Venita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus 0). Which best describes Venita’s error?

Answer:

becouse 4×960 will give you

3840

The equation your teacher has given you is an identity. We can prove this by transforming one side into the other. I'll transform the right hand side (RHS) into the left hand side (LHS).

This means I'll keep the LHS the same for each line. I'll only change the RHS. The goal is to get the same thing on both sides (I could go the other way around but I find this pathway is easier).

[tex]\tan^4(\theta)+\sec^2(\theta) = \sec^4(\theta)-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\sec^2(\theta)\right)^2-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\tan^2(\theta)+1\right)^2-\tan^2(\theta) \ \text{ ... see note 1}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+2\tan^2(\theta)+1-\tan^2(\theta)\\\\[/tex]

[tex]\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\tan^2(\theta)+1\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta)-1+1 \ \text{ ... see note 2}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta) \ \ \Large \checkmark\\\\[/tex]

So because we've arrived at the same thing on both sides, the original equation is an identity. It always true no matter what theta value you plug in, as long as theta is in the domain. So something like theta = pi/2 won't work because tan(pi/2) = undefined and sec(pi/2) = undefined. It's based on how cos(pi/2) = 0 and this value is in the denominator. Dividing by zero is undefined.

Consequently, this means all solutions to cos(theta) = 0 will be excluded from the domain. Everything else works.

Answer:

30. 2x²-x-1=0

or, 2x²-2x+x-1=0

or, 2x(x-1)+1(x-1)=0

or, (x-1)(2x+1)=0

so, x-1 = 0 or, x = 1

and 2x+1 = 0 or, 2x = -1 or, x = -1/2

so, x = 1 and 1/2

31. 3x²-14x=5

or, 3x²-14x-5=0

or, 3x²-15x+x-5=0

or, 3x(x-5)+1(x-5)=0

or, (x-5)(3x+1)=0

so, x-5=0 or, x=5

and 3x+1=0 or, 3x=-1 or, x=-1/3

so, x = 5 and -1/3

Answered by GAUTHMATH

Answer:

None

Step-by-step explanation:

No lines can be folded over to match up with the opposite side

Answer:

v = 3

General Formulas and Concepts:

Pre-Algebra  

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

12v + 10v + 14 = 80

Step 2: Solve for v

Answer: reduction

Step-by-step explanation:

ABCD-> 'ABCD

its bc 'ABCD got smaller compared to ABCD

Answer:

It is a reduction.

Step-by-step explanation:

Hope this helped.

Answer:

x is 3.[tex]\overline{72}[/tex]

Step-by-step explanation:

The given points on the line are;

R(-5, -6), S(1, 5) and T(x, 10)

The number of points required to find the equation of the line = 2 points

The slope, m, of the line using points R(-5, -6) and S(1, 5) is given as follows;

m = (5 - (-6))/(1 - (-5)) = 11/6

The equation of the line in slope and point form, using point S(1, 5) is therefore;

y - 5 = (11/6)·(x - 1) = 11·x/6 - 11/6

y - 5 = 11·x/6 - 11/6, given that the x-value is required, we have;

x = (y - 5 + 11/6) × 6/11 = 6·y/11 - 19/11

x = 6·y/11 - 19/11

At point T(x, 10), y = 10, therefore, we have;

x = 6×10/11 - 19/11 = 41/11 = 3.[tex]\overline{72}[/tex]

x = 3.[tex]\overline{72}[/tex].

Answer:

19 units

Step-by-step explanation:

count the squares around the shape for the slanted part treat it like a rectangle and just count the squares from the pointy spot to the other side where it stops

Answer:

2/5m - 1/5

Step-by-step explanation:

Given the equation :

2(1/5m - 2/5) + 3/5

First step:

Open the bracket by multiplying values in the bracket by 2

2/5m - 4/5 + 3/5

-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5

Hence,

2/5m - 4/5 + 3/5 = 2/5m - 1/5

= 2/5m - 1/5

Answer:

13.5

Step-by-step explanation:

Given

tan34° = [tex]\frac{x}{20}[/tex] ( multiply both sides by 20 )

20 × tan34° = x , then

x ≈ 13.5 ( to the nearest tenth )

Answer:

Four cars that can hold 3 passengers

Step-by-step explanation:

The number of cars on the Cyclone Coaster = 16 cars

The number of passengers some cars hold = 2 passengers

The number of passengers the other cars hold = 3 passengers

The number of people altogether the Cyclone Coaster has room for = 36 people

Let x represent the number of cars that can hold 3 passengers, and let y represent the number of cars that can hold 2 passengers, we have;

3·x + 2·y = 36...(1)

x + y = 16...(2)

The value of x can be found by making y the subject of equation (1) and equation (2) and equating both values of y given in x as follows;

The value of y from equation (1) is, y₁ = (36 - 3·x)/2 = 18 - 3·x/2

∴ y₁ = 18 - 3·x/2

The value of y from equation (2) is, y₂ = 16 - x

Equating both y values, to find the coordinates of the common point to both equations, gives;

At the common point y₁ = y₂

By the substitution property of equality

∴ 18 - 3·x/2 = 16 - x

3·x/2 - x = 18 - 16 = 2

x/2 = 2

∴ x = 4

The number of cars that can hold 3 passengers, x = 4

(From y₂ = 16 - x, we have

y₁ = y₂ = 16 - 4 = 12

y = 1

The number of cars that can hold 2 passengers, y = 12).

Answer:

40. A c=60

41 B z= 40

Step-by-step explanation:

The sum of the angles in a triangle is 180

40.  61+59+c = 180

Combine like terms

120+c = 180

c = 180-120

c =60

41.  90+50+z = 180

140 +z = 180

z = 180-140

z = 40

Answer:

dont understand clearly

Step-by-step explanation:

Answer:

We want to "chop and round" the periodic number 0.9 at 3 digits.

First, remember that we can write our periodic number as:

0.9 = 0.9999...

Such that the nine repeats infinitely.

Now we want to chop it at the third digit, and then round.

To chop at the third digit we just "cut" the number at the third digit after the decimal point, we will get:

0.9 ≈ 0.999

Now we round.

Remember that to round a number, we need to look at the last digit after the decimal point.

If the last digit is 5 or larger, we round up, adding 1 to the previous decimal.

If the last digit is 4 or smaller, we round down, don't adding anything to the previous decimal.

in our number:

0.999

The last digit is a 9, so we round up.

Then we add "1" to the previous decimal

but the previous decimal is a 9, so when we add 1, it will transform into a 10.

So it also adds one to the previous decimal, which also is a 9, so the process repeats, this time adding 1 to the decimal to its left, in this case, that decimal will be the first decimal at the left of the decimal point.

So after rounding, we will get:

0.999 ≈ 1

Then we can conclude that:

he 3 digit chopping and rounding approximately of the number 0.9 is 1"

Answer:

Step-by-step explanation:

The 2 2/5 is not showing up correctly, but I think it means that you are going 2 miles + 2/5 of a mile. If that is not true, leave me a note and I'll correct it.

So 75 and 30(n - 5) represent cents (I think) per 1/5 of a mile.

1 mile has 5 fifths.

2 miles has 10 fifths

2/5 has 2 fifths.

the total is 17 fifths so n = 17

C = 75 + 30(17 - 5)

C = 75 + 30(12)

C = 75 + 360

C = 435

That means you pay 4 dollars and 35 cents.

Answer:

probability that 2 cards drawn from a deck of 52 cards are both kings.

is probability that first card is a king times probability that second card is a king

with replacement 4/52*4/52 =0.592%

without replacement 4/52*3/51=0.452%

Step-by-step explanation:

Answer:

Step-by-step explanation:

peter can buy pack of nine pencils

6 divided by 1.68 =3.5

9 divided by 2.34=3.8

package 2 is just 0.3 more

it give 3 more pencils for 0.3

Part (i)

I'm going to use the notation T(n) instead of [tex]T_n[/tex]

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

Answer:

BW = 132.59

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 9 = 21 / BW

BW tan 9 = 21

BW = 21/ tan 9

BW = 132.5887818

BW = 132.59

Answer:

Step-by-step explanation:

Side BW is the height, aka as the side adjacent to the reference angle of 9 degrees. We have the side opposite the reference angle (21) and we are looking for the side adjacent to the reference angle. The trig ratio that we use for this, the one that relates the sides opposite and adjacent, is the tangent ratio, namely:

[tex]tan(9)=\frac{21}{BW}[/tex] and solving for BW:

[tex]BW=\frac{21}{tan(9)}[/tex] so

BW = 132.59

Answer:

hlo buddy

are u free now.. nhjm....

Answer: $25.85 assuming annual compounding.

Step-by-step explanation:

PV=470

I/Y=5.5

N=1

CPT_FV

Answer:

20.4

Step-by-step explanation:

cos(74) = x/74

x = 74×cos(74)

x = 20.4

Answered by GAUTHMATH

The answer is B

Eplanation:

V = pi * r² * (h/3)

Then from here you just make h the subject of the formula:

h = (V * 3)/(pi * r²)

h = (393*3)/[3.14* (10/2)²]

h = 15.01910828 ft

which is rounded to 15 ft...B

:)

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

[tex] {v}^{2} = {u}^{2} + 2as \\ {v}^{2} = 144 - 108 \\ {v}^{2} = 36 \\ v = 6 , -6 \: [/tex]

Answer:

12.73

Step-by-step explanation:

Set up ratio.

[tex]\frac{22}{100} =\frac{2.89}{x}[/tex]

Solve for x.

[tex]\frac{100}{22} =\frac{x}{2.8}[/tex]

[tex]\frac{100}{22} (2.8)=x[/tex]

x=12.73

Answer:

The radius of the circle if the circumference is 44 cm will be 7 cm.

Step-by-step explanation:

➝ Circumference of the circle = 44 cm

➔ Circumference = 2πr [For finding radius]

Finding the radius:-

➜ Let radius be r.

➜ 44 = 2 × 22/7 × r

➜ Multiply 2 × 22/7

➜ 44 = 44/7 × r

➜ Taking 7 to LHS.

➜ 44 × 7 = 44 × r

➜ 308 = 44 × r

➜ Taking 44 to LHS.

➜ 308/44 = r

➜ 308/44 = 7

➜ 7 = r

➜ r = 7

Answer:

40 oranges are there in 100 fruites.