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Yanka [14]
1 year ago
15

Can someone help me with these geometry questions? I can’t seem to understand them. If u find the answers, can u explain it too?

It’s urgent

Mathematics
1 answer:
rusak2 [61]1 year ago
6 0

<em>Question 5</em>

Vertical angles are <u>congruent</u>. Therefore, 3y=\boxed{150}. The sum of two supplementary angles equals \boxed{180^{\circ}}.

Therefore, 6x+150=\boxed{180}

<em>Question 6</em>

\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}

<em>Question 7</em>

<em />\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}

<em>Question 8</em>

<em />7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}

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Convert the polar coordinates (-3, -60°) to Cartesian coordinates.
notsponge [240]

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x

#Using the illustration above, we can express our polar coordinates as:

-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}

#Solve simultaneously to solve for x and y:

(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\  y \ in\  i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6

Hence, the Cartesian coordinates are (1.5,-2.6)

6 0
2 years ago
A LINE SEGMENT IS 5 INCHES MORE THAN FOUR TIMES THE LENGTH OF ANOTHER. THE DIFFERENCE IN THEIR LENGTHS IS 35 INCHES. HOW LONG AR
Georgia [21]
<h3>Answer:</h3>

One line segment is 10 cm and the other one is 45 cm


Hope this helps you!

Have an amazing day :)

<h3 />
6 0
3 years ago
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April
Svetlanka [38]

Answer:

  d.  May

Step-by-step explanation:

Working through the chain, we have ...

  Feb = 1.10×Jan

  Mar = 0.85×Feb = 0.935×Jan

  Apr = 1.20×Mar = 1.122×Jan

  May = 0.90×Apr = 1.0098×Jan

  Jun = 1.05×May = 1.06029×Jan

The multiplier that is closest to 1 is 1.0098, so May has sales closest to January.

_____

The percentage increase or decrease can be converted to a multiplier by adding it to 1. If p% is the percentage change, then adding it to an original value looks like ...

  original + p% × original = original × (1 +p%) . . . . . . . distributive property

And p% translates to a decimal number by replacing % with /100 or ×0.01.

  10% increase:   original × (1 + 10/100) = original × 1.10

  15% decrease:   original × (1 - 15/100) = original × 0.85

6 0
3 years ago
The price of the box of 15 stickers is $6. The price of the box of 25 stickers is $8. All prices are without tax, and the price
spayn [35]

<u><em>Answer:</em></u>

A box of 50 stickers would cost $13

<u><em>Explanation:</em></u>

<u>1- getting the equation representing the price:</u>

We have two variables; the number of stickers and the price of the box

We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)

<u>We are given that:</u>

A box of 15 stickers cost $6..........> first point is (15,6)

A box of 25 stickers cost $8 ........> second point is (25,8)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

<u>i. getting the slope:</u>

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2

The equation now became: y = 0.2x + c

<u>ii. getting the y-intercept:</u>

To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)

y = 0.2x + c

6 = 0.2(15) + c

c = 6 - 0.2(15) = 3

<u>The final equation is:</u>

y = 0.2x + 3

where y is the price of the box and x is the number of stickers it contains

<u>2- getting the price of a box with 50 stickers:</u>

To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1

<u>This is done as follows:</u>

y = 0.2(50) + 3 = 13

Therefore, a box of 50 stickers will cost $13

Hope this helps :)

5 0
3 years ago
Point (-5,2) is reflected over the y axis. Where is the new point located?
umka21 [38]
The new point is (5,2)
8 0
3 years ago
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