3. Find the measure of the angle indicated.

Answer: T is the longest side. T = 62

Step-by-step explanation:

R + S = 118

(57+61)

180-118=62

Answer:Nothing further can be done with this topic. 6y=22,x=−5y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Substitute the value of x (-5y) into the equation. Which gives you -5y-6y=22, add like terms and you get -11y=22. Divide both sides by -11 and you get y=-2

1. The functions are the same because each of the function has equations that are modeled after the horse diving into the water.

2. Given t = 20s, so using the equation modeled for Seb, we have

h(20) = -16(20^2) + 16(20) +18

After evaluating it we get -6062ft which is not possible since we cannot get a height in negative and jumping off at a height of 6062ft if it was in positive it wouldn't be done by a sane person.

3. Putting the value of t as 0 in the equation we get,

h(0) = -16(0^2) + 16(0) + 18

After evaluating it, we get 18ft and in this situation, we can say that in 0 seconds that is when the horse had not yet dived, the horse was at a height of 18ft.

4 a. Taking the value of h as 18 in Sabri's equation, we get

18 = -16(t - 0.5)^2 + 22

18 = 16t^2 - 4 + 22            (After solving {t - 0.5}^2)

t^2= 18 + 4 - 22/ 16

t^2= 0

t = 0seconds

b. The maximum height of Sabrina's height was 18ft, since this is the initial height of the horse diving booth.

What are functions?
In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable. To put it simply, a function is a type of rule that produces one output for every input it receives. Here, y=x2 serves as an illustration. A single output for y results from any input for x. Since x is the input value, we would state that y is a function of x.

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The numbers in order are 7, 8, 9, 11, 11, and 11.

Mode:

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all

Here we have to arrange the number in order.

Range:

The difference between the lowest and highest values.

Pu the six numbers in order from small to large.

7,8,9,11,11,11

So the median of the number is = (9 + 11) /2

= 10

The mode of these numbers is = 11

As 11 is three times in the series.

The range of the numbers is = 11-7 =4

Therefore the order is 7, 8, 9, 11, 11, 11.

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The difference between the record high and low temperatures for this state is 118 degrees Fahrenheit or 118°F

Given that,

104 f is the highest temperature ever recorded in a particular US state. The state's all-time low temperature is -14 f.

To find : The difference between the record high and low temperatures for this state.

Difference can be calculated as

Difference equals to highest temperature minus lowest temperature in the state

Difference = 104 -(-14)

= 104+14=118°F

Therefore, The difference in temperature between the state's record high and low readings is 118 degrees Fahrenheit, or 118°F.

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Given the relation (9,2)(4,5)(7,3)(10,-5), an ordered pair which would result in a relation that is not a function is: (10, 2).

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

Based on the ordered pairs shown above, we can reasonably infer and logically deduce that (10, 2) is an ordered pair which does not represent a function because the value of "a" has already been mapped to -5.

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The answer is:  " - 1,458 ".

Step-by-step explanation:
We are asked to simplify: " -2(3²)³ " ; into standard form.

Take note of the 'order of operations'—by using the mnemonic:
 "Please Excuse My Dear Aunt Sally."

  in which:
_______
Parentheses, if they occur, take top priority.
then :
Exponents, if they occur, take second priority.
then :

Multiplication—and/or:
Division—if they occur; take third priority; yet, multiplication does not necessarily take priority over division.  Rather, multiplication and/or division, if Either occurs, take the next priority—in the order in which they occur from the far left of the expression to the end.
then :
Addition—and/or:
Subtraction—if they occur; take the last priority; yet, addition does not necessarily take priority over subtraction.  Rather, addition and/or subtraction, if Either occurs, take the last priority—in the order in which they occur from the far left of the expression to the end.
____

Our given expression:  " -2(3²)³ " ;  is the same as:
  " - 2* (3²)³ " ;   We have parentheses, exponents, and multiplication;

 So; we need to find the value of:  " (3²)³ " ;  

and multiply that value by -2 ;

 So, let's start with calculating:  " (3²)³ " ;

Method 1)
 " (3²)³ = (3* 3)³ = 9³ = 9 * 9 * 9 = (9 * 9) * 9 = 81 * 9 = 729 " .

Method 2)
Note the multiplication property of exponents:
 (aᵇ)ᶜ = a⁽ ᵇ *ᶜ ⁾ ;

As such:   "  (3²)³ =  3⁽²*³⁾ = 3⁶ " ;

                             =  3 * 3 * 3 * 3 * 3 * 3 ;          

                             =  (3 * 3) * 3 * 3 * 3 * 3 ;

                            =   9 * 3 * 3 * 3 * 3 ;

                             =   (9 * 3) * 3 * 3 * 3 ;

                            =   (27) * 3 * 3 * 3 ;

                             =   (27)  *  (9)* 3 ;\

                             =  27 * 27 ;              

            ₁

             ₄  

              2 7
          *  2  7  
           ¹ 1 8 9          

        ⁺_5 4    
          7   2  9

                          =  729
____

Now,  multiply 729 by -2 ;

{Note that a negative value, when multiplied by a positive value, results in a negative value.}\

      ₁

      7 2 9

*       -   2      
-  1 4 5 8 ;  which is our answer to:  " -2(3²)³ " ; written in   standard form.

The answer is:  " - 1,458 ".

____

Hope this is helpful to you.

Best of luck to you!
____

Answer:

1. m∠5 + m∠6 = 180° ...........Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Answer:

∴ Shaquana bought 7 candies and 6 pretzels.

Step-by-step explanation:

Suppose all the snacks she bought were candies.

13 × $5 = $65

$65 - $53 = $12

$5 - $3 = $2

$12 ÷ $2 = 6 pretzels

∴ Number of candies Shaquana bought

= 13 snacks - 6 pretzels

= 7 candies

Answer:

6 pretzels and 5 candies

Step-by-step explanation:

Let c be the number of candies and p the number of pretzels.

We can determine the total cost by multiplying the candy price by it's price, $5/candy.  That would be $5*c.  We can do the same for the pretzels:  $3*p.

Thje total spent is:    ($5)c + ($3)p = $53.  Since the $ sign cancels out, let's rewrite this to simplify:   5c + 3p = 53.

We know that c + p = 13

Rearrange this to c = 13-p and then substitute this definition of c in the first equation:

5c + 3p = 53

5(13-p) +3p = 53

65 - 5p + 3p = 53

-2p = - 12

p = 6  Shaquana brought 6 pretzels.

Since c + p = 13, this means she bought 7 candies.

Check to see if this works:

Do 6 pretzels and 7 candies cost $53?

 (6 prezels)*($3/pretzel) =  $18

 (7 candies)*($5/candy) =  $35

               Total                =  $53  YES

$144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

Given that,

For the next 20 years, Bill intends to contribute the maximum $2,000 each year to his individual retirement account (ira).

We have to find how much will Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

We know that,

The worth of repeated payments at a specific future date, less a specified refund rate or a discount rate, is known as the future annuity value. The annuity amount increases with the discount rate.

According to the information provided, Future Value of Annuity equals:

FV= A×[(1+r)ⁿ-1]/r

Here,

A is periodic payment

r is rate per period

FV is future value

n is number of period

FV=2000×[(1+0.12]²⁰-1]/0.12

FV=2000×72.05244

FV=$144104.88

Therefore, $144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.

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Answer:

3043kg

Step-by-step explanation:

30kg

43g

is this right

Answer:

x-intercept is 5

y-intercept is -3

Step-by-step explanation:

For the x-intercept:

[tex]3x - 5(0) = 15[/tex]

[tex]3x = 15[/tex]

[tex]x = 5[/tex]

For the y-intercept:

[tex]3(0) - 5y = 15[/tex]

[tex] - 5y = 15[/tex]

[tex]y = - 3[/tex]

Answer:

Y intercept= -3

x-intercept = 5

Step-by-step explanation:

So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:

1. Subtract 3x from both sides to get -5y= -3x+15

2. then you would divide each side by -5 to get y= [tex]\frac{3}{5}[/tex] x -3

And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.

sorry if this was long

The answer that 12 times 1/3 will equal to -4 to 0, solving an equation.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

So the equation 12(x)-4 = 0

⇒12*x =4

⇒x=4/12

⇒x = 1/3

Hence, the equation will be solved and the number will be 1/3.

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A polynomial function with zeros of -1, -1, 2i is:

f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

We have been given a polynomial function with zeros of -1, -1, 2i

This means, (x + 1), (x + 1) and (x - 2i) are roots of polynomial.

Let f(x) be required polynomial function.

To find a polynomial consider an equation,

f(x) = 0

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

(x^2 + 2x + 1) * (x - 2i) = 0

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

x^3 + 2x^2 + x - 2ix^2 - 4ix - 2i = 0

x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i = 0

so, f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

Therefore, a polynomial with zeros of -1, -1, 2i is f(x) = x^3 + (2 - 2i)x^2 + (1 - 4i)x - 2i

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Answer:

Theusage is 585 minutes of call duration..

Explanation:

Fixed plan cost is M=$.39.95

Charge for first 500 minutes call: Free

Charge for call exceeding 500 minutes: $.0.35/minutes.

Let x minutes be the total call duration.

The bill is P=$.69.70 i.e. more than $.39.95, which indicates

call duration is more than 500 minutes.

The rule states that bill for call exceeding 500 minutes is

P=M+(x−500).0.35 or

69.70=39.95+(x−500).0.35 or (x−500).0.35=69.70−39.95 or

(x−500).0.35=29.75 or (x−500)=

0.35

29.75

or

(x−500)=85 or x=500+85=585 minutes.

The usage is 585 minutes of call duration .

Step-by-step explanation:

hope this helps

Answer:

[tex]\frac{1}{120}[/tex]

Step-by-step explanation:

To solve such a problem you need to simulate a situation in which this could happen in three picks and then make sure your equation takes into account that all three picks take place at the same time. One such situation could look like this:

1) At the start, the probability of picking one rotten apple with one pick is 2 out of 16 which 2/16.

2) After picking the first apple you have 15 apples left of which only 1 is rotten. So the chance to pick the second rotten apple is 1/15.

3) After you picked the second rotten apple you want the third one in the set to be good. As you are left with 14 apples of which all 14 are good, the probability of picking a good one is 14/14.

Now, because you are interested in ALL those 3 things happening at the same time, you need to multiply the probabilities. So this gives you the answer of:

[tex]\frac{2}{16} *\frac{1}{15} *\frac{14}{14} = \frac{1}{8} *\frac{1}{15} *1 = \frac{1}{120}[/tex]

You can achieve the same result if your picks are in a slightly different order. The result won't change as long as the outcome is the same (set of 2 rotten apples and 1 good apple). So if you first pick a rotten apple (2/16), then you happen to pick a good apple (14 out of 15 left are good so 14/15) and then pick the second rotten apple last (1/14) you will see it's gives the same result because you also end up with 2 rotten and 1 good apples:

[tex]\frac{2}{16} * \frac{14}{15} * \frac{1}{14} = \frac{1}{8} * \frac{1}{15} = \frac{1}{120}[/tex]

Answer:

[tex]y = \frac{3}{4} x - 3[/tex]

The slope is 3/4, and the y-intercept is -3.

Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches Mattie’s house.

The shortest distance between Caroline's and Mattie's house is 10 blocks.

If we assume this as a right angle triangle then height (BA) is 6 blocks long and base (BC) is 8 blocks

long.

Then, the shortest distance between Caroline's and Mattie's house will be the hypotenuse (AC) of this

triangle.

So, by applying Pythagoras theorem:

[tex](AC)^{2} = (BA)^{2} = (BC)^{2} = (6)^{2}+(8)^{2}[/tex] = 36+64 = 100

Thus, AC = [tex]\sqrt{100}[/tex] = 10 blocks.

Hence, the shortest distance we can take from Caroline's house to reach Mattie's house is 10 blocks.

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The number of students  that are studying abroad in 2001 is 150.38 thousand

The number of students that are studying abroad in 2018 is 467.53 thousand

The given equation that represents the growth in the number of students that are studying abroad is known as an exponential equation. An exponential equation is a non-linear equation.

The given exponential equation is 123.1(1.069)^x

Where:

Number of students studying abroad in 2001 = 123.1(1.069)^3= 150.38 thousand

Where x = 2001 - 1998 - 3

Number of students studying abroad in 2018 = 123.1(1.069)^20 = 467.53 thousand

Where x = 2018 - 1998 = 20.

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Negative numbers are sometimes rational numbers. As, this statement is only true in all the following statements.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them. the system of numbers

Following statements are given,

1. Positive numbers are always rational numbers.

2. Negative numbers are always irrational numbers.

3. Negative numbers are sometimes rational numbers.

4. Negative numbers are always integers.​

According to statement Positive numbers are always rational numbers

As this statement is not always true because though √2 is positive, it is not a rational number.

According to statement Negative numbers are always irrational numbers.

This is also not true as always as -4 is negative and it can be expressed in the form of [tex]\frac{-4}{1}[/tex] , hence it is rational.

According to statement Negative numbers are sometimes rational numbers.  As  it can be both -2 is a negative rational number and -√2 is negative irrational number.

According to statement Negative numbers are always integers.​This is not always true because [tex]\frac{-2}{3}[/tex] is a negative number with a fractional part, hence it is not an integer.

Hence, only 3rd statement is true ,

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Answer:

150≤x≤500

Step-by-step explanation:

Step-by-step explanation:

I assume you need the slope-intercept form

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

since we have the slope and a point, we can start with the point-slope form

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is a point on the line

so, we have

y - -7 = 3(x - -4)

y + 7 = 3(x + 4) = 3x + 12

and from there now the final equation :

y = 3x + 5

Answer:

y = -1/5x + 17/5

Step-by-step explanation:

Parallel lines have the same slope as m2 = m1.  Thus, the slope the of second line is -1/5.

We can find the y-intercept by plugging in (2,3) for x and y and our slope:

[tex]3 = -\frac{1}{5}(2)+b\\ 3=-\frac{2}{5}+b\\ \frac{17}{5}=b[/tex]

Answer:

Step-by-step explanation: I think you have to add all the numbers together then divide by all the numbers i think

Answer: A or C

Step-by-step explanation:

113.8 divided by 9 equal to 12.64

The calculation can be done simply by calculator however to so it manually the decimal is converted to fraction

converting to fraction

113.8 = 1138/ 10

dividing by three

= 1138/ 10 ÷ 9

= 1138/ 10 * 1/9

= 1138/ 90

= 569/45

= 12.64

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Answer:

Step-by-step explanation:

v = 1/3 (area of base) (height)

v = 1/3 (1/2*6*8) (7)

v = 1/3 (24) (7)

v = 8 (7)

v = 56 square inches