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1 year ago

BD bisects ZABC. Solve for x and find mABC. m/ABD = 11x - 10, m/CBD = 8x + 2

Mathematics

1 answer:

Tamiku [17]1 year ago

7 0

The value of x is 4 and the value of ∠ABC is 68°.

To solve this problem we first have to understand the concept of an angle bisector. Angle bisector is a straight line passes through the vertex of an angle dividing the angle in two equal angles.

According to the condition BD bisects ∠ABC

Therefore the two angles formed by the angle bisector are ∠ABD and ∠CBD.

The angle value of these two angles are equal.

Given:

m∠ABD=11x-10

m∠CBD=8x+2

Therefore from the above condition:

m∠ABD=m∠CBD

Substituting the values we get:

11x-10=8x+2

Solving the linear equation to find the value of x.

$or,11x-10=8x+2\\or,11x-8x=2+10\\or,3x=12\\or,x=4$

Now let us find the value of ∠ABC

m∠ABC=m∠ABD+m∠CBD

or,∠ABC=11x-10+8x+2

or,∠ABC=19x-8

Substituting the value x=4 in the equation we get:

m∠ABC=19×4-8

or,m∠ABC=68°

Therefore we can conclude that the value of xis 4 and the value of ∠ABC is 68°.

To learn more about angle bisectors:

brainly.com/question/12896755

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3 T-shirts cost $12. How much will 50 T-shirts cost?

LekaFEV [45]

Answer:

$200

Step-by-step explanation:

First, find the unit rate:

12/3= 4

Then multiply:

4*50= 200

Hope this helps!

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2 years ago

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How do you find the cube root

zvonat [6]

Use a calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as $ \sqrt[3]{64} = 4 $.The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of x is the same as x raised to the 1/3 power. Written as $ \sqrt[3]{x} = x^{\frac{1}{3}} $. The common definition of the cube root of a negative number is that 
(-x)1/3 = -(x1/3).[1] For example:

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

This was not copied from a website or someone else. This was from my last year report.


f -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

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3 years ago

The measure ∠BQS of is 80°. What is the m∠NQS? 42° 48° 128° 32°

fomenos

Answer:

m<NQS = 32°

Step-by-step explanation:

Given:

m<BQS = 80°

m<BQN = 48°

Required:

m<NQS

SOLUTION:

Angle BQN and angle NQS are adjacent angles having a common line, QN, and a common corner point, Q.

Therefore:

m<BQN + m<NQS = m<BQS (angle addition postulate)

48° + m<NQS = 80° (substitution)

m<NQS = 80 - 48° (Subtraction of 48 from each side)

m<NQS = 32°

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3 years ago

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inna [77]

Answer:

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Step-by-step explanation:

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3 years ago

Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?

Sonbull [250]

Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure. Please check the attached figure (a)

Answer:

Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.

Step-by-step explanation:

As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.

So,

Let suppose P(a, b) is the point.

The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is

P(a, b) → $P(\frac{x+2}{3}, \frac{y+4}{3})$

Hence,

A(1, 2) → A'(1, 2)

B(2, 3) → B'(4/3, 7/3)

C(4, 2) → C'(2, 2)

D(2, 1) → D'(4/3, 5/3)

The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.

Keywords: dilation, quadrilateral, segment

Learn more about dilation from brainly.com/question/7569824

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3 years ago