Find the value of each variable. Assume it is a 45 45 90 triangle. Round to the nearest tenth.

The weight in pounds of the fourth dog, is 55 lbs.

What is weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

As given, Ben is walking with three dogs that weigh an average of 75 pounds each. Ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds.

The total weight of the first three dogs is 225 pounds.

This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

\(\frac{d+225}{4} = 70\\d + 225 = 280\\d = 280 - 225\\d = 55 lbs\)

Therefore, the weight of the fourth dog is 55 lbs.

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To plot the function f(x) = -4x^2 + sin(5x) and its derivative, and to save the results in a file named "results.txt" with 2 decimal places.

You can use the following MATLAB code:

```matlab

x = -10:0.5:10; % Generate x values

f = -4*x.^2 + sin(5*x); % Calculate f(x)

df_dx = -8*x + 5*pi*cos(5*x); % Calculate the derivative

% Saving results to file

output = [x', f', df_dx'];

dlmwrite('results.txt', output, 'delimiter', '\t', 'precision', '%.2f');

1. First, we define the range of x values using the vector `-10:0.5:10` to cover the desired interval with a step size of 0.5.

2. Next, we calculate the values of f(x) and its derivative using the defined mathematical expressions.

3. We then plot the function and its derivative using the `plot` function. The red dashed line represents f(x), and the blue solid line represents its derivative.

4. To save the results, we create a matrix `output` that concatenates the x values, f(x), and the derivative column-wise.

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Answer:

1. 22

2. 22

3. 28

Step-by-step explanation:

Substitue the n in each expression with two, then solve the problem for the value

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

300

Step-by-step explanation:

5²•(4+2³)

5²•(4+8)

5²•(12)

5²•12

25•12

300

Answer:

300

Step-by-step explanation:

Answer: x = 15

Step-by-step explanation:

Since they are similar, corresponding angles are equal

m∠A = m∠E

m∠B = m∠F

m∠C = m∠G

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

m∠B = m∠F:

x - 5 = 2/3 x

Solve for x

1/3 x - 5 = 0

1/3 x = 5

x = 15

Zack should use a line with one arrowhead to map an abandoned line of reasoning.

A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.

The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.

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Answer:

15.9375 sq m

Step-by-step explanation:

First convert to meters

4 m 25 cm = 4.25 m

3m 75 cm = 3.75 m

Then multiply 4.25 * 3.75 = 15.9375

Step-by-step explanation:

let eqn be y = mx + b.

m = (-2 - 8)/(1 - 3) = 5

sub (3, 8):

8 = 5(3) + b

b = -7

therefore equation of the line is y = 5x - 7

Topic: coordinate geometry

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Answer:y = 5x - 7

Step-by-step explanation: /

Answer: T= 5 and s =17

Step-by-step explanation: Use the midpoint formula

Solve for T

^xm=^xC+^xD/2

15+t/2=10

15+t=20

Solve for S

^ym=^yC+^yD/2

s+3/2=10

s+3=20

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

First notice that angle C is a right angle, then:

Now, since this is a right triangle, we can find the measure of angle A using the trigonometric function sine:

In this case, we have the following:

Since the sum of the interior angles of a triangle equals 180, we can find the measure of angle B by solving the following equation:

therefore, angle A measures 48.6 degrees and angle B measures 41.4 degrees

We need to solve the next system of linear equations:

Let's pair the equations to eliminate 1 variable.

The first pair, add both equations:

The second pair:

Multiply the first equation by 5 and the second equation by -2:

Then, add both equations:

Now, solve the new system :

Multiply the first equation by 4 and multiply the second equation by -3:

Add both equations:

Solve for z:

To solve for x, replace the z value on one equation:

Finally, replace the z and x values:

Solve for y:

Hence, the result for each variable are:

x= 2

y= 2

z=6

Answer:

4 packages

Step-by-step explanation:

450 can be divided by 100 4 whole times, the extra cards cannot be added into a package

Answer: 4

Step-by-step explanation:

100 can go into 450 only 4 times

Hope this helped

The values of r and s is -1 and -4 respectively.

Given that:-

coordinates of j are (-8,-5)

coordinates of l are (6,-11)

coordinates of k are (r-4,2s)

Also, k is the mid-point of jl.

We have to find the values of r and s.

We know that, for  (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).

Here,

(x,y) = (-8.-5)

(z,w) = (6,-11)

(r-4,2s) = ((x+z)/2,(y+w)/2)

Hence,

(r-4,2s) = ((-8+6)/2,(-5-11)/2)

(r-4,2s) = (-1,-8)

Comparing the coordinates, we get:-

r - 4 = -1

r = -1+4 =3

2s = -8

s =-8/2 = -4

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Polynomial are expression that have a leading degree of 3. The other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3

Polynomial are expression that have a leading degree of 3. Given the following expression

Sum = –yz^2 – 3z^2 – 4y^4.

One of the polynomial = y – 4yz^2 – 3

Required

The other polynomial

Let the unknown polynomial be "a" such that:

a =  –yz^2 – 3z^2 – 4y^4 - (y – 4yz^2 – 3)

Expand

a =  –yz^2 – 3z^2 – 4y^4 - y + 4yz^2 + 3

a = 3yz^2 – 3z^2 – 4y^4 - y + 3

Hence the other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3

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Answer: D. or 3yz^2-3z^2-5y+7

Step-by-step explanation: got it right on edge

Answer:

Option a is the correct answer

Step-by-step explanation:

\( \huge( \sqrt[x]{2})^{ - 1} = {2}^{ - \frac{1}{x} } \)

Using the fundamental theorem of arithmetic, we have proven that (a, 6) [a, b] = ab for positive integers a and b.

To prove that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic, we'll proceed as follows:

Step 1: Prime factorization of a and 6:

Using the fundamental theorem of arithmetic, we can write a and 6 as products of their prime factors:

a = p1^k1 * p2^k2 * ... * pn^kn,

6 = 2^1 * 3^1.

Step 2: Finding the greatest common divisor (a, 6):

To find the greatest common divisor (a, 6), we consider the common prime factors between a and 6 and take the minimum exponent for each prime factor. In this case, the common prime factor is 2 with an exponent of 1. Therefore, (a, 6) = 2^1.

Step 3: Prime factorization of [a, b]:

Using the fundamental theorem of arithmetic, we can write [a, b] as a product of its prime factors:

[a, b] = p1^m1 * p2^m2 * ... * pn^mn.

Step 4: Finding the least common multiple [a, b]:

To find the least common multiple [a, b], we consider the prime factors between a and b and take the maximum exponent for each prime factor. In this case, we have already determined that the common prime factor is 2 with an exponent of 1. Therefore, [a, b] = 2^1.

Step 5: (a, 6) [a, b] = ab:

Substituting the values we found, we have:

(a, 6) [a, b] = 2^1 * 2^1 = 2^2 = 4.

Since ab = 4, we have proven that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic.

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If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

Answer:

1.75a + 8b

Step-by-step explanation:

0.75a + 10b + a - 2b ← collect like terms

= (0.75 + 1a) + (10b - 2b)

= 1.75a + 8b

Answer:

1.75a+8b

Step-by-step explanation:

Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b

                                                     =1.75a+8b

Hence, The required equivalent expression is 1.75a+8b

Answer:

slope = 2/5

Step-by-step explanation:

The slope of the green line would also be 2/5 because in a graph where the lines are parallel, they always have the same slope, since the lines that are graphed are parallel, the slope of the green line will be the same as the slope of the red line.

32% of the same people spend their time listening.

The total number of mentioned  people will be 100% or 1. Now, in the total people, the remaining ones who are not stated in the question, must be the listeners. Thus, calculating the remaining percentage of people, we will get the percentage of listeners in same people.

So, number of people who spend time speaking = 26%

Number of people who spend time speaking = \(\frac{26}{100}\)

Number of people who spend time speaking = 0.26

Number of people who spend time writing =  23%

Number of people who spend time writing = \(\frac{23}{100}\)

Number of people who spend time writing = 0.23

Number of people who spend time reading =  19%

Number of people who spend time reading = \(\frac{19}{100}\)

Number of people who spend time reading = 0.19

Total number of people involved in activities other than listening = 0.26 + 0.23 + 0.19

Total number of people involved in activities other than listening = 0.68

People who spend time listening = 1 - 0.68

People who spend time listening = 0.32

Percentage of people who spend time listening = 0.32 × 100

Percentage of people who spend time listening = 32%

Hence, 32% of the same people spend their time listening.

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Answer:

74.4%

Step-by-step explanation:

Given data

Initial price=$1.25

Final price= $2.18

Required

The percent increase

%increase= FInal-initial/ initial*100

substitute

%increase= 2.18-1.25/ 1.25*100

%increase= 0.93/ 1.25*100

%increase= 0.744*100

%increase= 74.4%

Hence the percent increase is 74.4%

Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c:  ordered pair (3, −4) isn't solution.

An unbalanced connection between two expressions or values is referred to in mathematics as an inequality. So, inequity results from imbalance. In mathematics, an inequality defines the connection between two non-equal quantities. Egality and inequality do not mean the same thing. Use the not equal sign whenever two values are not equal (). It is possible to compare values of any size using a variety of inequalities. By changing both sides until only the variables are left, it is possible to solve many straightforward inequality problems.

Here,

Given :  3x + 4y ≤ 20.

where x is the no of apples

and y is the no of grapes

Thus,

Part a:

where x is the no of apples

and y is the no of grapes

Part b:

Inequality signs means that 20 will be the maximum amount of the no of apples and no of grapes summation.

Part c: ordered pair (3, −4)

Thus,

putting in the inequality we find:

=> 3(-3)+ 4(-4)

=> -6 -16

=> -22

Thus , it is not a solution for inequality.

Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c:  ordered pair (3, −4) isn't solution.

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Answer:

The ladder makes an angle of 60 degree from the ground.

Step-by-step explanation:

Length of the ladder, L = 28 feet

distance of ladder, d = 14 feet

Let the angle formed with the ground is A.

According to the trigonometry

\(\cos A =\frac{d}{L}\)

\(\cos A =\frac{14}{28}\)

cos A = 0.5

A = 60 degree