When solving algebraic expressions involving fractions with different denominators, you just have to determine the LCM and multiply it across each term

Hey there!

[tex]\mathsf{x^2 - 11 = 25}[/tex]

[tex]\large\textsf{ADD 11 to BOTH SIDES}[/tex]

[tex]\mathsf{x^2 - 11 + 11 = 25 + 11}[/tex]

[tex]\large\textsf{CANCEL out: -11 + 11 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: 25 + 11 because that helps solve for the x-value}[/tex]

[tex]\mathsf{25 + 11 = \bf 36}[/tex]

[tex]\large\textsf{NEW EQUATION: }\mathsf{x^2=36}[/tex]

[tex]\large\textsf{Take the square root of the number (36)}[/tex]

[tex]\mathsf{x = \pm \sqrt{36}}[/tex]

[tex]\mathsf{\pm = \boxed{\bf plus-or-minus}}[/tex]

[tex]\mathsf{x = \sqrt{-36}\rightarrow \bf -6}[/tex]

[tex]\large\textsf{or}[/tex]

[tex]\mathsf{x = \sqrt{36} = \bf 6}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf x = 6 or x = -6}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

x² - 11 = 25

Add 11 to both sides.

x² - 11 + 11 = 25 + 11

Cancle out the 11 because when we add -11 to 11 that gives 0. On other side add 25 and 11 we get 36.

x² = 36

Take the square root of both sides of the equation and remember to use both positive and negative roots.

√x² = ± √36

x = ± 6

Write the solutions, one with a+ sign and one with a- sign.

[tex] x_1 = 6[/tex]

[tex]x_2 = -6[/tex]

This equation has two solutions which are :-

[tex] x_1 = 6[/tex]and [tex]x_2 = -6[/tex]

Answer:

7

Step-by-step explanation:

Exterior Angle Theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

In this case:

(4x + 7) + (97) = (17x + 13)

4x + 104 = 17x + 13

4x + 91 = 17x

91 = 13x

7 = x

Answer:

cost per serving can be used as a result of using your head to think

Answer:

y = - 2

Step-by-step explanation:

x = 0 lies on the y- axis

The only point on the y- axis where the function crosses is y = - 2

Then when x = 0, y = - 2

Answer:

1.likely. 11.likely

2. likely. 12.likely

3. likely. 13.likely

4. unlikely 14. unlikely

5. likely. 15. likely

6. likely

7. likely

8. likely

9. likely

10. likely

Step-by-step explanation:

im correct if I'm rwong

Step-by-step explanation:

answer what ?

all we can see is a grid of coordinates with a functional graph drawn into it.

and we know this function is called y=h(x).

that is it.

what answer is needed ? there is no question visible.

Explanation:

For any 30-60-90 triangle, the hypotenuse is always twice as long compared to the short leg. The short leg is always opposite the 30 degree angle.

The length of x is 6.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given problem,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = [tex]\frac{perpendicular}{hypotenuse}[/tex]

∅ = 30°

⇒ sin30 = [tex]\frac{3}{x}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{x}[/tex]  [ sin30 = [tex]\frac{1}{2}[/tex] ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ 6² = 3² + Base²

⇒ 6² - 3² = Base²

⇒ Base² = 25

⇒ Base = √25

⇒ Base = 5

Hence, we can conclude the value of x to be 6.

Learn more about right-angled triangle here:

https://brainly.com/question/3770177

#SPJ2

Answer:

(- 1, - 1 )

Step-by-step explanation:

Given the 2 equations

x = 4y + 3 → (1)

2x + y = - 3 → (2)

Substitute x = 4y + 3 into (2)

2(4y + 3) + y = - 3 ← distribute parenthesis and simplify left side

8y + 6 + y = - 3

9y + 6 = - 3 ( subtract 6 from both sides )

9y = - 9 ( divide both sides by 9 )

y = - 1

Substitute y = - 1 into (1) for corresponding value of x

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

solution is (- 1, - 1 )

Answer:

27 degrees

Step-by-step explanation:

First, we can draw this out. Since the altitude is 8000, we can make that the height, and it goes 16000 feet through the air, that can be the length. I have drawn this out, as shown in the image. Note that when drawing, because the airplane is going up and forward, that path should represent the hypotenuse. The angle of elevation is the angle connecting the length and the path, as shown by the angle x in the picture.

We know than tan(x) = opposite/adjacent, so tan(x) here = 8000/16000 = 1/2. Then, arctan(1/2) =x = 27 degrees

Answer:

I wanna say its B. Vera's only

Answer:

no  c

Step-by-step explanation:

Answer:

discounted price = original price ( 1 - discount rate)

Step-by-step explanation:

Answer: random sampling

Step-by-step explanation:

Because psychologists generally use college students as research participants, the research does not involve random sampling.

Random sampling is when each sample has an equal chance of being selected. Since the psychologists are targeting a particular set of students, the random sampling might not be applicable in this case.

Answer

There is a 68 percent that a student selected a random will score an 80 or higher on the next test.

Explanation

You just need to find the percentage of 17 out of 25, or 17/25.

You can do this by dividing 17 by 25.

17/25 equals 0.68, or 68 percent.

Answer:

k =  4

Step-by-step explanation:

If (x + 2) is a factor then f(- 2) = 0

f(x) = x³ - kx² + 2x + 7k , then

f(- 2) = (- 2)³ - k(- 2)² + 2(- 2) + 7k = 0      

     ⇒   - 8 - k(4) - 4 + 7k = 0

     ⇒  - 8 - 4k - 4 + 7k = 0

     ⇒ 3k - 12 = 0 ( add 12 to both sides )

     ⇒ 3k = 12 (divide both sides by 3 )

     ⇒ k = 4

Answer:

k = 4

Step-by-step explanation:

If x + 2 is a factor of x³ - kx² + 2x + 7k then

the value of x = -2

Solve for k

plug -2 as x in the expression.

expand the exponents

combine like terms

add 12 to both side

divide each side by 3

Respuesta:

5250

Explicación paso a paso:

Dado que :

Importe del préstamo, principal, p = 35000

Tasa de interés, r = 3% = 0.03

Tiempo, t = 5 años

Usando la fórmula de interés simple:

Interés = principal * tasa * tiempo

Interés = 35000 * 0.03 * 5

Intereses = 5250 pesos

Answer:

P is maximum at I = 2

Step-by-step explanation:

Here is the complete question

The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?

To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.

So, dP/dI =  d[100I/(I² + I + 4)]/dI

= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²

= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²

= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²

= [-100I² + 400]/(I² + I + 4)²

=  -100[I² - 4]/(I² + I + 4)²

Since dP/dI = 0,  -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4

I = ±2

Since I cannot be negative, we ignore the minus sign

To determine if this is a maximum point, we differentiate dP/dI. So,

d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI

= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²

= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴

= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴

Substituting I = 2 into d²P/dI², we have

= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴

= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴

= [-200(10)[24](5)]]/(10)⁴

= -240000/10⁴

= -24

Since d²P/dI² = -24 < 0 at I = 2,  this shows that it I = 2 is a maximum point.

So, P is maximum at I = 2

Answer:

[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (-1, 6), h = -1 and k = 6. Substitute:

[tex]f(x)=a(x-(-1))^2+(6)[/tex]

Simplify:

[tex]f(x)=a(x+1)^2+6[/tex]

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when x = -3. Substitute:

[tex](4)=a(-3+1)^2+6[/tex]

Solve for a. Simplify:

[tex]-2=a(-2)^2[/tex]

Hence:

[tex]\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}[/tex]

Therefore, our function in vertex form is:

[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]

Answer:

Step-by-step explanation:

The Midpoint formula is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] where the x's and y's come from the coordinates of the endpoints. Filling in:

[tex]M=(\frac{-2+(-1)}{2},\frac{-4+(-5)}{2})=(\frac{-3}{2},\frac{-9}{2})=(-1.5,-4.5)[/tex]

Answer:

ans is C................

Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Answer:

3/10 of a cup

Step-by-step explanation:

Find how many cups of strawberries each student got by dividing 6 by 20:

= 6/20

Simplify this by dividing each number by 2:

= 3/10

So, each student got 3/10 of a cup of strawberries

Hello!

[tex]\large\boxed{x = 4}[/tex]

7(x + 9) + 5 = 96

Distribute:

7x + 63 + 5 = 96

Combine like terms:

7x + 68 = 96

Subtract 68 from both sides:

7x = 28

Divide both sides by 7:

x = 4

Answer:

[tex]\fbox{x = 7}[/tex]

Step-by-step explanation:

7(x + 9) + 5 = 96

Solve for x.

Step 1 :- Distribute 7.

Step 2:- Add 63 and 5.

Step 3 :- Move constant to the right-hand side and change their sign.

Step 4 :- Subtract 68 from 96.

Step 5 :- Divide both side by 7.

Answer:

P = $80

Step-by-step explanation:

I = P*r*t

P = I/rt

Where,

simple interest, I = $20

Interest rate, r = 5%

Time, t = 5 years

P = I / rt

= 20 / 5% * 5

= 20 / 0.05 * 5

= 20 / 0.25

= 80

P = $80

Answer:-

The option B is the right answer.

Solution:-

[tex] \sf h = 2d = 2 \: • \: 2r = 4r[/tex]

[tex] \sf = \frac{1}{3} \pi {r}^{2} h[/tex]

[tex] \sf = \frac{1}{3} \pi {r}^{2} \: • \: 4r[/tex]

[tex] \sf = \frac{4}{3} \pi {r}^{3} \: \green✓ [/tex]

Answer:

Try harder at what you do. Talk to your teacher. Go to online study groups. Give me an example of a question and I will help you more.

Answer:

theta = 44.4 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig formulas

cos theta = opposite/ hypotenuse

cos theta = 15/21

Take the inverse of each side

cos^ -1 (cos theta) = cos ^-1 (15/21)

theta =44.4153086

theta = 44.4 degrees