what is the distance between the points 4,10 and -3,-14 on the coordinate plane

Answer:

A. y - 7 = -4(x + 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. In addition, I recall that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes], so -4 really should be replaced with ¼, but if your assignment says otherwise, then this is the answer.

To find the equation of a line perpendicular to y=-4x -1 that passes through (-2, 7), we take the negative reciprocal of -4 to find the slope of the perpendicular line. Plugging in the values (-2, 7) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).

To find the equation of a line perpendicular to a given line, we need to determine the slope of the perpendicular line. The given equation is in the form y = mx + b, where m represents the slope. The slope of the given line is -4. To find the slope of the perpendicular line, we take the negative reciprocal of -4, which is 1/4. Now that we have the slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Plugging in the values (-2, 7) for (x1, y1) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).

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Answer:

[tex]4\pi[/tex] or 12.56

Step-by-step explanation:

[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.

if we plug '2' in... [tex]\pi2^{2}[/tex]

which equals to [tex]4\pi[/tex]

if we multiply 4 with pi, it equals to 12.56

Answer:

Area of circle = 12.56 sq. units

Step-by-step explanation:

radius =  2

Area of circle = π r² sq. units

                       = 3.14 * 2 * 2 = 12.56 sq. units

Answer:

−27x2

Step-by-step explanation:

It's -27x to the second power so the small 2 at the end

Answer:

The complete factorization is 3x² (x - 5)² ⇒ 2nd answer

Step-by-step explanation:

* Lets revise how to factorize a trinomial

- Find the greatest common factor of the coefficients of the three terms

∵ The trinomial is 3x^4 - 30x³ + 75x²

- The greatest common factor of 3 , 30 , 75 is 3

∵ 3 ÷ 3 = 1

∵ 30 ÷ 3 = 10

∵ 75 ÷ 3 = 25

∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)

- Now lets find the greatest common factor of the variable x

∵ x² is the greatest common factor of the three terms

∵ x^4 ÷ x² = x²

∵ 10x³ ÷ x² = 10x

∵ 25x² ÷ x² = 25

∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)

- Lets factorize (x² - 10x + 25)

∵ √x² = x

∵ √25 = 5

∵ 2 × 5 × x = 10x

∴ x² - 10x + 25 is a completing square

∴ (x² - 10x + 25) = (x - 5)²

∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²

* The complete factorization is 3x² (x - 5)²

Answer:

3x^2 (x-5)^2

Step-by-step explanation:

3x^4 − 30x^3 + 75x^2

We can factor out a 3x^2 from each term

3x^2 (x^2 -10x +25)

The term inside the parentheses can be factored

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

3x^2 (x-5) (x-5)

3x^2 (x-5)^2

Answer:

f(1) = 24

Step-by-step explanation:

f(1) is the value of f(x) when x = 1, that is from the table

f(1) = 24

Answer:

4√7/5

Step-by-step explanation:

3×√7/5-√28/5+√63/5

3√7/5-2√7/5+3√7/5

4√7/5

The simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].

System of equations is a finite set of equations for which common solutions are sought.

We have,

[tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex]

Now,

Take LCM, of the given fraction,

We get,

[tex]\frac{3\sqrt{7} -\sqrt{28}+\sqrt{63}}{25}[/tex]

Now,

Simplify by rewriting every number in numerator in form of [tex]\sqrt{7}[/tex],

i.e.

[tex]\frac{3\sqrt{7} -\sqrt{4*7}+\sqrt{9*7}}{25}[/tex]

Now,

[tex]\frac{3\sqrt{7} -2\sqrt{7}+3\sqrt{7}}{25}[/tex]

Now,

Every digit is in the form of  [tex]\sqrt{7}[/tex],

So,

Simplify,

We get,

[tex]=\frac{4\sqrt{7}}{25}[/tex]

So,

This is the simplified form of the given equation.

Hence, we can say that the simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].

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Answer:

consistent  

Solution at (3,2)

Step-by-step explanation:

A consistent and independent solution to a system of linear equations is one point

A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)

An inconsistent solution is where there is no solution, the lines do not cross

Since the lines cross at exactly one point, this is a consistent and dependent solution

The solution is at x = 3  ( 3 units to the right of the origin)

and y = 2 ( 2 units up from the origin)

(3,2)

Answer:

Consistent :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

f(0) - f(-3) = area under f'(x) from x=0 to x=3.

We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.

A = 1/2 b h

A = 1/2 (3) (3)

A = 4.5

f(0) - f(-3) = 4.5

Since f(0) = 7:

7 - f(-3) = 4.5

f(-3) = 7 - 4.5

f(-3) = 2.5

Answer:

Step-by-step explanation: I believe you would just take 147 + 224 + 175 + 273 = 819pi cm2

So your answer would be 819pi cm2

The answer is 224 pi

.....................................

Answer:

$6240

Step-by-step explanation:

Find the rate by dividing property tax by the appraisal value.

[tex]\frac{3840}{160000}=0.024[/tex]

Now multiply the appraised value by this rate to find the property tax.

[tex]260000*0.024=6240[/tex]

The property tax on a home appraised at $260,000 is $6,240.

To find the property tax on a home appraised at $260,000, we can set up a proportion using the given information. The property tax on a $160,000 home is $3,840, so we have:

$160,000 : $3,840 = $260,000 : x

Using cross-multiplication, we can solve for x:

x = ($260,000 * $3,840) / $160,000

Calculating this, we find that the property tax on a home appraised at $260,000 is $6,240.

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Answer:

Option B is correct.

Step-by-step explanation:

A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.

Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship

a)

9/3 = 3

12/4 = 3

20/5 = 4

b)

25/20 = 5/4

30/24 = 5/4

40/32 = 5/4

c)

12/4 = 3

15/5 = 3

24/6 = 4

d)

4/3 = 4/3

9/6 = 3/2

12/16 = 3/4

So, Option B is correct.

Answer: Second Option

Step-by-step explanation:

It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.

That is, a and b are proportional if the quotient between b and a is always equal to a constant k.

[tex]\frac{b}{a}=k[/tex]

To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant

You can verify that the table where the quotient of b enters a is always constant is in the second table

[tex]\frac{b}{a}=\frac{5}{4}[/tex]

Answer:

(2.4 , -1)

Step-by-step explanation:

Too many commas in second ordered pair but this is how I will interpret the question:

Find the midpoint of (3.2,2.5) and (1.6,-4.5)

So just average x's  : (3.2+1.6)/2 =4.8/2=2.4

And

    just average y's : (2.5+-4.5)/2=-2/2=-1

The midpoint is (average x's , average y's)

Your midpoint is (2.4             ,     -1             )

answer (2.4 , -1)

Final answer:

The student missed the conversion from minutes to hours. The correct conversion is 26 hours × 60 minutes/hour × 60 seconds/minute, which equals 93,600 seconds.

Explanation:

Identifying the Missed Conversion Step

The student was attempting to convert 26 hours into seconds but arrived at an incorrect result of 1560 seconds. The error occurred because the student skipped the correct conversion ratio between minutes and hours. For such conversions, it is essential to use the correct conversion factors: 60 minutes per hour and 60 seconds per minute.

Correct Conversion Process

To convert 26 hours to seconds:

First, convert hours to minutes: 26 hours × 60 minutes/hour = 1560 minutes.

Then, convert minutes to seconds: 1560 minutes × 60 seconds/minute = 93,600 seconds.

Therefore, the correct number of seconds in 26 hours is 93,600 seconds.

Complementary means they add to 90°

f=90-g

f=4g

4g =90-g

5g=90

g=18

f=4g=4(18)=72

Answer: f=72°, g=18°

Answer:

B

Step-by-step explanation:

Noting the following rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

Given

([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )

Each term in the second factor is multiplied by each term in the first factor

= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis

= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]

Answer:

A

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1

= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms

= - 2x² - 8x + 12 → A

Answer:

[tex]\large\boxed{x=-\dfrac{2}{3}\ or\ x=1}[/tex]

Step-by-step explanation:

[tex]3x^2-x-2=0\\\\3x^2+2x-3x-2=0\\\\x(3x+2)-1(3x+2)=0\\\\(3x+2)(x-1)=0\iff3x+2=0\ \vee\ x-1=0\\\\3x+2=0\qquad\text{subtract 2 from both sides}\\3x=-2\qquad\text{divide both sides by 3}\\x=-\dfrac{2}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

Answer:

The length of the shorter piece is  13 inches

Step-by-step explanation:

Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.

Since the pipe is going to be the length of  L and S together, we can make this equation:

L+S=52

Also we know that the longer piece is three times the shorter piece or

L=3S

Substitute the second equation into the first equation.

L+S=52

3S+S=52

4S=52

Divide both sides by 4

4S/4=52/4

S=13 inches

The length of the shorter piece is 13 inches....

To find the length of longer piece, put the value S=13 in L=3S

L=3S

L=3(13)

L=39 inches

The length of the longer piece is 39 inches....

Kasey has $53.63 withheld from her weekly paycheck of $865 for Social Security, which is calculated by multiplying her weekly pay by the Social Security tax rate of 6.2%.

The question asks us to calculate how much is withheld from Kasey's paycheck for Social Security.

With a weekly pay of $865, we need to find 6.2% of that amount since that is the percentage deducted for Social Security taxes.

To find this amount, we multiply $865 by 0.062.

Calculation: $865 × 0.062 = $53.63

Therefore, $53.63 is withheld from Kasey's paycheck each week for Social Security.

Answer:

336

Step-by-step explanation:

Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !

where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1

8[tex]P_{3}[/tex]

= 8 ! / (8 - 3) !

= 8 ! / 5 !

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]

[ cancel 5(4)(3)(2)(1) on numerator/denominator

= 8 × 7 × 6 = 336

ANSWER

[tex]^8P_3 = 336[/tex]

EXPLANATION

Recall that;

[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]

The given expression is:

[tex]^8P_3[/tex]

We substitute n=8 and r=3

[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]

[tex]^8P_3 =\frac{8!}{(5)!} [/tex]

This simplifies to :

[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]

We cancel out the common factors to get:

[tex]^8P_3 = 8 \times 7 \times 6[/tex]

[tex]^8P_3 = 336[/tex]

Answer:

√113

or

10.6301458127

Step-by-step explanation:

Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order

d = √(x2 - x1)^2 + (y2 - y1)^2

The number next to the number does NOT mean multiply it mean like this

(x2, y2)  and (x1, y1) so you would plug them in like this:

d = √(-6 - 2)^2 + (4 - (-3))^2

d = √(-8)^2 + (7)^2

d = √(64 + 49

d = √113

or 10.6301458127

Answer with Step-by-step explanation:

The distance(d) between the points (a,b) and (c,d) is given by:

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here, we have to find distance between (2,-3) and (-6,4)

(a,b)=(2,-3) and (c,d)=(-6,4)

[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]

[tex]d=\sqrt{8^2+7^2}[/tex]

[tex]d=\sqrt{64+49}[/tex]

[tex]d=\sqrt{113}[/tex]

Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:

[tex]\sqrt{113}[/tex]

Answer:

f(5) = 17

Step-by-step explanation:

f(x) = 3x+2

Let x =5

f(5) = 3(5) +2

f(5) = 15+2

f(5) = 17

For this case we have the following equation:

[tex]3 (b + 4) + 8 = -3[/tex]

If we apply distributive property to the terms within the parenthesis we have:

[tex]3b + 12 + 8 = -3[/tex]

We add similar terms to the left side of the equation:

[tex]3b + 20 = -3[/tex]

Subtracting 20 from both sides of the equation:

[tex]3b = -3-20\\3b = -23[/tex]

Dividing between 3 on both sides of the equation:

[tex]b = - \frac {23} {3}[/tex]

In mixed number we have:

[tex]b = -7 \frac {2} {3}[/tex]

Answer:

[tex]b = -7 \frac {2} {3}[/tex]

Answer:

x = -2 or x = -3/2 thus B. & D. are the answer  

Step-by-step explanation:

Solve for x:

2 x^2 + 7 x + 6 = 0

Hint: | Factor the left hand side.

The left hand side factors into a product with two terms:

(x + 2) (2 x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x + 2 = 0 or 2 x + 3 = 0

Hint: | Look at the first equation: Solve for x.

Subtract 2 from both sides:

x = -2 or 2 x + 3 = 0

Hint: | Look at the second equation: Isolate terms with x to the left hand side.

Subtract 3 from both sides:

x = -2 or 2 x = -3

Hint: | Solve for x.

Divide both sides by 2:

Answer:  x = -2 or x = -3/2

Answer:

B and D

Step-by-step explanation:

Given

2x² + 7x + 6 = 0

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 6 = 12 and sum = + 7

The factors are + 4 and + 3

Use these factors to split the x- term

2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 → x = - 2 → D

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B

Answer:

x = 8

Step-by-step explanation:

Using the rule of logarithms

log x = log y ⇔ x = y

Given

log(3x + 2) = log(4x - 6), then

4x - 6 = 3x + 2 ( subtract 3x from both sides )

x - 6 = 2 ( add 6 to both sides )

x = 8

Answer:

Step-by-step explanation:

−7−4p+5

−4p+(−7+5)

Ans  

−4p−2

your answer is: -4p - 2

Explanation:

first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.

there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2

(this isn't the normal way of solving this, but I did my own way and got the same answer)

Answer:

In the photos

Step-by-step explanation:

First, create your trees (following instructions on the photo you attached). Then, circle the prime numbers in each tree you made. If the prime number shows up once put that number once on your prime factorization. If the prime number appears multiple times, put the number down and have an exponent (the exponent is determined by how many times that number appears).

Hope this helps a bit,

Flips

Answer:

Step-by-step explanation:

it's -2

The percentage change of 134 to 106 will be -20.89% .

Given ,

Number changed from 134 to 106 .

Now,

Here initially the number was = 134

After reduction the number was = 106

Percentage change = final - initial / initial * 100

Final number = 106

Initial number = 134

so,

Percentage change = 106 -134/134 * 100

Percentage change = -28/134 *100

Percentage change = -20.89%

Thus the percentage change is -20 .89% and the negative sign shows the declining nature of number .

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[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]

Answer:

A. The answer is our unit prices when our profit is 0

Step-by-step explanation:

The zeros are the x-intercepts, when the curve passes through the x-axis.

I'm going to call our function P

P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)

The answer is our unit prices when our profit is 0

The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.

The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.

The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.

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