What is the solution to the inequality? -2/3(2x - 1/2) ≤ 1/5x - 1 Express your answer in interval notation.

This is my answer and work, is this right? And how would I put this in interval notation.
-2/3(2x - 1/2) ≤ 1/5x - 1
2x – 1/2 ≥ 1/5x +3/2
2x ≥ 1/5x + 2
9/5x ≥ 2
x ≥ 10/9

That is 5 1/4 - 1 3/4

= 21/4 - 7/4

=14/4

= 3 1/2 inches

I believe its asking you the formula to find the rows numbers moving forward

Examle row 5 will be 16, I believe that is B. 4n - 1

Answer:

(1)  Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .

Step-by-step explanation:

We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.

To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).

We can see that distance between A and origin is [tex]\sqrt{5}[/tex] and distance between A' and origin is also [tex]\sqrt{5}[/tex]. Distance between A and A' is [tex]\sqrt{10}[/tex], which forms a right triangle.

To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).

Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.

Final answer:

The sequence of transformations is a rotation followed by a translation, which can map one triangle to another in the Euclidean plane.

Explanation:

A sequence of transformations that maps △ABC to △A′B′C′ can be described as a combination of basic transformations such as rotations, reflections, and translations. Based on the options given, the correct sequence to map △ABC to △A′B′C′ is a rotation followed by a translation. For example, if △ABC were rotated 90 degrees counterclockwise about the origin and then translated 2 units to the right, it could be mapped to a new position as △A′B′C′. It is important to note that the order of transformations can affect the outcome, and transformations are done in sequence.

Simplify as much as possible

1,750,932 x 2,355,435 = 4,124,206,515,420

4,124,206,515,420 x Y cannot be simplified anymore, therefore,

4,124,206,515,420 x Y is your answer

~Rise Above the Ordinary, Senpai

All we need to do here is simplify, since there is no given answer to y. The numbers you've provided are quite large, so I'd suggest just using a calculator, unless they're supposed to be decimals. The simplified answer to this is 412,320,615,420y.

Answer:

Option A : the interest for the shoe charge is $2.45.

Step-by-step explanation:

As given, Bank card is charging 1.4% monthly interest on credit card charges.

This amount is charged on $175.

We have the interest value as :

[tex]0.014\times175=2.45[/tex] dollars

Hence, the interest for the shoe charge is $2.45.

The expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

Which expression could be Amina's result?

From the question, we have the following parameters that can be used in our computation:

The list of options

Also, we have that

Her result shows two solutions that are complex numbers with imaginary parts

This can be expressed as

[tex]x = \dfrac{a \pm i\sqrt{b}}{c}[/tex]

From the list of options, the expresion that are of the above form are

[tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

hence, the expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]

Question

Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?

Given

Sue wants to buy a video that costs $24.95.

She has $3 in her pocket

a piggy bank full of quarters x

Find out the inequality can be used to represent the number of quarters sue needs to buy the game.

To proof

As given in the question

Sue wants to buy a video that costs = $24.95.

She has $3

The value of quaters in the piggy bank = x

1 $ = 4 quaters

First convert $24.95 in the quaters form

=  4 × 24.95

= 99.8 quaters

convert $3 in the quaters form

= 3 × 4

= 12 quaters

The equation become in the form

[tex]12 + x \geq 99.8[/tex]

x = 87.8 quaters

quarters sue needs to buy the game is  87.8 quaters.

Hence proved

Answer C, aka 3 is that line's slope.

Answer:

the slope of the line is 3

Step-by-step explanation:

Hello, I think I can help you with this

if you have two points of a line

[tex]P1=(x_{1},y_{1})\\ and\\P2=(x_{2},y_{2})[/tex]

you can find the slope using

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

Step 1

Let

P1( 1, 3) and P2(3,9)

put the values into the equation

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{9-3}{3-1}\\m=\frac{6}{2}\\ m=3[/tex]

the slope of the line is 3

I hope it helps,Have a great day.

Answer:

[tex]y =\frac{1}{6} + 0.25x[/tex]

[tex]0 \leq x \leq23.33[/tex]

[tex]0 \leq y \leq 6[/tex]

Step-by-step explanation:

The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.

The maximum amount of daily hours that the machine can work is 6 hours.

Therefore we can represent this situation by means of an equation of the form:

[tex]y =\frac{1}{6} + 0.25x[/tex]

Where

y = daily amount of hours the machine works.

x = number of daily cycles performed.

This equation is a linear function.  Because it has the form y = ax where a is a real number

The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.

The domain of the function is:

[tex]x\geq 0[/tex] (because you can not perform less than zero cycles a day)

[tex]x \leq23.33[/tex]. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.

So:

[tex]0 \leq x \leq23.33[/tex]

The range of the function is:

[tex]y \geq 0[/tex] (because you can not work less than 0 hours a day)

[tex]y \leq 6[/tex] (because the machine can not work more than 6 hours a day)

So

[tex]0 \leq y \leq 6[/tex]

your answer is A

hope this helps :)

A = [tex]\frac{1}{2}[/tex]bh

[tex]\frac{1}{2}[/tex] × (bh) = A

[tex]\frac{bh}{2}[/tex] = A

bh = A × 2

bh = 2A

b = [tex]\frac{2A}{h}[/tex]

The answer is a: b= [tex]\frac{2A}{h}[/tex]

Answer:

y=8x/9

Step-by-step explanation:

Given that 8 euros were worth $9 and

24 euros were worth $27.

Let y represent the number of Euros and x no of dollars.

Given that the relation is of the form y = kx+C

When x=0 y =0,

i.e. C =0

Hence equation is of the form y = kx

Substitute x=8 and y =9

We get 9 = 8k

Or k =8/9

Hence relation is y=8x/9 is the relation between x and y.

WE can verify this for 27 dollars worth 24 euros.

24 =8/9(27) is true.

Thus equation is verified.

B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

1. 4x = 7(x - 3)       1.Given

4x = (7)(x) + (7)(-3)

2. 4x = 7x - 21       2.Distributive property

4x - 7x = 7x - 7x - 21

3. -3x = -21            3.Subtraction property of equality

-3x : (-3) = -21 : (-3)

4. x = 7                  4.Division property of equality

The answer is B. If you look at a graph of -tan (which is cot), the places the graph crosses -1 are at pi/4 plus kpi. If you add pi to pi/4, you get 5pi/4, and these two answers are in B only.

Im adding an answer so the other guy that gave an answer gets his points.

Answer:

y= 126

Step-by-step explanation:

The given equation is: y= 3x-2x^2+5x^3

Substituting the value x=3 in the above equation,we get

   y= 3(3)-2(3)^2+5(3)^3

⇒y= 9-2(9)+5(27)

⇒y= 9-18+135

⇒y= 126

The answer is 3 hours  40 minutes

Initial salary =  $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

[tex]a_n = ar^{n-1}[/tex]

1) [tex]a_n = 50000(1.05)^{n-1}[/tex]

2) In order to find salary in 5 years we need to plug n=5, we get

[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]

= 50000(1.21550625)

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]

Plugging n=10, a = 50000 and r= 1.05.

[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]

[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]

= 628894.62678.

The length of the longest bridge in the world is found by adding the length of the second longest bridge namely the Tianjin Grand Bridge, and the stated difference between the two bridges' lengths. After calculation, the length of the longest bridge in the world is found to be 540,700 feet.

To find the length of the longest bridge in the world, we should add the length of the Tianjin Grand Bridge (the second longest in the world) and the difference between the two bridges. In this case, the length of the Tianjin Grand Bridge is 373,000 feet and it's stated that this is 167,700 less than the length of the longest bridge.

So, we have to do the following calculation: 373,000 feet (length of the Tianjin Grand Bridge) + 167,700 feet (difference in length) = 540,700 feet.

So, the length of the longest bridge in the world is 540,700 feet.

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To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. The derivative of sin(xy^2) with respect to x is cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx). Simplify the expression to find dy/dx.

To find dy/dx by implicit differentiation, we will differentiate both sides of the equation with respect to x.

We have the equation 5+4x=sin(xy^2). Taking the derivative of both sides, the left side will be 0 since it is a constant. On the right side, we use the chain rule.

The derivative of sin(xy^2) with respect to x can be written as cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx).

Simplifying further, dy/dx = (cos(xy^2) * (2xy^2 + x * 2y * dy/dx)) / (1 - x * 2y^2 * cos(xy^2)).

It is the transformation shown in (B)

(look at one point of the letter P and how it moves precisely 3 units. Also there is only the move, no flipping of the figure)

Answer is B.

B shows a translation of 3 units to the right

The answer is D, (3, -4)

When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.

To find the y-intercept, you have to substitute the point (8,2) into y = mx + b

2 = 1(8) + b

b = -6

The equation is y = x - 6

The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6

The equation of the required line in slope-intercept form is expressed as:

y-y0 = m(x-x0) where:

Given the equation of the line as y = -x

Get the slope of the line

mx = -x

m = -1

Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))

Get the required equation

Recall that;

y-y0 = m(x-x0)

y - 2 = 1(x-8)

y - 2 = x - 8

y = x - 8 + 2

y = x - 6

Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.

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The number that is divisible by 3 and 9 is 40,653.

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

We may face different situations every day where we use the division technique.

Given are numbers, we need to find which of them numbers are divisible by 3 and 9,

LCM of 3 and 9 is 9,

So numbers completely divisible by 9 will also be divisible by 3.

The only number from the option which is completely divisible by 9 is 40,653.

Hence, the number that is divisible by 3 and 9 is 40,653.

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The value of x is option C. 13.

The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.

Given is a triangle ABC.

A line PQ is drawn which is parallel to the line BC.

We have to find the value of x, which is the length of AQ.

Using the triangle Proportionality theorem,

AP / PB = AQ / QC

Substituting the values,

6 / 12 = x / 26

Cross multiplying,

12x = 6 × 26

x = 156 / 12

x = 13

Hence the value of x is 13.

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RPS is 90 degrees because of the vertical line theorem... opposite angles are always congruent.

Answer: RPS is 90 degrees

Step-by-step explanation:

Yes, this table represents a function.

Function--

It is  a set of ordered pair of the type: (x,y) in which each input variable i.e. x is mapped to a single output i.e. y.

i.e. each of the value of x is mapped to a single y.

Here after looking the table we observe that each of the value of the independent variable i.e. Hours of training is mapped to a single value of the dependent variable i.e. monthly pay.

x = - [tex]\frac{7}{4}[/tex] or x = 0

take out a common factor 2x

2x(4x + 7 ) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

4x + 7 = 0 ⇒ x = - [tex]\frac{7}{4}[/tex]