Please help me with this linear inequalities as graphs question!
I'd really appreciate if you added workings out and explained it a bit, as I'm terribly stuck.

The total number of digits used when the  first 2002 positive even integers are written is 4 digits

Using arithmetic sequence,

nth term = a + (n - 1)d

where

a = 2

d = 2

nth term = 2 + (2002 - 1)2

nth term = 2 + 4002

nth term = 4004

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Answer:

[tex]13.86[/tex]

Step-by-step explanation:

you should see 2 triangles with angle 60 bounded by two equal sides of 4

[tex]=2(\frac{1}{2} (4)(4)sin 60)\\=13.86[/tex]

Answer: If for every independent unit(aka x), you multiply the dependent unit by the same amount(aka y).

Step-by-step explanation:

EXAMPLE:

(0,2) (1,6) (2,18) (3,54) (4,162)

As you can see, each time x increases by unit, you multiply the y unit by 3.

As an example, if you increase x by 4, you multiply the y unit by 3^4 = 81.

If this pattern is consistent with your whole table, you have an exponential function.

Hope this is useful.

The length of the Rectangle is 9x +6 , Option D is the right answer.

A rectangle is a polygon with four sides , four angles and four vertices , The opposite sides are parallel and equal .

An expression representing the area of Rectangle is given

One of the side is 5x -8

The other side =  ?

As Area of Rectangle =  Length * Breadth

It can be calculated by Dividing Area by Breadth

(45x² - 45x -48 ) / (5x -8)

= 9x +6

Therefore the length of the Rectangle is 9x +6 ,Option D is the right answer.

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Answer:

9x + 6
INCLUDED WHOLE PAGE!!
☆
EDGE2022; Good Luck :3!!!

The inequality for sec (x) < cot (x) is;  π/2 < x < π

We are given that;

We want to find the intervals that the trigonometric inequality sec (x) < cot (x) always hold true.

This can also be expressed as;

1/cos (x) < 1/tan (x)

Now, this can happen only in the quadrant where tan (x) is negative and cos x is positive which is in fourth quadrant where;

π/2 < x < π

The inequality for sec (x) < cot (x) is;  π/2 < x < π

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Answer:

C on edge 22 for Pre-Calculus

Step-by-step explanation:

pi < x< 3pi/2

I retook the unit test, put C, and got a 100. I promise it's right

Answer:

m = 0.875

Step-by-step explanation:

the 3 angles lie on a straight line and sum to 180° , that is

4m + 83 + 4m + 90 = 180

8m + 173 = 180 ( subtract 173 from both sides )

8m = 7 ( divide both sides by 8 )

m = [tex]\frac{7}{8}[/tex] = 0.875

From the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2

the answers are -2.1 and 0.2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two systems of the equation:

y = log (−5.6x + 1.3)

y  = −1 − x

After plotting the above equation on the graph we will see two intersections point:

(-2.12, 1.12) and (0.221, -1.221)

So the least value is x = -2.12 ≈ -2.1

The greatest value is x = 0.221 ≈ 0.2

Thus, from the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2

the answers are -2.1 and 0.2.

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Answer:

V = 262.5 ft.

Step-by-step explanation:

Volume = length × width × height

6.25 × 14 × 3

6.25 × 42

262.5

Answer:

x = 3, x = 0

Given expression:

[tex]3^{2x-2}-28\left(3^{x-2}\right)+3=0[/tex]

rewrite expression

[tex]3^{2x} \times 3^{-2}-28\left(3^{x} \times 3^{-2}\right)+3=0[/tex]

treat [tex]\sf \s3^{x}\:as\:u[/tex], then expression

[tex]u^2 \times 3^{-2}-28\left(u \times 3^{-2}\right)+3=0[/tex]

multiply both sides by [tex]\sf 3^{2}[/tex]

[tex]u^2-28\left u+27=0[/tex]

factor expression

[tex]u^2-27\left u - u + 27=0[/tex]

factor out common terms

[tex]u(u-27) -1( u - 27)=0[/tex]

collect into groups

[tex](u-1)( u - 27)=0[/tex]

set to zero

[tex]u =1, \ u=27[/tex]

Substitute [tex]\sf 3^x = u[/tex], to find x

[tex]3^x = 1, \ 3^x = 27[/tex]

[tex]3^x = 3^0, \ 3^x =3^3[/tex]

[tex]x= 0, \ x = 3[/tex]

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The probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.

The combination is a way of selecting a smaller number of sets from a larger number of sets in no particular order.

If selecting r items from a set of n items, in no particular order, we use combinations, using the formula:

nCr = n!/{r!(n - r)!}.

In the question, we are asked the probability of a royal flush in a 5 card hand.

The number of ways of selecting 5 cards from a deck can be computed using a combination, 52C5, as we have 52 cards in a deck, 5 cards are to be chosen and the order is not in concern.

52C5 = 52!/{5!(52 - 5)!} = 52!/(5!.47!) = (52*51*50*49*48)/(5*4*3*2*1) = 2598960.

The number of hands that make a royal flush is only 4. 4 from each suit.

Therefore, the probability = 4/2598960 = 1/649740 or 0.0001539%.

Therefore, the probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.

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Answer: [tex]7\pi[/tex]

Step-by-step explanation:

The area of the entire circle is [tex](\pi)(3^{2})=9\pi[/tex]

The area of each of the smaller circles is [tex](1^{2})(\pi)=\pi[/tex], so their combined area is [tex]2\pi[/tex].

By subtracting areas, we get the area of the shaded region is [tex]7\pi[/tex].

62.5 seconds

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, since they have the same base, you can join them. Because it is division, you have to subtract the exponents.

4^(-11/3 -(-2/3)) = 4^-9/3 = 4^-3

Negative exponents turn the base into a fraction and 4^3= 64

so the answer is C. 1/64

use the 3rd icon to measure 30 and 60 degrees, Then connect them with a line and add a right angle.

Answer:

Not Possible

Step-by-step explanation:

It is not possible. While it does add up to 180, if one is 90 degrees, the rest must be 45 and 45, or your not getting anything.

Let me know if this helped !!

The inequality that represents the range of k so that inequality 1 has real solution is -3 < k < 5

Inequality 1

x^2 + (k + 1)x + k + 4 > 0

The discriminant is calculated using

D = b^2 - 4ac

So, we have:

D = (k + 1)^2 - 4 * 1 * (k + 4)

Evaluate

D = k^2 + 2k + 1 - 4k - 16

This gives

D = k^2- 2k - 15

Factorize the equation

D = (k+ 3)(k -5)

Solve for k

k = -3 and k = 5

Express the k values as inequalities

-3 < k < 5

Inequality 2

The inequality cannot be read, because of the image quality

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Answer:

The third picture

Step-by-step explanation:

Solve for x in both equations

2x<6

Divide both sides by 2:

x<3

3x+2>-4

Subtract 2 from both sides:

3x>-6

Divide both sides by 3:

x>-2

There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.

When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.

The circles are not filled in because the symbol is < and > rather than [tex]\leq and \geq[/tex]. When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.

Answer:

6xp^24

Step-by-step explanation:

Basically, there is 24 6xp's which is 6xp^24.

Hope I explained well enough.

Answer:

7.6 units

Step-by-step explanation:

   Use law of sines

12 / sin C = b / sin B

sin B  * 12 / sin C = b

sin (32) * 12 / sin(57) = b = 7.6

Answer:

20 vegetable plants

Step-by-step explanation:

In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!

Answer:

5:12

Step-by-step explanation:

because of the new wife

Using statistical concepts, it is found that it is an experimental study, as the music played corresponds to an experiment.

It is an study where an intervention is applied to a sample, and the effect of this intervention is studied.

In this problem, the music played is the intervention, and it's effect on the time that it takes for the infants to be asleep, hence it is an experimental study.

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By the ASA postulate, it can be said that the triangle ABC and triangle MRQ are congruent. Thus, option B is correct, Yes, they are congruent by either ASA or AAS.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Using Angle Sum Property, in ΔMRQ

<M + <R + <Q= 180

<M + 42 + 85 = 180

<M = 180 -42

<M= 53°

Now, In ΔMRQ and ΔABC  

<A= <R ,

<B = <M

AB = MR

Hence, By ASA criteria ΔMRQ ≅ ΔABC.

Thus, option B is correct, Yes, they are congruent by either ASA or AAS.

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Answer: Yes, they are congruent by either ASA or AAS.

Step-by-step explanation:

Answer:

180%

Step-by-step explanation:

Given:

The rectangle on the left is fully shaded in meaning that is 1 whole (100%)

The rectangle on the right is 4 / 5 shaded, 4 / 5 = 0.8 (80%)

Combining these will be 100 + 80 = 180%

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Step-by-step explanation:

Answer:

6 servings

Step-by-step explanation:

Box = 72 cups

1 serving size = 12 cups

72 ÷ 12 = 6

Answer:

Q1: 62

Q2: 13

Step-by-step explanation:

Just follow Order of operations, and you get the answers.

P arenthesis

E xponents

M ultiplication

D ivision

A ddition

S ubtraction

The measure of ∠A is 115˚.

Given that, ∠A and ∠B are supplementary angles. ∠A=(7x + 24)˚ and ∠B=(7x − 26)°.

Two angles are Supplementary when they add up to 180 degrees.

Now, ∠A+∠B=180°

⇒(7x + 24)˚+(7x − 26)°=180°

⇒14x− 2°=180°

⇒14x=182°

⇒14x=182°

⇒x=13°

Now, ∠A=7×13 + 24˚

⇒∠A=91˚+ 24˚=115˚

Therefore, the measure of ∠A is 115˚.

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Step-by-step explanation:

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The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.

To prove that the statement is true for all natural numbers, n, we can use mathematical induction.

The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.

Base Case (n = 1):

First, let's prove the statement for the base case, n = 1.

For n = 1:

d(1) + (1 + 1) = d(1) + 2

Now, consider a single square with 1 dot.

In this case, d(1) = 1.

So, we have:

1 + 2 = 3

Now, let's consider a pattern of 2 squares (n = 2).

The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.

So, the statement is true for n = 1.

Inductive Hypothesis (Assume true for n = k):

Now, assume that the statement is true for some arbitrary natural number k.

That is, assume that: d(k) + (k + 1) = d(k + 1)

Inductive Step (Prove true for n = k + 1):

To prove that the statement is true for n = k + 1.

d(k + 1) + (k + 2) = d(k + 2)

Now, consider a pattern of (k + 1) squares.

By the inductive hypothesis, assume that the statement is true for k squares:

d(k) + (k + 1) = d(k + 1)

Now, let's add one more square to the pattern.

This square will have (k + 2) dots.

So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:

d(k + 1) + (k + 2)

And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).

Therefore:

d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)

Now, simplify:

d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)

So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.

Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.

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Answer:

1578 + 1000 = 2578

2578 + 1000 = 3578

3578 + 1000 = 4578

4578 + 1000 = 5578

5578 + 1000 = 6578