which of the following values for x and y satisfy the following system of the equations?
{ x + 4y = 10
{5x + 10y = 20
a. x = 3, y = 2
b. x = 2, y - 3
c. x = -2, y = 3
d. x = 3, y = -2

Answer: The system of inequalities representing the situation are

x + y ≥ 20

10x + 20y ≤ 280

Step-by-step explanation:

Let x represent the number of $10 tickets that the radio station is giving away.

Let y represent the number of $20 tickets that the radio station is giving away.

They want to give away at least 20 tickets. This means that

x + y ≥ 20

The total cost of all the tickets they give away can be no more then $280. This means that

10x + 20y ≤ 280

Answer:

Step-by-step explanation:

Let x represent the original price of the model.

A builder of tract homes reduced the price of a model by 15%. This means that x was reduced by 15%. The amount by which x was reduced would be

15/100 × x = 0.15 × x = 0.15x

The new price would be

x - 0.15x = 0.85x

If the new price is $425,000, then it means that

0.85x = 425000

x = 425000/0.85

x = $500000

The amount that can be saved by purchasing the model at the new price would be

500000 - 425000 = $75000

Final answer:

The original price of the home was $500,000 before a 15% reduction. The new price is $425,000. Therefore, a buyer would save $75,000 by purchasing the home at the reduced price.

Explanation:

To find the original price of the home before the 15% reduction, we can use the formula for percentage decrease, which is:

Original Price = New Price / (1 - Rate of Decrease)

Here, the New Price is $425,000 and the Rate of Decrease is 15%, or 0.15 when converted to decimal form. Plugging the numbers into the formula gives us:

Original Price = $425,000 / (1 - 0.15) = $425,000 / 0.85

Original Price = $500,000

The amount that can be saved by purchasing the model at the reduced price is the difference between the original price and the new price:

Savings = Original Price - New Price

Savings = $500,000 - $425,000

Savings = $75,000

Answer: x= 1090 y=450

my question was "Tickets to a Broadway show cost $35 for adults and $10 for children. The total receipts for 1540 tickets at one performance were $42,650. How many adult and how many child tickets were sold?"

Step-by-step explanation:

to find y

take the original equation 35x+10y=42,650 and fill in the x which is 1090 in the equation

35(1090) +10y =42,650

38,150 +10y=42,650

-38,150         -38,150

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

10y = 4,500

divide 10 by both sides and u get

y= 450

have a great day! :)

Answer:

The probability that he picked 2 purpled socks is 0.33.

Step-by-step explanation:

Given:

Number of purple socks, [tex] n(P) = 6[/tex]

Number of orange socks, [tex] n(O) = 4[/tex]

Two socks are picked without replacement.

Now, total number of socks, [tex]n(T)=N(P)+n(O)=6+4=10[/tex]

Probability of picking the first cap as purple cap is given as:

[tex]P(P1)=\frac{n(P)}{n(T)}\\\\P(P1)=\frac{6}{10}=\frac{3}{5}[/tex]

Since there is no replacement, the number of socks decreases by 1. Also, if the first sock picked is purple, then number of purple socks is also decreased by 1.

Therefore, probability of picking the second cap as purple cap is given as:

[tex]P(P2)=\frac{n(P)-1}{n(T)-1}\\\\P(P2)=\frac{5}{9}[/tex]

Now, probability that both the picked caps are purple is given by their probability product. This gives,

[tex]P(P1\ and\ P2)=P(P1)\times P(P2)\\\\P(P1\ and\ P2)=\frac{3}{5}\times\frac{5}{9}\\\\P(P1\ and\ P2)=\frac{3}{9}=\frac{1}{3}=0.33[/tex]

Therefore, the probability that he picked 2 purpled socks is 0.33

Answer:

x = 3.5.

Step-by-step explanation:

This is an equilateral triangle ( as all angles = 60 degrees) so all 3 sides are of equal length.

Thus 2x - 3 = 4

2x = 7

x = 3.5.

Answer:

hi its me

Step-by-step explanation:

Answer:

[tex]FJ=18\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=12+8=20\ units[/tex]

[tex]FH=HF=12\ units[/tex]

[tex]FG=30\ units[/tex]

substitute the given values

[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]

[tex]FJ=12(30)/20\\FJ=18\ units[/tex]

Answer:

18 from k12

Step-by-step explanation:

Answer:

Step-by-step explanation:

No of ways in which 5 cards are chosen is [tex]N=^{52}C_5[/tex]

No of ways in which at most  4 cards are spades [tex]N_0=[/tex]Total ways-5 spades

[tex]=^{52}C_5-^{13}C_5[/tex]

Probability that at most 4 cards are spade [tex]P=\frac{N_0}{N}[/tex]

[tex]P=\frac{^{52}C_5-^{13}C_5}{^{52}C_5}[/tex]

[tex]P=\frac{2598960-1287}{2598960}[/tex]

[tex]P=\frac{2597673}{2598960}=0.9995[/tex]

The probability of being dealt 5 cards with at most 4 of them being spades from a standard deck is approximately 0.9995.

To determine the probability of being dealt 5 random cards with at most 4 of them being spades from a standard deck of 52 cards, follow these steps:

1. Understanding the total number of possible hands

⇒ C(52, 5) = 2,598,960

2. Calculating the number of desired outcomes

0 Spades: C(13, 0) × C(39, 5)

1 Spade: C(13, 1) × C(39, 4)

2 Spades: C(13, 2) × C(39, 3)

3 Spades: C(13, 3) × C(39, 2)

4 Spades: C(13, 4) × C(39, 1)

0 Spades:

⇒ 1 × 575,757 = 575,757

1 Spade:

⇒ 13 × 82,251 = 1,069,263

2 Spades:

⇒ 78 × 9,139 = 712,842

3 Spades:

⇒ 286 × 741 = 211,926

4 Spades:

⇒ 715 × 39 = 27,885

⇒ 575,757 + 1,069,263 + 712,842 + 211,926 + 27,885 = 2,597,673

3. Calculating the probability

⇒ P(at most 4 spades) = 2,597,673 ÷ 2,598,960

≈ 0.9995

Answer:

The study is an observational study because the study examines individuals in the sample, but does not try to influence the response variable.

Step-by-step explanation:

Final answer:

The described study, which involves asking a sample of people with heart arrhythmias about their caffeine consumption to explore a relationship between the two, is an observational study. In this type of study, there is no manipulation of variables or conditions, just observations and recordings of naturally occurring phenomena.

Explanation:

The study described is investigating if there is a relationship between heart arrhythmias and caffeine consumption by asking a sample of people with heart arrhythmia about their caffeine intake. This corresponds to an observational study, not an experiment. In an observational study, researchers collect data on existing behaviors and outcomes without manipulating any variables or conditions. Participants are observed in their natural settings, and their experiences or characteristics are recorded to find correlations or associations between factors.

By contrast, an experiment involves the researcher actively manipulating one or more independent variables to investigate the effects on a dependent variable, often involving random assignment to different conditions, such as treatment versus control groups.

In the context provided, because there is no manipulation of participants' caffeine consumption and no assignment to different conditions, but rather a collection of data through questionnaires, this study is classified as an observational study.

Answer:

The answer to your question is   3(25t² - 4)

Step-by-step explanation:

To factor this binomial, just look for the common factor between both terms.

                                75t² + 12

                                                      75     12      2

                                                      75      6     2

                                                      75      3     3

                                                      25      3     3

                                                      25      1      5

                                                        5       1      5

                                                         1

The greatest common factor is 3, that is the common factor.

Now, factor the polynomial

                                  3(25t² - 4)

Answer: 3(25t 2 + 4)

Step-by-step explanation:

Answer:

A) True

Step-by-step explanation:

Solution: When values of the ordered pair (v1, v2, ... , vn) are substituted in every equation of the linear system with variables x1, x2, ... , xn and these values satisfy each and every equation then it's called a solution.

Answer:

3y^7/ x 3y^5

Photomath

Answer:

They sold 16 French fries.

Step-by-step explanation:

Let x represent the number of large burgers that they sold on that day.

Let y represent the number of French fries that they sold on that day.

fast food sells large burgers for five dollars each and french fries for three dollars each that day and their total sales was $98.It means that

5x + 3y = 98 - - - - - - - - - - - - - -1

they sold six more french fries than burgers. It means that

y = x + 6

Substituting y = x+ 6 into equation 1, it becomes

5x + 3(x + 6) = 98

5x + 3x + 18 = 98

8x = 98 - 18 = 80

x = 80/8 = 10

y = x + 6 = 10 + 6

y = 16

Answer:

Sugar will dissolve to half of it's amount in 2.41 minutes.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

When the sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation

[tex]\frac{dA}{dt}=-kA, (k>0)[/tex]

If 25% of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve.

The given differential equation is [tex]\frac{dA}{dt}=-kA[/tex]

In other form, dA = -kA.dt

We further integrate the equation,

[tex]\int\limits {dA}\,=\int{-kA}\, dt[/tex]

[tex]\int\limits{\frac{dA}{A} }\,=-k\int\, dt[/tex]

lnA = -kt + c

Or [tex]A=e^{c-kt}[/tex]

A = [tex]e^{c}.e^{-kt}[/tex] -----(1)

Here [tex]e^{c}[/tex] is a constant.

For t = 0,

[tex]A=e^{c}[/tex]

Let [tex]e^{c}=A_{0}[/tex]

Therefore, equation (1) will become

A = [tex]A_{0}e^{-kt}[/tex]

If sugar dissolves 25% in 1 minutes then undissolved sugar will be

100 - 25 = 75%

Now from the equation

[tex]0.75A_{0}=A_{0}e^{-k\times 1}[/tex]

[tex]e^{-k}=0.75[/tex]

By taking natural log on both the sides

[tex]ln(e^{-k})=ln(0.75)[/tex]

k = 0.2877

Now we have to calculate the time to dissolve half of the sugar, that means half the sugar will be undissolved.

Form the equation,

[tex]0.5A_{0}=A_{0}e^{-0.2877t}[/tex]

[tex]0.5=e^{-0.2877t}[/tex]

ln(0.5) = [tex]ln(e^{-0.2877t})[/tex]

0.6931 = 0.2877t

t = 2.41 minutes

The question deals with logarithmic differential equations. After finding the value of the decay constant (k), it's used to find the time it takes for half of the sugar to dissolve.

The subject you're asking about is logarithmic differential equations. Let's start by writing the differential equation in its general form: dA/dt = -kA. This equation describes an exponentially decaying process, where the amount of undissolved sugar decreases proportionally to the amount of sugar left at any point in time (A).

From the problem, it's known that after 1 min 75% of the sugar remains, which means A = 0.75 and t = 1. We substitute these values into the equation to find the value of k.

Then we can use this information to calculate the time it takes for half of the sugar to dissolve. At this point A will be 0.5. We substitute A = 0.5 and the value of k from earlier into the equation and solve for t.

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Answer:

the apprentice can complete the job in 30 hours by working alone.

Step-by-step explanation:

Given:

Number of hours required to complete a job by welder = 18 hours

Number of hours welder work on job = 6 hours.

Number of hours required by apprentice to complete the job = 14 hours

We need to find Number of hours required to complete a job by apprentice alone.

Solution:

Let Number of hours required to complete a job by apprentice alone be 'a'.

Also let the job completed be = 1

Now we know that ;

Time required on job is equal to sum of Number of hours welder work on job and Number of hours required by apprentice to complete the job.

framing in equation form we get

Time required on job =  [tex]6+14 =20\ hrs[/tex]

Now we can say that;

each has done a fraction of the work so we will add to two fraction as number of hours of work done by Total number of hours required to do the work to complete 1 job.

so we can frame the equation as;

[tex]\frac{6}{18}+\frac{20}{a}=1[/tex]

By reducing the fraction we get;

[tex]\frac{1}{3}+\frac{20}{a}=1[/tex]

Now we will make the denominator common to solve the fraction we get;

[tex]\frac{1\times a}{3\times a}+\frac{20\times3}{a\times3}=1\\\\\frac{a}{3a}+\frac{60}{3a}=1[/tex]

Now denominators are same so we will solve the numerator we get;

[tex]\frac{a+60}{3a}=1[/tex]

Multiplying both side by 3a we get;

[tex]\frac{a+60}{3a}\times3a=1\times 3a\\\\a+60=3a[/tex]

Combining the like terms we get;

[tex]3a-a=60\\\\2a=60[/tex]

Dividing both side by 2 we get;

[tex]\frac{2a}{2}=\frac{60}{2}\\\\a=30\ hrs[/tex]

Hence the apprentice can complete the job in 30 hours by working alone.

Final answer:

The apprentice would take 21 hours to finish the welding job working alone. The problem is solved using the combined work rate of the welder and apprentice and then isolating the apprentice's work rate.

Explanation:

The student is asking how long it would take for an apprentice, working alone, to complete a welding job if the welder requires 18 hours to do the job alone, and together they have worked for 6 hours, after which the apprentice completes the remainder of the job in 14 hours. Let's represent the time it would take the apprentice to complete the job working alone as 'A' hours.

To solve this, we find the combined hourly rate of the welder and apprentice and use it to determine the apprentice's solo hourly rate. The welder completes the job in 18 hours, so his work rate is 1/18 job per hour. Together, they work for 6 hours, so they completed 6/18, or 1/3, of the job. We know that 1 whole job - 1/3 job leaves 2/3 of the job that the apprentice completes alone in 14 hours.

Therefore, the apprentice's rate is 2/3 job per 14 hours or 1/21 job per hour. Now we calculate the time it would take the apprentice to do the whole job alone (A hours) by setting up the equation 1/A = 1/21. By solving this equation for A, we find A = 21, meaning the apprentice would take 21 hours to finish the job working alone.

Answer:

[tex] A_n = [2^{n-1} , 3(2^{n-1}), 5(2^{n-1}), 7(2^{n-1}),....][/tex]

Step-by-step explanation:

For this case we need to produce an infinite collection of sets [tex] A_a, A_2, A_3,....[/tex] with the property that every [tex] A_i[/tex] has an infinite number of elements with [tex] A_i \cap A_j , i\neq j[/tex] and [tex] \cup_{i=1}^{\infty} A_i = N[/tex]

So for this case we need to create a set A who satisfy 3 conditions (Infinite number of elements, Disjoint and Union represent the natural numbers)

So if we define the nth term for the set A:

[tex] A_n = [2^{n-1} , 3(2^{n-1}), 5(2^{n-1}), 7(2^{n-1}),....][/tex]

We see that the set A represent all the odd multiplies of [tex] 2^{n-1}[/tex] and if we check the properties we have this:

Disjoint

If we select [tex] A_n , A_m[/tex] with [tex] n\neq m[/tex] and we can assume for example that [tex] n<m[/tex]  and if we have an element a in the intersection of the sets [tex] a \in A_n \cap A_m[/tex], so then needs to exists some odd numbers k and l such that

[tex] a = 2^{n-1} k = 2^{m-1}l[/tex]

And since we assume that [tex] n<m[/tex] then we have that [tex] n\leq m-1[/tex] and we can write:

[tex] 2^{m-1} =2^m 2^i , i\geq 0[/tex]

And then [tex] 2^{n-1} k= 2^n 2^i l[/tex] and if we divide by [tex] 2^{n-1}[/tex] we got:

[tex] k = 2 2^i l[/tex] so then k is not odd since the last statement contradicts this. So then we can conclude that [tex] A_n \cap A_m = \emptyset[/tex]

Union

For this case we need to show that  [tex] \cup_{i=1}^{\infty} A_i = N[/tex]

Since each element [tex] A_n[/tex] is a subset of the natural numbers then the unision of the sets represent N

For the other side of the explanation if we assume that [tex] a\in N[/tex] we can write [tex] a= 2^{n-1}k[/tex] for any [tex] n\in N[/tex] and k odd, and by this [tex] a\in A_n[/tex] and we chaek the property.

Infinite condition

For this case [tex] A_n = [2^{n-1} , 3(2^{n-1}), 5(2^{n-1}), 7(2^{n-1}),....][/tex]

is an infinite set since we don't have a limit for n so then we have infinite elements for this case.

And since all the properties are satisfied we end the problem.

If you want to find the area of the living room minus 1, it could be 8 m², 14 m², 19 m², or 24 m², depending on what you are looking for.

To find the area of the living room, you can use the provided information:

The area of the living room is:

9 m²

15 m²

20 m²

25 m²

You mentioned "The area of the living room - 1," which seems to imply you want to find the area of the living room, subtracting 1 from it. To do that, simply subtract 1 from each of the given options:

9 m² - 1 = 8 m²

15 m² - 1 = 14 m²

20 m² - 1 = 19 m²

25 m² - 1 = 24 m²

So, if you want to find the area of the living room minus 1, it could be 8 m², 14 m², 19 m², or 24 m², depending on what you are looking for.

for such more question on area

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Answer: The ball will hit the ground 5 seconds after being thrown.

Step-by-step explanation:

The correct function is: [tex]h (t) =-16t^2 +64t+80[/tex]

You can rewrite the Quadratic function given in the exercise with making [tex]h(t)=0[/tex]. Then this is:

[tex]0=-16t^2 +64t+80[/tex]

Now you can simplify the equation dividing both sides by -16. So you get:

 [tex]\frac{0}{-16}=\frac{-16t^2 +64t+80}{-16}\\\\0=t^2-4t-5[/tex]

To find the solution of the Quadratic equation, you can facfor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.

Therefore, you get this result:

[tex]0=(t-5)(t+1)\\\\t_1=5\\t_2=-1[/tex]

Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.

Part A

This line contains point G (as an endpoint) and it runs perpendicular to line FE. This line is in the bottom face of the rectangular prism. This line is also in the front face as well.

===================================================

Part B

AB is parallel to CD, GH and FE.

===================================================

Part C

Skew lines are lines that aren't parallel nor perpendicular nor intersecting. Skew lines can only be found in 3D space (not 2D space). Think of a line on the ground running from north to south. If we had a straight wire that did not bend at all run from north to south, then we would have two parallel lines. However, if we aim the wire to go from east to west, then the line on the ground and the wire will be skew lines. The line on the ground and the wire line do not intersect. The same story happens with AB and FE, along with AB and AG.

===================================================

Part D

The front face is plane AGF. We simply locate the three points A, G, F and note this is the front face. The back face is parallel to the front face. This face is plane GCH, and it contains point C.

note: we could say "plane AGFD" but we only need 3 points at minimum to uniquely determine a plane.

Any flat surface (plane) of a rectangular prism fits the description as they each have corners making right angles. Each edge of these faces can be seen as a line segment that would form a straight line if extended.

In a rectangular prism, each segment can be thought of as a part of a line. The plane that fits this description could be any of the flat surfaces of the prism, as they have each corner making a right angle. For example, consider you have a box (a rectangular prism). The front face of the box forms a plane, and each edge of this face can be seen as a line segment. Similarly, the top face of the box also forms a plane with all right angles. The edges of each face are line segments that are part of a straight line if extended. Therefore, all faces (planes) and edges (line segments) of the rectangular prism fit the description.

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Answer:

[tex]y = mx+b[/tex]

[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]

[tex] b = y_1 -m x_1[/tex]

Or equivalently:

[tex] b = y_2 - m x_2[/tex]

Step-by-step explanation:

If we are assuming that we have:

x independent variable

y dependent variable

And we want to find an equation of the line, we have the following general expression:

[tex]y = mx+b[/tex]

Where m represent the slope and b the y intercept. The general formula for the slope is given by:

[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]

Where [tex] (x_1,y_1) , (x_2,y_2)[/tex] are the minimum required points in order to estimate the slope.

In order to find the y intercept we just need to use one of the points selected [tex] (x_1,y_1) , (x_2,y_2)[/tex] and we can solve for b like this:

[tex] b = y_1 -m x_1[/tex]

Or equivalently:

[tex] b = y_2 - m x_2[/tex]

Answer:

x = 45.

Step-by-step explanation:

As the triangles are similar the corresponding sides are in the same proportion. Therefore:

18 / 2 = x / 5

x / 5 = 9

x = 5*9

x = 45.

Answer:

The decomposition is as shown in the attachment below

Step-by-step explanation:

Where A, B, C, D, E, F, G, H, I, J are numerical value of the coefficients that can be determined by method of comparing coefficients. Hence , there are two methods for solving partial fractions ; Cover up method and method of comparing coefficients.

The form of the partial fraction decomposition is as shown in the attachment.

Answer:

what do you need help with?

Step-by-step explanation:

Answer:

It would be 15 cm. because if the triangles are similar then BC = EF

Answer:

1. 20-15/0-8= -5/8

Step-by-step explanation:

2. In a positive slope the Y value increases as the X value increases (as the line moves towards the right it gets higher). In a negative slope the Y value decreases as the X value increases (as the line moves towards the right it gets lower). (Question 3 is in here)

4. It depends on the amount of time she's been driving

By considering the number of House members who voted in favor and against as variables and applying simple algebra, we find that 242 members voted in favor of the bill and 193 members voted against.

We can solve this question using simple mathematics or algebra. Let's consider the number of members who voted in favor as 'F' and against as 'A'. The total number of House members (435) is their sum (F + A). Moreover, we know there are 49 more members who voted in favor than against (F = A + 49).

Substituting the second equation into the first, we have: A + 49 + A = 435. If we simplify that by combining like terms, we get: 2A + 49 = 435. Subtracting 49 from both sides will result in 2A = 386. Dividing both sides by 2, we get A = 193. As we have 'A', we can now determine 'F' with the equation F = A + 49, which means F = 193 + 49 = 242. Thus, there were 242 members who voted in favor and 193 members who voted against.

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Answer:

The answer to your question is y = -11/2x - 19

Step-by-step explanation:

Data

Point (-4, 3)

⊥ to the line x- intercept of 22 and y-intercept of -4.

Process

1.- Find the equation of the perpendicular line

This line has passes through the points  (22, 0) and (0, -4)

Slope = [tex]\frac{-4 - 0}{0 - 22} = \frac{-4}{-22} = \frac{2}{11}[/tex]

2.- Find the slope of the new equation

Slope = [tex]\frac{-11}{2}[/tex]    because the lines are perpendicular

3.- Find the equation of the new line

            y - 3 = -11/2 (x + 4)

            y - 3 = -11/2x - 44/2

            y - 3 = -11/2 x - 22

            y = -11/2 x - 22 + 3

            y = -11/2x - 19

See the graph below

Answer:

Step-by-step explanation:

Final answer:

It takes 35 hours for the blood concentration of tadalafil to fall to 25% of its initial strength, given a half-life of 17.5 hours.

Explanation:

We can determine how long it takes for the blood concentration of a drug to fall to a certain percentage of its initial strength by knowing the drug's half-life. In this case, a half-life is the time required for the concentration of the drug to reduce to half its original value. For tadalafil 10mg/tab with a half-life of 17.5 hours, we want to calculate when the concentration falls to 25% of its initial strength.

To reach 25% of the original concentration, the drug needs to go through two half-lives (each half-life reduces the concentration by half):

Therefore, it will take 35 hours for the blood concentration of tadalafil to fall to 25% of its initial dosage, which corresponds to Option C.

Answer: the number of hot dogs that were purchased was 27

the number of bags of popcorn that were purchased was 13

Step-by-step explanation:

Let x represent the number of hot dogs that were purchased.

Let y represent the number of bags of popcorn that were purchased.

A group of 40 children attend a baseball game on a field trip. Each child received either a hot dog or a bag of popcorn. It means that

x + y = 40

Hot dogs were $2.25 and popcorn was $1.75. If the total bill was $83.50. It means that

2.25x + 1.75y = 83.50 - - - - - - - - - -1

Substituting x = 40 - y into equation 1, it becomes

2.25(40 - y) + 1.75y = 83.50

90 - 2.25y + 1.75y = 83.50

- 2.25y + 1.75y = 83.50 - 90

- 0.5y = - 6.5.y = - 6.5/ -0.5

y = 13

x = 40 - y = 40 - 13

x = 27

Answer:

D = -4

E = 2

Step-by-step explanation:

The procedure for completing the square method is given as:

x2 + bx + c = 0

x2 + bx = -c

x2 + bx + (b/2)2 = -c + (b/2)2

Aolving the LHS simultaneously,

(x + b)2 = -c + (b/2)2

Find the square root of both sides,

(x + b) = sqrt(-c + (b/2)2)

So for the equation, x2 - 8x + 12

x2 - 8x = -12

x2 - 8x + 16 = -12 + 16

(x - 4)2 = 4

So square root both sides,

(x - 4) = 2

Comparing this to the equation given,

(x - D) = E;

D = -4

E = 2

Answer:

a. The ball enters the green at Q (-13.46, -32.31)

b. 3.189s

c. 5.824s

d. Closest point =  (10.77, -16.15), it occurs 6.102s after the ball starts its journey

Step-by-step explanation:

he rightmost edge is taken as the right end of the horizontal diameter

Coordinates of the hole at H:(0,0)

Coordinates of the ball B:(-40,-50)

Coordinates of the point the ball exits green P:(35,0)

So, the line joining B and P is given by

Looking for the gradient of the line B P we have

(x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50))

 = 75/50=3/2

The line equation therefore = (y-(-50))/(x-(-50)) = 2/3

(y + 50)/(x+40) =2/3

y+50 = 2/3 (x+40)

The equation of a circle is given by

x^2+y^2 = 35^2

 solving the two equations we have

x = ((3y+150)/2)-40 = 1.5y-35

Substituting the value of x into the above equations we have (1.5y-35)2 + y2 = 352

3.25×y2+105×y = 0

From where we have y×(3.25×y + 105) = 0

From where y = 0 or y = -105/3.25 = -32.31m

Also x = 35 or x = -13.46

The line intersects the circle at

Q:(-13.46,-32.31) and P:(35,0)

a. The ball enters the green at Q (-13.46, -32.31)

b. The ball enters the green after (length BQ)/Velocity

Where length BQ is given as

√((-13.46-(-40))2+(-32.31-(-50))2) = √(26.532+17.692)  = 31.89ft

The ball enters after 31.89ft/10ft/s or 3.189s

c. To find out how long the ball spends inside the green we have

Q:(-13.46,-32.31) and P:(35,0)

Length QP2 = (-13.46-(35))2 + (-32.31- 0)2 = 3392.31 = 58.24m

Time spent in the green = 58.24/10 = 5.824s

d. The ball is closest to the cup at the point when the perpendicular from the cup intersects the line PQ

and this is at the center of the line PQ hence the locus of the point is

((-13.46 + (35-(-13.46))/2), (-32.31+(0-(-32.31))/2) =  (10.77, -16.15)

This occurs at (√( (10.77-(-40))2 + (-16.15(-50))2))/10 = 61.02ft/10ft/s = 6.102s after the ball starts its journey

As the cup of the 9th hole in the golf course is located as the dead in the center of the milled green circular shape that is 70 feet. A ball follows the straight-line path and exists at the fright most edge.  

Learn more about the hole of a golf course is located dead center in the middle.

brainly.com/question/2553954.

Answer:

[tex]11x+4y=264[/tex]

Step-by-step explanation:

an equation of the line in the form ax+by=c

y intercept is 66. at y intercept x is 0 . so y intercept point is (0,66)

x intercept is 24. at x intercept y is 0 . so x intercept point is (24,0)

slope m formula is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plug in the values in the formula and find out m

[tex]\frac{66-0}{0-24}=-\frac{11}{4}[/tex]

[tex]y=mx+b[/tex]

b is the y intercept 66

[tex]y=-\frac{11}{4} x+66[/tex]

multiply the whole equation by 4

[tex]4y=-11x+264[/tex]

add 11x on both sides

[tex]11x+4y=264[/tex]