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3 years ago

X + 4.2 = 7 what is x

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

In this question, you're solving for x.

Solve for x:

x + 4.2 = 7

You need to get x by itself, to do so, you would need to subtract 4.2 from both sides:

x = 2.8

Answer:

x = 2.8

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A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far

ValentinkaMS [17]

Answer:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

$\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}$ (1)

And this formula is expanded by definition of vectors in rectangular and polar form:

$(x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})$ (1b)

Where:

$x, y$ - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

$r_{1}, r_{2}$ - Length of each vector, in kilometers.

$\theta_{1}, \theta_{2}$ - Bearing of each vector in standard position, in sexagesimal degrees.

If we know that $r_{1} = 42\,km$ , $r_{2} = 28\,km$ , $\theta_{1} = 32^{\circ}$ and $\theta_{2} = 154^{\circ}$ , then the resulting coordinates of the final position of the surveyor is:

$(x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})$

$(x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km]$

$(x,y) = (10.452, 34.531)\,[km]$

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

$\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}$

$\theta \approx 16.840^{\circ}$

And the distance from the camp is calculated by the Pythagorean Theorem:

$r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}$

$r = 36.078\,km$

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

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3 years ago

Create a ratio table to solve the following rate problem.

rusak2 [61]

Answer:

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3 years ago

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The x axis of the point is being translated three units to the left (going from 6 to 3)
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8 0

2 years ago

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Jorge is mixing a special shade of orange paint. He mixed 1 gallon of red paint with 3 gallons of yellow paint. Based on this ra

astra-53 [7]

Answer:

a. b. c. and d. are true; e. is false

Step-by-step explanation:

1 gallon of red paint : 3 gallons of yellow paint

1 gallon of red paint + 3 gallons of yellow paint = 4 gallons of orange paint

a. 3/4 of a 4-gallon mix would be yellow paint.

True. 3 out of 4 gallon mix is yellow and 1 out 4 is red

b. Every 1 gallon of yellow paint requires 1/3 gallon of red paint.

1 gallon of red paint : 3 gallons of yellow paint

divide by 3 in both sides of :

1/3 gallon of red paint : 3/3 gallons of yellow paint

1/3 gallon of red paint: 1 gallon of yellow paint. True

c. Every 1 gallon of red paint requires 3 gallons of yellow paint.

True. 1 gallon of red paint : 3 gallons of yellow paint

d. There is 1 gallon of red paint in a 4-gallon mix of orange paint.

True. 1 out of 4 is red and 3 out of 4 is yellow.

e. There are 2 gallons of yellow paint in an 8-gallon mix of orange paint.

1 gallon of red paint + 3 gallons of yellow paint = 4 gallons of orange paint

Multiply by 2 each side of the equation

2(1 of red paint + 3 of yellow paint) = 2(4 of orange paint)

apply to each member of the parenthesis ()

2 of red paint + 6 of yellow paint = 8 of orange paint

Actually there are 6 gallons of yellow paint in a 8 gallon mix. So e. is false.

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3 years ago

The sum of two number is 14 and their different 6

STatiana [176]

8+6=14 and 14-8=6 so the 2 numbers are 8 and 6

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