given: 4x=12x+32 prove: =-4

[tex]\underline{\bf{Given \:equation:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex]

[tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex]

[tex]\sf We\:know,[/tex]

[tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex]

[tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex]

[tex]\underline{\large{\bf Identities\:used:-}}[/tex]

[tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex]

[tex]\boxed{\sf (√a)^2=a}[/tex]

[tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex]

[tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex]

[tex]\underline{\bf Final\: Solution:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex]

[tex]\bull\sf Apply\: Squares[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex]

[tex]\bull\sf Put\:values[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex]

[tex]\bull\sf Simplify[/tex]

[tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex]

[tex]\underline{\bf More\: simplification:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex]

[tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]

The value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Roots of a quadratic equation

Given the quadratic equation ax² + bx + c, the sum and product  of the roots are expressed as:

Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]

Taking the square of the expression will give:

Take the square root of both sides:

[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]

Substitute the product and the sum values into the expression to have:

[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Hence the value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Learn more on the roots of equation here: https://brainly.com/question/25841119

Answer:11cute and undred

Step-by-step explanation:cute11

Step-by-step explanation:

you can let

then connect this 2 points

Answer:

2x-1=5x

-1=3x

1.A. we take away 2x from both sides

2.A they are the same sine they both have the same solution of -1/3

Hope This Helps!!!

Answer:

Rewrite one side by combining like terms                                                                       A yes the equations are equivalent meaning they have the same solution

Step-by-step explanation:

Hope this helped

Answer:

2 5 and 6

Step-by-step explanation:

Any 2 sides have to add to more than the 3rd side.

Answer:

See below

Step-by-step explanation:

The population is all American households

The sample is 2,541 of those American households

Answer:

Answer is below and I solved them.

Step-by-step explanation:

Absences from school:

8*3*3*3*3 = 648

Day 4 = 648

8*3*3*3*3*3 = 1,944

Day 5 = 1,944

Absences from Band:

8*3*3+28+28 = 128

Day 4 = 128

8*3*3+28+28+28 = 156

Day 5 = 156

Hope that helps.

Please tell me.

Answer:

23 is the answer of this question

Step-by-step explanation:

bye

Mode means the number that pops up the most repeatedly. In this case it's B.) 2 3

Answer:

There is a relationship between Deforestation and Global Climate Change.

Step-by-step explanation:

Deforestation is a cause of global climate change.

Answer:

i think its 4*1

Step-by-step explanation:

hope this helps

have a great day

~Zero~

Answers

Explainations

By calculating the distance of a star to the Sun, astronomers can calculate the distance from Earth to the star.

Reasons

The given parameters are;

The distance from the star to the Sun = d

The angle formed by the ray to the Sun and the ray to Earth from the star, θ = 0.00001389 degrees

The average distance from Earth to the Sun = 1 AU

By trigonometric ratios, we have;

[tex]\displaystyle tan(\theta) = \mathbf{\frac{Opposite}{Adjacent}}[/tex]

Therefore;

[tex]\displaystyle tan(\theta) = \frac{1}{d}[/tex]

The expression to calculate for d for any star is therefore;

The angle given for θ for the referenced star is θ = 0.00001389

Therefore;

[tex]\displaystyle d = \frac{1 \, AU}{tan(0.00001389^{\circ}) } \approx 4,124,966.13 \, AU[/tex]

Learn more about trigonometric ratio here:

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Answer:

I.

II.

One and two are the correct ones

Step-by-step explanation:

Y goes up and down

X is side to side

so

x comes first in an ordered pair.

(I remember that by saying, "You need to find the room before you can ride the elevator)

Answer: How to calculate commission. This is a very basic calculation revolving around percents. Just take sale price, multiply it by the commission ...

Step-by-step explanation:

The null hypothesis is the one in which any statement which is the claim of the experiment is chosen to decide the results for .

The alternate hypothesis is the opposite of the null hypothesis.

Type I Error:  Type I Error occurs when H0 is true but it is rejected and Ha is accepted.

Type II Error:  Type II Error occurs when Ha is true but it is rejected and the false null hypothesis H0 is accepted which is wrong decision.

In this case the null hypothesis is

H0: On pulling the rip cord the parachute will open.

Ha: On pulling the rip cord the parachute will not open.

In this experiment the alternate hypothesis Ha :On pulling the rip cord the parachute will not open is accepted then type I error occurs.

In this experiment the null hypothesis H0 :On pulling the rip cord the parachute will not open is accepted then type II error occurs.

In this experiment Type I Error is a more serious error because the true null hypothesis H0: the parachute will open is rejected.

In this experiment Type II Error is a more serious error.

Type I and Type II Errors are independent of the confidence interval.

When the parachute has a backup in case of ripcord malfunctions then the confidence level of the hypothesis can be 100 percent. That is we are 100 percent sure that the parachute will land safely and there will be no accidents.

This is does not guard the type I and type II errors because these are made on the wrong decision.

The null and alternate hypotheses can be understood here

https://brainly.com/question/19132215

https://brainly.com/question/15681523

Type I and II Errors can be understood

https://brainly.com/question/7278657?section=related_q

https://brainly.com/question/16012410

[tex]y = \frac{x}{2} [/tex]

[tex]2x + 2y = \sqrt{180} \\ = > 2x + 2( \frac{x}{2} ) = \sqrt{180} \\ = > 2x + x = \sqrt{2 \times 2 \times 3 \times 3 \times 5} \\ = > 3x = 2 \times 3\sqrt{5} \\ = > 3x = 6 \sqrt{5} \\ = > x = \frac{6 \sqrt{5} }{3} \\ = > x = 2 \sqrt{5} [/tex]

[tex]x.y \\ = x \times \frac{x}{2} \\ = \frac{ {x}^{2} }{2} \\ = \frac{ {(2 \sqrt{5} )}^{2} }{2} \\ = \frac{4 \times 5}{2} \\ = \frac{20}{2} \\ = 10[/tex]

Answer:

10

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

b

Step-by-step explanation:

Given

2x + 2y = [tex]\sqrt{180}[/tex] = [tex]\sqrt{36(5)}[/tex] = 6[tex]\sqrt{5}[/tex]

and y = [tex]\frac{x}{2}[/tex] , then

2x + (2 × [tex]\frac{x}{2}[/tex] ) = 6[tex]\sqrt{5}[/tex]

2x + x = 6[tex]\sqrt{5}[/tex]

3x = 6[tex]\sqrt{5}[/tex] ( divide both sides by 3 )

x = 2[tex]\sqrt{5}[/tex]

and y = [tex]\frac{2\sqrt{5} }{2}[/tex] = [tex]\sqrt{5}[/tex]

Then

xy = 2[tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 2 × 5 = 10 → b

Answer:

Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?

Step-by-step explanation:

Multiply: 14(0.25). If you missed this problem, review Example 5.3.5.

Simplify: 100(0.2 + 0.05n). If you missed this problem, review Example 7.4.6.

Solve: 0.25x + 0.10(x + 4) = 2.5 If you missed this problem, review Example 8.6.8.

Imagine taking a handful of coins from your pocket or purse and placing them on your desk. How would you determine the value of that pile of coins?

If you can form a step-by-step plan for finding the total value of the coins, it will help you as you begin solving coin word problems.

One way to bring some order to the mess of coins would be to separate the coins into stacks according to their value. Quarters would go with quarters, dimes with dimes, nickels with nickels, and so on. To get the total value of all the coins, you would add the total value of each pile.Figure  9.3.1  - To determine the total value of a stack of nickels, multiply the number of nickels times the value of one nickel.For coins of the same type, the total value can be found as follows:

number⋅value=totalvalue(9.3.1)

where number is the number of coins, value is the value of each coin, and total value is the total value of all the coins.

You could continue this process for each type of coin, and then you would know the total value of each type of coin. To get the total value of all the coins, add the total value of each type of coin.

Let's look at a specific case. Suppose there are 14 quarters, 17 dimes, 21 nickels, and 39 pennies. We'll make a table to organize the information – the type of coin, the number of each, and the value.

Table  9.3.1

Type Number Value ($) Total Value ($)

Quarters 14 0.25 3.50

Dimes 17 0.10 1.70

Nickels 21 0.05 1.05

Pennies 39 0.01 0.39

6.64

How would you determine the value of each pile? Think about the dime pile—how much is it worth? If you count the number of dimes, you'll know how many you have—the number of dimes.

But this does not tell you the value of all the dimes. Say you counted 17 dimes, how much are they worth? Each dime is worth $0.10 —that is the value of one dime. To find the total value of the pile of 17 dimes, multiply 17 by $0.10 to get $1.70. This is the total value of all 17 dimes.

Answer:

False!

Step-by-step explanation:

Right angles are 90 degrees, for example EOA appears to be closer to a right angle but not HOA

Answer:

a) 335

b) 344

Step-by-step explanation:

The value of the variable x can be determined using the circle theorem to

determine the angle formed by x.

The correct responses are;

Reasons:

(1) From circle theorem, we have;

Therefore;

Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at center = Angle subtended by [tex]\widehat {BC}[/tex] at the center;

Therefore;

Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at the circumference = Angle subtended by [tex]\mathbf{\widehat {BC}}[/tex] at the circumference

Which gives;

(2) [tex]\displaystyle \widehat {AB} = \mathbf{\widehat {CD}}[/tex] given

Angle subtended by arc [tex]\widehat {CD}[/tex] at the center = x

Equal arcs subtend equal angles at the center of a circle.

Therefore;

Angle subtended by arc [tex]\mathbf{\widehat {AB}}[/tex] at the center = x

Angle at center = 2 × angle at circumference

Therefore;

x = 2 × 50° = 100°

x = 100°

(3) [tex]\displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}}[/tex] given

By definition, we have;

Angle subtended by [tex]\widehat {AC}[/tex] at the center = 3 × Angle subtended by [tex]\widehat {AB}[/tex] at the center

According to circle theorem, we have;

Angle at the center = 2 × Angle at the circumference

Let y represent the angle subtended at the circumference by [tex]\widehat {AB}[/tex], we have;

y = 20°

[tex]\widehat {AB}[/tex] = 2·y

[tex]\widehat {AC}[/tex] = 3 × [tex]\widehat {AB}[/tex] = 3 × 2·y = 6·y

Therefore;

[tex]\widehat {AC}[/tex] = 6 × 20° = 120°

[tex]\widehat {AC}[/tex] = 120°

[tex]\widehat {AC}[/tex] = 2·x

Therefore;

2·x = 120°

[tex]\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}[/tex]

x = 60°

Learn more circle theorems here:

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You should do 585 × 0.50 to find the markdown. Then subtract the markdown from the selling price to find the sale price.

Step-by-step explanation:

Answer:

2.45, 2.46, 2.47, 2.48, 2.49, 2.52, 2.52, 2.53 and 2.54 all round to 2.5 when being rounded to the nearest tenth.

Tenth = 0.1.

Hope that helps. x

Answer:

I think it's no

Step-by-step explanation:

because you will study hard

Using the tables to answer the question, the correct option is D.

Only table B represents a function

A relation/table will represent a function if each value of x is attached to a unique value of y.

That is, no value of x must be mapped to more than one value of y.

By considering the tables represented

Set A = {(-5, 2), (-8, 5), (-5, 8)}

As clearly shown above, when x = -5, y = 2 and 8. This means that there are more than 1 value of y for a single value of x, therefore, table A does not represent a function.

Set B = {(-5, 2), (-8, 5), (-11, 2)}

As shown above, all values of x have different values of y. Therefore, table B represents a function.

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