a right triangle has legs of 3 inches and 4 inches whose sides are changing. the short leg is increasing by 7 in/sec and the long leg is growing at 9 in/sec. what is the rate of change of the hypotenuse?

The sides of the triangle based on the information will be 5 unit, 5 units and 6 units.

From the information, we are given that the isosceles triangle and a square have the same perimeter and we want to find the side lengths of the triangle.

It should be noted that a isosceles triangle has two sides that are equal. In this case, the perimeter of the square and Triangle is the same. The perimeter will be:

= 4 + 4 + 4 + 4

= 16 units.

Therefore, the sides of the triangle will be calculated thus:

3x + 2x + 1 + 2x + 1 = 16

7x + 2 = 16

7x = 16 - 2

7x = 14

Divide

x = 14 / 7

x = 2

The sides will be:

3x = 3 × 2 = 6

2x + 1 = 2(2) + 1 = 5

2x + 1 = 2(2) + 1 = 5

Learn more about Triangle on

brainly.com/question/17335144

#SPJ1

Answer:

800 km/h

Step-by-step explanation:

speed = distance ÷ time

=1200km ÷ 1½

=800 km/h

This simplifies to x<3/2. So the graph of f(x) = –x^2 + 3x + 8 is increasing over the interval (-infinity,3/2)

Generally, The vertex form of a parabola that opens downward is

f(x) = a(x-h)^2 + k,

where (h,k) is the vertex of the parabola.

We know that the vertex of the parabola is at (1.5, 10) so we can use that to find the value of a and h. So,

f(x) = a(x-1.5)^2 + 10

Given that the parabola goes through (- 2, - 2) and (5, - 2), we can substitute these points into the equation to find a and k.

Substituting (-2, -2) into the equation:

-2 = a((-2) - 1.5)^2 + 10

Substituting (5, - 2) into the equation:

-2 = a(5 - 1.5)^2 + 10

Solving these two equations will give you a = -1/2 and k = -8

So the equation is f(x) = -1/2(x-1.5)^2 - 8

The graph of a parabola is increasing on the interval where the derivative is greater than 0.

To find the derivative, we use the power rule and the chain rule:

f'(x) = -1/2(2x-3)

= -x+3/2

So, the graph of f(x) is increasing when -x+3/2 > 0

Read more about interval

https://brainly.com/question/13708942

#SPJ1

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

1. Identify the two numbers you want to compare as the numerator and denominator

2. Divide the numerator by the denominator

3. The resulting answer is the ratio of the two numbers

To find a ratio in 8th grade math, divide the numerator by the denominator to get the ratio.

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

Margin of error is 0.017 pound(approximately.)

Now, According to the question:

We know that:

Formula of margin of error :

E = [tex]z^*[/tex] × [tex]\frac{s}{\sqrt{n} }[/tex]

where:

z* = critical value for confidence interval

s= standard deviation

n= sample size.

We have:

s= 0.15 pound

n= 300

Critical value for 95% confidence = 1.96

Then, Margin of error for 95% confidence interval will be :

E = (1.96)[tex]\frac{0.15}{\sqrt{300} }[/tex]

E = 0.0169740971 ≈ 0.017

Hence, Margin of error is 0.017 pound (approximately.)

Learn more about Margin of Error at:

https://brainly.com/question/10501147

#SPJ4

The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.The best method and reasoning to calculate the gas mileage is: D. 243.8 miles ÷ 7.71 gallon s

​The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.

The best method and reasoning to calculate the gas mileage is:

D. 243.8 miles ÷ 7.71 gallon s

because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

The mileage of the car is calculated by dividing the number of miles traveled by the amount of gas used.

mileage

= 243.8 /7.71

From the given parameters;

The unit of miles traveled is miles

The unit of gallons used is gallons

Because the miles traveled is divided by the gallons used, then the unit of the mileage would be miles per gallon

To learn more about mileage refer

https://brainly.com/question/24937565

#SPJ1

A day is a unit of time and cannot be divided into a fraction,  Therefore Wesley would need to run for at least 5 days to meet his goal of 19 miles.

To find out how many days Wesley needs to run to meet his goal, we need to divide the total distance he wants to run (19 miles) by the distance he runs each day (4.2 miles):

19 miles ÷ 4.2 miles/day = 4.52 days

Since a day is a unit of time and cannot be divided into a fraction, Wesley would need to run for at least 5 days to meet his goal of 19 miles.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

Answer:

There are many varying characteristics and exceptions to each type of protist.

They have been previously categorized based on what they are not.

Recent studies show that protists have not descended from one common ancestor.

Step-by-step explanation:

The minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of miles per hour is 4.8708 seconds.

We can solve this problem easily by using the Pythagorean Theorem. This is because the distances from the cop car to the road form two legs of a right triangle. This makes the total length of this zone the hypotenuse of this triangle and thus, this problem can be solved using the Pythagoras theorem.

= (150)^2 + (200)^2 = h^2

= 62500 = h^2

= h = 250

Our distance is in feet, but our speed is in miles per hour. Let's convert this distance into miles as well.

= 250 feet × 1 mile/5280 feet = 0.04735 miles

Then, when we use the formula  d = rt

= 0.04735 = 35t

= 0.04735/ 35 ≈ 0.001353

Since our speed was in miles per hour, this time is also in hours. We need to convert this to seconds before we can state our final answer.

= 0.001353 hours × 60 minutes/1 hour × 60 seconds/1 minute = 4.8708 sec

Learn more about the Pythagoras theorem on

https://brainly.com/question/343682?referrer=searchResults

#SPJ4

The horizontal asymptote is y = -2

What do you mean by asymptote?

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity. The curves visit these asymptotes but never overtake them.

The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.

Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.

The function given is, f(x) = (-2x²+3x+5)/(x²+1)

Horizontal asymptote is given by

y   = -2

So the horizontal asymptote of f(x) is, y = -2

Learn more about  asymptotes at

brainly.com/question/1851758

#SPJ4

The per-pound cost of ham, turkey, and roast beef is $8.29, $10.5, and $14.67. Here, ham is the least expensive meat.

The ratio is defined as the relationship between two magnitudes of similar size in terms of how often the first contains the second.

The cost of 1.75 pounds of ham is given as $14. 50. Let's consider the cost per pound of ham is x and this is calculated as follows,

[tex]\begin{aligned}\frac{1.75}{\$14.50}&=\frac{1}{x}\\1.75\times x&=\$14.50\\x&=\$8.29\end{aligned}[/tex]

The cost of 2.5 pounds of turkey is given as $26. Let's consider the cost per pound of turkey as y and this is calculated as follows,

[tex]\begin{aligned}\frac{2.5}{\$26.25}&=\frac{1}{y}\\2.5\times y&=\$26.25\\y&=\$10.5\end{aligned}[/tex]

The cost of 0.375 pounds of roast beef is $5.50. Let's consider the cost per pound of roast beef as z and this is calculated as follows,

[tex]\begin{aligned}\frac{0.375}{\$5.50}&=\frac{1}{z}\\0.375\times z&=\$5.50\\z&=\$14.67\end{aligned}[/tex]

From the above values we conclude, z>y>x. So the cost of ham is the least expensive.

To know more about ratios:

https://brainly.com/question/29061691

#SPJ4

The required number of ways to choose a pair of socks, provided that i get two socks of the same color are 50.

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

We have,

8 white, 6 brown, and 4 blue

So, We need to choose a pair of socks, provided that i get two socks of the same color.

The number of ways are;

Ways to choose 2 white =  C(8,2)  = 28

Ways to choose 2 brown = C(6,2)  = 16

Ways to choose 2 blue  = C(4,2)  = 6

So

28 + 16 +  6  =

50 ways

Thus, required total number of ways are 50.

To know more about Combination visit:

brainly.com/question/20211959

#SPJ4

Answer:

(a) 8800000

(b) Barcelona had the least population in 2018

(c) The difference in population is 2.9 x [tex]10^{7}[/tex]

Step-by-step explanation:

(a) Since '10' is raised to a positive power, the decimal will be moving in the forward direction, In other words, it will move towards the right. Therefore, the decimal will be moving 6 places forward. After which, the empty slot(s) will be occupied by zeros

8.8 x [tex]10^{6}[/tex] = 8800000

(b) First notice that three out of the five cities have population expressed in [tex]10^{6}[/tex] (where 6 is the least power). Then notice that out of those three cities, the smallest number corresponds to Barcelona (i.e. 5.5).

Therefore, Barcelona had the least population in 2018

(c) Population of:

Tokyo: 3.7 x [tex]10^{7}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

First, make sure the two numbers are expressed in the same standard form (meaning 10 is raised to the same power in both cases):

Tokyo: 3.7 x [tex]10^{7}[/tex] = 3.7 x 10 x [tex]10^{6}[/tex]  =37 x [tex]10^{6}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

Next step:

37 x [tex]10^{6}[/tex] - 7.7 x [tex]10^{6}[/tex]

= (37 - 7.7) x [tex]10^{6}[/tex]

= 29.3 x [tex]10^{6}[/tex]  

= 29 x [tex]10^{6}[/tex] (Corrected to 3 significant figures)

= 2.9 x 10 x [tex]10^{6}[/tex]

= 2.9 x [tex]10^{7}[/tex]

Using probability the value of p + q = -0.4

Probability is the likelihood of an event.

Given the Venn diagram and that the probabilities are independent events.

The probability of A or B is given by

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Also, the probability of A and B is given by P(A ∩ B) = P(A)P(B)

So, we have that

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = P(A) + P(B) - P(A)P(B)

From the Venn diagram, we have that

P(A) = p + q

P(B) = q + 0.6

P(A ∩ B) = q

P(A ∪ B) = 0.2

So, substituting these into the equation, we have that

P(A ∪ B) = P(A) + P(B) - P(A)P(B)

0.2 = p + q + q + 0.6 -  q

0.2 = p + 2q - q + 0.6

0.2 - 0.6 = p + q

-0.4 = p + q

So, the value of p + q = -0.4

Learn more about probability here:

brainly.com/question/25839839

#SPJ1

You can order 6 different one-topping pizzas. You can order 15 different one-topping pizzas.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

Case 1: one-topping pizzas

The number of different toppings is 6.

Selecting one topping is ₆C₁  = 6!/[1!5!] = 6

Case 2: two-topping pizzas

The number of different toppings is 6.

Selecting two topping is ₆C₂  = 6!/[2!4!] = 15

To learn more about combination and permutation, click on the below link:

https://brainly.com/question/29809260

#SPJ4

The larger possible angle of sin Ф = (5/9) is 34°.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

sin Ф = 5/9

Ф = [tex]sin^{-1}[/tex] (5/9)

Ф = 33.75

This means,

Ф =33° or 34°

Thus,

The larger angle is 34°.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer:

A = -5

B = -2

C = 3

The greatest number of police officers needed is 28.

In a scenario where there are n straight lines in a city, and none of the lines are parallel to each other, the maximum number of police officers needed at the intersections can be determined by using the summation formula. The summation formula for the series of numbers from 1 to n-1 is (n-1) * n / 2.

Thus, if there are 8 straight lines in a city, the maximum number of police officers needed at the intersections is (8-1) * 8 / 2 = 28. This is because there will be 8-1 = 7 intersection points in total, and at each intersection point, one police officer is needed.

It's important to note that this is the maximum number of officers needed and it assumes that all lines are intersecting at different points. In case of any parallel lines this number would be less.

Read more about Non-Parallel Lines:

https://brainly.com/question/22061724

#SPJ4

Buffalo Mild Wings offers the lowest price per wing.

Lowest Price:

Demands for the lowest possible price are more commonly seen in markets with limited liquidity or low trading volume, or from traders in companies with very small market caps. This is because investors trading illiquid securities are less likely to fill buy and sell orders. Markets for less traded securities are more limited and other parties can charge prices that may not be ideal for investors. For example, investors who want to trade currency options in foreign currencies (i.e. currencies other than dollars, euros, pounds or yen) often use the lowest possible price.

According to the Question:

Given:

Buffalo Bills has 8 wings for $7.

Buffalo Mild Wings has 12 wings for $10.

Wingers has 20 wings for $17.

To Find:

Which restaurant offers the lowest price per wing?

Solution:

Find the price per wing in Buffalo Bills:

8 wings = $7

1 wing = 7 ÷ 8

1 wing = $0.875

Find the price per wing in Buffalo Mild Wings:

12 wings = $10

1 wing = 10 ÷ 12

1 wing = $0.833

Find the price per wing in Wingers:

20 wings = $17

1 wing = 17 ÷ 20

1 wing = $0.85

Now,

Comparing  $0.875 , $0.833 and $0.85:

$0.833 < $0.85 < $0.875

⇒ $0.833 is the cheapest

⇒ Buffalo Mild Wings is the cheapest

Answer: Buffalo Mild Wings offers the lowest price per wing

Complete Question:

Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 8 wings for $7. Buffalo Mild Wings has 12 wings for $10. Wingers has 20 wings for $17. Which restaurant offers the lowest price per wing?

Learn more about Lowest Price:

https://brainly.com/question/29012342

#SPJ4

The number of possible values for m is 3.

An integer a is its own inverse mod m if a * a^(-1) = 1 (mod m)

For the first condition, 9 is its own inverse mod m, 99^(-1) = 1 (mod m)

so 99^(-1) = 1 + km for some integer k.

so 9*9^(-1) - 1 = km

so 8 = km

so m must be a divisor of 8.

For the second condition, 3 is not its own inverse mod m, 33^(-1) ≠ 1 (mod m)

so 33^(-1) = 1 + km for some integer k, k ≠ 0

so 3(3^(-1) - 1) = km

so 3(3^(-1) - 1) = km

so 3(1 - 3^(-1)) = km

so 3(1 - 9^(-1)) = km

so 3(8 - 9^(-1)) = km

so 38 - 39^(-1) = km

so 24 - 39^(-1) = km

so 24 - 27^(-1) = km

so 24 - 27^(-1) = km

so -327^(-1) = km

so -33^(-1) = km

so -33^(-1) = km

so 33^(-1) - 1 = km

so 33^(-1) = 1 + km

so 3*3^(-1) ≠ 1 (mod m)

The only positive integers that divide 8 are 1,2,4 and 8. Out of these, only 8 is not a solution. So the number of possible values for m is 3.

Therefore, The number of possible values for m is 3.

To learn more about the inverse mod,

Visit; brainly.com/question/30089810

#SPJ4

Answer:

6a-2b-3c+4d

Step-by-step explanation:

2a+4a = 6a

b-3b = -2b

-c-2c = -3c

-d+5d = 4d

Answer:

6a - b - 3c + 4d

Step-by-step explanation:

⭐What is a polynomial?

Whenever you add polynomials, the only terms you can perform addition or subtraction on are like terms.

⭐What are like terms?

We are asked to add the two given polynomials. Therefore, we have to add the like terms.

[tex]2a + b - c - d + (4a - 3b - 2c + 5d)[/tex]

a and a, b and b, c and c, and d and d all have the same variable with an exponent of 1.

When adding, make sure to utilize the correct addition rules.

⭐What are the rules for adding real numbers?

2a and 4a are positive. Therefore, 2a + 4a = 6a.

-3b is negative, but b is positive. -3b > b. Therefore, -3b + b = -2b.

-c and -2c are both negative. Therefore, -2c - c = -3c.

-d is negative, but 5d is positive. 5d > -d. Therefore, -d + 5d = 4d.

∴ [tex]2a + b - c - d + (4a - 3b - 2c + 5d) = 6a -b -3c + 4d[/tex]

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

C)  x = -1, y = 2

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}2x + 5y = 8\\4x + 3y = 2\end{cases}[/tex]

Multiply the first equation by -2:

[tex]\implies -2 \cdot 2x -2 \cdot 5y=-2 \cdot 8[/tex]

[tex]\implies -4x-10y=-16[/tex]

Add this to the second equation to eliminate x:

[tex]\begin{array}{crcrcr}& 4x & + & 3y & = & 2\\+&(-4x & - &10y&=&-16\\\cline{2-6}&&-&7y&=&-14\end{array}[/tex]

Solve for y:

[tex]\implies -7y=-14[/tex]

[tex]\implies \dfrac{-7y}{-7}=\dfrac{-14}{-7}[/tex]

[tex]\implies y=2[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 2x+5(2)=8[/tex]

[tex]\implies 2x+10=8[/tex]

[tex]\implies 2x=-2[/tex]

[tex]\implies x=-1[/tex]

Therefore the solution to the given system of linear equations is:

Answer:

c

Step-by-step explanation:

just trust me

Answer:

Step-by-step explanation:

A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.

making it a 33% chance of one of the toddler triplets to end up with their own coat.

100% divided by 3 = 0.33

There is exactly a 33% chance for one of the toddler triplets to end up with their coat.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of coat = 3

Red, green, and blue.

Now,

Each of them picks up a coat at random and goes out.

The chance of each of them getting their own coat.

= 1/3 x 100

= 33%

Thus,

There is a 33% chance that one of the toddler triplets ends up with their coat.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

For the series to converge, the limit as n approaches infinity of (x + 9)n must be less than 1.

Value is an important concept in economics and business that refers to the worth of a product, service, or asset. It is a measure of the relative worth of something compared to other similar items. Value can be determined by a variety of factors, such as the quality, condition, and availability of an item. It can also be based on a customer's perception or opinion of a product or service. Values can vary from person to person, and can even change over time. Ultimately, value is a subjective concept that is determined by the beliefs and preferences of individuals.

This can be expressed as x + 9 < 1, so the values of x for which the series converges is x < -8. The sum of the series for these values of x is the geometric series:

Sum = (x + 9)1 / (1- (x + 9)) = -8.

To know more about value click-
https://brainly.com/question/24281057
#SPJ4

Answer: a = 3, b = 1

Step-by-step explanation: There is nothing to be done except solving the equation together:

x - y = 2 => x - 2 = y (Equation 1)

x + y = 4 => 4 - x = y (Equation 2)

x - 2 = 4 - x ==> x should be 3 in this case. (a = 3)

If x or a is equal to 3, we can use this value to find y (or b).

Solving for the first equation:

x - y = 2 ==> (3 - y = 2)

y is equal to 1.

The equation representing the situation is y = 20.79+4x, where y is total cost and x is GB used.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Rick's Phone Service charges $20.79 for an activation fee plus $4 for every gigabyte (g) used.

If total charge for x GB used is y, then the equation to represent the situation is ;

y = 4x + 20.79

The graph of the equation is attached.

Learn more about equations, click;

https://brainly.com/question/29657983

#SPJ1

the value of p and d are P = [v1, v2, v3] = [[-1, 1, 1], [1, 1, 1], [1, 1, 1]] and

D = [[-3, 0, 0], [0, 12, 0], [0, 0, 12]]  To diagonalize a matrix A, initially the value of  eigenvalues and eigenvectors to be find. The eigenvalues of the matrix are λ = -3 and 12.

The eigenvectors for λ = -3 are obtained by the solutions to the equation given as:

(A - λI)v = 0 then,

(A + 3I)v = 0

hence

| 2 5 5 | |v1| | 0|

| 5 2 5 | . |v2| = | 0|

| 5 5 2 | |v3| | 0|

hence The solution obtained by the  equation is given by:

v1 = -v2 + v3

The eigenvectors for λ = 12 are obtained by the solutions to the equation:

(A - λI)v = 0

Which is:

(A - 12I)v = 0

Which is:

| -10 -5 -5 | |v1| | 0|

| -5 -10 -5 | . |v2| = | 0|

| -5 -5 -10 | |v3| | 0|

hence The solution obtained is :

v1 = v2 = v3

So the eigenvectors are:

v1 = [-1, 1, 1] for λ = -3

v2 = v3 = [1, 1, 1] for λ = 12

The matrix P is the matrix whose columns are of  the eigenvectors of A:

P = [v1, v2, v3] = [[-1, 1, 1], [1, 1, 1], [1, 1, 1]]

The matrix D is the diagonal matrix whose diagonal elements are of the eigenvalues of A:

D = [[-3, 0, 0], [0, 12, 0], [0, 0, 12]]

therefore , A can be diagonalized as A = PDP^-1

To know more about eigenvalues , click here:

brainly.com/question/29579848

#SJ4

Answer:

19

Step-by-step explanation:

If g(x) = [tex]x^{2} + 3[/tex], then we will substitute 4 in for x, giving us:

[tex]4^{2} + 3[/tex]

Simplifying:

[tex]16 + 3 = 19[/tex]

So g(4) = 19.

Hope this helped!