how should i explain this please help???

Work Shown:

4x + 13 ≥ 27

4x + 13-13 ≥ 27-13

4x ≥ 14

4x/4 ≥ 14/4

x ≥ 7/2

The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).

Note: 7/2 = 3.5

Answer:

Step-by-step explanation:

Answer:a, c and d

Step-by-step explanation:bc i got it right on edge

The number of 2 points and 5 points are 30 and 8 respectively.

Let the number of 5 points = x

Let the number of 2 points = x + 22

It was also stated that the test is worth 100 points and that each problem is worth either 2 points or 5 points.

This will be:

5x + 2(x + 22) = 100

5x + 2x + 44 = 100

7x + 44 =

Collect like terms

7x = 100 - 44

7x = 56

Divide

x 56 / 7

x = 8

Number of 5 points = 8

Number of 2 points = x + 22 = 8 + 22 = 30

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount in the account = x

Amount deducted every month = $14

The change in the account after 7 months.

= x - 7 x 14

= x - 98

Thus,

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

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The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

According to the question,

We have the following information:

[tex]64x^{3} +8[/tex]

The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.

So, we have the following expression:

[tex](4x)^{3} + 2^{3}[/tex]

Now, we can use the following identity to factor the given expression:

[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]

We have a = 8x and b = 2:

(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}

(8x+2) (16[tex]x^{2}[/tex]-16x+4)

Taking 4 as the common factor from the second bracket:

4(8x+2) (4[tex]x^{2}[/tex]-4x+1)

Now, finding the factors of second bracket:

4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)

4(8x+2) {2x(2x-1)-1(2x-1)}

4(8x+2) (2x-1) (2x-1)

4[tex](2x-1)^{2}[/tex] (8x+2)

Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

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The student pay initial fess of $20 and addition $10 per hour.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Plan 1:

students pay = $15 per hour.

Plan 2:

From the graph we can see that

slope= Rise/ Run = 10/ 1= 10

and, the graph line starts from 20.

Hence, the student pay initial fess of $20 and addition $10 per hour.

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In total there will be 397 dots after 100 minutes.

What do you mean by airthmetic sequences?

Arithmetic sequences are sequences of the form:

a, a+d, a+2d, a+3d, a+4d, …

a is the first term and d is the common difference

series. The n terms of the arithmetic progression are given by

[tex]a_{n}[/tex]  = a + (n - 1)d

The number d is called the common difference

Arithmetic progressions differ by d and any terms [tex]a_{n}[/tex] and [tex]a_{n-1}[/tex]

d = [tex]a_{n}-a_{n-1}[/tex] -  

According to the given pattern, in the first figure, number of dots is 1 , in the second figure, number of dots become 5 , similarly in the next the count is 9 and 14

So, the sequence become

1,5,9,14......

here first term , a = 1

common difference , d = 5-1 = 4

We need to find the number of dots after 100 minutes

So, here n = 100

We need to find [tex]a_{100}[/tex]

[tex]a_{100}[/tex] = a + (100 - 1) d = 1 + 99(4) = 1 + 396 = 397

Therefore, in total there will be 397 dots after 100 minutes.

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Answer:

Step-by-step explanation:

Answer:

3/12 or 40%

not 10000% sure on this tho

The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).

How to determine the midpoint of the line joining two points (a,b) and (p,q)?

To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.

To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.

so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.

Hence ans will be ,(-5/2,-11/2)

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Using the system of equations and use the elimination method the two numbers are 82 and 48.

What is the elimination method?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.

Here, we

let the first number = x

let the second number = y

according to the given conditions:

x + y = 130 ........(1)

x - y = 34 .........(2)

Using the elimination method we add both equations (1) and (2) and we get

2x = 164

x = 164/2 = 82

Now, we substitute the value of x in eq (1) and we get

82 + y = 130

y = 130-82

y = 48

Hence, using the system of equations and use the elimination method the two numbers are 82 and 48.

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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Answer:

n * 21 = m * 18       one runs n laps and one runs m laps to again be together at the same place

7 n = 6 m        divide by 3

one runs 7 * 18 = 126 min

the other runs 6 * 21 = 126 min

After 126 min they will be together at the start

Answer:

y=2x-22

Step-by-step explanation:

lets make the equation into slope intercept form

-2x+y=-8 let's move the -2x to the other side we get

y=2x-8

now let's create our equation with the points given

to create the equation you want to make it point slope form with the point given

y-0=2(x-11) distribute the 2 and we can remove the 0

y=2x-22

Answer:

BC = 6

Step-by-step explanation:

since BD = CD then Δ BCD is isosceles.

the line a through D is a perpendicular bisector of BC, then

BX = CX = 3 , so

BC = BX + CX = 3 + 3 = 6

By using the concept  of inequality, the correct options are

2nd, 4th and 5th option

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]

A one degree inequation is known as linear inequation.

Here,

The given inequation is

[tex]\frac{-2}{3}n \leq 16[/tex]

Now,

[tex]\frac{-2}{3}n \leq 16\\n \geq -16 \times \frac{3}{2}\\n \geq -24\\[/tex]

Since n is greater than or equal to 24, the arrow will point towards right

The circle will be closed as there is an equality

So the correct options are 2nd, 4th and 5th option

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Complete Question

The complete question has been attached here

See attachment, this took me a while so please say thanks and rate <3

A) The speed (in m/s) at which the ball hits the ground is; 23.43 m/s

B) The time (in s) that it takes the ball to remain in the air is; 3.67 s

C) The maximum height attained by the ball is; 16.51 m

A) The motion of the ball on the vertical axis is basically uniformly accelerated motion, with acceleration g = 9.81 m/s² and initial vertical velocity v_y = 18 m/s, so the vertical position of the ball at time t is:

y(t) = v_y*t - ¹/₂gt²

The formula for time when the ball hits the ground is;

t = 2v_y/g

t = (2 * 18)/9.81

t = 3.67 s

Thus, vertical velocity at time t is given by the formula;

v_y(t) = v_y - gt

v_y(t) = 18 - (9.81 * 3.67)

v_y(t) = -18 m/s (which shows it is in the opposite direction because of the negative sign)

Thus, the speed at which the ball hits the ground is the resultant of the vertical and horizontal velocity at time t;

v = √(v_x² + v_yt²)

v = √(15² + 18²)

v = 23.43 m/s

b) From a above, the time that the ball remains in the air is the time it takes to hit the ground which is t = 3.67 s

c) The time to reach maximum height is half the time it takes to reach the ground. Thus;

t = 3.67/2 = 1.835 s

Thus maximum height is given by the formula;

y(t) = v_y*t - ¹/₂gt²

y(1.835) = 18(1.835) - ¹/₂(9.81)(1.835²)

y = 16.51 m

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Answer:

S=3/8 miles

T=1/4 hour

V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour

The Perimeter of triangle CED  is 57 in.

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Rhombus: An equal-length parallelogram with four sides.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 34 into AC = 2CE =34 = 2CE

Calculate 34 = 2 CE=>  CE = 17

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 28 into BD = 2DE =>  28 = 2DE

Calculate 28 = 2DE  => DE = 14

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 26 into AB = CD =>  CD = 26

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 17, DE = 14, CD = 26.

PΔCDE = CE + CD + DE

PΔCDE = 17+ 26 + 14

PΔCDE = 57 in

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Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

Subtract 7 from both sides.

Subtract -7 from −3 to get −10.

Divide both sides by −2. Since −2 is negative, the inequality direction is changed.

Divide −10 by −2 to get 5.

Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   [tex]m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...[/tex]

Answer:

It's an example of the distributive property

The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]

Let the money deposited be x.

So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]

⇒ [tex]700=x(1+0.04)^{24}[/tex]

⇒ [tex]700=x(1.04)^{24}[/tex]

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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Answer:

Step-by-step explanation:

Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.

We are given the function as; h = 8 - 0.4j

Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.

We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.

The function  represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.

The equation of a line in slope-intercept form is given as;

y = mx + b

where;

m is Slope of line

b is y-intercept

If we rewrite our function slope-intercept form of equation, we will get;

h = -0.4j + 8

Thus;

Slope = -0.3

y-intercept = 8.

The graph is as plotted in the attached file

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