Which set of statements about the angles is true?

Which Set Of Statements About The Angles Is True?

Answers

Answer 1

Answer:

Answer choice 4

Step-by-step explanation:

Since alternate interior angles create congruent angles, angle 5 and 3 are congruent as well as 4 and 2, and since the only option that has these statements is answer choice 4, it is the correct answer.

Answer 2

Answer:

it is d

Step-by-step explanation:


Related Questions

7 days left until the launch of our new product and we have $668.00 left in our promotion budget we need to spend 85.00 on the last day how many dollars can we spend on the remaining days

Answers

Answer:

$97.16 per day

Step-by-step explanation:

Total amount you have = $668.00

You have to spent $85.00  on the last day.

$668.00-85.00

=$583

It means you have $583 for the remaining 6 days in the week.

If you spend equal amount of money each day , you can calculate it by dividing remaining amount and number of days

=583/6

=$97.16

It means you can spend $97.16 per day....

Two angles of a triangle have the same measure and the third one is 3 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.

The LARGEST angle has a measure of ___ degrees.

Answers

Answer:

62 DEGREES

Step-by-step explanation:

TWO ANGLES=2A

LARGEST ANGLE=A+3

2A+A+3=180

3A=180-3=177

A=177/3=59

LARGEST ANGLE=59+3=62

Answer:

The Largest Angle angle has a measure of 62 degrees.

Step-by-step explanation:

In triangle ABC, angle ABC equals to angle ACB.

and BAC is the largest angle.

Let angle measure of ABC and ACB angles be "x" degree.

then, measure of third angle i.e BAC will be "x + 3" degrees.

Since sum of all angles of any triangle is 180 degree.

so,  first angle + second angle + third angle = 180

       x  + x + (x + 3) = 180

        3x  = 180 - 3

         3x = 177

          x = 59 degrees

So, First angle = 59 degree

     Second angle = 59 degree

     Third Angle = 62 degree.

The Largest Angle angle has a measure of 62 degrees.

I need to find q, r, s, t
The function is g(x)=2x^2-8

Answers

Answer:

q=0

r=2

s=3

t=-3

Step-by-step explanation:

q represents the value we should get from evaluating d(-8).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(-8) we use this function here labeled d and replace x with -8:

[tex]d(-8)=-\sqrt{\frac{1}{2}(-8)+4}[/tex]

[tex]d(-8)=-\sqrt{-4+4}[/tex]

[tex]d(-8)=-\sqrt{0}[/tex]

[tex]d(-8)=0[/tex]

So q is 0 since d(-8)=0.

r represents the value we should get from evaluating f(0).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(0) we use this function labeled f and repalce x with 0:

[tex]f(0)=\sqrt{\frac{1}{2}(0)+4}[/tex]

[tex]f(0)=\sqrt{0+4}[/tex]

[tex]f(0)=\sqrt{4}[/tex]

[tex]f(0)=2[/tex]

So r is 2 since f(0)=2.

s represents the value we should get from evaluating f(10).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(10) we use this function labeled f and replace x with 10:

[tex]f(10)=\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]f(10)=\sqrt{5+4}[/tex]

[tex]f(10)=\sqrt{9}[/tex]

[tex]f(10)=3[/tex]

So s is 3 since f(10)=3.

t represents the value we should get from evaluating d(10).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(10) we use the function labeled d and replace x with 10:

[tex]d(10)=-\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]d(10)=-\sqrt{5+4}[/tex]

[tex]d(10)=-\sqrt{9}[/tex]

[tex]d(10)=-3[/tex]

So t is -3 since d(10)=-3

q=0

r=2

s=3

t=-3

which of the following binomials below is a factor of this trinomial x(x)-13x+36​

Answers

Answer:

(

x

+

4

)

(

x

+

9

)

=

0

Your answer would be x=-4 and x=-9.

Explanation::

(

x

+

4

)

(

x

+

9

)

x

times  

x

=

x

2

x

(

9

)

+

x

(

4

)

=

13

x

4

times  

9

=

36

=  

x

2

+

13

x

+

36

Answer:

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).

Step-by-step explanation:

To factore the given quadratic with leading coefficient one, you must find two numbers that add to be and multiply to be c.

a=1

b=-13

c=36

So we need two numbers that multiply to be 36 and add to be -13.

These numbers are -4 and -9 since

(-4)(-9)=36 and -4+-9=-13.

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).


Triangles ABD, CBD and ADC are all isosceles. Find the angle x.
AC = AD

Answers

     Measure of angle 'x' given in the picture will be 36°.

  From the picture attached,

In ΔABD,

m∠DAB = x° [Given]

AB ≅ BD [Isosceles triangle]

Therefore, opposite sides of the given triangles will measure the same.

m∠BAD = m∠BDA =

m∠BAD + m∠BDA + m∠ABD = 180° [By triangle sum theorem]

x° + x° + m∠ABD = 180°

m∠ABD = 180°- 2x°

m∠DBC + m∠ABD = 180° [Linear pair of angles]

m∠DBC + (180° - 2x) = 180°

m∠DBC = 2x°

In isosceles ΔBCD,

BD ≅ CD

Therefore, m∠DBC = m∠BCD = 2x°

In isosceles ΔACD,

Since, AC ≅ AD,

Therefore, m∠ACD = m∠ADC = 2x°

By applying triangle sum theorem in ΔACD,

m∠ACD + m∠DAC + m∠CDA = 180°

2x° + x° + 2x° = 180°

5x° = 180°

x = 36°

   Therefore, measure of 'x' will be 36°.

Learn more,

https://brainly.com/question/1153593

Elsie pays $8.99 for a one-pound canister of Georgia pecans. Write and solve a proportion to determine the cost of 4
ounces of the pecans she needs for a particular recipe. Round answer to the nearest cent.
(SHOW WORK)

Answers

Final answer:

To find the cost of 4 ounces of pecans, we set up a proportion comparing the cost to weight, resulting in $2.25 after rounding to the nearest cent.

Explanation:

To determine the cost of 4 ounces of pecans when a one-pound (16 ounces) canister costs $8.99, we set up a proportion where the cost is directly proportional to the weight.

The proportion is $8.99/16 ounces = $X/4 ounces, where X represents the cost of 4 ounces of pecans.

Multiplying both sides by 4 to solve for X gives us $X = (4 ounces × $8.99) / 16 ounces.

Simplifying this, we find that $X = $2.2475, which, when rounded to the nearest cent, gives us an answer of $2.25.

Evaluate |c^2 +b^2|, given a=5, b=-3, and c=-2.
2
6
10
13

Answers

Answer:

13

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

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

|c² + b²|

Put b = -3 and c = -2 to the expression:

|(-2)² + (-3)²| = |4 + 9| = |13| = 13

A side of a square is 8 3/2  inches. Using the area formula A = s2, determine the area of the square.

Answers

Answer:

Area=512 square inches

Step-by-step explanation:

According to the given data;

A side of a square = (8)³/² inches.

Area of a square = ?

To find the area of a square we use the formula:

Area = s²

Area=(8)³/²)²

Area = 8³

Area= 8*8*8

Area=512 square inches....

The product of two numbers is 144 and their difference is 10. What is the sum of the two numbers

Answers

Answer:

18+8=26

Step-by-step explanation:

Their sum would be 18 and * because they have  difference of ten. In order o get this you would have to multiply 1 X144 and so on.

Answer:

Step-by-step explanation:

Its 134 hope this helos

Find the selling price of a $50 item after a 50 % markup

Answers

Answer:

75 dollars

Step-by-step explanation:

If an item is 50 and you want to markup 50%, you must find 50% of 50 to find how much the item will go up by from 50.

So 50% of 50 means 50% times 50.

50%=.5 or 1/2

So .5(50)=25.

The item is going up by 25 dollars.

So we started at 50 dollars.

So 50+25 is going to be the new amount.

50+25=75 is the new amount.

Answer:

$75

Step-by-step explanation:

In this question, it's asking you to find the selling price of an item after the markup.

We know that:

Item is $50There is a 50% markup

With the information above, we can find the answer.

A markup is pretty much an increase in a price. This means that in this context, the item's price increased by 50%

We're going to need to find how much the selling price is after the markup.

We would multiply 50 by 1.5 to find the selling price.

[tex]50*1.5=75\\\\\text{Or you can do it this way}\\\\50*0.5=25\\\\50+25=75[/tex]

With either method, you're still going to get 75.

This means that the selling price of the item after applying the markup value is $75

I hope this helps you out.Good luck on your academics.Have a fantastic day!

you roll a fair 6 sided die what is p (not 5)

Answers

Answer:

5/6

Step-by-step explanation:

There are 6 possible rolls

1 2 3 4 5 6

Only one of 6 is a five

What is the truth value for the following conditional statement?

If the grass is red, then the snow is white.

T T → F
F T → T
F T → F
T F → T

Answers

Answer:  the correct option is

(B) F T → T.

Step-by-step explanation:  We are given to find the truth value of he following conditional statement :

"If the grass is red, then the snow is white."

Let us consider that

p : the grass is red. This is a false statement

and  

q : the snow is white. This is a true statement.

So, we get

p  →  q

F  → T, which is true (T).

Thus, the required answer is  F T → T

Option (B) is CORRECT.

For the parent function y=√x what effect does a value of k = -3 have on the graph?

Horizontal shift of 3 units to the right

Horizontal shift of 3 units to the left

Vertical shift of 3 units up

Vertical shift of 3 units down

Answers

Answer:

Vertical shift of 3 units down ⇒ last answer

Step-by-step explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ The parent function y = √x

∵ There is a translation by k = -3

- From the rules above k is for the vertical translation

∵ k = -3

- That means the parent function translated 3 units down

∴ The value of k = -3 makes the graph of the parent function translated

   3 units down

- For more understand look to the attached graph

# y = √x ⇒ the red graph

# y = √x - 3 ⇒ the blue graph

Swill sells 35 liters or milk in a day. How many liters of milk will be sold if he has to sell 125% more milk per day

Answers

Answer:

43.75 liters.

Step-by-step explanation:

125% = 1.25 as a decimal fraction.

number of liters of milk = 35 * 1.25

= 43.75 liters.

10x^3+40x^2+15x
------------------------------
5x

Answers

Answer:

Step-by-step explanation:

[tex]\dfrac{10x^3 + 40x^2 + 15x}{5x}\\ \dfrac{10x^3}{5x} +\dfrac{40x^2}{5x}+\dfrac{15x}{5x}[/tex]

2x^2 + 8x + 3 is your final answer.

Which expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?

Answers

Answer:

-9-3/1-(-7)

Step-by-step explanation:

Answer:

The slope of given line = -3/2

Step-by-step explanation:

Points to remember

slope of the line with end points (x1, y1) and (x2, y2) is given by,

Slope = (y2 - y1)/(x2 - x1)

To find the slope of the line

Here (x1, y1) = (-7, 3) and (x2, y2) = (1, -9)

Slope = (y2 - y1)/(x2 - x1)

 = (-9 - 3)/(1 - -7)

 = (-12)/8

 = -3/2

Therefore the slope of given line = -3/2

Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.

Answers

Answer:

Part 1) [tex]c=21.9\ units[/tex]

Part 2) [tex]B=61.1\°[/tex]

Part 3) [tex]A=28.9\°[/tex]

Part 4) [tex]C=90\°[/tex]

Step-by-step explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

substitute the given values

[tex]c^{2}=10.6^{2}+19.2^{2}[/tex]

[tex]c^{2}=481[/tex]

[tex]c=21.9\ units[/tex]

step 2

Fin the measure of angle B

we know that

In the right triangle

[tex]tan(B)=b/a[/tex]

substitute the given values

[tex]tan(B)=19.2/10.6[/tex]

[tex]B=arctan(19.2/10.6)=61.1\°[/tex]

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

[tex]B=61.1\°[/tex]

[tex]C=90\°[/tex]

substitute

[tex]A+61.1\°+90\°=180\°[/tex]

[tex]A=28.9\°[/tex]

Answer:

A = 28.9 degrees, B = 61.1 degrees, c = 21.9

Step-by-step explanation:

I got it correct on founders edtell

What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...

Answers

Answer:

-.1

Step-by-step explanation:

The common difference in the arithmetic sequence can be found by doing term minus a previous term.

So 0.26-0.36=-.1

or 0.16-0.26=-.1

or 0.06-0.16=-.1

or -0.04-0.06=-.1

or -0.14-(-0.04)=-.1

Evaluate the following vertices for the function f(x)=x+2y

Answers

Answer:

You might want to see if I read your ordered pairs right because it was really hard to see for me:

f(2,6)=14

f(-1,3)=5

f(6,4)=14

Step-by-step explanation:

I assume they meant to write f(x,y)=x+2y.

Doing f(2,6) now.  This means replace x with 2 and y with 6:

f(2,6)=2+2(6)=2+12=14

f(2,6)=14

Doing f(-1,3) now.  This means replace x with -1 and y with 3:

f(-1,3)=-1+2(3)=-1+6=5

f(-1,3)=5

Doing f(6,4) now. This means replace x with 6 and y with 4:

f(6,4)=6+2(4)=6+8=14

f(6,4)=14

Tha values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

Functions and values

Give the function expressed as:

f(x, y) = x + 2y

If the coordinate point is (2, 6), then;

f(2, 6) = 2 + 2(6)

f(2, 6) = 2 + 12

f(2, 6) = 14

If  the coordinate point is (-1, 3), then;

f(-1, 3) = -1 + 2(3)

f(-1, 3) = -1 + 6

f(-1, 3) = 5

If the coordinate point is (6, 4), then;

f(6, 4) = 6 + 2(4)

f(6, 4) = 6 + 8

f(6, 4) = 14

Hence the values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

Learn more on function and values here: https://brainly.com/question/4934333

jewels has 6.75 to ride the ferry around Connecticut m it will cost her 0.45 every time she rides. identify the dependent variable and independent variable in this scenario
the number of rides is the independent variable and the total cost is the dependent variable
the total cost is the independent variable and the number of rides is the dependent variable
the number of rides and the total cost are both independent variables
the number of rides and total cost are both dependent variables​

Answers

Answer:

Dependent would be the number of times she rides because it would add up to how many times she could ride. 6.75= x(.45)

Step-by-step explanation:

Final answer:

In Jewels' ferry ride scenario, the independent variable is the number of rides taken, and the dependent variable is the total cost incurred based on the rides. This follows the general rule where the dependent variable's outcome is determined by the choice made in the independent variable.

Explanation:

In the scenario described, Jewels has a certain amount of money to spend on ferry rides, and each ride costs a fixed amount. Here, the number of ferry rides she can take is the independent variable, as it can be chosen freely by Jewels. The total cost of the ferry rides is the dependent variable, as it depends on the number of rides she takes.

Therefore, the correct answer is that the number of rides is the independent variable and the total cost is the dependent variable.

As for the given reference information, in the vacation resort case, the number of hours the equipment is rented is the independent variable, and the total fee is the dependent variable. This is similar to Jewels' scenario because the basic principle in both instances is about the relationship between a variable you can control (number of rides or hours) and a variable that depends on this control (total cost or total fee).

For example, if Jewels decides to ride the ferry 5 times, the total cost would be 5 rides × $0.45 per ride = $2.25. This demonstrates how the dependent variable (total cost) changes in response to a change in the independent variable (number of rides).

2x^2+y^2=8xy find dy/dx

Answers

Answer:

2(x-2y)/(4x-y)  =  dy/dx

Step-by-step explanation:

2x^2+y^2=8xy

Take the derivative of each term, remembering that we take the 8xy as derivative by parts)

2 * 2x dx +  *2y dy = 8 ( x dy + dx *y)

4x dx +2y dy = 8x dy + 8y dx

Subtract 2y dy from each side

4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx

4x dx  = 8x dy - 2y dy + 8y dx

Subtract 8y dx from each side

4x dx -8y dx  = 8x dy - 2y dy + 8y dx-8y dx

4x dx -8y dx  = 8x dy - 2y dy

(4x-8y) dx = (8x-2y) dy

Factor out a 4 from the left side and a 2 from the right side

4(x-2y) dx = 2( 4x-y) dy

Cancel a 2

2(x-2y) dx = ( 4x-y) dy

Divide each side by (4x-y)

2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy

2(x-2y)/(4x-y) dx =  dy

Divide by dx

2(x-2y)/(4x-y) dx/dx =  dy/dx

2(x-2y)/(4x-y)  =  dy/dx

Sure would help a lot

Answers

Hello There!

X = 6

First, we would add 5 to both sides so adding 5 to -5 is 0 and adding 5 to 7 is 12 so we would get the equation 2x = 12

Next, we would divide 2x by 2 and divide 12 by 2 and we would get a quotient of 6.

Our final answer is x = 6

Answer:

x=6

Step-by-step explanation:

2x - 5 = 7

Add 5 to each side

2x-5+5= 7+5

2x = 12

Divide by 2

2x/2 = 12/2

x = 6

An 'A' is considered 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0. If you received the following grades in your first semester, what would your grade point average be?

English: 3.0 credits, B.
Biology: 4.0 credits, B.
Communications: 3.0, F.
New student seminar: 1.0, A.

Express your answer rounded to the hundredths place.

Answers

Answer:

Your grade point average would be 2.75(B- or C+)

Step-by-step explanation:

[tex]\frac{3+4+3+1}{4} \\\frac{11}{4} \\2.75[/tex]

Final answer:

Explaining the calculation of GPA based on given grades, resulting in an approximate value rounded to the hundredths place.

Explanation:

The grade point average (GPA) for the given grades can be calculated as follows:

English: 3.0 credits, B, which is 3.0 in GPA scale

Biology: 4.0 credits, B, which is 3.0 in GPA scale

Communications: 3.0, F, which is 0.0 in GPA scale

New student seminar: 1.0, A, which is 4.0 in GPA scale

Calculating the GPA:

(3.0 + 3.0 + 0.0 + 4.0) / 11 = 10.0 / 11 = 0.91

Therefore, the grade point average would be approximately 0.91 rounded to the hundredths place.

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents this scenario?



PLZ HELP IM TIMED

Answers

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of solved puzzles

y -----> the number of solved riddles

we know that

[tex]2x+y \geq 4[/tex]

The solution of the inequality is the shaded area above the solid line [tex]2x+y=4[/tex]

The slope of the solid line is negative [tex]m=-2[/tex]

The y-intercept of the solid line is the point (0,4)

The x-intercept of the solid line is the point (2,0)

therefore

The graph in the attached figure

Answer:

The graph that representss this scenario is attached.

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

x: number of solved puzzles

y: number of solved riddles

b) Point rules:

Each solved puzzle is worth two points: 2x

Each solved riddle is worth 1 point: 1y = y

Sum of points: 2x + y

The video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

Solve algebraically for y: y ≥ 4 - 2x

You want to draw the border line of the function, that is y = 4 - 2x

You have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.

x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)

y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

Addtional constrains: x and y cannot be negative, so add the constrains:

       x ≥ 0 and y ≥ 0

The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).

plz give brainliest


Ryan has 57 plastic blocks that are either yellow or green. In 57-X, what does x equal?​

Answers

Answer:

the amount of green blocks = X then you'll end up with the amount of yellow blocks

Answer:

so x can be either yellow or green

Step-by-step explanation:

Ryan has total 57 blocks (total yellow and green)

if x is either of yellow or green

then 57 -x will be either green or yellow (According to x is green or yellow)

x can be either yellow or green .

Simplify the expression.

-(10)^-2

Answers

Answer:

-1/100

Step-by-step explanation:

-(10)^-2

Exponents first

We need to make the negative in the exponent positive, which means move it to the denominator

-1

--------

10^2

-1

---------

100

Answer:

-1/100

Step-by-step explanation:

10^(-2) becomes 1/100.

-(10)^(-2) is -1/100.

Dimensions for an office floor plan is 15ft. By 15ft and 28ft. By 28ft. Tile runs $1 per square foot and carpeting $5 per square foot. What is the estimated total cost for the floor coverings installed

Answers

Answer:

$2520

Step-by-step explanation:

Taking the dimensions of the office floor from the plan to be;

[tex]15ft*28ft[/tex]

Area of the floor to be covered will be the product of the sides dimensions

[tex]=15*28=420ft^{2}[/tex]

Cost of putting tile on the floor

1ft²=$1

420ft²=?

=[tex]\frac{420*1}{1} =420[/tex]

=$420

Cost of putting a carpet on the floor

1ft²=$5

420ft²=?

[tex]=\frac{420*5}{1} =2100[/tex]

=$2100

Estimated cost

Total estimated cost =cost for putting tiles+cost for putting carpet

=$420+$2100=$2520

A researcher determined the amount of ducks that were in a pond over a four-year time span. The results are shown in the table below.
Year 1, 2, 3, 4
Ducks 64, 78, 92. 106

Year Ducks
1 64
2 78
3 92
4 106
Select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.


d= 64(1.22)^n-1

d=14n +64

d= 14n + 50

d + 50(1.14)^n-1

Answers

Answer:

Option C (d = 14n + 50).

Step-by-step explanation:

The observations for Year 1, 2, 3, and 4 are 64, 78, 92, and 106 respectively. It can be observed that the difference between second term and the first term is 78 - 64 = 14. This is also true for the third term and the second term. In fact, the difference between the terms is fixed. This means that the sequence is an arithmetic sequence, in which the difference between the terms is fixes for all the terms. The nth term in this case is defined as:

S = a + (n-1)*d; where S is the output at a given n, a is the first term, n is the position, and d is the common difference. In this question, S = ducks (d), a = 64, and d = 14. Therefore, plugging in the values in the above formula gives:

d = 64 + (n-1)*14.

d = 64 + 14n - 14.

d = 14n + 50.

Therefore, the model which best describes the amount of ducks that will be in the pond during the nth year is d = 14n + 50, i.e. Option C!!!

Answer: Third Option

[tex]a_n =14n+50[/tex]

Step-by-step explanation:

By subtracting consecutive terms from the number of ducks each year you will get a common difference of 144.

[tex]78-64 = 14\\92-78 = 14\\106-92 = 14[/tex]

This means that the data can be modeled by the equation of an arithmetic sequence

The arithmetic sequences have the following form:

[tex]a_n = a_1 + d(n-1)[/tex]

Where [tex]a_1[/tex] is the first term and d is the common difference between the consecutive terms.

So :

[tex]a_1 = 64[/tex]

[tex]d = 14[/tex]

Then the equation is:

[tex]a_n = 64 + 14(n-1)[/tex]

[tex]a_n = 64 + 14n-14[/tex]

[tex]a_n =14n+50[/tex]

what is the slope of the line shown below? (9, 1) (-3, -7)

Answers

Answer:

2/3

Step-by-step explanation:

To find the slope based off of two points, use the following formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in your values and simplify.

[tex]\frac{-7-1}{-3-9} \\\\\frac{-8}{-12}[/tex]

[tex]\frac{8}{12}[/tex]

[tex]\frac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

I like the line up and subtract strategy. At the end you just put 2nd number over 1st.

This is the slope formula; just a different way to think about the formula.

(9,1)

-(-3,-7)

=======

12, 8

So the slope is 8/12=2/3.

64 -[16 x (-3) – 2 x{17 – 25 }]​

Answers

Answer:

96

Step-by-step explanation:

64 -[16 x (-3) – 2 x{17 – 25 }]​   I'm going to take a couple of steps that are very small and they can be combines along with other steps. Combine 16*-3

64 - [-48 - 2*(17 - 25)]            Combine what is inside (17 - 25)

64 - [-48 - 2*(-8)]                    Combine -2*-8

64 - [-48 + 16]                         Combine what is in the brackets.

64 - [-32]                                 Remove the brackets

64 + 32                                    Combine

96

The trick in this question is the signs.

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