5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.

Answer:

The slope is 0, since it is a horizontal line

35 points omgggggggggggggggggg

Answer:

p=5

Step-by-step explanation:

3+ p= 8

subtract 3 on both sides

p=5

hope that helps :)

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

CD = 15

Step-by-step explanation:

We are given two quadrilaterals: CDEF and GIJH.

We know that CD = 3x - 6, and GI = x + 8.

We want to find the length of CD.

Notice how CD and GI both have one tick mark on them.
This indicates that these two are congruent, meaning that they have the same length.

Because of that, CD = GI.

If we substitute 3x - 6 for CD and x + 8 for GI, we get:

3x - 6 = x + 8

Now, we can solve this like a regular equation.

Add 6 to both sides.

3x - 6 = x + 8

    +6       +6

_________________

3x = x + 14

Subtract x from both sides.

3x = x + 14

-x    -x

_____________-

2x = 14

Divide both sides by 2.

2x = 14

÷2    ÷2

____________

x = 7

We found the value of x.

Now, substitute 7 as x in 3x-6 (the length of CD).

CD = 3x - 6 = 3(7) - 6 = 21 - 6 = 15

Therefore, CD = 15.

Answer:

12*3.25=39

Step-by-step explanation:

u multiply 12 by 3.25 and then u get ure answer witch is 39!!

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The simplified Expression of 2.5 x 10² / 5 x \(10^{-5}\) is 5 x \(10^6\).

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as \(3^4\), where 4 is the exponent and 3 is the base.

Given:

2.5 x 10² / 5 x \(10^{-5}\)

Now, using Exponents and powers

\(a^{-m}\) = 1/ \(a^m\)

So, 2.5 x 10² / 5 x \(10^{-5}\)

= 2.5 /5 x \(10^{2-(-5)}\)

= 25/50 x \(10^{2+5]\)

= 1/2 x \(10^7\)

= 0.5 x \(10^7\)

= 5 x \(10^6\)

Hence, the simplified Expression is 5 x \(10^6\).

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E=egg farm

x=distantce between  the Berto´s trains and the meeting point.

t=time where the trains meet up

⇒110 miles/h                                          ⇒85miles/h

[---------------------------E----------------------]-------------------------------------X

[............12 miles.......][........34 miles.....][------------ x ----------------------]

distance between Berto´s train and Eduardo´s train=

=12 miles+34 miles=46 miles.

S=d/t      ⇒d=S*t

S=seed

d=distance

T=time

Eduardo´s train;

46 miles+x=t*110 miles/h  ⇒x=t*110 miles/h-46 miles  (1)

Berto´s train;

x=t*85 miles/h  (2)

With the equations (1) and (2) we suggest this system equations:

x=t* 110 miles/h-46 miles

x=t*85 miles/h

we solve this system equiations :

t*110 miles/h-46 miles=t*85 miles/h

110t miles/h-85t miles/h=46 miles

25 t miles/h=46 miles

t=46 miles/25 miles/h=1,84 hour  (≈1 hour, 50 minutes, 24 seconds)

x=t*85 miles/h=156,4 miles

Solution: 1,84 hour

Answer:

1.84

Step-by-step explanation:

I did it on edge it was correct

Answer:

sorryyyyyy dont knowwwwwwww

since vectors v1 and v2 are parallel, the system xv1 + yv2 = v3 will have infinitely many solutions regardless of the specific values of v1, v2, and v3.

Geometrically, this is due to the fact that v1 and v2 span the same direction in space, so any combination of x and y will still lie on the same line or in the same direction.

Since vectors v1 and v2 are parallel, they lie on the same line or are scalar multiples of each other. Let's analyze the possible cases geometrically:

1. **Vectors v1 and v2 are collinear (lie on the same line):**

  In this case, any combination of x and y that satisfy the equation \(xv1 + yv2 = v3\) will lie on the same line as v1 and v2. This means there are infinitely many solutions for x and y.

2. **Vectors v1 and v2 are scalar multiples of each other:**

  If v1 and v2 are scalar multiples of each other, then they represent the same direction in space. In this case, any combination of x and y that satisfy the equation will give a vector that lies on this line (spanned by v1 and v2), which is also the direction of v3. Hence, again there are infinitely many solutions.

3. **Vectors v1 and v2 are not collinear but have different directions:**

  This scenario is not possible because you stated that v1 and v2 are parallel. If they have different directions, they would not be parallel.

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we know that

A=[2,4,6]

we have that

A ∩ Ø=Ø

therefore

Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

Answer:n the metric system, "milli" means 1/1,000 and "kilo" means 1,000. This means that a milligram is 1/1,000 of a gram, and a kilogram is 1,000 grams. So a kilogram is much heavier than a milligram; in fact, a kilogra

Step-by-step explanation:

The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

Do you have an image that can go along with your question?

Step-by-step explanation:

Mention more

Answer:

x = 4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

6x - 9 = 2x + 7

- Add 9 to both sides of the equation.

6x = 2x 16

- Subtract 2 from both sides.

4x = 16

- Divide by 4 to isolate the variable

x = 4

Answer:

2no is the answer pls mark me branilest

Answer:

its 2

Step-by-step explanation:

good luck!

Answer:

I would say 3n-8=n+2

Step-by-step explanation:

First it says the difference of three times a number. N is serving as the unknown number so, so far we have 3n then 8 so 3n-8 and then put an = and then it says 2 more than the number so put the n + 2

your answer should be 3n-8=n+2

i also took the test  :)

hope this helps

The expression representing the given word sentence is 3n-8 = n+2

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a statement the difference of three times a number and eight is two more than the number.

We need to convert it into a mathematical expression,

Therefore,

First it is saying, the difference of three times a number n, and 8

= 3n-8

Then, it says 2 more than the number so put the n + 2

Therefore,

3n-8 = n+2

Hence, the expression representing the given word sentence is 3n-8 = n+2

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Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

60in²

Explanation:

12 × 4 = 48

48in² for the rectangle

6 × 4 = 24

24/2 = 12

12in² for the triangle

12in² + 48in² = 60in² total

Answer:

B = 25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(9y - 5) = 10(3y + 17) - 40

Step 2: Solve for y

\(\huge\textsf{Hey there!}\)

\(\large\textsf{4(9y - 5) = 10(3y + 17) - 40}\\\\\large\textsf{4(9y) + 4(-5) = 10(3y) + 10(17) - 10(40)}\\\\\large\textsf{36y - 20 = 30y + 170 - 40}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{36y - 20 = (30 y)+ (170 - 40)}\\\\\large\textsf{36y - 20 = 30y + 130}\\\\\large\textsf{SUBTRACT 30y to BOTH SIDES}\\\\\large\textsf{36y - 20 - 30y = 30y + 130 - 30}}\\\\\large\textsf{Cancel out: 30y - 30y because that gives you 0}\\\\\large\textsf{Keep: 20 - 30y because helps solve for the y-value}\)

\(\large\textsf{NEW EQUATION: 6y - 20 = 130}\\\\\large\textsf{ADD 20 to BOTH SIDES}\\\\\large\textsf{6y - 20 + 20 = 130 + 20}\\\\\large\textsf{Cancel out: -20 + 20 because that gives you 0}\\\\\large\textsf{Keep: 130 + 20 because that helps solve for the y-value}\\\\\large\textsf{130 + 20 = \bf 150}\\\\\large\textsf{NEW EQUATION: 6y = 150}\\\\\large\textsf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\dfrac{6y}{6}= \dfrac{150}{6}}\\\\\large\textsf{Cancel: }\mathsf{\dfrac{6}{6}\large\textsf{ because that gives you 1}}\)

\(\large\textsf{Keep: }\mathsf{\dfrac{150}{6}}\large\textsf{ because it helps solve for the y-value}\\\\\large\textsf{\bf y = }\mathsf{\dfrac{150}{6}}\\\\\large\textsf{OR }\\\\\mathsf{\dfrac{150}{6} }\large\textsf{ = \bf y}\\\\\\\large\textsf{SIMPLIFY ABOVE AND TOU YOU HAVE YOUR Y-VALUE}\uparrow\\\\\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf y = 25} (Option B.)}}}\huge\checkmark\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}\)

The five theorems of congruent triangles are SSS, SAS, AAS, RHS, and ASA.

Triangle congruence means :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

" ≅ " is the congruence symbol.

For triangles, there are five primary congruency rules:

By these we can proof two triangles are congruent or not

The question is incomplete so I've answered in general

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Answer:

The scatterplot that shows the strongest negative linear association would have the points on the plot in a downward slope from left to right. The closer the points are to forming a straight line going from the upper left to the lower right, the stronger the negative linear association is. The points on the scatterplot with the strongest negative linear association will be closely clustered along a line, indicating a clear and strong relationship between the two variables being plotted.

Answer:

18.09

Step-by-step explanation:2.4x2.4, then x3.14  

Answer:

answers below

Step-by-step explanation:

If you are trying to find the area the answers are:

Earth= 289.52918

Saturn=6,532.5021

The formula for area for a sphere is:

4 x pie x r2

If you are trying to find the volume the answers are:

Earth=57.90584

Saturn=46,647.01596

The formula for volume for a sphere is:

4/3 x pie x r3

Also the radius (r) is half of the diameter, so you divide the diameter by 2.

Answer:

B

Step-by-step explanation:

Answer: -68

Expression :4(-45) +112

Step-by-step explanation:

-180+112= -68

Answer:

Twelve and one fourth feet

Step-by-step explanation:

9 and 3/4 feet =9.75

2 and 2/4 feet =2.50

9.75 + 2.50

= 12.25/12 and 1/4 feet

In the question, it's σ = 10 and not μ = 10.

Answer:

A) σ_x = 1.4142

B) σ_x = 1.4135

C) σ_x = 1.4073

D) σ_x = 1.343

Step-by-step explanation:

We are given;

n = 50

σ = 10

A) Formula for standard error of the mean for infinite size is;

σ_x = σ/√n

Thus;

σ_x = 10/√50

σ_x = 1.4142

B) When population is finite, we use correction factor and thus, we have;

σ_x = [√((N - n)/(N - 1)] × σ/√n

N = 50,000

Thus;

σ_x = [√((50000 - 50)/(50000 - 1)] × 10/√50

σ_x = 1.4135

C) N = 5000

Thus;

σ_x = [√((5000 - 50)/(5000 - 1)] × 10/√50

σ_x = 1.4073

D) N = 500

Thus;

σ_x = [√((500 - 50)/(500 - 1)] × 10/√50

σ_x = 1.343