All categories

3 years ago

Warm-Up

Mathematics

1 answer:

Sveta_85 [38]3 years ago

4 0

Answer:

Graph # 3

Step-by-step explanation:

-2x + 5y > 15 Let x = 0 solve for y

-2(0) + 5y = 15 change the > to an =

5y = 15

y =3 Point (0, 5) is on the graph

Graph # 3 is correct because the y-intercept is 5

x y

0 3 -2(0) + 5y = 15; 5y = 15

5 5 -2(5) + 5y = 15; -10 + 5y = 15; 5y = 25; y = 5

10 7 -2(10) + 5y = 15; -20 + 5y = 15; 5y = 35; y = 7

The graph > the line is dotted and you will shade above the line

You might be interested in

Sonia read 2 pages of book per minute. If sonia read all the pages of the book at the same rate, which equation shows the tital

Fudgin [204]

2x=y
two times the number of minutes = the amount of pages

5 0

3 years ago

A store sells 4 cans of fruit cocktail for $9. How much would it cost you to buy 3 cans of fruit cocktail?

horsena [70]

Answer:

9:4=2.25 3x2.25=6.75 i think lol

6 0

4 years ago

Read 2 more answers

Solve y′′=sin(x) if y(0)=0 and y′(0)=5. y(x)=?

Ksenya-84 [330]

Answer:

$y(x)=6x-sin(x)$

Step-by-step explanation:

Rewrite the differential equation as:

$\frac{d^{2} y }{dx^{2} } =sin(x)$

Integrate both sides with respect to x:

$\int\ \frac{d^{2} y }{dx^{2} } dx = \int\ sin(x) dx$

$\frac{dy}{dx} =-cos(x)+C_1$

Integrate one more time both sides with respect to x:

$\int\ \frac{dy}{dx} = \int\ -cos(x)+C_1 dx$

$y(x)=-sin(x)+C_1x+C_2$

Now that we find the solution, let's find its derivate:

$y'(x)=C_1-cos(x)$

Evaluating the initial conditions:

$y(0)=C_1(0)+C_2-sin(0)=0\\C_2=0$

$y'(0)=C_1-cos(0)=5\\C_1=5+1=6$

Replacing the value of the constants that we found in the differential equation solution:

$y(x)=6x-sin(x)$

6 0

3 years ago

7a - 17 = 9a + 1 (Finding Common Denominators)

MA_775_DIABLO [31]

Answer:
3a−17=1

3a=18

a=6

8 0

3 years ago

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find t

sp2606 [1]

Answer:

Length of DE is : 18√2 units

Step-by-step explanation:

The length of a side of a triangle is 36.

To calculate : The length of the segment DE

Now, the two parts of triangle have equal area ∴ Area(ADE) = Area(BDEC)

$\implies Area(ADE)=\frac{1}{2}\times Area(ABC) \\\\\implies \frac{Ar(ADE)}{Ar(ABC)}=\frac{1}{2}$

In ΔABE and ΔABC,

∠A = ∠A (Common angles)

∠ABE = ∠ABC (Corresponding angles are always equal)

By AA postulate of similarity of triangles, ΔABE ~ ΔABC.

Hence by area side proportionality theorem

$\frac{Ar(ADE)}{Ar(ABC)}=(\frac{DE}{BC})^2\\\\\implies \frac{1}{2}=\frac{DE^2}{36^2}\\\\\implies DE^2=\frac{36^2}{2}\\\\\bf\implies DE=18\sqrt{2}\textbf{ units}$

Hence, length of DE is 18√2 units

8 0

3 years ago