If the area of a rectangular field is x2 – 3x + 4 units and the width is 2x – 3, then find the length of the rectangular field.

Answer:

Steps shown in picture provided

Answer:

8

Step-by-step explanation:

x=16

x(16)-8=8

Answer:

√2

Step-by-step explanation:

tan(x) = -1

x = arctan(-1)

x = -π/4

Now since x is between 3π/2 and 2π use use the general form

nπ-π/4

taking n = 2

2×π-π/4

= 7π/4

now tan (7π/4) = -1

so sec (7π/4) = √2

Answered by GAUTHMATH

Answer:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle

Answer:

-21 =x

Step-by-step explanation:

9(3x+3)=10(3x+9)

Distribute

27x +27 = 30x +90

Subtract 27x from each side

27x+27 -27x = 30x-27x +90

27 = 3x+90

Subtract 90 from each side

27-90 = 3x +90-27

-63 = 3x

Divide by 3

-63/3 = 3x/3

-21 =x

Answer:

x = -21

Step-by-step explanation:

9(3x+3) = 10(3x+9)

27x + 27 = 30x + 90

-30x + 27x = 90 - 27

-3x = 63

x = -21

Answer:

5.25 kg of the mashed potatoes were eaten.

Step-by-step explanation:

(3/4) * 7 = 5.25

I hope this is helpful :)

The area divided by XYZ is 16/9

i.e. [tex]\frac{A}{[XYZ]} = \frac{16}{9}[/tex]

The given parameters can be represented as:

[tex]r = -\frac{4}{3}[/tex] --- the ratio of dilation

The area of the second triangle is as follows:

[tex]A =r^2 * \triangle XYZ[/tex]

Make [tex]r^2[/tex] as subject

[tex]r^2 = \frac{A}{\triangle XYZ}[/tex]

Substitute value for [tex]r^2[/tex]

[tex](\frac{4}{3})^2 = \frac{A}{\triangle XYZ}[/tex]

[tex]\frac{16}{9} = \frac{A}{\triangle XYZ}[/tex]

Rewrite as:

[tex]\frac{A}{\triangle XYZ} = \frac{16}{9}[/tex]

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Answer:

Step-by-step explanation:

Let each side of triangle XYZ have length s. We therefore have:

s = YZ = YQ + QR + RZ = x + 2y

Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:

3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.

The system of equations:

x + 2y = s

2x + y = 3/4s

Multiply the second equation by 2, then subtract the first equation.

3x = 1/2s, so x = 1/6s.

Now we have y = 3/4s-2x = 5/12s.

A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]

= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]

={23/48* [XYZ]} / [XYZ]

= 23/48

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

A system of equations, involving two linear lines has solutions as follows:

In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.

We are asked to comment on her conclusion.

To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.

Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.

Thus, the slope for:-

Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.

Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.

Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

Learn more about the system of equations at

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Answer:

94.5 yd^3

Step-by-step explanation:

The volume of a rectangular prism is given by the formula:

A = lwh

Where:

l = length

w = width

h = height

Volume is how much space a 3d figure occupies.

USE THE FORMULA WITH THE GIVEN DIMENSIONS:

A = (7)(4.5)(3)

= (31.5)(3)

= 94.5

Volume is measured in cubic yards, in this case.

Therefore your answer is 94.5 yd^3

I hope I helped!

Answer:

Step-by-step explanation:

length = 7 yd

Width = 4.5 yd

height = 3 yd

Volume of rectangular prism = length * width * height

                                                = 7 * 4.5 * 3 = 94.5 yd³

Answer:

Step-by-step explanation:

Total amount in cents (unsimplified): 5N +17(10-N)

Simplified: 170-5N

Answer:

The answer is n = - 4.. I hope it will help :)

Answer:

[tex]\displaystyle lne^4 = 4[/tex]

General Formulas and Concepts:

Algebra II

Natural Logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle lne^4[/tex]

Step 2: Evaluate

Answer:

Step-by-step explanation:

We have 3 identical pumps working to fill a pool. If it takes them working  together 8 hours to fill the pool, the equation is:

[tex]\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=\frac{1}{8}[/tex] and

[tex]\frac{3}{x}=\frac{1}{8}[/tex] . Cross multiply to get

x = 24, which is the number of hours it will take one pump to do the job all alone. If this be the case, and we have 4 pumps WORKING AT THE SAME TIME, filling the pool will be the number of hours it takes one pump divided by 4.

4 pumps can do the job in 6 hours.

Answer: B. θ = 36°

Step-by-step explanation:

Concept:

Here, we need to know the idea of the Law of sines.

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.

The Law of sines: a / sinA = b / sinB = c / sinC

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

a = 10 m

c = 11.2 m

C = 41°

Given formula

a / sinA = c / sinC

Substitute the value into the formula

10 / sinA = 11.1 / sin (41)

Cross-multiply to simplify the equation

sinA × 11.1 = 10 · sin (41)

Divide 11.1 on both sides

sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1

sinA = 10 · sin (41) / 11.1

Apply arcsine or the inverse of sine (basically representing the division of sine)

A = sin⁻¹ (10 · sin (41) / 11.1)

A = 36°

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]End = (4, 9)[/tex]

Step-by-step explanation:

Given

[tex]Start = (2,6)[/tex]

Transformation: 2 units right and 3 units down

Required

The new point

First, we take the right translation;

When a point is translated right by 2 units, the rule is:

[tex](x,y) \to (x + 2, y)[/tex]

So, we have:

[tex](2,6) \to (2 + 2, 6)[/tex]

[tex](2,6) \to (4, 6)[/tex]

Next, we take the down translation;

When a point is translated down by 3 units, the rule is:

[tex](x,y) \to (x, y + 3)[/tex]

So, we have:

[tex](4,6) \to (4, 6+3)[/tex]

[tex](4,6) \to (4, 9)[/tex]

Hence, the endpoint is:

[tex]End = (4, 9)[/tex]

Answer:

203 ft.

Step-by-step explanation:

Since we are given the measurements of two sides, we can use trig to find the angle (or our reference angle, we'll call it x) the sides form.

SOH-CAH-TOA

We'll use cosine since the adjacent and hypotenuse were given for our reference angle.

Cos(x) = (adj/hyp)

Cos(x) = (396/445)

[Cos(x)]cos^-1 = (396/445)(cos^-1)

x ≈ 27.1409 (Nearest ten-thousandth)

And now we find the missing side using our now known angle.

SOH-CAH-TOA

Tan(x) = (opp/adj)

Tan(27.1409) = (opp/396)

0.5126 ≈ (opp/396)

(0.5126)(396) ≈ (opp/396)(396)

Opp = 203

Missing Side = 203 ft

Answer:

135

Step-by-step explanation:

(n−2) × 180° = sum of the interior angles  where n is the number of sides

There are 6 sides

(6 -2) * 180

4*180

The sum is 720

2x+2x+3x+3x+3x+3x = 720

16x = 720

Divide by 16

16x/16 = 720/16

x = 45

Angle E = 3x= 3(45) = 135

Answer:

First one: function

Second one: not a function

Step-by-step explanation:

A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function

For the first one no x value repeats meaning each input has it's own output therefore it is a function

For the second one the x value 8 has more than 1 output therefore the second one is not a function

Answer:

Step-by-step explanation:

please make it a brainliest answer.

They should use the conversion factor

1 mile = 5280 feet

To go from feet to miles, you divide by 5280

So,

4224 ft = 4224/5280 = 0.8 miles

The distance between their homes is exactly 0.8 miles

Answer:

bc=  7

Step-by-step explanation:

Answer:

(4x4) + (6x11) = 82 for area

4+4+10+11+7+6= 42

Step-by-step explanation:

You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)

Answer:

Step-by-step explanation:

The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.

Use the  tan of the angle so formed (which is 30 degrees)

Tan(30)= opposite / height (which is the line you just drew).

Tan(30) = 3.5 / h

Tan(30) = 0.5774

Tan(30) = 3.5 / h                multiply both sides by h

h*Tan(30) = 3.5                  Divide by tan30

h = 3.5 / Tan(30)

h = 3.5 / 0.5774

h = 6.062

Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.

Area of 1 triangle = 1/2 * b * h

area of 1 triangle = 1/2 * 7 * 6.062

Area of 1 triangle = 21.2176

There are 6 such triangles so multiply that number by 6

Answer:  6 * 21.2176

Answer:  127.31

Answer:

A

Step-by-step explanation:

a geometric sequence is where we multiply a factor from element to element.

a1 = $900

a2 = 981 = a1 × f = 900 ×

a3 = 1069.29 = a2 × f = a1 × f × f = s1 × f²

[tex]an = 900 \times {f}^{n - 1} [/tex]

so, now let's try and get f.

remember, 981 = 900 × f

f = 981/900 = 109/100 = 1.09

just to control, we check for s3 :

900 × (1.09)² = 900 × 1.1881 = 1069.29

correct.

so,

a13 = 900 × (1.09)¹² = 2,531.398304

s13 is then the sum of all a1, ..., a13

there is a nice formula for sums of finite sequences

s13 = 900 × (1-f¹³) / (1-f) = 900×(1-(1.09)¹³) / (1-1.09) =

= 900×(1-3.065804612) / (-0.09) =

= 900×(-2.065804612) / (-0.09) = 20,658.04612

.

Answer:

Step-by-step explanation:

This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):

[tex]sin^{-1}[sin(2x+30)]=sin^{-1}(1)[/tex]

On the left, the inverse sin "undoes" or cancels the sin, leaving us with

2x + 30 = sin⁻¹(1)

The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:

2x + 30 = 90 and

2x = 60 so

x = 30

You're welcome!

Answer:

Step-by-step explanation:

The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:

by finding the slope. Remember, that slope is the same thing as rate of change.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:

[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]

Answer:

C x=8

Step-by-step explanation:

Chúc bạn ngày mới tốt lành

Answer:

3?

Step-by-step explanation:

A little confused by the question but is it just

1/5 2/5 3/5 4/5

1     2     3     4

so theres 3 in between

so, start floor = x

x + 7 - 9 - 4 + 8 - 2 = 14

x = 14

the elevator started on the 14th floor.

to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14