Find the 87th term of this sequence: 157, 150, 143, ...

Answers

Answer 1

Answer:

                [tex]\bold{a_{87}=-445}[/tex]

Step-by-step explanation:

[tex]a_1=157\\a_2=150\\\\d=150-157=-7\\\\a_n=a_1+d(n-1)\\\\a_{87}=157+(-7)(87-1)=157-7\cdot86=-445[/tex]


Related Questions

Which is the best estimate of 22 x 97 by using rounding or compatible numbers? F. 1.800 G. 2,000 H. 2.300 1. 2.400​

Answers

Answer:

G

Step-by-step explanation:

2,134 is the answer to 22 times 97.

So, the estimate would have to be; G. 2,000

( 2,134 rounds to 2,000.)

Is 8:3 and 32:12 equivalent fractions

Answers

Answer:

Yes.

Step-by-step explanation: 8/3 is equal to 32/12, but simplified. Hope this helps!

Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x^2-25

Answers

9514 1404 393

Answer:

asymptotes: x = ±5; y = 0zero: x = 0

Step-by-step explanation:

The function will have a zero where the numerator is zero:

  5x = 0

  x = 0 . . . . divide by 5

The zero of the function is x=0.

__

The function will have vertical asymptotes where the denominator is zero:

  x^2 -25 = 0

  x^2 = 25 . . . . add 25

  x = ±5 . . . . . . take the square root

The function will have vertical asymptotes at x = -5 and x = 5.

__

When x gets large, the magnitude of the function is approximately ...

  5x/x^2 = 5/x

As x approaches infinity, this value approaches zero.

The function will have a horizontal asymptote at y = 0.

1. David uses 1 tbsp of sugar for every 1.25 cups of water when he makes lemonade complete the table below by filling in the missing values

Answers

Answer:

Step-by-step explanation:

David uses 1 table spoon of sugar for every 1.25 cups of water to prepare lemonade.

Therefore, Number of table spoons of sugar required (S) ∝ Cups of water required (w)

⇒ S ∝ w

⇒ S = kw

⇒ k = [tex]\frac{S}{w}[/tex]

⇒ k = [tex]\frac{1}{1.25}[/tex] = 0.8

So the formula to calculate the amount of water will be,

S = 0.8w

⇒ w = [tex]\frac{S}{0.8}[/tex]

where k = proportionality constant

Now we can complete the table with the help of the formula.

Sugar (tbsp)                   Water (cups)

      1                                     1.25                                                                      

      7                                    8.75    

      3                                    3.75

      5                                    6.25

f(x)= 3x^2-7 over
4x^2-3

-find f(2)

Answers

Answer:

5/13

Step-by-step explanation:

f(x) = [tex]\frac{3x^{2}-7 }{4x^{2}-3 }[/tex]

Substitute x for 2.

[tex]\frac{3(2)^2-7}{4(2)^2-3}[/tex]

Solve

[tex]\frac{3(4)-7}{4(4)-3}[/tex]

[tex]\frac{12-7}{16-3}[/tex]

f(2)= [tex]\frac{5}{13}[/tex]

The value of f(2) is 5/29.

What is Function?

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 3x² -7/ 4x² - 3

Now, find the value of the function at x= 2

So, f(2)= 3(2)² -7/ 4(2)² - 3

f(2) = 3 x 4 -7 / 4 x 8  - 3

f(2) = 5/29

Hence, the value of f(2) is 5/29.

Learn more about function here:

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Solve proportion 2/4.5=t/0.5

Answers

0.2 or 2/9 in fraction form I believe.

PLEASE HELP I AM BEING TIMED.

A frame designer is making a triangular frame. she has two sides of length 20 inches and 28 inches. What are the possible lengths for the third side?

Answers

the answer is in the question. it says 2 sides lengths of 20 in. and 1 side of 28 in.
um uh. it might be- well shii- probably- maybe- um well..

1 x 1
2 x 2
4 x 4
16 x 16
200 x 19.56

Answers

Answer:

we should solve it or what should we do...

Which of the following must always be true about vertical angles

Answers

Answer:

It is always a strait line going up.

Step-by-step explanation:

Answer:

vertical angels

angles opposite each other where two lines cross.

plz mark brainliest

Step-by-step explanation:

can someone explain to me how to do this

Answers

Answer:

x=45

Step-by-step explanation:

We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102. [tex]6y=108[/tex], which means that y=18. [tex]2\cdot(18)+6=36+6=42[/tex]. Since one line is a straight angle, it is 180 degrees we can do [tex]3x=180-45=135[/tex], so x=45.

Answer:

y = 18

x = 46

measures of the angles:

8y - 102 = 42

2y + 6 = 42

3x = 138

Step-by-step explanation:

So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is,  they will have the same measure.

Using this we know that opposite angles have to be congruent:

so

(2y + 6) = (8y -102)

now there is an algebra equation that can be solved by inverse operations and simplifying

2y + 6 = 8y - 102

    +102      +102

2y + 108 = 8y

-2y             -2y

108 = 6y

/6        /6

18 = y

Also, remember that two adjacent angles that form a line will add up to 180,

so

3x + (2y + 6) = 180

*note: I could have also used (8y - 102) but I choose to use (2y + 6)

so now substitute in the value of y that was found

y = 18

3x + (2 * 18 + 6) = 180

simplify

3x + ( 36 + 6) = 180

3x + 42 = 180

now use inverse operations

3x + 42 = 180

     -42     -42

3x = 138

/3      /3

x = 46

Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *

Answers

Answer:

Step-by-step explanation:

Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;

1, 2, 4...

The nth term of an arithmetic sequence is expresses as;

[tex]T_n = ar^{n-1}[/tex] where;

a is the first term

r is the common ratio

n is the number of terms

To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).

from the sequence above;

a = 1

r = 2/1 = 4/2 = 2

T4 = 1(2)^{4-1}

T4 = 2^3

T4 = 8

Hence the hydra will have 8 heads on the third day.

To know the number of heads at the end of 10 days, we will find the 11th term of the progression

T11 = 1(2)^{11-1}

T4 = 2^10

T4 = 1024

He will have 1024 heads after 10 days of trying to kill the monster.

The number of heads that would the Hydra have on the third day is 8

And, at the end of 10 days of trying to kill it is 1024.

The calculation is as follows:

a = 1

r = 2 by 1 = 2  

T4

= 8

So the hydra will have 8 heads on the third day.

Now  

To know the number of heads at the end of 10 days, we will determine the 11th term of the progression

= 1024

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Max is x years . Brother is 8 years older , sister is 12 years younger.total age.is 50 years.how old are they ?

Answers

Answer:

30

Step-by-step explanation:

12 + 8 = 20 so that means 50-20= 30 so max is 30 years old

x+8=b
x-12=s
X+b+s=50 then
x+x+8+x-12=50
So 3x-4=50
Then 3x=54
So x=18
Then the brother is 26 and the sister is 6
Check 26+18+6=50

Find the measure of the "?" or "X". Explain or show your

Answers

Answer:

66⁰ + x = 111⁰

x = 111⁰ - 66⁰

x = 45⁰

Answer:

First, I am taking the interior angle E as 'y' to be able to use the angle sum property to find 'x'.

So we can find 'y' by using 'linear pair'.

So Exterior angle 'E'+y=180 Degree.

=  111+y=180

By transposing: y=180-11

And y= 69 degrees.

And now have angles y & 'Angle G' we can use Angle sum property to find 'x'

ACCORDING TO ANFLE SUM PROPERTY OF TRIANGLE: "THE SUM OF ALL THE ANGLES OF A TRIANGLE IS 180 DEGREE"

THEREFOR, y+x+angle G=180 degrees.

=  69 degrees+66 degrees+x=180 degrees

=  135 degrees+x=180 degrees

by transposing,

x= 180 degrees-135 degrees

And, x= 45 degrees

ANOTHER METHOD:

BY USING EXTERIOR ANGLE PROPERTY.

ACCORDING TO EXTERIOR ANGLE PROPERTY OF TRIANGLE: "An exterior angle of a triangle is equal to the sum of its interior opposite angles"

So, Exterior Angle E= x+ Angle G

=  111 degrees= x+ 66 degrees

By transposing, x= 111 degrees-66 degrees

=  x=45 degrees.

So no matter whichever method is used, the value of x= 45 degrees.

Maki gave the cashier $50 to pay for 3 necklaces. The cashier gave her $4.25 in change. If each necklace cost the same amount, what is the cost in dollars and cents for each necklace?

Answers

Answer:

15.25

Step-by-step explanation

We can make an equation based on the data. 3x + 4.25 = 50

3x = 45.75

x = 15.25

Answer:

15.25

Step-by-step explanation:

The graph shows the height in feet of an object above the ground T seconds after it was launched from the ground.

Answers

Answer:

the answer is D

Step-by-step explanation:

The equation y = -16x² + 64x represents the given parabola that represents the height in feet of an object above the ground T seconds after it was launched from the ground.

What is function?

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is a graph that shows the height in feet of an object above the ground {T} seconds after it was launched from the ground.

The given graph is a parabola. A quadratic equation represents a parabola.

The quadratic equation will have two roots at the point on which it cuts the {x} axis.

Consider the equation in option {C} as -

y = -16x² + 64x

For the point (4, 0), we can check the graph as -

0 = - 16 x 4 x 4 + 64 x 4

0 = 0

For the point (0, 0), we can check -

0 = 0 + 64 x 0

0 = 0

Therefore, the equation y = -16x² + 64x represents the given parabola that represents the height in feet of an object above the ground T seconds after it was launched from the ground.

To solve more questions on functions, visit the link below-

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Need help ASAP!!!!!!!

Which pair of numbers has an LCM of 60?
a. 2 and 12
b.5 and 12
c.6 and 12
d.3 and 12


Pls answer ASAP

Answers

Answer: 5 and 12

Step-by-step explanation:

i did the quiz

1. (3x + 7) + (8x + 2)

Answers

11x+9


Step by step:
Remove the parenthesis
3x+7+8x+2
Collect like terms
11x+7+2
Add 7+2
11x+9

Which pair of lines are perpendicular

Answers

Answer:

D

Step-by-step explanation:


-9/6 + (-3/5) help please tytyytytytyyty

Answers

Answer:

-2.1

Step-by-step explanation:

Answer:

-2 1/10

Step-by-step explanation:

[tex] - \frac{9}{6} + ( - \frac{3}{5} ) = - \frac{3}{2} + ( - \frac{3}{5} ) = - \frac{15 + 6}{10} = - \frac{21}{10} = - 2 \frac{1}{10} [/tex]

( need help asap for a test) Ms. Smith bought a 5 pound bag of candy for her 6th grade classroom. She gave away 2 pounds of candy to her students during the first unit of instruction and ate 6 ounces of candy during planning.

(16 ounces = 1 pound)

How many ounces of candy does Ms. Smith still have in her bag?

A.
38 ounces

B.
42 ounces

C.
48 ounces

D.
54 ounces

Answers

Answer:

c

Step-by-step explanation:

5-2=3 3•16=48 48-6=42

PLS HELP ILL MARK YOU BRAINEST DUE IN 20 MINSS

Answers

Answer:

well the numbers are 58 60 62 64 and 66

Step-by-step explanation:

it's because when u add these 5 numbers u get 310 hope this helps

Answer: 62

Step-by-step explanation:

Given triangle ABC, determine the location of A' after a translation 2 units left and a reflection over the x-axis.

Answers

Answer:

(0,-3)

Step-by-step explanation:

left 2 puts you at (0,3) and flipping over x axis makes the y value negative, so it's (0,-3)

reciprocal of the fraction 3/7 is​

Answers

Answer:

A simple example - the reciprocal fraction of 3/7 is 7/3. As you can see, a reciprocal of a fraction is just flipping the numerator and denominator.

Step-by-step explanation:

Answer:

7/3

Step-by-step explanation:

reciprocal, refliprical is a great way to remember how to solve. You just flip the fraction.

Anna runs three over4 mile in six minutes. Assuming she runs at a constant rate what is her speed in miles per hour

Answers

Answer:

7.5 mph

Step-by-step explanation:

6 times 10 is 60 minutes which is an hour

3/4 times ten is 7.5

What is the slope of a line that is parallel to the line y=2/3x+5

Answers

Answer: 2/3

Step-by-step explanation: The slopes of parallel lines are equal/the same but they have different y intercepts

There are 2 computers for every 3 iPads in this technology room

Answers

I’m confused on the question, what are u asking

Answer:

The Ans Is 2:3

Step-by-step explanation:

help if u can please

Answers

Money with Tom = ×

Money with Aaron = x + 8

Their sum = $20

This can be written as :

= x + x + 8 = 20

= 2x + 8 = 20

= 2x = 20 - 8 ( transposing +8 from LHS to RHS changes +8 to -8 ) .

= 2x = 12

= x = 12 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 ) .

= x = 6

Which means ,

Tom has = x = $6

Aaron has = x + 8 = $6 + $8 =

= $14

Therefore , Tom has = $6 and Aaron has = $14 .

-13 = r/9 + 8

r =


r equals what

Answers

-5=r/9

-45=r

Step-by-step explanation:

you're just trying to get the r alone. so you have to subtract the 8 and multiply the nine. you're just reversing the problem.

-x + 7 <10
Solving inequalities

Answers

Answer:

x>-3

Step-by-step explanation:

−x+7<10

Step 1: Subtract 7 from both sides.

−x+7−7<10−7

−x<3

Step 2: Divide both sides by -1.

−x−1<3-1

x>−3

I need help please and thank you

Answers

Answer:#7 is 20%. #8 is 67.5 people

Step-by-step explanation: For #7 you would just divine 14/70 to get .20 converted to a percentage is 20%. For #8 you would convert 37.5% to a decimal of .375 and multiply that to 180 people to get the answer of 67.5 people.

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Individuals became slaves as aform of punishment for certain crimes orfor failure to pay tribute. Prisoners of warwho were not used as human sacrificesalso became slaves. An individual couldvoluntarily sell himself or his children intoslavery to pay back a debt. Slaves had theright to marry, to have children, tosubstitute another individual in their place, and to buy their freedom. Their ownerswere responsible for housing and feeding their slaves, and generally, slaves couldnot be resold. They were usually freed when their owners died and could alsogain freedom by marrying their owner. Aztecs were not born slaves and could notinherit this status from their parents.Which Of The Following Statement BEST explains slavery in The Aztec Empire? Select TWO correct answers.A. Slaves Could Not Buy There Own Freedom or have friends to purchase them.B. Slaves were Born as property, So Their Children were also Considered property.C. 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