what's the equation in point slope form of the line that passes through the point (3, 1) and has a slope of -2

Answer:

In order to determine the density of a solid , it is necessary to determine the mass and the volume

Step-by-step explanation:

Answer:

density of a solid?

Answer

Density of a solid

Mass/Volume

So (i) measure the mass, and (ii) measure the volume, and then take the quotient.

Of course, the mass is easy to measure. The volume is a little harder to assess, especially if it is an irregularly shaped solid, however, volume displacement of a liquid would be a quite feasible means.

Step-by-step explanation:

Density of salt is in the picture above please mark me brainliest

:)

Answer:

1. s = 19

2. 17

3. R

4. Angle bisector

5. 53°

Step-by-step explanation:

1. If VY is a midsegment of triangle WXZ, then by midsegment theorem,

[tex]VY=\dfrac{1}{2}WX.[/tex]

Since [tex]WX=s+55[/tex] and [tex]VY=s+18,[/tex] then

[tex]s+18=\dfrac{1}{2}(s+55)\\ \\2(s+18)=s+55\\ \\2s+36=s+55\\ \\2s-s=55-36\\ \\s=19[/tex]

2. A triangle has two sodes of length 18 and 2 units.

Let c units be the length of the third side. Then

[tex]18+c>2\\ \\2+c>18\\ \\2+18>c[/tex]

So,

[tex]c>-16\\ \\c>16\\ \\c<20[/tex]

Hence, [tex]16<c<20,[/tex] and the smallest possible whole-number length for the third side is 17 units.

3. In triangle QSR, the smallest angle is opposite to the smallest side. The smallest side is the side with length of 49 m, then the smallest angle is angle R.

4. Given ∠VYW≅∠WYX.

Definition of angle bisector: An angle bisector in a triangle is a line segment that bisects one of the vertex angles of a triangle.

Thus, YW is angle Y bisector.

5. Consider two right triangles ACD and ABC. In these triangles,

Then, by HL postulate, triangles ACD and ABC are congruent. Congruent triangles have congruent corresponding sides, then

∠ACD ≅ ∠ACB

and

m∠ACB = m∠ACD = 53°

Answer:

y-3=14/17(x-2)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(17-3)/(19-2)

m=14/17

y-y1=m(x-x1)

y-3=14/17(x-2)

Answer -

46.2/6 = 7.7

107.9/14 =7.7

it's show proportional relationship

a/b =K

k is proportionality constant

46.2/6 = 7.7 = K

Answer:

Charnessa has 4 times as many apples as Luke. Luke has -8 apples.

Hope this is what you were looking for :)

Answer:

81/16

Step-by-step explanation:

Answer:

9p

Explanation:

4p + 5p are like terms since they have the same variable p

All you have to do is add the numbers

(4+5)p = 9p

-x + 2y = -4

-x = -2y - 4

x = 2y + 4

5(2y + 4) - 4y = 8

10y + 20 - 4y = 8

6y + 20 = 8

6y = -18

y = -3

-x + 2y = -4

-x + 2(-3) = -4

-x - 6 = -4

-x = 2

x = -2

The coordinate pair is (-2, -3) (x = -2, y = -3.)

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Answer:

The net effect of amount in John account after 5 months is  $A - $200

Step-by-step explanation:

Given as :

The amount of money withdraws by John each month from his account = $40

Let The total amount of  money did John had in his account = $A

Let the amount left in John account after 5 months of withdraw = $x

So, According to question

∵ Each month the money withdraw from account = $40

∴ In 5 months , the money withdraw = $40 × 5

I.e In 5 months , the money withdraw = $200

So, The left money in account after withdraw in 5 months = $A - The amount withdraw in 5 months

I.e x = $A - $200

So, The balance in account after 5 months = x =  $A - $200

Hence, The net effect of amount in John account after 5 months is             $A - $200  Answer

Answer:

Step-by-step explanation:

The school store sells packs of 12 pens for $2.40.  

Select the three unit rates that describe this sale.

There is more than one correct answer

$0.20 per pen

$2.40 per pack of pens

5 pens per dollar

120 pens per $24

HOPE THIS HELPED ;3

Answer:

x=(3+sqrt(7)*i)/4, (3-sqrt(7)*i)/4.

Step-by-step explanation:

Apply the quadratic formula.

Answer:

[tex]x = \frac{3 +/- i \sqrt{7} }{4}[/tex]

Step-by-step explanation:

[tex]2x^{2} -3x + 2 = 0[/tex]

a =2 b = -3 c = 2. Substitute these into the quadratic formula [tex]x = \frac{-b +/- \sqrt{b^{2}- 4ac} }{2a}[/tex].

[tex]x = \frac{-(-3)+/- \sqrt{(-3)^{2} - 4(2*2)} }{2(2)}[/tex] Simplify.

[tex]x = \frac{3+/-\sqrt{(9)^{2} - 4(4) } }{4}[/tex] Keep simplifying...

[tex]x = \frac{3+/-\sqrt{9-16} }{4}[/tex] Simplify again...

[tex]x = \frac{3 +/-\sqrt{-7} }{4}[/tex] There will be an imaginary number because the number under the [tex]\sqrt{}[/tex] is negative, so

[tex]x = \frac{3+/-i\sqrt{7} }{4}[/tex]

Hey, I'd like to give you a professional response.

First we need to re-group terms.

1. 2(3+g)−g=−4(g+1)

Let's also expand the terms.

6+2g−g=−4g−4

Simplify 6+2g-g to 6 + g.

6+g=-4g-4

Add 4g to BOTH sides.

6+2g−g=−4g−4

Simplify 6+g+4g to 6+5g.

6+5g=-4

Now subtract 6 from both sides.

5g = -4-6

Simplify -4 - 6 to -10.

Now you have 5g = -10.

g = -10/5 (Divide both sides by 5)

Simplify -10/5 to 2.

G = 2

Let's check our answer.

First let g = 2.

2+2 X (3-2) = -4 X (-2 + 1)

2 + 2 X 1 = -4 X (-2 +1)

2 + 2 X 1 = -4 x -1

2+2 = -(-4)

Remove the parentheses,

4 = 4 This problem has been checked.

Answer:

OPTION D: NEITHER

Step-by-step explanation:

The given equation is: 7x - 2y = - 5

To find a solution to this, we substitute the options and compare LHS and RHS.

OPTION A: (1, 5)

LHS = 7(1) - 2(5) = 7 - 10 = -3

RHS = - 5

LHS [tex]$ \ne $[/tex] RHS.

So, this option is eliminated.

OPTION B: (-1, 1)

LHS = 7(-1) - 2(1) = -7 - 2 = - 9

RHS = - 5

Again, LHS [tex]$ \ne $[/tex] RHS.

So, this Option is eliminated as well.

OPTION C: It says both A and B. Clearly, this is eliminated as well.

Therefore, the answer is: OPTION D: NEITHER.

NOTE: This is a two variable equation. So, we need a minimum of two equations to determine the solution. Since, only one equation is given here, we use the help of options.

Answer:

Part 1) The length of the apothem is 13.32'

Part 2) The perimeter of the decagon is 86.5'

Step-by-step explanation:

we know that        

A regular decagon has 10 equal sides and 10 equal interior angles

A regular decagon can be divided into 10 congruent isosceles triangle

(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)  

 The vertex angle of each isosceles triangle is equal to

[tex]\frac{360^o}{10}=36^o[/tex]

To find out the side length of the decagon, we can use the law of cosines

so

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

c is the length side of decagon

a and b are the radii

we have

[tex]a=14'\\b=14'\\C=36^o[/tex]

substitute the values

[tex]c^2=14^2+14^2-2(14)(14)cos(36^o)[/tex]

[tex]c^2=392-(392)cos(36^o)[/tex]

[tex]c^2=392-(392)cos(36^o)[/tex]

[tex]c=8.65'[/tex]

To fin out the perimeter of decagon multiply the length side by 10

so

[tex]P=8.65(10)=86.5'[/tex]

To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle

see the attached figure to better understand the problem

[tex]r^2=a^2+(c/2)^2[/tex]

substitute the given values

[tex]14^2=a^2+(8.65/2)^2[/tex]

solve for a

[tex]a^2=14^2-(8.65/2)^2[/tex]

[tex]a=13.32'[/tex]

Answer:

The correct answer is A. Debit Revenue and Credit Income Summary

Step-by-step explanation:

Let's recall that at the end of the accounting year, closing entries transfer the balances from the temporary accounts to a permanent account with the purpose that those temporary accounts will begin the next accounting year with zero balances.

However, an intermediate account called Income summary is created and used in the closing stage of the accounting year to register all income and expense balances and determine the net result for the period (income or loss).

Upon saying that, usually revenue accounts have a credit balance.  To make it zero we want to decrease the balance.  We will debit the revenue account and credit the Income Summary account.  This credit to income summary should be exactly the total revenue from the income statement.

The correct answer is A. Debit Revenue and Credit Income Summary

Answer:

Step-by-step explanation:

During the closing process, which of the following would likely occur?

Question options:

Debit Revenue and Credit Income Summary

Answer:

Step-by-step explanation:

This kinda looks like the limiting definition of a derivative.  

Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x.  That looks like this:

f(2 + h) = 2(2 + h) - 3 which simplifies to

f(2 + h) = 4 + 2h - 3 which simplifies to

2h + 1

From that we are subtracting f(2).  What we are doing with that is evaluating f(x) with 2 in place for x.  That looks like this:

f(2) = 2(2) - 3 which simplifies to

f(2) = 4 - 3 which simplifies to

f(2) = 1.  Now put those together over h to get:

[tex]\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2[/tex]

Option B

12 over quantity x minus 7, x ≠ 7, x ≠ −3

Solution:

Given that we have to simplify quantity 12 x plus 36 over quantity x squared minus 4 x minus 21

So we have to simplify,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 }[/tex]

We have to find the restrictions on the variable

The above given Rational function is defined, for

[tex]{x}^{2} - 4x - 21\ne0\\\\(x+3)(x-7)\ne0\\\\x\ne -3,x\ne7[/tex]

In order to simplify the above expression, we need to factor both the numerator and the denominator

[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 4x - 21}[/tex]

For the denominator, we need to split the middle term of the quadratic to get factored form,

[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 7x + 3x- 21}[/tex]

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ x(x - 7) + 3(x- 7)}[/tex]

Fcatoring the denominator part,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ (x + 3)(x - 7)}[/tex]

Cancel out common factors to get,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12}{x - 7} \\\\where\\\\x\ne -3,x\ne7[/tex]

Thus option B is correct. 12 over quantity x minus 7, x ≠ 7, x ≠ −3

The simplified expression is 12 / (x - 7) with restrictions x ≠ 7, x ≠ -3. The correct answer is option b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3.

The expression((12x + 36) / (x² - 4x - 21)) and finding the restrictions on the variable.

First, we factor both the numerator and the denominator.

The numerator can be factored as 12(x + 3).

The denominator can be factored by finding two numbers that multiply to -21 and add to -4, which are -7 and 3.

Thus, the denominator factors to (x - 7)(x + 3). Our expression then simplifies to (12 / (x - 7)), after cancelling out the (x + 3) terms.

To find the restrictions on the variable, we note that the original denominator, (x² - 4x - 21), cannot be zero, as division by zero is undefined.

Setting (x - 7)(x + 3) to zero gives us the restrictions x ≠ 7 and x ≠ -3, to ensure the denominator is not zero.

Therefore, the simplified expression is 12 / (x - 7), with the restrictions x ≠ 7, x ≠ -3.

Answer:

[tex]15x\geq 105[/tex]

Step-by-step explanation:

Hence, the inequality represents how long Johnny needs to work to afford his new bike is

[tex]15x\geq 105[/tex]

What is the inequality?

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Here given that,

Johny earns $[tex]15[/tex] per hour dog walking. So, he wants to earn at least $[tex]105[/tex] to buy a new bike.

So, the inequality is

[tex]15x\geq 105[/tex]

Hence, the inequality represents how long Johnny needs to work to afford his new bike is

[tex]15x\geq 105[/tex]

To know more about the inequality

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Answer:

4.9%

Step-by-step explanation:

To find the percentage you first find the decrease in price, divide it by the original price then multiply it by 100.

(14. 44-13. 72)

= -------------------- ×100

14. 44

0. 72

= -------- × 100

14. 44

= 0. 72× 6. 925207759

= 4. 986149584

~ 4. 9

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

[tex]4x-5y=3[/tex]

[tex]3x+5y=13[/tex]

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]3x+5y=13[/tex][tex]......[2][/tex]

Adding Equation 1 and Equation 2

[tex]4x-5y+3x+5y=3+13[/tex]

[tex]7x=16[/tex]

[tex]x=[/tex][tex]\frac{16}{7}[/tex]

Putting [tex]x=[/tex][tex]\frac{16}{7}[/tex] in Equation [1]

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]y=[/tex][tex]\frac{43}{35}[/tex]

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]3x+5y=13[/tex][tex]......[2][/tex]

Solving the equation 2 for x variable

[tex]3x=13-5y[/tex]

[tex]x=\frac{13-5y}{3}[/tex]

Plugging [tex]x=\frac{13-5y}{3}[/tex] in equation [1]

[tex]4(\frac{13-5y}{3}) -5y=3[/tex]

[tex]y = \frac{43}{35}[/tex]

Putting [tex]y = \frac{43}{35}[/tex] in Equation 2

[tex]3x+5y=13[/tex][tex]......[2][/tex]

[tex]x = \frac{16}{7}[/tex]

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

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The substitution and graphing methods are less efficient methods than elimination method for this system as there is extra amount of steps we have to take to solve the same system of equations 4x-5y=3  , 3x+5y=13

We have equations

4x-5y=3  ... (1)

3x+5y=13 ...(2)

Substituting the value of 5y = 13-3x from equation (2) into equation(1)

4x-(13-3x)=3

4x-13+3x=3

7x= 3+13

7x= 16

x = [tex]\frac{16}{7}[/tex]

Substitute the value of x = [tex]\frac{16}{7}[/tex] in y value, we get

[tex]5y=13-3(\frac{16}{7} )\\y=\frac{43}{35}[/tex]

4x-5y=3

3x+5y=13

Adding both the equations, we get

[tex]7x=16\\x=\frac{16}{7}[/tex]

Put the value of x in any one of the above equation, we get

[tex]3\frac{16}{7} +5y=13\\y=\frac{43}{35}[/tex]

So, the Elimination method is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation and it is less time consuming.

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Answer:

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-4)/(-2-10)

m=-9/-12

m=9/12

m=3/4

------------------------

m=(y2-y1)/(x2-x1)

m=(8-1)/(7-(-7))

m=7/(7+7)

m=7/14

m=1/2

-------------------------

m=(y2-y1)/(x2-x1)

m=(3-1)/(2-1)

m=2/1

m=2

Final answer:

The slope of a line between two points is found using the formula slope (m) = (y2 - y1) / (x2 - x1), with an example given for points A (10,4) and B (-2,-5), resulting in a slope of 3/4.

Explanation:

The slope of a line passing through two points (A and B) can be determined using the formula slope

(m) = (y2 - y1) / (x2 - x1).

This formula calculates the rate of change in the y-values with respect to the x-values, resulting in a description of the steepness of the line.

For example, let's find the slope for points A (10,4) and B (-2,-5). Applying the formula, we have:

m = (y2 - y1) / (x2 - x1) = (-5 - 4) / (-2 - 10) = (-9) / (-12) = 3/4

The slope between points A and B is 3/4. This process can be repeated for other pairs of points to find the respective slopes.

Answer:

Circumference is 12.56 km

Explanation:

C = 2πr (with radius)

C = 2(3.14)(2)

C = 12.56 km

The circumference of a circle with a radius of 2 km is calculated using the formula C = 2πr. Using π ≈ 3.14159, the circumference is approximately 12.57 km.

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. Given the radius (r) of 2 km, we can substitute this value into the formula to find the circumference:

C = 2π(2 km)
C = 4π km
By using the approximation π ≈ 3.14159, we can calculate the circumference as:

C = 4 × 3.14159 km
C ≈ 12.56636 km

Therefore, the circumference of the circle is approximately 12.57 kilometers.

Answer:

5x^2-6x-10

Step-by-step explanation:

(2x^2-2x)-(-3x^2+4x+10)

2x^2-2x+3x^2-4x-10

5x^2-2x-4x-10

5x^2-6x-10

Answer: 14 cakes

Step-by-step explanation:

We have the following data:

Number of gallons the baker has: [tex]4 gallons \frac{16 cups}{1 gallon}=64 cups[/tex]

Number of cups the baker used for one cake: [tex]4,5 cups[/tex]

Now, we can use the Rule of three  to find the maximum number of cakes the baker can completely decorate:

[tex]4.5 cups[/tex]-----​[tex]1 cake[/tex]

[tex]64 cups[/tex]-----​[tex]?[/tex]

Then:

​[tex]?=\frac{(64 cups)(1 cake)}{4.5 cups}[/tex]

​[tex]?=14,2 cakes \approx 14 cakes[/tex]

Answer:

Step-by-step explanation:

line l

Answer:

The “blank” is 4

Step-by-step explanation:

4 1/4= 16/x+ 1/4

We want to get rid of the 1/4. So we subtract it from both sides and get

4= 16/x

We know that if we put 16 divided by 4, you get 4.

This gives you 4= 16/4.

This is your final answer.

Area of the rectangle: 14.5 x 22 = 319 square meters.

Area the goat can reach ( area of a circle): 3.14 x 2.5^2 = 19.625 square meters.

Now subtract the area of the circle from the area of the rectangle:

319 - 19.625 = 299.375 square meters.  (Round the answer as needed.)

Option A and Option B

The equivalent expressions for 24k + 36q - 12 are 12(2k + 3q - 1) and 3(8k + 12q - 4)

Solution:

Given that we have to factor 24k + 36q - 12

To factor a number or expression containing variables means to break it up into smaller numbers or expressions that can be multiplied together to get the original number or expression

Given expression is:

24k + 36q - 12

So for numbers 24 , 36 and 12: the factors that divides all these numbers 24, 36 and 12 completely are 12 and 3 and also 2

In the above expression we take 12 common term

12(2k + 3q - 1)

So option A is correct

We can also take out 3 as common term

3(8k + 12q - 4)

So option B is also correct

Thus the equivalent expressions are: 12(2k + 3q - 1) and 3(8k + 12q - 4)

Answer:

Sample Response: George did not put parentheses around the total snack amount to be subtracted from his $15. He needed to total the purchases and then subtract that amount from $15.

Step-by-step explanation: