use these two graphs to answers questions for 4 and 5


why do these graphs represent functions? explain.​

Answer:

157.5°

Step-by-step explanation:

Total size of interior angles=(2n-4)90°

(2x16-4)90= 2520

size of one interior angle= (2n-4)90°/n

2520/16

Answer= 157.5°

NB n is the number of sides

The size of the interior angle of a regular 16-sided polygon would be 157.5 degrees.

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal.

The formula for finding the sum of the measure of the interior angles is,

S = (n - 2) × 180.

We have to give that,

A regular-sided polygon has 16 sides.

Using the formula for a regular polygon of n sides would be,

Each interior angle = \(\dfrac{(2n - 4) \times 90 deg}{n}\)

Here, we have the sides of the regular polygon;

n = 16

Hence substitute n = 16 in above formula,

Each interior angle = \(\dfrac{(2n - 4) \times 90 deg}{n}\)

                                \(= \dfrac{(2\times 16 - 4) \times 90 deg}{16}\)

                                \(= \dfrac{(28) \times 90 deg}{16}\)

                              \(= 157.5 \ \text{degree}\)

Therefore, The size of the interior angle would be, 157.5 degrees.

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Answer:

Step-by-step explanation:

Step one:

given data

we are told that before tax the bill is pretax= $78

the tax is 8%

and he left 20% of the pretax for the attendant.

Step two:

let us find the amount he paid for eating with tax

=8/100*78

=0.08*78

=$6.24

with tax the meal cost  is

= 78+6.24

=$84.24

let us solve for the tip he left  (note: it is 20% of the pretax)

=20/100*78

=0.2*100

=$15.6

the tip is $15.6

Step three:

the total amount he paid after eating plus tax and tip is

78+6.24+15.6

=$99.84

Answer:

99.84

Step-by-step explanation:

Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute

Answer:

41.5

Step-by-step explanation:

you use the trigonometric equations. in this case, we will use SOH:

sin 49=opposite/adjacent

sin 49=x/55

55 sin 49=x

41.50=x

Therefore, x is equals to 41.50. And it is already to it's nearest hundredth.

The value of x is  41.25.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

We use the sin function.

Sin 49 = DE/DF

Sin 49 = x / 55

0.75 = x / 55

x = 0.75 x 55

x = 41.25

Thus,

The value of x is  41.25.

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Answer:

C. 24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

9 ÷ 3[12 - 4]

3[8] = 24

Answer:

69

Step-by-step explanation:

just cause

Answer:

Given a triangle ABC, Pythagoras' Theorem shows that:

\(c^2=a^2+b^2\)

Thus,

\(c = \sqrt{a^2+b^2}\)

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.

\(d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2\)

\(d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }\)

Therefore when given the hypotenuse with endpoints at

\((x_{1}, y_{1}) and {(x_{2}, y_{2})\)

We know that the third point of the right triangle will be at

\((x_{2}, y_{1})\)

and that the two side lengths will be defined by the absolute values of:

\((x_{2} - x_{1}) = a\)

\((y_{2} - y_{1}) = b\)

All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

          x³ + 8x² + 100x = -800

x³ + 8x² + 100x + 800 = 0

Then the factor of the equation will be

x³ + 8x² + 100x + 800 = 0

x² (x + 8) + 100(x + 8) = 0

        (x² + 100)(x + 8) = 0

Then all the solution of the equation will be

x = 10i, -10i, and -8.

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

Substitution method - the points are (-6, -11/2),(-4,-3), (-8/5,0), (0,2) and (4,7)

what is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

we are given the equation,

5x - 4y = -8

case I

when x = -6

5(-6) - 4y  = -8

-30 - 4y = -8

-4y = -8 + 30

-4y = 22

y = -(22/4)

y = -11/2

(x,y) = (-6, -11/2)

case II

when y = -3

5x - 4(-3) = -8

5x + 12 = -8

5x = -8 -12

5x = -20

x = -20/5

x = -4

(x,y) = (-4,-3)

case III

when y = 0

5x - 4y = -8

5x - 4(0) = -8

5x = -8

x = -8/5

(x,y) = (-8/5,0)

case III

when x = 0

5(0) - 4y = -8

0 - 4y = - 8

y= 8/4

y = 2

(x,y) = (0,2)

case IV

when x = 4

5(4) - 4y = -8

20 - 4y = -8

-4y = -8-20

-4y = -28

y = 28/4

y = 7

(x,y) = (4,7)

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The solutions of provide logarithmic equations are present in below :

1) x = 9 ; 2) x = 0 ; 3)p = 7/9 ; 4) k= 2 ; 5) a= -1 ; 6) r = -1/2 ; 7) n = 2 ; 8) x = 1/35 ; 9) m = -2 ; 10) x = 84 ; 11) v = -6, -6 ; 12) x = -4, -7

The logarithmic number is associated with exponent and power, such that if xⁿ = m, then it is equal to logₓ m = n. That is exponential value are inverse of logarithm values. Some basic properties of logarithmic numbers:

Now, we solve each logarithm equation one by one. Assume that 'log' is the base-10 logarithm where absence of base.

1) log (5x) = log (2x + 9)

Exponentiate both sides

=> 5x = 2x + 9

=> 3x = 9

=> x = 9

2) log (10 − 4x) = log (10 − 3x)

Exponentiate both sides,

=> 10 - 4x = 10 - 3x

simplify, => x = 0

3) log (4p − 2) = log (−5p + 5)

Exponentiate both sides,

=> 4p - 2 = - 5p + 5

simplify, => 9p = 7

=> p = 7/9

4) log (4k − 5) = log (2k − 1)

Exponentiate both sides,

=> 4k - 5 = 2k - 1

simplify, => 2k = 4

=> k = 2

5) log (−2a + 9) = log (7 − 4a)

Exponentiate both sides,

=> - 2a + 9 = 7 - 4a

simplify, => 2a = -2

=> a = -1

6) 2log₇( −2r) = 0

=> log₇( −2r) = 0

using the property, log꜀a = n <=> cⁿ = a

=> ( 7⁰) = - 2r

=> -2 × r = 1 ( since a⁰ = 1 )

=> r = -1/2

7) −10 + log₃(n + 3) = −10

=> log₃(n + 3) = −10 + 10 = 0

using the property, log꜀a = n <=> cⁿ = a

=> 3⁰ = n + 3

=> 1 = n + 3

=> n = 2

8) −2log₅ ( 7x ) = 2

=> log₅ 7x = -1

=> 5⁻¹ = 7x

=> x = 1/35

9) log( −m) + 2 = 4

=> log( −m) = 2

Exponentiate both sides,

=> -m = 2

=> m = -2

10) −6log₃ (x − 3) = −24

simplify, log₃ (x − 3) = 4

=> (x - 3) = 3⁴ ( since log꜀a = n <=> cⁿ = a )

=> x - 3 = 81

=> x = 84

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

=> log₁₂ (v²+ 35) - log₁₂ (−12v − 1) = 0

Using the quotient property of logarithm,

\(log_{12}( \frac{v²+ 35}{-12v-1}) = 0 \)

\(\frac{v²+ 35}{-12v - 1} = {12}^{0} = 1 \)

\(v²+ 35 = −12v − 1\)

\(v²+ 35 + 12v + 1 = 0\)

\(v²+12v + 36 = 0\)

which is a quadratic equation, and solve it by middle term splitting method,

\(v²+ 6v + 6v + 36= 0\)

\(v(v + 6) + 6(v + 6)= 0\)

\((v + 6) (6 + v)= 0\)

so, v = -6, -6

12) log₉(−11x + 2) = log₉ (x²+ 30)

=> log₉ (x²+ 30) - log₉(−11x + 2) = 0

Using the quotient property of logarithm,

\(log₉(\frac{x²+ 30 }{−11x + 2}) = 0\)

\( \frac{x²+ 30}{-11x + 2} ={9}^{0} = 1 \)

=> x² + 30 = - 11x + 2

=> x² + 11x + 30 -2 = 0

=> x² + 11x + 28 = 0

Factorize using middle term splitting,

=> x² + 7x + 4x + 28 = 0

=> x( x + 7) + 4( x + 7) = 0

=> ( x + 4) (x+7) = 0

=> either x = -4 or x = -7

Hence, required solution is x = -4, -7.

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Complete question:

kuta software infinite algebra 2 logarithmic equationsSolve each equation.

1) log 5x = log (2x + 9)

2) log (10 − 4x) = log (10 − 3x)

3) log (4 − 2) = log (−5 p + 5)

4) log (4k − 5) = log (2k − 1)

5) log (−2a + 9) = log (7 − 4a)

6) 2log₇ −2r = 0

7) −10 + log₃(n + 3) = −10

8) −2log₅ 7x = 2

9) log −m + 2 = 4

10) −6log₃ (x − 3) = −24

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

12) log₉(−11x + 2) = log₉ (x²+ 30)

The distance between the tips of the minute and hour hands of a large clock is changing at a rate of approximately 0.0084 feet per minute at 6:20 pm.

To find the rate at which the distance between the tips of the two hands is changing, we can use the concept of related rates. Let's consider the minute hand and the hour hand as they move on the clock face.

At 6:20 pm, the minute hand is pointing at the 4 on the clock, and the hour hand is pointing between the 6 and 7 on the clock. We can calculate the angle between the two hands by taking the difference in their positions. The minute hand has moved 20 minutes past the 6, which corresponds to 1/3 of the clock's circumference, or 2π/3 radians. The hour hand has moved 1/3 of the way between the 6 and 7, which corresponds to 1/12 of the clock's circumference, or π/6 radians.

The distance between the tips of the hands can be found using the law of cosines. Considering the minute hand as the side a (length 1 foot), the hour hand as the side b (length 1/2 feet), and the angle between them as θ (π/6 - 2π/3), we can use the formula: c^2 = a^2 + b^2 - 2ab*cos(θ).

By substituting the given values, we have c^2 = (1)^2 + (1/2)^2 - 2(1)(1/2)*cos(π/6 - 2π/3).

Simplifying, c^2 = 5/4 - √3/2.

Differentiating both sides with respect to time, we have 2c(dc/dt) = 0 - (-√3/2)(dθ/dt).

Since the minute hand moves at a constant rate of 2π radians per hour, dθ/dt = 2π/60 = π/30 radians per minute.

Substituting the values, we get 2c(dc/dt) = (√3/2)(π/30).

Simplifying, dc/dt = (√3/4π) feet per minute.

Therefore, at 6:20 pm, the distance between the tips of the minute and hour hands is changing at a rate of approximately 0.0084 feet per minute.

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Answer:

\( V = U + at\)

Step-by-step explanation:

Given the following data;

Initial velocity = 0 (since the stone is starting from rest).

Final velocity = 32 m/s

Acceleration = g = 10 m/s²

Time = 3.2 seconds

To show that the speed of the stone when it hits the ground is 32 m/s, we would use the first equation of motion;

\( V = U + at\)

Where;

Substituting into the formula, we have;

\( 32 = 0 + 10*3.2\)

\( 32 = 0 + 32 \)

\( 32 = 32 \)

Proven: 32 m/s = 32 m/s

Answer:

(6, -13)

Step-by-step explanation:

The rule is (x+2, y-8) so,

4+2=6

-5-8=-13

That would give you (6, -13)

Hope this helps

Answer:

Activity 68

a. ∠1, ∠3, ∠4 : its ∠1

b.  ∠2, ∠4, ∠5 : its ∠5

c.  ∠5, ∠6, ∠8 : its ∠8

Activity 69

A

1. 13, 15, 28 : No because sum of the 2 sides is not larger than the third

2. 4, 9, 14 : No because sum of 2 sides is not larger than the third

3. 15, 20, 25 : yes because sum of 2 sides is larger than the third

also

its a right triangle. its a 3 4 5 right triangle where 5 is the hypotenuse

B.

The third side must be shorter than 12 + 23 = 35 and longer than 23 — 12 = 11. So the range is 11 to 35 units, not including 11 or 35.

Activity 70

shortest side = smallest angle on the opposite side

longest side = largest angle  on the opposite side

B is 30 A is 60  C is 90

1. ∠B ∠A ∠C

2. ∠E ∠D ∠F

gathmath

quora

toppr

Answer:

B. 88.8

Step-by-step explanation:

let x represent class y

(x+71.2)/2=80   multiply each side by 2

x+71.2=160      subtract 71.2 by both sides

x=88.8

or

trial an error

replace x with each of the numbers and see if it plugs in.

example:

(80.5+71.2)/2=80

151.7/2=80

75.85=80?

false. incorrect

another example:

(88.8+71.2)/2=80

160/2=80

80=80?

true. correct

Answer:

3 Blouses cost $450

Step-by-step explanation:

1,200 ÷ 8 = 150

150 x 3 = 450

Answer: $450

Step-by-step explanation:

First divide 1,200 by 8 (150) Then times that by 3 to get the answer

Answer:

Step-by-step explanation:

f(1) = 160

f(n + 1) = -2 * f(n)

n = 1

f(2) = -2*f(1)

f(2) = -2*160

f(2) = - 320

f(3) = - 2*f(2)

f(3) = -2 * - 320

f(3) = 640

f(4) = -2 * f(3)

f(4) = -2 * 640

f(4) = - 1280

Answer:

Step-by-step explanation:

$68

--------------- * 15 months = $85

12 months

15 months will cost $85.  Total cost (m) = ($5.67/mo)*m, where m represents the number of months of service purchased.

Answer:

800

Step-by-step explanation:

2×4=8

add the 0 form 20 and 40

800

Answer:

800 students

Step-by-step explanation:

just multiply 20 by 40 to get how many students in all because each class has 40 students and there's 20 classes in all. so the answer is 800.

Answer:  How many hours did Jacob work in his second week if he earned $117?​

Step-by-step explanation:

We can start by setting up a proportion to relate the number of hours worked to the amount earned:

hours worked / amount earned = constant of proportionality

Let's call the constant of proportionality "k". Then we have:

15 / 146.26 = k

Solving for k, we get:

k = 9.75

Now we can use this value of k to find the number of hours Jacob worked in his second week:

117 / 9.75 = 12

Therefore, Jacob worked 12 hours in his second week if he earned $117.

{Hope This Helped! :)}

B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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The value of the discriminant is 0 and the number of real solutions is 1

For the given equation, 36x^(2)-24x+4=0, we can find the value of the discriminant and the number of real solutions using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation.

The discriminant is the part of the formula under the square root, b^(2)-4ac.

In this equation, a = 36, b = -24, and c = 4. Plugging these values into the discriminant, we get:

Discriminant = (-24)^(2)-4(36)(4) = 576-576 = 0

Since the discriminant is equal to 0, there is only one real solution to this equation.

Therefore, the value of the discriminant is 0 and the number of real solutions is 1.

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Answer:
A' = (-5,4)
B' = (-4,4)

C' = (-4,5)

D' = (-1,2)

E' = (-2,1)

Step-by-step explanation:

For the 90 degrees counterclockwise rotation (x,y) will be (-y,x) so just switch places and put the negative sign.

There are 48 possible poker hands that contain all four aces, and the probability of getting one of these hands is 0.002%.

A poker hand that contains all four aces can be formed in 48 ways.

This is because there are 48 cards remaining in the deck after the four aces are removed, and any one of these cards can be chosen to complete the hand.

The number of ways to choose 5 cards from a deck of 52 is 52C5 = 2,598,960.

So the probability of getting a hand with all four aces is 48/2,598,960 = 0.0000185, or about 0.002%.

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The profitability index for this project is approximately 0.65, indicating that it may not be a favorable investment as the PI is less than 1.

The profitability index (PI) is a ratio that measures the present value of future cash flows of a project per dollar of initial investment.

To calculate the PI of a project with an initial investment of $194,000 and a net present value of -$68,000, you would divide the present value of future cash flows by the initial investment.

PI = Present Value of Future Cash Flows / Initial Investment

Since the net present value is negative, we can assume that the present value of future cash flows is less than the initial investment.

PI = (-$68,000) / $194,000

PI = -0.35

The PI of the project is negative (-0.35), which means that the project is not expected to be profitable and may result in a net loss. Therefore, it may not be a wise investment decision.
The profitability index (PI) is a financial metric used to evaluate the attractiveness of an investment. It is calculated by dividing the present value of future cash flows by the initial investment. In this case, the initial investment is $194,000 and the net present value (NPV) is -$68,000. To calculate the PI:

PI = (NPV + Initial Investment) / Initial Investment
PI = (-$68,000 + $194,000) / $194,000
PI = $126,000 / $194,000
PI ≈ 0.65

The profitability index for this project is approximately 0.65, indicating that it may not be a favorable investment as the PI is less than 1.

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Step-by-step explanation:

here's the answer to your question

Answer:

x = -4.7

Step-by-step explanation:

√4x+9 = 1-√2

2x + 9 = 1 - √2

2x = -8 - √2

2x / 2 =  -8 - √2 / 2

x = -4.7

Answer:

9,007,308

Hope this helps.

Answer:

(nine million, seven thousand, three hundred and eight)

Answer:

This is absolutely amazing! I love the passion in your anger. I can tell that this was a real life experience, and if it wasn't, your songwriting abilities are at a peak. at the melody that I read it in, it sounded sort of indie pop.

Step-by-step explanation:

Incredible story, loved it.

and the "your probably with that girl" really gave Olivia Rodrigo! love it so much.

Answer:

I love it.

Step-by-step explanation:

I really like it but one thing I learned about songwriting, make sure you are putting it through eyes.