solve the system of the equations using the elimination or substitution method

Answer:

a₂ = 12.5 m/s²

Step-by-step explanation:

Applying the 2º Newton's Law:

∑F = m * a

F₁ = m₁ * a₁

F₁ = m₁ * 12.5

F₁ = 12.5m₁

F₂ = m₂ * a₂

2F₁ = 2m₁ * a₂

a₂ = F₁ / m₁

So:

a₂ = 12.5m₁ / m₁

a₂ = 12.5 m/s²

Step 1

Given;

Required to solve the problem using completing the square method

Step 2

Move 10 to the left.

Simplify

Step 3

Add 64 and subtract 64

Step 4

Complete the square

Step 5

Find the value of n

Hence,

n= -8+(2√2)i

or

n= -8-(2√2)i

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

Since line YZ is parallel to chord line WX and the length of WX is 50, then the length of XZ must be half of WX, which is  A) 25.

Parallel refers to the concept of running multiple processes at the same time. It is often used in computing and engineering to describe the process of running multiple operations simultaneously. It is also used to refer to multiple paths of data or information travelling in the same direction, such as in a computer network. Parallel computing is a form of computation in which multiple processes are run concurrently, either on the same computer or across multiple computers. This allows for faster execution of tasks and better utilization of resources, such as processors and memory.

Since diameter line YZ is parallel to chord line WX, we can use the property of parallel lines that the opposite angles are equal. Thus, we have:

angle ZWX = angle ZYX (corresponding angles)

angle ZYX = 90 degrees (as YZ is a diameter)

angle ZWX = 90 degrees (as WZ is a chord of the circle)

Therefore, triangle WZX is a right triangle with right angle at Z. Using the Pythagorean theorem, we can find the length of XZ as:

[tex]XZ^2 = WX^2 - WZ^2[/tex]

[tex]XZ^2 = 50^2 - (YZ/2)^2[/tex] (as YZ is the diameter and WZ = YZ/2)

[tex]XZ^2 = 2500 - YZ^2/4[/tex]

[tex]XZ^2 = 2500 - (XZ^2/4)[/tex](as YZ = 2XZ)

[tex]5XZ^2/4[/tex] [tex]= 2500[/tex]

[tex]XZ^2 = 2000[/tex]

[tex]XZ = (2000) = 20(5)[/tex]

Therefore, the length of XZ is approximately 44.72 units, which is not one of the answer choices. However, if we assume that the diameter YZ is 100 units (so that WZ = 50 units), then [tex]XZ^2 = 50^2 - 25^2 = 1875[/tex], and [tex]XZ = (1875) = 25(3)[/tex]. This value is approximately 43.30 units, which is closest to answer choice (A) 25. Therefore, the answer is (A) 25.

To learn more about parallel, visit

brainly.com/question/30195834

#SPJ1

Answer:

y = (-3/5)x - (31/5)

Step-by-step explanation:

3x + 5y = 11

-3x              -3x

------------------------------

5y = -3x + 11

÷5    ÷5    ÷5

-----------------------

y = (-3/5)x + (11/5)

y - y₁ = m(x - x₁)

y - (-5) = (-3/5)(x -(-2))

y + 5 = (-3/5)(x + 2)

y + 5 = (-3/5)x - (6/5)

    -5                 -5

-----------------------------------

y = (-3/5)x - (31/5)

I hope this helps!

The number 25×10 to the power of -3 written in the standard form is 2.5×10⁻⁴.

The given number is;

25×10 to the power of -3

This can be written as;

= 25×10⁻³

Now, as per the standard form, the number should contain only one digit to the left of decimal.

Thus, shifting one decimal to the left of the 5 and converting the power by adding one to the current power,.

The number becomes;

= 2.5×10⁻⁴.

Thus, the number written in the standard form is 2.5×10⁻⁴.

To know more about the scientific notations, here

https://brainly.com/question/1767229

#SPJ10

She uses 800 mL of solution A; that is, 2% of those 800 mL is alcohol

Alcohol on a:

2% of 800 = 2*800/100 = 16mL

If we use x mL of b, the amount of alcohol is:

5% of x = 5*x/100 = x / 20

Total amount of alcohol: 16 + x/20

Total amount of solution mixture: 800 + x

The ratio:

(16 + x/20) / (800 + x) = 3%

(16 + x/20) / (800 + x) = 3/100

1600 + 5x = 2400 + 3x

Solving for x:

5x - 3x = 2400 - 1600

2x = 800

x = 400 mL

She used 400 mL of solution b

Answer:

x=4/15

Step-by-step explanation:

first you need to make common denominators for 1/5 and 1/3

the common denominator is 15

5*3=15, 3*5=15. 1*3=3, 1*5=5

new equation:3x-3/15=x+5/15

now subtract x from both sides: 3x-3/15=x+5/15

                                                     -x          -x

                                                     2x-3/15=5/15

now you can add 3/15 to 5/15

2x=8/15

now for the last step, divide by 2 because there are 2 x's

2x/2=x         8/15 /2=4/15

x=4/15

Answer:

4/15

Step-by-step explanation:

3x-1/5 = x+1/3

make a common denominator

3x -3/15 = x + 5/15

next you can take away one x from both sides

2x - 3/15 = 5/15

then we want to have x alone on one side and everything else on the other

2x = 5/15 + 3/15

2x = 8/15

1x = 8/15 ÷ 2

1x = 8/30

simplify that

x = 4/15

Answer:

t=44 hrs.

Step-by-step explanation:

1. a. you are asked to find the total hours the 2 girls work in a week.

b. it needs to be a greater number than 26

2. variables: h= hours per week

t= total hrs.

3. h= hrs. per week

t= total hrs.

4. 44=26+h

-26 -26

18=h

5. 44=26+18

44=44

6. The total hours the two work in a week is 44 hours.

1089822 is the combined population of the four insect groups.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

Given Data

Insect population

Population of honeybees = 7.3498(10⁴)

Population of honeybees = 73498

Population of ants = 6.822(10³)

Population of ants = 6822

Population of termites = 9.8(10⁵)

Population of termites = 980000

Population of aphids = 2.9502(10⁴)

Population of aphids = 29502

Combined population = 73498 + 6822+980000+29502

Combined population = 1089822

1089822 is the combined population of the four insect groups.

To learn more about exponents, visit:

https://brainly.com/question/24813773

#SPJ9

Answer: z=23/9

Step-by-step explanation:

I will use cross multiplication

[tex]\frac{1}{9} =\frac{z}{23} \\23(1)=9(z)\\23=9z\\\frac{23}{9} =\frac{9z}{9} \\z=\frac{23}{9}[/tex]

I hope this helps.

The simplified expression of (4⁴)⁻¹  is one over four raised to the fourth power

The expression can be simplified as follows:

(4⁴)⁻¹

Therefore, the expression can be simplified using laws of indices.

[tex](a^{c} )^{b} = a^{cb}[/tex]

and

[tex](a^{-b} )^{c} = \frac{1}{a^{bc} }[/tex]

Therefore, using the laws of indices, the expression can be simplified below:

(4⁴)⁻¹  = 4⁻⁴

Hence,

4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴

Hence,

(4⁴)⁻¹  = 1 / 4⁴ = (1 / 4)⁴

learn more on simplification here: https://brainly.com/question/28296328

#SPJ1

Answer:

y = (1/3)x + 4

Step-by-step explanation:

(0, 4) and (-3, 3)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁           3 - 4           -1            1

m = ------------- = ------------ = --------- = --------

         x₂ - x₁          -3 - 0         -3           3

y - y₁ = m(x - x₁)

y - 4 = (1/3)(x - 0)

y - 4 = (1/3)x - 0

   +4            +4

----------------------------

y = (1/3)x + 4

I hope this helps!

Answer: [tex](\sqrt{9}-2 )^{-2} = 1 \\ (1-6)^{2}=(-5)^{2} = 25\\ 1+25=26[/tex]

26

Step-by-step explanation:

1) First, lets solve the first part --> (√9 - 2)^-2 will make 1.

2) Then, --> (1-6)^2= (-5)^2= 25

3) Sum this up --> 1+25=26.

Hope all clear!!

The east distance from town to house is 6.464 miles.

STEP - BY - STEP EXPLANATION

What to find? The east distance from town to house.

To solve;

Let us first make a sketch to get the clearer picture of the problem.

Attach below is the sketch.

Observe that the house is far east of the center of the town= 3miles + x

We need to find the value of x.

Using Pythagoras theorem;

hypotenuse²= adjacent² + opposite²

From the diagram above,

hypotenuse = 4

adjacent=x

opposite=2

Substitute the values into the formula and solve for x.

4² =x² + 2²

16 = x²+4

Subtract 4 from both-side of the equation.

x²=16 - 4

x²=12

Take the square root of both-side of the equation.

x = 3.464

But recall that, the east distance from town to house = 3+ x

Substitute the value of x.

Hence, the east distance from town to house = 3+ 3.464 = 6.464 miles

Let's begin by listing out the information given to us:

Sandra has 1/4 of a roll of ribbon

To make 3 bows, she will use the amount of ribbon shown below:

The given figure can be drawn as,

From the figure,

Since angle of incidence will be equal to angle of reflection, [tex]\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}[/tex]Therefore, the height of cactus is 6 m.

line A and line B are showing that object A and B are moving with a different rate.

they both are moving with constant speed but we can see that line A has a large slope as compare to line B, that means object A has more speed than the object B.

so the speed of object A is greater than the object B.

all the statements prove that a line is parallel to b.

If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.

Lines can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points then it is known as a transversal line.

line intersects lines a and b at points P and Q respectively. The line l is the transversal here.

∠1,∠2,∠7 and ∠8 are the exterior angles and ∠3,∠4,∠5 and ∠6 denote the interior angles.

The angle pairs formed due to intersection by a transversal are named as follows:

Corresponding Angles: ∠1 and ∠6; ∠4 and ∠8; ∠2 and ∠5; ∠3 and ∠7 are the corresponding pair of angles.

Alternate Interior Angles: ∠4 and ∠5 ; ∠3 and ∠6 denote the pair of alternate interior angles.

Alternate Exterior Angles: ∠1 and ∠7; ∠2 and ∠8 are the alternate exterior angles.

Same side Interior Angles: ∠3 and ∠5; ∠4 and ∠6 denote the interior angles on the same side of the transversal or co-interior or consecutive interior angles.

learn more about parallel line here :

brainly.com/question/16701300

#SPJ13

The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5 the first term of the sequence 12.

Formula\sa {n}=a {1}+(n-1) The nth term in the series is d a n.

The first term present in the sequence is a 1.

d is the common distinction between the terms.

an = a1 + (n-1)d

⇒ a1 = an - (n-1)d

= a70 - (70-1) (1.5)

= 115.5 - 69 (1.5)

= 12

The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive terms is always two, so the sequence 3, 5, 7, 9... is arithmetic.

The formula for an arithmetic sequence is given as an=a1+(n1)d, where n is a general term, a1 a 1 is the initial term, and d is the common difference. To find the general word in the series, do this.

To know more about arithmetic sequence, visit:

https://brainly.com/question/10396151

#SPJ9

Option C. The way that the change would affect the mean and the median is that The mean will increase and the median will not change.

We will find the mean and the median before the 40 was added and after it was added

Before it was added

Mean = 16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 / 9

= 213 / 9

= 23.67

The median is 24

After we have added 40 the mean would be

16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40 / 10

= 253 / 10

= 25.3

The median would be 24 + 24 / 2

= 48 / 2

= 24

Hence we can see that the mean got to be higher while the median still remained as 24.

The solution is C.

Read more on mean and median here:

https://brainly.com/question/14532771

#SPJ1

Answer:

B

Step-by-step explanation:

If we look at the x-axis, the function increases and decreases. Therefore, the domain is all real numbers.

If we look at the y-axis, the same is occurring. Therefore the range is also all real numbers.

The frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.

So, the frequency for the particular 5 classes is as follows:

The following five classes will appear most frequently overall:

Therefore, the frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.

Know more about frequency here:

brainly.com/question/254161

#SPJ3

By solving a system of equations we can see that Olivia spent $14 and Camiller spent $37.

Let's define two variables:

We know that " Camille spent $14 less than three times what Olivia spent" so we can write:

y = 3*x - 14

And "In total, they spent $54"

x + y = 54

Then we have a system of equations:

y = 3*x - 14

x + y = 54

Replacing the first equation into the second one, we get:

x + 3x- 14 = 54

4x - 14 = 54

4x = 54 + 14

4x = 68

x = 68/4 = 17

Now that we know the value of x, we can try to find the value of y.

y = 3x - 14 = 3*17 - 14 = 37

So Olivia spent $14 and Camiller spent $37.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer:

34

Step-by-step explanation:

[tex]26+8 \\ \\ =2(13+4) \\ \\ =2(17) \\ \\ =34[/tex]

Answer:

Four Students have failing grades, with a remainder of 4.

28:4 R:4

Step-by-step explanation:

With 32 students in the class. A 7:1 ratio doesn't work perfectly. 7*4=28. 28:4.

32 students - 28 possible students to fail = 4 Remainder since 7:1 ratio doesn't fulfill 32 students.

Answer: Provided the geometric diagram, we have to find the unknown angle DCF.

Assuming, that the line segments AC and EF are parallel and the same is true for the line segments DE and CB.

The new diagram is:

Therefore the answer is:

or 61 degrees.

Answer:

C. translated 1 unit to left and then rotated 180° counterclockwise about the

origin

Explanation:

In the graph:

• The vertices of Figure A are: (0,4), (-9,3) and (-9,6)

• The vertices of Figure A' are: (1,-4), (10,-3) and (10,-6)

If Figure A is translated 1 unit to the left, the vertices are:

Next, a rotation of 180° counterclockwise about the origin gives:

These are the vertices of Figure A'.

Thus, the correct transformation is: translated 1 unit to left and then rotated 180° counterclockwise about the origin.

The correct choice is C.

y = x - 3

y = - x -1

They intersect at