Which of the following statements must be true about the diagram? Check all that apply.

Answer:

f(g(x) = 1x² + 4x + 3

Explanation:

Question: f(g(x))

Given following:

While solving such function questions, solve from right to left.

⇒ f(x + 2)

⇒ (x + 2)² - 1

⇒ x² + 4x + 4 - 1

⇒ x² + 4x + 3

The exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

a) As the base of the exponent is greater than 1 so it is exponential growth.

b) 500 in the equation represents the initial value.

c) We have another exponential equation:

[tex]\rm b_2(t) = 800(1.6)^t[/tex]

For exponentikal gropwth:

1 + r = 1.6

r = 0.6 or

r = 6%

In the equation:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

The number of bacteria initially was 500 and from the second the number of bacteria initially was 800.

Thus, the exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

Learn more about exponential decay here:

brainly.com/question/14355665

#SPJ1

The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

The transformation rule for triangle P by translating using the vector [tex](^{\ 2}_{-7})[/tex] is (x, y) ⇒ (x + 2, y - 7)

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Answer:

y-intercept = -12

Step-by-step explanation:

The y-intercept is the "y" value when x = 0. You can find the y-intercept by plugging 0 into the equation and simplifying.

y = 4x - 12                                      <----- Original equation

y = 4(0) - 12                                    <----- Plug 0 in "x"

y = 0 - 12                                        <----- Multiply 4 and 0

y = -12                                           <----- Subtract 12 from 0

The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s

An equation is an expression that shows the relationship between two or more variables and numbers.

1 mile = 5280 ft, 1 min = 60 sec

30 mile = 30 mile * 5280 ft per mile = 158400 ft

58.2 min = 58.2 min * 60 sec per min = 3492 sec

Speed = distance / time = 158400 ft / 3492 sec = 45.36 ft/s

The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

You can purchase 10 gallons of Gasoline.

We have only $20 to spend on gasoline each week. If the price of gasoline is $2 a gallon

Here, we have $20

Cost per gallon $2

Number of gallons: 20/2 =10 gallons

Learn more about Gasoline:

https://brainly.com/question/1288131

#SPJ4

Using relations in a right triangle, the trigonometric function that should be used is given by:

b) tan.

The relations in a right triangle are given as follows:

Hence, if the opposite and adjacent side are know, the tangent function should be used, and option b is correct.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

#SPJ1

Answer: [tex]60cm^2[/tex]

Step-by-step explanation:

Looking at the figure, you can see that the length is 5cm + 3cm = 8cm and the width is 2cm + 5cm + 2cm = 9cm.

The formula for area is length x width, therefore you do 8x9 which is 72.

Next, we solve for the two "dips" in the rectangle. We can do that by subtracting the area of the "mini-rectangles" from the whole figure:

72-2(2x3) = 60

Thus, 60cm^2 is your answer.

Answer:

12

Step-by-step explanation:

B x H x 1/2 = area of a triangle

we can break this figure into 4 different triangles and since we have the length of the chords (dotted lines) in the diamond we can easily solve it.

half of QS is 2 and half of PR is 3

2 x 3 = 6

6 / 2 = 3

since there are four triangles multiply 3 by 4 (3 x 4)

and you get 12.

Flo should walk 60 extra minutes of time per day to accomplish her goal of walking 12,000 total steps per day.

Calculating the Time for Which Flo Walks Each Day

Flo walks 6,000 steps per day.

She walks 100 steps per minute.

⇒ Time taken by Flo to cover 6,000 steps = [tex]\frac{6000}{100}[/tex] minutes

⇒ Time taken by Flo to cover 6,000 steps, m₁ = 60 minutes

Hence, Flo walks for 60 minutes or 1 hour per day.

Calculating the Extra Hours of Walking

Steps to be covered by Flo each day = 12,000

Time required to walk 12,000 steps per day, m₂ = [tex]\frac{12000}{100}[/tex] minutes

⇒ m₂ = 120 minutes

Extra hours of walk per day = (m₂-m₁) minutes

= (120 - 60) minutes

= 60 minutes

Thus, Flow should walk 1 hour extra to be able to accomplish a goal of walking 12,00 steps per day.

Learn more about time here:

https://brainly.com/question/14381704

#SPJ4

Graph C depicts the relation between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements )

Graph is the statistical representation of data , It helps to observe large data systematically.

It is given that

Sale of one sweater gives $3

The relation between the amount raised for funding , M and the number of shirts sold , n is given by

M = 3n

It has to be found that which graph exactly depicts the relation and the condition as given

Graph C depicts the relation given as , The graph is between No. of sweaters ( Nombre de chandails vendus ) and the fund raised in the campaign (Campagne de financements ) , and for every 100 sweater , $300 is earned .

Therefore Graph C is the answer.

To know more about Graph

https://brainly.com/question/14375099

#SPJ1

The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The graph of √(5x - x²) was translated 9 units left and 2 units up, then reflected over the x axis to get the new graph.

The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Answer:

$25.00

Step-by-step explanation:

20% of $125 = $25

The area of the triangle, trapezoid, rectangle and total area are 7. 5 ft², 10. 5 ft², 0.8 ft² and 18. 8 ft² respectively.

1. Area of a triangle = 1/2 base × height

Area = 1/2 × 5 × 3

Area = 1/2 × 15

Area = 7. 5 ft²

2. Area of trapezoid = [tex]\frac{a + b}{2} h[/tex]

a = 4ft

b = 0. 2ft

h = 5ft

Area = [tex]\frac{4 + 0.2}{2}* 5[/tex]

Area = [tex]\frac{4.2}{2} * 5[/tex]

Area = 2.1 × 5

Area = 10. 5 ft²

3. Area of rectangle = length × width

Area of rectangle = 0. 2 × 4

Area of rectangle = 0. 8 ft²

4. Total area of tree = area of triangle + area of trapezoid + area of rectangle

Total area of tree = 7. 5 + 10. 5 + 0. 8

Total area of tree = 18. 8 ft²

Thus, the area of the triangle, trapezoid, rectangle and total area are 7. 5 ft², 10. 5 ft², 0.8 ft² and 18. 8 ft² respectively.

Learn more about area of a rectangle here:

https://brainly.com/question/25292087

#SPJ1

The probability that he will be rejected to at least one of the colleges is 0.51.

Given probability that he will admit in A is 0.7, probability that he will not be admit in B is 0.5, probability that atleast one of his applications got rejected is 0.6.

We have to find the probability that he will be rejected to at least one of the colleges.

Probability that he will admit in A =0.7

Probability that he will not admit in A=1-0.7=0.3

Probability that he will not admit in B =0.5

Probability that he will admit in B=1-0.5=0.5

Probability  that he will be rejected to at least one of the colleges=probability that he will admit in A* probability that he will not admit in B+ probability that he will admit in B* probability that he will not admit in A+ probability that he will not admit in A* probability that he will not admit in B

=0.7*0.5+0.5*0.3+0.5*0.3

=0.35+0.15+0.15

=0.51

Hence the probability that he will be rejected to at least one of the colleges is 0.51.

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

Hello

6x² - 2x + 6 - (6x² - 7x - 2)

= 6x² - 2x + 6 - 6x² + 7x + 2

= 5x + 8

Sally to get to the next town in 2/3 hour.

According to the statement

The distance covered by sally to get next town is 20 miles

Speed at which sally drive is 30 miles per hour

We know that the

TIME = DISTANCE / SPEED

Substitute the values in it and

TIME = 20 / 30

TIME = 2/3 hour

So, Sally to get to the next town in 2/3 hour.

Learn more about SPEED here https://brainly.com/question/4931057

#SPJ4

Answer:

98

Step-by-step explanation:

From the statement of similarity, we can write this proportion.

TV/MV = UV/LV

28/x = 16/56

16x = 28 × 56

x = 7 × 14

x = 98

Answer:

See below

Step-by-step explanation:

285714 / 1000 000    which simplifies to 142,857 / 500,000

Answer:

6h² + 3h + 5

Step-by-step explanation:

7h² + 2h + 5 - h² + h

= 7h² - h² + 2h + h + 5

= 6h² + 3h + 5

The correct option regarding whether the table represents a proportional relationship is:

The relationship is proportional because the ratio of m to k is constant.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the ratio of m to km is given as follows:

k = 11/17.699 = 26/41.834 = 34/54.706 = 0.6215.

Since the values are equal, the correct option is:

The relationship is proportional because the ratio of m to k is constant.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

B. 11.4

Step-by-step explanation:

By using the line segment formula

AC = √(9-(-2)^2+(2-5)^2

AC = √130

AC = 11.4

Answer:

2

Step-by-step explanation:

Let the missing length be " x ".

( 3 + 1 ) / 6 = x / 3

4 / 6 = x / 3

Cross multiply,

x * 6 = 4 * 3

6 = 2 * 3

4 = 2 * 2

x * 2 * 3 = 2 * 2 * 3

Divide 2 * 3 on both sides,

x = 2

Using the normal distribution, it is found that there is a 0.3156 = 31.56% probability that the sample proportion will be less than 14%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given, respectively, by:

p = 0.15, n = 294

Hence the mean and the standard error are given, respectively, by:

The probability is the p-value of Z when X = 0.14, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.14 - 0.15}{0.0208}[/tex]

Z = -0.48

Z = -0.48 has a p-value of 0.3156.

0.3156 = 31.56% probability that the sample proportion will be less than 14%.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

The next Answers are x > 0, and all real numbers

The correct function shown in graph is,

⇒ f (x) = log₁₀ x

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function is shown in figure.

Now, Points on the graph are (1, 0) , (5, 1) and (0.2, -1)

Hence, From the option 4;

⇒ f (x) = log₁₀ x

Put x = 1;

⇒ f (x) = log₁₀ 1

⇒ f (x) = 0

Thus, The correct function shown in graph is,

⇒ f (x) = log₁₀ x

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ5

Answer:

012

Step-by-step explanation:

please mark brainliest if correct

Answer:

The 17th term of the given Arithmetic progression -6,-1,-4 will be 74.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

As per the given Arithmetic progression,

-6, -1, -4.

First term a = -6

Common difference d = -1 - (-6) = 5

The nth term of AP is given as a + (n - 1)d.

This 17th term will be as, -6 + (17 - 1)5

⇒ -6 + 16 × 5 = 74

Hence "The 17th term of the given Arithmetic progression -6,-1,-4 will be 74".

For more about Arithmetic progression

https://brainly.com/question/20385181

#SPJ2

Answer:

-3*4^2/3.

Step-by-step explanation:

[4 -⅓ ( 64 ⅓ - 64 ⅔) ]​

= 1/4^1/3 ( 4 - 4^2)

= 1 / 4^1/3 * -12

= -12/ 4^1/3

= -12 * 4^2/3 / 4

= -3*4^2/3

Answer:

40 km on the highway

30 km on the city roads

Step-by-step explanation:

Let x = highway

Let y = city road

The time formula: time = distance / speed.

1) Since we do not know the distance travelled on the highway and city roads but we do know the total time taken, we can say x + y = 70. Set the distances x and y and all equated to 2 hours, since we do not know them, nor do we know the time. This is called a system of equations.

x + y = 70

x/80 + y/20 = 2

2) Solve the system of equations using substitution.

x = 70 - y

---------------

70 - y/80 + y/20 = 2

70 + 3y/80 = 2

y = 30

---------------------------------

x + 30 = 70

x = 70 - 30

x = 40

Therefore, the delivery truck travelled 40 km on the highway and 30 km on the city roads.