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3 years ago

Find the point at which the line f(x)=2x+10 intersects the line g(x)=−3x−5 .

Mathematics

1 answer:

k0ka [10]3 years ago

8 0

9514 1404 393

Answer:

(x, y) = (-3, 4)

Step-by-step explanation:

A graphing calculator answers this question quickly. The point of intersection is (-3, 4).

The lines intersect where f(x) = g(x).

2x +10 = -3x -5

5x = -15 . . . . . . . . add 3x-10

x = -3 . . . . . . divide by 5

f(-3) = 2(-3) +10 = 4 . . . . . find the y-coordinate

The point is (-3, 4).

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If it takes earth 24 hours to complete a full rotation it takes saturn approximately 10 hours, 39 minutes and 24 seconds to comp

Igoryamba

The correct answer is:

639.4 minutes.

Explanation:

Saturn takes 10 hours, 39 minutes and 24 seconds to make a complete rotation.

10 hours × 60 minutes per hour = 600 minutes.

600 minutes + 39 minutes = 639 minutes.

24 seconds out of 60 seconds per minute = 24/60 = 0.4.

This gives us 639+0.4 = 639.4 minutes.

8 0

3 years ago

Divide 28 cans into 2 groups so the ratio is 3 to 4

zysi [14]

$\bf \cfrac{\textit{first group}}{\textit{second group}}\qquad 3:4\qquad \cfrac{3}{4}\implies \cfrac{3\cdot \frac{28}{3+4}}{4\cdot \frac{28}{3+4}}\implies \cfrac{3\cdot \frac{28}{7}}{4\cdot \frac{28}{7}}\implies \cfrac{12}{16}$

7 0

3 years ago

2 The following functions are equivalent.

uysha [10]

2x2 − 12x + 21. Axis of symmetry. 2.

8 0

3 years ago

It is known that 2.2< sq root 5 <2.3. Find all possible values of the expression: a sq root 5 +2 3- sq root 5 It is known

NISA [10]

Answer:

4.2 < sq. 5< 4.3

Step-by-step explanation:

since square root of 5 was +2 you just add +2 to both sides and you will get your answer, however it is different with different operations.

5 0

3 years ago

Write the equation of the line that passes through

Gnom [1K]

Answer:

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 2) and (6, 3):

$m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}$

Therefore, the slope of the line is $\frac{\displaystyle 1}{\displaystyle 7}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

Plug in one of the given points and solve for b:

$2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b$

Add $\frac{\displaystyle 1}{\displaystyle 7}$ to both sides to isolate b:

$2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b$

Therefore, the y-intercept of the line is $\frac{\displaystyle15}{\displaystyle 7}$ . Plug this back into $y=\frac{\displaystyle 1}{\displaystyle 7}x+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

I hope this helps!

3 0

3 years ago