a matrix

A matrix can be written by

A=co-efficient of x of 1st linear equation co-efficient of y of 1st linear equation constant of 1st terms linear equation

co-efficient of x of 2st linear equation co-efficient of y of 2st linear equation constant of 2st terms linear equation

co-efficient of x of 3st linear equation co-efficient of y of 3st linear equation constant of 3st terms linear equation $3\times 3$

which is a $3\times 3$ matrix.

Therefore A can be written as

A= $\left[\begin{array}{lll}3&-2&-2\\7&3&26\\-1&-11&46\end{array}\right] 3\times 3$

Matrix "A" is a $3\times3$ matrix so that it has 3 rows and 3 columns

A square matrix has equal rows and equal columns

Since matrix "A" has equal rows and columns Therefore it must be a square matrix

Therefore the given system of linear equation forms a square matrix

7 0

2 years ago

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A store has 2 times as hooded sweatshirt as crewneck sweatshirts. The total number of sweatshirts is 36. How many hooded sweatsh

svlad2 [7]

Answer:

Answer below

Step-by-step explanation:

It would be 36×2=72

since we're doubl8ng it so there would be 72 hooded sweatshirts

6 0

2 years ago

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