The graph of the problem depicts the rate of the temperature change.
How to graph the temperature change?To graph temperature change, you can use a line graph. The horizontal axis represents time, while the vertical axis represents temperature. You plot points on the graph corresponding to the recorded temperature at specific times, and then connect the points to form a line.
The slope of the line represents the rate of temperature change, with a steep line indicating a rapid increase or decrease in temperature and a gentle slope indicating a slow change. The line graph helps to visually represent changes in temperature over time and can be used to analyze patterns and trends.
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Choose the best method for solving and solve. Show your work.
y = -x-6
x + 3y = -18
The final solution to the given simultaneous equation is (0, -6)
Solving simultaneous equationsA finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Given the set of equations below:
y = -x-6
x + 3y = -18
Using the substitution method;
Substitute equation 1 into 2 to have:
x + 3(-x - 6) = -18
x - 3x - 18 =-18
-2x = 0
x = 0
Since y = -x- 6
y = -0 - 6
y = -6
Hence the solution to the system of equation is (0, -6)
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I Need Help ASAP!!!!!!!!!!
The difference in simple interest at 13% and 12% p.a. of a sum in one year is $ 110. Then the sum is (a) $11,000 (b) $13,000 (c) $15000 (d) 12000
Based on the information provided, it can be concluded the sum is $11,000.
How to know what is the sum?To know what is the sum, let's calculate the difference in the interest rate:
13% - 12% = 1%
This means the difference between the two interest rates presented is 1%. Based on this, let's calculate the 1% of the sums given:
11,000 x 0.01 = 11013,000 x 0.01 = 13015,000 x 0.01 = 15012,000 x 0.01 = 120Based on the above, the correct sum is $11,000 because only in this one 1% is equivalent to $110.
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Help……………………………………..
The correct option is the third one. The statement "The [tex]\lim_{x \to \0} f(x)=4[/tex] because both the left hand and the right hand limit is equal to 4" identifies and explains the function of limit.
What is a limit?The limit function in mathematics is a way of finding the value that a function or sequence approaches as the input values approach a certain point. It is used to determine the behavior of a function as the input values approach a certain point or their maximum or minimum values.
Where the above two limits say that when we approach zero from the negative side (the first one) and from the positive side (the second one), we must get the same value.
Remember that the limit is an approximation through near points.
Then, regardless the fact that f(0) = -2, we can see that as x approaches 0 from both sides, the value of the function approaches 4.
Thus, we can conclude that the limit of f(x) when x tends to zero is equal to 4.
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The Tour de France is not a 3500 km race, it is a 3500 km cycling race. The diameter of the bike wheels used in the race must be between 55 cm and 75 cm. To find the minimum number of rotations
The minimum number of rotations required for a 3500 km race is 52,800 rotations.
This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).
We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
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Evaluate the expression 52 × (7.2 + 16) − 8.
The evaluation of the expression is 1198.4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Expression; 52 × (7.2 + 16) − 8
Now,
=52*23.2-8
=1206.4-8
=1198.4
Therefore, the algebra will give 1198.4.
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In the graph shown, which of the following values represents the x-value where line l and
the line y = 2x - 1 intersect?
-1
0
1
2
Answer:
2 or -1
Step-by-step explanation:
[tex]1. \: y + 1 = 2x \\ 2. \: \frac{y + 1}{2} = x \\ 3. \: x = \frac{y + 1}{2} [/tex]
[tex]1. \: y = 2 \times 0 - 1 \\ 2. \: y = - 1[/tex]
the dencity of apple juice is
Answer:
density of apple juice
1.034-1.051g.cm‐³
Explain how the coordinates of a point and its reflection across the x-axis are the same and how they are different
Answer: The coordinates of a point in the plane are represented by a pair of values, (x, y), where x is the horizontal position and y is the vertical position.
When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate changes. This is because the x-axis acts as a mirror, flipping the point over to the opposite side of the axis.
So, the coordinates of the reflected point would be (x, -y).
In summary, the x-coordinates of a point and its reflection across the x-axis are the same, while the y-coordinates are different (one is positive, and the other is negative).
Step-by-step explanation:
The population of a certain animal species decreases at a rate of 12.5% per year. In 2021, at the beginning of the study, you counted 97 of the animal species you are studying in their natural habitat. Write a function that models the change in the animal population.
P should stand for the population in a certain year. P = 97*(0.875) is the function to model the population change (year-2021).
P should stand for the population in a certain year. To simulate how the animal population changes over time, we can utilise a function. The 12.5% annual reduction rate will be considered by the function. This can be stated mathematically as P = 97*(0.875), which is how it will appear in the equation (year-2021). In this equation, the number 97 stands in for the population in 2021, and the number 0.875 denotes the 12.5% annual decline rate. The exponent (year 2021) represents the number of years that have passed since 2021, allowing the equation to take the population decline over a number of years into consideration. As a result, the equation can be used to determine the animal species' population at the start of a particular year.
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Lindsay invests $2200 in one account and $1000 in an account paying 4 % higher interest. At the end of one year she had earned $168 in interest. At what rates did she invest?
Answer:
4% and 8%
Step-by-step explanation:
You want to know the interest rates that yield $168 on investments of $2200 at one rate and $1000 at a rate 4% higher.
SetupLet r represent the lower interest rate. Then x+0.04 is the higher rate, and the total interest earned is ...
2200r +1000(r +0.04) = 168
SolutionSimplifying the equation, we have ...
3200r +40 = 168
3200r = 128 . . . . . . . . subtract 40
r = 128/3200 = 0.04 = 4% . . . . . divide by the coefficient of r
The rates of interest on Lindays's investments were 4% and 8%.
x=5-2y
3x+2y=17
solve the system of equations!!
show your work!! :)
Answer: (x = 6, y = -0.5)
Step-by-step explanation:
Substitute into one of the equations: 3(5 - 2y) + 2y = 17
Apply Multiplicative Distribution Law: 15 - 6y + 2y = 17
Rearrange unknown terms to the left side of the equation: -6y + 2y = 17 - 15
Combine like terms: -4y = 2
Divide both sides of the equation by the coefficient of variable: y = 2 / (-4)
Remove the parentheses: y = -2 / 4
Calculate the product or quotient: y = -0.5
Substitute into one of the equations: x = 5 - 2 * (-0.5)
Remove the parentheses: x = 5 - 2 * -0.5
Calculate the product or quotient: x = 5 + 1
Calculate the sum or difference: x = 6
The solution of the system is: {x = 6, y = -0.5}
Hope this helps!
Two families attend a performance of the Circus Mage. The cost of a ticket for adult is
1.5 times higher than that of a child ticket. Clothilde buys a ticket for her, for her
husband and for her 2 children. She pays $90 in all, taxes included. Her friend Naomie
buys tickets for her 4 children and herself. Clothilde thinks that going to the circus
costs her less than Naomie. Is she right?
Answer: NO
Step-by-step explanation:
Adult tickets cost $27
Child tickets cost $18
$18 x 4 child tickets = $72 + $27 adult ticket = $99
A school set up a new sports club. In the first week, 8 girls and 7 boys went to the club. In the second week, another 2 girls and some more boys joined the club. The number of boys in the club was now double the number of girls. How many boys joined the club in the second week?
an anchor weighing 100 lbs in water is attached to a chain weighing 3 lb/ft in water. find the work done to haul the anchor and chain to the surface of the water from a depth of 25 ft.
In linear equation, 3437.5 feet - lbs is the work done to haul the anchor .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Anchor weighing = 100 lbs
given 3 lb/ft
the combined weight = 3( 25 -y ) + 100
= 175 - 3y
the workdone on small solution is = (175 - 3y)Δy
w = ∫₀²⁵ (175 - 3y) dy
= 175[y]²⁵₀- 3/2[y²]²⁵₀
= 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]
= 3437.5 feet - lbs
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if x,y,z are different and =mod x x^2 1+x^3
y y^2 1+y^3 = 0 then show than 1+xyz=0
z z^2 1+z^3
Given that x, y, z are different and satisfy the equations:
x^3 + x^2 - x = 0
y^3 + y^2 - y = 0
z^3 + z^2 - z = 0
We can multiply the first equation by y, the second by z, and the third by x to obtain:
x^3y + x^2y - xy = 0
y^3z + y^2z - yz = 0
z^3x + z^2x - zx = 0
Adding these three equations together, we get:
x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0
Expanding and simplifying, we find that:
x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0
Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:
x^2 - x + y^2 - y + z^2 - z = 0
We can also write this as:
(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0
This expression can be factorized as:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
Since x, y, and z are all different, we have that:
(x - 1)(x + 1) ≠ 0
(y - 1)(y + 1) ≠ 0
(z - 1)(z + 1) ≠ 0
Therefore, we have:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
So, we can conclude that:
xyz = -1
And,
1 + xyz = 0
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Mark is planning a birthday party at the local skating rink.The table shows the rates that are charged for parties at the skating rink.Is the number of guests proportional to the cost?If so, what is the constant of proportionality, and what does it mean in this situation? Is the graph a straight line?
The constant of proportionality is, 12
Yes, The graph of equation is a straight line.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Mark is planning a birthday party at the local skating rink.
And, The table shows the rates that are charged for parties at the skating rink.
Let two points on table are (5, 60) and (10, 120)
Now, The equation of line is,
⇒ y - 60 = (120 - 60) / (10 - 5) (x - 5)
⇒ y - 60 = 60/5 (x - 5)
⇒ y - 60 = 12(x - 5)
⇒ y - 60 = 12x - 60
⇒ y = 12x
Thus, The number of guests proportional to the cost.
And, Constant of proportionality = 12
And, The graph of y = 12x is a straight line.
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Complete question is shown in figure.
Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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Help please i need answer asap
The correct matching of the given numbers is as follows:
√30 - Real, Irrational root-26 - Real, Rational, Integer√64 - Real, Rational Root, Whole Number1/4 - Real, Rational0.36336333633336.... - Real, Irrational decimal0.42424242..... - Real, Rational decimal✓ 7, or 7i - Imaginary NumberWhat are real and imaginary numbers?Natural numbers, whole numbers, integers, rational numbers, and irrational numbers can all be classified as real numbers.
An imaginary number is created by multiplying a real number by i where i = (-1). To calculate the square root of negative values, we employ imaginary numbers. For instance, (√-7) Equals (-1) √7
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Which figure would best model the sandbox to help determine the amount of sand needed?
You need to buy 80 cubic feet of sand to fill the sandbox.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The sandbox is a rectangular prism.
Length is 10 feet.
Width is 8 feet
Height is 1 feet.
Volume of prism=Length×Width×Height
=10×8×1
=80 cubic feet.
Hence, you need to buy 80 cubic feet of sand to fill the sandbox.
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The complete question is given in the attachment.
Solve this problem pls
Answer:
[tex]\frac{43}{15}[/tex]x + 30
Step-by-step explanation:
3[tex]\frac{2}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - 3[tex]\frac{3}{4}[/tex])
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - [tex]\frac{15}{4}[/tex])
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + [tex]\frac{60}{20}[/tex]
[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + 30
[tex]\frac{55}{15}[/tex]x - [tex]\frac{12}{15}[/tex] x + 30
[tex]\frac{43}{15}[/tex]x + 30
Archive invested an amount of money in a savings account that pays compound interest at a rate of 6% per annum. After 11 years there is £13,288.09 in the savings account (rounded to the nearest 1p). How much did Archive initially invest?
Answer: 7000 (4 s.f)
Step-by-step explanation:
[tex]x[/tex] x [tex]1.06^{11} = 13,288.09[/tex]
[tex]x = \frac{13,288.09}{1.06^{11} }[/tex]
[tex]x = 7000[/tex] (4 s.f)
This is a question where you make the equation by yourself using compound interest. If you have any further questions, feel free to ask me :)
please help asap, show your work then choose an answer
Note that where the figure below contains two semi-circles that are tangent to each Other at point B and ray DE is tangent to both semicircles at points E and F, it is correct to state that ED = 6√2 (Option A).
What is a Semi Circle?A semicircle is a one-dimensional point collection that forms half of a circle in mathematics. It is a circular arc with a circumference of 180°. It just has one symmetry line.
Solving the ED, we have:
ΔDEM ~ ΔDFP
This means that MD/PD = EM/FP
MD/(MD + 9) = 3/6
6MD = 3MD + 27 (Collect like terms over the equation)
3MD = 27
MD = 9 (If both sides are divided by 9)
Note that
ED = √[MD²-EM²]
ED = √9²-3²]
ED = 6√2
Thus, it is correct to state that ED = 6√2
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Norachai and Rain each improved their yards by planting rose bushes and grass. They bought their supplies from the same store. Norachai spent $209 on 11 rose bushes and 11 bunches of grass. Rain spent $40 on 3 rose bushes and 2 bunches of grass. What is the cost of one rose bush and the cost of one bunch of grass?
The cost of one rose bush is $2 and the cost of one bunch of grass is $17.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Norachai and Rain each improved their yards by planting rose bushes and grass.
Let the cost of rose bushes be x and the cost of bunches of grass be y.
Norachai spent $209 on 11 rose bushes and 11 bunches of grass.
Now, 11x+11y=209
x+y=19 --------(i)
Rain spent $40 on 3 rose bushes and 2 bunches of grass.
3x+2y=40 --------(ii)
Substitute x=19-y in equation (ii), we get
3(19-y)+2y=40
57-3y+2y=40
57-40=y
y=17
Substitute y=17 in equation (i), we get
x=2
Therefore, the cost of one rose bush is $2 and the cost of one bunch of grass is $17.
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the patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add 7 1/4% tax to the cost of the meal. Mr patterson was very happy with the food and service so he gave a 20% tip to the waitress. How much does the lunch cost, including tax and tip?
the lunch cost, including tax and tip 67.31$.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.
total cost after the tax = 52.30*(1 + 7 1/4)%
total cost after the tax = 52.30* 7.25/100 + 52.30
total cost after the tax = 3.79 + 52.30
total cost after the tax = 56.09
Since,
Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.
Thus,
Total cost after the tip = 56.09(1 +20/100)
Total cost after the tip = 56.09 * 1.2
Total cost after the tip = 67.308
Therefore, the lunch cost, including tax and tip 67.31$.
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Solve the inequality.
X/10 >5
Answer:
x > 50
Step-by-step explanation:
[tex]\frac{x}{10}[/tex] > 5 ( multiply both sides by 10 to clear the fraction )
x > 50
how far from the base of a building must a 15-ft ladder be placed so that it reaches 12 ft up the wall?
The base of the ladder must be placed 3 ft from the base of the building. The total length of the ladder is 15 ft.
1. The ladder must reach 12 ft up the wall, so we need to calculate the distance from the base of the building to 12 ft.
2. The total length of the ladder is 15 ft.
3. Subtract the length of the ladder (15 ft) fromthe desired height (12 ft) to get the distance from the base of the building.
4. 12 ft - 15 ft = -3 ft
5. Since the distance cannot be negative, the base of the ladder must be placed 3 ft away from the base of the building.
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numbers that summarize a sample of data are called and numbers that summarize populations are called
Numbers that summarize a sample of data are called "sample statistics," and numbers that summarize populations are called "population parameters."
A sample statistic is a single value that describes a characteristic of a sample, such as the mean, median, or standard deviation. Sample statistics are used to make inferences about the population from which the sample was drawn.
A population parameter, on the other hand, is a single value that describes a characteristic of an entire population, such as the population mean, population standard deviation, or population proportion. Population parameters are usually not known and must be estimated from a sample.
For example, if you have a sample of 100 students' heights, the mean height of the sample (a sample statistic) can be calculated and used to make inferences about the mean height of the population of all students.
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Find the perimeter of ABCD.
The perimeter of ABCD is, √18 + 5 + √29 + √10
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The diagram of ABCD is shown.
Now, The coordinate of the ABCD are,
⇒ A = (- 3, 2)
⇒ B = (0, 5)
⇒ C = (3, 1)
⇒ D = (-2, - 1)
Hence, Distance between A and B is,
⇒ f = √(- 3 - 0)² + (2 - 5)²
⇒ f = √9 + 9
⇒ f = √18
Distance between B and C is,
⇒ g = √(3 - 0)² + (1 - 5)²
⇒ g = √9 + 16
⇒ g = √25
⇒ g = 5
Distance between C and D is,
⇒ h = √(- 2 - 3)² + (- 1 - 1)²
⇒ h = √25 + 4
⇒ h = √29
Distance between D and A is,
⇒ i = √(- 3 + 2)² + (2 + 1)²
⇒ i = √1 + 9
⇒ i = √10
Hence, The perimeter of ABCD is,
⇒ f + g + h + i
⇒ √18 + 5 + √29 + √10
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If M(-4,3) and N(1,0) are two fixed points and P(x, y) is a moving point which moves such that PM^2 -PN^2=20, find the locus of the point P.
The locus of point P is a circle with center at the midpoint of points M and N, and radius equal to half the distance between the two points.
How do we determine the value?The midpoint of M and N is given by:
((-4+1)/2, (3+0)/2) = (-1.5, 1.5)
The distance between M and N is given by the distance formula:
√((1-(-4))^2 + (0-3)^2) = sqrt(25 + 9) = √(34)
So, the radius of the circle is √(34)/2.
Hence, the equation of the locus of point P is given by:
(x-(-1.5))^2 + (y-1.5)^2 = (√(34)/2)^2
or
(x+1.5)^2 + (y-1.5)^2 = (√(34)/2)^2
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2. Decide whether ∆ABC and ∆DEF are similar, not similar, or cannot be determined for the given information. Include your reason.
Answer:
By AA similarity Triangle ABC and DEF are similar.
What is Similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
First in Triangle ABC
using Angle Sum Property
<C= 180 - <A - <B
<C = 180 - 77 - 48
<C = 55 degree
and, In Triangle DEF
using Angle Sum Property
ND= 180- <E- <F
<D = 180- 55 - 48
<D = 77
As, In both Triangle ABC and DEF all angles triangles are Equal.
<A = <D= 77
<B = <E = 48
<C = <F= 55
So, by AA similarity Triangle ABC and DEF are similar.
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