Students were asked to write an expression equivalent to the expression below:
30a+12b-6a+ 2(9b+c+15)
Their answers are as follows:
36a-30b+2c +30
Ben wrote: 36a - 30b + 2c + 30
Martin:
24a+30b+2c +30
Sara wrote: 24a + 30b + 2c + 15
Martin wrote: 24a + 30b+2c +30
Which, if any, of those students wrote expressions that are equivalent to the original expression?
In the space provided below, either prove why each student's response is equivalent, or explain and correct the student's error.
Sara
| Ben:
Allie wrote: 2(12a + 15b+c+15)
24a+30b+ac+15
Allie:
2(13a +156+c+15)

Answer:

1±i sqrt(7/2)

Step-by-step explanation:

For this equation you would need to use quadratic formula: x=(-b+-square root b^2-4ac)/2a

Answer:the answer is option E (see pic)

Step-by-step explanation:

One root would be: x =(4-√88)/-4=1+1/2√ 22 = 1.345

The length of the rectangle is 8m and width of the rectangle is 7m

Given that the length and width of a rectangle are consecutive integers

Let the length of the rectangle be x+1 meter

Let the breadth of the rectangle be x meter

Also given that perimeter of the rectangle is 30 meters

To find length and breadth of the rectangle

We know that perimeter of the rectangle is P = 2 (l+b)

30 = 2 (x+x+1)

15 = 2x + 1

2x = 14

x = 7

x+1 = 8

Hence, the length of the rectangle is 8m and width of the rectangle is 7m

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Let x = number of hours washing cars

Let y = number of hours landscaping

System of equations:

[tex]10x+8y=84\\\\x=2y[/tex]

Answer: No

Step-by-step explanation:

The sum of the interior angles of a polygon with n sides is given by [tex]180(n-2)[/tex]. Setting this equal to 850 degrees,

[tex]180(n-2)=850\\\\n-2=\frac{85}{18}\\\\n=\frac{121}{18}[/tex]

Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.

Answer:

a = -4

b=-29

Step-by-step explanation:

First write the radicals in simplest form.

i² = -1

[tex]\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)[/tex]

                                                          [tex]\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i[/tex]

   [tex]\sf \boxed{a = -4 }\\\\\boxed{b=-29}[/tex]

The first four terms of the sequence are 6, -24, 96 and -384

How to determine the first four terms?

The sequence is given as:

an=6(-4)^n-1

When n = 1, we have:

a(1)=6(-4)^(1-1)

This gives

a(1) = 6

When n = 2, we have:

a(2)=6(-4)^(2-1)

This gives

a(2) = -24

When n = 3, we have:

a(3)=6(-4)^(3-1)

This gives

a(3)=96

When n = 4, we have:

a(4)=6(-4)^(4-1)

This gives

a(4)=-384

Hence, the first four terms of the sequence are 6, -24, 96 and -384

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The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

Total rupees withdraw from saving account is $149

Let total amount in account before withdrawing is X= $500

Amount left after withdraw the money is calculated by a

AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT

So, put the values then

Y= X($500) - $149

Y= $500 - $149

Y= $351

If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

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The sale price of the car as a percentage of the original price is 142%

Sale price as a percentage of the original price = sale price / buying price

= 1280/900 × 100

= 1.42222222222222 × 100

= 142.22%

Approximately,

142%

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Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7)  = 44.92937 which is 44.93 rounded to 2 decimal places

Using the cosine ratio, the value of AD in the diagram is: 2√3π in.

If we have the following given in a right triangle like triangle ADC in the diagram:

AC = 4π (hypotenuse)

AD = ? (adjacent side)

The cosine ratio, CAH would be applied, which is:

Cos 30 = adjacent/hypotenuse

Cos 30 = AD/4π

AD = cos 30 × 4π = √3/2 × 4π [cos 30 = √3/2]

AD = 2√3π in.

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Answer:

V = 343

Step-by-step explanation:

V = lwh

= 7(7)(7)

= 49(7)

= 343

Answer:

c = 75.36 cm

Step-by-step explanation:

The equation of the circumference is:

[tex]c=\pi d[/tex]  In which "d" represents the measurement of the diameter

in this case d= 24cm, π = 3.14

Calculate the circumference:

[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]

Hope this helps

A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Given information;

A circle has a diameter of 24cm.

"d" represents the measurement of the diameter, so

d= 24cm, π = 3.14

Radius = d/ 2 = 12

Calculate the circumference:

The circumference of the circle = 2πr

= 2 ( 3.14 ) ( 12)

= 75.36

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Answer:

x=7 and x = 1

Step-by-step explanation:

This is pretty much a quadratic in disguise.
If we multiply both sides by x, we get:
x^2-7=6x
move 6x to the left
x^2-6x-7 = 0
We can either use the quadratic formula, or we can use factoring.
with factoring*, we get:
(x-7)(x+1) = 0 , and so the solution to the equation is x=7, and x=-1

*in a equation: x^2+ax+b = (x+c)(x+d), c+d equals a, and c*d equals b

On to the quadratic formula, a=1, b=-6, and c=-7, so:
(6±sqrt(36+4*7))/2 = x
=(6±8)/2
=3±4
x=7 and x = 1

Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

Step-by-step explanation:

[tex]10x+45 > 120\\10x+45-45 > 120-45\\10x > 75\\\frac{10x}{10} > \frac{75}{10} \\x > 7.5[/tex]

Therefore, Mel has to work at least 7.5 hours or 8 total hours.

Answer:

ksb said did bud did did it did did gc victory in suf did did zudbxudng jc fn facing did fjgduf bdyrut during their fyrhfb hi f f7djdufj fhdf. Is A

Answer:

y = -x + 1

(Image of what graph looks like is attached)

Step-by-step explanation:

x = 1 - y can be rewritten into y = mx + b format.

x = 1 - y (subtract 1 from both sides)

x - 1 = -y (multiply by -1 to both sides)

y = -x + 1

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The total weight of the packed box is 9 lb 6 oz

According to question:

The weight of 12 jars is 12 times the weight of one jar

The weight of jars and box together is the sum of those weights.

... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz

... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz

... = 9 lb 6 oz

1 ounce (oz) is equal to 0.0625 pounds (lb).

1 oz = (1/16) lb = 0.0625 lb

The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:

m(lb) = m(oz) / 16

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The graph has been shifted to the left and moved up and stretched as scaling is done ,

Reflecting , Rotating , Dilating a function to form a new function is called Transformation.

The graph of the function f(x) = 1/ x is given

and a transformed function is given

The graph has been shifted to the left and moved up and stretched as scaling is done ,

Therefore three types of transformation are done on the parents function.

The transformation can be seen through the graph attached.

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here u go hope this helps

Answer: After working for 33 [tex]\frac{1}{3}[/tex] hours a week

Step-by-step explanation:

     Let us write equations to represent these two places. Let x be hours worked and y be money earned.

   Tim Hortons:

$200 + $5x = y

    McDonalds:

$300 + $2x = y

    Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.

$200 + $5x > $300 + $2x

$5x > $100 + $2x

$3x > $100

x > [tex]\frac{100}{3}[/tex]

x > 33.3334

    Tim Hortons is the better employer after an employee has worked for 33 [tex]\frac{1}{3}[/tex] hours a week.

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The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.

Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.

Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.

Hence, x -2 = 0 and x= 2.

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Answer: THE PERSON ABOVE IS CORRECT!!

The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

Answer:

Yes

Step-by-step explanation:

To find out whether or not a graph is a function, we can do the vertical line test. If the vertical line only touches one point, then the graph is a function. This is because in a function, an input can only have one output.

Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13

Step-by-step explanation:

Answer:

Tan p is 20/21

Tan q is 21/20

Step-by-step explanation:

Tan is short for tangeant.

tangeant means opposite/adjacent

the opposite of vertices p is 20.

the adjacent of vertices p is 21.

so tan p= 20/21

The opposite of vertices q is 21

the adjacent of vertices q is 20

so tan q is 21/20

The required equation of parabola is y = (-1/4)(x-9)² +4

What is a Parabola ?

A parabola is a U shaped Curve , whose all point are at same distance from a point called as Focus and a line called as Directrix.

Let (x,y) be any point on the parabola.

the distance between (x,y) and the focus and the distance between (x,y) and directrix is equal.

The focus is at (9,0) and a directrix at y= - 4

[tex]\rm \sqrt {(x-9)^2 + (y -0)^2[/tex]  = | y +4|

[tex]\rm {(x-9)^2 + (y -0)^2 = (y-4)^2[/tex]

(x-9)²  + y² = y² +16 -4y

On solving this

4y = - (x-9)² +16

y = (-1/4)(x-9)² +4

Therefore this is the required equation of parabola .

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The distance from Bobby to the plane is 154.7 yards.

Sine law can be used to find the distance of the plane to Bobby.

Therefore,

x / sin 40 = 240 / sin 95

cross multiply

Hence,

x sin 95 = 240 sin 40

divide both sides by sin 95

x  =  240 sin 40 / sin 95

x = 240 × 0.64278760968 / 0.99619469809

x = 154.08 / 0.9961

x = 154.683264732

x = 154.7 yards

Therefore, the distance from Bobby to the plane is 154.7 yards.

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Answer:

Complementary angles are:

∠ORS and ∠SRQ

Supplementary angles are:

∠ORP and ∠PRQ

Answer: 9

Step-by-step explanation:

[tex](f \circ g)(0)=f(g(0))\\\\g(0)=2\\\\\implies f(g(0))=f(2)=\boxed{9}[/tex]

Step-by-step explanation:

x + 2x + 7x

72 = 9x

72 - 9 = x

63 = x

63 ÷ 3 = 21

piece 1 = 21

piece 2 =21+2 = 23

piece 3 =21+7 = 28

21+23+28 = 72 This proves the above is correct.