Solve the system using elimination.
2x+8y = 6
3x -8y = 9

Step-by-step explanation:

The given geometric sequence:

- 8, - 40, - 200, - 1000

Here, first term(a) = - 8, common ration(r) = [tex]\dfrac{-40}{-8}[/tex] = 5

To find, an explicit formula for the given geometric sequence = ?

We know that,

The explicit formula for the geometric sequence

[tex]a_{n} =ar^{n-1}[/tex]

∴ An explicit formula for the given geometric sequence

[tex]a_{n} =(-8)(5)^{n-1}[/tex]

[tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]

∴ An explicit formula for the given geometric sequence, [tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]

Answer:

what the guy above me said

Step-by-step explanation:

The inequality representing Marisa's goal to buy a phone costing at least $200, with $125 already saved and a plan to save $10 each week, is 125 + 10w \\geq 200, where w is the number of weeks of additional savings.

To write an inequality that represents Marisa's situation, we need to consider the amount she has already saved, the additional amount she plans to save weekly, and the minimum amount she needs for the phone. Marisa wants a phone that costs at least $200 and has saved $125. She plans to save $10 each week. We can use the variable w to represent the number of weeks she will save additional money.

Marisa's current savings plus the additional amount she plans to save for w weeks needs to be at least $200. This situation can be represented by the following inequality:

125 + 10w \\geq 200

Here, 125 represents the amount already saved, 10w represents the additional amount saved after w weeks, and the inequality symbol \\geq (greater than or equal to) establishes that Marisa's total savings must be at least $200.

Step-by-step explanation:

By Wien’s Law we have

              [tex]\lambda =\frac{2898}{T}[/tex]

          where λ is in μm and T is in K

Given that

             T = 6000 K

Substituting

              [tex]\lambda =\frac{2898}{6000}=0.483\mu m[/tex]

Option C is the correct answer.

Final answer:

By using Wien's Law with the given temperature of the Sun (6000K), we calculate the peak emission wavelength as 0.483 micrometers, which corresponds to option c. 0.48 µm.

Explanation:

The student asked about the wavelength most emitted by the Sun as predicted by Wien's Law, given the temperature of 6000K using the equation λ = 2898/T, where λ is the wavelength in micrometers and T is the temperature in Kelvin. According to Wien's displacement law, the temperature and peak wavelength of emission of an object are inversely proportional.

Plugging in the given temperature (T = 6000K) into the equation λ = 2898/T, we calculate the peak emission wavelength to be 2898/6000 = 0.483 µm.

So, the correct answer is c. 0.48 µm.

Answer: D

Step-by-step explanation:

it makes the most sense ( do ont know how to explain but I do know it is right. )

Answer:

D.) No, product means multiplication, and the student wrote a division expression.

Step-by-step explanation:

did the assignment. good luck! <3

Answer: $4,884.75

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount deposited.

P represents the principal or amount deposited.

R represents interest rate

T represents the duration of the savings in years.

From the given information,

P = 4500

R = 2.85

T = 3 years

I = (4500 × 2.85 × 3)/100 = $384.75

The total amount that they will have in savings after 3 years is

4500 + 384.75 = $4884.75

Answer: the shortest side is 10 centimeters.

The length of each of the other sides is 10 centimeters each.

Step-by-step explanation:

Let x represent the length of the shortest side of the triangle.

Two sides of the triangle are each twice as long as the shortest side. This means that the length of the two sides would be 2x.

The perimeter of a triangle is the sum of each side of the triangle.

The puzzle piece in the shape of a triangle has perimeter 25 centimeters. This means that

x + 2x + 2x = 25

5x = 25

x = 25/5

x = 5

The length of each of the two sides is

2x = 2 × 5 = 10

The length of the shortest side of the triangle is 5 centimeters.

Let's denote the length of the shortest side of the triangle as "x" centimeters. According to the problem, the other two sides are each twice as long as the shortest side. Therefore, the lengths of the other two sides are "2x" centimeters each.

Now, we can use the information given about the perimeter to set up an equation:

Perimeter = Sum of all sides

Given that the perimeter is 25 centimeters:

25 = x + 2x + 2x

Now, combine like terms on the right side:

25 = 5x

To solve for x, divide both sides by 5:

x = 25 / 5

x = 5

So, the length of the shortest side of the triangle is 5 centimeters.

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Answer:

Step-by-step explanation:

Answer:

A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.

Step-by-step explanation:

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)

A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.

B) We are interpolating. There are no concerns about interpolation.

C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.

D) We are extrapolating. There are no concerns about extrapolation.

The answer is A

assuming we are looking for the value of y within the range of x, we are interpolating. Take for instance, the range of  xi between 60 and 65, what is the value of y at point 62.5. This is interpolation.

But then we have the data sets of temperature of a particular place within 1 to 15 days in a month. if we are asked to look for its temperature on the 31st of that particular month, we are extrapolating, which might take a different pattern from the line of best bit

Using a least-squares line to predict y values for x values beyond the range of the data is called extrapolation. This process is risky because the pattern of data may change outside of the existing range, leading to inaccurate predictions.

When using a least-squares line to predict y values for x values beyond the range of x values found in the data, we are extrapolating. This is because we are making predictions outside of the range of the existing data set. However, extrapolation comes with certain risks. The pattern of the data may not remain constant beyond the data we have, leading to inaccurate predictions.

Therefore, answer A is the most accurate: 'We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.'

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(1) Vertical asymptote: [tex]x=-4[/tex]

(2) Domain: [tex]x>-4[/tex]

(3) X intercept: [tex](-2,0)[/tex] and Y intercept : [tex](0,1)[/tex]

(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.

Explanation:

The parent function is [tex]f(x)=\log _{2} x[/tex]

The transformed function is [tex]g(x)=\log _{2}(x+4)-1[/tex]

(1) Vertical asymptote:

The vertical asymptote of a function can be determined by equating

[tex]x+4=0[/tex]

Thus, [tex]x=-4[/tex]

The vertical asymptote is [tex]x=-4[/tex]

(2) Domain:

The domain of a function is the set of all independent x-values.

[tex]x+4>0[/tex]

Thus, [tex]x>-4[/tex]

The domain of a function is [tex]x>-4[/tex]

(3) X and Y intercepts:

To determine the x intercept, let us substitute y=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]

[tex]\begin{equation}\begin{aligned}\log _{2}(x+4)-1 &=0 \\\log _{2}(x+4) &=1 \\x+4 &=2^{1} \\x &=-2\end{aligned}[/tex]

Thus, the x intercept is [tex](-2,0)[/tex]

To determine the y intercept, let us substitute x=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]

[tex]\begin{equation}\begin{aligned}y &=\log _{2}(0+4)-1 \\&=\log _{2} 4-1 \\&=2-1 \\&=1\end{aligned}[/tex]

Thus, the y intercept is [tex](0,1)[/tex]

(4) To determine the transformation:

The transformed function [tex]g(x)=\log _{2}(x+4)-1[/tex] is shifted 4 units to the left and shifted 1 unit downwards.

Multiply the price of popcorn by the number of bags so 6b.

Multiply the price of candy by the number bought, so 3.25c

Add those together to get total :

6b + 3.25c

Now the most she can spend is 50 so set the equation to less than it equal to what she can spend:

6b + 3.25c <= 50

Final answer:

The inequality representing Samantha's budget for purchasing popcorn and candies is 6b + 3.25c ≤ 50.

Explanation:

To formulate the inequality representing the possible values for the number of bags of popcorn (b) and the number of candies (c) Samantha can purchase without exceeding her $50 budget, we can set up an expression based on the given prices for each item.

The cost of the popcorn bags is $6, and the cost of each candy is $3.25.

The inequality that represents this scenario would be:

6b + 3.25c ≤ 50

This inequality denotes that the total cost of b popcorn bags and c candies, which is the sum of $6 times the number of popcorn bags plus $3.25 times the number of candies, should be less than or equal to $50.

Samantha must choose combinations of b and c that satisfy this inequality to stay within her budget.

Answer:

39 °F

Step-by-step explanation:

There's 4 hours difference between given times so the change in the temperature would be 4 × 8 = 32° F if the temperature drops 8 °F every hour therefore the temperature would be 71 - 32 = 39 °F

Answer:

Option A:        [tex]$ \sum_{n = 1}^{15} {\textbf{- 9 + 6 n}} $[/tex]

Step-by-step explanation:

We are given with the series - 9  - 3  + 3   +  9 +  . . . .  +  81.

Note that the second term is obtained by adding 6 to the first term.

Each consecutive term is obtained by adding 6 to its previous term.

Therefore, we should be adding six two times to get the third term from the first term.

Putting it Mathematically, we get: - 9 + 6n

This gives all the terms of the sequence. Since, we have to add all the terms we take the summation.

Also, note that 81 is the 15 th term.

Therefore, - 9  - 3  + 3   +  9 +  . . . .  +  81 =    [tex]$ \sum_{n = 1}^{15} {- 9 + 6 n} $[/tex]

Hence, the answer.

Final answer:

The sequence -9, -3, 3, 9, ..., 81 increases by 6 each time and follows the arithmetic sequence formula -9 + 6(n-1), which simplifies to -15 + 6n. The summation notation that represents this sequence is the sum of -15 + 6n from n = 0 to 15.

Explanation:

The given sequence is -9, -3, 3, 9, ..., 81, and we can see that it is increasing by 6 each time (an arithmetic sequence). The nth term of an arithmetic sequence can be written as a + (n-1)d, where a is the first term and d is the common difference. Here, the first term a is -9 and the common difference d is 6. Plugging these values into the formula gives us the nth term as -9 + 6(n-1). We can simplify this to -9 + 6n - 6, which further simplifies to -15 + 6n.

To find the last term which is 81, we can set the nth term equal to 81: -15 + 6n = 81. Solving for n gives us n = 16, meaning there are 15 terms before it (since we start counting from n = 0).

The summation notation for the given sequence is then the sum of the terms from n = 0 to n = 15 of the general term -15 + 6n.

Answer: there are 25 red flowers in Sakura's garden.

Step-by-step explanation:

In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. This means that if there are 10 red flowers, there would be 20 yellow flowers. if there are 20 red flowers, there would be 40 yellow flowers. Therefore, the ratio of red flowers to yellow flowers in the garden is

5/10 = 10/20 £= 20/40 = 1/2 = 1:2

Total ratio = 2 + 1 = 3

If there are 75 total red and yellow flowers, then the total number of red flowers are in Sakura's garden would be

1/3 × 75 = 25

Answer:

25

Step-by-step explanation:

Step-by-step explanation: Understand it as a ratio. 5:10. Add both ratios together, 15. Make an expression, 15x=75. x=5, Then multiply 10 and 5 by 5 and that will give you the ratio of 25:50 red to yellow flowers.

The required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]

The standard exponential function is expressed as:

[tex]y=ab^x[/tex] where:

Given the following parameters:

a = 800

b = 1/4

Substitute into the formula to have;

[tex]y=800(\frac{1}{4} )^t[/tex]

Hence the required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]

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Answer:

It's 800(3/4)^t

Step-by-step explanation:

Answer:

Step-by-step explanation:

Triangle VWX is a right angle triangle.

From the given right angle triangle,

VX represents the hypotenuse of the right angle triangle.

With m∠X as the reference angle,

WX represents the adjacent side of the right angle triangle.

VW represents the opposite side of the right angle triangle.

To determine m∠X, we would apply

the tangent trigonometric ratio. It is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan X = 2/1 = 1

m∠X = Tan^-1(1)

m∠X = 45°

Answer:

[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]

Step-by-step explanation:

The polynomial function has zeros

x=1, x=2,x=-3,x=-1

This means the factored form of the polynomial is

[tex]p(x) = (x - 1)(x + 1)(x + 3)(x - 2)[/tex]

We expand to get:

[tex]p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)[/tex]

We expand further to get:

[tex]p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)[/tex]

[tex]p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6[/tex]

This simplifies to:

[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]

This is the standard form of the polynomial since it is written in descending powers of x.

Answer:

55.96 miles

Step-by-step explanation:

Distance = Speed X time

Car first moved east for 1 hr , distance = 40 x 1 = 40 miles

Car then moved north-east for 30 min, distance = 40 x 0.5 = 20 miles

From trigonometry,

sin 45 = [tex]\frac{y}{20}[/tex] ; y = 20 sin 45 ; y= 14.14 miles

cos 45 = [tex]\frac{x}{20}[/tex] ; x = 20 cos 45 ; x = 14.14 miles

using Pythagoras theorem;

[tex]z^{2}[/tex] = [tex]y^{2}[/tex] + [tex](40+x)^{2}[/tex]

    = [tex]14.14^{2}[/tex] + [tex](40+14.14)^{2}[/tex]

     = 3131.08

[tex]z^{2}[/tex] = [tex]\sqrt{3131.08}[/tex]

z = 55.96 miles

Answer:

Ethan can type 12 pages before the meeting starts.

Step-by-step explanation:

Given:

Number of pages he can type =2

Number of hours he can type 2 pages = [tex]\frac{1}8\ hrs[/tex]

We need to find number of pages he can type in [tex]\frac34\ hrs[/tex]

Solution:

Now first we will  find number of pages in 1 hour

So we can say;

In [tex]\frac{1}8\ hrs[/tex]  = 2 pages

In 1 hour = number of pages he can type in 1 hour

By Using Unitary method we get;

number of pages he can type in 1 hour = [tex]\frac{2}{\frac18} =\frac{2\times8}{1}=16\ pages[/tex]

Now we can say that;

In 1 hour = 16 pages

So [tex]\frac34\ hrs[/tex] = number of pages he can type in [tex]\frac34\ hrs[/tex]

Again By using Unitary method we get;

number of pages he can type in [tex]\frac34\ hrs[/tex] = [tex]16\times \frac34 = 12\ pages[/tex]

Hence Ethan can type 12 pages before the meeting starts.

Final answer:

Ethan has 3/4 hours to type and can complete two pages every 1/8 hour, resulting in a total of 12 pages typed before the meeting starts.

Explanation:

Ethan can type two pages every 1/8 hour. To find out how many pages he can type before the start of the meeting, we need to calculate the total pages he can type in the waiting time of 3/4 hours. Here's the step-by-step calculation:

Calculate the number of 1/8 hour intervals in 3/4 hours by dividing: (3/4) ÷ (1/8) = (3/4) × (8/1) = 6.

Since he types two pages every 1/8 hour, we find the total number of pages by multiplying the number of intervals by 2: 6 × 2 = 12 pages.

Therefore, Ethan can type a total of 12 pages before the meeting starts.

Answer:

47 ducks and 7 cows

Step-by-step explanation:

Ducks have 2 legs and cows have 4 legs.

If all the animals are ducks,

number of legs= 54(2)= 108

Difference in number of legs= 122 -108= 14

Difference in no. of legs per animal= 4 -2 = 2

Number of cows=14 ÷2 = 7

Number of ducks= 54-7= 47

Thus, he have 47 ducks and 7 cows.

Let's check:

Total number of feet= 7(4)+ 47(2) = 122 ✓

You could also first assume that all the animals are cows. The answer would be the same.

Answer:

100

Step-by-step explanation:

Answer:

25,000

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

should be the 3rd choice

Step-by-step explanation:

even though the 2nd choice is technically correct for a rhombus, but this property does not explain the first part of this 2 part question.

We are looking for an answer that supports pert 1 of the question.

by definition, a rhombus is a parallelogram with 4 sides of equal length, which means 2 adjacent sides will have the same length, which explains the answer in the first part because JK and KL are adjacent sides

Answer: the number of adult and student tickets sold are (45, 29)

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of student tickets that were sold.

On Wednesday, a total of 74 tickets were sold. This means that

x + y = 74

x = 74 - y- - - - - - - - - - - - - - 1

If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that

15x + 11y = 994- - - - - - - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

15(74 - y) + 11y = 994

1110 - 15y + 11y = 994

- 15y + 11y = 994 - 1110

- 4y = - 116

y = - 116/ - 4

y = 29

Substituting y = 29 into equation 1, it becomes

x = 74 - 29 = 45

The number of adult tickets and student tickets sold is (x, y) = (45, 29)

To determine the number of adult tickets x and student tickets y sold, we need to solve the system of equations given by the following conditions:

1. The total number of tickets sold is 74:

x + y = 74

2. The total revenue from the tickets is $994, with adult tickets sold for $15 each and student tickets sold for $11 each:

15x + 11y = 994

We can solve this system of equations using the substitution or elimination method. Here, we will use the elimination method.

First, let's write the two equations clearly:

x + y = 74

15x + 11y = 994

To eliminate one of the variables, we can multiply the first equation by 11, so the coefficients of  y in both equations will be the same:

[tex]\[ 11(x + y) = 11 \cdot 74 \][/tex]

11x + 11y = 814

Now we have:

11x + 11y = 814

15x + 11y = 994

Next, we subtract the first modified equation from the second equation to eliminate y

(15x + 11y) - (11x + 11y) = 994 - 814

15x + 11y - 11x - 11y = 180

4x = 180

x = 45

Now, substitute x = 45 back into the first original equation to find y

x + y = 74

45 + y = 74

y = 29

Therefore, the number of adult tickets and student tickets sold is:

(x, y) = (45, 29)

Answer:

0.40

Step-by-step explanation:

to find out the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8

Let A = sum of dice is 8

B = one lands in 5

P(B/A) = P(AB)/P(A) by conditional probability

P(AB) = sum is 8 and one is 5

So (5,3) or (3,5)

P(A) = sum  is 8.

i.e. (2,6) (2,6) (3,5) (5,3) (4,4)

Required probability

= n(AB)/n(A)

=[tex]\frac{2}{5} =0.40[/tex]

Answer:

The answer is:

22 tacos per tray

Step-by-step explanation:

Number of trays:

Number of Tacos is 88:

Put 22 Taco's in each tray:

Tray 1.  22 Tacos

Tray 2. 22 Tacos

Tray 3. 22 Tacos

Tray 4. 22 Tacos

Example of dividing:

All 4 trays Add up to 88 tacos total

I hope this helped! <3

Answer:

Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.

Step-by-step explanation:

Given system of equation are

7x+9y=-4..............(1)

5x-2y=6...............(2)

Equation (1)×5 - equation (2)×7

35x +45y-(35x-14y)= -20-42

⇔ 35x+45y-35x+14y = -62

⇔59 y = -62

[tex]\Leftrightarrow y =-\frac{62}{59}[/tex]

Putting the value of y in equation (1)

[tex]7x +9.(-\frac{62}{59} )= -4[/tex]

[tex]\Leftrightarrow 7x += -4+\frac{558}{59}[/tex]

[tex]\Leftrightarrow 7x = \frac{322}{59}[/tex]

[tex]\Leftrightarrow x =\frac{322}{59\times 7}[/tex]

[tex]\Leftrightarrow x =\frac{46}{59}[/tex]

Therefore  [tex]x =\frac{46}{59}[/tex] and  [tex]y =-\frac{62}{59}[/tex]

Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.

Answer:

D.)He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

Step-by-step explanation:

I just got this right for the exam review on edge

Answer:

a negative correlation between the temperature and the amount of snow still on the ground

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

Explanation:

When it comes to "correlations," a negative one refers to an "inverse" relationship between two variables. So, this means that as one variable increases, the other decreases and vice-versa.

The question is asking for two options that are "casual" (common) when it comes to "negative correlation." So, the answers are:

a negative correlation between the temperature and the amount of snow still on the ground

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

Answer:

Step-by-step explanation:

These are the two relationships that are most likely to be causal. Causal relationships are those in which one aspect is the cause of the second one being described. Moreover, a negative correlation is one in which one aspect of the relationship increases while the other one decreases. In the first example, as the temperature goes up, this causes the amount of snow on the ground to go down. In the second example, as you upload more pictures to a website, there is less storage space.

Answer:

seven eights mean; 8888888

they can repave one fifty six mile per hour; 156/hour

Step-by-step explanation:

To calculate total time to repave

8888888/156 = 56980.02 hours require

Answer:

576 cm²

Step-by-step explanation:

Given:

Number of sections in a suncatcher (n) = 6

Each section is in the shape of a parallelogram.

Base of parallelogram = 12 cm

Height of parallelogram = 8 cm

Now, area of a parallelogram is given as:

Area of parallelogram = Base × Height

Area of 1 parallelogram = 12 cm × 8 cm = 96 cm²

Now, there are 6 parallelogram shaped sections.

So, area of the sections = area of 1 section × total number of sections

∴ Area of 6 sections = 96 cm² × 6 = 576 cm²

Therefore, the total area of the sections of a suncatcher is 576 cm².

Answer:

the order is Helen Olivia Francessca

Step-by-step explanation:

ik im late but i hop this helps C:

The order of percentage of correct questions from least to greatest.

80% < 84% < 88%

Helen < Olivia < Francesca.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of questions in the test = 25.

Helen:

Percentage of the number of questions correct.

= 20/25 x 100

= 80%

Francesca:

Percentage of the number of questions correct.

= 22/25 x 100

= 88%

Olivia:

Percentage of the number of questions correct.

= 84%

Thus,

Arranging the percentage in increasing order.

80% < 84% < 88%

Helen < Olivia < Francesca.

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