two different possibilities for the angle measures of an isosceles triangle.

The rate at which the distance between the car and the truck is changing when the car is 9 m from the intersection and the truck is 40 m from the intersection is about 19.187 m/s

The rate of change of a function is an indication of how fast the function's output changes per unit change in the input of the function.

Let y represent the distance of the car from the intersection, and let x represent the distance of the truck from the intersection, we get;

The distance between the car and the truck, d, can be obtained from Pythagorean Theorem as follows;

d² = y² + x²

2·d·d/dt = 2·y·dy/dt + 2·x·dx/dt

dy/dt = The speed of the car = 48 km/h = 40/3 m/s

dx/dt = The speed of the truck = 60 km/h = 50/3 m/s

y = The distance of the car from the intersection = 9 m

x = The distance of the truck from the intersection = 40 m

d² = 9² + 40² = 1681

d = √(1681) = 41

d = 41 m

Therefore;

2×41×d/dt = 2×9 × 40/3 + 2 × 40 × 50/3 = 4720/3

d/dt = 4720/3/(2 × 41) = 2360/123 ≈ 19.187

d/dt ≈ 19.187 m/s

The rate of change distance between the car and the truck d/dt is about 19.187 m/s

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Answer: 108

Step-by-step explanation: Let the total number of sweets be x

Therefore, Anna  - (x/3)+8

After Anna, remaining amount is x - ((x/3)+8) = 2x/3 + 8

Betty took (2x/3 + 8)/2 + 18 = x/3 + 22

Remaining = x - ((x/3)+8) - (x/3 + 22) = x/3 -30

Candy took the rest which is 6 i.e.

x/3 - 30 = 6

x/3 = 36

x = 108

Answer:

Step-by-step explanation:

At equilibrium price and quantity, the answer is 1. The quantity supplied equals the quantity demanded.

This means that the market is in a state of balance, where the quantity of a good or service that producers are willing to supply is exactly the same as the quantity that consumers are willing to buy. As a result, there is no excess supply or excess demand, and the price of the good or service is stable.

Answer:

three sides measuring 4 ft, 8 ft, and 10 ft

Step-by-step explanation:

To choose which dimensions that can create more than one triangle, we consider the given values carefully and how possible it will be to construct.

The only dimensions given in the option that will be possible to create more than one triangle from it, is three sides measuring 4 ft, 8 ft, and 10 ft.

4 ft, 8 ft, and 10 ft are in simple multiple of 2

4 ft, 8 ft, and 10 ft  = 2 (2 ft, 4 ft, and 5 ft ), with this we can construct two triangles with three sides measuring 2 ft, 4 ft, and 5 ft.

Answer:

d

Step-by-step explanation:

To find the value in the blank, we need to use the next exponential properties:

Power of a power:

Using this rule:

Product of the exponents:

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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The college student can spend $35 in December to achieve his goal of a mean spending of $60 per month for the remaining five months.

To find out how much the college student can spend in December, we need to consider the total amount he has already spent in the first four months and his goal of having a mean spending of $60 per month for the remaining five months.

Let's calculate the total amount spent in the first four months:

Total spent = $65 + $55 + $70 + $75 = $265

The student's goal is to spend a mean of $60 per month for the remaining five months. Since there are five months remaining, the total amount he plans to spend is:

Total planned spending = $60 * 5 = $300

To find out how much he can spend in December, we subtract the total spent in the first four months from the total planned spending:

Amount he can spend in December = Total planned spending - Total spent

= $300 - $265

= $35

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Let us use the equality postulate.

Since each class fills 3/4 bus, we will say:

1 class = 3/4 buses

For us to get the number of classes riding on the 5 1/4 buses for the field trip, we will express this as:

x classes = 5 1/4 buses

Solving both expression

1 class = 3/4 buses

x classes = 5 1/4 buses

you will need to cross multiply from here:

3/4 * x = 1 * 5 1/4

3/4 x = 21/4

multiply both sides by 4

3x/4 * 4 = 21/4 * 4

3x = 21

Divide both sides by 3:

3x/3 = 21/3

x = 7

Therefore 7 classes are riding on the bus.

On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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Step-by-step explanation:

Mathematically the statement can be written as

SUPPLEMENTARY Angles add up to 180°

x+y=180°....(1)

let y be the larger angle and x be the smaller angle.

y=x+88°....(2)

plug in the (2) in the first equation

\(x + (x + 88) = 180 \\ 2x + 88 = 180 \\ 2x = 180 - 88 \\ 2x = 92 \\ \frac{2x}{2} = \frac{92}{2} \\ x = 46\)

the measure of the larger angle is y=x+88°

\(y = 46 + 88 \\ y = 134\)

The bigger angle is equal to 134°

HOPE THIS HELPS!!!!

Answer: 134°

here's your answer

Therefore, Heather can make a maximum of 4 biscuits with the given ingredient quantities.

To determine how many biscuits Heather can make, we need to compare the amount of each ingredient required for a single biscuit to the total amount of ingredients she has.

Let's calculate the number of biscuits she can make based on the ingredient quantities provided:

First, we need to find the ratio of each ingredient required per biscuit:

Flour: 100g per biscuit

Butter: 120g per biscuit

Icing sugar: 80g per biscuit

Chocolate: 25g per biscuit

Next, we divide the total amount of each ingredient by the respective ratio to find the maximum number of biscuits she can make:

Flour: 2kg / 100g = 20 biscuits

Butter: 1kg / 120g = 8.33 biscuits (approximately)

Icing sugar: 340g / 80g = 4.25 biscuits (approximately)

Chocolate: 200g / 25g = 8 biscuits

Since we can only make a whole number of biscuits, the limiting factor is the icing sugar. Heather can only make 4 biscuits since she has 4.25 times the required amount of icing sugar.

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the counting number just before C5F16 is 3,072.

Answer:

5.4 = 7.56

1.5 = 2.1

Step-by-step explanation:

Just find the answer for 40% of the given meters.

Answer:

Find the perimeter of a park that measures 7 miles by 910 miles. Get the answers you need, now! ... Advertisement tasha005111 is waiting for your help. Add your answer and earn points. kaylapoo34 kaylapoo34 Answer: the answer is 130. Step-by-step explanation: ... 15 Niles and Bob sailed at the same time for the same length of time.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

x is greater than or equal to 3

Step-by-step explanation:

4x-5>7 (equation)

4x>12 (add 5 to both sides)

x>3 (divide both sides by 4)

There's two ways of answering this. You can either check if the points marked on the graph matches each option, or you can also get the equation of the line from the graph.

I'll do the second way. To do this we can see that points (3,12) and (1,4) are marked on the line. And we know that the general equation of a line is:

'm' is the slope and b is the point where the line crosses the 'y' axis. We can see from the graph that b = 0, since the line goes through the origin. So our equation will be something like this:

Finally, to find the slope we use the points. If we have two pair of points (x1,y1) and (x2,y2), the slope is:

In this case, this is:

So, the equation for this graph is:

The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

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Answer:

A= \(R2\) \(\pi\)

Step-by-step explanation:

Answer:

  t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

  sin(12t) = 141/197

  12t = arcsin(141/197)

  t = arcsin(141/197)/12

  t ≈ 0.0664731 . . . . . . . radians

__

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)

Answer:

(B) 2x + 90 = 180 is an equation that could be used to find x.

Step-by-step explanation:

Observing at the triangle, we can see that..

- We are aware of two angel measurements, both of which are 45 degrees.

One triangle is exactly 180 degrees and if you add both 2 angel measurements from the triangles...

45 + 45 = 90 degrees

180 - 90 = 90 degrees

As a result, we know that x = 90. Now we find the equation. Lets look at equation B. ( 2x + 90 = 180 )

Step 1 : 90 should be subtracted from both sides.

2x + 90 − 90 = 180 − 90

2x = 90

Step 2 : Divide both sides by 2.

(When I use the symbol /, it signifies I'm dividing.)

2x/2  = 90/2

x = 45

Step 3: Examine your solution to see whether it is right.

2x + 90 = 180

2(45) + 90 = 180

90 + 90 = 180 ✓

This shows that 2x + 90 = 180 is an equation that could be used to find x.

Hope this helps! :D

Answer:

Respond to the post by acknowledging the person’s argument and explaining why he disagrees.

Step-by-step explanation:

did this on edge

have a good day!!

Answer:

The correct answer is C.) Respond to the post by acknowledging the person’s argument and explaining why he disagrees.

Step-by-step explanation:

I just did the assignment on edge 2020 and got it right

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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Answer:

Step-by-step explanation:

Y = mx +b        / Slope intercept form

  mx - y = -b      / Standard form

6m -2 = -b   / Plug in ( 6,2)

-9m -10 = -b / Plug in  ( -9, 10)

 Solve the system of equation for m and b.

 6m -2 = -9m -10  , then   15m = -8      m = -8/15

     b = -6m +2     ,then         b= -6 ( -8/ 15) +2 = 78/15

    -8/15 X -  y = - 78/15

     8X +15y = 78  / Equation of in standard form

Note: This is a different methods of solving this problem. All methods find their roots coming from the basic premises.

Equation of a line in the slope intersect form is

   Y = mx +b

   To convert to standard form of ax + by =c

      Simply move over the parameters

       mx - y = -b        where a = m , and c = -b

      Then we feed coordinates of 2 points in there

       make a 2 equation with 2 unknown( m,b) to

       solve.

Answer:

5) The third side must be more than 4 and less than 14.

6) The third side must be more than 3 and less than 13.

Step-by-step explanation:

The third side must be more than the difference and less than the sum of the two numbers.

5) 9-5=4

9+5=14

So the third side must be more than 4 and less than 14.

6) 8-5=3

8+5=13

So the third side must be more than 3 and less than 13.

Answer:

15 square meters.

Hope this helped!

Answer:

average=9 hours

Step-by-step explanation:

10hours on Friday

12 hours on Saturday

300 mins to hours= 300÷60=5

5 hours on Sunday

average=10+12+5

average=27

average=27÷3

average=9 hours

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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We need to find the unit rate for this situation.

The graph represents a linear equation. Therefore, the unit rate will be found by getting the slope of the line.

The slope is given by the next formula:

Where m= slope

P1(x1,y1) and P2(x2,y2) are points for the graph

Let's use the given points P1(1,7) and P=(5,35)

Replacing the values:

Then

Hence, we found that the unit rate for the situation is given by 7 miles per gallon.

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?