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adoni [48]
1 year ago
14

In △ABC, ∠ABC = 60 degrees .

Mathematics
1 answer:
ira [324]1 year ago
5 0

A given<u> shape</u> that is <em>bounded</em> by three <u>sides</u> and has got three <em>internal angles</em> is referred to as a <u>triangle</u>. Thus the <em>value</em> of <u>PB</u> is 8.0 units.

A given <em>shape</em> that is <u>bounded</u> by three<em> sides</em> and has got three <em>internal angles</em> is referred to as a <u>triangl</u>e. Types of <u>triangles</u> include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The sum of the<em> internal angles</em> of any <u>triangle</u> is 180^{o}.

In the given question, point<u> P</u> is <u>center</u> of the given <u>triangle</u> such that <APB = <APC = <BPC = 120^{o}. Such that <u>line</u> PB <em>bisects</em> <ABC into two <u>equal</u> measures of 30^{o}.

Thus;

<ABP = 30^{o}

Thus,

<ABP + <APB + <BAP = 180^{o}

30 + 120 + <BAP = 180^{o}

<BAP = 180^{o} - 150

<BAP = 30^{o}

Apply the <em>Sine rule</em> to determine the value of PB, such that;

\frac{a}{SinA} = \frac{b}{SinB}

\frac{8}{Sin 30} = \frac{PB}{Sin 30}

BP = \frac{8*Sin 30}{Sin 30}

    = 8

BP = 8.0

Therefore, the value of <u>PB</u> = 8 units.

For more clarifications on Sine rule, visit: brainly.com/question/27174058

#SPJ1

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The art teacher has 7 bottles of glue that are each 2/5 full. He combines them so he will have fewer bottles. How many bottles o
Katen [24]

Teacher will have 3 bottles of glue after he combines

<em><u>Solution:</u></em>

Given that,

The art teacher has 7 bottles of glue that are each 2/5 full

He combines them so he will have fewer bottles

<em><u>To find: bottles of glue does he have after he combines them</u></em>

From given,

Total bottles = 7

Each is 2/5 full

Therefore, multiply 7 with 2/5 to get total bottles of glues he will have after combining

Number\ of\ bottles\ of\ glues = 7 \times \frac{2}{5}\\\\Number\ of\ bottles\ of\ glues = \frac{14}{5} = 2.8 \approx 3

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7 0
3 years ago
Consider h(x)=x^2+8+15. identify its vertex and y-intercept.
OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

x = \frac{-b}{2a}

x = \frac{-8}{2(1)}

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

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