What is the growth rate for the following equation in Big O notation? n
n 3
+1000n
​
O(1) O(n) O(n 2
) O(log(n)) O(n!)
Previous que

Answer:

Step-by-step explanation:

Domain of a function is given by the set of x-values (Input values) on the graph.

Range of a function is given by the set of y-values (output values) on the graph.

From the graph attached,

Set of time will represent the "domain" and set of snowfall will represent the "range" of the function graphed.

a). Domain of the function: 0 ≤ x ≤ 5

b). Range of the function: 0 ≤ y ≤ 10

Answer:

\(\frac{2x+4}{x^{2}-x-6 } \\\frac{2x+4}{x^{2} +2x-3x-6} \\\frac{2x+4}{x(x+2)-3(x+2)} \\\frac{2x+4}{(x-3)(x+2)}\)

Step-by-step explanation:

The statement describes the incidence measure of occurrence, which refers to the number of new cases of a disease or condition that occur in a defined population over a specific period of time.

This statement describes the incidence rate of flu among students living in Dunedin hostels.
The incidence rate is a measure of occurrence that calculates the number of new cases (in this case, students getting sick with the flu) in a specific population (150 students in Dunedin hostels) over a specific time period (3 months). This rate helps us understand the frequency at which the flu is affecting this particular group of students

For similar question on population.

https://brainly.com/question/28683624

#SPJ11

If a circle graph was constructed from the results, the lake activity has a central angle of 54° is Paddleboarding.

To find the lake activity with a central angle of 54° in the circle graph, we need to determine the percentage of campers who chose that activity.

The total number of campers surveyed is 100, and the number of campers who chose paddleboarding is 54. Therefore, the percentage of campers who chose paddleboarding is:

54/100 x 100% = 54%

To convert this percentage to a central angle in degrees, we can use the formula:

Central angle = Percentage * 360°

So, the central angle for paddleboarding is:

54% x 360° = 194.4°

Therefore, the correct option is d. Paddleboarding.

Learn more about circle graphs, here:

https://brainly.com/question/30289738

#SPJ1

To prove the conjecture "If -1/3n = 12, then n = -36," we can use a two-column proof. The proof will involve algebraic steps to show that when -1/3n is equal to 12, n is indeed equal to -36.

-1/3n = 12 | Given

-1n = 12 * 3 | Multiply both sides by 3

-n = 36 | Simplify

n = -36 | Multiply both sides by -1

In the two-column proof above, we start with the given equation -1/3n = 12.

We then multiply both sides of the equation by 3 to eliminate the fraction, resulting in -1n = 12 * 3, which simplifies to -n = 36. Finally, we multiply both sides by -1 to isolate n, giving us n = -36.

By following the logical steps of algebraic manipulation, we have shown that if -1/3n is equal to 12, then n is indeed equal to -36. Thus, the two-column proof validates the conjecture.

Learn more about equation visit:

brainly.com/question/29538993

#SPJ11

Answer: 1. 35 5/6 - 4 1/2

2. 1 5/8 - 2/3

3. 1 5/8 + 2/3

4. 35 5/6+4 1/2

Step-by-step explanation:

1. E=Eli. J=Jamison

E=J+4 1/2

35 5/6=J+4 1/2

J=35 5/6 - 4 1/2

2. s=cups of strawberries

b=cups of blueberries

m=more cups of b than s

m=b-s

m=1 5/8 - 2/3

3. o=original length of patio.

i=increase in length of patio

t=total length of patio after increase.

o+i=t

1 5/8 + 2/3=t

4. p=pine tree. a=palm tree. i=inches taller

p+i=a

35 5/6+4 1/2=a

Answer: 20%

Explanation:

1. Turn it into a fraction (224/280)

2. Divide the numerator (224) by the denominator (280). (224÷280=0.8)

3. Subtract 1 by 0.8 (or 100% by 80%) that should give you the answer 0.2 (20%)

Checking work:

280x0.2=56

280-56=224

The angle of incidence can be calculated using the formula below:
cosθ= cos(SL-LST) x cosδ x cosH + sinδ x sinH
Where:
SL: Standard meridian of the local time zone
LST: Local standard time
δ: Declination of the sun
H: Hour angle of the sun
Hour angle (H) = (15 × (local solar time - 12))°
The equation for local solar time is LST =

Standard Time + EOT + (LST-Standard Time of the central meridian).
EOT is the Equation of time.

South-facing horizontal surface

cosθ = cos(30°-1hr) x cos(23.81°) x cos(30°-29°) + sin(23.81°) x sin(30°-29°)
θ= 72.92°

South-facing vertical surface

cosθ = cos(30°-1hr) x cos(23.81°) x cos(90°-29°) + sin(23.81°) x sin(90°-29°)
θ= 81.19°

Inclined surface tilted 65° from the vertical and facing 30° east of south.

cosθ = cos(30°-1hr) x cos(23.81°) x cos(65°) + sin(23.81°) x sin(65°) x cos(30°-29°-30°)
θ= 56.95°

The angle of incidence is calculated using the formula below:
cosθ= cos(SL-LST) x cosδ x cosH + sinδ x sinH

South-facing horizontal surface

cosθ = cos(30°-1hr) x cos(23.81°) x cos(30°-29°) + sin(23.81°) x sin(30°-29°)
θ= 72.92°

South-facing vertical surface

cosθ = cos(30°-1hr) x cos(23.81°) x cos(90°-29°) + sin(23.81°) x sin(90°-29°)
θ= 81.19°

Inclined surface tilted 65° from the vertical and facing 30° east of south.

cosθ = cos(30°-1hr) x cos(23.81°) x cos(65°) + sin(23.81°) x sin(65°) x cos(30°-29°-30°)
θ= 56.95°

The angle of incidence at 10:00 AM (standard time) on July 15 for Alexandria, Egypt (31°N, 29°E) are as follows:

South-facing horizontal surface = 72.92°, South-facing vertical surface = 81.19° and Inclined surface tilted 65° from the vertical and facing 30° east of south = 56.95°.

To know more about Declination of the sun visit :

https://brainly.com/question/32788837

#SPJ11

Answer:

the first one because negative 1 repeat twice

Answer:

the highest common factor of 12 , 15 and 60 is 3

Step-by-step explanation:

So thus 3 is the HCF that is why i underlined it

Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.

Part A: k = 8.4

To find the value of k, we must solve for k in the equation.

We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).

We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

For more questions related to system

https://brainly.com/question/847634

#SPJ1

Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.

Part A: k = 8.4

We must answer for k in the equation in order to determine its value.

We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).

After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

To know more about Equation, visit:

https://brainly.com/question/2972832

#SPJ1

The complete question is,

EXIT TICKET

After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.

Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.

Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.

The area of the square is 1/4inches² in square inches

The area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.

The square has side of length = 6/12

this can be simplified as 1/2

so

area of the square = (1/2 × 1/2) inches ²

area of the square = 1/4inches²

Thus, the area of the square is calculated using area = s × s, as 1/4inches²

Know about area of square here: https://brainly.com/question/24487155

#SPJ1

Answer:

  7) perimeter = 16 units; area = 12 square units

  8) perimeter = 8 +√13 +√29 ≈ 17.0 units; area = 8 square units

Step-by-step explanation:

You want the perimeter and area of figures defined by their coordinates.

The figure is the brown rectangle in the attachment. It is seen to have a width of 2 units and a height of 6 units. The perimeter and area formulas are ...

  P = 2(W+H) = 2(2+6) = 16 . . . . units

  A = WH = (2)(6) = 12 . . . . square units

The perimeter of the figure is 16 units; the area is 12 square units.

The figure is the blue triangle in the attachment. It is seen to have a base length of 8 units, and a height of 2 units. Vertex T is 3 units from one end of the triangle, and 5 units from the other end.

The lengths of the sides can be found from the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

For side ST, its length is ...

  d = √((3 -0)² +(-2 -0)²) = √(9 +4) = √13 ≈ 3.606

For side TU, the side length is ...

  d = √((8 -3)² +(0 -(-2))²) = √(25 +4) = √29 ≈ 5.385

Side length SU can be seen to be 8 units with no calculation required.

The perimeter is the sum of the side lengths:

  ST +TU +UT = 3.606 +5.385 +8.000 = 16.991 ≈ 17.0 . . . . units

The area formula is

  A = 1/2bh

  A = 1/2(8)(2) = 8 . . . . square units

The perimeter of the figure is about 17.0 units; the area is 8 square units

This question is about probability. The answer for this question is 34,09%.

Suppose there was survey that state that the number of hours spent per week on house hold course of adult has mean 26,3 and standard deviatiador 7,4 and, sample are 46.

First, we need to know the base formula for probability given a mean and standard deviation.

First we need to know the z-score with this formula:

z-score =( x -μ )/ δ

Where:

X = individual data

μ = population mean

δ = population standard deviation.

But in this case, we were asked about the probabilty mean of 46 people. Then, we can use this formula :

Z-score =(x- μ) / (δ /√n)

Where :

X = sample mean

μ = population mean

δ = population standard deviation

Then we can find the z-score in z-table value.

Given :

X = 26,75

μ = 26,3

δ = 7,4

n = 46

Question :

Probability mean more than 26,75

Answer :

Z-score = (x- μ) / (δ /√n)

Z-score = (26,75 - 26,3)/ (7,4/√46)

Z-score = (0,45)/ (1,09)

Z-score = 0,4128

if we look in z-score table, we get number 0,6591.The probability that the mean hours spent per week on household chores by a sample of 46 adults will be more than 26.75 is 1 substract by the value of z-score ,

So, the probability mean for working adult more than 26,75 is 1 - 0,6591 = 0,3409 = 34,09%

brainly.com/question/15352354

#SPJ4

If two independent events a and b have p(a) > 0, p(b) > 0. The statement that a and b are mutually exclusive events is false.

If two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event occurring. In other words, the probability of A and B both occurring is equal to the product of their individual probabilities: P(A and B) = P(A) x P(B).

Mutually exclusive events, on the other hand, are events that cannot occur at the same time. If one event occurs, then the other event cannot occur. The probability of both events occurring is zero: P(A and B) = 0.

So, two events A and B can be independent without being mutually exclusive, and they can be mutually exclusive without being independent. The only requirement for independence is that P(A and B) = P(A) x P(B), while the requirement for mutual exclusivity is that P(A and B) = 0.

To find more questions on Probability

https://brainly.com/question/7965468

#SPJ4

1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

For more information about general solution of differential equation, visit:

https://brainly.com/question/30078609

#SPJ4

Answer:

486 Calories

Step-by-step explanation:

175/9 = # of Calories for EACH Starburst

25 x 175/9

4375 / 9 = 486 1/9

Answer: 486 calories

Step-by-step explanation:

175 / 9 = 19.4444444444 calories per piece

25 starbursts = 19.4444444444 * 25= 486.111111111

Rounded = 486 calories

Answer:

12/2-3

Step-by-step explanation:

12/2-3

Answer:

12/2-3

Step-by-step explanation:

12/2-3

Cooper left his dinner server a 19% tip.

To find the percent tip, we need to first subtract the cost of the meal from the total amount paid, which will give us the tip amount:

Tip amount = Total amount paid - Cost of the meal

Tip amount = $33.32 - $28

Tip amount = $5.32

Now we can calculate the percentage of the tip by dividing the tip amount by the cost of the meal and multiplying by 100:

Percent tip = (Tip amount / Cost of the meal) x 100

Percent tip = ($5.32 / $28) x 100

Percent tip = 0.19 x 100

Percent tip = 19%

Therefore, Cooper gave a 19% tip on his dinner.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

Answer:

C

Step-by-step explanation:

Please mark me brainlist

Answer:

-9

hope it helped and stay safe

Answer:

The correct option is;

f(x) = 3·sin x/8·π + 2

Step-by-step explanation:

The given parameters for the sinusoidal function are;

Amplitude of oscillation = 3

Frequency of oscillation = 1/8·π

Midline of oscillation= 2

The general form of sinusoidal equation is y = A·sin(B(x - C)) + D

Where;

A = The amplitude

B = The frequency

C = The horizontal shift

D = The midline or vertical shift

Substituting the given values into the general form of sinusoidal equation, we have;

f(x) = y =  3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2

Which gives;

f(x) = 3·sin(x/8·π) + 2.

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

To learn more about polar curve, refer:-

https://brainly.com/question/28976035

#SPJ11

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

Learn more about Stratified random sampling:

https://brainly.com/question/20544692

#SPJ11

The amount invested in the account that pays a 5% interest is $2100 and the amount invested in the account that pays a 7.5% interest is $1400.

0.05a + 0.075b = (0.06 x $3500)

0.05a + 0.075b = $210 equation 1

a + b = $3,500 equation 2

Where:

a = amount invested in the account that paid a 5% interest

b = amount invested in the account that paid a 7.5% interest

In order to determine this value, multiply equation 2 by 0,05

0.05a + 0.05b = 175 equation 3

0.025b = 35

b = $1400

a + $1400 = $3500

a = $3500 - 1400

a = $2100

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Question 8

1) \(\triangle ACE\) with \(\overline{AC} \cong \overline{EC}\), \(\overline{BC} \cong \overline{DC}\) (given)

2) \(\angle C \cong \angle C\) (reflexive property)

3) \(\triangle ACD \cong \triangle ECB\) (SAS)

Question 9

1) \(\overline{PQ}\) and \(\overline{PR}\) are the legs of isosceles \(\triangle PQR\), \(\overline{PS} \cong \overline{QR}\) (given)

2) \(\angle PSQ\) and \(\angle PSR\) are right angles (definition of perpendicular lines)

3) \(\angle Q \cong \angle R\) (angles opposite the legs of an isosceles triangle are congruent)

4) \(\overline{PS} \cong \overline{PS}\) (reflexive property)

5) \(\angle PSQ \cong \angle PSR\) (all right angles are congruent)

6) \(\triangle PSQ \cong \triangle PSR\) (AAS)

Question 10

1) \(\overline{AB} \cong \overline{CD}\), \(\overline{AB} \perp \overline{BC}\), \(\overline{CD} \perp \overline{AD}\) (given)

2) \(\overline{AC} \cong \overline{AC}\) (reflexive property)

3) \(\angle ABC\) and \(\angle ADC\) are right angles (perpendicular lines form right angles)

4) \(\triangle ABC\) and \(\triangle ADC\) are right triangles (a triangle with a right angle is a right triangle)

5) \(\triangle ABC \cong \triangle CDA\) (HL)

6) \(\overline{AD} \cong \overline{CB}\) (CPCTC)

The solution to the equation \(3 = \frac{2y-4}{7} + \frac{5y+2}{4}\) is \(y = \frac{20}{13}\).

To solve the equation, we first simplify the expression on the right-hand side by finding a common denominator. The common denominator for 7 and 4 is 28. So we rewrite the equation as:

\[3 = \frac{2(4y-8)}{28} + \frac{5(7y+2)}{28}\]

Next, we combine the fractions by adding the numerators and keeping the common denominator:

\[3 = \frac{8y-16+35y+10}{28}\]

Simplifying the numerator, we have:

\[3 = \frac{43y-6}{28}\]

To eliminate the fraction, we can cross-multiply:

\[28 \cdot 3 = 43y-6\]

Simplifying the left side of the equation, we get:

\[84 = 43y-6\]

To isolate the variable, we add 6 to both sides:

\[90 = 43y\]

Finally, we divide both sides by 43 to solve for \(y\):

\[y = \frac{90}{43}\]

The fraction cannot be simplified any further, so the solution to the equation is \(y = \frac{90}{43}\).

Learn more about  equation here:

https://brainly.com/question/29269455

#SPJ11

The value that completes the blank in the ordered pair is - 4

From the question, we have the following equation

y = 3x - 7

Also, we have the following incomplete ordered pair

(1, )

Complete the blank with a variable y

So, we have the ordered pair to be (1, y)

The ordered pair (1, y) means x = 1

So, we subtsitute 1 for x in the equation y = 3x - 7

y = 3(1) - 7

This gives

y = 3 - 7

Evaluate

y = -4

Substitute y = -4 in the ordered pair (1, y)

So, we have

(1 -4)

Hence, the complete value is (1 -4)

Read more about linear equations at

https://brainly.com/question/2030026

#SPJ1