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2(x - 2)² - 5(x - 2) - 5

Answer:

Step-by-step explanation:

Effective interest rate, r = [tex](1+\frac{i}{n} )^{n}-1[/tex]
Here,
r = effective annual rate
i = nominal rate
n = number of periods

r = [tex](1+\frac{0.0489}{12} )^{12}-1[/tex]

 = 0.05001099558

 = 5.001099558 %

Answer:

1. B

2. D

3. A

4. B

5. A

6. C

7. B

8. D

9. B

10. A

Step-by-step explanation:

Using linear approximation, the function y = √33 is approximated as 5.744

The concept behind the linear approximation formula is the equation of a tangent line. We know that the slope of the tangent that is drawn to a curve y = f(x) at x = a is its derivative at that point. i.e., the slope of the tangent line is f'(a). Thus, the linear approximation formula is an application of derivatives. Let us learn more about this formula in the upcoming sections.

In equation y = √33

We can apply linear approximation to this

y = √33 = 5.744

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Using the scale of 7 millimeters : 3 meters as used by Rick the actual parking lot is 39 meters wide

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

solving for the width of the actual parking

7 millimeters = 0.007 meters

91 millimeters = 0.091 meters

0.007 = 3

0.091 = ?

cross multiplying

0.007 * ? = 3 * 0.091

? = 0.273/0.007

? = 39 meters

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Answer:

[tex] \huge{ \bold{y - 3 = 7(x +9)}}[/tex]

Step-by-step explanation:

The equation of a line in point-slope form is represented by the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

(x1, y1) is the point and m is the slope

From the question the point is (-9,3) and m = 7

So we substitute the given variables into the formula and solve

We have

[tex]y - 3 = 7(x - - 9) \\ y - 3 = 7(x + 9)[/tex]

Hope this helps you

The equation in point-slope form is y=4x-25.

A line passing through the point (x 1, y1) has a slope of "m," and its point slope form is given by the equation y - y1=m (x - x1).

A horizontal line's equation is of the form y=b when it passes through the points (a, b).

Step 1: Write down the  line's slope, "m," and the coordinates (x 1, y 1) of the point that is given and is on the line.

Step 2: Replace the given values in the calculation for the point slope: y - y1 = m. (x - x1).

Point-slope form is y=mx+b.

To get the equation of the line in standard form, simplify in step three.

Given, m(slope)= 4.

The point is (8,7)= (x1,y1)

y-7=4(x-8)

y-7=4x-32

y=4x-32+7

y=4x-25

Hence, the equation in point-slope form is y=4x-25.

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The length of diagonal falls between 4 and 5.

Given,

Length of diagonal = [tex]\sqrt{18}[/tex]

                                = 4.24

which is between whole numbers 4 and 5 and closer to 4.

Hence, The length of diagonal falls between 4 and 5 and closer to 4.

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Using inequality the number of 105  of 120-kilogram crates that can be loaded into the shipping container.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to one another.

The greatest weight that container can hold = 27500

Shipment weight already  in the container =14900

Amount of weight that may be loaded = 27500 - 14900 = 12600

Weight of each crates = 120 kg

Let x be the maximum number of 120 kg crates that can be loaded to the container then,

Weight of 'x' number of 120 kg crates = 120x

Therefore, the required inequality is as follows

=>120x< 12600

(since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).

Then the inequality is ,

=> x [tex]\leq \frac{12600}{120}[/tex]

=> x ≤ 105.

Thus, a maximum of 105 crates can be loaded into the container.

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Answer:

f = -8

Step-by-step explanation:

We know the slope formula is:

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Because we already know the slope and three other points, we can let point f represent y2 and solve for it:

[tex]\frac{1}{8}=\frac{f-(-6)}{-8-8}\\ \frac{1}{8}=\frac{f+6}{-16}\\ -2=f+6\\ -8=f[/tex]

Answer: x = 14

Step-by-step explanation: Because these are vertical angles we know they are equal.

5x-10 = 60

Add 10 on both sides

5x = 70

Divide by 5 on both sides

x = 14

Answer A, B, D

Step-by-step explanation:

Answer:

h = 3

Step-by-step explanation:

y-6 = 4/7 (x-(-4)

y - 6 = 4/7 (x+4)

y - 6 = 4/7 x + 16/7

y = 4/7 x + 16/7 + 6

y = 4/7 x + (16+42)/7

y = 4/7 x + 58/7

10 = 4/7 x + 58/7

4/7 x = 10 - 58/7

4/7 x = (70-58)/7

4/7 x = 12/7

7/4 * 4/7 x = 12/7 * 7/4

x = 3

(1) The explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2) The explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.

(1)

The given sequence is 5, 0, -5, -10,...

Note the difference between two consecutive terms of the sequence is the same, which is -5.

Therefore, the sequence is an arithmetic sequence with a common difference of d = -5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 5 and d= -5 into the equation,

aₙ = 5+ (n-1)(-5)

   = 5 - 5n + 5

aₙ = 10 - 5n

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 10 - 5n

a₂₁ = 10 - 5(21)

a₂₁ = 10 - 105

a₂₁ = -95

Hence, the explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2)

The given sequence is 3, 4.5, 6, 7.5, 9,...

Note that the difference between two consecutive terms is 1.5, therefore, the sequence is an arithmetic sequence with a common difference of

d = 1.5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 3 and d= 1.5 into the equation,

aₙ = 3 + (n-1)1.5

aₙ = 3+1.5n-1.5

aₙ = 1.5n+1.5

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 1.5(21) + 1.5

a₂₁ = 31.5 + 1.5

a₂₁ = 33

Hence, the explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

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Answer:

Step-by-step explanation:

Expressing the complex number 2i(i +3) in a + bi form gives -2 + 6i

Complex numbers are numbers that are expressed as a + ib,

where a and b are real numbers and i is an fictitious number called "iota."

i has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Real number) and the imaginary number 3i.

The multiplication of 2i(i + 3)

= 2i^2  + 6i

= -2 + 6i

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If the faculty went on a weight watchers diet plan and now weight an average of 185 pounds in 2021.  The faculty's average weight loss per year : 185 pounds and 155 pounds.

First step is to find the difference between the initial weight and the final weight

Difference = Initial weight - Final weight

Difference = 215 pounds - 185 pounds

Difference = 30 pounds

Now let find the lost per year

2018

Lost per year = 215 pounds - 30 pounds

Lost per year = 185 pounds

2021

Lost per year = 185 pounds - 30 pounds

Lost per year = 155 pounds

Therefore the loss is 185 and 155 pounds.

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Answer:

$35

Step-by-step explanation:

money on clothes is 10%, that means it's $5
you get this by dividing the 50 by 100 to figure out how much 1% is, and then multiply with 10.

money on games is 20%, that means it's $10
again, you figure out how much 1% of 50 is and then multiply by 20 to figure out what 20% is.
50 / 100 = 0.5
0.5 * 20 = 10

So far you spent $5 on clothes, $10 on games, that's $15 in total.
When the rest is spent on books, you need to see how much is left of the $50.
50 - 15 = 35

So you spent $35 on books.

The value of composition of function (goh) (-3) is [tex]\frac{8}{5}[/tex].

A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. The definition of a composite function is a function made up of two functions, one of which acts as an independent variable for the other function. It can be defined as:

[tex](fog)(x)=f(g(x))\\(gof)(x)=g(f(x))[/tex]

When dealing with the composition of functions, the order of the functions is crucial since (f∘g)(x) is not equivalent to (g∘f)(x).

Finding the composition of function by putting x=h(x) in function g(x),

[tex](goh)(x)=g(h(x))\\\\=\frac{4-x+1}{4-x-2}\\\\=\frac{5-x}{2-x}[/tex]

Now, putting x = -3,

[tex](goh)(-3)=\frac{5-(-3)}{2-(-3)} \\\\=\frac{8}{5}[/tex]

Therefore, the value of composition of function (goh) (-3) is  [tex]\frac{8}{5}[/tex] .

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The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.

Hence, The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.

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Answer:f(-10)= -60

Step-by-step explanation:

Answer:

f(- 10) = - 300

Step-by-step explanation:

substitute x = - 10 into f(x) , that is

f(- 10) = - 3(- 10)² = - 3(100) = - 300

The solution of the inequality z + 1 ≥ 29 for z , is z ≥ 28  .

Inequality can be defined as a relationship between two expressions or values that are not equal to each other.

For Example : x > 3.

In the question ,

it is given that

the inequality is " z + 1 is greater than it equal to 29 ",

we have to solve this inequality for z ,

So inequality can be rewritten as

z + 1 ≥ 29

Subtracting 1 from both sides of the inequality , we get

z + 1 -1 ≥ 29 - 1

z ≥ 29 - 1

z ≥ 28 .

Therefore , The solution for z + 1 ≥ 29 , is z ≥ 28  .

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Answer:

Step-by-step explanation:

Answer: I think it (7,4.1)

Step-by-step explanation:

Answer:

7.3.0

Step-by-step explanation:

11 times the product of 19 and a number g?

11*(19g)

= 209g

The solutions of the given equations are,

(i) [tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]

(ii)  x = 0, x = 2π, x = 4π, x = 6π, x = 8π.

(iii)

[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]

What is solution of the equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.

(i) cosec x = 1      for 0 ≤ x ≤ 360°

Since, the general solution for

cosec x = 1 is, [tex]x = \frac{\pi }{2} +2n\pi[/tex]

The range for the solution is 0 ≤ x ≤ 360°

Hence,

[tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]

(ii) sec x = 2

Since, the general solution for

sec x = 1  is, x = 0 + 2πn

The range for the solution is 0 ≤ x ≤ 360°

Hence,

x = 0, x = 2π, x = 4π, x = 6π, x = 8π.

(iii) cot x = 4

⇒ [tex]x = cot^-^1(4)[/tex]

The range for the solution is 0 ≤ x ≤ 360°

Hence,

[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]

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Answer:

B.

Step-by-step explanation:

635/100 = 127/20

=>6 3/10

Answer:

None

Explanation:

A unique triangle can be defined as a triangle that can be formed in one way.

The various conditions that a triangle must satisfy so that it is unique :

a) A triangle where the length of the three sides is known or given is a unique triangle.

b) A triangle where two side lengths and their included angle is given is a unique triangle.

c) A triangle where two angles and their included side is given is a unique triangle.

d) A triangle where two angles and a non - included side length is known is a unique triangle.

In the above question, we are given angles 40°, 40° and 100 degrees

3 angles are known, no side length is given. The angles above can form a triangle called the obtuse triangle because their sum = 180° and one of the angles is great we than 90°

However, this does not satisfy the criteria that makes a triangle unique.

Therefore, no unique triangle(s) can be drawn with interior angles measuring 40°, 40°, and 100°.

70 Cos 20° rounded up to 1d.p is 65.8 and as a fraction is 658/10.

What is a fraction?

This refers to the value that is part of a whole number. It has a numerator (upper part) and a denominator (lower part) eg.1/2.

What is Decimal point?

This refers to a dot that is used to demarcate a whole number from the fractional part of a number. eg. 12.6.

The number of points/ values after the decimal point is called the decimal place. Example: 3.7  ( 1 decimal place), 4.26 ( 2 decimal places).

From the question:

Calculate 70cos 20° rounded to 1 d.p.

=70 * 0.9397

=65.78

rounded to 1 d.p.

=65.8

As fraction:

65.8 =65.8/10

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The sentence is true because the expressions are equivalent.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=7 and b=3.

The linear equations are considered equivalent when they are equal.

The given equations are 5y+4−3y = 2y+4. Solving theses equations, you have:

5y+4−3y = 2y+4

2y+4 = 2y+4

Like the both equation present the slope and the constant term equal, the expressions are equivalent.

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