Write the point-slope form of the equation for a line that passes through (6, -1) with a slope of 2

Answer:

x = 42/31, y = -37/62

Step-by-step explanation:

5x + 8y =2

4x -6y =9

Multiply the first equation by 4

4(5x + 8y) =2*4

20x +32y = 8

Multiply this equation by -5

-5(4x -6y) =9*-5

-20x +30y = -45

Add them together

20x +32y = 8

-20x +30y = -45

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

62y = -37

Divide by 62

62y/62 = -37/62

Multiply the first equation by 3

3(5x + 8y) =2*3

15x +24y =6

And the second equation by 4

4(4x -6y) =9*4

16x -24y = 36

Add them together

15x +24y =6

16x -24y = 36

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

31x = 42

Divide by 31

31x/31 = 42/31

x = 42/31

Answer with explanation:

Consider two linear equation in two variable,

ax + by =c

p x +q y=r

The equations have an infinite number of solutions , means the two lines are Coincident, when it follows the following law

[tex]\frac{a}{p}= \frac{b}{q}= \frac{c}{r}[/tex]

                                      --------------------------------------(1)

Now, equation of two lines are

1. y= 6 x -b

→6 x -y -b=0

2. -3 x +y= -3

⇒-3 x+y+3=0

By the above law,that is law 1, the two lines will be coincident

[tex]\frac{6}{-3}=\frac{-1}{1}= \frac{-b}{3}\\\\2=1= \frac{b}{3}[/tex]

Which is not possible that is ,2≠1.

→→→Hence the two lines can never be coincident for any value of b.

Answer:

1st graph in edgnuity

Step-by-step explanation:

Answer:

1st graph

Step-by-step explanation:

i got it correct

Answer:

Following are the statements:

a. logₐb - logₐc = logₐb/logₐc

False.

b. logₐB - logₐc = logₐ(b/c)

True.

c. log₄(5x+16) = log₄5x+log₄16 = 2 +log₄5x

False.

d.  log₄(5x*16) = log₄5x+log₄16 = 2 +log₄5x

True.

e. logₐ(3x)₂ = 2 logₐ3 + logₐx

False.

f. logₐ(3x)₂ = 2 logₐ3 + 2 logₐx

Answer:

a. False

b. True

c. False

d. True

e. False

f. True

Step-by-step explanation:

By properties of logarithms:

a. False: ㏒ₐb-㏒ₐc ≠ (㏒ₐb / ㏒ₐc) does not exists that property

b. True: (㏒ₐb)-(㏒ₐc) = ㏒ₐ(b/c)  Logarithm of a Quotient

c. False: Does not exists the property:  ㏒ₐ(c+b) = ㏒ₐc + ㏒ₐb

so

㏒₄(5x+16) ≠ ㏒₄5x + ㏒₄16 but,  ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x  

because ㏒₄16 = 2.

d. True:  Logarithm of a Product: ㏒ₐ(c×b) = ㏒ₐc + ㏒ₐb

so

㏒₄(16×5x) = ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x

e. False: Logarithm of a Power: ㏒ₐ(c×b)ⁿ = n ㏒ₐ(c×b) = n (㏒ₐc + ㏒ₐb) = n ㏒ₐc + n ㏒ₐb

so

㏒ₐ(3x)² ≠ 2 ㏒ₐ3 + ㏒ₐx

f. Correct use of property in point e.

Answer:

Monthly Expense = $270.83

Step-by-step explanation:

The semi-annual premium is paid twice a year so,

Automobile insurance premium for whole year = 650*2

= $1300

Monthly premium will be paid 12 times a year so,

Health insurance premium for whole year = 125*12 = $1500

Annual premium is only paid once a year.

So adding all the premiums will give us the total premiums for whole year.

Total amount of premium for a year = $1300+$1500+$450

= $3250

The premium amount for whole year is $3250. To find the monthly expense, we will divide it by 12.

So monthly expense is:

= 3250/12

= $270.83 ..

To find the monthly expense, calculate the total annual premium for each insurance and divide by 12. The monthly expense is $187.5.

To find the monthly expense, we need to calculate the total annual premium for each insurance and divide it by 12 (since there are 12 months in a year).

For automobile insurance, the semiannual premium is $650, so the annual premium is $650 * 2 = $1300.

The monthly premium for health insurance is $125.

For life insurance, the annual premium is $450.

Now, let's calculate the total monthly expense: ($1300 + $125 + $450) / 12 = $187.5.

So, the monthly expense is $187.5.

Answer:

Average = -1°C

Step-by-step explanation:

The data recorded is;

6, -7, -5, 5, -8, 3 (in °C)

Average = [tex]\frac{6 - 7 - 5 + 5 - 8 + 3}{6}[/tex] = -1°C

Answer:

Average temperature listed will be (-1).

Step-by-step explanation:

As we know average of any given set of numbers is = [tex]\frac{\text{Sum of all the numbers}}{\text{Total numbers }}[/tex]

Now the given set of temperatures is 6, -7, -5, 5, -8, 3

Now Sum of all numbers = 6 + (-7) + (-5) + 5 + (-8) + 3

= (-6)

Total numbers = 6

Now average temperature will be = [tex]\frac{-6}{6}=(-1)[/tex]

Therefore, average temperature listed will be (-1).

Answer: It depends on you if it seems easier for you, you should try both and see which one works better for you.

Answer:

Geometry nation helps when you need to go more in depth and need practice problems. While the textbook might give you good definitions it may seem more monotone.

Answer: it can’t be converted to a fraction

Step-by-step explanation:

Answer:

[tex]\large\boxed{3x-4y=-48}[/tex]

Step-by-step explanation:

The standard form of an equation of a line

[tex]Ax+By=C[/tex]

We have the eqution in the point-slope form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]

Convert it to the standard form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]           multiply both sides by 4

[tex]4y-16=3(x+8)[/tex]           use the distributive property

[tex]4y-16=3x+32[/tex]          add 16 to both sides

[tex]4y=3x+48[/tex]           subtract 3x from both sides

[tex]-3x+4y=48[/tex]           change the signs

[tex]3x-4y=-48[/tex]

Answer:

25/9

Step-by-step explanation:

Fraction is 25/9 and it's simplified.

Hope my answer has helped you if not i'm sorry.

Answer:

(5e)^4

Step-by-step explanation:

5e•5e•5e•5e

There are 4 sets of 5e being multiplied together

(5e)^4

Answer:

thanks for the points

Step-by-step explanation:

Answer:

Option 1 and 3 are correct.

Step-by-step explanation:

The corresponding angles are the matching angles when two lines are crossed by another line which is called traversal.

Looking in the figure following are corresponding angles

8 and 6

4 and 2

7 and 5

3 and 1

Now, looking at the options

Option 1  5 and 7

and Option 3  6 and 8 are only given corresponding angles.

So Option 1 and 3 are correct.

Answer:The age of daughter is 12 years  and age of son is 24 years

Step-by-step explanation:

Given :

Present age of father = 52 years

Let the present age of daughter be x

So according to the question son's age is twice that of daughter's

So present age of son =2x

Now after 4 years the sum of their ages = 100

i.e. x+4 + 2x+4 + 52 +4 =100

3x+ 64 = 100

Subtracting both sides by 64 we get

3x + 64 - 64=100 -64

3x = 36

Dividing LHS and RHS by 3 we get

x=12

i.e. Present age of daughter  = x = 12 years

Present age of son = 2x = 2× 12= 24 years

Answer:

r² + 9r + 6

Step-by-step explanation:

+3|  +1    +6   -21   -18

   |         +3   +27  +18  

      +1    +9    +6     0

Answer:

=1r² +9r + 6 + 0

=r² +9r + 6    (simplified)

Read on if you want to know how it was done.

To do synthetic division, you first need to get the constant of the divisor and change the sign.

Then list the coefficients of the dividend.

Drop the first coefficient.

Multiply it by the divisor, and write the answer under the next coefficient and add. Repeat till the end.

The answer should be one degree less, the original polynomial.

For this case we must build a quotient such that when multiplied by the divisor, it eliminates the terms of the dividend until it reaches the remainder.

According to the figure we have that the quotient is:

[tex]r ^ 2 + 9r + 6[/tex]

Answer:

Quotient:

[tex]r ^ 2 + 9r + 6[/tex]

See attached image

b. state taxes are the most likely to pay for universities and police.

Answer:

B

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

30 % × $40 = 30 ÷ 100 × 40 = $12

The value of the Percentage 30% of $40 is: $12

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Thus:

30% of $40 is calculated as:

30/100 * 40

= 1200/100

= $12

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Answer:

50 degrees

Step-by-step explanation:

As the kite is triangular, the sum of all angles will be 180 degrees.

Let x be the first angle.

Then according to the statement second angle is four times as large as the first, second angle will be:

4x

And according to the statement, the third angle is 55 degrees ° more than the sum of the other two angles, third angle will be:

x+4x+55

So,

x+4x+x+4x+55=180

10x+55=180

10x= 180-55

10x=125

x=125/10

x=12.5 degrees

So first angle is 12.5 degrees.

Second angle = 4(12.5)

=50 degrees

Third angle = x+4x+55

= 12.5+50+55

= 117.5 degrees

To check if the sum of angles is 180 degrees

= 12.5+117.5+50 = 180

Hence, second angle is 50 degrees ..

Answer:

[tex]\large\boxed{D.\ 2160\pi\ units^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cylinder:}\\\\V=\pi r^2H\\\\r-radius\\\H-height\\\\\text{We have}\ r=12\ \text{and}\ H=15.\ \text{Substitute:}\\\\V=\pi(12^2)(15)=\pi(144)(15)=2160\pi[/tex]

The volume of the cylinder is [tex]\( 2160 \pi \)[/tex] units³.

To find the volume of the cylinder, we'll use the formula for the volume of a cylinder, which is given by:

[tex]\[ V = \pi r^2 h \][/tex]

Where:

- V is the volume of the cylinder,

- r is the radius of the cylinder, and

- h is the height of the cylinder.

Given:

- Height h = 15 units

- Radius r = 12 units

We'll substitute these values into the formula:

[tex]\[ V = \pi \times (12)^2 \times 15 \][/tex]

[tex]\[ V = \pi \times 144 \times 15 \][/tex]

[tex]\[ V = 2160 \pi \][/tex]

So, the volume of the cylinder is [tex]\( 2160 \pi \)[/tex] cubic units.

The correct answer is option D: [tex]\( 2160 \pi \)[/tex] units³.

Answer:

2 and 10

Step-by-step explanation:

In order to solve these types of problems, you should first subtract the difference of the two pieces. You get 4. Divide by 2 (two pieces) and there are 2 and 2. Add the 8 back to one of them, and you get 10 ad 2.

Answer:

Step-by-step explanation:

The variance is the square of the standard deviation.  Here, the variance is 17^2, or 289.

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points A(-3, 0) and B(-6, 5). Substitute:

[tex]m=\dfrac{5-0}{-6-(-3)}=\dfrac{5}{-3}=-\dfrac{5}{3}[/tex]

The line passes through the origin, therefore the y-intercept is equal to 0.

Therefore we have the equation:

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

Convert to the standard form [tex]Ax+By=C[/tex]

[tex]y=-\dfrac{5}{3}x[/tex]         multiply both sides by 3

[tex]3y=-5x[/tex]                add 5x to both sides

[tex]5x+3y=0[/tex]

The equation of the line parallel to AB passing through the origin is 5x - 3y = 0.

The equation of the line that passes through the origin and is parallel to AB is 5x - 3y = 0.

To find the equation of a line parallel to AB passing through the origin, we first need to find the slope of AB, which is (5 - 0) / (-6 + 3) = 5 / -3 = -5/3.

Since the line passing through the origin and parallel to AB has the same slope, its equation will be of the form y = mx. Substituting the point (0, 0) into y = -5/3x gives us y = -5/3x, which simplifies to 5x - 3y = 0.

Answer:

B

Step-by-step explanation:

Using the rule of radicals/ exponents

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

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]\sqrt[3]{x^5 y}[/tex]

= [tex]\sqrt[3]{x^5}[/tex] × [tex]\sqrt[3]{y}[/tex]

= [tex]x^{\frac{5}{3} }[/tex] [tex]y^{\frac{1}{3} }[/tex] → B

Let

[tex]P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}[/tex]

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

[tex]P(1):\ 1 = \dfrac{1\cdot 2}{2}=1[/tex]

So, the base case is ok. Now, we need to assume [tex]P(n)[/tex] and prove [tex]P(n+1)[/tex].

[tex]P(n+1)[/tex] states that

[tex]P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}[/tex]

Since we're assuming [tex]P(n)[/tex], we can substitute the sum of the first n terms with their expression:

[tex]\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}[/tex]

Which terminates the proof, since we showed that

[tex]P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}[/tex]

as required

Answer:

Option C.

Step-by-step explanation:

We know that

f(t) = 1.5t + 50

represents the approximate population of trout in Sky Lake

And

g(t) = 0.1t^2 - 4t + 70

represents the approximate population of trout in Lake Cyan

The total trout population in the area is described as

f(t) + g(t)

f(t) + g(t) =  [1.5t + 50] + [0.1t^2 - 4t + 70]

f(t) + g(t) =  [1.5t + 50+ 0.1t^2 - 4t + 70]

f(t) + g(t) =  [0.1t^2 -2.5t + 120]

f(t) + g(t) =  0.1t^2 -2.5t + 120

Option C.

Answer:

- [tex]\sqrt{11}[/tex]

Step-by-step explanation:

Radical roots occur in conjugate pairs

Thus if [tex]\sqrt{11}[/tex] is a root then

- [tex]\sqrt{11}[/tex] is also a root

The other root of the given polynomial is  [tex]-\sqrt{11}[/tex].

"Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero."

Given roots of a polynomial f(x) are - 4, 2, 1, [tex]\sqrt{11}[/tex].

We know, for the root of an equation, radical roots are always in pair.

If a polynomial has two roots, one is [tex]\sqrt{x}[/tex] then the other one must be [tex]-\sqrt{x}[/tex].

Similarly, the root of the given polynomial is [tex]-\sqrt{11}[/tex].

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Answer:

0 is the answer.

Step-by-step explanation:

This would be the same answer as the last problem of yours I answered, since the denominator has to be 0 in the equation -5/7s≠0

s≠0

So  the non permissible replacement is 0.

Hope this helps!

Answer:

answer is (1,0)

Step-by-step explanation:

Let the coordinates of D be (a,b).The diagonals of a parallelogram bisect each other.The midpoint of AC should be the same as the midpoint of BD.Compare corresponding coordinatesThis implies that:, , , Therefore the coordinates of D are: (1,0)

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Answer:

multiplication property of equality

Step-by-step explanation:

Given:

[tex]-\frac{1}{2}p = 4[/tex]

The rule is that whatever is done on one side of the equation is done on the other side of the equation two.

In order to isolate p, both sides of equation will be multiplied by -2.

This is called the multiplication property of equality ..

Following are the calculation to the radius of circle B:

Therefore, the answer is "BN".

Learn more:

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