The augmented matrix of a system of linear equations is given: , determine value(s) of k if 2 k - 2 if the system has no solution there are no values of k that will make the system inconsistent. The system has one solution for all values of k except k = 4.The system has infinitely many solutions if k = 0, a unique solution if k ≠ 0 and k ≠ 4, and no solutions if k = 4
To determine the value(s) of k for each case, we will perform row reduction on the augmented matrix and analyze the resulting echelon form.
1 3 1 | 0
2 k - 2 | 0
R2 - 2R1 -> R2
1 3 1 | 0
0 k - 4 | 0
Case (a): If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions. If k ≠ 4, then we can use back-substitution to find the solution(s):
k - 4 = 0 => k = 4
Since this contradicts our assumption, there are no values of k that will make the system inconsistent.
Case (b): If k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions.
Case (c): If k = 0, then the second row reduces to 0 = 0, which means we have a free variable and infinitely many solutions. If k ≠ 0 and k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the system is inconsistent with no solutions.
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1. Find the length of the curve.
r ( t ) = 6 cos ( t ) i − sin ( t ) j + 5 sin ( t ) k , 0 ≤ t ≤ 1
2. If r ( t ) = 〈 sin ( t ) , cos ( t ) , ln ( cos ( t ) ) 〉 , 0 ≤ t ≤ π/4 , find ds/d t , where s is the arc length function of r(t).
Answer choices
a. sec(t)
b. sec^2(t)
c. tan(t)
d. tan^2(t)
e. 1+tan^2(t).
ds/dt = sec(t)
To find the length of the curve, we need to find the arc length. The arc length of the curve r(t) is given by:
LENGTH = $\int_{0}^{1} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)} dt$
To find ds/dt, we can take the derivative of the above equation with respect to t:
$\frac{ds}{dt} = \frac{d}{dt} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}$
$\frac{ds}{dt} = \frac{6^2\cos(t)\sin(t) + 10\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$
$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$
$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{1+tan^2(t)}}$
Thus, ds/dt = sec(t).
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What is the common factor of the numerator and denominator in the expression (x+1)(x+7)(x+7)(x−1)
Answer:So the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2, and the simplified expression is (x+1)(x−1).
Step-by-step explanation:
To find the common factor of the numerator and denominator of the expression (x+1)(x+7)(x+7)(x−1), we need to factorize it completely.
(x+1)(x+7)(x+7)(x−1) = (x+1)(x−1)(x+7)(x+7)
Now we can see that the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2.
Therefore, we can simplify the expression by dividing both the numerator and denominator by (x+7)^2:
(x+1)(x−1)(x+7)(x+7)/(x+7)(x+7) = (x+1)(x−1)
So the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2, and the simplified expression is (x+1)(x−1).
What is one hundredth more than 2.89?
Answer:
2.90
Step-by-step explanation:
One hundredth is 0.01. 2.89+0.01= 2.90.
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HELPP ME
Some of the radicals below are like terms, while others are not: √2, − 3√2, 2√3, 5√2, 2√5, √32
List the Like Terms here
3b) Combine those like terms to write one single simplified radical (do not type!):
3c) Explain why the leftover terms are NOT like terms with the others.
The like terms are √2, − 3√2 and 5√2. The radicals are 2√3 and 2√5, √32.
What are radicals?The radical and root of a number are the same thing. The root can be an nth root, a square root, or a cube root. Hence, a radical is any number or phrase that employs a root. The Latin word Radix, which meaning root, is where the word "radical" originates. The radical can be used to explain various types of roots for a number, including square, cube, fourth, and so on. The index number or degree is the number that appears before the radical.
Similar terms are ones whose exponent power and variables are the same. These variables' coefficients might differ. Terms with algebraic similarities are those that are comparable to one another.
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You go to the park on a windy day to fly a kite. You have released 40 feet of string. The string makes an angle of 30°with the ground. How high is the kite in the air?
Answer:
20 feet
Step-by-step explanation:
You can use trigonometry to solve this problem. The height of the kite can be found using the sine function. The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the 30° angle is the height of the kite (h), and the hypotenuse is the length of the string (40 feet). So we have:
sin(30°) = h / 40
Solving for h, we get:
h = 40 * sin(30°)
Since sin(30°) = 0.5, we have:
h = 40 * 0.5
So, h = 20 feet.
The kite is 20 feet high in the air.
Answer:
To solve this problem, we can use trigonometry. Let's assume that the height of the kite from the ground is h. Then, we can use the tangent function to find the value of h.
We know that the tangent of an angle is equal to the opposite side over the adjacent side. In this case, the opposite side is the height of the kite (h) and the adjacent side is the distance from you to the point directly below the kite on the ground, which is 40 feet.
So we have:
tan(30°) = h/40
Multiplying both sides by 40, we get:
h = 40 tan(30°)
Using a calculator, we can find the value of tangent of 30 degrees, which is approximately 0.5774. So:
h = 40 × 0.5774 ≈ 23.1
Therefore, the height of the kite in the air is approximately 23.1 feet.
1. What are the six primary sources of greenhouse gas emissions in the United States? 2. What are the seven types of greenhouse gases of climate change? 3. What are the four types of Machine learning?
The six primary sources of greenhouse gas emissions in the United States are:
Electricity productionTransportationIndustryCommercial and residentialAgricultureLand use and forestry2. The seven types of greenhouse gases of climate change are:
Carbon dioxide (CO2)Methane (CH4)Nitrous oxide (N2O)Fluorinated gasesChlorofluorocarbons (CFCs)Hydrofluorocarbons (HFCs)Sulfur hexafluoride (SF6)3. The four types of Machine learning are:
Supervised learningUnsupervised learningSemi-supervised learningReinforcement learningLearn more about greenhouse
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when an integer m is divided by 5 the remainder is 3. When m is divided by 7 the remainder is 1. If m is greater than 40 but less than 80, what is one possible value of m.
One possible value of m is 53.
A possible value of m can be found using the Chinese Remainder Theorem. The Chinese Remainder Theorem states that if two numbers a and b are relatively prime, then there exists an integer x such that:
x ≡ a (mod m)
x ≡ b (mod n)
In this case, we have:
m ≡ 3 (mod 5)
m ≡ 1 (mod 7)
Both 5 and 7 are prime so we can start by finding the smallest positive integer that is congruent to 3 (mod 5) and 1 (mod 7). This integer is 18:
18 ≡ 3 (mod 5)
18 ≡ 1 (mod 7)
Now, we can add multiples of 5*7 = 35 to 18 until we find a value of m that is greater than 40 but less than 80:
18 + 35 = 53
53 is greater than 40 but less than 80, so one possible value of m is 53.
Therefore, one possible value of m is 53.
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Help pls !!!!!!!!!!!!!!!!!!!!!!
Answer:
I think 2nd option..........
PLEASE HELP ASAP
how much percent is 2882.45 of 3374.60?
( include working out and show answer as percentage )
Answer:
97271.1577
Step-by-step explanation:
multiply 3374.60 by 2882.45%
Evaluate det (A) by a cofactor expansion along a row or column of your choice. A=[[-6,0,2],[2,4,1],[-1,0,3]]
The determinant of matrix A is -6.
A. To evaluate det(A) by a cofactor expansion along a row or column of your choice, we can choose any row or column and multiply each element by its corresponding minor and sign.
For example, let's choose the first row:
det(A) = (-6)(4*3-0*1) + (0)(2*3-(-1)*2) + (2)(2*0-(-1)*4)
det(A) = (-6)(12) + (0)(6) + (2)(4)
det(A) = (-72) + (0) + (8)
det(A) = -64
Therefore, the determinant of matrix A is -64.
B. Alternatively, we could have chosen any other row or column and the result would have been the same. For example, if we chose the third column:
det(A) = (2)(4*0-2*0) + (-1)(-6*3-2*0) + (3)(-6*0-2*4)
det(A) = (2)(0) + (-1)(-18) + (3)(-8)
det(A) = (0) + (18) + (-24)
det(A) = -6
Therefore, the determinant of matrix A is -6.
Note that the determinant of a matrix is a scalar value, and it is the same regardless of which row or column we choose to expand along.
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Louise has 3 and 3/4 feet of green yarn and 2/4 yards of white yarn to make an art project. How many more feet of green yarn than white yarn does Louise have? ASAP PLS
Louise has 2 1/4 feet more of green yarn than white yarn.
What is the fractions ?
A fraction is a way to represent a part of a whole or a ratio between two quantities.
To compare the amounts of green and white yarn, we need to express the amounts in the same units. Let's convert 2/4 yards of white yarn to feet, since the green yarn is already measured in feet.
1 yard = 3 feet
2/4 yard = 2/4 * 3 feet/yard = 1.5 feet
Now we can compare the amounts of green and white yarn in feet:
Amount of green yarn = 3 3/4 feet
Amount of white yarn = 1.5 feet
To find how many more feet of green yarn Louise has than white yarn, we can subtract the amount of white yarn from the amount of green yarn:
3 3/4 feet - 1.5 feet = 2 1/4 feet
Hence, Louise has 2 1/4 feet more of green yarn than white yarn.
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A water faucet leaks 35
of a liter of water in 34
of an hour. Which TWO statements are correct for this situation?
Answer:
To determine which two statements are correct for this situation, we need to analyze the given information.
The water faucet leaks 35 of a liter of water in 34 of an hour, which means that:
In one hour (60 minutes), the faucet will leak:
60/34 x 35 = 61.76 milliliters (ml) of water.
In one minute, the faucet will leak:
35/34 = 1.0294 ml of water.
In one day (24 hours), the faucet will leak:
24 x 61.76 = 1482.24 ml or 1.48224 liters of water.
In one week (7 days), the faucet will leak:
7 x 1.48224 = 10.37568 liters of water.
Based on this information, the correct statements are:
The faucet leaks approximately 61.76 milliliters of water in one hour.
The faucet leaks approximately 10.37568 liters of water in one week.
A third grade class is making paper cups and snowman crafts of popsicle sticks. It takes 271 popsicle sticks to make eight pencil cups and 15 snowmen. It takes 373 popsicle sticks to make 14 pencil cups and 15 snowmen. How many popsicle sticks are needed for one snowman?
The total number of popsicle sticks needed to make one snowman using the given conditions for system of equations is equal to 9.
Let us consider 'x' is the number of popsicle sticks required to make one pencil cup.
And 'y' represents the number of popsicle sticks required to make one snowman.
The required set up two equations are,
8x + 15y = 271 ___(1)
14x + 15y = 373 ___(2)
Multiplying both sides of equation (1) by 14 and both sides of equation (2) by -8 we get,
112x + 210y = 3794
-112x - 120y = -2984
Add both the above equations to eliminate the x variable we get,
⇒ 112x + (-112x) + 210y + (-120y) = 3794 + (-2984)
Simplifying the equation we get,
⇒90y = 810
Dividing both sides by 90 we get,
⇒ y = 9
Therefore, number of popsicle sticks required to make one snowman is equal to 9.
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equals zero, which expression is equ (25-4x^(2))/(6x^(2)+9x-15)*(6x^(2)-2x-4)/(2x^(2)-x-10)
The solver for this expression is x = -5/2, 5/2, 2, -1/3, 1, 2.
To solve this expression, we will first need to factor the numerator and denominator of each fraction.
For the first fraction, we can factor the numerator as follows:
[tex]25 - 4x^2 = (5 + 2x)(5 - 2x)[/tex]
The denominator can be factored as follows:
[tex]6x^2 + 9x - 15 = (2x + 5)(3x - 3)[/tex]
For the second fraction, the numerator can be factored as follows:
[tex]6x^2 - 2x - 4 = (2x - 4)(3x + 1)[/tex]
The denominator can be factored as follows:
[tex]2x^2 - x - 10 = (2x + 5)(x - 2)[/tex]
Now we can simplify the expression by canceling out any common factors:
[tex](5 + 2x)(5 - 2x)/(2x + 5)(3x - 3) * (2x - 4)(3x + 1)/(2x + 5)(x - 2)[/tex]
[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(2x + 5)(3x - 3)(2x + 5)(x - 2)[/tex]
[tex]= (5 + 2x)(5 - 2x)(2x - 4)(3x + 1)/(3x - 3)(x - 2)[/tex]
Since the expression is equal to 0, we can set each factor equal to 0 and solve for [tex]x[/tex]:
[tex]5 + 2x = 0 \\5 - 2x = 0 \\2x - 4 = 0 \\3x + 1 = 0 \\3x - 3 = 0 \\x - 2 = 0 \\[/tex]
Solving for x, we get the following solutions:
[tex]x = -5/2 \\x = 5/2 \\x = 2 \\x = -1/3\\ x = 1 \\x = 2 \\[/tex]
Therefore, the solver for this expression is [tex]x = -5/2, 5/2, 2, -1/3, 1, 2[/tex].
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please help me i have a test and i did not study.
The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value: (0, 3), (2, 2), (-1, 1).
What are ordered pair?An ordered pair (a, b) is a pair of objects in mathematics. Because the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b, the order in which the items occur in the pair is important. The unordered pair a, b, on the other hand, equals the unordered pair b, a.
Ordered pairs are sometimes known as 2-tuples, or sequences of length 2 (or, in computer science, sometimes, lists). 2-dimensional vectors are occasionally used to refer to ordered pairs of scalars.
The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value.
Some of the input, output pair are:
(0, 3)
(2, 2)
(-1, 1)
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Teresa can paddle her kayak 6 miles per hour in still water. It takes her as long to paddle 9 miles upstream as it takes her to travel 27 miles downstream. Determine the speed of the river's current.
The speed of the river's current is 3 miles per hour.
How To determine the speedTo determine the speed of the river's current, we can use the formula d = rt, where d is the distance, r is the rate, and t is the time.
We can set up two equations, one for upstream and one for downstream, and solve for the speed of the river's current.
For upstream:
9 = (6 - c)t
For downstream: 27 = (6 + c)t
Since it takes her the same amount of time to paddle 9 miles upstream as it does to travel 27 miles downstream, we can set the two equations equal to each other:
9 = (6 - c)t = 27 = (6 + c)t
Simplifying and solving for c:
9(6 + c) = 27(6 - c) 54 + 9c = 162 - 27c 36c = 108 c = 3
Therefore, the speed of the river's current is 3 miles per hour.
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Sketch the figure in the side length of an equilateral triangle is 5 centimeters
Fοr an equilateral triangle, sketch is drawn fοr side length = 5 cm.
What are triangles?Triangles are a particular sοrt οf pοlygοn in geοmetry that have three sides and three vertices. Three straight sides make up the twο-dimensiοnal figure shοwn here. An example οf a 3-sided pοlygοn is a triangle. The tοtal οf a triangle's three angles equals 180 degrees. One plane cοmpletely enclοses the triangle.
An equilateral triangle in geοmetry is a triangle with equal-length sides οn all three sides.
In the well-knοwn Euclidean geοmetry, an equilateral triangle is alsο equiangular, meaning that each οf its three internal angles is 60 degrees and cοngruent with the οthers.
The given triangle has a side length οf 5 cm.
Sο, each sire measures the same.
Therefοre, the sketch is drawn fοr the same.
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Which comparison is not correct?
-7 < -2
-1 > -5
7 > -9
5 < -8
[tex]5 < - 8[/tex]
__________
A bank has to be guarded 24 hours a day. 9 guards are ordered to split each day’s guard duty equally. How long will each guard spend on guard duty in one day?
Answer:8/3
Step-by-step explanation:
Total number of hours: 24
Total number of guards: 9
Equation: Total number of hours/ total number of guards
24/9= 8/3 hour shifts or 2.66667 hour shifts for each guard.
I think it's B but I'm not sure
Use the solid figure to determine whether each statement is true or false. A?
b?
c?
d?
e?
f?
To make the solid figure true using column A and column B are as follow,
1.ice cube → cube
2.tissue roll → cylinder
3.match box →rectangular prism
4.volleyball →sphere
5.can of sardines →cylinder
6.milk box → rectangular prism
7.volcano →cone
8.toblerone →triangular prism
9.bus→rectangular prism
10.roof of a nipa hut→ triangular pyramid
Solid figure represents the following shape,
1. Ice cube represents the cube shape as all the sides are of same length.
2. Tissue roll represents the cylindrical shape.
3. Match box is an perfect example for rectangular prism.
4. Volleyball represents the spherical shape.
5. Can of sardines is one of the perfect example of cylinder.
6. Milk box is also one of the example of rectangular prism
7.volcano represents the cone.
8.toblerone is representing triangular prism.
9.bus is a example of rectangular prism
10.roof of a nipa hut it is an example of triangular pyramid
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The above question is incomplete, the complete question is:
Choose the solid figure in Column B to make each statement is true of column A.
Column A.
1.ice cube
2.tissue roll
3.match box
4.volleyball
5.can of sardines
6.milk box
7.volcano
8.toblerone
9.bus
10.roof of a nipa hut
Column B.
A. cone
B. cube
C. cylinder
D. rectangular prism
E. sphere
F. square pyramid
G. triangular prism
H. triangular pyramid
I am unsure how to solve problems H through L and it's due by Friday!!! pls help! (solve for variable listed on paper from equation)
Answer:
Step-by-step explanation:
(h)
[tex]KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}[/tex]
(g)
[tex]s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v[/tex]
(i)
[tex]s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t[/tex]
(j)
[tex]\frac{pV}{T} =nR\\T=\frac{pV}{nR}[/tex]
(k)
[tex]a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }[/tex]
(i)sinθ[tex]=\frac{a}{b}[/tex]
θ=[tex]\frac{a}{sin(b)}[/tex]
Jian made some designs using equilateral triangles, as shown below. He noticed that as he added new triangles, there was a
relationship between n, the number of triangles, and p, the outer perimeter of the design. The table below lists the outer
perimeters for the designs shown.
Number of 1 2 3 4
triangles
Outer
Perimeter
3 4 5 6
n
A
Р
Write a rule for finding p, the outer perimeter for a design that uses n triangles.
The perimeter is the tοtal length οf a shape's bοundary, and the rule fοr finding the οuter perimeter οf Jian's equilateral triangle designs is p = n + 1.
What is a perimeter?The perimeter οf a twο-dimensiοnal shape is the tοtal length οf its bοundary, which is the sum οf the lengths οf all its sides. It is typically measured in units such as centimeters, inches, οr meters.
Fοr example, the perimeter οf a square with side length s is 4s, since it has fοur sides οf equal length. The perimeter οf a rectangle with length l and width w is 2l + 2w, since it has twο pairs οf sides οf different lengths.
Nοw, let's cοnsider the relatiοnship between the number οf triangles and the οuter perimeter οf Jian's design. Frοm the table, we can see that the οuter perimeter increases by 1 as the number οf triangles increases by 1. Specifically, the οuter perimeter is always 1 mοre than the number οf triangles used in the design.
Therefοre, we can write the rule fοr finding the οuter perimeter p in terms οf the number οf triangles n as:
p = n + 1
This rule tells us that if we knοw the number οf triangles used in a design, we can find the οuter perimeter by adding 1 tο that number.
Hence, The perimeter is the tοtal length οf a shape's bοundary, and the rule fοr finding the οuter perimeter οf Jian's equilateral triangle designs is p = n + 1.
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Solve the proportion.
$\frac{x}{4}=\frac{2}{5}$
$
The value of x from the proportion is x = 1.6
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A
Now , the value of A is
( x / 4 ) = ( 2 / 5 )
On simplifying , we get
Multiply by 4 on both sides , we get
x = ( 2 * 4 ) / 5
x = 8/5
On further simplification , we get
x = 1.6
Therefore , the value of x is 1.6
Hence , the proportion is x = 1.6
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HELP PLEASE AND THANK YOU
Answer:
5n = 1.75
Step-by-step explanation:
We are given 1.75 and n 5 times, so
5n = 1.75
Answer: n=0.35
Step-by-step explanation:
Divide 1.75 into fifths and that equals 1 n
Kim went to the store she bought fewer than 20 pieces of fruit she bought three more apples then oranges how many of each kind of fruit Kim could gave him bought? how many how many pieces of fruit in all?
The number of fruits that Kim bought in all, given the apples and oranges was ;
8 oranges 11 apples How to find the number of fruits ?Let's call the number of oranges that Kim bought "O" and the number of apples that Kim bought "A".
From the problem, we know that Kim bought fewer than 20 pieces of fruit, so we can write:
A + O < 20
A = O + 3
Simplifying:
2O + 3 < 20
2O < 17
O < 8.5
Since O represents the number of oranges, we know that Kim bought fewer than 8.5 oranges. Since she can't buy a fraction of an orange, this means that she must have bought either 8 oranges or fewer.
Now we can use the equation A = O + 3 to find the number of apples she bought:
A = 8 + 3 = 11
So Kim bought 8 oranges and 11 apples.
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The points F(8,-1), G(2,1), H(1, -2), and I(7,-4) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.
The points F(8,-1), G(2,1), H(1, -2), and I(7,-4) form a quadrilateral. The desired slopes and lengths are follows:
Slopes:The type of quadrilateral that BEST identifies the given points is a parallelogram.
To find the slopes and lengths of the quadrilateral, we will use the slope formula and the distance formula.
Slope formula: m = (y2 - y1)/(x2 - x1)
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Slopes:
FG: m = (1 - (-1))/(2 - 8) = -1/3
GH: m = (-2 - 1)/(1 - 2) = 3
HI: m = (-4 - (-2))/(7 - 1) = -1/3
IF: m = (-1 - (-4))/(8 - 7) = 3
Lengths:
FG: d = √((2 - 8)² + (1 - (-1))²) = √(40) = 2√(10)
GH: d = √((1 - 2)²+ (-2 - 1)²) = √(10)
HI: d = √((7 - 1)^2 + (-4 - (-2))²) = √(40) = 2√(10)
IF: d = √((8 - 7)² + (-1 - (-4))^2) = √(10)
From the above calculations, we can see that the slopes of FG and HI are equal, and the slopes of GH and IF are equal. This means that the opposite sides of the quadrilateral are parallel. Additionally, the lengths of FG and HI are equal, and the lengths of GH and IF are equal. This means that the opposite sides of the quadrilateral are also congruent.
Therefore, the type of quadrilateral that BEST identifies the given points is a parallelogram.
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One Monday in December, it was `-8`ºC in Harbin, China and `-2`ºC in Beijing, China. Which city was colder on that day?
Harbin was colder than Beijing on that particular day in December because the temperature difference between the two cities was -6ºC.
To figure out which city was colder, we need to compare the difference between the temperatures of the two cities. The temperature difference is the numerical value we get when we subtract one temperature from the other.
In this case, the temperature in Harbin was -8ºC and the temperature in Beijing was -2ºC. To find out which city was colder, we need to calculate the temperature difference between the two cities.
To do this, we subtract the temperature in Beijing from the temperature in Harbin:
-8ºC - -2ºC = -6ºC
So the temperature difference between the two cities is -6ºC. This means that Harbin was colder than Beijing on that day.
We can see that the temperature difference is negative, which tells us that the temperature in Harbin was lower than the temperature in Beijing.
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Please help me you can use any strategie
The responses which represents the area of the rectangle are 23 ⅝ and 198/8
The correct answer choice is option A and B
What is the area of a rectangle?Area of a rectangle = Length × Width
Length = 5 ¼ metros
Width = 4 ½ metros
Area of a rectangle = Length × Width
= 5 ¼ metros × 4 ½ metros
= 21/4 × 9/2
= (21 × 9) / (4 × 2)
= 189 / 8 square metros
= 23 5/8 square metros
Hence, the area of the rectangle is given by 189 / 8 square metros or 23 5/8 square metros.
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Julian makes and sells wallets. He estimates that his income can be modeled by y = 18x - 140, where x is the number of wallets he sells. He estimates that his costs to make the wallets can be modeled by y = 7x+160. How many wallets does Julian need to make in order to break even?
Therefore , the solution of the given problem of equation comes out to be julian must sell at least 28 wallets in order to make even.
How do equations operate?Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical fraction equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection between each sign part and the number of lines. The significance of a symbol usually contradicts itself.
Here,
For Julian to break even, his revenue must match his expenses. Therefore, we can equalise the two equations and find x:
=> 18x - 140 = 7x + 160
7x is subtracted from both lines to yield:
=> 11x - 140 = 160
140 added to both ends results in:
=> 11x = 300
When we multiply both parts by 11, we get:
=> x = 27.27 (rounded to two integer places) (rounded to two decimal places)
We can round up to the nearest whole amount because Julian cannot sell a fraction of a wallet. Julian must therefore sell at least 28 wallets in order to make even.
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