Find the 56th term of the following arithmetic sequence 7,10,13,16

The equation of line in standard form that pass through the point (1, -3) and (-2, -1) is (-2x/3)-y=7/3 where -2/3 is x-intercept and -1 is the y-intercept.

A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.

we are given with;

x1=1, y1=-3

x2=-2, y2=-1

equation of line in standard form:

Ax+By=C

so using formula:

(y−y1)=(y2−y1)(x−x1)/(x2−x1)

(y−(-3))=((-1)−(-3))(x-1)/(-2−1)

(y+3)=(2)(x−1)/(-3)

(y+3)=(2x−2)/(-3)

y+3=(-2x/3)+(2/3)

y=(-2x/3)+(2/3)-3

y=(-2x+2-9)/3

y=(-2x-7)/3

(2x/3)+y=-7/3

rearranging;

(-2x/3)-y=7/3

This is our required answer.

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There are 2 decorations that Jasmine makes.

What are word problems?

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

You can tackle any word problem by following these five steps:

Since we have given that

Length of a meter of ribbon used = 1/4

[tex]\frac{1}{4} = \frac{1}{4}.100 = 25[/tex]

Length of a meter cut into equal pieces = 1/2

[tex]\frac{1}{2} =\frac{1}{2}.100= 50[/tex]

So, Number of decorations that Eli make is given by

Length of total ribbon / Length of ribbon used

= 50 / 25

= 2

Hence, there are 2 decorations that Jasmine makes.

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The solution of the system of equations is (x, y) = (9/2, -7/10).

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To solve a system of equations, we can use any of the following methods:
Substitution method,
Elimination method,
Matrix method.
Let's use the substitution method to solve the given system of equations.
We can solve the first equation for z:
z = 7 - 3x - 2y
Substituting this expression into the third equation, we get:
3x + 2y + 3(7 - 3x - 2y) = 1
This simplifies to:
-5x - 3y + 21 = 1
Adding 5x and 3y to both sides, we get:
21 = 5x + 3y + 1
Subtracting 1 from both sides, we get:
20 = 5x + 3y
Dividing both sides by 5, we get:
4 = x + 3/5 y
Substituting this expression into the first equation, we get:
3(x + 3/5 y) + 2y + 7 = 7
This simplifies to:
2y = -7/5
Dividing both sides by 2, we get:
y = -7/10
Substituting this value into the expression for x, we get:
x = 4 - 3/5(-7/10)
This simplifies to:
x = 4 + 21/10
x = 9/2

Hence, the solution of the system of equations is (x, y) = (9/2, -7/10).

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Answer:

1 – cos²x = Sin²x

Step-by-step explanation:

Sinx + 1 = cos x

by squaring both sides

(Sinx + 1)² = (cos x )²

Sin²x + 1 = cos²x

1 – cos²x = Sin²x

i hope this helped

Step-by-step explanation:

Jim paid £70 for a bike. Then pays £10 per month.

a) Write down an expression for the total amount paid after m months.

cost = 10m + 70

_______________________________________

b) Factor the expression.

10m + 70

common factor is 10 so:

10(m + 7)

Answer:

Step-by-step explanation:

100

As per the unitary method, the number of tulip were 21.

Unitary method:

In algebra, unitary method defines how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

Given,

Here we have There were 35 bunches of rose and tulip. Each bunch had 12 of the roe flower. There 7 more bunches of tulip than rose.

Now we need to find how many tulip were there.

Let number of bunches of roses be x.

And then the number of bunches of tulips will be x + 7

The total number of bunches of flowers = 35                                                                          

So, it can be written as,

=> x + x + 7 = 35

When we simplify this one then we get,

=> 2x + 7 = 35

Now, we have to subtracting both sides by 7

=> 2x = 28

Then dividing both sides by 2

=> x = 14

So, the number of bunches of roses = 14

Then the number of bunches of tulips = 14 + 7 = 21

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Answer:

1 -3/4

2. P(00,3)

3. Q(4,0)

4. 6

Step-by-step explanation:

1. 3x+4y=12

 4y= -3x+12

 y= -(3/4)x+ 3 , so gradient = -3/4

2. Y intercept is P (0,3)

3. X intercept is Q(4,0)

4. Area = 3×4÷2=6

Answer: -23

Step-by-step explanation:

When you're adding to a negative the negative number decreases, so if you're adding 12 from negative 35, you're taking away 12 negative numbers, hence why the answer is -23

hope that helped :)

I think you're answer is right angle

Answer: You are correct

Step-by-step explanation: You are correct with both answers because 9x + 7 and 7 + 9x will equal the same thing. Here's an example

X=3

9(3) + 7

27+ 7

34

7 + 9(3)

7+27

34

34=34

It only equals 34, no matter the order. So, it has one solution.

I hope this helps!

Answer:

Equivalent

Step-by-step explanation:

The expressions 9x+7 and 7+9x are equivalent .The equation has infinite many solutions

The required fraction cup of sugar do Evelyn need to add is 8/3.

Multiply the numerators and denominators independently to track down the item. At the point when you need to duplicate divisions, increase the 2 numerators together first and compose it on top. Then increase the denominators together and compose it on the lower part of the portion. Improve on your response on the off chance that you would be able so it is in the least terms.

As question says Evelyn need 3(1/3) cup og sugar

To find many cup of sugar do Evelyn need to add.

Let the required sugar be x

Then,

2/3 + x = 3(1/3)

x = 10/3 - 2/3

x = 8/3 cup of sugar need.

Thus, required cup of sugar is 8/3.

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8 seed packets

First, we need to figure out how many plants Emma can grow with each seed packet. To do this, divide 6 plants (the number of plants Emma currently has) by 3 seed packets (the number Emma had to begin with). This will give us a unit rate of "2 plants per seed packet".

Now that we know the unit rate, we can use it to figure out how many seed packets Emma needs to have 16 plants in her backyard. Divide 16 plants (the number of plants Emma wants to have) by 2 plants per seed packet (the unit rate). This will give us 8 seed packets.

Therefore, Emma needs 8 seed packets to have a total of 16 plants in her backyard.

If you have any additional questions or need further assistance, please let me know.

Answer:

Step-by-step explanation:

Rewrite equations: x+y=6;2x−3y=4

Solve x+y=6 for x: x+y+−y=6+−y (Add -y to both sides)

x=−y+6

Substitute −y+6 for x in2x−3y=4: 2x−3y=4

2(−y+6)−3y=4

−5y+12=4 (Simplify both sides of the equation)

−5y+12+−12=4+−12 (Add -12 to both sides)

−5y=−8

−5y/−5=−8/−5 (Divide both sides by -5)

y=8/5

Substitute 8/5 for y in x=−y+6:

x=−y+6

x=−8/5 +6

x=22/5 (Simplify both sides of the equation)

Answer: x=22/5 and y=8/5

The maximum miles that Emma can ride without exceeding her spending limit is 17.3 miles

What are Linear Inequalities?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It depicts the data which is not equal in graph form.

The linear expression formed using the given description will be 2.75 + 0.65x

where x is the total number of miles

and the linear inequality formed will be 2.75 + 0.65x < 14

Refer to the graph below

So, the maximum miles that Emma can ride without exceeding her spending limit is 17.3 miles

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Answer:

A

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

After reviewing the derivative of the tangent double , the correct order of the derivative is (a) .

In the question ,

the derivative of the  double tangent is given ,

we have to select the correct order of the derivative .

the function is tan(2x) .

Step 4:   tan(2x) = Sin(2x)/cos(2x)

Step 3 :

expanding sin(2x) and cos(2x) using identity ,

we get ,

= 2sinxcosx/(cos²x - sin²x)

Step 5 :

dividing the numerator and denominator by cos²x .

= [2sinxcosx/cos²x]/[cos²x/cos²x - sin²x/cos²x]

Step 1 : simplifying further,

we get ,

= [2sinx/cosx]/[1 - sin²x/cos²x]

Step 2 : writing sinx/cosx = tanx

we get ,

tan2x = 2tanx/(1 - tanx)

Therefore , the correct order for the given derivative is (a) 4, 3, 5, 1, 2  .

The given question is incomplete , the complete question is

Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order

(a) 4, 3, 5, 1, 2

(b) 4, 5, 3, 1, 2

(c) 3, 4, 5, 1, 2

(d) 3, 4, 1, 5, 2

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The possible elevation of Salton city will be;

⇒ x < - 2 feet

Where, x is the elevation of Salton city.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

New Orleans is 2 feet below sea level.

And, Salton City has an elevation that is lower than New Orleans.

Now,

New Orleans is 2 feet below sea level.

And, Salton City has an elevation that is lower than New Orleans.

Let the elevation of Salton city = x feet

Thus, We get;

The possible elevation of Salton city will be;

⇒ x < - 2 feet

Where, x is the elevation of Salton city.

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Answer:

log base 28 of (7x4)

log base 28 of (28)

which equals 1

Answer:

The slope is 1/6.

Step-by-step explanation:

The slope of the given equation is -6. Perpendicular lines have negative reciprocal slopes.

Answer:

In any right triangle, the sine of one acute angle is equal to the cosine of the other angle.

Step-by-step explanation:

The measure of the largest angle is 96 degrees.

What is a ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3

The measure of the largest angle in the triangle is 96 degrees.

To find the measure of the largest angle, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

Let's call the measures of the three angles x, y, and z, where x is the measure of the smallest angle, y is the measure of the middle angle, and z is the measure of the largest angle.

We are given that the ratio of the angles is 3:5:8, which means that x:y:z = 3:5:8.

We can set up the following equation to represent the sum of the measures of the angles in the triangle:

x + y + z = 180

We can also set up the following equation to represent the ratio of the angles:

x : y : z = 3 : 5 : 8

We can use these two equations to find the measure of the largest angle.

First, let's multiply the second equation by 3, 5, and 8 to get:

3x = 15y = 24z

Then, we can substitute these equations into the first equation to get:

15y + 24z = 180

Solving for z, we get:

z = 180 / (15+24) = 180 / 39 = 96

Therefore, the measure of the largest angle is 96 degrees.

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The hot air balloon is rising at 600 feet per minute and  the blimp are rising at 250 feet per minute

How fast is the hot air balloon rising?

From the question, we have the following parameters that can be used in our computation:

The height of a balloon over time is represented by the graph

On the graph, we have the following points

(x, y) = (0, 0) and (2, 1200)

The rate is calculated as

Rate = (1200 - 0)/(2 - 0)

Evaluate

Rate = 600

Hence, the rate of rising is 600 feet per minute

How fast is the blimp rising?

From the question, we have the following parameters that can be used in our computation:

The height of a blimp over time is given by y = 250x

The above equation is a linear equation

A linear equation can be represented as

y = mx + c

Where

slope = m

This means that the slope of y = 250x is 250

The slope represents the rate

Hence, the rate of rising is 250 feet per minute

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Answer:

y=-3/1x-2

y=9/3x+8

Step-by-step explanation:

Slope is -3/1 using rise over run, it's just negative because the graph is slanted down. The slope is 9/3 using rise over run. Then the y-intercepts are -2 and 8.

-Hope this helped & Happy Holidays!

Answer: When you solve the equations and work them out, you get the answer of $4000.

The approximate ordered pair for f(x) = g(x) is given as; (4, 22) from the graph. Option A

We know that there are two equations that can be shown from the set of equations that have been written here and the set of equations that we have are;

f(x) = −2x + 30

g(x) = 3x + 10

We are now trying to see the points at which the equation can be said to be equal. This refers to the point where  f(x) = g(x). How can we be able to obtain this point? If we are to get this point then we must go back and look at the graph very well.

As we are looking at the graph very well we should fix our eyes on any point where the line of two functions can be seen to intersect. Once that happens, we can say that we have reached the point where the two functions can be said to be equal. This point is read from the graph as (4, 22)

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The inequality expression is :16 + 8B ≥ 50

Least amount that could be spent = $4500

What is  inequality expression?

An algebraic inequality is a mathematical statement that uses the inequality sign to relate an expression to a value, a variable, or another expression. "Greater than" and "greater than or equal to" are two verbs that can be translated as inequalities.

need at least 50  total rooms.

Room already booked = 16  

Number of Blocks booked = B

Each Block = 8

8B  - Addition room Booked

Total room booked = 8B + 16

Total room booked  ≥   need at least 50  total rooms

8B  + 16  ≥ 50

=> 16 + 8B ≥ 50  , option B is correct

=> 8B ≥ 34

=> 4B ≥ 17

minimum B = 5

Cost = 900 * 5 = 4500 $

least amount of additional money Joe can spend to get the rooms they need in  dollars  = 4500  

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The value of the angle m∠BDC is 105°.

Let separate the triangles and find missing angle in triangle with given angles.

CAD = 45°

CDA = 30°

Then, CAD+CDA+ACD = 180°

45°+30°+ACD=180°

ACD=180°-75°

       =105°

by applying third angle theorem,

∠CAD=∠DBC=45°

∠ADC=∠BCD=30°

Then, ∠DBC+∠BCD+∠BDC=180°

45°+30°+BCD=180°

BCD=180°-75°

      =105°

Hence, The value of the angle m∠BDC is 105°.

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Answer: 18x-12

Step-by-step explanation:

Add 10x +8x (because they both have x at the end so its fine to add them

then do -5-7= -12