Which expression is equivalent?

Answer: [tex]\frac{\sqrt{65}}{4}[/tex]

Step-by-step explanation:

By the Pythagorean theorem, the unknown side has length

[tex]\sqrt{9^{2}-4^{2}}=\sqrt{65}[/tex]

Therefore,

[tex]\tan \theta=\boxed{\frac{\sqrt{65}}{4}}[/tex]

You define complex numbers as the reals, i, as usually defined, and their linear combinations using real coefficients, then,

The reals are complex numbers, even if you haven’t fully defined their properties.

If you define complex numbers as the form (a,b) with and a, b are real numbers, then you can say that each real number a is isomorphic with that complex number,

if b=0 once you define their properties.

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Of course, (0,1) will be i. You’ll have to define the multiplication rule, etc.

In actual usage, we gloss over the distinction, and real numbers are complex numbers with no imaginary part.

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Answer:

[tex]\displaystyle{y-1=5(x+6)}[/tex]

Step-by-step explanation:

A point-slope form is written in the equation of  [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]

Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:

[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)

Answer:

y - 1 = 5 ( x + 6 )

Step-by-step explanation:

       Here,

          m ⇒ slope

    y = 5x - 4 ← equation of the old line

         Now it is clear to us that,

         m ⇒ slope of the line ⇒ 5

         c  ⇒ y-intercept ⇒ -4

                 That is, m = 5

                   y - y₁ = m ( x - x₁ ).

        m = slope

           ( -6 , 1 ) ⇔ ( x₁ , y₁ )

        Let us solve this now

         y - y₁ = m ( x - x₁ )

         y - 1 = 5 ( x - ( -6) )

         y - 1 = 5 ( x + 6 )

                y - 1 = 5 ( x + 6 )

The function that is graphed is f(x) = |x - 3| + 1

The parent absolute function is:

f(x) = |x|

From the graph, we have the following transformations:

This is represented as:

(x, y) = (x - 3, y + 1)

So, we have:

f(x) = |x - 3| + 1

Hence, the function that is graphed is f(x) = |x - 3| + 1

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The verbal description matches option D; Gene earns 2% interest after depositing $150 into his account.

The function is a type of relation, or rule, that maps one input to specific single output.

The function given;

f(x) = 0.02 x +150

Gene earns 2% interest after depositing $150 into his account.

Thus, this verbal description matches the function given as it represents, the total account balance Gene.

Hence, Option D is the correct answer.

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Answer:

x=1

Step-by-step explanation:

Original Equation:

[tex]-5(5x+3)-5x+1= -44[/tex]

Distribute the -5

[tex]-25x-15-5x+1= -44[/tex]

Add like terms

[tex]-30x-14=-44[/tex]

Add 14 to both sides

[tex]-30x=-30[/tex]

Divide both sides by -30

[tex]x=1[/tex]

Answer:

x = 1

Step-by-step explanation:

-5(5x+3) - 5x + 1 = -44

(-5*5x -5*3) - 5x + 1 = -44

(-25x - 15) - 5x + 1 = -44

-25x - 5x - 15 + 1 = -44

-30x - 14 = -44

-30x = -44 + 14

-30x = -30

x = -30/-30

x = 1

Check:

-5(/5*1) + 3) - 5*1 + 1 = -44

-5(5+3) - 5 + 1 = -44

-5*8 - 5 + 1 = -44

-40 - 5 + 1 = -44

-45 + 1 = -44

Answer:

The answer is option c

Answer:

The answer is B.

BC = EF

the side has to lie between the two angles

Answer: y=[tex]\sqrt[3]{x}[/tex]-4

Step-by-step explanation:

By critically observing the basketball hoop (see attachment), we can logically deduce that the basket's height from Lisa's horizontal sight is the same as the length of the shortest leg of the right-angle triangle:

Shortest leg = 8.5 - 5

Shortest leg = 3.5 feet.

In Geometry, the sum of all the angles in a triangle is equal to 180°:

x + y + z = 180

x + y + 90 = 180

x + y = 180 - 90

x + y = 90° (complementary angle).

Therefore, the angle of depression is complementary to the angle of elevation.

Also, you should use the inverse tangent function because the lengths of the opposite and adjacent sides of the right-angle triangle are known.

Angle of depression = tan⁻¹(Opposite/Adjacent)

Angle of depression = tan⁻¹(3.5/10)

Angle of depression = 19.29° ≈ 19°.

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Answer:

3.5

congruent

inverse tangent

19

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

Answer:

[tex] \tt \: x.( - 1).( - x).(1)[/tex]

[tex] \longrightarrow \tt ( - x). (- x)[/tex]

[tex] \longrightarrow \boxed{\tt{x}^{2} }[/tex]

------- HappY LearninG <3 --------------

Answer:

x= 1.5, y= 3.5

or x= -5, y= 10

Step-by-step explanation:

Let's solve by substitution.

Label the two equations:

y= 2x² +6x -10 -----(1)

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

Substitute (2) into (1):

2x² +6x -10= -x +5

2x² +6x +x -10 -5= 0

Simplify:

2x² +7x -15= 0

Factorise:

(2x -3)(x +5)= 0

2x -3= 0 or x +5= 0

2x= 3 or x= -5

x= 1.5

Now that we have found the value of x, we can find the value of y through substitution.

Substitute into (2):

y= -1.5 +5 or y= -(-5) +5

y= 3.5 or y= 10

Supplementary:

Do check out the following should you wish to learn more about solving quadratic equations!

The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

a - 5 = 0

a = 5

3) The final equation of the parabola is;

y = 5(x - 3)² - 5

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Answer:

5 (rounded)

Step-by-step explanation:

by using the Pythagorean theorem you can calculate b

[tex]a^{2} + b^{2} = c^{2}[/tex]

here we have a and c

first lets times it by themselves

16 + b^2 = 36

now lets isolate b^2

b^2 = 36-16

= 20

now we have to get rid of the exponent ^2

b = 4.47....

rounding it would be 5!

Hope that helps :>

The measure of [tex]\theta[/tex] is 68 degrees

The complete question is in the attached image

The value of [tex]\theta[/tex] is calculate using the following cosine function

[tex]\cos(\theta) = \frac 38[/tex]

Evaluate the quotient'

[tex]\cos(\theta) = 0.375[/tex]

Take the arc cos of both sides

[tex]\theta = \cos^{-1}(0.375)[/tex]

Evaluate the arc cos

[tex]\theta = 67.97[/tex]

Approximate to the nearest degree

[tex]\theta = 68[/tex]

Hence, the measure of [tex]\theta[/tex] is 68 degrees

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The statement that apply is that the volume of the cone is One-third the volume of the cylinder

volume of a cone = 1 / 3 πr²h

where

Volume of a cylinder = πr²h

where

The cone and the cylinder has the same base and height. Therefore, the radius and height are the same .

volume of the cylinder = 84π

Therefore, the volume of the cone is One-third the volume of the cylinder.

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Answer: Give me the full answer and i will be able to answer it

Step-by-step explanation:

Answer: 5.3

Step-by-step explanation:

[tex]12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3[/tex]

Answer:

Step-by-step explanation:

***I hope this helps and the explanation is helpful!***

Step-by-step explanation:

5 x 0.7 = 3.5

The length of GH is 15.

GH = IG

GH = 5x - 10

IG = 3x

5x - 10 = 3x

5x - 3x = 10

2x = 10

x = 10/2 = 5

GH = 5x - 10

= 5 * 5 - 10 = 25 - 10

GH = 15

<ABD = < DBC

<ABD = 10y°

<DBC = (8y + 4)°

10y° = (8y + 4)°

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 4/2 = 2

The value of y is 2

<DBE = <DBC + <CBE

<DBC = 10y°

<CBE = <DBC = 10y°

y = 2

<DBC = <CBE = 10y° = 10*2° = 20°

<DBE = 20° + 20° = 40°

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The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

An equation is an expression that shows the relationship between two or more numbers and variables.

A unit rate is a ratio between two different units with a denominator of one.

If For every 1 student out of school, there are 10 students going to school, hence:

Unit rate = 10/1 = 10 students going to school per 1 student out of school

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

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Answer:

-x^3-5x^2+10x-4

Step-by-step explanation:

(−x + 1) (x ^ 2 + 6x − 4) = (-x)(x ^ 2 + 6x − 4) + 1(x ^ 2 + 6x − 4)

= -x^3-6x^2+4x+x^2+6x-4 = -x^3-5x^2+10x-4

Answer:

x= -2, -11

Step-by-step explanation:

Answer:

$2

Step-by-step explanation:

If the total is $12, and he spent $6 on a notebook, he has $6 left for his 3 pencils. If each pencil costs the same, he paid $2 for each pencil.

The weight of 45 bushels of soya beans is 1.2247 Tons

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion factor of soyabeans is 36.744 (bu/t). Hence:

45 bushels = 45 bushels / 36.744 (bu/t) = 1.2247 Tons

The weight of 45 bushels of soya beans is 1.2247 Tons

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