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2 years ago

In the diagram alongside angel ABD measure 30 ,angel CDE measure 40 and angel CED measure 55 . Find the measure of angel BAC

Mathematics

1 answer:

jeka942 years ago

6 0

The measure of the angle BAC is 55 degrees

<h3>Lines and angles</h3>

An angle is the point where two lines meet. From the given diagram, the sum of the angle in the triangle BAC is 180 degrees

Determine the measure of <BCA

<BCA = (40+55)

<BCA = 95 degrees

Determine the measure of <BAC

<BAC = 180 - (95+30)

<BAC = 180 - 125

<BAC = 55 degrees

Hence the measure of the angle BAC is 55 degrees

Learn more on lines and angles here; brainly.com/question/25716982

#SPJ1

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A train traveling at a constant speed takes a passenger from Elm to Millwood, stopping at Centre along the way. It takes 2004-01

ZanzabumX [31]

The complete problem is as following:
A train traveling at a constant speed takes a passenger from Elm to Millwood, stopping at Centre along the way. It takes 5 times as long to go from Centre to Millwood as it does to go from Elm to Centre. The entire trip is 48 miles. How far is the ride from Centre to Millwood? Name a geometric postulate or theorem used to find the solution.
A) 8 miles ; segment addition postulate
B) 8 miles; segment bisector theorem
C) 40 miles; segment addition postulate
D) 40 miles; segment bisector theorem
=======================================================
Solution ;
Let the time taken from Elm to Centre = x ⇒⇒⇒ segment (1)

∴ the time taken from Centre to Millwood = 5x ⇒⇒⇒ segment (2)

∴ Total time of all the trip = x + 5x = 6x
The entire trip is 48 miles and the train traveling with constant speed
∴ speed = distance over the time = $\frac{48}{6x} = \frac{8}{x}$
So, the distance from Centre to Millwood = speed * time = $\frac{8}{x} * 5x = \framebox{40 \ miles}$
As seen in the answer, we have added the segment (1) to segment (2)
So, The geometric postulate used to find the solution is segment addition postulate

So, the correct option is C) 40 miles; segment addition postulate

=======================================================
Another solution :
From Elm to Centre = x ⇒⇒⇒ segment (1)
From Centre to Millwood = 5x ⇒⇒⇒ segment (2)
∵ The train traveling with constant speed
∴ Distance is proportional with the time
By using the ratio and proportional as following

$Segment (1) : segment (2) : Total \\ \ \ 
. \ \ \ \ \ \ \ x \ \ \ \ \ \ : \ \ \ \ \ 5x \ \ \ \ \ \ \ : \ \ 6x \\
. \ \ \ \ \ \ \ ? \ \ \ \ \ \ : \ \ \ \ \ \ \ ? \ \ \ \ \ \ \ \ : \ \ \ 48$

∴ segment (2) = $\frac{48 * 5x}{6x} = \framebox {40 miles}
$

we have used the postulate of segment addition to add x and 5x.

So, the correct option is C) 40 miles; segment addition postulate

4 0

4 years ago

Reil [10]

<u>Answer:</u>

x = 5.00 cm

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

• area of the rectangle = $x$ x $(x + 1)$

= $x^2 + x$

• area of the circle = π r²

= $\frac{22}{7}$ x $(x + 2)^2$

= $\frac{22}{7}$ x $(x^2 + 4x + 4)$

∴ $x^2 + x$ + $\frac{22}{7}$ x $(x^2 + 4x + 4) = 184$

⇒ $x^2 + x$ + $\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184$

⇒ $\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0$

• Using quadratic formula, where

a = $\frac{29}{7}$

b = $\frac{95}{7}$

c = $\frac{-1200}{7}$ ,

$x=\frac{-b \pm \sqrt{b^2-4c}}{2}$

$x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}$

$x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28$

As length (x) cannot be a negative number,

x = 5.00 cm

7 0

2 years ago

20. Lee uses Bill Payer from his bank account to pay his internet bill. Lee pays the same amount each month.

NARA [144]

It's the same amount each month, for a year. So:
total money ÷ times money was taken out= how much has been taken out.

$600÷12=50

3 0

3 years ago

A farmer planted 2/5 of his 60 acres in beans and 4/10 of his 60 acres in corn. What fraction of the 60 acres had been planted i

yanalaym [24]

The answer is that 48 have been planted with bean and corn and 24 acres is beans and another 24 acres is corn

5 0

3 years ago

Which equation shows a y- intercept of -5

Assoli18 [71]

Hi there!

»»————-　★　————-««

I believe your answer is:

Option B) $y=x-5$

»»————-　★　————-««

Here’s why:

Most options (Second, Third, and Fourth) are in slope intercept form.

⸻⸻⸻⸻

$\boxed{\text{Slope-Intercept Form}}\\\\y=mx + b\\\\\boxed{\text{Key:}}\\\\m - \text{The Slope}\\\\b- \text{The Y-Intercept}$

⸻⸻⸻⸻

We are looking for the equation where '-5' is in b's place.

⸻⸻⸻⸻

$\boxed{\text{Which equation shows a y-intercept of -5?}}\\\\---------\\\text{A}) -5y = x\\\\\text{This equation in slope-intercept form is }y=\frac{1}{5}x.\\\\\text{The 'b' part is not shown. This means that the line passes through the}\\\text{origin.}\\\\---------\\\\\text{B})\text{ }y = x-5\\\\\text{This option shows a slope of one and a y-intercept of -5.} \\\\\text{Therefore, \boxed{\text{option B is the correct answer.}}}\\\\----------\\\text{Option C has a y-intercept of 5, and Option D has a}\\$

$\text{y-intercept of 1.}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

8 0

3 years ago