Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet.
Old garden area = New garden area
x2 = (2x)(x – 16)
x2 = 2x2 – 32x
0 = x2 – 32x
What is the value of x that makes sense in this context?
What are the dimensions of the new garden?

The property that Antonio has used is what is called the Subtraction property of equality.

This is the property that tells us in mathematics that is a number is subtracted from an inequality, they would still remain the same.

2x + 1 = 11 is the same thing as also writing  2x = 10. The difference is that the like terms were on the same side.

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Using Trigonometry, the approximate distance from the observatory to the island is evaluated to be 322 feet.

Given Information

It is given that,

The height of the observatory = 150 feet

The angle of depression from the top of the observatory = 25°

We can calculate the horizontal distance of the observatory from the island using Trigonometry

What is Trigonometry?

The area of mathematics known as Trigonometry is concerned with certain functions of angles and how to use them in computations. There are six popular Trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.

Calculating the Horizontal Distance Using Trigonometry

As per the rules of the Trigonometry,

[tex]tan \alpha = \frac{Perpendicular/ Opposite Side}{Base}[/tex]

Here,

[tex]\alpha[/tex] = 25°

Perpendicular = 150 ft.

Base = Horizontal Distance

Thus, [tex]tan 25 =\frac{150}{Horizontal Distance}[/tex]

∴ x ≈ 322 ft.

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[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Which equation represents a line with slope: [tex]\bf{\dfrac{1}{2}[/tex] and y-intercept: [tex]\bf 3[/tex]?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

[tex]\bf{Equation: y=mx+b[/tex]

[tex]\bf{Equation\:with\:the\:given\:information: y=\dfrac{1}{2}x+3}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{y=\dfrac{1}{2}x+3}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Three types of financial institutions and the services they offer include:

Commercial banks:

Insurance company:

Investment banks:

Commercial banks are one of the largest and they offer deposit services to people and companies. They then use these deposits to make loans.

Insurance companies act to protect their clients from financial losses arising from unforeseen circumstances. They also help with wealth accumulation if a claim is not made.

Investment banks are very important for stock issuance, and mergers and acquisitions where they act as financial advisors and facilitators.

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Answer:

this is the example answer.

Step-by-step explanation:

(Answers may vary.)

Bank: Wells Fargo is a commercial bank that provides services for individuals, small businesses, and corporations. The bank manages IRAs (traditional and Roth), which are retirement funds that invest in different stocks and bonds to earn interest. Traditional IRAs offer tax-deferred growth. An individual doesn't have to pay taxes on earnings until he or she is ready to make withdrawals (i.e., after retirement). Roth IRAs offer tax-deferred growth until retirement and tax-free withdrawals while in retirement. The bank offers merchant services for small businesses. The bank processes payments via credit cards, debit cards, checks, gift cards, and international payments. Wells Fargo also gives small businesses options on how to accept customer payments: online shopping carts, mobile apps, and onsite payment processing equipment.The bank offers affordable student loans to cover the cost of tuition, books, computers, and housing. Students are not required to make loan payments until six months after leaving school. The bank offers two types of interest rates on student loans: variable and fixed. Variable interest rates range from 3% to 8% and fixed rates range from 5% to 10%.

Credit union: Navy Federal Credit Union has more than 5 million members. It is available for anyone who is affiliated with the Armed Forces, Coast Guard, National Guard, or the Department of Defense, or anyone who has a family member who is already a Navy Federal member. It offers a fixed-rate home equity loan for members. Home equity loans use a borrower’s home as collateral for the loan. These loans are usually used to pay for major expenses such as home repairs, college education, medical bills, and so on. The borrower can borrow up to 100 percent of the home's property value, with the agreement that the fixed-rate loan will be paid off in 20 years (longest term available). This credit union guarantees no hidden closing costs on the loan. It offers motorcycle, boat, and leisure vehicle loans. The loans require zero down payment and promise to cover the cost of the vehicle/boat, taxes, title, and tags. This is a good loan for someone who has not saved any money prior to choosing to buy a vehicle.It also offers prepaid Visa cards, which are useful for students and young adults who are learning to control expenses. Unlike most prepaid cards, this credit union states there are no hidden monthly fees, activation charges, or purchase fees. The prepaid cards can be loaded up to $10,000 and are protected by the credit union's zero liability policy. There are spending limits associated with the program: an ATM withdrawal limit per day of $600 and a spending limit of $3,000 per day.

Financial service company: First Financial advertises itself to be a leading provider of bad credit auto loans. It markets to individuals and companies who have bad credit ratings and cannot qualify for loans with banks and credit unions.It offers auto loans for anyone who earns $1,500 if the borrower’s credit score is less than 650. People who have filed bankruptcy can also obtain loans. The company’s website does not quote an interest rate or loan term.It offers business loans to high-risk merchants with bad credit. The website does not quote interest rates or loan terms.It offers merchant cash advances, which provide quick cash for businesses. The site does not provide detailed information about this service.

Answer:

Step-by-step explanation:

Comment

Start with the right hand side.

1/2(3 - x)

This reads as The difference between 3 and a number. You put it the way you read it difference between 3 and a number = 3 - x The 1/2 affects both terms. So that makes b and d incorrect.

The left side is a bit harder. You want the sum of 6 + something. Read the rest of the given

6 + 2(x +4)

Now that is all equal to

6 + 2(x + 4) = 1/2 (x - x)

The answer is A

Thw statement that's true for the function g is g(-13) = 20.

From the information given, the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

In this case, g(-13) = 20. Here, x = -13 is in the domain and 20 is also in the range. Therefore, this is true for g.

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There are 28 ways for Mary to put the plants on the sills.

We can use the Binomial Theorem to solve this problem.

We have 6 plants and 3 sills, so we have6 + 3 − 1 = 8 total objects.

Since we have 8 objects, we can use the Binomial Theorem to expand [tex](x + y)^{8}[/tex].

The coefficient   [tex]x^{6} y^{2}[/tex] will be the number of ways for Mary to put the plants on the sills. We can expand [tex](x + y)^{8}[/tex]

using the Binomial Theorem:

[tex](x + y)^{8}=(\left\ {{8}\atop {0}} \right. )x^{8}+ (\left\ {{8}\atop {1}} \right. )x^{7}y+(\left\ {{8}\atop {2}} \right. )x^{6}y^{2} +(\left\ {{8}\atop {3}} \right. )x^{5}y^{3} +(\left\ {{8}\atop {4}} \right. )x^{4}y^{4}+(\left\ {{8}\atop {5}} \right. )x^{3}y^{5} +(\left\ {{8}\atop {6}} \right. )x^{2}y^{6} +(\left\ {{8}\atop {7}} \right. )x^{1}y^{7} +(\left\ {{8}\atop {8}} \right. )y^{8}[/tex]

Since we are only interested in the coefficient of [tex]x^{6} y^{2}[/tex] , we can ignore all terms that do not have [tex]x^{6}[/tex] and  [tex]y^{2}[/tex].

Therefore, we are left with [tex](\left\ {{8}\atop {2}} \right. )x^{6}y^{2}[/tex]

[tex](\left\ {{8}\atop {2}} \right. )=\frac{8!}{2!(8-2)!} =\frac{8!}{2!6!} =\frac{8*7*6!}{2!6!} =28\\[/tex]

Therefore, there are 28 ways for Mary to put the plants on the sills.

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StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

What is partial fraction?

Partial fractions are the fractions used for the decomposition of a rational expression.

Given:

(4x + 40)/ (x + 2)(x + 6) = A/(x + 2) + B/(x + 6)

4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = x(A+B) + 6A +2B

On comparing

4= A+B

A= 4-B

and, 6A +2B =40

3A + B =20

3(4-B) + B =20

12  - 3B + B =20

-2B = 8

B= -4

and, A= 8

Hence, StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

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Answer:

C.

Step-by-step explanation:

photo below

Answer:

⅓ ×½ which will give you ⅙

Step-by-step explanation:

because

The probability that Manu will win the coin flip amongst others is 4/7

To determine the probability that Manu will win, we need to consider the possible outcomes of the coin flips.

Let's break down the scenarios:

Scenario 1: Manu wins on the first flip

- The probability of Manu winning on the first flip is 1/2, as he needs to flip heads right away.

Scenario 2: Manu wins on the second flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the second flip is (1/2) * (1/2) * (1/2) = 1/8.

Scenario 3: Manu wins on the third flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips tails (1/2 probability)

- Juan flips heads (1/2 probability)

- Carlos flips heads (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the third flip is (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/64.

The pattern continues, and we can see that Manu's probability of winning decreases exponentially with each subsequent flip.

Therefore, the total probability of Manu winning is the sum of the probabilities from each scenario:

1/2 + 1/8 + 1/64 + ...

This is an infinite geometric series with a first term (a) of 1/2 and a common ratio (r) of 1/8.

Using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Sum = (1/2) / (1 - 1/8)

Sum = (1/2) / (7/8)

Sum = (1/2) * (8/7)

Sum = 4/7

Therefore, the probability that Manu will win is 4/7.

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Answer:

Step-by-step explanation:

Out of every 20 students, there are 9 that gain admission to s.h.s.

Overall, there are 12,000 students. To find how many groups of 20 students there are, we divide 12,000 by 20. We get 600.

Since there are 9/20 students, we multiply 600 * 9. We get 5,400.

So, out of the 12,000 students, 5,400 gained admission.

Hope this helps.

The assumptions in each case of this statistics problem is given as follows:

ts < tc Do not reject H0

P value > α Do not reject H0

There is insufficient data to determine that the mean scores of the two groups of pupils differ.

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Answer:

None

Step-by-step explanation:

We can eliminate the x's by add the 2 equations :

2y = 18

Divide both sides by 2 :

y = 9

Substitute this value into equation 1 to solve for x :

-3x + (9) = 6

Subtract 9 from both sides :

-3x = -3

Divide both sides by -3 :

x = 1

Substitute these values into equation 2 to check :

-3(1) + 6 = 12 ❌❌

So it has no solution

Answer:

i'm not realy sure what you mean by a table

8x=2x+2

subtract 2x from each side

6x=2

divide by 6

x=1/3

Hope This Helps!!!

Step-by-step explanation:

So if you want to make a table to find the solution, you'll need 3 columns, one will be the value of x, the other two will be the value of the equation (left and right) and then you'll need to look where the two equations are equal, and the solution is whatever the x-value is. It'll look something like this:

[tex]x\ \ \ \ |\ 2x+2\ |8x\\-3\ \| -4\ \ \ \ \ | -24\\-2\ \| -2\ \ \ \ \ |-16\\-1\ \| 0\ \ \ \ \ \ \ \ \ | -8\\0\ \ \ \ \|2\ \ \ \ \ \ \ \ \ | 0 \\1\ \ \ \ \| 4\ \ \ \ \ \ \ \ \ | 8\\2\ \ \ \ \|6\ \ \ \ \ \ \ \ \ | 16\\3\ \ \ \ \|8\ \ \ \ \ \ \ \ \ | 24[/tex]  

As you can see, none of rows (the two right most columns with the equations) are ever equal, on the same row. This is because the solution is not an integer. If you solve it algebraically. You'll get this:

Original equation

8x = 2x+2

Subtract 2x from both sieds

6x = 2

Divide both sides by 6

x = 2/6

Simplify the fraction

x=1/6

Answer: 18

Step-by-step explanation:

(3+6)/2*4

Answer:

18 square feet.

Step-by-step explanation:

   a = 6 ft

   b = 3 ft

   h = 4 ft

a & b are the length of the parallel lines. h is the height between the parallel lines.

[tex]\sf \boxed{\text{\bf Area of trapezoid =$ \dfrac{(a+b)*h}{2}$}}[/tex]

                                  [tex]\sf =\dfrac{(6+3)*4}{2}\\\\=\dfrac{9*4}{2}\\\\= 9 * 2\\\\= 18 \ ft^2[/tex]

When a customer has a 6 pound Chihuahua, the cost that will be charged is $5.00.

a. If a customer has a 6 pound Chihuahua, how much would you charge?

It should be noted that from the information given, for dogs that weigh 0 to 15 pounds, the amount charged is $5.00.

b. If a customer has a 65 pound Labrador, how much would you charge?

It should be noted that for dogs over 45 pounds, the amount that's charged is $9.00

There, the amount charged will be $9.00.

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Answer:

spider : 5

beetle : 6

Step-by-step explanation:

Total number of legs --> 8 + 6 = 14 ( 1 set )

Number of sets that can fit --> 76 ÷ 14 = 5 R 6

Since each set has a beetle and a spider,

Number of spider -->5 × 1 = 5

Since there are additional 6 legs:

Number of beetles --> ( 5 × 1 )+ 1 = 6

Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn - one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins

The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.

Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.

It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.

Also, let [tex]\%R_{A}[/tex] be the quantity of nonzero elements in [tex]R_{A}.[/tex]

Let [tex]C_{1}=\left(\begin{array}{l}1\\ -1\\ 0\\ 0\end{array}\right)[/tex].

Parity demands that [tex]\%R_{A}[/tex] and[tex]\%R_{B}[/tex] must equal 2 or 4.

Case 1: [tex]\%R_{A}[/tex]=4 and [tex]\%R_B[/tex]=4. There are [tex]\left(\begin{array}{l}3\\ 2\end{array}\right)[/tex]=3 ways to put 2-1's in [tex]R_A[/tex], so there are 3 ways.

Case 2: [tex]\%R_{A}[/tex]=2 and [tex]\%R_B[/tex]=4. There are 3 ways to position the -1 in [tex]R_A[/tex], 2 ways to put the remaining -1 in [tex]R_B[/tex] (just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of [tex]\%R_{A}=4,\%R_{B}=2[/tex] for a complete of 24 ways.

Case 3: [tex]\%R_A=\%R_B=2[/tex]. There are 3 ways to put the -1 in [tex]R_{A}[/tex]. Now, there are two cases on what happens next.

Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192

Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.

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The linear equality y < 3x + 2 is represented by the graph attached.

An equation is an expression that shows the relationship between two or more numbers and variables.

An inequality is the non equal comparison of two or more numbers and variables.

The linear equality y < 3x + 2 is represented by the graph attached.

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Answer:

[tex]h(-6)=-(-6)-4\\h(-6)=2[/tex]

Step-by-step explanation:

The congruency statement that describes the figure is: D. ΔRST ≅ ΔBAC.

A congruency statement is a statement that states that two triangles are congruent to each other.

180 degrees rotation around the origin will give us the rule: (x, y) → (-x, -y)

Therefore, applying this rule to triangle RST that was rotated, we would have:

R'(-1, -1)

S'(-3, -4)

T'(-5, 0)

Translating R'S'T' 3 units up, using the rule, (x, y + 3) will give us:

B(-1, 2)

A(-3, -1)

C(-5, 3)

Therefore, we can conclude that, D. ΔRST ≅ ΔBAC.

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Answer:its D just took test:)

Step-by-step explanation:

I honestly have no idea how to slove this question

For real,I don't know. OK

BTW,you nice,keep going

Answer:

third option listed

Step-by-step explanation:

We know that Johnny does not ever stay/wait at the same distance from the wall, as that would look like a flat line (the y-value / distance would be unchanging, it would be constant)

So, the only possibly correct option is C, because all other options describe him pausing

But why is it not A? We know that at "0" y we are at the gym wall, and that each point is a point that he turns around and runs the opposite way. He first runs away, back, away, back, away, back--which we know because of the direction of the line over time. We also can tell that each period of "away, back" is the same distance, and it takes the same time to travel that distance, by looking at the length of each line.

hope this helps!! have a lovely day :)

Answer:

the 3rd answer option

Step-by-step explanation:

as we can see, time is on the x-axis.

(0, 0) means start of the action (0 seconds) with 0 distance to the gym wall.

then we see that for 2 seconds Johnny increases the distance to the gym wall up to 3 units (the line goes to (2, 3)).

then we see that for the next 2 seconds he returns to the gym wall (0 distance).

then for 3 seconds he increases the distance to the gym wall to 5 units. the line goes to (7, 5). and then for the next 3 seconds he returns to the gym wall (0 distance). then for 4 seconds he increases the distance to the gym wall to 7 units. the line goes to (14, 7). abd then for the next 4 seconds he returns to the gym wall (0 distance).

P(1) = P(-1)

P(1) = 3 - a + b
P(-1) = -3 + a + b

-> 3 - a + b = -3 + a + b
-> 3 - a + b + 3 - a - b = 0
-> 6 - 2a = 0
-> a = 3.

P(2) = 24 - 2a + b -> 24 - (2a - b) = 16 -> 2a - b = 8
-> 6 - b = 8
b = -2.

So, a = 3 and b = -2

Recheck : P(1) = 3 - 3 + (-2) = -2
P(-1) = -3 + 3 + (-2) = -2 => P(1) = P(-1) (true)

P(2) = 24 - 6 + (-2) = 16.

Answer:

A linear relationship can be represented by a straight-line graph and by an equation of the form y=mx+b. In the equation, m is the slope of the line, and b is the y-intercept. Used to track changes over short and long periods of time. When smaller changes exist, this graph is better to use than bar graphs.

Step-by-step explanation:

Radius = 14 cm

π = 22/7 (Because the value of the circle's radius is the multiples of 7).

• Perimeter :

= 2 . π . r

= 2 . 22/7 . 14

= 28 . 22/7 (Divide 28 and 7 with 7)

= 4 . 22/1

= 4 . 22

= 88 cm is the answer

Answer: [tex]\cos 34^{\circ}[/tex] and [tex]\sin 56^{\circ}[/tex]

Answer:

Holocene

Step-by-step explanation:

The Holocene began 11,700 years ago after the last major ice age.

The blank space in the task content should be filled with; a 270° rotation about point P.

It follows from the transformation described in the task content that; Triangle KLM from which triangle K'L'M' is rotated 270 degrees about point P and then translated down and to the right.

It therefore follows from observation. that the first transformation is; a 270° rotation about point P.

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