There are 162 people waiting in line to ride a roller coaster when the line closes for the day. Each roller coaster car holds 12 people. After loading c cars on the roller coaster, there are 6 people still in line. Write an equation to represent the number of cars, c, that have been loaded on the roller coaster. Solve the equation to find the number of cars on the roller coaster.

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:

40%

Step-by-step explanation:

We are given that last month, Joe's puppy weight 5.4 pounds while this month, the puppy weighed 7.56 pounds.

We are to find the percentage increase of the weight of the puppy

We know that the formula of percentage increase if given by:

Percentage increase = (new value - initial value)/initial value × 100

So substituting the given values to get:

Percentage increase in puppy's weight = [tex]\frac{7.56-5.4}{5.4} \times 100[/tex] = 40%

Answer:

(-2, 6) on edge

Step-by-step explanation:

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:

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{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:

100

Step-by-step explanation:

550=L+R

2/9=L/R

=========

Solve the second for L:   2R/9=L

Plug this into the first:  550=2R/9 +R

(2/9+1=11/9)  So          :   550=11R/9

Now multiply both sides by 9/11:   550(9)/11=R

R=50(9)=450

L=550-R=550-450=100

There are 100 lefties

The number of left-handed students in the school is 100, calculated by dividing the total student population by the sum of the ratio parts and then multiplying by the number of parts for lefties.

To calculate the number of left-handed students in a school with 550 students and a ratio of lefties to righties of 2:9, you first add the parts of the ratio together (2 + 9 = 11 parts). Knowing that 11 parts represent all students, 1 part is equal to 550 students divided by 11, which is 50 students. Because there are 2 parts for lefties, you multiply 50 students by 2 parts to find out that there are 100 left-handed students in the school.

Answer:

The speed was [tex]61\frac{miles}{hour}[/tex]

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

s------> the speed in miles per hour

d ----> the distance in miles

t ----> is the time in hours

we know that

[tex]s=\frac{d}{t}[/tex]

we have

[tex]d=305\ miles[/tex]

[tex]t=5\ hours[/tex]

substitute

[tex]s=\frac{305}{5}[/tex]

[tex]s=61\frac{miles}{hour}[/tex]

Answer:

First option.

Step-by-step explanation:

In this case you need to remember that an angle formed by two intersecting chords is equal to the sum of the intercepted arcs divided by 2. This is:

[tex]Angle\ formed\ by\ two\ intersecting\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex]

You can identify in the figure that the angle ∠1 is an angle formed by two intersecting chords. Therefore, since the intercepted arcs are SP and QR, you can say the following:

[tex]m\angle 1=\frac{1}2}(mSP+mQR)[/tex]

You can observe that this matches with the first option.

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:

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

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

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 ..

Answer: 500 as 49 is closer to 500 by 1, if it was 550 then it would have been 600. It's basically just estimation or rounding it off to the nearest hundred

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)

Read more on Brainly.com - https://brainly.com/question/12816305#readmore

Answer with explanation:

Using Sine Rule for Congruence of Triangles

    [tex]\Rightarrow\frac{a}{\ SinA}=\frac{b}{\ Sin B}=\frac{c}{\ Sin C}\\\\\Rightarrow\frac{15}{\ Sin29^{\circ}}=\frac{20}{\ Sin B}\\\\\Rightarrow\frac{15}{0.49}=\frac{20}{\ Sin B}\\\\\Rightarrow \ SinB=\frac{20 \times 0.49}{15}\\\\\Rightarrow \ SinB=\frac{9.8}{15}\\\\\Rightarrow \ SinB=0.65\\\\B=41^{\circ}[/tex]

Using Angle Sum Property of Triangle

⇒∠A+∠B+∠C=180°

⇒29°+41°+∠C=180°

⇒∠C=180°-70°

⇒∠C=110°

→Again Using Sine Rule

[tex]\Rightarrow \frac{b}{\ Sin B}=\frac{c}{\ Sin C}\\\\\Rightarrow \frac{20}{\ Sin 41^{\circ}}=\frac{c}{\ Sin 110^{\circ}}\\\\\Rightarrow \frac{20}{0.65}=\frac{c}{0.94}\\\\\Rightarrow \frac{20 \times 0.94}{0.65}=c\\\\\Rightarrow c=\frac{18.8}{0.65}\\\\\Rightarrow c=28.92[/tex]

Length of third Side =28.92 unit

So,Perimeter of Triangle

=Sum of sides of triangle

=a +b +c

       =15 + 20 +28.92

       = 63.92 unit  

Answer:

b on edge

Step-by-step explanation:

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!

Following are the calculation to the radius of circle B:

Therefore, the answer is "BN".

Learn more:

brainly.com/question/17125936

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

Read more on about percentage at: https://brainly.com/question/843074

#SPJ6

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:

[tex]f^{-1}(x)=2(+/-)2\sqrt{(7+x)}[/tex]

Step-by-step explanation:

we have

[tex]2(x-2)^{2}=8(7+y)[/tex]

step 1

Exchange x for y and y for x

[tex]2(y-2)^{2}=8(7+x)[/tex]

step 2

isolate the variable y

[tex](y-2)^{2}=4(7+x)[/tex]

take the square root both sides

[tex]y-2=(+/-)\sqrt{4(7+x)}[/tex]

[tex]y=2(+/-)\sqrt{4(7+x)}[/tex]

step 3

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=2(+/-)\sqrt{4(7+x)}[/tex]

[tex]f^{-1}(x)=2(+/-)2\sqrt{(7+x)}[/tex]  ----> equation of the inverse

Answer:

y=2+√28+4x

Step-by-step explanation:

Hello! My name is Zalgo and I am here to help you out on the beautiful day!. The answer to your question would be that 17000 grams is the same weight as 1 kilogram since 1 kilogram is the same weight as 1000 grams.

I hope that this helps! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Thanks! X3)

Final answer:

To convert 17 kilograms to grams, multiply 17 by 1000 to get 17000 grams.

Explanation:

To find the number of grams in 17 kilograms, we need to understand the relationship between kilograms and grams. One kilogram is equal to 1000 grams. Therefore, to convert kilograms to grams, we multiply by 1000.

Step-by-step conversion:

So, 17 kilograms is equal to 17000 grams.

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt[3]{9x^4}\cdot \sqrt[3]{3x^8}\implies (9x^4)^{\frac{1}{3}}\cdot (3x^8)^{\frac{1}{3}}\implies 9^{\frac{1}{3}}\cdot x^{4\cdot \frac{1}{3}}\cdot 3^{\frac{1}{3}}\cdot x^{8\cdot \frac{1}{3}}[/tex]

[tex]\bf 9^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}\cdot x^{\frac{4}{3}}\cdot x^{\frac{8}{3}}\implies (3^2)^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}\cdot x^{\frac{4}{3}+\frac{8}{3}}\implies 3^{\frac{2}{3}}\cdot 3^{\frac{1}{3}}\cdot x^{\frac{12}{3}} \\\\\\ 3^{\frac{2}{3}+\frac{1}{3}}x^4\implies 3^{\frac{3}{3}}x^4\implies 3x^4[/tex]

Answer:

[tex]3x^4[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{9x^4} \cdot \sqrt[3]{3x^8}[/tex]

To simplify it we multiply all the terms inside the cube root

[tex]\sqrt[3]{9x^4} \cdot \sqrt[3]{3x^8}[/tex]

[tex]\sqrt[3]{9x^4 \cdot 3x^8}[/tex]

Now we apply exponential property

[tex]a^m \cdot a^m = a^{mn}[/tex]

[tex]x^4 \cdot x^8 = x^{12}[/tex]

[tex]\sqrt[3]{9x^4 \cdot 3x^8}[/tex]

[tex]\sqrt[3]{27x^{12}}[/tex]

Now we take cube root

[tex]\sqrt[3]{27}=3[/tex]

[tex]\sqrt[3]{x^{12}}=\sqrt[3]{x^3 \cdot x^3 \cdot x^3 \cdot x^3}=x^4[/tex]

[tex]\sqrt[3]{27x^{12}}[/tex]

[tex]3x^4[/tex]

Answer:

Reflection

Step-by-step explanation:

reflect it over the y axis it will be congruent

Answer:

reflection

Step-by-step explanation:

if the triangle is reflected it will keep its exact shape and only be flipped over.

(pls mark brainliest)

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: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:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem

[tex]a=1[/tex]

[tex]b=2[/tex]

[tex]b=1+r[/tex]

[tex]r=2-1=1=100\%[/tex]

using a graphing tool

The graph in the attached figure

Answer:

1 / y^7

Step-by-step explanation:

Y^-9•y^-8•y^10

= y^10 / y^9•y^8

= y^10 / y^17

= 1 / y^7

Answer: The answer is y^-7