Matilda and Lorraine work in the mail room of a large company sorting letters. Matilda has already sorted 50 letters and continues sorting at a rate of 50 letters per hour. Lorraine has already sorted 80 letters and continues sorting at a rate of 40 letters per hour.

Which function can Matilda and Lorraine use to determine the total number of letters they have sorted after x hours? How many letters will they have sorted after 6 hours?

A.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 100x + 120. Thus, they will have sorted 720 letters in 6 hours.
B.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 130. Thus, they will have sorted 670 letters in 6 hours.
C.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 130x + 90. Thus, they will have sorted 870 letters in 6 hours.
D.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 30. Thus, they will have sorted 570 letters in 6 hours.

Answer:198 Girls were there

Step-by-step explanation:

Total number of people tthat attended the study = 392

Number of adults = 105

Number of boys = 89

Number of Girls= Total number of people attended the study - ( Number of adults + Number of boys)

392- ( 105+89)

392- 194

=198 Girls

Answer:

not factorable

Step-by-step explanation:

To factor a trinomial of the type x^2 + ax + b, you need to find two numbers that add to a and multiply to b.

You have 1x^2 + 9x + 2.

In this case, a = 9 and b = 2.

There are no two integers whose sum is 9 and whose product is 2, so this trinomial is not factorable.

Answer:

5

yStep-by-step explanation:

The diameter of the base of the tree is 0.3 meters.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that in forest management, conifer trees that exceed a height to base diameter ratio of 80 to 1 are considered unstable and the height of the tree is 24 meters.

The diameter is calculated as:-

Diameter = 24 / 80

Diameter = 0.3 meters

Hence, the diameter of the tree is 0.3 meters.

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Answer:

Runner A run's the fastest

Step-by-step explanation:

There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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Answer:

27.5

Step-by-step explanation:

y = kx

55 = 120k

k = 55/120

y = 55/120 x 60

y = 55/2

y = 27.5

The resultant velocity and acceleration of the skier at t=4.00 sec on the ski jump path are 12.8 m/s and 45.9 m/s², respectively.

To find the resultant velocity, first find the velocity vector components using the parametric equations:

vx = 7.00t, vy = 0.48t³ - 6.00t²/√(t⁴+1)

At t=4.00 s, vx = 28.0 m/s and vy = 10.50 m/s. The resultant velocity is the magnitude of the velocity vector, given by:

|v| = √(vx² + vy²) = 12.8 m/s

To find the acceleration vector components, differentiate the velocity vector components with respect to time:

ax = 7.00 m/s², ay = 1.44t² - 12.00t/√(t⁴+1) - 6.00t³(t⁴+1)^(-3/2)

At t=4.00 s, ax = 7.00 m/s² and ay = 45.9 m/s². The acceleration vector magnitude is:

|a| = √(ax² + ay²) = 46.1 m/s².

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The focal length of the lens is -15 cm. The negative sign indicates that the lens is a diverging lens.

To find the focal length of the lens, we can use the lens formula:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the image distance, and u is the object distance.

Given:

Object height (h_o) = 1.00 cm

Object distance (u) = 12 cm

Image height (h_i) = 5.00 cm

We can use the magnification formula to relate the object and image heights:

Magnification (m) = h_i / h_o

Given:

m = h_i / h_o = 5.00 cm / 1.00 cm = 5.00

Now, let's substitute the values into the lens formula:

1/f = 1/v - 1/u

Since the image is upright, the image distance (v) will be positive.

1/f = 1/v - 1/u

1/f = 1/v - 1/12

To find the value of v, we can use the magnification formula:

m = v / u

5.00 = v / 12

v = 5.00 * 12

v = 60 cm

Now, substitute the values of v and u into the lens formula:

1/f = 1/60 - 1/12

Simplifying:

1/f = (1 - 5) / 60

1/f = -4/60

1/f = -1/15

Taking the reciprocal of both sides:

f = -15 cm

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

arc length= central length/360 (circumference)

GJ=90/360 (2π20)

GJ= 31.42

31.42

The length of arc GJ is 11.5133 unit.

In geometry, the arc length refers to the length of a portion of a curve or an arc of a circle. It is the distance along the curve between two endpoints of the arc.

We have,

m <GHJ = 66 and GH = 10 unit

Now, using arc length formula

= nπr / 180

= 66 x 3.14 x 10/ 180

= 11.5133 unit

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Answer:its 5

Step-by-step explanation: cuz

Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

Answer:

A C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Leah wants to earn at least 120 dollars a month and she has two job options. This is written as

5x + 8y > 120

She also can't work more than 20 hours, leading us to the second equation

x + y = 20

First we solve for one variable

y = 20 - x

then substitute it into the first equation

5x + 8(20 - x) = 120

Solve for x

5x + 160 - 8x = 120

3x = 40

     x = 40/3

Then we solve for y

y = 20 - x

     y = 20/3

x < 40/3

y > 20/3

B and D will not work because their x+y is greater than 20.

E will also not work because the value is less than 120

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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Answer:

Hi friend! the answer is 64/3 or 21.3333333 or 21 1/3

Step-by-step explanation:

Answer:

64/3

Step-by-step explanation:

becaseu of math bro

Answer: 0.14

Step-by-step explanation:

1) Find the total #of seniors. To do this add up 25+5+5 = 35.

2)Since we know the number of seniors that work just do 5/35. This simplifies to 0.14 rounded to the nearest hundreth.

The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x=9

Step-by-step explanation:

2x=15+3

2x=18

x=18/2

x=9

The lines given by the equations y - 4 = 3(x + 5) and y + 3 = -1/3(x + 1) are perpendicular to each other.


To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes. The given equations are:

1) y - 4 = 3(x + 5)

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

Both equations are in slope-intercept form (y = mx + b), where m represents the slope. By comparing the coefficients of x, we can determine the slopes of the lines.

For equation 1, the slope is 3. This means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

For equation 2, the slope is -1/3. This means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 1/3.

Now, let's analyze the slopes:

Since the slopes of the two lines are not equal, the lines are not parallel.

To determine if the lines are perpendicular, we can use the fact that the product of the slopes of perpendicular lines is -1.

The product of 3 and -1/3 is -1, which means the lines are perpendicular.

Therefore, the lines given by the equations y - 4 = 3(x + 5) and y + 3 = -1/3(x + 1) are perpendicular to each other.

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a. The three exponential graphs can be analyzed to determine the values of a and b in their corresponding equations.

b. The three logarithmic graphs can also be analyzed to determine the values of a and b in their corresponding equations.

a. Analyzing the exponential graphs allows us to compare their corresponding equations and identify the values of a and b. The general form of an exponential function is given by y = ab^x, where a represents the initial value or y-intercept, and b represents the base or growth factor of the exponential function. By examining the graphs, we can determine the values of a and b by observing the initial value and the rate of growth or decay.

b. Similarly, analyzing the logarithmic graphs helps us compare their corresponding equations and determine the values of a and b. The general form of a logarithmic function is y = αlog_a(x), where α represents the coefficient or scaling factor, and a represents the base of the logarithm. By studying the graphs, we can identify the values of α and a by looking at the scaling of the logarithmic curve and the base of the logarithm.

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The solution to the initial value problem dy/dt = -4y + 20, y(0) = 11 is y(t) = 4e^(-4t) + 5.

The initial value problem, we can use the method of separation of variables.

First, separate the variables by writing the equation as dy/(4y - 20) = -dt.

Next, integrate both sides of the equation. The integral of dy/(4y - 20) is (1/4)ln|4y - 20| + C1, and the integral of -dt is -t + C2.

Combining the integrals, we have (1/4)ln|4y - 20| = -t + C.

Now, applying the initial condition y(0) = 11, we can substitute t = 0 and y = 11 into the equation. This gives (1/4)ln|4(11) - 20| = -0 + C, which simplifies to ln|24| = C.

Therefore, the final solution is (1/4)ln|4y - 20| = -t + ln|24|. Solving for y, we get 4y - 20 = 24e^(-4t), which further simplifies to y(t) = 4e^(-4t) + 5.

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Answer:

x = 82°

Step-by-step explanation:

Similar Triangles

Two triangles are similar if their corresponding sides are always in the same ratio.

In similar triangles,  corresponding angles are always congruent.

From inspection of the given diagram, the two triangles are similar as their corresponding sides are in the same ratio.  Therefore, their corresponding angles are equal:

⇒ 2x - 19° = x + 63°

⇒ 2x - 19° - x = x + 63° - x

⇒ x - 19° = 63°

⇒ x - 19° + 19°= 63° + 19°

⇒ x = 82°

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

Slope = (4-7)/(7-1)

Slope = -3/6

Slope = -1/2

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

you know who else like the shape my mom

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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Answer:

x^6/2

Step-by-step explanation:

simplify the expression, 4x^4x^3/8x, you make it 4x^7/8x

and it simplifys to 4x^6/8 which then becomes x^6/2

extra note:

a^x * a^y = a^ x+y

(see attachment below)

I hope this helps :)