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Given:

The equation of a line is

[tex]y=-\dfrac{2}{3}x+2[/tex]          ...(i)

The perpendicular line passes through the point (-1,4).

To find:

The equation of the perpendicular line.

Solution:

The slope intercept form of a line is:

[tex]y=mx+b[/tex]            ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

[tex]m=-\dfrac{2}{3}[/tex]

Product of slopes of two perpendicular lines is -1.

Let the slope of perpendicular line is [tex]m_1[/tex].

[tex]m\times m_1=-1[/tex]

[tex]-\dfrac{2}{3}\times m_1=-1[/tex]

[tex]m_1=\dfrac{3}{2}[/tex]

The slope of the perpendicular line is [tex]m_1=\dfrac{3}{2}[/tex] and it passes through the point (-1,4). So, the equation of the line is:

[tex]y-y_1=m_1(x-x_1)[/tex]

[tex]y-4=\dfrac{3}{2}(x-(-1))[/tex]

[tex]y-4=\dfrac{3}{2}(x+1)[/tex]

[tex]y-4=\dfrac{3}{2}x+\dfrac{3}{2}[/tex]

Add 4 on both sides.

[tex]y-4+4=\dfrac{3}{2}x+\dfrac{3}{2}+4[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{3+8}{2}[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex]

Therefore, the equation of required line is [tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex].

Answer:

the answer should be 24ft

Step-by-step explanation:

Answer:

24 ft

Step-by-step explanation:

1/2hb

4=h

12=b

plug in

1/2(4)(12)= 24

Answer:

Not sure what you're asking but 120.4 is

one hundred

two tens

and four tenths

Answer:

one jar of pickles is $1.50, 49-47.50 =1.50

Step-by-step explanation:

Answer: 5(2x+13)

Step-by-step explanation: Hope this was helpful....

Answer:113

Step-by-step explanation:

Answer:

ty should save $62.50 a month to meet his goal

To write slope intercept form from 2 numbers, you take the 3 and covert it to 3/1, or rise/run form. Then you find the y-intercept. Now listen, this is very complicated. Ready? It's the y-coordinate. 10. Veery complicated.

So y=3/1+10

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hope it helps

Answer:

i think its the third section choice

Step-by-step explanation:

P = L × B

54 = L × 7

54 = 7L

Therefore, L = 54 ÷ 7

L = 7.71

Answer:

130°

Step-by-step explanation:

20° + 30° =50°

a triangles full angle is 180°

180° - 50° = 130°

Answer:

54x ²+21x-20

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

please mark me as brainliest

Answer:

Yes, No, No, No

Step-by-step explanation:

To decide whether the point lies on the circle, what you need to do it simply substituting the x and y values into the equation and check if it add up to be 25

(-5)² + 0² = 25, = RHS  [Yes]

1² + (√7)² = 8, ≠ RHS [No]

(√21)² + (-3)² = 30, ≠RHS [No]

0² + 7² = 49, ≠RHS [No]

Answer: 33

If you put all the numbers In order from least to greatest and find the middle number you'll get the answer

Answer:

-3x - 6

Step-by-step explanation:

x - (4x + 6) becomes x - 4x - 6 after we've distributed the multiplication.

We can simplify this result as follows:  -3x - 6

Answer:

1. Exponential

2. Linear

Step-by-step explanation:

1. Exponential

Principal = 15000

Rate, r = 6.5% compounded annually

A = P(1 + r)^t

A = 15000(1 + 0.065)^t

A = 15000(1.065)^t

2. Linear

Let initial amount in bank = x

Amount added per week = 2

Number of weeks or period = t

A = x + 2t

Answer:

[tex]\mathbf{\dfrac{2b- 1}{2b}}[/tex]

Step-by-step explanation:

[tex]\text{The given equation is:}[/tex]

[tex]\dfrac{a}{b}+ (\dfrac{1}{4} \times \dfrac{1}{b}) = \dfrac{1}{2}[/tex]

[tex]\text{To find:}[/tex]

[tex]\dfrac{1}{2} } \div {\dfrac{a}{b} }[/tex]

[tex]\text{From the given equation:}[/tex]

[tex]\dfrac{a}{b}+ (\dfrac{1}{4b}) = \dfrac{1}{2}[/tex]

[tex]\dfrac{a}{b} = \dfrac{1}{2} - (\dfrac{1}{4b})[/tex]

[tex]\dfrac{a}{b} = \dfrac{4b- 2}{(2) (4b)}[/tex]

[tex]\dfrac{a}{b} = \dfrac{4b- 2}{8b}[/tex]

[tex]\text{Now; the value of}[/tex] [tex]\dfrac{a}{b} \div \dfrac{1}{2}[/tex]

∴

[tex]\implies \dfrac{4b- 2}{8b} \div \dfrac{1}{2}[/tex]

[tex]\implies \dfrac{4b- 2}{8b} \times \dfrac{2}{1}[/tex]

[tex]\implies \dfrac{4b- 2}{4b}[/tex]

[tex]\implies \dfrac{2b- 1}{2b}[/tex]

Answer:

pi = V - r^2

Step-by-step explanation:

subtract r^2 from both sides !!!

Answer:

The standard error between the sample mean is approximately 0.3412

Step-by-step explanation:

The equation for the standard error of a difference in sample mean of equal sample sizes is given as follows;

[tex]SE(\overline x_1 - \overline x_2)={\sqrt{\dfrac{s_{1}^{2} }{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]

The given parameters are;

The number of sample of southern grass cicadas, n₁ = 20

The mean body length of the southern grass cicadas, [tex]\overline x _1[/tex] = 16.22 mm

The standard deviation, s₁ = 1.34 mm

The number of sample of citrus cicadas, n₂ = 20

The mean body length of the citrus cicadas, [tex]\overline x _2[/tex] = 13.41 mm

The standard deviation, s₂ = 0.73 mm

[tex]SE(16.22 - 13.41)={\sqrt{\dfrac{1.34^{2} }{20}+\dfrac{0.73^{2}}{20}}} \approx 0.3412[/tex]

The standard error between the sample mean, SE ≈ 0.3412

Answer:

use math papa

Step-by-step explanation:

Answer:

the answer is A because thats the answer

Answer: The answer I got was D) 31

Step-by-step explanation:

Hope this helps!!!!!

Answer:

B. 15x-35

Step-by-step explanation:

multiply 5 by both 3x and -7

5(3x-7)

5(3x) 5(-7)

15x-35

Answer:

your answer will be option B

Step-by-step explanation:

hope it helps

Answer:

6

Step-by-step explanation:

OOO OOO = 6

Answer:

the second one

Step-by-step explanation:

the y cannot be inside of the parenthesis  

Answer: A

Step-by-step explanation: In all of the other equations your including y in the multiplication, BUT it is supposed be added

Answer:

It is x=7.

Step-by-step explanation:

(7)+8=15 You can subtract and you can get 7!!!

Answer:

X = 7

Step-by-step explanation:

If we take the equation

x + 8 = 15

and then subtract 8 on both sides we get

x = 7

so therefore x is 7 to make the value true.

Answer:

38.70

Step-by-step explanation:

if you divide it it u can get the answers.

40÷15.48