HELP!


Solve by completing the square: 2x^(2)+x-21

Answer:

8 years.

Step-by-step explanation:

Mara is 6.

6+8=14

Alberto is 20.

20+8=28

14*2=28.

In 8 years, Alberto will be twice Mara's age.

Answer:

This is called "completing the square"

It is a technique to  solve a quadratic equation. It involves "moving all

of the constants to the right" , then doing a "move" on the left hand side. This move "creates a perfect square".. This is done by taking 1/f of the "B" term and squaring it... this will "un-balance" the  sides of the equation... to balance it out you have to "add" some stuff to the right hand side... when done the left side will be "a perfect square" .. last step will be take the square root of both sides.

Step-by-step explanation:

[tex]x^2 + 12x + 15 = 0[/tex]

[tex]x^2 + 12x + 15 -15 = -15[/tex]

[tex]x^2 + 12x = -15[/tex]

[tex]b = 12 ... (1/2 b)^2 = 6^2 = 36[/tex]

[tex]x^2 + 12x + 36 = -15 + 36[/tex]

[tex]x^2 + 12x + 36 = 21[/tex]

[tex](x+ 6)^2 = 21[/tex]

[tex]\sqrt{(x+ 6)^2 } =[/tex] ± [tex]\sqrt{21}[/tex]

[tex]x+ 6[/tex]= ± [tex]\sqrt{21}[/tex]

x = -6 ±[tex]\sqrt{21}[/tex]

Answer:

Step 1: -15

Step 2: b = 12, c = 36

Step 3-4: x² + 12x + 36 = -15 + 36, which simples to (x + 6)² = 21

If there is a step that has you solve for x, it should be -6 + √21 or -6 - √21.

Step-by-step explanation:

Step 1 is pretty simple. All we have to do is subtract 15 from 0 to get the first blank.

x² + 12x = 0 - 15

x² + 12x = -15

Step 2:

b is the coefficient on x, which is 12.

Then, use the formula mentioned:

[tex]c = ( \frac{b}{2})^{2} \\ c = ( \frac{12}{2} )^{2} \\ c ={6}^{2} \\ c = 36[/tex]

As a result of that, c is 36.

Now to substitute and simplify. (Steps 3-4)

x² + 12x + 36 = -15 + 36

To factor an equation, think about it like this: Find two numbers that add to the coefficient of x, and multiply to the constant. So what two numbers add to 12, and multiply to 36? That would be 6 & 6 (6 + 6 = 12; 6 × 6 = 36).

(x + 6)² = -15 + 36

Add 36 to -15 to get 21.

(x + 6)² = 21

That should solve steps 1-4, but I will go on ahead and give the final answer to the entire problem.

(x + 6)² = 21

Yes, you are about see what I just factored be expanded back over again. It's part of the process.

x² + 12x + 36 = 21

Now subtract 21 from both sides.

x² + 12x + 36 - 21 = 21 - 21

x² + 12x + 15 = 0

Now onto the hard part of this: the quadratic formula. a = (the understood) 1, b = 12, and c = 15.

x = (-b ± √b² - 4ac)/2a

x = -12 ± √12² - 4(15)/2

x = -12 ± √144 - 60/2

x = -12 ± ✓84/2

x = -6 + √21 or -6 - √21

The correct option is B)

Let the fourth vertex D =(x,y)

We know that the diagonals of a parallelogram bisect each other. So, the.

The midpoint of AC is the same as the midpoint of BD.

Midpoint of two points (x 1 ,y 1 ) and (x 2,y 2) is  calculated by the formula ( 2x 1+x 2, 2y 1+y2 )

So, the midpoint of AC= Midpoint of BD

=>( 2−2+8, 23+3)=( 26+x, 27+y

=>( 6, 26)=( 26+x, 27+y)

=>6+x=6;7+y=6

=>x=0;y=−1

Hence, D=(0,−1)

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Answer:

Teresa tiene 1 chocolate.

Ella le da 1/3 del chocolate a Miguel, entonces ahora Teresa tendrá un chocolate menos un tercio de chocolate, es decir, ella tiene:

1 - 1/3 = 3/3 - 1/3 = 2/3 de un chocolate.

Ahora le da 1/4 a diego, entonces lo que le sobra va a ser:

2/3 - 1/4

recordar que tenemos que tener el mismo denominador en ambas fracciones, entonces podemos reescribir esto como:

(4/4)*(2/3) - (3/3)*(1/4)

(a cada fracción la multiplico y divido por el denominador de la otra)

8/12 - 3/12 = (8 - 3)/12 = 5/12

Es decir, Teresa finalmente tiene 5/12 del chocolate.

Entonces la parte de chocolate que repartió es lo que le falta, que se obtiene como:

1 - 5/12 = 12/12 - 5/12 = 7/12

Ella repartió 7/12 de su chocolate.

La fracción de chocolate que repartió Teresa es 7/12

Let we have to add two fractions as:

[tex]\dfrac{a_1}{b_1} + \dfrac{a_2}{b_2}[/tex]

Then we will find Lowest Common Multiple (LCM) of [tex]b_1[/tex] and [tex]b_2[/tex]

That will help to make the denominators same.

Once the denominators become same, the numerators can add up directly, giving us the final result of addition.

For this case, we're provided that:

So, the total part she gave is addition of those fractions.

Total part of chocolate Teresa gave = 1/3 + 1/4

LCM of 3 and 4 is 12 since 12 is the smallest number whose factors are 3 and 4 both(this is what LCM of two numbers denote).

Converting each fraction such that it has denominator 12, we get;
[tex]\dfrac{1}{3} \times\dfrac{4}{4} = \dfrac{4}{12}\\\\\dfrac{1}{4} \times\dfrac{3}{3} = \dfrac{3}{12}\\[/tex]

And their addition is:

[tex]\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}[/tex]

Thus, the portion of the chocolate that Teresa distributed is 7/12.

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Answer:

- 3 + 2y

Step-by-step explanation:

[tex]\frac{-\frac{15}{2} +5y}{\frac{5}{2} }[/tex]

[tex]\frac{2}{5}( -\frac{15}{2} +5y} )[/tex]

[tex]-3+2y[/tex]

Step-by-step explanation:

Division by a fraction such as 5/2 is equivalent to multiplication by the reciprocal of the fraction (2/5).

Multiplying (-15/2 + 5y) by 2/5 yields:

-3 + 2y (answer)

Answer:

ii

Step-by-step explanation:

from what you've written in the comments I think this question requires you to find the equation that can be expressed in two variables,so the best way to do this is to solve the pairs as simultaneous equations and see the ones that will give you two answers x and y

if you solve the first pair you will have

x + y = 5

2x+2y=10

2(x + y =5)

1(2x+2y=10)

2x+2y=10

2x+2y=10--

now from this you will see that it cannot be expressed as two variables because the answer is just zero..

for the second equation it can be expressed as two variables

x - y = 8

3x-3y =16

3(x-y =8)

1(x-3y=16)

3x-3y=24

x - 3y=16

2x/2=8/2

x=4

x-y=8

4-y=8

-y=8-4

-y/-1=4/-1

y=-4...

so you see it can be expressed as two variables..

if you solve the third one it will also give you an answer which is zero so it can't be expressed as two variables.

and the fourth one also cannot.

I hope this helps and if you don't understand feel free to ask..and sorry if it's wrong

Answer:

Answer and Explanation: Given polynomial expression is: (5x2+3x−5)−(x2 −6x−4) ( 5 x 2 + 3 x − 5) − ( x 2 − 6 x − 4).

Step-by-step explanation:

Answer:

25x^2 -20x +4

Step-by-step explanation:

(5x-2)^2

FOIL

(5x-2)(5x-2)

25x^2 -10x -10x +4

25x^2 -20x +4

Answer:

R’ = {(1,a) , (2,b)}

Step-by-step explanation:

For us to get the inverse, we switch the places of the x and y variables

The x variable goes to the place of the y variable and the y variable goes to the place of the x variable

we have this as;

R’ = {(1,a) , (2,b)}

Answer: 105750

Step-by-step explanation:

From the sequence 9, 33, 57, 81, 105, the following can be derived:

a = First term = 9.

d = Common difference = 33 - 9 = 24

n = Number of terms = 94

The sum of the nth term will be:

= n/2[2a + (n – 1)d]

= 94/2 [(2 × 9) + (94 - 1) × 24]

= 47 [18 + (93 × 24)]

= 47[18 + 2232]

= 47 × 2250

= 105750

Therefore, the sum of the 94 terms of the sequence is 105750.

Answer:

x = -3

y = 1

z = -2

Step-by-step explanation:

-2x + 3y + z = 7

-4x - y -2z = 15

x + 2y +3z = -7

|-2 3 1|

|-4 -1 -2|

|1 2 3|

Determinant of this from online determinant calculator is;

D = 21

For Dx, we have;

|7 3 1|

|15 -1 -2|

|-7 2 3|

Determinant of this from online determinant calculator is;

Dx = -63

For Dy, we have;

|-2 7 1|

|-4 15 -2|

|1 -7 3|

Determinant of this from online determinant calculator is;

Dy = 21

For Dz, we have;

|-2 3 7|

|-4 -1 15|

|1 2 -7|

Determinant of this from online determinant calculator is;

Dz = -42

From creamers rule;

x = Dx/D

y = Dy/d

z = Dz/d

Thus;

x = -63/21

x = -3

y = 21/21

y = 1

z = -42/21

z = -2

Thus,

x = -3

y = 1

z = -2

Answer:

Step-by-step explanation:

If the position function is

[tex]h(t)=-40t^2+200t[/tex] and we are looking for time when the height is 0, we sub in a 0 for h(t) and solve for t:

[tex]0=-40t^2+200t[/tex] and the easiest way to do this is to factor by taking the GCF of -40t:

0 = -40t(t - 5) and by the Zero Product Property,

-40t = 0 or t - 5 = 0. Solving for t, we get

t = 0 (which is before the object is launched) and

t = 5 (which is how long it takes the object to go from the ground, up to its max height, and then back to the ground again).

Your choice is c) 5

Answer:

Check the explanation for the answer please. Thank you!

Step-by-step explanation:

a. Nina is correct, because the formula P = 2l + 2w would be a correct perimeter formula. Alexander, however, is wrong, because the formula P = 2(l + w) would be an incorrect perimeter formula.

b. P = L + L + W + W would be another correct perimeter formula, as it is the same thing to P = 2l + 2w.

c. One reason the paint was empty after their calculations were correct would be because of their argument before determining the perimeter amount of paint that they need. Another reason the paint was empty after their calculations were correct was because of the fact that they probably don't know how to perfectly do the paint within the perimeter. [I might be wrong about this, but it should be an opinion question anyway.] DO NOT WRITE/TYPE THE PARENTHESIS INTO THIS PROBLEM!!!

Hope this helped!

Answer:

second and fourth has real solution.

Step-by-step explanation:

hope this helps.

Answer:

C.52

Step-by-step explanation:

In a parallelograms opposite sides are congruent

This means that side SP = side RQ as they are opposites

Hence 1/4y = 13

Note that we've just created an equation that we can use to solve for y.

We now solve for y algebraically using the equation we've just created

1/4y = 13

Divide both sides by 1/4

1/4y / 1/4 = y

13 / 1/4 = 52

We're left with y = 52

If PQRS is a parallelogram, the value of y in the parallelogram PQRS is 52. Therefore, option C, 52, is the correct answer.

To find the value of y in the parallelogram PQRS, we can use the properties of parallelograms.

In a parallelogram, opposite sides are equal in length. Therefore, PQ is equal to RS, and QR is equal to SP.

Given that PQ = 11 and RS = 11, we can conclude that QR = SP.

Substituting the given values, we have:

1/4 y = 13

To isolate y, we multiply both sides of the equation by 4:

4 * (1/4 y) = 4 * 13

This simplifies to:

y = 52

Using the property of a parallelogram where opposite sides are equal, we determine that QR is equal to SP. Substituting the given values, we find that 1/4 y is equal to 13. By multiplying both sides of the equation by 4, we isolate y and find that its value is 52.

Therefore, option C, 52, is the correct answer.

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answer ..........(114,0.16)

Answer:

I dont mind answering but what is the question comment the question and i will solve it for you ;)

Answer:

D

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 3x - 2 + x² + 1 ← collect like terms

= x² + 3x - 1 → D

The combination function (f+g)(x) is x²+3x-2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=3x-2 and g(x)=x²+1.

Here, (f+g)(x)=f(x)+g(x)

= (3x-2)+x²+1

= x²+3x-2

Therefore, the combination function (f+g)(x) is x²+3x-2.

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Answer:

[tex]a_n=a_{n-1}+8,n\geq 1[/tex]

[tex]a_1=-11[/tex]

Step-by-step explanation:

We are given that a sequence

-11,-3,5,13,...

[tex]a=a_1=-11[/tex]

[tex]a_2=-3[/tex]

[tex]a_3=5[/tex]

[tex]a_2-a_1=-3-(-11)=-3+11=8[/tex]

[tex]a_3-a_2=5-(-3)=5+3[/tex]

[tex]a_3-a_2=8[/tex]

Common difference between two consecutive terms is equal.

Hence, the sequence is Arithmetic.

Common difference, d=8

[tex]a_2=a_1+8=-3[/tex]

[tex]a_3=a_2+8=5[/tex]

[tex]a_4=a_3+8=13[/tex]

:

:

:

[tex]a_n=a_{n-1}+8, n\geq 1[/tex]

[tex]a_1=-11[/tex]

9514 1404 393

Answer:

  [tex]a_n=\dfrac{1}{2}n^3-\dfrac{1}{2}n^2+6n-3[/tex]

Step-by-step explanation:

The first differences are 8, 13, 21. The second differences are 5, 8. The second differences are not constant, so this is not a quadratic sequence.

If we assume it is a cubic sequence, a calculator tells us the formula is ...

  [tex]a_n=\dfrac{1}{2}n^3-\dfrac{1}{2}n^2+6n-3[/tex]

Answer:g∘f(x)=g(f(x))=g(−3x+4)=(−3x+4)2. In x=−2 we have g∘f(−2)=(−2⋅−3+4)2=102=100.

Step-by-step explanation:

yuhhh babyyyy

Answer:

(x-3)^2+(y-16)^2=9

Step-by-step explanation:

Answer:

The answer is 9

Step-by-step explanation:

(x-3)^2+(y-16)^2=9

Hope this helps :)

Answer:

1

Step-by-step explanation:

Answer:

Ruby is sphere

Shriya's is incorrect

Abhishek's is correct

Step-by-step explanation:

Ruby's definition matches a sphere because it is 3D and Shriya's is wrong.

Answer:

Rs . 28 and Rs.56

Step-by-step explanation:

Explaination in figure

Please mark me as brainliest

1*24= 24....

when any number is multiplied by one it gines the same no. for eg 241526×1=241526..

doesn't matter how greayer or smaller the number is....

Answer:

Step-by-step explanation:

y = 1/2x + 3

9514 1404 393

Answer:

  48

Step-by-step explanation:

The measure of the angle where the chords cross is the average of the measures of the intercepted arcs.

  (70 +x)/2 = 59

  x = 2×59 -70

  x = 48

Answer:

x = 0

Step-by-step explanation:

a = 10

=> x + a = 10

=> x + 10 = 10

=> x = 10 - 10

=> x = 0