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write an equations in slope-intercept form of the line that passes through the point(5,9) with slope 7

vovangra [49]

Answer:

$y=7x-26$

Step-by-step explanation:

1) Write it in the slope-intercept form of $y=mx+b$ , where m is the slope and b is the y-intercept.

$y=7x +c$

2) Substitute the given coordinates into $y=7x +b$ , and then solve for c.

$9=7(5) +b\\9=35+b\\9-35=b\\b= -26$

3) Substitute c into $y=7x +b$

$y=7x-26$

Therefore, the answer is $y=7x-26$ .

6 0

2 years ago

Find function domain f(x) = sqrt( 2sin x - 1 )

vekshin1

Answer:

{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}

Step-by-step explanation:

sinx can run from -1 to +1

2sinx can run from -2 to +2

2sinx -1 can run from -3 to +1

However, the square root is imaginary when x < 0. So, the condition is

2sinx -1 ≥ 0

2sinx ≥ 1

sinx ≥ ½

x ≥ π/6 (30°)

So, in the interval [0, 2π], π/6 ≤ x ≤ 5π/6

However, the sine is a cyclic function and repeats itself every 2π.

Over all real numbers, the condition is (π/6 +2πn) ≤ x ≤ (5π/6 + 2πn).

The domain is then

{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}

5 0

3 years ago

The figure below shows a brick in the shape of a rectangular prism. 6 cm 8 cm 14 cm (a) Use the calculator to find the surface a

umka21 [38]

Answer:

The Total Surface Area = 2(84+48+112) = 2× 244

= 488 cm²

Step-by-step explanation:

Volume of brick = 8×14×6

= 672cm³

6 0

2 years ago

Simplify (1-cosΘ)(1+cosΘ) / (1-sinΘ)/(1+sinΘ)?

Vedmedyk [2.9K]

$\frac{(1-cosx)(1+cosx)}{(1-sinx)(1+sinx)} \\ \\ \frac{1-cos^2x}{1-sin^2x} \\ \\ \frac{sin^2x}{cos^2x} \\ \\ tan^2x$

3 0

4 years ago

Need some help with number word problems, tysm if you do :)

lord [1]

Answer:

Read below

Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

6x=y
x+y=42

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+3=y
4x-4=3y

A.

4+3=7

12-6≠21 (incorrect)

B.

7+3=10

28-3≠30 (incorrect)

C.

13+3=16

52-4=48 (correct)

D.

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+4=y
5x+3=4y

A.

13+4=17

65+3=68 (correct)

B.

-23+4= -19

-115+3≠ -76 (incorrect)

C.

17+4=21

85+3≠84 (incorrect)

D.

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

x+y=23
y-3x=3

A.

5+18=23

18-15=3 (correct)

B.

8+15=23

15-24≠3 (incorrect)

C.

-13+36=23

36+39≠3 (incorrect)

D.

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

x+y=26
y-2x=2

A.

8+18=26

18-16=2 (correct)

B.

9+17=26

17-18≠2 (incorrect)

C.

7+19=26

19-14≠2 (incorrect)

D.

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

4 0

4 years ago