Answer:
7
Step-by-step explanation:
Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?
The lengths of the legs of a 45°-45°-90° triangle can be described by the expressions 3x − 10 and x + 2. What is the length of the legs of the triangle?
Answer:
8
Step-by-step explanation:
3x - 10 = x + 2
2x = 12
x = 6
3x - 10 = 3(6) - 10 = 8
The length of each leg of the triangle is 8.
The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?
The calculated number of plants the flower bed can contain is 120
Calculating hw many plants can be planted in itFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 16 m by 9 m
So, the area of the flower bed is
Area = 16 * 9
Evaluate
Area = 144
Also, we have
Each plant requires a space of 1.2m x 1m?
This means that
Plant area = 1.2 * 1
Plant area = 1.2
So, we have
Plants = 144/1.2
Evaluate
Plants = 120
Hence, the number of plants is 120
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Answer:
Step-by-step explanation:
To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.
The area of the flower bed is calculated by multiplying its length and breadth.
So, the area of the flower bed is 16m x 9m = 144 sq.m.
Each plant requires a space of 1.2m x 1m = 1.2 sq.m.
Therefore, the number of plants that can be planted in the flower bed is:
144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.
So, you can plant 120 plants in the rectangular flower bed.
Solve for y
Finally, solve the proportion for y.
y/8 = 10/y
y = √ [?]
M
Enter the square root NOT simplified.
=
The square root of y is not simplified and can be represented as:
y = √([tex]2^4 \times[/tex] 5) or y = 4√5.
To solve the proportion y/8 = 10/y for y, we can cross-multiply:
y [tex]\times[/tex] y = 8 [tex]\times[/tex]10
This simplifies to:
[tex]y^2[/tex] = 80
To solve for y, we can take the square root of both sides of the equation:
[tex]\sqrt{y^2[/tex] = √80
Since the square root of [tex]y^2[/tex] is simply y, we have:
y = √80
The square root of 80 can be further simplified by breaking it down into its prime factors. Since 80 can be expressed as 2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]5, we can simplify the square root:
y = [tex]\sqrt(2 \times 2 \times 2 \times 2 \times 5)[/tex]
Therefore, the square root of y is not simplified and can be represented as:
y = [tex]\sqrt{(2^4 \times 5)[/tex] or y = 4√5.
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Answer:
[tex]y = \sqrt{80\\} =4\sqrt{5}[/tex]
Step-by-step explanation:
A natural food company produces and sells organic almond milk for $9.00 per gallon. This company
estimates its fixed costs to be 1121 dollars per month and the variable cost to produce each gallon of
almond milk is $7.50.
What is the margin of profit if 1494 gallons of almond milk are produced and sold each month?
A Select an answer of $
Okay, here are the steps to solve this problem:
Fixed costs per month: $1121
Variable cost per gallon: $7.50
Selling price per gallon: $9.00
Monthly sales (gallons): 1494
Cost of goods sold = Variable cost per gallon * Monthly sales
= $7.50 * 1494 gallons
= $11,105
Gross margin = Revenue - Cost of goods sold
= $9 * 1494 gallons
= $13,446
- $11,105 (Cost of goods sold)
= $2,341
Margin of profit = Gross margin - Fixed costs
= $2,341 - $1121
= $1,220
So the margin of profit if 1494 gallons are produced and sold each month is $1,220.
The answer is:
B $1,220
Troys toy box is 4 ft x 3ft x 5 ft. What is the Volume of his toy box?
Answer:
60 ft^2
Step-by-step explanation:
To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.
4 x 3 x 5 = 15x 4 = 60
Answer:
60 ft³
Step-by-step explanation:
V = 4 ft × 3 ft × 5 ft
V = 12 ft² × 5 ft
V = 60 ft³
#CMIIWGiven the regression line Ŷ = –6 + 0.41(X), make predictions for each of the following:
a. X = 25
b. X = 50
c. X = 75
For the "regression-line", Ŷ = -6 + 0.41(X), the predicted value,
(a) when X=25 is 4.25,
(b) when X=50 is 14.50,
(c) when X=75 is 24.75.
The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).
(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:
Ŷ = -6 + 0.41(25)
Ŷ = -6 + 10.25
Ŷ = 4.25
So, the predicted value of Y when X = 25 is 4.25.
(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:
Ŷ = -6 + 0.41(50)
Ŷ = -6 + 20.50
Ŷ = 14.50
So, the predicted value of Y when X = 50 is 14.50.
(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:
Ŷ = -6 + 0.41(75)
Ŷ = -6 + 30.75
Ŷ = 24.75
So, the "predicted-value" of Y when X = 75 is 24.75.
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There are 3 feet in a yard. How many centimeters are in a yard?
Please help quick! will mark brainliest!
Answer:
7, 14
Step-by-step explanation:
Look at the first column of numbers: 2.8 m in 2 min.
We can get a unit rate from those numbers:
2.8 m / 2 min = 1.4 m/min
He walks at a rate of 1.4 m/min
Now multiply the unit rate by each number of minutes to find the number of meter.
Let's do the second column as a check: time = 3 min
1.4 m/min × 3 min = 4.2 m
4.2 m is the number on the table, so our unti rate is correct.
5 min:
1/4 m/min × 5 min = 7 m
10 min:
1.4 m/min × 10 min = 14 m
How do I covert 45 degrees to a radian
Step-by-step explanation:
There are pi radians in 180 degrees
you want 1/4 of 180 degrees (45/180 = 1/4)
so this would be 1/4 pi radians or pi / 4 radians
45 * pi / 180 = pi/4
One candle, in the shape of a right circular
cylinder, has a height of 7.5 inches and a
diameter of 5 inches. What is the volume of the
candle? Round your answer to the nearest
cubic inch.
Answer:
147
Step-by-step explanation:
V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188
At a conference of educators, there ore 189 people total, and 128 are teachers. If the rest are principals, then how many principals are present?
Answer:
61 principals
Step-by-step explanation:
189 total - 128 teachers = 61 principals
NO LINKS!!! URGENT HELP PLEASE!!!
3. A virus has infected 400 people in the town and is spreading to 25% more people each day. Write an exponential function to model this situation, then find the number of 3000 people are infected.
4. The population of a small town was 10,800 in 2002. Since then, the population has decreased at a rate of 2.5% each year. Write an exponential function to model the situation, then find when the popuation reaches half the 2002 value?
Step-by-step explanation:
3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:
P(t) = 400 * 1.25^t
Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.
To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:
P(t) = 400 * 1.25^t
P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))
P(t) ≈ 2,343
Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.
4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:
P(t) = 10,800 * 0.975^t
Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.
To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:
5,400 = 10,800 * 0.975^t
0.5 = 0.975^t
log(0.5) = t * log(0.975)
t ≈ 28.2
Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.
Answer:
3) 9.03 days
4) 27.38 years
Step-by-step explanation:
Question 3To model the spread of the virus over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]
where:
P(t) is the number of infected people after t days.P₀ is the initial number of infected people.r is the daily growth rate (as a decimal).t is the time elapsed (in days).Given the virus has infected 400 people in the town and is spreading to 25% more people each day:
P₀ = 400r = 25% = 0.25Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 400(1 + 0.25)^t[/tex]
[tex]P(t) = 400(1.25)^t[/tex]
To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:
[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]
Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.
Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.
[tex]\hrulefill[/tex]
Question 4To model the population of the town over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]
where:
P(t) is population after t days.P₀ is the initial population.r is the annual decay rate (as a decimal).t is the time elapsed (in days).Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:
P₀ = 10,800r = 2.5% = 0.025Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 10800(1 -0.025)^t[/tex]
[tex]P(t) = 10800(0.975)^t[/tex]
To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:
[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]
Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.
Which point would be a solution to the system of linear inequalities shown below?
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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Which expression is equivalent to 4^7/8
4^1/4?
What’s the constant term of the polynomial 2x^3-5x^2+8*x+3
The constant term of the polynomial 2x³-5x²+8x+3 is 3.
A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.
The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.
The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.
Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.
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Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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HELP PLEASE PHOTO INCLUDED
Answer:
Eat that cookie and you will not regret about it
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
The amount of poster board left over will be 1275 square inches, the equation used is A = (b₁ + b₂)h/2.
To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,
we need to find the area of the trapezoid window and subtract it from the area of the poster board.
The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.
Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.
Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.
To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.
Finally, we subtract the area of the window from the area of the poster board using the equation:
1500 - 225 = 1275 square inches.
Therefore, the amount of poster board left over will be 1275 square inches.
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The complete question is
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
The Martinez family has a large lot. They have decided to create a square garden in
one corner of the lot. They want to put a walkway around the garden. The walkway
will be 5 feet wide on one side of the square and 8 feet wide on the other side. The
total area of the garden and the walkway must be 700 square feet.p
The length of a side of the square garden is 5.75 feet.
How to calculate the length(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700
Simplifying and solving for x, we get:
2x^2 + 46x - 177 = 0
Using the quadratic formula, we can solve for x:
x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))
x = (-46 ± 26) / 4
x = 5.75
The length of a side of the square garden is 5.75 feet.
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Venessa bought 80 apples for 4$.out of these apples 25 precent were rotten and had to be thrown away Vanessa sold the remaining apples at 6 cents per apple. What is the profit or loss percentage
The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.
Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.
Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.
Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.
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the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
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Draw the following shapes on geoboard paper. Find the area of each shape by partitioning it into sub-shapes and finding the areas of the sub-shapes. Remember to label your answers.
Draw the following shapes on geoboard paper. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle. Think about how you can use rectangles to determine the areas of right triangles that are inside the rectangles.
Answer:
I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.
To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:
1. Draw the given shape on geoboard paper.
2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.
3. Identify the right triangles that are inside the rectangles.
4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.
5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.
6. Add up the areas of the triangles and rectangles to find the total area of the shape.
Remember to label your answers with the correct units (square units).
Find the area of the composite figure
The area of the composite shape is 125units²
What is area of shape?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A composite shape can be defines as a shape created with two or more basic shapes.
The composite shape can be divided into 2 equal squares and a rectangles.
Area of the square = l²
= 5× 5 = 25
For two squares it will be;
25 × 2
= 50 units²
area of the rectangle = l× w
where w is the width
A = 15 × 5
= 75 units²
Therefore the area of the composite shape = 50 + 75 = 125 units²
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Use technology or a z-score table to answer the question. The odometer readings on a random sample of identical model sports cars are normally distributed with a mean of 120,000 miles and a standard deviation of 30,000 miles. Consider a group of 6000 sports cars. Approximately how many sports cars will have less than 150,000 miles on the odometer? O 300 951 O 5048 O 5700
Approximately 5048 sports cars will have less than 150,000 miles on the odometer
Mean = 120,000
Standard deviation = 30,000
Total group = 6000
Total Miles = 150,0000
An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.
Calculating the Z score -
z = x - u/a
= 15,0000 - 12,0000/30000
= 30000/30000
= 1
Using the standard normal table, to determine the value -
P ( Z<1) = 0.8413
Calculating the total number of cars -
= P value x total group of cars
= 6000 x 0.8413
= 5047.7 or 5048
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NO LINKS!!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Sines
1. A = 29°, C = 63°, c = 24
2. A = 72°, B= 35°, c = 21
Answer:
1) B = 88°, a = 13.1, b = 26.9
2) C = 73°, a = 20.9, b = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Question 1Given values:
A = 29°C = 63°c = 24As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies B=180^{\circ}-A-C[/tex]
[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]
[tex]\implies B=88^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies a=13.0876493...[/tex]
[tex]\implies a=13.1[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies b=26.9194211...[/tex]
[tex]\implies b=26.9[/tex]
[tex]\hrulefill[/tex]
Question 2Given values:
A = 72°B = 35°c = 21As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]
[tex]\implies C=73^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies a=20.8847511...[/tex]
[tex]\implies a=20.9[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies b=12.5954671...[/tex]
[tex]\implies b=12.6[/tex]
Work out the area of the shaded shape on the millimetre (mm) grid.
State the units with your answer.
The diagram is not drawn to scale.
The requried area of the shaded shape is 5 square millimeters.
From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:
= 5 * 1 = 5 square millimeters.
Thus, the requried area of the shaded shape is 5 square millimeters.
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A spinner has 3 equal sections: red, white, and blue. John spins the spinner and tosses a coin. Which shows the sample space for spinning the spinner and tossing the coin?
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.
Given that:
A coin is tossed.
A spinner has 3 equal sections: Red, White, and Blue.
The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The total number of samples is calculated as,
Total samples = 2 x 3
Total samples = 6
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.
Thus, the correct option is D.
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the temperatures at midday on march 1st in five cities are shown in the bar chart below. What is the difference in temperature between rome and munich?
The difference in temperature between Rome and Munich is given as follows:
6ºC.
How to obtain the difference in temperatures?The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.
The bar graph in the context of this problem gives the temperature for each town.
From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:
Rome: 11 ºC.Munich: 5 ºC.Hence the difference in temperature between Rome and Munich is given as follows:
11 - 5 = 6ºC.
Missing InformationThe graph is given by the image presented at the end of the answer.
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i need the answer for this asap Please!
The system of inequalities for the graph is
a) y < 3x - 4
b) y = x + 3
Given data ,
Let the inequality equations be represented as A and B
where
Let the first point be P ( 0 , 3 )
Let the second point be Q ( -3 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 3 - 0 ) / ( 0 + 3 )
m = 1
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 0 = 1 ( x + 3 )
y = x + 3
And , the second equation is
Let the first point be R ( 0 , -4 )
Let the second point be S ( 2 , 2 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -4 - 2 ) / ( 0 - 2 )
m = -6/-2
m = 3
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 2 = 3 ( x - 2 )
Adding 2 on both sides , we get
y = 3x - 4
Since , it is a dotted line ,
y < 3x - 4
And , the solution to the inequality is point of intersection
where A ( 3.5 , 6.5 ) is the solution
Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution
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Need help, show work please
Using the first two points we can get an exponential model:
[tex]y = (225/23)*(23/15)^x[/tex]
How to find the exponential equation?
The general exponential equation can be written as:
[tex]y = A*(b)^x[/tex]
We can replace any two values of the table to get the system of eqautions:
[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]
Taking the quotient between the second and the first equation we get:
[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]
Replacing that on the first equation we will get:
[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]
Then an exponential model is:
[tex]y = (225/23)*(23/15)^x[/tex]
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