Solve the system of equations.
−
2
�
+
9
�
=
11
−
5
�
+
2
�
=
−
34
​

−2x+9y=11
−5x+2y=−34
​

The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

What is the slope?

The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):

m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333

Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:

b = y₁ - m * x₁

b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666

Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:

y = mx + b

y = 5.3333x + 9.6666

Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

To learn more about slope, Visit

https://brainly.com/question/16949303

#SPJ1

Answer:

[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

The first and last data points of the given table are:

Substitute the data points into the slope formula to find the slope of the trend line:

[tex]\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Substitute the found slope and the first data point into the slope-intercept formula and solve for b:

[tex]\implies 15=\dfrac{16}{3}(1)+b[/tex]

[tex]\implies 15=\dfrac{16}{3}+b[/tex]

[tex]\implies b=15-\dfrac{16}{3}[/tex]

[tex]\implies b=\dfrac{45}{3}-\dfrac{16}{3}[/tex]

[tex]\implies b=\dfrac{45-16}{3}[/tex]

[tex]\implies b=\dfrac{29}{3}[/tex]

Therefore, the equation of the trend line in slope-intercept form is:

[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]

a) Dilation 1 has a scale factor of 3 units.

b) Dilation 2 has a scale factor of 4 units.

c) Dilation 3 has a scale factor of 0 units.

What is a scale factor?

A scale factor is a number used to multiply the dimensions of a shape to enlarge or reduce its size. In geometry, the scale factor is used to create similar figures by preserving their shape while changing their size. If a figure is scaled up by a scale factor of 'k', its dimensions are increased by a factor of 'k'. If a figure is scaled down, its dimensions are reduced by a factor of 'k'.

For the triangle, the scale factor would be 3 units.

For the square, the scale factor would be 4 units.

For the line, the scale factor would be 0 units.

Hence,

a) Dilation 1 has a scale factor of 3 units.

b) Dilation 2 has a scale factor of 4 units.

c) Dilation 3 has a scale factor of 0 units.

To learn more about the scale factor, visit:

https://brainly.com/question/25722260

#SPJ1

You and your friend are approximately 181.23 meters apart at that point in time.

To find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".

d² = 250² + 195² - 2 X 250 X 195 X cos(18)

d = √(250² + 195² - 2 X 250 × 195 X cos(18))

d ≈ 181.23 m

So you and your friend are approximately 181.23 meters apart.

The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).

In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.

We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).

We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".

Learn more about Distance Between Friends On Mountain here:

https://brainly.com/question/9794375

#SPJ4

Answer:

Below

Step-by-step explanation:

Interest for a WHOLE 12 months would be   14 000 * .025 = 350

but Jane had the account for   9 out of 12 months

9/12  * 350 = 262.50 dollars

Answer:

1. x = 20

2. m<ABK = 137

Step-by-step explanation:

1.

(3x - 5) + (4x + 2) + (2x + 3) = 180

9x  = 180

x = 20

2.

3x - 5 + 4x + 2

7x - 3

7(20) - 3

140 - 3

m<ABK = 137

James and Sandra drank the most soda from their cup.

The information that was given gave specific amount that each person drank from their soda, but James and Sandra were not given a specific amount, so one can only assume they drank the most since their own percentage of drink is not disclose.

Percentage is a way to express a number as a fraction of 100. It's often denoted using the symbol "%". For example, 50% means 50 per 100, or one half

learn more about percentage: https://brainly.com/question/24877689

#SPJ1

Using the cosine ratio, the measure of angle A, to the nearest hundredth is: 75.52°.

The cosine ratio, also known simply as the cosine, is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.

It is defined as cos(θ) = adjacent side/hypotenuse, where θ is the angle between the adjacent side and the hypotenuse.

Reference angle (∅) = A

Length of adjacent side = 2

Length of hypotenuse = 8

Therefore:

cos A = adj./hyp. = 2/8

cos A = 1/4

A = cos^(-1)(1/4)

A = 75.52°

Learn more about the cosine ratio on:

https://brainly.com/question/15793827

#SPJ1

The peak to peak value of a sine wave is twice the peak value. Therefore, total number of the peak to peak value of this waveform is 2 x 80 VAC = 160 VAC.

The peak to peak value of a sine wave is an important measure of the waveform's amplitude. It is calculated by multiplying the peak value of the waveform by two. The peak value of this particular waveform is 80 VAC, so the peak to peak value of the waveform is 2 x 80 VAC = 160 VAC. This peak to peak value is a measure of the total number voltage swing of the waveform, from its lowest point to its highest point. The peak to peak value of this waveform is a useful parameter for understanding the waveform's strength and potential for causing electrical damage. As such, it is important to measure and understand the peak to peak value of any sine wave in order to successfully manage its power and potential for causing harm.

learn more about number here

https://brainly.com/question/10547079

#SPJ4

Answer:

Step-by-step explanation:

Part A:

To find the value of the remaining angles, we can use the fact that the sum of the angles in a triangle is 180°.

First, let's find the value of <1. We have:

<4 + <1 + <2 = 180°

4 + <1 + (180° - 5 - 4) = 180°

4 + <1 + 171° = 180°

<1 = 5°

Next, let's find the value of <7. We have:

<7 + <5 + <6 = 180°

<7 + 135° + (180° - 10 - 5) = 180°

<7 + 135° + 165° = 180°

<7 = 0°

Finally, let's find the value of <9. We have:

<9 + <10 + <11 = 180°

<9 + 11° + (180° - 10 - 11) = 180°

<9 + 11° + 159° = 180°

<9 = 0°

Part B:

The angle <4 is supplementary to angle <1, meaning they add up to 180°.

The angle <7 is congruent to angle <5, meaning they have the same measure.

The angle <9 is congruent to angle <10, meaning they have the same measure.

Answer:

1:3:5

Step-by-step explanation:

[tex]\frac{7}{7}=1\\\\\frac{21}{7}=3\\ \\\frac{35}{7}=5[/tex]

1:3:5

the probability of rolling an odd number or rolling a 2 is 2/3

The probability of rolling an even number or a 4 is 2/3

Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur. The probability of an event can also be expressed as a percentage or as a fraction.

If you roll a six-sided die. The probability of rolling 1, 2, 3, 4, 5 and 6 are as follows:

P (1) = 1/6

P (2) = 1/6

P (3) = 1/6

P (4) = 1/6

P (5) = 1/6

P (6) = 1/6

a. Since there are three odd numbers, P(odd) = 3/6 = 1/2

Thus, the probability of rolling an odd number or rolling a 2 will be:

P(odd or 2) = P(odd) + P(2)

                  = 1/2 + 1/6 = 2/3

b. Since there are three even numbers, P(even) = 3/6 = 1/2

Thus, the probability of rolling an even number or a 4 will be:

P(even or 4) = P(even) + P(4)

                  = 1/2 + 1/6 = 2/3

Learn more about probability on:

brainly.com/question/251701

#SPJ1

The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Given that the cards are selected with replacement.

The probability of selecting a spade card is:

P(S) =13/52

Now, a heart card is selected.

Since, the previous card is replaced in the deck the total number of cards is 52.

The probability of selecting a heart card is:

P(H) = 13/ 52

The probability of selecting a spade and then selecting a heart is:

P = 13 / 52 × 13/52

P = 0.0625

Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

The relationship the ratios of sin x° and cos y° share is The ratios are both identical (five thirteenths and five thirteenths). Option B

Trigonometric Identities are defined as the qualities involving trigonometry functions and also holds true for all the values of the variables given in the equation.

The different types of trigonometric identities are given as;

From the information given, we have that

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

But;

Hypotenuse= 13

Opposite = 5

Adjacent = 12

Substitute the value

sin x = 5/13

cos y = 5/13

Hence, the values are identical

Learn about trigonometric identities on:

https://brainly.com/question/7331447

#SPJ1

Answer:

B!

Step-by-step explanation:

took the testt

54.10Answer:

Step-by-step explanation:

The size of the input is doubled, the time taken to execute the loop will also double.

The time complexity of this pseudocode is O(n). This can be determined by analyzing the number of times the loop is executed. The loop is entered once and is then executed n times, where n is the number of times the loop is executed. This can be expressed mathematically as T(n) = 1 + n. Since the loop is executed a constant number of times, regardless of the size of the input, the time complexity of the pseudocode is O(n). This means that the execution time of the loop grows linearly with the size of the input. Thus, if the size of the input is doubled, the time taken to execute the loop will also double.

Learn more about number of time here:

https://brainly.com/question/30061892

#SPJ4

The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.

First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850

Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850

Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33

You can learn more about calculating total cost at

https://brainly.com/question/9063096

#SPJ4

According to the concept of fraction the value of the quantity at any time t is -4.

A fraction is a mathematical representation of division of two numbers. In this case, we will be using fractions to solve an initial value problem.

The initial value problem is ′=−2,(0)=−4.

This means that the rate of change of the quantity is -2 and its starting value at time 0 is -4.

To solve this problem, we need to find the value of the quantity at some other time.

Here the first step is to find the general solution to the differential equation ′=−2.

This can be done by integrating both sides, which gives us

=> −2.

Integrating, we get

=> −2 + C, where C is an arbitrary constant.

Next, we use the initial value to find the value of C.

We know that when t=0, the value of the quantity is -4, so we can substitute these values into the general solution to get

=> -4 = -2 + C.

Solving for C, we get C = -2.

Finally, we substitute C into the general solution to get

=> -2 -2 = -4.

To know more about fraction here.

https://brainly.com/question/10354322

#SPJ4

The choice that  is equivalent to the product given is 2√10

What are surds ?

Surds in mathematics are the square root values that can't be further condensed into whole numbers or integers. Numbers with surds are illogical.

Surds are the square roots of numbers ( √) that are not able to be divided into whole or rational numbers. It cannot be precisely described by a fraction. A surd, then, is a root of a whole number with an irrational value.

√8 •√5

= √(8*5) = √40

= √(10*4)

= √4  * √10

= 2√10

The choice that  is equivalent to the product given is 2√10

To learn more about the surds from the given link

https://brainly.com/question/840021

#SPJ1

B and C

Right pyramid has 8, Right triangular prism has 9

Elimination.... my biggest enemy

Welp let's dive in.

Elimination is sort of like subtraction BUT it's subtraction of equations.

In Elimination we want to make sure that we are looking for a common/ opposite coefficient.

If we see 5x and 5x stacked on each other, GREAT! or maybe -5x and 5x stacked on each other.

Why am I happy? Welll that just made the whole process easier. You see, if you see those stacked on top of each other, that means free elimation. You can just cancel them out because it becomes zero.

then we solve the problem same old same old.

P.S: If it's opposites coefficients we add the equations if it's the same we subract.

In your elimination, we have the same coefficients.

(yay)

so we can minus ad and ad

6c with 5c and 111 with 103

c=8

so we pick an equation and sustitute every c with 8

6*8+ad=111

48+ad=111

ad=63

questiojns? feel free to ask

The simplification are as follows:

Simplification in mathematics refers to the process of making an expression, equation, or mathematical problem easier to understand, solve, or manipulate by reducing its complexity. This can be achieved by combining like terms, cancelling out common factors, reducing fractions, or using the properties of arithmetic operations.

The goal of simplification is to transform a complex expression into a simpler form that can be more easily understood or used in further mathematical analysis.

learn more about simplification: https://brainly.com/question/28595186

#SPJ1

The number of cupcakes that the customer can buy as inequality will be 3.5C + 2 < 44.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars.

The inequality can be written as:-

3.5C + 2 < 44.

Where C is the number of cupcakes and $2 is the charge for the box. Which should be lesser than the total amount.

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ1

The inequality equation is x ≤ 8 , where x is the number of cupcakes

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of cupcakes be represented as A

Now , the equation will be

The cost of each cupcake = $ 3.50

The cost per box of cupcake = $ 2.00

So , the total cost of x cupcakes = x ( 3.50 + 2.00 )

The total cost of x cupcakes = 5.50x

Now , The amount of money with Rebecca = $ 44

So , the maximum number of cupcakes she can buy is

total cost of x cupcakes < amount of money with Rebecca

Substituting the values in the equation , we get

5.50 x ≤ 44

Divide by 5.50 on both sides of the equation , we get

x ≤ 44/5.50

x ≤ 8 cupcakes

Hence , the inequality equation is x ≤ 8

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

The numerical length of PQ is 20

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the line segments are: -

OQ=11  O P = 9

The numerical value of PQ will be calculated as below.

OP+OQ=PQ

11+9=PQ=11+9=PQ

Therefore PQ=20=PQ

To know more about length visit:

https://brainly.com/question/8552546

#SPJ4

Answer:

C

Step-by-step explanation:

create two inequalities:

3 < x + 3   and  x + 3 < 6

0 < x         and  x < 3

An exponential function would better approximate the data described about the volume of a gas.

The relationship between the volume of a gas and its temperature is described by the Ideal Gas Law, which states that the volume of a gas is proportional to its temperature raised to the power of the ratio of specific heat to the universal gas constant. Therefore, as the temperature of a gas increases, its volume will increase exponentially.

The data given in the problem, with the volume increasing as the temperature increases, supports the use of an exponential function to model the relationship between temperature and volume. On the other hand, a linear function, which models a constant rate of change, would not accurately capture the exponential increase in volume as the temperature increases.

Learn more about An exponential function:

https://brainly.com/question/30127596

#SPJ4

Answer:

Below

Step-by-step explanation:

5 out of 8 are NOT blue     5/8=.625

The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.

The ratio of base and height according to angled of elevation will be -

tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.

The formula will be -

Perpendicular ÷ base of observer = perpendicular ÷ base of chimney

6/4 = height/238

Rewriting the equation according to height of chimney

Height = (6 × 238)/4

Performing multiplication on Right Hand Side of the equation

Height = 1428/4

Performing division on Right Hand Side of the equation

Height = 357

Thus, chimney is 357 feet tall.

Learn more about height calculations -

https://brainly.com/question/27243378

#SPJ4

Answer:

1). 3a^4c^3 or D

2). -1/25 or C

3). -z/y^7 or D

4). 3 or A

5). -4^-4 or A

Step-by-step explanation:

I took the quick check already so enjoy your 100% :)

y = tan(x) - (π/2 + πn)

This equation represents a tangent function with a domain of all real numbers, except for multiples of pi/2 plus pi.

The equation y = tan(x) - (π/2 + πn) represents a tangent function with a domain of all real numbers except for multiples of pi/2 plus pi. This equation is useful for finding the tangent value of any given x-value, as long as it is not equal to a multiple of pi/2 plus pi. The equation works by subtracting the multiple of pi/2 plus pi from the x-value, and then finding the tangent of the new value. This allows the tangent of the x-value to be found, regardless of whether or not it is equal to a multiple of pi/2 plus pi.

Learn more about equations: https://brainly.com/question/2972832

#SPJ4