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Liono4ka [1.6K]
2 years ago
5

Friday's temperature was 15° warmer than Tuesday's temperature. Find the temperature

Mathematics
1 answer:
artcher [175]2 years ago
5 0

Answer:

the answer is 84 degrees

Step-by-step explanation: add 15 degrees to 69 degrees

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XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3
nataly862011 [7]
<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = \frac{1}{2} x b x h      -------------(i)

Where;

A = 18\sqrt{3}

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18\sqrt{3} =  \frac{1}{2} x b x 6

18\sqrt{3} =  3b

<em>Divide through by 3</em>

6\sqrt{3} =  b

Therefore, b = XZ = 6\sqrt{3}

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}

\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}

\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}

\frac{1}{12}  = \frac{1}{2|OZ|}

\frac{1}{6} = \frac{1}{|OZ|}

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

5 0
2 years ago
Write an equation for the line that is parallel to the given line and that passes through the given point. y = –6x + 2; (–1, 2)
kap26 [50]
Parallel=same slope
Y=mx+b
Sub in the slope and point to solve for b
2=-6(-1)+b
2=6+b
2-6=b
-4=b
The equation is y=-6x-4; the answer is B
Hope this helps!
6 0
3 years ago
A line that includes the point (4,1) has a slope of 1 7 . What is its equation in point-slope form?
Sergeeva-Olga [200]

Answer:

y = 17x-67

Step-by-step explanation:

The one point form of line also called slope point form is given by

(y-y_1)=m(x-x_1)

where (x1, y1) is the point and m is slope

Given: (x1, y1) = (4,1) and m= 17

Substituting these values in above equation to find equation in point-slope form

(y-1)=17(x-4)

y-1 = 17x-68

y = 17x-67

the point -slope form of equation y = 17x-67

5 0
2 years ago
What is 2 plus 2 add 14 subtract 6
olasank [31]

What is 2 plus 2 add 14 subtract 6

2+2+14-6=

12

3 0
2 years ago
Read 2 more answers
A basketball player made 80 out of 100 attempted free throws. What percent of free throws was​ made?
Mrac [35]

Percent of free throws = (number of free throws made / total attempts) x 100

Percent = (80/100) x 100 = 80%

The answer is 80%

5 0
2 years ago
Read 2 more answers
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