Choose the answer based on the most efficient method as presented in the lesson. If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then what should the next step be? subtract 3 add 8 subtract 5x

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:

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:

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

[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:

x=2.5&.5

Step-by-step explanation:

The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a

12+or-sqrt((-12^2)-4(4)(5))

12+or-sqrt(144-80)

12+or-sqrt(64)

(12+8)/8 and (12-8)/8

x=2.5 and x=.5

Answer: [tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex] or [tex]x=2.5,\:x=0.5[/tex]

Step-by-step explanation:

[tex]4x^2-12x=-5[/tex]

[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]

[tex]4x^2-12x+5=-5+5[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x^2-12x+5=0[/tex]

Solve with Quadratic Formula

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]a=4,\:b=-12,\:c=5:\quad x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\frac{-\left(-12\right)+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]

[tex]\frac{12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=12+\sqrt{64}[/tex]

[tex]\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=\sqrt{64}[/tex]

[tex]\sqrt{64}=8[/tex]

[tex]=\frac{12+8}{8}[/tex]

[tex]=\frac{20}{8}[/tex]

[tex]=\frac{5}{2}[/tex]

[tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex]

Answer:

D. 15

Step-by-step explanation:

Use proportions.

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

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:

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:

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:

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:

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:

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:

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)

CHECK THE COMPLETE QUESTION BELOW;

Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza with t toppings, her total cost can be found using this expression: 0.90(2.25d + 1.40t + 6). What is the total cost for Lindy and her friends to order 4 drinks and a medium pizza with 3 toppings? A. $17.28 B. $16.52 C. $15.69 D. $28.40

Answer:

OPTION A. is correct

A)$17.28

Step-by-step explanation:

From the question we were giventhis expression as the total cost for all.

0.90(2.25d + 1.40t + 6).

We know that Lindy and her friends to order 4 drinks and a medium pizza with 3 topping

Then we can say d= 4 and t= 3 ,

Then we can substitute into below expresion

0.90(2.25d + 1.40t + 6).

0.90[2.25(4)+1.40(3)+6]

= 0.90[9+4.2+6]

= 17.8

Hence the total cost for Lindy = $ 17.28

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

Answer:

10a²b²6ab²

Step-by-step explanation:

Distribute the 2ab the other values

The correct answer is Maxine

Explanation:

One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.

Gina: [tex]\frac{3}{8} = 0.375[/tex]  

Maxine: [tex]\frac{2}{3} = 0.666[/tex]

Shari: [tex]\frac{2}{4} = 0.5[/tex]

Vanessa: [tex]\frac{3}{12} = 0.25[/tex]

According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).

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!

1st 2nd and last

Step-by-step explanation:

simplify your inequality

6x >= 3 + 4(2x -1)

6x >= 3 + 8x - 4

2x >= 1

x >= 1/2

so indeed the

1st one , the 2nd and the last one

first, second, last

Hope it helps

Answer:

Step-by-step explanation:

[tex]5(y - 3.8) = 4.7(y - 4)[/tex]

Distribute 5 through the parentheses

[tex]5y - 19 = 4.7(y - 4)[/tex]

Distribute 4.7 through the parentheses

[tex]5y - 19 = 4.7y - 18.8[/tex]

Move ' 4.7 y ' to L.H.S and change it's sign

[tex]5y - 4.7y - 19 = - 18.8[/tex]

Move constant to R.H.S and change it's sign

[tex]5y - 4.7y = - 18.8 + 19[/tex]

Collect like terms

[tex]0.3y = - 18.8 + 19[/tex]

Calculate

[tex]0.3y = 0.2[/tex]

Divide both sides of the equation by 0.3

[tex] \frac{0.3y}{0.3} = \frac{0.2}{0.3} [/tex]

Calculate

[tex]y = 0.67[/tex]

Hope this helps...

Best regards!!

Answer:

[tex]y = 0.67[/tex]   (To 2 dps)

y = 0.7 (To 1 dps)

y = 1 (To nearest whole no.)

Step-by-step explanation:

[tex]5(y-3.8) = 4.7 (y-4)[/tex]

Distribute the terms

[tex]5y - 19 = 4.7y-18.8[/tex]

Combining like terms

[tex]5y - 4.7y = -18.8+19[/tex]

Adding and subtracting

[tex]0.3y = 0.2[/tex]

Dividing both sides by 0.3

[tex]y = 0.2/0.3[/tex]

[tex]y = 0.67[/tex]

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:

117 R=0

Step-by-step explanation:

819:7= 117 R=0

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).

Step-by-step explanation:

your answer is C

HOPE IT HELPS YOU MATE

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:

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:

-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!