solve the simultaneous equations
2x + 5y = -4

The first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

To find the first four terms of a geometric sequence with a first term (a1) of 3 and a common ratio (r) of 2, we can use the formula for the nth term of a geometric sequence:

\(an = a1 * r^(n-1)\)

Substituting the given values, we have:

a1 = 3

r = 2

Let's calculate the first four terms (n = 1, 2, 3, 4) using the formula:

\(a1 = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3\\a2 = 3 * 2^(2-1) = 3 * 2^1 = 3 * 2 = 6\\a3 = 3 * 2^(3-1) = 3 * 2^2 = 3 * 4 = 12\\a4 = 3 * 2^(4-1) = 3 * 2^3 = 3 * 8 = 24\)

Therefore, the first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

In summary, the terms of the sequence are obtained by multiplying the first term (a1) by the common ratio (r) raised to the power of (n-1), where n represents the term number.

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Answer:

The equations are:

\(4H + 3P = 13.75\)

\(2H + 5P = 11.25\)

\(Hotdog = 2.50\)

\(Pretzel = 1.25\)

Step-by-step explanation:

Let:

\(H = hot\ dog\)

\(P =Pretzel\)

For Tina:

\(4H + 3P = 13.75\)

For Doug:

\(2H + 5P = 11.25\)

Solving for the price of both items:

We have:

\(4H + 3P = 13.75\) --- (1)

\(2H + 5P = 11.25\) --- (2)

Multiply (2) by 2

2 * (\(2H + 5P = 11.25\))

-------------------

\(4H + 10P = 22.50\) --- (3)

Subtract (3) from (1)

\(4H + 3P = 13.75\)

\(4H + 10P = 22.50\)

----------------------

\(4H - 4H + 3P - 10P = 13.75 - 22.50\)

\(3P - 10P = 13.75 - 22.50\)

\(-7P = -8.75\)

Solve for P

\(P = \frac{-8.75}{-7}\)

\(P = 1.25\)

Substitute 1.25 for P in (2)

\(2H + 5P = 11.25\)

\(2H + 5 * 1.25 = 11.25\)

\(2H + 6.25 = 11.25\)

Collect Like Terms

\(2H = 11.25-6.25\)

\(2H = 5\)

Solve for H

\(H = \frac{5}{2}\)

\(H = 2.50\)

Solution:

Given the figure;

The reflection rule across the x-axis is;

Thus, the point A(3,1) after reflection is;

Then, dilated by a factor of 2 using the point (-2,1) as the center of dilation.

Thus;

CORRECT OPTION: (B) A"(8,-3)

solution

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The answer to your question is 2

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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Answer:

So if you have an angle that is 20 degrees, then the complement angle measures 70 degrees.

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer:

43.6 has 3 significant figures.

Given:

\(\sqrt{z+5}+4\leq 13\)

Move 4 to the right side:

\(\sqrt{z+5}\leq 9\)

Simplify

\(z+5 \leq 81\)

Move 5 to the right side:

\(z\leq 76\)

Find singularity points

Find non-negative values for radicals:  \(z\geq -5\)

Combine the intervals

\(z\leq 76 \ \text{and} \ z\geq -5\)

Merge overlapping intervals

\(-5\leq z\leq 76\)

Answer:

Answer:

You need to cook 14 entrees.

Step-by-step explanation:

In the given problem, Dave has been asked to cook 14 of the 28 entrees that the kitchen has received an order for. Therefore, he needs to cook 14 entrees.

The total number of different signals consisting of flags is 216

Given data ,

The number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags can be calculated using combinatorial principles.

There are 3 choices for the top flag (white, red, or blue), 2 choices for the second flag (since we've already used one color for the top flag), and 1 choice for the third flag.

Similarly, there are 3 choices for the fourth flag, 2 choices for the fifth flag, and 1 choice for the sixth flag. Finally, there are 3 choices for the seventh flag, 2 choices for the eighth flag, and 1 choice for the ninth flag.

Using the multiplication principle, we can multiply the number of choices at each step to get the total number of different signals:

3 × 2 × 1 × 3 × 2 × 1 × 3 × 2 × 1 = 3! × 3! × 3!

where "!" represents the factorial operation, which is the product of all positive integers up to a given number.

So, the total number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags is:

3! × 3! × 3! = 6 × 6 × 6 = 216

Hence , the number of signals is 216

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Answer:

34,500

Step-by-step explanation:

34,528 rounds down rather than up because 528 is closer to 500 than 600 so it will round down to 34,500

Answer:

34,500

Step-by-step explanation:

34,528 = 34,500 because when you round the 5 in the hundred place the 2 isn't high enough to make the 5 round up so its 34,500.

5-10 round up 1-4 round down.

Step-by-step explanation:

it means reaching your saving goal + 35% of it

lets assume your saving goal is 100 $

so reaching 135% of your saving goal means that you have saved 135 $

100 × 135% = 135

Answer:

pluto

Step-by-step explanation:

In order to prove that the triangles are congruent by SAS, we need two congruent pairs of sides and the angles between these sides also congruent.

Let's analyze each sentence:

A.

We need one pair of congruent angles, with this proff we would have the angle needed, but the question didn't say the triangle is isosceles. This theorem states that the opposite angles to the congruent sides in a isosceles triangle are congruent.

B.

We still don't know that the triangles are congruent, so we can't use the reason CPCTC.

C.

These angles are not vertical angles.

D.

With this statement we have one of the required pair of congruent sides to prove the triangles congruent.

Therefore the correct option is D.

Answer:

4 hours and 20 minutes!

Answer:

Step-by-step explanation:

PM or AM?

If it is 9:30 AM to 1:50 PM, it is 4 hours and 20 minutes.

if it is 9:30 PM to 1:50 AM, it is also 4 hours and 20 minutes.

If it is 9:30am to 1:50 AM, it is 16 hours and 20 minutes.

We know a line intercepts the x-axis of a graph whenever y = 0

Therefore to determine the x intercept of the graph of the equation

y = 0.5x+ 5

we set y = 0, then

0 = 0.5x + 5

Solving the equation...

-5 = 0.5x

-5/0.5 = -10 = x

Answer:

A Margin of​ error : Generally margin can be defined as a statistical concept that informs the researcher or any person carrying statistical active the percentage by which his /her result will differ from the  real population value.

B Margin of error is used to establish a confidence​ interval by adding and  subtracting the statistical value (i.e  sample proportion or sample mean ) from the margin of error

C Generally the confidence interval tell the researcher the probability by which  a population parameter(sample proportion or sample mean) will fall between two set of values(Upper limit and  the lower limit )

Step-by-step explanation:

Answer:

Rigid motion.

Step-by-step explanation:

please this was my opinion

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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The Event of choosing a letter from F to D is

n(A) = 4

A series of possible results from an experiment that have been given a probability is called an event. Separate events in an experiment may not be equally probable, since they may involve vastly dissimilar sets of outcomes, and a single result may be a component of many different events.

Given that a bag contains eight different balls, each of which is labeled from A to H. Given that a ball is selected at random, and the letter it lands on is written down as the result. Given that there is an equal chance of drawing any one of the balls, the sample space for drawing one ball is

Generally, the equation for S is  mathematically given as

S = {A,B,C,D,E,F,G,H} and n(S) = 8

Therefore

G = The event of choosing a label from D to F

Where

F= {A,B,C,D}  

Sample size

n(A) = 4

In conclusion,

n(A) = 4

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Answer:

x = 72

Step-by-step explanation:

A circle is 360 degrees

2x-61+ x-11 + 3x = 360

Combine like terms

6x-72=360

Add 72 to each side

6x-72+72 = 360+72

6x =432

Divide each side by 6

6x/6 = 432/6

x =72

part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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The size of angle DAB in the quadrilateral is 48°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

\(\angle \text{A} +\angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ\)

\(\angle \text{A} +38^\circ + \angle\text{C} + 226^\circ = 360^\circ\)

\(\angle \text{A} + \angle\text{C} + 264^\circ = 360^\circ\)

\(\angle \text{A} + \angle\text{C} = 360^\circ- 264^\circ\)

\(\angle \text{A} + \angle\text{C} = 96\)

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

\(\angle\text{A} + \angle\text{A} = 96\)

\(2\angle\text{A} = 96\)

\(\angle\text{A} = \dfrac{96}{2}\)

\(\angle\text{A} = 48^\circ\)

Therefore, the size of angle DAB is 48°.

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