I don’t understand how to do it

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:

Step-by-step explanation:

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

Answer A, B, D

Step-by-step explanation:

The solution to the equation by linear combination is (b)  The solution is (4, 0).

From the question, we have the following system of equations

2x + y = 8

x – y = 4

By linear combination, we start by eliminating one of the variables

This is done by adding the equations

So, we have

2x + x - y + y = 8 + 4

Evaluate the like terms

3x = 12

Divide both sides

x = 4

Substitute x = 4 in x – y = 4

4 – y = 4

So, we have

y = 4 - 4

Divide

y = 0

Hence, the solution is (b) (4, 0)

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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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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.

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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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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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°.

Answer: I think it (7,4.1)

Step-by-step explanation:

Answer:

7.3.0

Step-by-step explanation:

Answer: what picture

Step-by-step explanation:

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

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:

1. B

2. D

3. A

4. B

5. A

6. C

7. B

8. D

9. B

10. A

Step-by-step explanation:

The relative maxima and relative minima for  f(x) = x⁵ - 4x³ + 3x² - 8x - 6 is   is -1.871 and  1.518

The given  function is  f(x) = x⁵ - 4x³ + 3x² - 8x - 6  ,now  differentiation function with respect to x we get  

=5x⁴ - 12x² + 6x - 8

Now solving the given  equation for the critical values are:

x₁ = 0.176 + 0.73i

x₂ = 0.176 - 0.73i

x₃ = 1.518

x₄ = -1.871

Now, taking derivative of the 5x⁴ - 12x² + 6x - 8  , with respect to x we get

= 20x³ - 24x + 6

now replacing the value of  x by   1.58, we get

20 * 1.58³ - 24 * 1.58 + 6

= 46.966, which is positive so it is the  minima

Again  replacing the value of  x by   -1.871, we get

=>20 * -1.871³ - 24 * -1.871 + 6

=> -169.9, which is negative so it is the maxima

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The percent of decrease is 63.16%

How to calculate the percentage of decrease?

First, we calculate the amount of decrease

= $3,800 - $1,400

= $2,400

Next we dividing the amount of decrease by original price (old price)

= $2,400 ÷ $3,800

= 0.6316

And then convert the result into a percentage by multiplying by 100%

= 0.6316 × 100%

= 63.16%

Thus, the percent of decrease is 63.16%

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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 %

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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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:

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

11 times the product of 19 and a number g?

11*(19g)

= 209g

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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Answer:

B.

Step-by-step explanation:

635/100 = 127/20

=>6 3/10

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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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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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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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]