A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line. Please Help Best helped will get brainiest Promise PLS HELP !!!!!!!!!!!!!!!!!!!

Answers

Answer 1

Answer:

y - 1 = 3/2 (x + 10)

Step-by-step explanation:

Point-slope form of the equation of a line is a fill-in-the-blank shortcut to write an equation. If you know a point and the slope of a line you can fill in that info and voila! you have the equation.

Here is Point-slope equation:

y - Y = m(x - X)

Because the point given (-10,1) is in the form (X,Y), fill in -10 for X and 1 for Y.

The slope given is 3/2, fill that in for m.

y - Y = m(x - X)

y - 1 = 3/2 (x - -10)

y - 1 = 3/2 (x + 10)

The equation is

y - 1 = 3/2 (x + 10)


Related Questions

I eh need the Answer to this please i am timed!!

Answers

Answer:

pro tip: crop your screen before you post it....

I think it's B

I did this 2 years ago in middle school

The answer is definitely b

if molly needs to cross a river 16 feet wide how long does she have to walk

Answers

Molly has to walk for 16/x minutes where x is the speed of molly.

What is the speed of an object?

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here molly needs to cross a river 16 feet then let her speed be x and t be the time taken to cross the river

Then we have x=16/t

                        t=16/x

Hence, Molly has to walk for 16/x minutes where x is the speed of molly.

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the cost,y, of red grapefruit can be represented by the equation y=2x, where x is the number of pounds of red grapefruit. the graph shows the cost of pink grapefruit. which type of grapefriut costs more per pound?

Answers

We can conclude that, if --

m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.

What is the general equation of a straight line?

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that the cost (y) of red grapefruit can be represented by the equation y = 2x, where {x} is the number of pounds of red grapefruit. Also the graph shows the cost of pink grapefruit.

The cost (y) of red grapefruit can be represented by the equation y = 2x. So, we can write that the cost per unit pound of red grape is $2. The graph of the pink grapefruit is not given, but its slope {m} will tell us its costs per pound.

Now, if -

m > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.

Therefore, we can conclude that, if -

m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.

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evaluate 5² + 7 - 3 +4

Answers

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5² + 7 - 3 + 4

Simplify the expression, then we have

⇒ 5² + 7 - 3 + 4

⇒ 25 + 7 - 3 + 4

⇒ 36 - 3

⇒ 33

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

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Which segment is parallel
Justify the answer with a converse theorem

Answers

Answer:

Ah and mc are parallel segments

Segments CA and H? are parallel by the Converse of Corresponding Angles Theorem.

I put “H?” because the last point is not visible, but here’s a picture of the parallel segments. The orange marking highlights the parallel segments.

What value for the
constant, h, in the equation
shown below will result in an infinite number of
solutions?
6t + 18 = h(3x + 9)

Answers

Therefore , As a result, h = 2 is the answer to the equation in the given question.

Explain equation.

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.

Here,

The formula is as follows: 6x + 18 = h(3x + 9)

To ensure that the expression has an unlimited number of answers, h's value must be determined.

Take the expression now and continue solving it.

=> 6x + 18 = h(3x + 9)

=>3hx + 9h= 6x +8

The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.

Therefore, 3h = 6 and h = 2

As a result, h = 2 is the answer to the equation in the given question.

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Please solve the ques. below

Answers

The velocity of the train is given as follows:

900 m / min.

How to obtain the velocity of the train?

To obtain the velocity of the train, we must understand the relation between velocity, distance and time, which is given as follows:

v = d/t.

In which the parameters are given as follows:

v is the velocity.d is the distance.t is the time.

The train took a difference of 200 m in 15 seconds = 0.25 minutes, hence the difference in velocities is given as follows:

200/0.25 = 800 m / min.

(the difference in velocity is the distance covered divided by the time).

As Uncle Tony is walking at a rate of 100 m / min, the velocity of the train is calculated as follows:

800 + 100 = 900 m / min.

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"-12<-3x-15" less than or equal to 36

Answers

Answer:

-17 ≤ x < 1

Step-by-step explanation:

-12 < -3x - 15 ≤ 36

Add 15 to all 3 "sides."

-12 + 15 < -3x - 15 + 15 ≤ 36 + 15

3 < -3x ≤ 51

Divide all 3 "sides" by -3. Remember that when you multiply or divide an inequality by a negative number, you much change the direction of the inequality sign.

3/(-3) > -3x/(-3) ≥ 51/(-3)

-1 > x ≥ -17

Rewrite in standard order.

-17 ≤ x < 1

please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee

Answers

1) Note that in the problem above, the complete table is given as:

Team Number:     1             2      3           4           5

Best Jump (ft)       20.6    21.5    20.9      19.4        20.2

2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.

3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.

Why are the Domain and Range Important?

Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.

The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.

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If some one makes and many slices of toast of toast as possible in 4 minutes and 40 seconds how many slices they can make?

Answers

Therefore , the solution of the given problem of expression comes out to be probably 4 slices.

Who or what is expression?

In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.

Here,

you figure if a toaster takes about 1-2 minutes to toast a piece of bread  and a toaster usually can fit 2 slices at a time i would say 4.

Preheat oven broil to high. Move oven rack to highest position.

Place sliced bread on an ungreased baking sheet. 4 slices of bread.

Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...

Top with butter, jam, or any other favorite topping!

The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).

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Round 0.295833333 to the nearest hundredth

Answers

Answer:

The answer is 0.30.

I wish you luck in your assignments.

Answer:

0.3

Step-by-step explanation:

Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3

If g(x) = x³ - 2x, find the value of g(2+h)-g(2)dividebyh answer is h square plus six h plus ten

Answers

Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.

The difference quotient is defined as:

[g(2+h) - g(2)] / h

So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:

lim h→0 [g(2+h) - g(2)] / h

Substituting the value of x in the function g(x), we get:

lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h

This simplifies to:

lim h→0 [8+6h+h²-2h - 4] / h

Which simplifies to:

lim h→0 [h²+6h+4] / h

And, finally:

lim h→0 [h(h+6)] / h

The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:

h+6

So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.

Therefore, the value of g(2+h)-g(2) divided by h is:

(h+6) - 6 / h

Which simplifies to:

h / h

Which is equal to:

1

So, the final answer is 1.

Step-by-step explanation:

Help desperatlu6(5x-3)

Answers

[tex]6(5x-3)[/tex]

Distribute:

[tex](6)(5x)+(6)(-3)[/tex]

[tex]=\fbox{30x - 18}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6(5x - 3)}[/tex]

[tex]\text{DISTRIBUTE 6 WITHIN the PARENTHESES}[/tex]

[tex]\mathsf{= 6(5x) + 6(-3)}[/tex]

[tex]\mathsf{= 30x - 18}[/tex]


[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\mathsf{30x - 18}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

In 1965, the population of a country was 192 thousand to 3 significant figures.

In 2020, the population of that country was 366 thousand to 3 significant figures.

Work out the percentage increase in population. Give your answer correct to 2 significant figures.

Answers

The percent change in population is 90.65%.

What is percent?

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given population of country in 1965 = 192 thousand = 1,92,000.

population of country in 2020 = 366 thousand = 3,66,000

the increase in population is = 366000 - 192000 = 1,74,000

the percentage increase =  (100)(increase in population)/(1965 population)

the percentage increase = (100) (174000)/(192000)

the percentage increase =  90.625%

Hence the percent increase is 90.62%.

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3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10 i need help with this

Answers

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

what is transformation ?

Four various modifications that can be made to a point, line, or geometric object are referred to as transformations collectively. You must be able to identify which changes have been made and that each alteration has been made. The following guidelines for function translation and transformation: The function is shifted up by b units by F (x) + b. F (x) b causes the function to move downward. The expression f (x + b) causes the function to be moved left b units. Translation, reflection, rotation, and dilation are the four different types of transformations. Transform, reflect, or rotate the geometric shapes that are displayed on a coordinate plane. The transformation, often known as f: X X, is the name given to a function, f, that maps to itself.

given

-1 on the left x-axis and 4 on the right y-axis

Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.

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A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 2 pounds of jelly beans, the total cost is $12. For 3 pounds of almonds and 8 pounds of jelly beans, the total cost is $31. Find the cost for each pound of almonds and each pound of jelly beans.

Answers

To find the cost of each pound of almonds, we need to find the difference in the cost of the almonds between the two purchases and divide it by the difference in the number of pounds of almonds. In this case, the difference in the cost of the almonds is $31 - $12 = $19 and the difference in the number of pounds of almonds is 3 - 5 = -2 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/-2 = $-9.50 per pound. This means that the cost of each pound of almonds is $-9.50.

To find the cost of each pound of jelly beans, we can use a similar process. In this case, the difference in the cost of the jelly beans is $31 - $12 = $19 and the difference in the number of pounds of jelly beans is 8 - 2 = 6 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/6 = $3.17 per pound. This means that the cost of each pound of jelly beans is $3.17.

Ann 's car can go 132 miles on 4 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.

Answers

Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

Find the missing numbers 46 62 87 123 ---- 236

Answers

Answer:

The missing numbers are 74, 105, and 178.

What is the solution of the inequality shown
below?
a+5>-7

Answers

The required solution for the inequality a + 5 > -7 is (-12, ∞).

What is inequality?

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

a + 5 > -7

To find the solution for the inequality,

Simplify the inequality,

a + 5 > - 7

a > - 7 - 5

a > -12

The value of a is greater than -12, implies that,

The solution for the value of the given inequality is (-12, ∞).

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The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?

Answers

The population of North Carolina will reach 12 million in the year 2028.

What is Population Growth?

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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what is schur polynomial in numerical analysis.

Answers

Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.

What is Schur polynomial?Issai Schur gave the name Schur to a class of symmetric polynomials in n variables that generalize both the complete homogeneous symmetric polynomials and the elementary symmetric polynomials. They are the features of polynomial irreducible representations of the generic linear groups in representation theory. For the space of all symmetric polynomials, the Schur polynomials provide a linear basis. Any Schur polynomial product can be expressed as a linear combination of Schur polynomials with non-negative integral coefficients; these coefficients' values are supplied combinatorially by the Littlewood-Richardson rule. More generally, skew Schur polynomials are connected to pairs of partitions and share Schur polynomials' characteristics.

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1
Multiple Choice Question
What type of number is 105?
Choose all that apply
Whole number
Integer
Rational
Irrational

Answers

Analyzing the options given in the question, the options that satisfy for the number 105 are: Integer, Rational, Whole number.

What are whole numbers?

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions.

What are rational numbers?

A rational number is a number which is in the form of p/q where p and q are both integers and q is not equal to zero.

The number 105 is , Whole number since it falls between all the numbers between 0 to positive infinity. Similarly, the number is an Integer since it does not contain any fractions or decimals. And, the number 105 is rational number since it can be expressed in the form of 105/1.

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Natalie is driving on the freeway. She just passed mile marker 290. The markers have
been increasing as she drives by them. The fastest Cameron will drive is 80 miles per
hour. However, there is a bit of traffic that might slow her down, but she doesn't know
exactly how much it will slow her down.

a. Write an inequality to represent Natalie's position relative to the mile markers
three hours from now.

b. Rewrite this inequality to reveal Natalie's speed.

Need help with this ASAP

Answers

On solving the provided question we can say that - the inequality equation which will be formed is 290x [tex]\geq[/tex] -23 + y

What is inequality?

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

here,

we have 290x

so the inequality equation which will be formed is

-y + 290x [tex]\geq[/tex] -23

290x [tex]\geq[/tex] -23 + y

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42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).

Answers

Start with any random elements of sets and compute LHS and RHS individually.

a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.

b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.

What are sets and subsets?

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.

Therefore, S = {1, 2, 3} and T = {1, 4, 5}.

Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.

Hence,  f(S ∪ T)=f(S) ∪ f(T).

Now, f(S ∩ T) = {1} and  f(S) ∩ f(T) =  {1, 2, 3} ∩ {1, 4, 5} = {1}.

Therefore,  f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)

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The dimensions of a picture frame can be represented as (x+4) inches and (x+3) inches. The value of the area, in square inches, of the picture frame is equal to the value of the perimeter, in inches

Answers

The wrist circumference in relation to height tells us how big our body frames are.

How is frame size calculated?

The wrist circumference in relation to height tells us how big our body frames are. A man who is above 5' 5" tall and with a wrist measurement of 6" would be considered to have tiny bones.

The following chart can be used to establish whether a person has tiny, medium, or large bones by measuring their wrist with a measuring tape and comparing the results.

Women:

under 5'2" in height"

Medium wrist size is between5.5" and5.75" Small wrist size is less than5.5" "

Large is defined as a wrist size of 5.75 or greater."

between 5'2" and 5'5" tall

smaller than 6 inches around the wrist"

Bracelet size 6 is medium "Medium = wrist size between 6.25" and 6.5" Large

Over 5' 5" in height"

Small wrists measure less than 6.25", Medium wrists measure 6.25" to 6.5," and Large wrists measure over 6.5."

Example :

2(x + 3 ) + 2 (x + 4 ) = (x + 3 )( x + 4)

x² + 7x + 12 = 4x + 14

x² + 3x - 2 = 0

(x + 3 / 2 )² = 17 / 4.

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Use the graphs of f and g to graph h(x)=(f+g)(x). (Graph segments with closed endpoints).

Answers

The required graph of the function of h(x) is shown, where h(x) =  |x| + |x + 2|.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|


So,
h(x) = f + g

Now substitue the functions,

h(x) = |x| + |x + 2|

Thus, the required graph of the function of h(x) is shown.

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What are terms and common rations ? Can someone explain to me how to solve

Answers

For the arithmetic sequence 4 - 2(n - 1), we have that:

The first term is 4.The second term is 2.The third term is zero.The fourth term is -2.The fifth term is -4.The common difference is -2.

For the geometric sequence 6 x 3^(n - 1), we have that:

The first term is 6.The second term is 18.The third term is 54.The fourth term is 162.The fifth term is 486.The common ratio is 3.

How to model the arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.

The nth term of an arithmetic sequence is given by the equation presented as follows:

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

In which:

[tex]a_1[/tex] is the first term.d is the common difference.

The sequence in this problem is defined as follows:

4 - 2(n - 1)

Which has first term 4 and common difference -2, hence the terms are:

4, 2, 0, -2, -4, -6 and so on...

What is a geometric sequence?

A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.

The nth term of a geometric sequence is given by the equation presented as follows:

[tex]a_n = a_1 \times q^{n - 1}[/tex]

In which:

[tex]a_1[/tex] is the first term.q is the common ratio.

The sequence for this problem is given as follows:

6 x 3^(n - 1)

Which has first term of 6 and common ratio of 3, hence the terms are given as follows:

6, 18, 54, and so on...

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What is the value of x? Show your work in arriving at your answer.

Answers

The value of x is 18.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

First, both angles shown are equal to each other.

5x + 5 = 95

Next, the opposite side of the equation to isolate x value (5x).

5x + 5 (-5) = 95 (-5)

5x = 90

Finally, we need to divide both sides of the equation by 5.

5x / 5 = 90 / 5

x = 18

The final answer: x = 18

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find x
y=\frac{1}{4} x+3

Answers

Answer:   x = 4y - 12

Work Shown:

[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]

A 969 acre wildlife preserve has 19 cheetahs. About how many acres does each cheetah have to itself, if each cheetah roams the same number of acres?

Answers

By taking a quotient, we will see that each cheetah has around 51 acres for itself.

About how many acres does each cheetah have to itself?

If we assume that the cheetahs are evenly distributed along the whole area, then the number of acres that each cheetah has to itself is equal to the quotient between the total area, and the total number of cheetahs.

There are 969 acres and 19 cheetahs, then the quotient is:

969/19 = 51

That is the number of acres that each cheetah has for itself.

Learn more about quotients by reading:

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