6.21(3.1) answer for number 6

Answer:

  25%

Step-by-step explanation:

The ratio of rise to run is ...

  rise/run = 6 ft/24 ft = 1/4

Expressed as a percentage, this is ...

  1/4 × 100% = 25%

_____

Comment on this grade

Interstate highways are limited to a 7% grade. Most local jurisdictions limit the grade of a road to somewhere between 12% and 15%.

Answer:  see proof below

Step-by-step explanation:

You will need the following identities to prove this:

[tex]\tan\ (\alpha-\beta)=\dfrac{\tan \alpha-\tan \beta}{1+\tan \alpha\cdot \tan \beta}[/tex]

[tex]\cos\ 2\alpha=\cos^2 \alpha-\sin^2\alpha[/tex]

LHS → RHS

[tex]\dfrac{2\tan\ (45^o-A)}{1+\tan^2\ (45^o-A)}\\\\\\=\dfrac{2\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)}{1+\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)}{1+\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{1+\bigg(\dfrac{1-2\tan\A+\tan^2 A}{1+2\tan A+\tan^2A}\bigg)}\\[/tex]

[tex]=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{(1+2\tan A+\tan^2A)+(1-2\tan A+\tan^2 A)}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{2+2\tan^2A}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{2\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}\\\\\\=\dfrac{\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}[/tex]

[tex]=\dfrac{1-\tan A}{1+\tan A}}\times \dfrac{(1+\tan A)^2}{1+\tan^2A}\\\\\\=\dfrac{1-\tan^2 A}{1+\tan^2 A}\\\\\\=\dfrac{1-\dfrac{\sin^2 A}{\cos^2 A}}{1+\dfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{\bigg(\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A}\bigg)}{\bigg(\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}\bigg)}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A+\sin^2 A}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{1}\\\\\\=\cos^2 A-\sin^2 A\\\\\\=\cos 2A[/tex]

cos 2A = cos 2A   [tex]\checkmark[/tex]

Answer:

Step-by-step explanation:

Using Pythagoras Theorem, hypotenuse = 5

[tex]h = \sqrt{a^{2}+ b^{2}[/tex]

[tex]h = \sqrt{9+16 }\ = \sqrt{25}\ = 5[/tex]

sin x = height / hypotenuse = 3 / 5

cos y = base / hypotenuse = 3 / 5

sin x = cos y = 3 / 5

Answer:

Bottom right option

Step-by-step explanation:

To find this, we can calculate:

1/2 * 4.32 * 10⁻⁴

= (1/2 * 4.32) * 10⁻⁴

= 2.16 * 10⁻⁴

The diameter of a new cell is 2.16×10−⁴millimeters

First step is to calculate 4.32×10−⁴ to the original numbers

4.32×10−⁴ =0.000432

Second step is to determine the diameter of a new cell

New cell diameter=0.000432×1/2

New cell diameter=0.000216

New cell diameter=2.16×10−⁴millimeters

Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters

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Answer:

7

Step-by-step explanation:

Step-by-step explanation:

The three main types of exercise are cardiovascular exercise, strength training and stretching. All three types of exercise are important for physical fitness. Cardiovascular aerobic exercise is repetitive, rhythmic exercise that increases your heart rate and requires you to use more oxygen.

Answer:

6.67

Step-by-step explanation:

Answer:

x-axis

Step-by-step explanation:

Answer:

It is the x-axis

Step-by-step explanation:

In  a graph, the horizontal part of it is called the x axis.

Here is an definition: horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates

Answer:

31 Pikachu bags were sold.

19 peanut bags were sold.

Step-by-step explanation:

Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.

We know that the number of Peanuts sold is 50-x (as the total needs to be 50)

We know that the total revenue is:

Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts

Using our definitions above:

Total Revenue = x * $3.68 + (50-x) * $0.76

We know that the revenue needs to be $128.52.

$128.52 = x * $3.68 + (50-x) * $0.76

Let's remove the $ signs.

128.52 = x * 3.68 + (50-x) * 0.76

Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.

128.52 = x*3.68 + 50*0.76 - x*0.76

128.52 = x*3.68 + 38 - 0.76*x

Subtracting 38 from both sides

90.52 = 3.68*x - 0.76*x

We can simplify the right side.

90.52 = 2.92*x

We can divide both sides by 2.92:

31 = x

And flip it:

x = 31

So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is

50-x = 50-31 = 19

31 Pikachu bags were sold.

19 peanut bags were sold.

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]

Let the number of peanut bags be x

Then, Number of pikachu bags = 50 - x

Given,

Then,

⇛ Total cost he gets from peanut bag = $0.76 × x

⇛ Total cost he gets from pikachu bag = $3.68(50 - x)

According to question,

⇛ $0.76x+ $3.68(50 - x) = $128.52

Solving this equation,

⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)

⇛ 184 - 2.92x = 128.52

⇛ 184 - 128.52 = 2.92x

⇛ 55.48 = 2.92x

Flipping the equation,

⇛ 2.92x = 55.48

⇛ x = 55.48 / 2.92

⇛ x = 19

Then,

⇛ 50 - x = 50 - 19 = 31

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Answer:

x = 75

Step-by-step explanation:

FGE is a straight line so it equals 180 degrees

FGA + AGC + CGE = FGE

x + 90 + 15 = 180

Combine like terms

x+ 105 = 180

Subtract 105 from each side

x = 180-105

x = 75

Answer:

x = 75º

Step-by-step explanation:

The Vertical Angle Theorem shows that:

∠CGE ≅ ∠DGF

So:

∠DGF = 15º

∠AGD = 90º

90º - 15º = 75º

x = 75º

Answer:

convert them to decimasls

Step-by-step explanation:

convert thhem to decimals to make it easier

Answer:

1/2 2/4 4/8 6/12 9/18

Step-by-step explanation:

Answer:

x = 180 - [(180 - 3x) + (180 - 2x)]

Step-by-step explanation:

Start off by finding the angles of the triangle

Angle F = 180 - 3x

The angle across from I (which I will call I) = 180 - 2x

Angle G = 180 - (F + I)

Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G

Therefore x =  180 - (F + I) or otherwise said as:

x = 180 - [(180 - 3x) + (180 - 2x)]

I hope this is helpful :)

Answer:

The first one

Step-by-step explanation:

This line is the best fit for the scatter plot because it touches a lot more points than the second

Answer:

The first line

Step-by-step explanation:

Hey there!

Well the first lie is a positive slope just like the dots whereas,

the second line is a negative slope.

Therefore, the first line is the line of best fit.

Hope this helps :)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The amount left in the bank account is -$50.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount in the bank account = $150

Cost of the bike = $200

The amount left in the bank account.

= 150 - 200

= -$50

Thus,

The amount left in the bank account is -$50.

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Answer:

1. EF = 65m

2. DF = 73m

Step-by-step explanation:

1. EF = height of the building = h = 33 / tan 27 = 65m

2. DF = sqrt (65² + 33²) = 73m

The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

From the triangle DEF, we find the value of EF by using tan function.

tan function is a ratio of opposite side and adjacent side.

tan(27)= 33/FE

0.5095 = 33/FE

Apply cross multiplication:

FE=33/0.5095

FE=64.76

Now DF is the hypotenuse, we find it by using pythagoras theorem.

DF²=DE²+EF²

DF²=33²+64.76²

DF²=1089+4193.85

DF²=5282.85

Take square root on both sides:

DF=72.68

In a triangle the the sum of three angles is 180 degrees.

∠D + 27 +90 =180

∠D + 117 =180

Subtract 117 from both sides:

∠D =63 degrees.

Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

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Answer:

she bought 7 cards

Step-by-step explanation

7x5=35 and im sure there is tax

Answer:

approximately 5.36

Step-by-step explanation

20 - 9.28 = 10.72

BD = EC

10.72/2 = 5.36

Answer: 24

Step-by-step explanation:

Colleen painted 7 windows, some of which were her mother's.

Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.

If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.

8+7+3+3+3=24

The total windows in the house are 21.

It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.

In our given problem, the algebraic relation between different members work output and total windows can be expressed as:

Windows painted by colleen and her mother = 7

Windows painted by father = (Windows painted by colleen and her mother + 1)

                                          = (7 + 1) = 8

∴ Windows painted by father = 8

Now, as given,

2 Windows painted by mother = Windows painted by father

∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4

and Windows painted by colleen = 7 - 4 = 3

Colleen and her 2 brothers paint equal windows;

∴  They painted 3 windows each.

The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:

⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21

Hence the total windows in the house are 21.

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Answer:

3^1 or 3

3^5 * 3^-4 are 3^5-4

so, 3^1!

Hope it helps!

Answer:

3^1

Step-by-step explanation:

Since the bases are the same and we are multiplying we can add the exponents

a^b * a^c = a^(b+c)

3^5 * 3^-4

3^ (5+-4)

3^1

Answer:

[tex]\Large \boxed{b=2}[/tex]

Step-by-step explanation:

-5+2(10b-2)=31

Expand brackets.

-5+20b-4=31

-9+20b=31

Add 9 on both sides.

20b=40

Divide both sides by 20

b=2

Answer:

Step-by-step explanation:

-5+2(10b-2)=31

Multiply the terms in the bracket

That's

- 5 + 20b - 4 = 31

Group like terms

Send the constants to the right side of the equation

That's

20b = 31 + 4 + 5

Simplify

20b = 40

Divide both sides by 20

We have the final answer as

Hope this helps you

Answer:

36

Step-by-step explanation:

There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)

A cube has 12 edges.

12x3=36

Answer:

A. 0

Step-by-step explanation:

In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices.  Since four is the smallest number, the other two must have four left as well.  That means Donavan drank 1 spoiled milk and 2 flat sodas.  Therefore, he drank 0 purified water.

Answer:

2

Step-by-step explanation:

A coefficient is the number placed before the variable. The variable gets multiplied by the coefficient.

The format is not exactly clear with the expression in the question.

Assuming the expression is '8 * 2n', the coefficient would be 2.

'n' is getting multiplied by '2'.

'8' does not have a variable next to it, so it is just a term in the expression.

The product of 8 and 2 is 16. 16 is not in the expression.

If the expression was '8.2n', 8.2 would be the coefficient.

Brainilest Appreciated.

Answer:

VW=35

YZ=50

Step-by-step explanation:

As they are similar triangles with a ratio of 1:2 and we know VW:XZ=1:2, we can make the equation:

2(4y+7)=12y-14

8y+14=12y-14

4y=28

y=7

So, VW=4(7)+7=35.

Similarly, you can find YZ through VT:

2(7x-17)=8x+2

14x-34=8x+2

6x=36

x=6

Therefore, YZ=8(6)+2=50.

Answer:

T≥2

Step-by-step explanation:

3t+9≥15

3T≥15-9

3T≥6

T≥2

Answer:

t ≥ 2

t ∈ [2 ; +oo)

Step-by-step explanation:

3t + 9 ≥ 15

3t ≥ 15 - 9

3t ≥ 6

t ≥ 6 : 3

t ≥ 2

t ∈ [2 ; +oo)

Answer:

f(4) = 3

Step-by-step explanation:

f(x) = -[tex]x^{2}[/tex] + 8x - 13

To find f(4), substitute 4 for all instances of x:

f(4) = -(4[tex])^{2}[/tex] + 8(4) - 13

Simplify the exponent:

f(4) = -16 + 8(4) - 13

Multiply:

f(4) = -16 + 32 - 13

Combine terms:

f(4) = 3

Answer:

3

Step-by-step explanation:

You plug in 4.

f(4)= -(4)^2+8(4)-13

f(4)= -16+32-13

f(4)= 16-13

f(4)=3

Answer:

Definitely the bottom left

Step-by-step explanation:

Answer:

d = √8

d ≈ 2.82843

Step-by-step explanation:

Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Simply plug in our coordinates into the distance formula:

[tex]d = \sqrt{(-3 + 5)^2+(-8 + 6)^2}[/tex]

[tex]d = \sqrt{(2)^2+(-2)^2}[/tex]

[tex]d = \sqrt{4+4}[/tex]

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

To find the decimal, simply evaluate the square root:

√8 = 2.82843

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 5 , - 6 ) ⇒ ( x₁ , y₁ )

B ( -3 , - 8 )⇒( x₂ , y₂ )

Now, let's find the distance between these two points:

AB = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]

Plug the values

⇒[tex] \mathsf{ \sqrt{( - 3 - ( - 5) )^{2} + {( - 8 - ( - 6))}^{2} } }[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

⇒[tex] \mathsf{ \sqrt{ {( - 3 + 5)}^{2} + {( - 8 + 6)}^{2} } }[/tex]

Calculate

⇒[tex] \mathsf{ \sqrt{ {(2)}^{2} + {( - 2)}^{2} } }[/tex]

Evaluate the power

⇒[tex] \mathsf{ \sqrt{4 + 4} }[/tex]

Add the numbers

⇒[tex] \mathsf{\sqrt{8} }[/tex]

Simplify the radical expression

⇒[tex] \mathsf{ \sqrt{2 \times 2 \times 2}} [/tex]

⇒[tex] \mathsf{2 \sqrt{2} }[/tex] units

Hope I helped!

Best regards!

Answer:

36 degrees

Step-by-step explanation:

Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.

(3x+30)+(6x-12)=90

9x+18=90

9x=72

x=8

AOB = 6x-12, so substituting

8 in for x gives us 48-12=36

Answer:

[tex]d=\sqrt{73}[/tex]

Step-by-step explanation:

[tex]Q(5, -1)[/tex]

[tex]P(-3, 2)[/tex]

Using the distance formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_2+y_1)^2}[/tex]

[tex]d=\sqrt{(-3-5)^2+(2-(-1))^2}[/tex]

[tex]d=\sqrt{(-8)^2+(3)^2}[/tex]

[tex]d=\sqrt{64+9}[/tex]

[tex]d=\sqrt{64+9}[/tex]

[tex]d=\sqrt{73}[/tex]

[tex]d\approx 8.5[/tex]

Answer:C and F are correct

Step-by-step explanation:

got it right on edge