1. Triangle ABC is similar to triangle DEF.
D
А
80
4 cm
B
С
10 cm
20 cm
E
What is the measure of ZD?

Given:

The piecewise function is

[tex]f(x)=\begin{cases}x+4 & \text{ if } -4\leq x<3 \\ 2x-1 & \text{ if } 3\leq x<6 \end{cases}[/tex]

To find:

The range of given piecewise function.

Solution:

Range is the set of output values.

Both functions [tex]f(x)=x+4[/tex] and [tex]f(x)=2x-1[/tex] as linear functions.

Starting value of [tex]f(x)=x+4[/tex] is at x=-4 and end value is at x=3.

Starting value: [tex]f(-4)=-4+4=0[/tex]

End value: [tex]f(3)=3+4=7[/tex]

Starting value of [tex]f(x)=2x-1[/tex] is at x=3 and end value is at x=6.

Starting value: [tex]f(3)=2(3)-1=5[/tex]

End value: [tex]f(6)=2(6)-1=11[/tex]

Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.

Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.

So, the range of the given piecewise function is [0,11).

Therefore, the correct option is A.

Raymond's account balance after depositing two deposits of $100 , purchase of $86.72 with overdrawn amount $32.55 is equal to $80.73.

As given in the question,

Raymond's bank account has:

Overdrawn amount in bank = $32.55

Deposits amounts by Raymond's = 2 × ( $100 )

                                                       = $200

Purchase amount = $86.72

Account balance in Raymond's account = ( $200 - $32.55 - $86.72 )

                                                                  = ( $200 - $119.27 )

                                                                  = $80.73

Therefore, Raymond's account balance after depositing two deposits of $100 , purchase of $86.72 with overdrawn amount $32.55 is equal to $80.73.

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The mean waste recycled per person per day for the population of new- york is 1.9 < u < 2.3 .

Given that,

The mean waste recycled per person per day = 2.12

Standard Deviation = 0.250

c = 0.9 , So  [tex]\alpha[/tex] =1-c =0.10

n = 9<30 so we use t critical value.

From t table we get the critical value = 1.859

90% confidence interval for the mean u

So,

X = 2.1 , s = 0.25 , n= 9

2.1 - 1.86 (0.25/[tex]\sqrt{9}[/tex]) < u < 2.1 =1.86 (0.25/[tex]\sqrt{9}[/tex])

1.954  < u < 2.225

1.9 < u < 2.3 .

Therefore,

From 1.9 < u < 2.3 we get that the population is approximately normal.

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Answer:

Dragons are real because all the other animals on the calendar for real.

Step-by-step explanation:

Hope this helps.

Answer:

Step-by-step explanation:

9 is the answer

Answer: 5 minutes

60 minutes to start -20 minutes used =40 minutes left

40 minutes left/ 8 questions = 5 minutes on average per question

32% of the same people spend their time listening.

The total number of mentioned  people will be 100% or 1. Now, in the total people, the remaining ones who are not stated in the question, must be the listeners. Thus, calculating the remaining percentage of people, we will get the percentage of listeners in same people.

So, number of people who spend time speaking = 26%

Number of people who spend time speaking = [tex]\frac{26}{100}[/tex]

Number of people who spend time speaking = 0.26

Number of people who spend time writing =  23%

Number of people who spend time writing = [tex]\frac{23}{100}[/tex]

Number of people who spend time writing = 0.23

Number of people who spend time reading =  19%

Number of people who spend time reading = [tex]\frac{19}{100}[/tex]

Number of people who spend time reading = 0.19

Total number of people involved in activities other than listening = 0.26 + 0.23 + 0.19

Total number of people involved in activities other than listening = 0.68

People who spend time listening = 1 - 0.68

People who spend time listening = 0.32

Percentage of people who spend time listening = 0.32 × 100

Percentage of people who spend time listening = 32%

Hence, 32% of the same people spend their time listening.

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Answer: b=7

Step-by-step explanation:

6b+7+7b-8=90

6b+7b+7-8=90

13b-1=90

13b=91

b=7

The value of function f(x) = 3x² + 8x-10 at f(2) is  18 .

We have given an function f(x) = 3x² + 8x-10

Putting x = 2 into this function , we get

 f(2) = 3(2)²+ 8x -10

        =3(4) + 8(2) -10

        = 12 + 16 -10

        = 18

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The equation of the amount of pay and the number of hours it takes to get your car fixed will be P = 50x + 100.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

You had to take your car to the shop for a weird noise. The mechanic charges a flat rate of $100 for looking at your car and $50 an hour to fix the problem.

Let P represents the amount of pay and x be the number of hours. Then the linear equation is given as,

P = 50x + 100 where p is amount

The equation of the amount of pay and the number of hours it takes to get your car fixed will be P = 50x + 100.

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Answer:

it's the last one

Step-by-step explanation:

the last one is the correct one

Answer: 26/168 hours are spent watching TV a week.

Step-by-step explanation:

Weekdays: 2 * 5 = 10

Weekends: 8 * 2 = 16

Week total hrs: 24 * 7 = 168

10 + 16 = 26

26/168

Step-by-step explanation:

60+40=100

70+30=100

80+20=100

hope it helps

It is already in the simplest form.

The measure of C'T' is √17 units after the rotation .

Rotation of a graph is a transformation in which the figure is rotated around a fixed point.

The given triangle is CAT and it has the coordinates as C(0,0) , A(-2,1) and T(-1,4).

So when the figure is rotated about a fixed point the side lengths will remain same as the original figure.

C'T' = CT = √17 (the value of CT is given)

Hence the length of  C′T′ is √17 units .

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Answer:

30

Step-by-step explanation:

All triangles have a measure of 180 on the inside. I found this by taking 180 and subtracting it by the sum of 53 and 97 which is 150. 108-150=30.

Answer:

The answer is 30

the inside of a triangle always adds up to 180.

Step-by-step explanation:

97 + 53 = 150

180-150 + 30

2 Answers:

Choice B) irrational

Choice F) Natural

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

Reason:

Let's go through the answer choices.

Answer:

Denominator, opposite of the numerator

Step-by-step explanation:

When divided by negative, it's the inverse (+/-) and changes signs.

2 parts to a fraction

Numerator

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

Denominator

Hope this helps! :)

The values of x will be 2 and -1.

Given that:-

[tex]14x+17=2(x+3)^2-5[/tex]

We have to find the value of x.

As it is a quadratic equation, there will be two values of x.

Opening the bracket and solving the equation further, we get,

[tex]14x+17=2(x^2+9+6x) -5\\14x+17 = 2x^2 +18+12x-5\\2x^2-2x-4 = 0\\2(x^2-x-2) =0\\x^2-x-2 = 0[/tex]

Using middle-term split theorem to solve the quadratic equation, we get,

[tex]x^2-x-2 = 0\\x^2+x-2x-2=0\\[/tex]

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

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

Hence, either x + 1 = 0 or x - 2 = 0 or both of them are 0.

x + 1 = 0

x = -1

and,

x - 2 = 0

x = 2

Hence, the values of x are 2 and -1.

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Answer:

congruent

Step-by-step explanation:

Smallest possible value of the least common multiple is 6

a =12 and  b=54

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted as GCD(x,y)=[tex]\frac{x*y}{LCM(x,y)}[/tex]

GCD[12, 54] =[tex]\frac{(12*54)}{106}[/tex]=6

LCM[12, 54] =108

Also a =42 and b= 24 will give the same GCD of 6, but the LCM[42, 24] =168 which is greater than the first one.

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The circle graph/pie chart is made for the given bar graph.

A pie chart is a type of graph that displays data in a circular graph. The slices of pie represent the relative amount of information and are a type of pictorial data representation.

Now, as the data given in the bar graph.

The basketball is played the number of students is 4.

That is 40% of the total.

The football is played the number of students is 3.

That is 30% of the total.

The baseball is played the number of students is 2.

That is 20% of the total.

The soccer is played the number of students is 1.

That is 10% of the total.

Thus, the pi cart for the all data percentage is formed.

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Check the picture below.

the function is the Cost function for the bagels, of course that'd depend on the price of each bagel, so the cost C(x) is dependent on how many independent bagels Naomi is buying, as you can see in the table in the picture.

now, if Naomi gets 10 bagels, that simply means that x = 10, thus the price is C(10), or namely C(10) = 1.25(10), so Naomi better check her pockets for $12.50 for the bagels, hopefully she'll get some cream cheese too and cocoa.

Answer:

40billion for the tip question

Answer: 6 metres

Step-by-step explanation:

It can be written as 48=8x

48/8=x

x=6

Using proportions, the amounts are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

We have that the amount of Twix is triple the amount of Milky ways, hence:

There are 5 fewer Snickers then Twix, hence:

Hence the amounts are given as follows:

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Answer:

C. 445

Step-by-step explanation:

Directly proportional means that y = kx for some constant k. So you can start by substituting;

712 = 8k

k = 89

y = 5(89)

y = 445

Hope this helps! :)