4.
Which of the following equations has
both -1 and 4 as solutions?
A) x²+4x+4 B) x2-4x+3
C) x2-3x-4 D) x2+3x-4

Answer:

parabola opens up

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then parabola opens up

• If a < 0 then parabola opens down

y = (x + 3)² - 4 ← is in vertex form

with a = 1

Since a > 0 then parabola opens up

Answer:

$2.30

Step-by-step explanation:

Answer:

$1449.15

Step-by-step explanation:

currently paying 815

to pay next year: 41% increase + 25 extra per month

⇒ 141%·815 + 12·25

    = 1149.15 + 300

    = 1449.15

Answer:

Im pretty sure its 3 cups

Step-by-step explanation:

Answer:

3/151

Step-by-step explanation:

That's the answer

Answer:

= [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Result in decimals: 0.66666666666667

x = mutiply

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

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

= [tex]\frac{2}{3}[/tex]

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

33.20% probability that the sample mean would differ from the population mean by greater than 1 gallon

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Answer:

sqrt299

Step-by-step explanation:

Because the loading dock and the ground are perpendicular we know that they are at a 90° angle. Therefore we can use the equation :

a=5

b= ?

c=18

(Then we can move all of the numbers together but what you do to one side you must do to the other)

 Therefore,

 (Now to make b a single variable we must square root both sides)

 Therefore,

Now with all of these as numbers, we can plug this into a calculator *For all of those who have teachers who need EVERY Step see below I continue

  Where  and

(approximately)

m-18

Answer:

it is D

Step-by-step explanation:

I have to show you, but if I do it don't on the paper

1. [tex] \frac{5}{12} = \frac{35}{n} \\ 5n = 35 \times 12 \\ 5n = 420 \\ n = \frac{420}{5} \\ n = 84[/tex]

2. [tex] \frac{n}{52} = \frac{180}{120} \\ 120n = 180 \times 52 \\ 120n = 9360 \\ n = \frac{9360}{120} \\ n = 78[/tex]

Answer:

D. (19,12)

Step-by-step explanation:

For each bus stop, the X coordinate increases 4, and the Y coordinate increases 2.

Name                x      y      Point

bus station:     3   4     (3,4)

1st bus stop:     7  6     (7,6)

2nd bus stop:    11  8     (11,8)

3rd bus stop:     15  10     (15,10)

4th bus top:     19  12     (19,12)

Answer:

Step-by-step explanation:

19,12

Answer:

Step-by-step explanation:

24)

3x - 10 > 2

3x - 10 + 10 > 2 + 10

3x > 12

3x/3 > 12/3

x > 4

5x - 15 < -5

5x - 15 + 15 < -5 + 15

5x < 10

5x/5 < 10/5

x < 2

B)  x > 4 or x < 2

25)   1.5/60 = 12/x

x = 12(60) / 1.5

x = 480

B) 480 miles

This distance from Old Faithful to Mammoth Hot Springs is actually about 52 miles by road, so there must have been MASSIVE number of road closures to get this result...or else their scale is incorrect. 1.5 inch to 6.0 miles would be a much more accurate scale making the distance 48 miles.

Answer:

9 quarts

Step-by-step explanation:

Answer:

for me the picture is blurry sorry

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Answer:

This is 0.8 to the nearest tenth.

Step-by-step explanation:

FYI, to round to the nearest tenth, look at the second number after the decimal point. If it is 5 or more then round the first number after the point up one e.g.. If the answer was 0.850375,you round up which is 0.9 to the nearest 10th.

If the second number after the decimal point is less than 5 (in this case) you round down to 0.8.        (BRAINLIETS PRETTY PLEASEEEE OvO)

Answer:

x = 24°

Step-by-step explanation:

Using 180-degree formula, we can find x.

=> 84 + 4x = 180°

=> 4x = 180 - 84

=> 4x = 96

=> 24°

Therefore, x = 24°

Hoped this helped.

Answer:

[tex] {\boxed {\sf{x = 24 \degree}}}[/tex]

Step-by-step explanation:

In the given figure we have two consecutive interior angles.

We know that each pair of consecutive interior angles is supplementary.

So,

Therefore, x = 24°

Answer:

C.) 10.44030650

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use distance formula:

Substitute the values and calculate:

Correct choice is C

Answer:

ture

Step-by-step explanation:

Answer:

21.6171

Step-by-step explanation:

Have a great day!

1. The given equation is probably supposed to read

y'' - 2y' - 3y = 64x exp(-x)

First consider the homogeneous equation,

y'' - 2y' - 3y = 0

which has characteristic equation

r² - 2r - 3 = (r - 3) (r + 1) = 0

with roots r = 3 and r = -1. Then the characteristic solution is

[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]

and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.

Now we use variation of parameters, which gives a particular solution of the form

[tex]y_p = u_1y_1 + u_2y_2[/tex]

where

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]

and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is

[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]

Then we find

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]

so it follows that the particular solution is

[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]

and so the general solution is

[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]

2. I'll again assume there's typo in the equation, and that it should read

y''' - 6y'' + 11y' - 6y = 2x exp(-x)

Again, we consider the homogeneous equation,

y''' - 6y'' + 11y' - 6y = 0

and observe that the characteristic polynomial,

r³ - 6r² + 11r - 6

has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields

r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)

and from this we see the characteristic solution is

[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]

For the particular solution, I'll use undetermined coefficients. We look for a solution of the form

[tex]y_p = (ax+b)e^{-x}[/tex]

whose first three derivatives are

[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]

[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]

[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]

Substituting these into the equation gives

[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]

[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]

[tex]-24ax+26a-24b = 2x[/tex]

It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is

[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]

and the general solution is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]

Answer:

c

Step-by-step explanation:

its in the middle of all the data

Answer:

1. 4

2. 6

3. 10

4. 30

5. 48

6. 55

7. 68

8. 148

9. 102

10. 38

Answer:

0.400

Step-by-step explanation:

Slope = 0.800/2.000 = 0.400

 x-intercept = 4/2 = 2

 y-intercept = 4/-5 = -0.80000

Answer:

By deleting the question, or getting it deleted.

Step-by-step explanation:

Answer:

2/5m - 1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...

  0.15q + 0.05(390 -q) = 0.08(390)

  0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify

  q = 117 . . . . . . . . . . . . . . . . . . multiply by 10

  390-q = 273

The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).

__

Additional comment

You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.

Answer:

f ( 3 ) = 81

Step-by-step explanation:

→ Substitute in x = 3

9 × 3² - 3

→ Simplify

9 × 9 - 3

→ Simplify again

78

If z = (6x + 2y)⁹, then the partial derivatives of z are

• with respect to x :

∂z/∂x = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂x

∂z/∂x = 9 (6x + 2y)⁸ • 6

∂z/∂x = 54 (6x + 2y)⁸

• with respect to y :

∂z/∂y = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂y

∂z/∂y = 9 (6x + 2y)⁸ • 2

∂z/∂y = 18 (6x + 2y)⁸