The work of a student trying to solve the equation 4(2x − 1) = 11 + 3x + 5 is shown below:

Step 1: 4(2x − 1) = 11 + 3x + 5
Step 2: 8x − 4 = 16 + 3x
Step 3: 8x + 3x = 16 − 4
Step 4: 11x = 24
Step 5: x = 2.18

In which step did the student first make an error and what is the correct step?

Step 2: 8x − 1 = 16 + 3x
Step 2: 8x − 8 = 6 + 3x
Step 3: 8x − 3x = 16 + 4
Step 3: 8x + 3x = 16 − 8

In which step did the student first make an error and what is the correct step?

Step 2: 8x − 1 = 16 + 3x
Step 2: 8x − 8 = 6 + 3x
Step 3: 8x − 3x = 16 + 4
Step 3: 8x + 3x = 16 − 8

Answer:

88 degrees

Step-by-step explanation:

Since x and z have the same angel their degrees is the same

Answer:Set it up as two equations.  Start off by stating that x= the number of adult tickets, and y= the number of student tickets.

6x+4.5y=2175

x+y=430

State that y = 430-x, and substitute it into the second equation 6x +4.5(430-x)= 2175.

Solve for x.  Then plug in what you get for x into the x+y=430 equation and solve for y.  Your number of adult tickets should equal 160, and your number of child tickets should equal 270.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

because it's right and you'll get it right so it is a

Answer:

13/16

Step-by-step explanation:

Answer:

2912

Step-by-step explanation:

the answer is 2912 toys.....

Answer:

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

For m to be equal to n,

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

Multiply both sides by 3:

[tex]6s = 2s - 1[/tex]

Minus 2s on both sides:

[tex]4s = - 1[/tex]

Divide by 4 on both sides:

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

Answer:

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

Answer: 61/100 would be the answer

Answer:

9 days before only 8 mg is still emitting radiation.

Step-by-step explanation:

The exponential model is:

[tex]y(t) = a(0.5)^{\frac{t}{28}}[/tex]

In which a is y(0), that is, the initial quantity.

10 mg is ingested by a patient

This means that [tex]a = 10[/tex], and thus:

[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]

How many days before only 8 mg is still emitting radiation?

This is t for which y(t) = 8. So

[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]

[tex]8 = 10(0.5)^{\frac{t}{28}}[/tex]

[tex](0.5)^{\frac{t}{28}} = \frac{8}{10}[/tex]

[tex](0.5)^{\frac{t}{28}} = 0.8[/tex]

[tex]\log{(0.5)^{\frac{t}{28}}} = \log{0.8}[/tex]

[tex](\frac{t}{28})\log{0.5} = \log{0.8}[/tex]

[tex]\frac{t}{28} = \frac{\log{0.8}}{\log{0.5}}[/tex]

[tex]t = 28\frac{\log{0.8}}{\log{0.5}}[/tex]

[tex]t = 9[/tex]

9 days before only 8 mg is still emitting radiation.

Answer: we need to survey 2285 Americans.

Step-by-step explanation:

When population proportion (p) is known, then the formula to evaluate the sample size( minimum) is given by :-

[tex]n=p(1-p)(\frac{z^*}{E})^2[/tex], where E = margin of error , z* = critical z-value.

Given: p= 0.61, E=0.02, Critical z value for 95% = 1.96

Required sample size: [tex]n=(\frac{1.96}{0.02})^2(0.61)(1-0.61)[/tex]

[tex]=(98)^2(0.61)(0.39)\\\\=9604(0.61)(0.39)\\\\\approx$$2285[/tex]

Hence, we need to survey 2285 Americans.

Answer:

y = 18 / (x + 2)²

Step-by-step explanation:

Inversely proportional

y * (x + 2)² = k

when x=1, y=2

k = 2 * (1 + 2)²

k = 18

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

y * (x + 2)² = 18

Divide both sides by (x + 2)²

y = 18 / (x + 2)²

Answer:

B

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

take 64 degree as reference angle

using cos rule

cos 64=adjacent/hypotemuse

0.43=QR/10

10*0.43=QR

4.3=QR

Answer:

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Given the following data;

Present value, P = $300

Interest rate, r = 8%

Number of times, n = 1/4

Note: Future value = 2 * P = 2*300 = $600

Compound interest is generally calculated based on the interest rate on a loan, principal and the accumulated interest gained from previous periods. This interest is compounded for a certain number of times such as daily, weekly, quarterly or annually.

To find how long she would have to invest her money in order to double it, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Answer:

Exactly 4 pitches: 15/100

= 0.15

Answer:

1.5 amps

Step-by-step explanation:

P = V.I

60 = 40.I

60/40 = 40.I/40

I = 1.5

Answer:

yes it is.

x = 4 and y = -3

Step-by-step explanation:

Solve simultaneously using elimination method:

equation 1 - equation 2

3x + y = 9 equation 1

-2x + y = 5 equation 2

_________

x = 4

plug 4 into any of the 2 equations and solve for y.

3(4) + y = 9

12 + y = 9

12-12 + y = 9-12

y = -3

Answer:

1 3/7

Step-by-step explanation:

5 / 7 ÷ ½

Copy dot flip

5/7 * 2/1

10 /7

Changing from an improper fraction

7/7 + 3/7

1 3/7

Answer:

Yes, they lie on the line NP

Answer:

they lie in the line MO

Step-by-step explanation:

Answer:

6(2x + 3y)

Step-by-step explanation:

6 is the largest greatest common factor you can take out. As all powers are 1, nothing else can be done.

The factorize form of the expression  12x + 18y is 6(2x+3y)

An expression is combination of variables, numbers and operators.

The given expression is  12x + 18y

Twelve times of x plus eighteen times of y

x and y are the variables in the expression

Let us factorize the expression

The Gcd of 12 and 18 is 6

So take 6 as common from the expression

6(2x+3y)

Hence, the factorize form of the expression  12x + 18y is 6(2x+3y)

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Answer: I think your answer is right

Step-by-step explanation:

Answer:

length : 8 m

width : 13/2 = 6.5 m

Step-by-step explanation:

area of rectangle = l(ength)×w(idth) = 52

l = 2w - 5

=> (2w - 5)×w = 52

=> 2w² -5w - 52 = 0

we know, when transforming this quadratic equation into a multiplication of two expressions of w, that we need to have 2w and w (to make 2w²), and then which 2 numbers multiply to 52 and add to -5 (when one is multiplied by 2 due to 2w) : -13 and 4

=> (2w - 13)×(w + 4) = 0

=> 2 solutions for w :

2w-13 = 0

2w = 13, w = 13/2

w+4 = 0, w = -4

negative values for a side length of a shape do not make sense, so the only usable solution is w = 13/2

=> l = 2w - 5 = 13 - 5 = 8