What are the 3 possible solution that you can obtain when solving a system of linear equations

Answer:

The person has a speed of 12 miles per hour.

Step-by-step explanation:

The ratio is 12 miles to 1 hour.

This means, that in every hour, the person can move 12 miles and has a speed of 12 miles per hour.

Answer:

13.67

Step-by-step explanation:

Answer: t × 9

Step-by-step explanation:

Answer: t × 9

Step-by-step explanation:

When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.

If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.

However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.

In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.

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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{105°}}}}}\)

Step-by-step explanation:

Given, < 2 = 105°

To find : < 1

When two lines interest the angles formed opposite to each other are called vertically opposite angles. Vertically opposite angles are always equal to each other.

So,

<1 = 105 °

Hope I helped!

Best regards!

Answer:

\(\Huge \boxed{\angle 1 = 105 \° }\)

Step-by-step explanation:

\(\angle 1\) and \(\angle 2\) are vertical angles.

\(\angle 2= 105 \°\)

Vertical angles are equal in measure.

\(\angle 1= \angle 2\)

\(\angle 1= 105 \°\)

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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Answer:

4 kilometers

plz give brainliest

Step-by-step explanation:

Answeri think 40 kilo

Step-by-step explanation:

Answer:

y=(x+7)(x-8)(x-15)

Step-by-step explanation:

yw

An equation for a polynomial function with given intercepts is

\(P(x)=x^3-16x^2-41x+840\)

Given :

The intercepts at the horizontal axis at -7, 8, and 15.

so, the x intercepts are -7, 8, and 15.

Lets write the x intercepts in factor form

if 'a' is x intercept then (x-a) is a factor

x intercepts are -7, 8, and 15.

the factors are

\((x-(-7)) (x-8)(x-15)\\(x+7)(x-8)(x-15)\)

Now to write the polynomial we multiply all the factors

\(P(x)=(x+7)(x-8)(x-15)\\P(x)=\left(x^2-x-56\right)\left(x-15\right)\\P(x)=x^3-16x^2-41x+840\)

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Based on the converse of corresponding angles theorem, the value of x would be: 20.

The converse of corresponding angles theorem states that if two corresponding angles that lie on two lines that are crossed by a transversal are congruent to each other, then the lines are parallel lines.

Therefore, based on the converse of corresponding angles theorem, lines m and n will be parallel to each other if:

3x + 5 = 65

Solve for the value of x that makes both measures equal:

3x + 5 - 5 = 65 - 5 [subtraction property of equality]

3x = 60

3x/3 = 60/3 [division property of equality]

x = 20

Therefore, based on the converse of corresponding angles theorem, the value of x would be: 20.

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Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

The number we are looking for is x - 6.

To determine the number that, when subtracted from x, results in 6, we can set up the equation:

x - y = 6

Here, y represents the unknown number we are trying to find. To isolate y, we can rearrange the equation:

y = x - 6

Therefore, the number we are looking for is x - 6.

It's important to note that in mathematics, without specific values or additional information about x, we cannot determine a unique solution. The expression "6 - xx - 66 + x6 - ( x - 6)" you provided is not clear and does not allow us to solve for x or the unknown number directly. If you have specific values or additional context, please provide them, and I'll be glad to assist you further.

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The researcher is referring to the between-groups source of variation.

Therefore, the researcher is referring to the between-groups source of variation.

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Answer:

yes they both form a proportion

In order to calculate efficiency

Option A

528 ÷ 24 = 22 mi/gal

Option B

690 ÷ 30 = 23 mi/gal

Option C

840 ÷ 42 = 20 mi/gal

Option B, gives the best fuel efficiency because the car can travel further using 1 gallons of fuel than others.

the total cost of the carpet for Courtney's new house will be $24.89.

To find the total cost of the carpet, we need to multiply the cost per yard by the number of yards.

Cost per yard = $2.62

Number of yards = 9.5

Total cost of carpet = Cost per yard x Number of yards

Total cost of carpet = $2.62 x 9.5

Total cost of carpet = $24.89

what is number?

A number is a mathematical object used to represent quantity, magnitude or a value. Numbers can be used for various purposes, such as counting, measuring, and performing mathematical operations like addition, subtraction, multiplication, and division. Numbers can be classified into different categories, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers, depending on their properties and characteristics. Numbers are an essential part of everyday life and are used in many fields, including science, engineering, economics, and finance, among others.

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The correct option is A. m ≤ (8)(20)

The inequality which gives the possible values of 'm' is m ≤ (8)(20).

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

According to the question;

Terrence's car contains 8 gallons of fuel.

Terrence can drive the car 'm' miles using the fuel currently in the car.

The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).

Then,

The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.

Thus, total miles covered by the car are less than the maximum value which is given by the inequality-

m ≤ (8)(20)

Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).

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The complete question is-

Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?

answer choices

A. m ≤ (8)(20)

B. m ≥ (8)(20)

C. 8 ≤ 20m

D. 8 ≥ 20 m

The estimated mean amount of money spent per household on internet service each month is $59.95 with confidence interval.

To calculate the estimated mean amount of money spent per household on internet service each month, we first need to find the lower and upper bounds of the confidence interval. The lower bound is $47.45 and the upper bound is $72.45. We then take the average of these two numbers to get the estimated mean. The average of $47.45 and $72.45 is

($47.45 + $72.45) / 2

= $59.95.

Therefore, the estimated mean amount of money spent per household on internet service each month is $59.95.

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Answer:

19%=0.19+$4,350/16=$272+$1,600=$1872+0.19=1872.19/12=$156+$4,50=

$375.50

Answer: C. $309.

Step-by-step explanation:

Answer:

i took the test⬇️

Answer:

(3, - 2 )

Step-by-step explanation:

The solution is at the point of intersection of the 2 lines

The lines intersect at (3, - 2 ) ← solution

Check by substituting  x = 3 into the left side of the given equation

- 2(3) + 4 = - 6 + 4 = - 2 ← True

Penelope must purchase 30 ride tickets in order to spend $35 in all. The equation that represents this scenario is:0.5x + 20 = 35

Let x be the number of ride tickets that Penelope purchases. Each ride ticket costs $0.50, so the cost of the tickets is 0.5x dollars. In addition, she pays $20 to get into the carnival. Thus, the total cost of her trip to the carnival is:

Total Cost = Cost of Ride Tickets + Cost of Admission
Total Cost = 0.5x + 20

We know that Penelope spends $35 in all, so we can set the total cost equal to $35 and solve for x:

0.5x + 20 = 35

Subtracting 20 from both sides, we get:

0.5x = 15

Dividing both sides by 0.5, we get:

x = 30

Therefore, Penelope must purchase 30 ride tickets in order to spend $35 in all. The equation that represents this scenario is:

0.5x + 20 = 35

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There exists a unique solution to the equation ax = b in f.

Since a is non-zero in the field f, there exists a unique multiplicative inverse for a in f, which we denote by \(a^{(-1).\)

Now, suppose that there are two solutions to the equation ax = b, say x and y. Then we have:

ax = b

ay = b

Subtracting the second equation from the first, we get:

ax - ay = b - b

a(x - y) = 0

Since a is non-zero, it follows that x - y = 0, i.e., x = y. Therefore, there can be at most one solution to the equation ax = b.

To show that there exists a solution, we can simply divide both sides of the equation ax = b by a to obtain:

\(x = a^{(-1)b\)

Since \(a^{(-1)\)exists in f, so does x. Therefore, there exists a unique solution to the equation ax = b in f.

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After solving the quadratic equation, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

Let's assume that one leg of the right triangle is x units. According to the problem, the other leg is 4 more than twice the length of x, which can be represented as 2x + 4 units.

Using the Pythagorean theorem, we can set up the equation:

\(x^2 + (2x + 4)^2 = 26^2\)

Expanding and simplifying the equation:

\(x^2 + 4x^2 + 16x + 16 = 676\)

\(5x^2 + 16x - 660 = 0\)

We can now solve this quadratic equation to find the value of x. By summing the lengths of the legs (x + 2x + 4), we can determine the final answer.

After solving the quadratic equation, we find two possible solutions: x = 11 and x = -12. Since the lengths of the sides cannot be negative, we consider x = 11 as the valid solution.

Therefore, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

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Answer:

make 1/4 2/8... Then Add, 3/8+2/8= 5/8.

Answer:

the correct answer is 5/8

the explanation is in the picture.

I hope it helps.

Answer:

by phythagoras theorem

(c+b)^2=(8)^2+(6)^2

(b+c)^2=64+36

(b+c)^2=100

b+c=√100

b+c=10.

by phythagoras theorem

(8)^2=(a)^2+(b)^2

64-b^2=a^2. {1}

by phythagoras theorem

(6)^2=(a)^2+(c)^2

36-c^2=a^2. {2}

In equation 1 and 2,

64-b^2=36-c^2

64-36= -c^2+b^2

28= b^2-c^2

28=(b+c)(b-c)

28=10(b-c)

b-c=28/10

b-c=2.8.

b+c=10

b-c=2.8

subtract both equations

c=3.6

option A is correct.

Output: y(t) = yₛ(t) + yₜ(t)

Steady-state: α = 2/9, s = -3

Transient: c₁ = 2/9, s ˉ₁ = -1, c₂ = -2/9, s ˉ₂ = -3

To solve the given differential equation and find the output of the system, we will follow these steps:

Step 1: Find the characteristic equation:

The characteristic equation is obtained by substituting y(t) = e^(st) into the differential equation:

s²e^(st) + 6se^(st) + 8e^(st) = 0

s² + 6s + 8 = 0

Step 2: Solve the characteristic equation for s:

Using the quadratic formula, we have:

s = (-6 ± √(6² - 4(1)(8))) / (2(1))

s = (-6 ± √(36 - 32)) / 2

s = (-6 ± √4) / 2

s = (-6 ± 2) / 2

s₁ = -4/2 = -2

s₂ = -8/2 = -4

Step 3: Determine the steady-state component:

The steady-state component is given by yₛ(t) = αe^(st). Since the input x(t) = e^(-t)u(t), the steady-state output will have the same form as the input, but with a different amplitude α. We can determine α by substituting the steady-state output and input into the differential equation:

2αe^(st) + 6αse^(st) + 8αe^(st) = 2e^(-t)

(2s + 6 + 8)e^(st) = 2e^(-t)

(2s + 14)e^(st) = 2e^(-t)

Comparing the exponents, we have:

2s + 14 = 0

s = -7

Step 4: Determine the transient component:

The transient component is given by yₜ(t) = c₁e^(sˉ₁t) + c₂e^(sˉ₂t). To find c₁ and c₂, we can use the initial conditions y(0) = -1 and dy/dt(0) = 1. Substituting these values into the transient equation and its derivative, we get:

yₜ(0) = c₁ + c₂ = -1 ... (1)

dyₜ/dt(0) = sˉ₁c₁ + sˉ₂c₂ = 1 ... (2)

Using sˉ₁ = -2 and sˉ₂ = -4 from earlier calculations, we can solve equations (1) and (2) simultaneously to find c₁ and c₂.

Solving the equations yields:

c₁ = 2/9

c₂ = -2/9

Overall, the calculations show that the system's output consists of a steady-state component (yₛ(t)) and a transient component (yₜ(t)), with specific values for the real and imaginary parts of α, s, c₁, and c₂.

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Answer:

2x=10

Step-by-step explanation:

7x-14=21

x=5

2x=10 (divide both sides by two)

2x/2  10/2

x=5

Yky. we'd to provide the other options but to do this you need to +14 to both side. 21+14 then -14+14 cancel. so it's now

7x=35 then you divide 7 in both sides 7 cancels 35/7 =5

x=5

Answer:

  T'''(2, 6)

Step-by-step explanation:

The transformations used in this problem are ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

  (x, y) ⇒ (x +h, y +k) . . . . translation h right and k up

  (x, y) ⇒ (y, x) . . . . . . reflection over the line y=x

__

Applying these transformations to point T(-5, -4), we have ...

1.  T(-5, -4) ⇒ T'(5, 4)

2. (h, k) = (1, -2), so we get ...

  T'(5, 4) ⇒ T"(5 +1, 4 -2) = T"(6, 2)

3. T"(6, 2) ⇒ T'''(2, 6) . . . . straightforward application of the separate transformations