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NeTakaya
3 years ago
8

In a doctor's office, the receptionist's annual salary is $159,000 less than that of the doctor. Together, the doctor and the re

ceptionist make $227,000 per year. Find each person's annual income.
Mathematics
1 answer:
Ann [662]3 years ago
8 0

Answer:

The salary of Doctor = $193,000

The salary of Receptionist = $34,000

Step-by-step explanation:

Given as,

Together ,the Doctor salary and the Receptionist salary = $ 227,000 per year

And the salary of Receptionist = The Doctor salary -$159,000 per year

Let the salary of Doctor = x

So, the Receptionist salary = x - $159,000 per year

And x + Receptionist salary = $ 227,000 per year

       x + x - $159,000 per year = $ 227,000 per year

Or,   2x = $ 386,000 per year

Or,     x = $ \frac{386000}{2}

Or,     x = $ 193,000

And the salary of Receptionist = $193,000 - $159,000 = $34,000

Hence,  The salary of Doctor = $193,000

And,       The salary of Receptionist = $34,000

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point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below
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Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a  sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

  • To find angle CAB and;
  • Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using  cosine rule to determine angle CAB, we have:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}

Here:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}

\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}

\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = 0.3451}

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

  • assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;          

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)      

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

\mathbf{Tan \theta = \dfrac{GF}{BF}}

\mathbf{Tan \ 35.19  = \dfrac{1.8 \ m }{BF}}

\mathbf{BF  = \dfrac{1.8 \ m }{Tan \ 35.19}}

\mathbf{BF  = \dfrac{1.8 \ m }{0.7052}}

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0
3 years ago
PLS HELP I WILL HELP BACK 15 POINTS WILL GIVE BRAINLIEST Write the equation of a polynomial, in standard form, that has:
djyliett [7]

Answer:  -5x^3 -13x^2 -6x + 15ix + 39ix + 18i

Step-by-step explanation:

An equation with zeros at these numbers could be put in form x = number.

So, (x-3) could be set to 0 to get x=3.

So, you can look at these "answers" they give you and work backward to get:

(x-3)(x+2/5)(x-3i)

Multiply first two together.

x^2+2/5x-3x-6/5

simplify

x^2 - 2 3/5x -6/5

Change first term to have same denominator by multiplying by "1" in the form of -5/-5

-5x^2/-5 - 13/5x -6/5

Divide all terms by 1/5 (which is the same as multiplying each term by 5)

(-5x^2 -13x -6)

Now multiply by (x-3i)

-5x^3 -13x^2 -6x + 15ix + 39ix + 18i

4 0
2 years ago
TWVU is a trapezoid with midsgment FG find the value of x please help
photoshop1234 [79]

Answer:

Find each measure.

1. 

SOLUTION:  

The trapezoid ABCD is an isosceles trapezoid. So,

each pair of base angles is congruent. Therefore,

ANSWER:  

101

2. WT, if ZX = 20 and TY = 15

SOLUTION:  

The trapezoid WXYZ is an isosceles trapezoid. So, the

diagonals are congruent. Therefore, WY = ZX.

WT + TY = ZX

WT + 15 = 20

WT = 5

ANSWER:  

5

COORDINATE GEOMETRY Quadrilateral

ABCD has vertices A(–4, –1), B(–2, 3), C(3, 3),

and D(5, –1).

3. Verify that ABCD is a trapezoid.

SOLUTION:  

First graph the points on a coordinate grid and draw

the trapezoid.

Use the slope formula to find the slope of the sides of

the trapezoid.

The slopes of exactly one pair of opposite sides are

equal. So, they are parallel. Therefore, the

quadrilateral ABCD is a trapezoid.

ANSWER:  

ABCD is a trapezoid.

4. Determine whether ABCD is an isosceles trapezoid.

Explain.

SOLUTION:  

Refer to the graph of the trapezoid.

Use the slope formula to find the slope of the sides of

the quadrilateral.

The slopes of exactly one pair of opposite sides are

equal. So, they are parallel. Therefore, the

quadrilateral ABCD is a trapezoid.

Use the Distance Formula to find the lengths of the

legs of the trapezoid.

The lengths of the legs are equal. Therefore, ABCD

is an isosceles trapezoid.

ANSWER:  

isosceles;

5. GRIDDED REPSONSE In the figure, is the

midsegment of trapezoid TWRV. Determine the value

of x.

SOLUTION:  

By the Trapezoid Midsegment Theorem, the

midsegment of a trapezoid is parallel to each base

and its measure is one half the sum of the lengths of

the bases.

 are the bases and   is the 

midsegment. So,

Solve for x.

16 = 14.8 + x

1.2 = x

ANSWER:  

1.2

CCSS SENSE-MAKING  If ABCD is a kite, find

each measure.

6. AB

SOLUTION

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2 years ago
The line passes through the point (-2,-5) and has a slope of -3.
JulsSmile [24]

Answer:

y = - 3x  -11

Step-by-step explanation:

(x₁ , y₁) = (-2 , -5)   & m = -3

y - y₁ = m (x - x₁)

y - [-5] = (-3)(x -[-2])

y + 5   = (-3)(x + 2)

y + 5  = -3x - 6

      y = -3x - 6 - 5

      y = - 3x  -11

4 0
2 years ago
12 is what % less than 24
Alex777 [14]
50% less or half, hope this help
6 0
3 years ago
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