MATHEMATICS MIDDLE SCHOOL

If r(x) = 3x - 1 and s(x) = 2x , which expression is equivalent to (r/s) (6)

Answers

Answer 1

Answer:

Step-by-step explanation:

(r/s)(x)=3x-1

(r/s)(6)=18-1/12

=17/12

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Solve the equation sin^2 x=3 cos ^2 x

Answers

Answer:

Step-by-step explanation:

Answer:

Explanation:

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$\bf \textit{Pythagorean Identities} \n\n sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \n\n[-0.35em] \rule{34em}{0.25pt}\n\n sin^2(x)=3cos^2(x)\implies sin^2(x)=3[1-sin^2(x)] \implies sin^2(x)=3-3sin^2(x) \n\n\n sin^2(x)+3sin^2(x)=3\implies 4sin^2(x)=3\implies sin^2(x)=\cfrac{3}{4}$

$\bf sin(x)=\pm\sqrt{\cfrac{3}{4}}\implies sin(x)=\pm\cfrac{√(3)}{√(4)}\implies sin(x)=\pm\cfrac{√(3)}{2} \n\n\n sin^(-1)[sin(x)]=sin^(-1)\left( \pm\cfrac{√(3)}{2} \right)\implies x= \begin{cases} (\pi )/(3)\n\n (2\pi )/(3)\n\n (4\pi )/(3)\n\n (5\pi )/(3) \end{cases}$

that is, on the interval [0, 2π].

Caleb draws 14 dogs on each of 4 posters.He draws 18 cats on each of 6 other posters. If he draws 5 more dogs on each poster with dogs, how many dogs ad cats does he draws?

Answers

14x4=56

18x6=108

5x4=20

total = 184

my answer is 184 because you have to multipy

At Raging River Sports, polyester-fill sleeping bags sell for $79. Down-fill sleeping bags sell for $149. In one week the store sold 14 sleeping bags for $1456.A.Let x represent the number of polyester-fill bags sold and let y represent the number of down-fill bags sold. Write a system of equations you can solve to find the number of each type sold.

B.Explain how you can solve the system for y by multiplying and subtracting.

C.Explain how you can solve the system for y using substitution.

D.How many of each type of bag were sold?

Answers

Answer:

x 79 + y149=1456

x +y = 14

multiplying the second equation by 79 and subtracting it to the first equation.

Solving for x in the second equation and Replacing x in the first equation, then solve for y.

Down-fill sleeping bags(y) = 5

Polyester-fill sleeping bags (x) =9

Step-by-step explanation:

Hi, the sum of the product of each type of sleeping bag multiplied by its cost is equal to 1456 (equation1)

The sum of both sleeping bags sold is equal to 14 (equation 2)

x 79 + y149=1456

x +y = 14

B. multiplying the second equation by 79 and subtracting it to the first equation.

79x + y149=1456

79x +79y = 1106

_____________

70y = 350

y = 350/70

y = 5

C. solving for x in the second equation:

x = 14-y

Replacing x in the first equation:

79 (14-y)+ 149y=1456

1106-79y +149y =1456

149y-79y = 1456-1106

70y =350

y = 350/70

y = 5

Replacing the value of Y in any equation:

x +y = 14

x+ (5) =14

x =14-5

x = 9

Down-fill sleeping bags(y) = 5

Polyester-fill sleeping bags (x) =9

A.
x+y=14
79x+149y=1456

B.
-79(x+y=14)
79x+149y=1456

-79x-79y=-1106
79x+149y=1456
70y=350
y=350/70
y=5

79x+149(5)=1456
79x+745=1456
79x=1456-745
79x=711
x=711/79
x=9

C.
x=-y+14
79(-y+14)+149y=1456
-79y+1106+149y=1456
-79y+149y=1456-1106
70y=350
y=350/70
y=5

x=-y+14
x=-5+14
x=9

D.
9 polyester-fill
5 down-fill

What is the decimal representation of 5/11

Answers

Answer:

$(5)/(11)=0.\overline{45}$

Step-by-step explanation:

Given: $(5)/(11)$

We need to change given fraction into decimal.

$x=(5)/(11)-------(1)$

$11x=5$

Multiply both sides by 9

$99x=45-----------(2)$

Add equation (1) and (2)

$99x+x=45+(5)/(11)$

$100x=45.45.....$

Divide both sides by 100

$x=0.454545.....$

$(5)/(11)=0.454545.......=0.\overline{45}$

0.45 is the answer but
0.45454545454is it

Five eighths plus eleven twelves

Answers

$five \ eighths \to (5)/(8) \n\n eleven \ twelves \to (11)/(12) \n\n (5)/(8)^((3)+(11)/(12)^((2)= \n\n =(15)/(24)+(22)/(24)= \n\n =\boxed{\boxed{(37)/(24)}}$

5/8 + 11/12
make the denominator the same
48 divided by 12 = 4
48 divided by 8 = 6
5 x 6 = 30
11 x 4 = 44
30/48 + 44/48
30 + 44 = 74
74 - 48 = 26
So the answer is 1 and 26/48 in its proper form.
Simplified, it would be 1 and 13/24. Mixed = 37/24 since you'll be adding 24.

PLEASE HELP I GIVE THANKS

Answers

$\$55-\$25=\$30\n\$30/\$1.5=20$

20 balloons

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