Grace, Chelsea, and Roan are simplifying the same polynomial expression. Which
student's work is correct and why?
Grace
Chelsea
3(2 - x) - 2(6x - 8)
= 6 - 3x – 12x + 16
3(2 - x) – 2(6x – 8)
= 6 - 3x – 12x - 16
Roan
3(2 - x) - 2(6x - 8)
= 6 - 3x + 12x - 16
= -3x - 12x + 16 + 6
= -3x – 12x – 16 + 6
= -3x + 12x – 16 + 6
= -15x + 22
= -15x – 10
= 9x - 10​

Answer:

Sin 24 = 0.4067366431 = 0.4

Cos 45 = [tex]\frac{\sqrt{2} }{2}[/tex] = 0.7071067812 = 0.7

Tan 88 = 28.63625328 = 28.6

[tex]\bold{\text{Answer:}\quad \dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]

Step-by-step explanation:

[tex].\quad \dfrac{-5x}{8x+7}-\dfrac{6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}+\dfrac{-6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}\bigg(\dfrac{3x+1}{3x+1}\bigg)+\dfrac{-6x^3}{3x+1}\bigg(\dfrac{8x+7}{8x+7}\bigg)\\\\\\=\dfrac{-15x^2-5x}{(8x+7)(3x+1)}+\dfrac{-48x^4-42x^3}{(8x+7)(3x+1)}\\\\\\=\large\boxed{\dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]

Answer:

D. 15

Step-by-step explanation:

Use proportions.

[tex]\frac{35}{25} = \frac{21}{x} \\\\35x = 525\\x = 15[/tex]

Answer:

Toa

48/55

Step-by-step explanation:

O/A

48/55

Answer:

I hope it helps you......

Answer:

Copy this onto a piece of graph paper

Step-by-step explanation:

when graphing you want to make sure  that the slope is correct and the y-intercept is the same

Answer:

7.3%

Step-by-step explanation:

Let M = Maths

E = English

P(M ∪ E) = P(M) + P(E) - P( M ∩ E)

From the question:

P(M ∪ E) = 35.7%

P(M) = 18%

P(E) = 24%

P( M ∩ E) = unknown

35.7% = 18% + 24% - P( M ∩ E)

35.7% = 42% - P( M ∩ E)

P( M ∩ E) = 42% - 35.7%

P( M ∩ E) = 7.3%

Therefore, the probability that a student who receives an A in Math course will also receive an A in English course is 7.3%.

Answer:

117 R=0

Step-by-step explanation:

819:7= 117 R=0

Answer:

Amount of car in 2012 = $1,242.55 (Approx)

Step-by-step explanation:

Given:

Rate of depreciation(d) = 18% = 0.18

Amount of car in 1998 = $19,995

Find:

Amount of car in 2012

Computation:

Number of year(n) = 14 year

[tex]Amount\ of\ car\ in\ 2012 = Amount\ of\ car\ in\ 2012 [1-d]^n[/tex]

Amount of car in 2012 = 19,995[1-0.18]¹⁴

Amount of car in 2012 = 19,995[0.82]¹⁴

Amount of car in 2012 = 19,995[0.0621432458]

Amount of car in 2012 = 1,242.5542

Amount of car in 2012 = $1,242.55 (Approx)

Answer:

(B)[tex]2^1[/tex]

Step-by-step explanation:

We are to simplify the given expression: [tex]\dfrac{2^2 \cdot 2^3}{2^4}[/tex]

Step 1: Apply the addition law of indices to simplify the numerator.

[tex]\text{Addition Law: }a^x \cdot a^y=a^{x+y}[/tex]

Therefore:

[tex]\dfrac{2^2 \cdot 2^3}{2^4} \\\\=\dfrac{2^{2+3}}{2^4}\\\\=\dfrac{2^5}{2^4}[/tex]

Step 2: Apply the Subtraction law of indices to simplify the expression

[tex]\text{Subtraction Law: }a^x \div a^y=a^{x-y}\\\\\implies \dfrac{2^5}{2^4} =2^{5-4}\\\\=2^1[/tex]

The correct option is B.

Answer:

.0000416

Step-by-step explanation:

Since 10 is squared by a negative number, the number (4.16) will be smaller. To find the answer, move the decimal 5 places to the left

Answer:

0.0000416.

Step-by-step explanation:

When 10 is raised to a negative power, that means that the decimal point will be moved to the left a certain number of units.

In this case, it is 10^-5, so the decimal point will move to the left by 5 units.

4.16 * 10^-5 = 000004.16 * 10^-5 = 0.0000416.

Hope this helps!

Answer:(2x+1)(5x+3)

Step-by-step explanation:

Answer:

The values of x = 8 and x = -3 are the x-intercepts of this equation. The width of the archway is 11 units.

Step-by-step explanation:

Let be [tex]y = -x^{2}+5\cdot x +24[/tex], which is now graphed with the help of a graphing tool, the outcome is included below as attachment. The values of x = 8 and x = -3 are the x-intercepts of this equation, that is, values of x such that y is equal to zero. Algebraically speaking, both are roots of the second-order polynomial.

The width of the archway ([tex]d[/tex]) is the distance between both intercepts, which is obtained by the following calculation:

[tex]d = |x_{1}-x_{2}|[/tex], where [tex]x_{1} \geq x_{2}[/tex].

If [tex]x_{1} = 8[/tex] and [tex]x_{2} = -3[/tex], then:

[tex]d = |8-(-3)|[/tex]

[tex]d = 8 +3[/tex]

[tex]d = 11[/tex]

The width of the archway is 11 units.

Answer:

k = - 3

Step-by-step explanation:

Given that (x - 1) is a factor of the polynomial then x = 1 is a root

Substitute x = 1 into the polynomial and equate to zero, that is

4(1)³ + 3(1)² - 4(1) + k = 0, that is

4 + 3 - 4 + k = 0

3 + k = 0 ( subtract 3 from both sides )

k = - 3

Answer:

B.

Step-by-step explanation:

Well we know that

[tex]224=2^{5} *7[/tex]

so we can get the 2 outside of the radical

[tex]x^{11} =(x^{5} )^{2} *x[/tex]

and we can get the x^2 outside too.

[tex]y^8=y^5*y^3[/tex]

and we also can get y outside.

so we have:

[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]

Answer:

A: The triangle in question is not a right triangle.

Step-by-step explanation:

If the triangle is a right triangle, then the Pythagorean theorem would hold

a^2 + b^2 = c^2

3^2 + 4^2 = 6^2

9+16 = 36

25 = 36

This is not true so this is not a right triangle

Answer:

A: The triangle in question is not a right triangle.

Step-by-step explanation:

We can use Pythagorean theorem to check.

a² + b² = c²

3² + 4² = 6²

9 + 16 = 36

25 = 36 (not true)

Answer:

[tex] Area = 400.4 m^2 [/tex]

Step-by-step Explanation:

Given:

∆UVW,

m < U = 33°

m < V = 113°

VW = u = 29 m

Required:

Area of ∆UVW

Solution:

Find side length UV using Law of Sines

[tex] \frac{u}{sin(U)} = \frac{w}{sin(W)} [/tex]

U = 33°

u = VW = 29 m

W = 180 - (33+113) = 34°

w = UV = ?

[tex] \frac{29}{sin(33)} = \frac{w}{sin(34)} [/tex]

Cross multiply

[tex] 29*sin(34) = w*sin(33) [/tex]

Divide both sides by sin(33) to make w the subject of formula

[tex] \frac{29*sin(34)}{sin(33)} = \frac{w*sin(33)}{sin(33)} [/tex]

[tex] \frac{29*sin(34)}{sin(33)} = w [/tex]

[tex] 29.77 = w [/tex]

[tex] UV = w = 30 m [/tex] (rounded to nearest whole number)

Find the area of ∆UVW using the formula,

[tex] area = \frac{1}{2}*u*w*sin(V) [/tex]

[tex] = \frac{1}{2}*29*30*sin(113) [/tex]

[tex] = \frac{29*30*sin(113)}{2} [/tex]

[tex] Area = 400.4 m^2 [/tex] (to nearest tenth).

Answer:

.

Step-by-step explanation:

Answer:

Rectangle

Step-by-step explanation:

You graph them. From Point A to Point B it's rise 2 run 6 just like Point C to Point D. From Point D to Point A it's rise 3 run -1 just like Point C to Point B

Answer:

  105.07°

Step-by-step explanation:

The angle of v1 is ...

  arctan(5/2) ≈ 68.199°

The angle of v2 is ...

  arctan(-3/4) ≈ -38.870°

The angle difference between the two vectors is ...

  68.199° -(-38.870°) = 105.07°

Answer:

A i think its a A try. it it that looks correct

Answer:

Its B, 1.2EE6/1.1EE4

Step-by-step explanation:

The density is 109.9, and this is the only equation that gives you this answer

i also took the test!

1.  √7 × √7  = √[7×7] = √[7²] = 7

2. √18 × √2  = √[18×2] = √36 = √[6²] = 6

3. √45  = √[9×5] = √9 × √5 = √[3²] × √5 = 3√5

4. [tex]\dfrac{\sqrt{50}}{5}=\dfrac{\sqrt{25\cdot2}}{5}=\dfrac{\sqrt{25}\cdot\sqrt2}{5}=\dfrac{5\cdot\sqrt2}{5}=\bold{\sqrt2}[/tex]

5. 2√2 × 4√5  = (2×4) × (√2×√5) = 8×√[2×5] = 8√10

6. √48 - √12  = √[16×3] - √[4×3] = √16×√3 - √4×√3 = 4√3 - 2√3 = 2√3

7. (2 - √3)(1 + √3) = 2×1 + 2×√3 + (-√3)×1 + (-√3)×√3 =

                                     = 2 + 2√3 - √3 - √[3×3] = 2 + √3 - 3 = √3 - 1

Answer: [tex]-5x^{2} -5x-10[/tex]

Step-by-step explanation:

[tex](2x^{2} -5x-7)-(7x^{2} +3)[/tex]  

subtract by terms.

2x^2 - 7x^2 = -5x^2  

-5x  is the only term so leave it alone

-7-3= -10

-5x^2 -5x -10

Answer:

-5x-48

Step-by-step explanation:

First, simplify the first half,

(2x2-5x-7) --> (4-5x-7) --> (-5x-7+4) --> (-5x-13)

Then, simplify the second half,

(7x2+3) --> (7x5) --> (35)

Finaly put them together

-5x-13-35, subtract like terms

-5x-48

This is the most simplifyed it can get because of the variable.

Hope this helps, if you have a question if you are confused,

Have a good day and if you can, please give me brainliest, it will help a lot. :)

Answer:

Expanded expression of the area of the rectangle = 10x² - 4x + 6 square units

Step-by-step explanation:

Area of a rectangle = Length × Width

Area of the rectangle = 2 × (5x² - 2x + 3)

= 2 × 5x² - 2× 2x + 2×3

= 10x² - 4x + 6 square units

Answer:

469.4ft² of 469.4 square feet

Step-by-step explanation:

In the above question, we are given ∆ WXY

In the question, we have the following values already:

Angle W = 27°

Angle X = unknown

Angle Y = 40°

Side w = unknown

Side x = unknown

Side y = 38ft

Area of the triangle= it is unknown as well

First Step

We would determine the third angle = Angle X

Sum of angles in a triangle = 180°

= Angle X= 180° - (27 + 40)°

= 180° - 67°

Angle X = 113°

Second step

Determine the sides w and x

We find these sides using the sine rule

Sine rule =

a/ sin A = b/ Sin B

Hence for triangle WXY

w/ sin W = x/ sin X = y/ sin Y

a) side w

w/ sin W= y/ sin Y

w/sin 27 = 38/sin 40

Cross Multiply

sin 27 × 38 = w × sin 40

w = sin 27 × 38/sin 40

w = 26.83879ft

w = 26.84ft

Finding side x

x / sin X= y/ sin Y

x/ sin 113 = 38/sin 40

Cross Multiply

sin 113 × 38 = x × sin 40

x = sin 113 × 38/sin 40

x = 54.41795ft

x = 54.42ft

To find the area of triangle WXY

We use heron formula, which is given as:

= √s(s - w) (s - x) (s - y)

Where S = w + x + y/ 2

s = (38 + 26.84 + 54.42)/2

s = 59.63

Area of the triangle

= √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)

Area of the triangle = √220343.61423

Area of the triangle = 469.40772706541ft²

Therefore, approximately to the nearest tenth , the Area of ∆WXY =469.4yd²

Answer:

1/8-7/8= -3/4

Step-by-step explanation:

1/8-7/8 is just like 7/8-1/8 but is the opposite

7/8-1/8=6/8 or 3/4

1/8+6/8=7/8

1/8-1/8=0

0-6/8= -6/8 or -3/4

Answer:

126 $

Step-by-step explanation:

1- 18000 / 100 = 180

2- 180 x 0.7 = 126$

Answer:

Step-by-step explanation:

[tex]m\angle OFB=m\angle OCB=90^o\\\\so\ from\ BCOF:\\\stackrel{\big{\frown}} {CDF} =m\angle COF=360^o-2\cdot90^o-82^o=98^o \\\\\\ \stackrel{\big{\frown}} {CGF} =360^o-\stackrel{\big{\frown}} {CDF} =360^o-98^o=262^o[/tex]

Answer:

11

Step-by-step explanation:

Given:

3/2y - 3 + 5/3z

When

y=6

z=3

3/2y - 3 + 5/3z

Substitute the value of y and z

3/2(6) - 3 + 5/3(3)

=18/2 - 3 + 15/3

=9-3+5

=6+5

=11

8% lower means the gauge is showing 92% of the original pressure

( 100% - 8% = 92%)

Divide the pressure the gauge is showing by 92%

33.58 / 0.92 = 36.5

The actual pressure is 36.5

Answer:

-4

Step-by-step explanation:

When looking at the graph look at the y axis and look to see where the line passes through

Answer:

-4 is the y intercept.

Step-by-step explanation:

Brainliest? Have a great day!