Simplify image below 20 POINTS!

Step-by-step explanation:

First let solve the inequality

[tex]5 {x}^{2} + 2x - 3 < 0[/tex]

Factor by grouping

[tex]5 {x}^{2} + 5x - 3x - 3 < 0[/tex]

[tex]5x(x + 1) - 3(x + 1)[/tex]

So the factor are

[tex](5x - 3)(x + 1)[/tex]

So the factor are

[tex]x = \frac{3}{5} [/tex]

and

[tex]x = - 1[/tex]

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

[tex] |x - b| < c[/tex]

works as

b is the midpoint between 2 roots. And c is the

[tex] |x + b| = c[/tex]

We know that the midpoint between both roots is-1/5.

so

[tex] |x - ( - \frac{1}{5} )| < c[/tex]

[tex] |x + \frac{1}{5} | < c[/tex]

Let use roots 3/5

[tex] | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} [/tex]

-1 works as well.

[tex] | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} [/tex]

So the absolute value equation is

[tex] |x + \frac{1}{5} | < \frac{4}{5} [/tex]

Answer:

12000

Step-by-step explanation:

8000+4000=12000

Answer:

4

Step-by-step explanation:

because BC=CD as it is parallel that means all the sides are equal

The value of CD is 20/3.

The correct option is (A).

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

In ACB and ECD,

angle CAB= angle DEC

angle CBA= angle EDC

angle DCE = angle ACB

By, AA similarity criteria,

ΔACB~ΔECD

Now,

AC/CE= BC/CD

3/5=4/CD

CD= 20/3

Learn more about similarity property here:

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Answer:

A.

Step-by-step explanation:

Answer:

going up in even numbers

Step-by-step explanation:

its like the two times table, and it goes up in even numbers

Answer:

any number you can take

Step-by-step explanation:

like 4'6'8''12

Answer:

Step-by-step explanation:

You will have to interpret the question with the aid of a diagram and make out the relevant angles and either make use of cosine rule,sine rule etc....Your knowledge on angles should be sound

Answer:

2

Step-by-step explanation:

=3+5×5-25+3-4

=3+25-25+3-4

=28-22-4

=28-26

=2

Answer:

2

Step-by-step explanation:

3 + 5 * 5 - 50 / 2 + 3 - 4

3 + (5 * 5) - 50 / 2 + 3 - 4  => Multiplication what ever comes first

3 + 25     (-50 / 2) + 3 - 4  => Division left to right

(3 + 25)     - 25  +( 3 - 4)  => Addition what ever comes first

28  - 25 - 1 => Substraction  left to right

2

Leave comment if you're curious.

Answers and Step-by-step explanation:

Question 8:

Since angle BCD is opposite angle DAB, this means that they are similar angles as the shape is a parallelogram, and so BCD is 115 degrees, or answer D

Question 3:

We can use process of elimination on this question - The first choice is all squares are rhombuses, which is true. The second question is all rectangles are squares, which is not true, therefore the answer is B

Question 4:

m angle 2 is equal to 106, as it is similar to question 8, and angle 3 is equal to 360 (the total degrees of the shape) - 106 - 106, then divided by 2 and divided by 2 again.

This will equal to angle 3 being 37 degrees, and the answer will be C

Question 5:

We can draw a rectangle from this graph. We can also tell that, in theory, the diagonals are the same, that rules out answer B, and also 5x-5 = x+11

We can then find out x.

+5 on both sides

5x = x+16

-x on both sides

4x = 16

x = 4.

Therefore, each of the sides will be 4+11 = 15, and the answer being C

Answer:

72+12

Step-by-step explanation:

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  C. The order in which numbers are added does not affect the sum.

Step-by-step explanation:

In symbols, the commutative property of addition is ...

  a +b = b +a

The order in which numbers are added does not affect the sum.

Answer:

90,000+9,000+700+60+3

Answer:

90,000 + 9,000 + 700 + 60 + 3 I hope this helped

Answer:

B) Both functions have a y-intercept of -2.

Step-by-step explanation:

Hi there!

A) Both functions are always increasing.

⇒ False

Let's first take a look at the given equation, [tex]y=3x-2[/tex]. This is a linear equation, and it is organized in slope-intercept form: [tex]y=mx+b[/tex]. m is the slope and b is the y-intercept. When m is positive, it is always increasing.

In [tex]y=3x-2[/tex], 3 is m, and because it's positive, this line is always increasing on a graph.

However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).

B) Both functions have a y-intercept of -2.

⇒ True

In the given equation [tex]y=3x-2[/tex], this is true. -2 is the y-intercept.

On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.

C) Both functions are symmetric about the y-axis.

⇒ False

The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form [tex]y=b[/tex], which isn't the case here with [tex]y=3x-2[/tex]. [tex]y=3x-2[/tex] has a slope.

D) Both functions are linear relationships.

⇒ False

Sure, [tex]y=3x-2[/tex] is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.

I hope this helps!

The comparison of both resistors is defined by an inequality. Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]

Given that:

[tex]R = 100 \Omega[/tex] ---- the reference resistor

First, we calculate the resistance of both resistors

Resistor A differs by [tex]0.15\Omega[/tex] means that:

[tex]R_A = 100\Omega + 0.15\Omega[/tex]

[tex]R_A = 100.15\Omega[/tex]

Resistor A has a resistance of [tex]100.15\Omega[/tex]

Resistor B differs by [tex]-0.78\Omega[/tex] means that:

[tex]R_B = 100\Omega -0.78\Omega[/tex]

[tex]R_B = 99.22\Omega[/tex]

Resistor B has a resistance of [tex]99.22\Omega[/tex]

By comparing the calculated values, we can conclude that:

Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]

Read more about inequality comparison at:

https://brainly.com/question/11772136

Answer:

100 yojan=how much km

1287.48

please brainlist

Define relation.

Let A and B are only two non-empty set,then A*B is cartesian product of A*B.Then any subset of A*B is known as the relation fromA to B.

Answer:

4y

Step-by-step explanation:

Answer:

perimeter=4y

Step-by-step explanation:

y+y+y+y=4y

..........

Answer:

15.2

[tex] {c }^{2} = {a}^{2} + {b}^{2} \: \\ {c}^{2} ={6}^{2} + {14}^{2} \\ {c}^{2} = 36 + 196 \\ {c}^{2} = 232 \\ \sqrt{c } = \sqrt{232} \\ c = 15.23154621[/tex]

Answer:

14,712 ft difference

Step-by-step explanation:

15,062 - 350 = 14,712

Answer:

Step-by-step explanation:

Difference in elevation is 15,062-(-350)=15,062+350=15,412

Depending on the length of the two sides of the triangle the length could be smaller than 1.

The answer that is not true is :

B. It is always greater than 1

Answer: 2 13/ 15

Step-by-step explanation:

Answer:

50cm

Step-by-step explanation:

oh apdiya I just wanted to let you

The range of the exponential function is: B. [tex]g(x)>-6[/tex]

Recall:

Range of any function includes all possible values of y (output)

Domain of any function includes all possible values of x (input).

Thus:

The values of y in the exponential function greater than -6 on the y-axis as shown in the graph given.

Therefore:

Range of the exponential function given in the graph is: B. [tex]g(x)>-6[/tex].

Learn more about exponential function here:

https://brainly.com/question/19554225

p ∧ q (i.e. "p and q") is true only if both p and q are true. This is the case for the first two rows, but not the third.

Similarly, (p ∧ q) ∧ r is true only if both p ∧ q and r are true. We know when p ∧ q is true, so (p ∧ q) ∧ r is true only when all three of p, q, and r are true. This happens only in the first row.

All other cases are false.

The table should look like this:

[tex]\begin{array}{c|c|c|c|c}p&q&r&p\land q&(p\land q)\land r) \\---&---&---&---&--- \\T&T&T&\boxed T&\boxed T\\&&&&\\T&T&F&\boxed T&\boxed F\\&&&&\\T&F&T&\boxed F&\boxed F\end{array}[/tex]

Answer:

Part A)

[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]

Part B)

After three months, the revenue is increasing at a rate of $391,560 per month.

Step-by-step explanation:

A product is introduced into the market. The quantity per month q sold is given by the function:

[tex]q(t) = 5000t - 120t^2[/tex]

And the price p (in dollars) of the product is given by the function:

[tex]p(t) = 120-t^2[/tex]

Part A)

R(t), or the revenue, will be the product of the quantity sold and its respective price during the month. Hence:

[tex]\displaystyle R(t) = q(t)\cdot p(t)[/tex]

Substitute:

[tex]\displaystyle R(t) = \left(5000t-120t^2\right)\left(120-t^2\right)[/tex]

To find R'(t), take the derivative of both sides with respect to t:

[tex]\displaystyle R'(t) = \frac{d}{dt}\left[ \left(5000t-120t^2\right)\left(120-t^2\right)\right][/tex]

Since the function is a product of two expressions, we can consider using the Product Rule:

[tex]\displaystyle \frac{d}{dx} \left[uv\right] = u'v+uv'[/tex]

Hence:

[tex]\displaystyle R'(t) = \frac{d}{dt}\left[5000t-120t^2\right]\left(120-t^2\right) + \left(5000t-120t^2\right)\frac{d}{dt}\left[120-t^2\right][/tex]

Differentiate. Therefore:

[tex]\displaystyle R'(t) = (5000-240t)(120-t^2)+(5000t-120t^2)(-2t)[/tex]

(We may simplify if we desire, but this is not required by the problem.)

Part B)

To find the rate of change of revenue with respect to time three months after the introduction, we can evaluate R'(t) at t = 3. Hence:

[tex]\displaystyle R'(3) = (5000-240(3))(120-(3)^2)+(5000(3)-120(3)^2)(-2(3))[/tex]

Evaluate:

[tex]R'(3) = 391560\text{ dollars/month}[/tex]

In conclusion, after three months, the revenue is increasing at a rate of $391,560 per month.

(Note: it is increasing because the final value is positive.)

Answer:

98376

Step-by-step explanation: