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3 years ago

Need some help? Image should convey the rest.

Mathematics

1 answer:

KonstantinChe [14]3 years ago

7 0

Answer:

30+(4x-4)=180-90(angle sum of triangle)

30+4x-4=90

4x+30-4=90

4x+26=90

4x=90-26

=54

x=54÷4

=13.5

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The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.

pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

c = 8

The equation of tangent line at (-6,8) is:

y = 8

6 0

3 years ago

Rectangle poster is 3 times as long as wide perimeter is 24 in

Alexxandr [17]

w= width

l = 3w

P = 2(l+w)

substitute

24 = 2(3w+w)

24 = 2(4w)

24 =8w

3 =w

The width is 3 inches

the length is 9 inches

3 0

4 years ago

katrin2010 [14]

Answer:

230 - 151 + 180 + (43 - 12) = 290

Step-by-step explanation:

Use PEMDAS.

Evaluate the expression in the parentheses:

230 - 151 + 180 + (43 - 12)

43 - 12 = 31

230 - 151 + 180 + 31

Add and Subtract From Left to Right:

230 - 151 + 180 + 31

79 + 180 + 31

259 + 31

290

None of the given options are correct. 

6 0

3 years ago

Basic functions sample work! Help please

frosja888 [35]

Answer:

See the attachment.

Step-by-step explanation:

Function notation: This means the description of the curve is written in the form ...

f(x) = <an expression that describes the curve in terms of independent variable x>

The name of the function does not have to be "f", though f, g, h are traditional for generic functions. In specific cases, the function name might be related to the value the function delivers: cost(n) might be the function that tells you the cost of producing n items, for example.

The functions shown (square root, reciprocal) should be shapes you have memorized. You can check the scale factor at specific values you know, for example, √4 = 2, or 1/1 = 1. Hence both functions have a scale factor of 1 (no scaling).

___

The domain is the horizontal region where the function is defined. Square root is not defined for negative numbers; reciprocal is not defined for 0. Hence the descriptions of the respective domains must exclude these values.

___

The range is the vertical extent of the values each function produces. The domain and range are the same for both functions shown here.

___

Asymptotes are lines the function approaches but does not reach. The square root function has no such lines. (It reaches vertical at x=0.)

The reciprocal function has a vertical asymptote as x=0 (the value of x that makes the function denominator zero). And, it has a horizontal asymptote at y=0, a value that can be approached, but not reached, as x gets large in either the positive or negative directions.

___

End behavior: The square root function heads off toward (∞, ∞). The reciprocal function heads toward the value defined by the horizontal asymptote: y=0 as x gets large in magnitude.

3 0

3 years ago

Solve using elimination 2x+5y=34 x+2y=14

Darina [25.2K]

2x + 5y = 34

x+2y = 14

Multiply the second equation by two to create like terms for one variable.

2(x+2y = 14)

2x + 4y = 28

2x + 5y = 34

2x + 4y = 28 -- Subtract.

y = 34.28 = 6

Solve for x

x + 2(6) = 14

x + 12 = 14

x = 2

Check:

2 + 2(6) = 14

2 + 12 = 14

14 = 14

Answer:

X = 2

Y = 6

8 0

4 years ago