The first term of a sequence is 4 and the common ratio is –2. What is the formula for the sequence based on term number

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-3x+6\\y=9\end{array}\right\ \text{put the value of}\ y\ \text{to the first equation}\\\\9=-3x+6\qquad\text{subtract 6 from both sides}\\3=-3x\qquad\text{divide both sides by (-3)}\\-1=x\to x=-1[/tex]

Answer:

w=6

Step-by-step explanation:

P=2(L)+2(w)

48= 2(18)+2w

48=36+2w

12=2w

w=6

checking;

48= 2(18)+2(6)

48= 36+12

48= 48

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Round the answer as needed

To find the original number that increased by 130% equals 69, we divide 69 by 2.30, which reveals that the original number is 30.

The student is asking how to find a number that, when increased by 130%, results in 69. To solve this problem, let's represent the original number as x. The increase by 130% of the original number would be x + 1.30x (which equals 2.30x), and this sum is equal to 69. To find x, we divide 69 by 2.30:

x = 69 / 2.30

We calculate this as:

x = 30

Therefore, the number which when increased by 130% equals 69 is 30.

The store wants to make a 20% profit:

Multiply the cost of the toy by 1.20 ( cost plus 20%).

6.25 x 1.20 = $7.50

This means when the toy is sold at 25% off, it needs to be $7.50 to make the 20% profit.

When the item is 25% off, that means it would sell for 75% of the original price.

Now to find what the price needs to be before the 25% off divide the profit price by 75%

7.50 / 0.75 = $10

K = $10

Final answer:

To find the price at which the toy should be sold to maintain a 20% profit after a 25% discount, use the cost price and profit margin to calculate the selling price.

Explanation:

To compute the price at which the toy should be priced at a 25% discount and still make a profit of 20%, follow these steps:

Calculate the cost price after a 20% profit margin: $6.25 + 0.20 * $6.25 = $7.50

Set up the equation: $7.50 = (100% - 25%) * $k

Solve for k: $k = $7.50 / 0.75 = $10

Answer:

100>=500-15x

Step-by-step explanation:

He needs at least 100, so it's greater than OR equal to 100. He starts with 500 and goes down 15 each week. The x stands for the amount of weeks that are in the school year. Sorry for the terrible formatting on the greater than or equal to.

To write an inequality representing Daniel's lunch account scenario, where he begins with $500 and must have at least $100 by year-end despite spending $15 weekly, the inequality would be: 500 - 15x >= 100.

The question involves writing an inequality to represent the condition where Daniel must have at least $100 in his school lunch account by the end of the school year, given he starts with $500 and spends $15 each week on lunches. To frame the inequality, let's denote the number of weeks Daniel buys lunch as x. Given he spends $15 per week, the total expenditure over x weeks will be $15x. Initially having $500 and requiring at least $100 by the end of the school year, the inequality will be:

500 - 15x ≥ 100.

This inequality states that even after spending $15 each week for x weeks, Daniel must have at least $100 remaining in his account. To find how many weeks he can afford to buy lunch while meeting this requirement, one would solve for x in the inequality.

Answer:

420°

Step-by-step explanation:

To convert from radian to degree measure

degree measure = radian measure × [tex]\frac{180}{\pi }[/tex]

Hence

degree = [tex]\frac{7\pi }{3}[/tex] × [tex]\frac{180}{\pi }[/tex]

Cancel π on numerator/ denominator

= [tex]\frac{7(180)}{3}[/tex] = 420°

To convert 7π/3 radians to degrees, multiply by the conversion factor 180°/π to get 420°.

To convert the radian measure to degrees, we can use the conversion factor that 1 radian is equivalent to 57.3°.

Given the radian measure 7π/3, we multiply this by the conversion factor to find the degree measure.

The conversion is as follows:

7π/3 radians × (180°/π) = 7×180°/3 = 420°.

Therefore, 7π/3 radians is equivalent to 420° when converted to degrees.

Answer:

B = 135

A = 60

C = 75

Hope this helps

Answer:

∠B = 135°

∠A = 60°

∠C = 75°

Step-by-step explanation:

Since, Straight Line PQ always has angle 180°

∴ ∠PBS = 180 - ∠ABC

             = 180° - 45° = 135° = ∠B

Since, ∠RAS and ∠BAC are vertically opposite to each other.

So, ∠RAS = ∠BAC

Also ∠RAS = 60°

∴ ∠BAC = 60° = ∠A

The straight line ∠PCQ always has angle 180°.

∴ ∠PCR = 180 - ∠RCQ

⇒ ∠PCR = 180 - 105° = 75° = ∠C

That's true: if a triangle has two congruent angles, then it's an isosceles triangle.

An isosceles triangle has two congruent sides, which are opposite to the congruent angles, and a base, which is the side opposite to the non-congruent angle.

Answer:

Step-by-step explanation:

{z+1}/{z-1} = i.

z+1 = i (z-1)

z+1 =iz -i

z - iz  = -1 -i

z ( 1 -i) = - 1 -i

z = (- 1 - i ) /(1-i) = - (1+i)/(1-i)

z = - (1+i)(1+i)/(1-i)(1+i)

z = - (1+2i +i²)/ ( 1²-i²).........i² = -1

z =-2i/2

z = - i      (one solution)

All the complex numbers z satisfying the equation {z+1}/{z-1} = i is z = -i.

Complex numbers are numbers which are of the form [tex]a + ib[/tex], where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^2[/tex]= -1.

Given equation is,

(z + 1) / (z - 1) = i

Multiplying both sides by (z - 1),

z + 1 = i (z - 1)

Let z = (a + bi)

Substituting,

(a + bi + 1) = i (a + bi - 1)

(a + bi + 1) - i (a + bi - 1) = 0

a + bi + 1 - (ai + b(i)² - i) = 0

a + bi + 1 - ai - b(i)² + i = 0

Now i² = -1

a + bi + 1 - ai + b + i = 0

Combining the like terms,

(bi - ai + i) + (a + 1 + b) = 0

i (b - a + 1) + (a + b + 1) = 0

Left hand side is a complex number.

A complex number is a + bi = 0, when a = 0 and b = 0.

So, we get,

(b - a + 1) = 0 and (a + b + 1) = 0

b - a = -1 and a + b = -1

So, combining,

a + b = b - a

a + a = b - b

2a = 0

a = 0

Substituting,

b = -1

So the complex number, z = a + bi = -i

Hence the complex number z = -i.

Learn more about Complex Numbers here :

https://brainly.com/question/20566728

#SPJ3

Hello There!

the distance between 0 and -53 on a number line would be 53 spaces. This is because they are exactly 53 spaces away from each other.

Answer:

0

Step-by-step explanation:

Each time two cubes are rolled, the sum can be a number from 2 (rolling 1 and 1) to 12 (rolling 6 and 6). It is impossible to get a sum of more than 12, so there is zero probability of getting a sum of 47.

Answer: 0

Answer:

The correct answer would be true.  Reversing the statement clause and inserting a "not" in a if- then statement will also make the new statement true. For example, "If I eat this, then give me five dollars". The reverse would be " If I do not eat this, then do not give me five dollars". Both sentences mean the same.

Step-by-step explanation:

Answer:

its true

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Evaluate (h + k)(x) then substitute x = 2 into the result

(h + k)(x) = h(x) + k(x)

h(x) + k(x) = x² + 1 + x - 2 = x² + x - 1, thus

(h + k)(2) = 2² + 2 - 1 = 4 + 2 - 1 = 5

To find the value of (h + k)(2), substitute x = 2 into h(x) and k(x) and then add the results. The result is 5.

To find the value of (h + k)(2), we first need to find the values of h(2) and k(2). To find h(2), we substitute x = 2 into the function h(x) = x² + 1. h(2) = (2)² + 1 = 4 + 1 = 5. Next, to find k(2), we substitute x = 2 into the function k(x) = x - 2. k(2) = 2 - 2 = 0. Now, we can find (h + k)(2) by adding the values of h(2) and k(2). (h + k)(2) = h(2) + k(2) = 5 + 0 = 5.

https://brainly.com/question/29752390

#SPJ2

Answer:

B 0.55

Step-by-step explanation:

the student is a sophomore - so youre looking at the sophomore row, 77 sophomores total

the student attended the volleyball game - 42 sophomores attended the game

42 / 77 students total = about 0.55

Option: B is the correct answer.

              B.   0.55

Let A denote the event that the student is a sophomore.

and B denote the event that the student attend the volleyball game.

and A∩B denote the event that the student is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find the probability : P(B|A)

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Based on the table provided to us we have:

[tex]P(A)=\dfrac{77}{137}[/tex]

and

[tex]P(A\bigcap B)=\dfrac{42}{137}[/tex]

Hence, we have:

[tex]P(B|A)=\dfrac{\dfrac{42}{137}}{\dfrac{77}{137}}[/tex]

i.e.

[tex]P(B|A)=\dfrac{42}{77}=0.55[/tex]

Answer:

-11x-4 is the answer if the expression to simplify is (-7x+1)-(4x+5).

Step-by-step explanation:

We are first going to distribute to get rid of the ( ):

-7x+1-4x-5

Pair up like terms:

-7x-4x+1-5

Combine the like terms:

-11x-4

Answer:

The answer would be 6.

for a vertically opening parabola, its axis of symmetry will come from the x-coordinate of its vertex, thus

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-6}{2(1)}~~,~~-7-\cfrac{(-6)^2}{4(1)} \right)\implies (3~~,~~-7-9)\implies (3~~,~~-16) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=3}~\hfill[/tex]

Answer:

45

Step-by-step explanation:

Um, If we say that all the numbers are 44, and now we add 50, then we will get 270. Find the mean of 270. We get 45.

Final answer:

To find the new average after adding 50 to a set of 5 numbers with an average of 44, multiply the average by the number of elements, add the new number, then divide by the total number of elements to get the new average of 45.

Explanation:

The average of a set of 5 numbers is 44. To find the sum of the original set, multiply the average by the number of elements: 44 x 5 = 220. When 50 is added, there are now 6 numbers in the set. To find the new average, divide the new sum (220 + 50 = 270) by the total number of elements (6) to get 45 as the new average.

Answer:

A. x-9 and x+9 because these are perfect squares. 9 times -9 is -81. x times x is x^2. 9 + -9 is 0

Answer:

4

because if you cross off one number at a time from each side you are left with 2 number 4s and 4+4/2=4

The range of the function y=3/x+8 is all real numbers except 8, since the function approaches 8 but never reaches it due to the vertical asymptote at x=0.

The range of the function y=3/x+8 refers to all possible output values (y-values) that the function can produce. To find the range, it is essential to consider the values that x can take. Since x is in the denominator, x cannot be 0, as division by zero is undefined. Therefore, the function has a vertical asymptote at x=0.

As x approaches both positive and negative infinity, y approaches the constant 8, because the term 3/x approaches 0. Thus, the function can get close to, but never equal, the value of 8. Also, since 3/x can take any value except 0, the range of the function is all real numbers, excluding 8.

The final range of the function y=3/x+8 is therefore: {y | y ≠ 8}, meaning all real numbers that are not equal to 8.

Answer:

Correct answer is f(x) = (625^x)^1/4

Step-by-step explanation:

We know that

625 = 5^4

This means

f(x) = (625^x)^1/4

f(x) = (5^(4x))^1/4

But we know this is equivalent to

f(x) = (5^(4x*(1/4))) =

= 5^(x)

Correct answer is f(x) = (625^x)^1/4

Answer:

An important property of every line is its steepness, or slope.

The important property of every line is its steepness, or slope.

In terms of mathematics, the slope or gradient of a line represent the number that explained both the direction and the steepness of the line.

The steepness, incline, or grade of a line should be determined by the absolute value of the slope. A slope should have a greater absolute value indicates a steeper line.

learn more about the line here:

https://brainly.com/question/24489361

Answer:

t[c(h)] = 700h

Step-by-step explanation:

Got it wrong, and it told me what was right lol

The function is given by:

                            t[c(h)] = 700h

Emma burns 350 calories per hour biking.

The function is given by:

                 c(h) = 350h.

Also, when her little sister tow in the bike then the she  burn twice as many calories.

This could be represented by the function:

                             t(c) = 2c

where c is the number of calories burned per hour.

Now, we are asked to find the function that calculate he number of calories she will burn per hour while biking with her sister in the bike trailer i.e. we are asked to find the composition function:

[tex]t(c(h))[/tex]

Hence, we have:

[tex]t(c(h))=t(350h)\\\\i.e.\\\\t(c(h))=2(350h)\\\\i.e.\\\\t(c(h))=700h[/tex]

Answer:

[tex]y = \frac{1}{2}x+\frac{5}{2}[/tex]

Step-by-step explanation:

The perpendicular bisector of a line passes through the mid-point of the line and the product of slopes of the line and perpendicular bisector will be -1.

So,

[tex]Mid-point\ of\ BC = (\frac{6+8}{2},  \frac{8+4}{2})\\= (\frac{14}{2},  \frac{12}{2})\\= (7,6)[/tex]

The line will pass through (7,6)

Now,

[tex]Slope\ of\ BC = m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{4-8}{8-6}\\= \frac{-4}{2}\\= -2[/tex]

Let

m_2 be the slope of perpendicular bisector

So,

m_1*m_2 = -1

-2 * m_2 = -1

m_2 = -1/-2 = 1/2

The standard equation of line is:

y=mx+b

Where m is slope

So putting the value of slope and point to find the value of b

[tex]6 = \frac{1}{2}*7 +b\\ 6 = \frac{7}{2} + b\\b = 6 - \frac{7}{2}\\ b = \frac{12-7}{2}\\b = \frac{5}{2}\\So,\ the\ equation\ of\ perpendcular\ bisector\ of\ BC\ is:\\y = \frac{1}{2}x+\frac{5}{2}[/tex]

..

Answer:

x=(2/5) or x=0.4

Step-by-step explanation:

3x+5=7-2x

3x=2-2x

5x=2

x=(2/5) or x=0.4

Answer:

y = - 3x + 3

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 and c = 3, hence

y = - 3x + 3 ← equation of line

Hey there!

What I am assuming you are looking to do is convert this into a linear equation. I will guide you on how to do just that.

The linear equation form is:

y = mx + b

Note in particular m represents the slope and b represents the y-intercept.

Our answer would be y = -3x + 3

Answer:

6 square units (rounded to nearest whole number)

Step-by-step explanation:

Area of triangle is found by the formula 1/2 * base * height

But we can't easily figure this out using this formula, instead we use another formula for area of a triangle:

[tex]A=\frac{1}{2}abSinC[/tex]

Where

A is the area

a and b are the two side given (3 and 5 in our case)

C is the angle between a and b (53 degrees given)

We can substitute into the formula and figure out:

[tex]A=\frac{1}{2}abSinC\\A=\frac{1}{2}(3)(5)Sin53\\A=5.99[/tex]

The area is 5.99, to the nearest whole number, the area is 6

Answer:

14 days

Step-by-step explanation:

1. Convert the amount of work person A and B can do respectively in one day into fractions.

                                        A = 1/16                  B = 1/12

2. Get both fractions to a common denominator using the least common multiple. This is 48.

                                1/16 × 3 = 3/48        1/12 × 4 = 4/48

3. Add both fractions to find out how much work will be done in two days.  We are doing this because we are working in a pattern, and this will allow us to multiply, which is more time efficient than repeatedly adding 3 and then 4.

                                               3/48 + 4/48 = 7/48

4. Figure out how many sets of two days work (7/48) will get them to 48/48 (100% done) or closest to it without being under. This would be 7 sets.

                                               7/48 × 7 = 49/48

5. Multiply 7 by 2. We are doing this because we worked in sets of two days to account for A working and then B, since they are taking turns.

                                                    7 × 2 = 14

6. It will take them 14 days.

Answer:

a=1, b=-12

Step-by-step explanation:

This is a rational function with a hole at x=3 and a vertical asymptote at x=-4.

The denominator of this rational function must be:

[tex](x - 3)(x + 4)[/tex]

When we expand using the distributive property, we get:

[tex] {x}^{2} + 4x -3 x - 12[/tex]

This simplifies to

[tex] {x}^{2} + x - 12[/tex]

Therefore the graphed rational function is:

[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} + x - 12 } [/tex]

Comparing this to

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

We have

[tex]a = 1[/tex]

and

[tex]b = - 12[/tex]