f(x) = x² + 2ax + a² - a
g(x) = 4 - x²

Let variable a be a real number. Find the range of values of a such that the equation f(x) = g(x) has two different solutions.

***The answer should be -2 < a < 4, but I don't know why.

Answer:

A number multiplied by a variable.

Step-by-step explanation:

For example, 4 is a coefficient.

[tex]4x[/tex]

Answer:

Step-by-step explanation:

37.203

-29.800

=36.203+1-29.800=36.2003-1+0.200=7.403

Answer:

Subtraction,... Below,...!

Step-by-step explanation:

37.203 - 29.800 = 7.403

Subtract like you where subtracting 37203 - 29800 you add the extra 0's to align the would-be decimal points...

37203 - 29800 = 7403

Answer: 7.403

Chow,...!

9514 1404 393

Answer:

  (x, y, z) = (-9, -1, 8)

Step-by-step explanation:

My calculator tells me the reduced row-echelon form of ...

  [tex]\left[\begin{array}{ccc|c}-3&-2&-3&5\\1&2&-1&-19\\-2&1&-2&1\end{array}\right][/tex]

is ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&-9\\0&1&0&-1\\0&0&1&8\end{array}\right][/tex]

This means the solution is (x, y, z) = (-9, -1, 8).

_____

Additional comment

In case you haven't learned how to use your graphing calculator to solve matrix equations, you can solve this system easily as follows:

Subtract 2 times the first equation from 3 times the third equation. This eliminates the x and z terms and gives you the value of y. (y=-1)

Substitute that value into the first and second equations. This gives you two equations in the sum and difference of x and z. (You may need to divide the coefficients by the common factor.) Add these sum and difference equations to find one of the variables, then substitute to find the other.

Answer:

[tex]x=-1\\y=3\\z=-4\\[/tex]

Step-by-step explanation:

Please see attached document.

Answer:

5, i think

Step-by-step explanation:

1. 3x = 15 and divide all by 3 (the number with a variable or letter

Answer:

Domain: {-2, -1, 0, 1, 2}

Range: {-5, -1, 3, 7, 11}

Step-by-step explanation:

Given the function, f(x) = -4x + 3:

We could simply substitute the given x-values into the function to solve for its corresponding y-values:

x = -2:

f(-2) = -4(-2) + 3

f(-2) = 8 + 3

f(-2) = 11

x = -1:

f(-1) = -4(-1) + 3

f(-1) = 4 + 3

f(-1) = 7

x = 0:

f(0) = -4(0) + 3

f(0) = 0 + 3

f(0) = 3

x = 1:

f( 1 ) = -4( 1 ) + 3

f( 1 ) = -4 + 3

f( 1 ) = -1

x = 2:

f(2) = -4(2) + 3

f(2) = -8 + 3

f(2) = -5

Attached is a screenshot of the table containing the same solution displayed in this post.

D, Because there are two negative numbers must be before zero and three positive numbers must be after zero so the right answer is D i'm sure

-0.5 is between -1 and 0

7/4 = 1.75 is between 1.5 and 2

0.75 is between 0 and 1

-9/4 = -2.25 is after -2

1.25 is between 1 and 1.5

9514 1404 393

Answer:

  2

Step-by-step explanation:

The products of chord lengths are the same for the intersecting chords:

  AQ×BQ = CQ×DQ

  6×12 = CQ×(38 -CQ)

This gives a quadratic in CQ:

  CQ² -38CQ +72 = 0 . . . . . write in standard form

  (CQ -2)(CQ -36) = 0 . . . . . factor the quadratic

  CQ = 2 or 36 . . . . . . . values of CQ that make the factors zero

The minimum length of CQ is 2 units. (DQ will be 36.)

Answer:

igneous

Step-by-step explanation:

igneous rocks are made out of molten lava or magma

Answer:

sedimentary rock/igneous rock and Metamorphic rock

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To write the equation of line when slope and one point is given

[tex]y2 - y1 = m(x2 - x1)[/tex]

here m = 3/4

(x1,y1) = 3,-2

Substitute all the values in Formula

[tex]y + 2 = \frac{3}{4} (x - 3) \\ y + 2 = \frac{3}{4} x - \frac{9}{4} \\ y = \frac{3}{4} x - \frac{9}{4} - 2 \\ = \frac{3}{4} x - \frac{17}{4} \\ 4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

multiply by 4 on both sides

[tex]4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

Answer:

option 2: f(x) = 4x + 4

Step-by-step explanation:

Graph is positive, so with this you should already know that options: 1, 3, 4 are incorrect since those are negative.

However, let's break it down more.

To write the function for a line, you use y = mx+b

m stands for the rise/run

b stands for the y-intercept

Rise over run is 4/1, or just 4

With this we know that option 3 is not correct, yet again

Our y intercept is 4

With this we know that option 1 is not correct, yet again

This just leaves option 2 and 4 with the correct slope and y-intercept, yet as we said before this is a positive slop, so again, 4 is incorrect

Answer:

no of course yes its no yes

Step-by-step explanation:

Answer:

x = 3/5

Step-by-step explanation:

5th root of Y is notated in exponential notation as Y^(1/5), which is Y to the one fifth (1/5) power.

So, the 5th root of 19^3 is (19^3)^(1/5) = 19^(3 * 1/5) = 19^(3/5), since (A^a)^b = A^(a*b).

Answer:

decimal: 2.25

fraction: 9/4

Step-by-step explanation:

Answer:

Fraction: 15/4

Decimal: 3.75

Answer:

4 hours and 30 minutes 288/64 = 4,5

Step-by-step explanation:

Answer:

A is function.

Step-by-step explanation:

-11.9 -1 = -12.9

Your answer is negative 12.9

Answer:

-12.9

Step-by-step explanation:

Hope this helps you! :)

Answer:

VU, VT, TU

Step-by-step explanation:

List the side lengths of triangle TUV from shortest to longest.

A. VU, VT, TU

B. VT, TU, VU

C. VT, VU, TU

D. VU, TU, VT"

Answer:

f(x)=4−(x−7)

3

Let y=f(x)

So, x=f

−1

(y) ---- ( 1 )

y=f(x)

⇒ y=4−(x−7)

3

⇒ (x−7)

3

=4−y

⇒ x−7=

3

4−y

⇒ x=7+

3

4−y

⇒ f

−1

(y)=7+

3

4−y

.................. [ From ( 1 ) ]

∴ f

−1

(x)=7+

3

4−x

Answer:

A) = 5

B) = 3

C) = [tex]2\sqrt{3}[/tex]

D) = 2.2894

Step-by-step explanation:

A)  [tex]x^2=25[/tex]

[tex]\sqrt{x^2} = \sqrt{25} \\x= 5[/tex]

5*5 = 25

B)  [tex]x^3 = 27[/tex]

[tex]\sqrt[3]{x^3} = \sqrt[3]{27} \\x=3[/tex]

3*3*3 = 27

C)  [tex]x^2 = 12\\[/tex]

[tex]\sqrt{x^2} = \sqrt{12} \\x=2\sqrt{3} \\[/tex]

[tex]2\sqrt{3}[/tex] * [tex]2\sqrt{3}[/tex] = 12

D)  [tex]x^3 = 12[/tex]

[tex]\sqrt[3]{x^3} = \sqrt[3]{12} \\x=2.2894.....\\[/tex]

2.2894 * 2.2894 *2.2894 = 12

No exact solution

Answer:

no

Step-by-step explanation:

Answer:

ok?

Step-by-step explanation:

Answer:

12m perimeter

Step-by-step explanation:

all side are 3m so 3x4 = 12m

Answer:

it is a

Step-by-step explanation:

2-5

y=mx+b

-3=3(3)+b

-3=9+b

-12=b

Given function :-

[tex]\bf \implies g(x) = \dfrac{3}{x}+7[/tex]

[tex]\bf \implies y = \dfrac{3}{x}+7[/tex]

[tex]\bf \implies x = \dfrac{3}{y}+7[/tex]

[tex]\bf\implies \dfrac{3}{y}= x -7 \\\\\bf\implies y =\dfrac{3}{x-7} [/tex]

[tex]\implies\boxed{\red{\bf f^{-1}(x) = \dfrac{3}{x-7} }}[/tex]