Calculate the length of the legs of the triangle.

There were originally 10 puppies in the litter, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
We can represent the number of original puppies as "x", and the sequence of events can be represented as:

Sold half of the puppies, so they have x/2 left - 1 sold to the local pet shop.

Sold half of the remaining puppies, so they have (x/2 - 1)/2 left sold to poodle palace.

One puppy was given to Grace, so they have ((x/2 - 1)/2- 1 = x - 2 / 4 - 1 remaining.

Since they are left with x - 2 / 4 - 1  puppies in the end, we can set this equal to 1 (the remaining puppy given to Grace), and solve for x:

x - 2 / 4 - 1  = 1

x - 2 = {1 + 1} * 4
x = 8 + 2
x = 10

Therefore, there were originally 10 puppies in the litter.

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There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

Assume that there are n total secretaries employed by the business.

Either we can select 2 secretaries and 1 non-secretary member, or we can select all 3 members to be secretaries in order to form a committee with at least 2 secretaries.

Out of n, there are binom n2 ways to select two secretaries, and binom n-21 ways to select a non-secretary member from the remaining n-2 non-secretaries.

This means that there are binom n ways to form a committee with 2 secretaries and 1 non-secretary member.

There are binom ways to select each of the three members to serve as a secretary.

There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

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Answer:

9 science books

Step-by-step explanation:

Step 1) 36 - 17 = 19

Step 2) 19 - 10 = 9

Answer: The answer is 3 slices

Step-by-step explanation:

if you cut a pizza into 12 peices and devide it by 4 people each person gets 3

If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.

Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.

If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.

Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.

So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.

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The average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67.

To find the average value fave of the function f(x) = 3x2 + 4x on the interval [-1, 2], solve the definite integral of f(x) over the interval and then divide by the interval length.

The definite integral of f(x) over the interval [-1, 2] can be calculated as follows:

[tex]∫[-1,2] (3x^2 + 4x) dx = [x^3 + 2x^2] between x = -1 and x = 2 = (23 + 2(22)) - ((-1)^3 + 2(-1)^2) \s= 14[/tex]

The interval length is 2 - (-1) = 3.

As a result, the average value fave of f(x) on the interval [-1, 2] is as follows:

fave =[tex](1/3) * ∫[-1,2] (3x^2 + 4x) dx \s= (1/3) * 14 \s[/tex]= 4.67 (rounded to two decimal places) (rounded to two decimal places)

As a result, the average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67

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The plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.

The first step in solving this problem is to recognize that we can use the formula

=> speed = distance/time

to find the time it took for the plane to travel at each speed. Let's denote the time the plane traveled at the first speed (110 mph) as t1, and the time it traveled at the second speed (125 mph) as t2.

We know that the total distance traveled was 595 miles, and the total time taken was 5 hours. Using the formula for average speed, we can write:

Average speed = total distance / total time

Therefore,

Average speed = 595 / 5 = 119 mph

Now we can use the information about the two speeds to set up a system of equations. The first equation relates the total distance traveled at the first speed to the time it took:

110t₁ = d₁

where d1 is the distance traveled at the first speed. Similarly, the second equation relates the total distance traveled at the second speed to the time it took:

125t₂ = d₂

where d₂ is the distance traveled at the second speed.

The total time taken is the sum of the times taken at each speed:

t₁ + t₂ = 5

We now have three equations and three unknowns (t₁, t₂, and d₂). We can use the first two equations to eliminate d₁ and d₂, and then solve for t₁ and t₂.

Multiplying the first equation by 125/110, we get:

125/110 * 110t₁ = 125/110 * d₁

125t₁/110 = d₂

Substituting d₂ in the third equation, we get:

t₁ + 125t₁/110 = 5

Multiplying both sides by 110, we get:

121t₁ = 550

Solving for t₁, we get:

t₁ = 4.55 hours

Substituting t₁ in the third equation, we get:

t₂ = 0.45 hours

Therefore, the plane flew at 110 mph for 4.55 hours and at 125 mph for 0.45 hours.

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Complete Question:

A plane left Kennedy Airport tuesday morning for a 595−mileˏ 5−hour trip.

For the first part of the tripˏ the average speed was 110 mph.

For the remainder of the tripˏ the average speed was 125 mph. How long did the plane fly at each speed.

Answer:

y = (2/3)x + 3

Step-by-step explanation:

first we need to find the y-intercept

we can do this by using what is given, the point (-3,1) and the slope (2/3)

using the slope-intercept formula: y = mx + b.

m = slope

b = y intercept

we can plug in the x and y values we were given

so,

1 = (2/3)(-3) + b

we can now easily solve for b

1 = (2/3)(-3) = b

first multiply

1 = -2 + b

then add 2 to both sides, this way we isolate b

3 = b

now that we have the y intercept we can write the equation of the line

y = (2/3)x + 3

if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.

1 = (2/3)(-3) + 3

multiply first

1 = -2 + 3

add the like terms

1 = 1

The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.

The root of the function is calculated by setting the function equal to zero.

The given function is f (x) = ( x - 6 )²( x + 2 )²

we will separate the two equation and set them equal to zero.

( x - 6 )² = 0  ----  equation  ( 1 )

or

( x + 2 )² = 0 -------- equation ( 2 )

from the first equation, x = 6

from the second equation, x = - 2

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The complete question is below:

Find the roots of f(x) = (x - 6)² (x + 2)²

The number of machines used in order to get to the number 450 from the number 900 is 9.

An expression contains more than one term with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

900 to 450

We need a number of machines such that 450 is the last output starting from 900.

Now,

If we subtract 50 from each consecutive number we get,

900, 850, 800, 750, 700, 650, 600, 550, 500, 450

So,

We use 9 machines to get 450 from 900.

Thus,

9 machines should be used in order to get to the number 450 from the number 900.

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Answer:

The system of equation is y=12x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x - 10 - 4 = 6

5x - 14 = 6

5x = 20

x = 4

Option C is the solution

Answer:

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

Recall triangle angle sum property, the sum of three interior angles is 180°.

Add up the three angle measures, then solve the equation for x:

Substitute the value of x and find the value of each angle:

Quadratic equation gives us the fuel efficiencies of the two cars for the given values of fuel consumption and total distance driven.

Let's denote the fuel efficiency of the first car as x miles per gallon, and the fuel efficiency of the second car as y miles per gallon.

We know that the first car consumed a total of a gallons of gas, and the second car consumed b gallons of gas. If we assume that the fuel efficiencies are constant, then the total distance driven by both cars can be calculated using the formula:

distance = fuel consumed / fuel efficiency

So, the total distance driven by both cars is:

(a/x) + (b/y) = total miles

We also know that the sum of their fuel efficiencies was:

x + y = total miles per gallon

We have two equations and two unknowns, so we can solve for x and y. First, we can solve the second equation for x:

x = total miles per gallon - y

Substituting this expression for x into the first equation, we get:

(a / (total miles per gallon - y)) + (b / y) = total miles

Multiplying both sides by y(total miles per gallon - y) to eliminate the denominators, we get:

ay + b(total miles per gallon - y) = total miles * y(total miles per gallon - y)

Expanding the left side and simplifying, we get a quadratic equation in y:

(total miles^2 - a - b) y^2 + (total miles * a) y - ab = 0

Using the quadratic formula, we can solve for y:

y = [(total miles * a) ± sqrt((total miles * a)^2 + 4ab(total miles^2 - a - b))] / 2(total miles^2 - a - b)

We can then use the equation x = total miles per gallon - y to find the value of x. The gives the fuel consumption of both cars.

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Dilation Starting with our fundamental equation, x^2+y^2=r^2, we can dilate a circle. The point can be found by multiplying the parameters of the vertices in the bounding box by the scale factor when distorting a figure that is centered at the origin.

What does triangle mean?

A triangle is made up of three vertices, three angles, and three sides. A triangle's internal angles add up to 180 degrees. The triangle's third side is longer than the two sides added together. The base plus the height multiplied by half equals the triangle's area.

What are a few examples of dilation?

Dilation refers to a change in size without a change in shape of an object. Depending on the scale, the object's size could grow or shrink.

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Answer: 20 centimeters

Step-by-step explanation:

The radius is half the diameter so then the radius is 20 centimeters.

The distance between the center of the circle to its circumference is the radius. The diameter is always double the radius. Hence, the formula is derived by dividing the diameter by 2.

When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.

An expression is combination of variables, numbers and operators.

Given that Marcia's cost, in dollars, to wash her car can be calculated using the expression

0.25m +1.50

Zero point two five plus one point five.

In the expression m represents the number of minutes the car wash will run.

We need to find the value of expression when m is 20

0.25(20)+1.50

5+1.50

6.5

When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.

Hence, Marcias cost $6.5 to wash her car for 20 minutes.

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A fair coin and a fair six-sided die, the sample space can be represented as:

{ (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6) }

where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.

The sample space for this experiment can be described as the set of all possible outcomes of the coin toss and die cast. One way to represent the sample space is to use the Cartesian product of the sample space for the coin toss and the sample space for the die cast.

where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.

Each element in this sample space represents a possible outcome of the experiment, where the first element represents the outcome of the coin toss and the second element represents the outcome of the die cast. This sample space contains 12 possible outcomes, each with an equal probability of 1/12.

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Answer:

Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X

Step-by-step explanation:

Self-explanatory

Every value of y in Table A is 2.5 times  x value

and

every value of y in table B is 3 times x value

An equation to find the temperature after x number hours of waking up for Jackie is Temperature ( x ) = 4 x + 70

The equation which takes the form y = mx + b means that in relation to the temperature when Jackie woke up:

y = current temperature after x hours

x = number of hours after waking up

m = change in temperature per hour

b = starting temperature when Jackie woke up

The equation to find the temperature after x hours is therefore:

Temperature ( x ) = 4 x + 70

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The value of x to the nearest tenth are as follows;

x = 47.0 units.

x = 25.1 units.

x = 23.8 units.

x = 29.7 units.

x = 21.1°.

x = 39.6°.

x = 58.0°.

x = 72.9°.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = x.

Adjacent side = 25.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan45 = 25/x

x = 25Tan62

x = 47.0 units.

For right-angled triangle 3, we have:

Sin26 = 11/x

x = 11/0.4384

x = 25.1 units.

For right-angled triangle 4, we have:

Sin48 = x/32

x = 32sin48

x = 23.8 units.

For right-angled triangle 5, we have:

Cos12 = 29/x

x = 29/0.9782

x = 29.7 units.

For right-angled triangle 6, we have:

Cosθ = 14/15

θ = cos⁻¹(0.9333)

θ = 21.1°.

For right-angled triangle 7, we have:

Tanθ = 19/23

θ = tan⁻¹(0.8261)

θ = 39.6°.

For right-angled triangle 8, we have:

Cosθ = 9/17

θ = cos⁻¹(0.5294)

θ = 58.0°.

For right-angled triangle 9, we have:

Sinθ = 43/45

θ = sin⁻¹(0.9556)

θ = 72.9°.

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Step-by-step explanation:

Sure, I'd be happy to help!

5 feet 7 inches is equivalent to 170.18 cm.

The percentage of winners driving a Chevrolet who won with an average speed of at least miles per hour is fifty percent (50%).

We can infer that for a Chevrolet car,

the percentage of average speed (in miles/hour) for the range of 150-159.9 is 25%,

the percentage of average speed (in miles/hour) for the range of 160-169.9 is 18.75%,

and the percentage of average speed (in miles/hour) for the range of 170-179.9 is 6.25%.

Thereby, the percentage of winners of the race who were driving a Chevrolet and had an average speed of at least 150 miles/hour is,

50%.

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Answer:

Brand b

Step-by-step explanation:

brand a is 0.165 per ounce

brand b is 0.143 per ounce

brand c is 0.166 per ounce

The system using substitution has its solution to be (-1.8, -1.2)

From the question, we have the following parameters that can be used in our computation:

3x-2y=3

y=6+4x

By susbstitution, we have the following equation

3x - 12 - 8x = 3

Evaluate the like terms

so, we have the following representation

-5x = 9

Divide by 5

x = -1.8

So, we have

y= 6 + 4 * -1.8

Evaluate

y = -1.2

Hence, the value of y is -1.2

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Answer:

maximum score = 92

Step-by-step explanation:

the maximum score is the largest value in the data set.

maximum score = 92

The order of the place value in increasing order is equal to units , tens , hundreds , thousands , ten-thousand and so on.

Therefore, the order of the place value in ascending order of the place of the digit is given by units , tens , hundreds , thousands , ten-thousand and so on.

The given question is incomplete, I answer the question in general according to my knowledge:

What is the order of the place value ?

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