An avocado tree has a sale price of $27.95 dollars; this is 65% off the original price. What percent of the original price was the discount and how much was deducted from the original price?

Answer:

[tex]A.\ a_n=n^2+1[/tex]

Step-by-step explanation:

[tex]Check:[/tex]

[tex]a_n=n^2+1\\\\a_1=1^2+1=1+1=2\qquad CORRECT\\\\a_2=2^2+1=4+1=5\qquad CORRECT\\\\a_3=3^2+1=9+1=10\qquad CORRECT\\\\a_4=4^2+1=16+1=17\qquad CORRECT\\\\a_5=5^2+1=25+1=26\qquad CORRECT[/tex]

Used PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

First Power, next Addition

Answer: A.

Step-by-step explanation:

2, 5, 10, 17, 26

First, check the difference between each term:

2 → 5 = +3

5 → 10 = +5

10 → 17 = +7

17 → 26 = +9

Since the difference (d) is not the same, this is not an arithmetic sequence.

Now, check the second tier {3, 5, 7, 9}

3 → 5 = 2

5 → 7 = 2

7 → 9 = 2

The difference (d) of the second tier is the same, so it is an exponential sequence.

--> the only option that is an exponential sequence is option A.

Answers: -4, 5

Step-by-step explanation:

[tex]e^{x^{2}}=e^{x}*e^{20}[/tex]

[tex]e^{x^{2}}=e^{x+20}[/tex]

x² = x + 20

x² - x - 20 = 0

(x + 4)(x - 5) = 0

x + 4 = 0      x - 5 = 0

 x = -4            x = 5

**************************************************

Answers:

Step-by-step explanation:

domain: there are no restrictions on the x-value so x = All Real Numbers

range: since the new graph has a reflection then y < 0

y-intercept is when x = 0:

horizontal asymptote: y ≠ 0 so the H.A. is y = 0

graph:  The parent graph is: y = 2ˣ

The new graph of y = -2ˣ⁻³ has the following transformations:

***************************************************************************

graph: see attachment

(0, 0) and (-1/3, 1)

(-1, ∞)

x = -1

Answer:

x = 5

Step-by-step explanation:

in ΔABC , AB = BC , hence triangle is isosceles, thus

∠A = ∠C = 73° ( base angles are equal )

the sum of the 3 angles in a triangle = 180°

subtract the sum of the base angles from 180 for ∠B

∠B = 180° - (73 + 73)° = 34°

⇒ 6x + 4 = 34 ( subtract 4 from both sides )

6x = 30 ( divide both sides by 6 )

x = 5

Answer:

Short-response question = 20.

Step-by-step explanation:

Let x be number of short response questions and y be the number of essay questions.

We have been given that there are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. Using our given information we can form a system of equations as:

[tex]x+y=22...(1)[/tex]  

[tex]4x+10y=100...(2)[/tex]

Now we will solve our system of equations using substitution method.

From equation 1 we will get,

[tex]y=22-x[/tex]

Upon substituting [tex]y=22-x[/tex] in equation 2 we will get,

[tex]4x+10(22-x)=100[/tex]

[tex]4x+220-10x=100[/tex]

[tex]4x-10x=100-220[/tex]

[tex]-6x=-120[/tex]

[tex]x=\frac{-120}{-6}[/tex]    

[tex]x=20[/tex]  

Therefore, there are 20 short-response questions on the exam.

Answer:

D. 20

Step-by-step explanation:

I got it right on prepworks

Answer:

(D)68

Step-by-step explanation:

If 1 litre =4.23 cups

and 1 cup = 8 ounces

Therefore: 1 litre = 4.23 X 8 Ounces = 33.84 Ounces

2 litres = 2 x 33.84 Ounces

           =67.68 Ounces

           =68 Ounces (To the nearest whole number)

The number of ounces in 2 liters will be 68 ounces. Thus, the correct option is D.

Given that:

1 liter = 4.23 cups

1 cup = 8 ounces

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The number of cups in 2 liters is calculated as,

⇒ 2 x 4.23

⇒ 8.46 cups

The number of ounces in 8.46 cups is calculated as,

⇒ 8.46 x 8

⇒ 67.68 or 68 ounces

Thus, the correct option is D.

More about the conversion link is given below.

https://brainly.com/question/9414705

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First question:

By definition of sine and cosine, we have

[tex]\sin30^\circ=\dfrac h{\sqrt5}\implies h=\dfrac{\sqrt5}2[/tex]

[tex]\cos30^\circ=\dfrac g{\sqrt5}\implies g=\dfrac{\sqrt{15}}2[/tex]

Second question:

By definition of tangent, we have

[tex]\tan60^\circ=\dfrac{5\sqrt2}x\implies x=\dfrac{5\sqrt2}{\sqrt3}=\dfrac{5\sqrt6}3[/tex]

Then by Pythagoras' theorem,

[tex](5\sqrt2)^2+x^2=y^2\implies y=\sqrt{(5\sqrt2)^2+\left(\dfrac{5\sqrt6}3\right)^2}=\sqrt{50+\dfrac{50}3}=\sqrt{\dfrac{200}3}=\dfrac{10\sqrt6}3[/tex]

6+4x=y or y=4x+6

Plug in to second equation: -5x-(4x+6)=21

-9x-6=21

-9x=27

x=-3

Plugging in, you get that y=-12+6 or -6.

Therefore, the solution is (-3,-6)

Answer:

Money  club have after the show is  $358 .

Step-by-step explanation:

As given

The art club at a school raised $248 at a car wash.

They spent $206 to set up an art show, and raised $316 at the art show by selling artwork the members had made.

Than

Money club have after the show =  school raised money at a car wash +  Raised money at the art show  -  spent money to set up an art show.

Money club have after the show =  248 +  316 - 206

Money club have after the show =  564 - 206

Money club have after the show =  $358

Therefore  money  club have after the show is  $358 .

Answer:

It is 358.

Step-by-step explanation:

The club started with $248, and then spent $206.

248−206=42

The club had $42, left after they spent for the art show.

Then, they raised another $316, at the show.

42 + 316 = 358

Answer: 358

[tex]7x+10=\dfrac{1}{3}(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=\dfrac{1}{3}\cdot12x-\dfrac{1}{3}\cdot3+14x\\\\7x+10=4x-1+14x\\\\7x+10=18x-1\qquad\text{substitute 10 from both sides}\\\\7x=18x-11\qquad\text{subtract 18x from both sides}\\\\-11x=-11\qquad\text{divide both sides by (-11)}\\\\\boxed{x=1}[/tex]

Answer:

I believe the correct awnser is x=1 I took the test

Answer:

[(x+3)(x+2)] /[(2x+3)(x-3)]  

Step-by-step explanation:

 [(2x²+x-6)/(x²-x-6)]/[(4x²-9)/(x²+5x+6)]

= (2x²+x-6)/(x²-x-6) × (x²+5x+6) /(4x²-9)                           Factor

= [(2x-3)(x+2)]/[(x-3)(x+2] × [(x+3)(x+2)] /[(2x+3)(2x-3)]     Cancel terms

= (2x-3)/(x-3) × [(x+3)(x+2)] /[(2x+3)(2x-3)]                        Cancel terms

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

[tex]\dfrac{\frac{2x^2+x-6}{x^2-x-6}}{\frac{4x^2-9}{x^2+5x+6}}=(*)\\---------------------\\2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)\\-----------\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)\\-----------\\x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)\\-----------\\4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)\\----------------------[/tex]

[tex](*)=\dfrac{(x+2)(2x-3)}{(x+2)(x-3)}\cdot\dfrac{(x+2)(x+3)}{(2x-3)(2x+3)}=(**)\\----------------------\\(x+2)-canceled\\(2x-3)-canceled\\----------------------\\(**)=\dfrac{(x+2)(x+3)}{(x-3)(2x+3)}\\\\Answer:\ \boxed{\boxed{\dfrac{(x+2)(x+3)}{(2x+3)(x-3)}}}[/tex]

The correct answer is A.

Hope this helps,

Davinia.

The inverse of the function g(x)=-4/3x+2 is

[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

The given function is:

[tex]g(x) = -\frac{4}{3}x + 2[/tex]

To find the inverse of the function g(x), follow the steps below

Make x the subject of the formula

[tex]g(x) = -\frac{4}{3}x+2\\\\ -\frac{4}{3}x = g(x) - 2\\\\-4x=3g(x)-6\\\\x = -\frac{3}{4}g(x)+\frac{6}{4} \\\\x = -\frac{3}{4}g(x)+\frac{3}{2}[/tex]

Replace x by [tex]g^{-1}(x)[/tex] and replace g(x) by x

The inverse function therefore becomes:

[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

The inverse of the function g(x)=-4/3x+2 is [tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

Learn more here: https://brainly.com/question/12220962

Answer

3/7 - three sevenths

Step-by-step explanation:

Multiply both numerators and both denominators

4*3=12 and 7*4=28

first one is your numerator

second one is your denominator

12/28

Then simplify

12/4=3 and 28/4=7

3/7

Answer:

(B) ASA

Step-by-step explanation:

we will verify each options

option-A:

we can see that there is no consecutive two angles

so, this postulates can not be true

so, this is FALSE

option-B:

We can see that

one angle and then side and another angle are equivalents

so, this is TRUE

option-C:

We can see that

one side and two angles are equivalents

so, this is FALSE

option-D:

we can see that

one side and two angles are equivalents

so, this is FALSE

Answer:

B

Step-by-step explanation:

So firstly, we need to find how much the entire trip will cost. To do this, add the product of 16 and 35 (since tickets are 35 per student, and there are 16 students) with 960:

[tex](35*16)+960\\560+960\\\\\$ 1520[/tex]

The total cost of the trip is $1520. Next, we know that the sweatshirts will be making a profit of $19 per article sold so divide 1520 by 19:

[tex]1520\div 19=80[/tex]

The students need to sell 80 sweatshirts total to get enough money for the trip. Now, to know how many sweatshirts each student needs to sell individually, divide 80 by 16 (since there are 16 students):

[tex]80\div 16=5[/tex]

In short, each student must sell 5 sweatshirts to pay for the entire trip.

Answer:

2, and 10

Step-by-step explanation:

Let's work through each one.

First, plug -10 into the equation:

-10² + 20 = 12 x -10?

-10² = 100

100 + 20 = 120

12 x -10 = -120

120 = -120?    False!

But, using these same calculations, we can see that 10 is a correct answer.

Because everything's the same up to 12 x 10 = 120.

120 = 120

Same with 2 and -2

-2 does not work, but 2 does.

2² + 20 = 12 x 2?

4 + 20 = 24?

24 = 24?    True!

The solution of the given quadratic equation is x = 2 and x = 10.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

Given a quadratic equation, x²+20 = -12x

x²-12x+20 = 0

On factorizing the equation,

x²-10x-2x+20 = 0

x(x-10)-2(x-10) = 0

(x-10)(x-2) = 0

x = 10 or x = 2

Hence, the solution of the given quadratic equation is x = 2 and x = 10.

For more references on quadratic equation, click;

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Answer:

b^2-4ac >0  the roots are real

Step-by-step explanation:

b^2-4ac >0  the roots are real

b^2-4ac = 0 there is 1 root

b^2 -4ac <0 the root are complex

Answer:

239 ft³

Step-by-step explanation:

Multiply the squared radius by π:

2*2*3.14=12.56 ft².

Multiplying the height:

12.56*19≅239 ft³.

The least common multiple of 7 and 3 is 21, so both the football and volleyball teams will have games on the same day again in 21 days.

The question requires us to determine when the football and volleyball teams will have games on the same day again. Since the football team plays every 7 days and the volleyball team plays every 3 days, we are looking for the least common multiple (LCM) of 7 and 3, which represents the number of days until both teams will have games on the same day again.

To find the LCM of 7 and 3, we can list the multiples of each number until we find a common multiple:

Multiples of 7: 7, 14, 21, 28, ...

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...

The first common multiple we encounter is 21. Therefore, both teams will have games on the same day again in 21 days.

Answer:

8 square units

Step-by-step explanation:

Base area= Length* width

Base area= 4* 2

Base area= 8 square units

Answer:

8 square units

Step-by-step explanation:

Base area= Length* width

Base area= 4* 2

Base area= 8 square units

Answer: [tex]\bold{[\dfrac{\pi}{4},\dfrac{5\pi}{4}]}[/tex]

Step-by-step explanation:

Step 1: Create a table

x    |   5sinx + 5cosx = y

0    |       0    +     5     =   5

[tex]\frac{\pi}{2}[/tex]   |        5    +     0    =   5

π    |        0    +    -5    =  -5

[tex]\frac{3\pi}{2}[/tex]    |       -5    +     0    =  -5

2π |        0    +      5    =   5

Notice that y = 5 at 0 and [tex]\frac{\pi}{2}[/tex] , so there will be a vertex at their midpoint.  Similarly at y = -5.

Midpoint of 0 and [tex]\frac{\pi}{2}[/tex]  is [tex]\dfrac{\pi}{4}[/tex] . Midpoint of π and [tex]\frac{3\pi}{2}[/tex] is [tex]\dfrac{5\pi}{4}[/tex]

(graph is attached to confirm interval)

Answer:

A) 1/2QP=UT

D) SU II RP

Step-by-step explanation:

A & D ARE THE ANSWERS

The correct statements are 1/2QP=UT and SU||RP.

In this question, we are given that points S, U, and T are the midpoints of the sides of triangle PQR. We need to determine which statements are correct.

Answer:

total earning is  $64.80

Step-by-step explanation:

Price of one work = $18.00

Payment  by owner = 1/4 of $18.00

                                 = 18/4

                                  = $4.50

Earning by tip =  20% of $18.00 =  20/100 x18 = 3.60

Total earning from one work   =   $4.50+$3.60

                                                = $ 8.10

Earning from 8 tips =  8x8.10

                                = $64.80

Let the Distance traveled by the tourist by walking be : D miles

Given : Tourist walks at a rate of 4 Miles per Hour

[tex]\mathsf{\implies Tourist\;travels\;D\;Miles\;in : \frac{D}{4}\;Hours}[/tex]

Given : The Total Distance of Mountain Path = 31 Miles

Distance traveled by the tourist by hiring a Taxi is : (31 - D) Miles

Given : The Taxi travels at a constant speed of 50 miles per hour

[tex]\mathsf{\implies Tourist\;travels\;(31 - D)\;Miles\;in : (\frac{31 - D}{50})\;Hours}[/tex]

Given : The Tourist reaches the destination 2 Hours after he started

Time taken by Walking + Time Taken by travelling in Taxi = 2 Hours

[tex]\mathsf{\implies \frac{D}{4} + \frac{31 - D}{50} = 2}[/tex]

[tex]\mathsf{\implies \frac{D}{2} + \frac{31 - D}{25} = 4}[/tex]

[tex]\mathsf{\implies (\frac{25D + 2(31 - D)}{50}) = 4}[/tex]

[tex]\mathsf{\implies (\frac{25D + 62 - 2D}{50}) = 4}[/tex]

[tex]\mathsf{\implies ({23D + 62}) = 200}[/tex]

[tex]\mathsf{\implies 23D = 200 - 62}[/tex]

[tex]\mathsf{\implies 23D = 138}[/tex]

[tex]\mathsf{\implies D = 6}[/tex]

⇒ Distance traveled by the tourist by walking = 6 Miles

⇒ Distance traveled by the tourist by hiring a taxi = (31 - 6) = 25 Miles

⇒ The Distance for which tourist has to pay for cab driver is 25 Miles

The distance traveled by taxi = 25 miles

Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration

• At constant velocity motion:

the speed of vo = v = constant

acceleration = a = 0

An equation of constant velocity motion

[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]

x = distance = m

v = speed = m / s

t = time = seconds

x1, x2 = distance traveled

t1, t2 = travel time

1 = tourist, 2 = taxi

[tex]\rm x1=v1.t1=4t1\\\\x2=v2.t2=50.t2\\\\t1+t2=2~hours\\\\t1=2-t2[/tex]

Total distance = x1 + x2

[tex]\rm 31~miles=4t1+50t2\\\\31=4(2-t2)+50t2\\\\31=8-4t2+50t2\\\\23=46t2\\\\t2=0.5[/tex]

then:

[tex]\rm x2=v2.t2\\\\x2=50\times 0.5\\\\x2=\boxed{\bold{25~miles}}[/tex]

The distance of the elevator

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resultant velocity

brainly.com/question/4945130

the average velocity

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Answer:

d. 40

Step-by-step explanation:

x/4 - 7=3

Add 7 to both sides

x/4 - 7+7=3+7

x/4 = 10

Multiply by 4 on each side

x/4*4 = 10*4

x = 40

Answer:The Answer of this probelm is D 40.

Step-by-step explanation:

x/4 - 7=3

First you need to add 7 to both sides

x/4 - 7+7=3+7

x/4 = 10

second you need to multiply by 4 on each side

x/4*4 = 10*4

Once you finish this should be your final answer right here x = 40

Hope this helps

Answer:

42° and 48°

Step-by-step explanation:

Complementary angles sum to 90°, hence

x + 10 + x + 4 = 90

2x + 14 = 90 ( subtract 14 from both sides )

2x = 76 ( divide both sides by 2 )

x = 38

x + 10 = 38 + 10 = 48° and x + 4 = 38 + 4 = 42°

Answer:     Arithmetic , Divergent

Step-by-step explanation:

Given sequence is  

{aₙ} =  {  4 , 10/3  , 8/ 3 , 2 , . . .   }

To check whether the sequence is geometric or not , we divide second term by first term  to find the common ratio . Then we again divide third term by second term to get common ratio .

The common ratio we get would same , then it is geometric .

         10/3               10            5

r₁  =  -----------  =     ------    =   ------

             4                12             6

        8/3                8                  3                4

r₂=   ----------   =  ----------  *   ------------   =     -----

           10/ 3             3              10                  5

Thus the common ratio are not same . So the sequence is not geometric .

Now we check for arithmetic .

We take difference of second and first term and then difference of third and second term . If it will be same then it is arithmetic . This is called common difference , d .

             10                       -  2

d₁   =    ------     - 4   =       -------

              3                          3

                8            10             - 2

d₂   =    ------    -   --------    =   ---------

               3             3                 3

Thus the common difference is same .

So the given sequence is arithmetic .

To find whether it is convergent or divergent , we need to write sum of n terms first .

Formula for finding sum of n terms of arithmetic sequence is

            n

sₙ =     -----  [ 2a + ( n - 1 ) d]

             2

We have a = 4 , d = - 2/3 .

Plug  in this formula we get

              n                                                    n                2             2

sₙ  =     ------- [ 2 * 4 + ( n - 1 ) ( -2/3) ]  =     ------ [  8 -   -----  n  +   ------  ]

              2                                                    2                3               3

           n          26              2

sₙ  =   ------  [    ------    -    ------- n  ]

           2           3                3

To check whether it is convergent or divergent , we take limit sₙ approaches to infinity .

                               n       26       2

lim   sₙ   =     lim    { ---   [  ---  -  ------ n ] } =     - ∞

n → ∞           n→∞      2        3       3

As the sequence diverge , thus the series is divergent .

Thus given series is arithmetic , divergent .

Second is the  correct option .

[tex]7x+10=13(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=(13)(12x)+(13)(-3)+14x\\\\7x+10=156x-39+14x\\\\7x+10=170x-39\qquad\text{subtract 10 from both sides}\\\\7x=170x-49\qquad\text{subtract 170x from both sides}\\\\-163x=-49\qquad\text{divide both sides by (-163)}\\\\\boxed{x=\dfrac{49}{163}}[/tex]

[tex]\heartsuit[/tex]  If x = 4 is the Only Solution of the Equation x² + bx + 16 = 0

[tex]\heartsuit[/tex]  Then the Value x = 4 should satisfy the Given Equation

⇒ (4)² + b(4) + 16 = 0

⇒ 16 + 4b + 16 = 0

⇒ 4b + 32 = 0

⇒ 4b = -32

⇒ b = -8

Answer:

200

Step-by-step explanation:

150/3=50 so she sorts 50 items per minute, then 50*4=200

Answer:

Number of recyclable items sort in 4 minutes by Faye = 200

Step-by-step explanation:

Given that Faye can sort 150 recyclable items in 3 minutes.

   Number of recyclable items sort in 3 minutes = 150

   [tex]\texttt{ Number of recyclable items sort in 1 minute =}\frac{150}{3}=50[/tex]

Number of recyclable items sort in 4 minutes = 4 x Number of recyclable items sort in 1 minute

Number of recyclable items sort in 4 minutes = 4 x 50 = 200

Number of recyclable items sort in 4 minutes by Faye = 200