By substituting the equations for x and y into the equation z = x + y, simplifying the expression, and solving for z in terms of a, it can be demonstrated that the two equations demonstrate that z = x + y.
To prove that the two equations show that z = x + y, we need to perform the following steps:
Substitute the given equations for x and y in the equation z = x + y:
z = (2a + 3b) + (4a - 5b)
Simplify the right-hand side of the equation by combining like terms:
z = 6a - 2b
Substitute the value of b in terms of a from the equation 2a + 3b = 7:
2a + 3b = 7
3b = 7 - 2a
b = (7 - 2a)/3
Substitute the value of b in terms of an into the equation z = 6a - 2b:
z = 6a - 2((7 - 2a)/3)
Simplify the expression by combining like terms and solving for z:
z = (12a - 14)/3
z = 4a - 4.67
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Check all statements that are true about the Pythagorean Theorem
Only used on Right Triangles
The hypotenuse is the shortest side of the triangle
The legs are sides a and b of the triangles
The last step is to take the square root of both sides
Exponents are NOT a part of the pythagorean theorem
The true statements about the Pythagorean theorem are :
a) Only used on Right Triangles
b) The legs are sides a and b of the triangles
c) The last step is to take the square root of both sides
Given data ,
The Pythagorean Theorem is a mathematical theorem that applies only to right triangles, and it states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the two other sides, called the legs.
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse
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I. Solve each equation by factoring.
1) p² = -6p
3) k² - 28 = -3k
5) 2m² + 13m + 15 = 0
2) x² = -49 - 14x
4) r² =9r-8
6) 3m² +20m-32=0
The solution of the equation is determined as;
1. p = 0 or - 6.
2. x = -7 twice
3. k = -7 or 4
4. r = 1 or 8
5. m = -3/2 or -5.
6. m = 4/3 or -8
What is the factorization of the equation?The expression can be factorized as follows;
1. p² = -6p
p(p + 6) = 0
p = 0 or p + 6 = 0
p = 0 or - 6
2. x² = -49 - 14x, factorize as follows;
put the both constant and variables on one side;
x² + 14x + 49 = 0
(x + 7)(x + 7) = 0
x = -7 twice
3. k² - 28 = -3k, factorize as follows;
k² + 3k - 28 = 0
k² + 7k - 4k - 28 = 0
(k + 7)(k - 4) = 0
k = -7 or 4
4. r² = 9r - 8, factorize as follows;
r² - 9r + 8 = 0
r² -r - 8r = 0
(r - 1)(r - 8) = 0
r = 1 or 8
5. 2m² + 13m + 15 = 0, factorize as follows;
2m² + 3m + 10m + 15 = 0
(2m + 3)(m + 5) = 0
2m = -3 or m = -5
m = -3/2 or -5
6. 3m² + 20m - 32 = 0, factorize as follows;
3m² - 4m + 24 m - 32
(3m - 4)(m + 8) = 0
3m = 4 or m = -8
m = 4/3 or -8
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the matrices form a basis for the linear space write the matrix of the linear transformation such that relative to this basis.
Answer: )Step-by-step explanation:
When you say that the matrices form a basis for the linear space, I assume you mean that they form a basis for the vector space of matrices with the same dimensions.
To write the matrix of the linear transformation relative to the given basis, follow these steps:
1. Identify the basis matrices for the linear space.
2. Apply the linear transformation to each basis matrix.
3. Express the transformed matrices as linear combinations of the basis matrices.
4. Write the coefficients of these linear combinations as columns in the matrix of the linear transformation.
By following these steps, you will have the matrix of the linear transformation relative to the given basis. Note that I cannot provide specific numbers or examples since no specific matrices or transformations were provided in your question.
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Please help answer this question.
The angle that has a cosine of 3/5 is: ∠A
How to find trigonometric ratios?The three main trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
The given fraction is actually 3/5. This can also be written as 6/10. Thus:
From the given triangle, we can say that:
cos A = 6/10
Thus, it represents angle A.
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if the probability that a tire has ana expected life of at least 30000 miles is 0.85, find the probailities that amoong 20 such tirse
If the probability that a tire has an expected life of at least 30000 miles is 0.85, then the probability that a tire will have a life of less than 30000 miles is 0.15.
Using this information, we can find the probability that among 20 tires, a certain number will have a life of less than 30000 miles. This can be done using a binomial distribution, where the probability of success (a tire having a life of at least 30000 miles) is p = 0.85 and the number of trials is n = 20.
The probability of having k tires with a life of less than 30000 miles is given by the formula:
[tex]P(k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]
where (n choose k) represents the number of ways to choose k items out of n, and is calculated by the formula:
(n choose k) = n! / (k! * (n-k)!)
Using this formula, we can find the probabilities of having 0, 1, 2, ..., 20 tires with a life of less than 30000 miles.
For example, the probability of having exactly 3 tires with a life of less than 30000 miles is:
P(3) = (20 choose 3) * 0.85^17 * 0.15^3
= 1140 * 0.085 * 0.003375
= 0.02736
Similarly, we can find the probabilities of having any other number of tires with a life of less than 30000 miles.
Note that the sum of all these probabilities is equal to 1, since one of these outcomes must occur.
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Find the probability that a randomly
selected point within the square falls in the
red-shaded triangle.
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
0.13
Step-by-step explanation:
You want the probability that a point in the figure lies in the red shaded area.
ProbabilityThe desired probability is the ratio of the red area to the entire area.
Red areaThe red area is half a 4×4 square, so is (4×4)/2 = 8 square units.
Total areaThe area of the whole figure is that of an 8×8 square, so is (8×8) = 64 square units.
RatioThe ratio of the areas is ...
red/whole = 8/64 = 1/8 = 0.125 ≈ 0.13
The probability that a randomly selected point falls in the red area is about 0.13.
<95141404393>
annalisa can rent a bike from one store for $22.25 per hour with no additional charge for a helmet. at another store, the bike rental fee is $21.00 per hour, and there is flat fee of $9.00 for the helmet. if annalisa would pay the same amount at the either store to rent a bike and helmet, for how many hours is the rental?
Answer:
7.2 hours
Step-by-step explanation:
You want the number of rental hours that will result in the same charge if one store rents for $22.25 per hour, and the other store rents for $21.00 per hour with an added $9 charge.
CostThe cost for h hours at the first store is ...
cost = 22.25h
The cost for h hours at the second store is ...
cost = 21.00h +9.00
The costs are the same when ...
22.25h = 21.00h +9.00
1.25h = 9.00 . . . . . . . . . . . . . subtract 21h
h = 9.00/1.25 = 7.20 . . . . . . . divide by 1.25
Annalisa will spend the same at each store for a rental of 7.2 hours.
__
Additional comment
The cost at either place for a 7.2 hour rental is $160.20.
<95141404393>
Leroy buys 5 single tickets
He uses a voucher that reduces the ticket by a quarter
How much does he pay?
Please Help
The calculated amount paid by Leroy is 4.75
Calculting how much he pays?From the question, we have the following parameters that can be used in our computation:
Ticket = 5
Reduction = A quarter
using the above as a guide, we have the following:
Amount paid = 5 - A quarter
Evaluate
Amount paid = 4.75
Hence, the amount paid = 4.75
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HELP PLEASE IM TIMED
The amount of fabric needed to make the tent is given as follows:
C. 18,350 sq. in.
How to obtain the amount of fabric needed?
The amount of fabric needed is given by the surface area of the figure presented in this problem.
The surface area is given by the sum of all areas that compose the figure in the context of the problem.
The figure is composed as follows:
Rectangle of dimensions 2a + c and b -> 198 inches and 75 inches.Two triangles of base c and height d -> base 50 inches and height 70 inches.Hence the surface area is given as follows:
S = 198 x 75 + 2 x 0.5 x 50 x 70
S = 18,350 sq. in.
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pls help !!!!!!!!!!!!
Answer:
[tex]C.\quad \dfrac{\sqrt{17}}{6}[/tex]
Step-by-step explanation:
We are given
[tex]\tan\theta = - \dfrac{\sqrt{19}}{\sqrt{17}} \\\\[/tex]
Square both sides
[tex]\tan^2\theta = \left(- \dfrac{\sqrt{19}}{\sqrt{17}} \right)^2 = \dfrac{19}{17}[/tex]
[tex]\tan \theta = \dfrac{\sin\theta}{\cos\theta}\\\\\tan^2 \theta = \dfrac{\sin^2\theta}{\cos^2\theta}\\[/tex]
Substituting for [tex]tan^2 \theta[/tex] and switching sides we get
[tex]\dfrac{\sin^2\theta}{\cos^2\theta} = \dfrac{19}{17}\\\\\text{Add 1 to both sides:}\\\\ \\ \dfrac{\sin^2\theta}{\cos^2\theta} + 1 = \dfrac{19}{17} + 1 \\\[/tex]
[tex]\dfrac{\sin^2\theta + cos^2\theta}{\cos^2\theta} = \dfrac{19 + 17}{17} = \dfrac{36}{17}[/tex]
[tex]\sin^2\theta + cos^2\theta = 1[/tex]
giving
[tex]\dfrac{1}{\cos^2\theta} = \dfrac{36}{17}[/tex]
[tex]\dfrac{17}{36} = \cos^2\theta\\\\ \cos^2\theta = \dfrac{17}{36}\\\\ \cos\theta = \sqrt{\dfrac{17}{36}}\\\\ \cos\theta = \dfrac{\sqrt{17}}{6} \\\\[/tex]
This is choice C. You had it right
A bakery has 9 different types of pastries for breakfast and either coffee, tea, or orange juice for beverages. How many different breakfast choices are there?
Given bakery can offer 27 distinct types of breakfasts.
The number of pastries available must be multiplied by the number of beverages available in order to determine how many distinct breakfast options are available at the bakery.
The overall amount of varied breakfast options is nine pastries and three beverage selections.
3 drinks plus 9 pastries equal 27 distinct breakfast options.
As a result, the bakery offers 27 distinct breakfast options.
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The table below shows a proportional relationship between v and w.
V
36
63
144
w
4
7
16
Find the constant of proportionality from v to w. Express
your answer as a fraction in reduced terms.
The constant of proportionality is expressed as a fraction in reduced terms as: k = 1/9.
What is the Constant of Proportionality?The constant of proportionality is a constant which represents the rate at which one variable vary directly with another variable, proportionately.
For example, if x and y are the two variables, and y is dependent on x, therefore:
Constant of proportionality (k) = y/x.
The table given as shown in the attachment shows a relationship between v and w. Therefore, we have:
Constant of proportionality (k) = 16/144 = 7/63 = 4/36
Constant of proportionality (k) = 1/9
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prove that : Cos² (180-x) + 2 CosxCos (90+ x) tan (360-x) = Sin ²x + 1
The trigonometric identity cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x
What is a trigonometric identity?A trigonometric identity is a mathematical expression that contains trigonometric ratios.
To prove that : cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = sin²x + 1 , we proceed as follows
We need to show that Left hand side L.H.S = right hand side R.H.S
Now
cos(180 - x) = -cosx, cos(90 + x) = -sinx, tan(360 - x) = -tanxSo, substituting the values of the variables into the equation, we have that
L.H.S = Cos²(180 - x) + 2CosxCos(90 + x)tan(360 - x) = (-Cosx)² + 2Cosx(-sinx)(-tanx)
= (Cosx)² + 2Cosxsinxtanx
Now tanx = sinx/cosx,
So, substituting the values of the variables into the equation, we have that
(Cosx)² + 2Cosxsinxtanx = (cosx)² + 2cosxsinxsinx/cosx
= cos²x + 2sin²x
= cos²x + sin²x + sin²x
Now the trigonometric identity cos²x + sin²x = 1.
So, we have that
cos²x + sin²x + sin²x = 1 + sin²x = R.H.S
So, cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x
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How to slove this proof ?
To prove that DE is parallel to FB, we can use the property that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
We can see triangles AED and CFB with DE and FB as their respective midsegments. Then, we can show that these triangles are similar and that their corresponding sides are proportional. This will imply that DE and FB are parallel.
Proof:
ABCD is a parallelogram, E is the midpoint of AB and F is the midpoint of DC.
Given
Construct triangles AED and CFB with DE and FB as their midsegments, respectively.
Definition of midsegment
AE = ED and CF = FB
Given that E and F are midpoints
AD = BC
Opposite sides of a parallelogram are congruent
∠AED = ∠DCF
Opposite angles of a parallelogram are congruent
∠ADE = ∠CDB
Alternate interior angles formed by parallel lines and a transversal
Triangles ADE and CFB are similar
By angle-angle similarity (AA)
AD/CF = DE/FB
Corresponding sides of similar triangles are proportional
Substituting AD = BC and simplifying, we get:
BC/CF = DE/FB
Since CF = FB (given), we have:
BC/FB = DE/FB
Therefore, BC = DE
Since the corresponding sides of similar triangles are proportional, we can equate BC/CF and DE/FB to get this result.
Hence, DE is parallel to FB
If a line segment joining the midpoints of two sides of a triangle is parallel to the third side, then it is half its length.
Therefore, DE is parallel to FB, as required.
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Okay, so “the radius of a circle is 1 yard, what’s the circles circumference?” (Please don’t round it needs exact)
Can you also include the formula for solving + the formula for solving when given diameter? Thanks sm!!
Answer:
2π yards
Step-by-step explanation:
You want the circumference of a circle with a radius of 1 yard.
CircumferenceWhen the radius is given, the formula for circumference is ...
C = 2πr . . . . . circumference for radius r
When the diameter is given, the formula for circumference is ...
C = πd . . . . . circumference for diameter d
ApplicationFor a radius of 1 yard, the circumference is ...
C = 2π(1 yard) = 2π yards
The circle's circumference is 2π yards.
__
Additional comment
The diameter is twice the radius, so ...
d = 2r
That is, the diameter of the given circle is 2 yards. Using the second formula, we get ...
C = π(2 yards) = 2π yards
Rearranging the second formula, we can get the equation ...
π = C/d
That is, π (pi) is the ratio of the circumference to the diameter.
PLEASE HELP!!! Amusement Park: Coffee and Crime
Directions: Answer the following problems showing as much work as you can.
As you are drawing up the plans to build a coffee shop in your amusement park, a co-worker comes to you with a concern. He heard a news report that indicated that a coffee shop would bring more crime into the amusement park. To support this claim, your co-worker presented the following data and scatterplot (with the least squares line shown) for 8 counties in the state:
County
Shops
Crimes
A
9
4000
B
1
2700
C
0
500
D
6
4200
E
15
6800
F
50
20800
G
5
2800
H
24
15400
The scatterplot shows the positive linear relationship between “Shops” (the number of coffee shops of this particular chain in the county) and “Crimes” (the number of annual property crimes for the county). In other words, counties with more of these coffee shops tend to have more property crimes annually.
Does the relationship between Shops and Crimes appear to be linear? Would you consider the relationship between Shops and Crimes to be strong, moderate, or weak?
Compute the correlation coefficient. Does the value of the correlation coefficient support your choice in part (a)? Explain.
The equation of the least-squares line for these data is: Predicted Crimes = 1434 + 415.7(Shops). Based on this line, what is the estimated number of additional annual property crimes for a given county that has 3 more coffee shops than another county?
Do these data support the claim that building a coffee shop will necessarily cause an increase in property crimes? What other variables might explain the positive relationship between the number of coffee shops for this coffee shop chain and the number of annual property crimes for these counties?
If the following two counties were added to the data set, would you still consider using a line to model the relationship? If not, what other types (forms) of model would you consider?
County
Shops
Crimes
I
25
36900
J
27
24100
The linear pattern between Shops and Crimes is established through the visible increasing trend formed by data points within the scatterplot.
How to explain the informationThis is further reinforced by the noteworthy clustering of evidence along the least squares line, implying an undeniable relationship exists between the number of coffee shops and cases of reported property crime in these counties.
Moreover, the correlation coefficient, at 0.94, strongly accentuates the strong positive link that has been deduced between both external and internal variables. .
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need help with this just need a little help with it
2x - 8 = 2(2x - 15) and 11 are the correct equation and answer respectively.
Similarity theorem of triangleThe given diagram is a triangle. From the figure, the triangles QLK is similar to triangle QRP.
Hence, the correct expression to solve for x will be:
RP = 2LK
Substitute the expression given
RP = 2x - 8
LK = 2x - 15
Substitute to have:
2x - 8 = 2(2x - 15)
Simplify to have:
2x - 8 = 4x - 30
2x - 4x = -30 + 8
-2x = -22
x = 11
Hence the correct equation and answer to solve for x using the triangle are 2x - 8 = 2(2x - 15) and 11 respectively.
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find the equation of the tangent line to the curve at the given point. y = 9x − 6 x , (1, 3)
To find the equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3), follow these steps: 1. Find the derivative of the function: dy/dx r,
Represents the slope of the tangent line at any point (x, y) on the curve.
y = 9x - (6/x)
dy/dx = d(9x)/dx - d(6/x)/dx
Using the power rule for the first term and the quotient rule for the second term:
dy/dx = 9 - (-6/x^2)
dy/dx = 9 + 6/x^2
2. Find the slope of the tangent line at the given point (1, 3) by plugging x = 1 into the derivative:
m = 9 + 6/1^2
m = 9 + 6
m = 15
3. Use the point-slope form of a linear equation to find the equation of the tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope:
y - 3 = 15(x - 1)
4. Solve for y to get the equation of the tangent line:
y = 15(x - 1) + 3
y = 15x - 15 + 3
y = 15x - 12
The equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3) is y = 15x - 12.
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please answer fast i’m
doing ixl!
what is m
Answer:
Step-by-step explanation:
dior dior
18. How are sequential circuits different from combinational circuits?
The main difference between sequential and combinational circuits is that sequential circuit have internal memory and state, while combinational circuits do not.
Sequential circuit and combinational circuits are both types of digital circuits that are used in electronics and computer engineering. The main difference between the two is that sequential circuits use feedback and memory elements to store and propagate information, while combinational circuits do not.
Combinational circuits are made up of logic gates that are connected together to perform a specific function, such as addition or subtraction. The output of a combinational circuit depends only on the current inputs, and there is no internal memory or state.
In contrast, sequential circuits use feedback to store and propagate information, and the output of a sequential circuit depends not only on the current inputs but also on the past inputs and the internal state of the circuit. Sequential circuits include flip-flops, registers, and counters, which are used to store and manipulate data over time.
In summary, the main difference between sequential and combinational circuits is that sequential circuits have internal memory and state, while combinational circuits do not.
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A piece of art is in the shape of a rectangular pyramid like the figure shown.
How much glass is needed to cover the entire pyramid?
102.53 ft2
144.53 ft2
198.06 ft2
289.06 ft2
The amount of glass needed to cover the entire pyramid is given as follows:
144.53 ft².
How to obtain the amount of glass?The amount of glass needed to cover the entire pyramid is given by the surface area of the pyramid.
The surface area of any prism is given by the sum of the areas of all the parts of the prism.
The pyramid in this problem is composed as follows:
Rectangle of dimensions 7 ft and 6 ft.Two triangular faces of base 7 ft and height 7.79 ft.Two triangular faces of base 6 ft and height 8 ft.The areas are calculated as follows:
Rectangle: multiplication of dimensions.Triangle: half the multiplication of the base by the height.Hence the surface area of the pyramid is given as follows:
S = 7 x 6 + 2 x 0.5 x (7 x 7.79 + 6 x 8)
S = 144.53 ft².
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Will give BRAINLYST HELP Point t is the in center of pQR
25. If point A is the incenter then point A is the point of concurrence of the angle bisectors of a triangle
26. ST = 15
27. x = 8
28. ∠ QRT = 24 degrees
29. ∠ RPT = 31 degrees
What is incenter?This is a point where the angle bisectors of the triangle intersect. The incenter is also the center of the circle
since incenter is the center of the triangle therefore
ST = WT = UT = 16
The incenter is meeting point of angle bisectors too hence we have that
∠ QRT = ∠ PRT = 24 degrees.
Also, ∠ RPT = ∠ RPQ / 2 = 62 / 2 = 31 degrees
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Shaquana invested $230 in an account paying an interest rate of 4 3/8% compounded continuously. Brianna invested $230 in an account paying an interest rate of 4 3/4% compounded monthly. After 18 years, how much more money would Brianna have in her account than Shaquana, to the nearest dollar?
Answer: &1,552.50
Step-by-step explanation: Step 1: Multiply Shaquana and Briana deposits of $230 times both interest rates.
Step 2: Shaquana dollar amount adds up to $1006.25. Brianna’s dollar amount adds up to $1,092.50.
Step 3: Multiply both totals times 18yrs.
Step 4: Subtract 18,112.50 from 19,665 and you find that Brianna will have $1552.50 more than Shaquana.
Brianna would have $290 more in her account than Shaquana after 18 years.
The final amount in Shaquana's account is:
[tex]A=230e^0^.^0^4^3^7^5^\times^1^8[/tex]
[tex]A=230e^0^.^7^8^7^5[/tex]
A=230×1.082
= $249
For Brianna, we have:
P = $230
r = 4.75% / 12 = 0.0039583333
t = 18 × 12 = 216 months
So, the final amount in Brianna's account is:
A = $230×(1 + 0.0039583333)²¹⁶
A=230(1.00395)²¹⁶
A=230×2.34
A=538.2
Therefore, the difference in the final amounts is:
$538.2 - $249= $289.2
So, Brianna would have $290 more in her account than Shaquana after 18 years.
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rewrite 9x (8x7) using the associative law of multiplication
Answer:
504
Step-by-step explanation:
use pemdas
multiply 8 and 7 first then u have 56 so multiply it by 9
The expression 9x (8x7) can be rewritten as (9x8) x7 or 72x7 by using the associative law of multiplication. This law states that the way numbers are grouped doesn't affect the result of multiplication.
Explanation:The question asks to rewrite 9x (8x7) using the associative law of multiplication. The associative law of multiplication, in basic terms, states that the way in which numbers are grouped in multiplication does not change the result.
To apply this law to the given expression, we just need to change the grouping of the numbers. Instead of grouping (8x7) together, we could group (9x8) together. So, the content loaded rewrite of 9x (8x7) using the associative law of multiplication would be: (9x8) x7 or we can write it as 72x7.
This does not change the result of the multiplication, thus demonstrating the associative property. This is a helpful principle to understand, as it is commonly applied in a variety of mathematical operations and can simplify complex equations.
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A researcher is curious about the average IQ of all currently registered voters in the state of Iowa. If the average could be attained, it would be an example of a:
"A researcher is curious about the average IQ of all currently registered voters in the state of Iowa. If the average could be attained, it would be an example of a population parameter."
In statistical terms, a population parameter refers to a characteristic of a whole population. In this case, the researcher is interested in the average IQ of all registered voters in Iowa, which would be a population parameter. The researcher would need to gather IQ data from every registered voter in the state and calculate the mean IQ to obtain the population parameter.
However, it's important to note that obtaining the true population parameter is often impractical or impossible due to logistical constraints, so researchers typically rely on samples to estimate population parameters with a certain level of confidence.
This question should be provided as:
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which of the following is a type i error in this context? null hypothesis: the patient does not have the disease. alternative hypothesis: the patient does have the disease.
In this context, a type I error would occur if the null hypothesis was rejected when it is actually true, meaning that the patient does not have the disease but is diagnosed with it.
This would be a false positive result. It is important to note that a type I error is related to the level of significance chosen for the hypothesis test, and it represents the probability of rejecting the null hypothesis when it is true.
In this case, if the level of significance was set at 0.05, for example, there would be a 5% chance of making a type I error. It is also important to consider the consequences of making a type I error in a medical context, as it could lead to unnecessary treatments or interventions that could harm the patient.
Therefore, it is crucial to carefully design hypothesis tests and choose appropriate levels of significance to minimize the risk of making such errors.
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One spring day, Chloe noted the time of day and the temperature, in degrees Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 54° F. For the next 2 hours, the temperature rose 2° per hour. For the next 4 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 63° at midnight. On the set of axes below, graph Chloe's data.
The graph of Chloe's temperature of the day is plotted
Given data ,
To graph Chloe's data, we can use a line graph with time (in hours) on the x-axis and temperature (in degrees Fahrenheit) on the y-axis. Here is the graph:
The graph has five line segments:
From 6 a.m. to 8 a.m., the temperature rises from 54°F to 58°F. This is a line with a slope of 2/2 = 1, passing through the points (6, 54) and (8, 58).
From 8 a.m. to 12 p.m., the temperature rises from 58°F to 70°F. This is a line with a slope of 3/4, passing through the points (8, 58) and (12, 70).
From 12 p.m. to 2 p.m., the temperature stays at 70°F. This is a horizontal line passing through the point (12, 70).
From 2 p.m. to 4 p.m., the temperature drops from 70°F to 68°F. This is a line with a slope of -1/2, passing through the points (2, 70) and (4, 68).
From 4 p.m. to 12 a.m., the temperature drops from 68°F to 63°F. This is a line with a slope of -5/8, passing through the points (4, 68) and (12, 63).
Hence , the graph is plotted
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an oil storage tank ruptures at time and oil leaks from the tank at a rate of liters per minute. how much oil leaks out during the first hour?
Answer:
If this is the full question, 60x
Step-by-step explanation:
Let x = # of liters leaked per minute. There are 60 minutes in an hour.
If this isn't the full question and you forgot to write the # of liters leaked per minute, just multiply that number by 60.
If the linear transformation T(x)=Ax is one-to-one, then the columns of A form a linearly dependent set
The statement is false.
In fact, the correct statement is the opposite: if the linear transformation T(x) = Ax is one-to-one, then the columns of A form a linearly independent set.
To see why, suppose that T(x) = Ax is one-to-one, which means that for any two distinct vectors x1 and x2, we have T(x1) = Ax1 and T(x2) = Ax2, and Ax1 ≠ Ax2. This implies that x1 ≠ x2, since if x1 = x2, then we would have Ax1 = Ax2, which contradicts the assumption that Ax1 ≠ Ax2.
Now suppose that the columns of A are linearly dependent, which means that there exist scalars c1, c2, ..., cn, not all zero, such that c1a1 + c2a2 + ... + cnan = 0, where a1, a2, ..., an are the columns of A. Then we can rewrite this equation as A(c1e1 + c2e2 + ... + cnen) = 0, where e1, e2, ..., en are the standard basis vectors. Since not all of the ci's are zero, there exists a non-zero vector c = (c1, c2, ..., cn) such that Ac = 0. But this means that T(c) = Ac = 0, which contradicts the assumption that T(x) is one-to-one, since c ≠ 0 but T(c) = 0. Therefore, the columns of A must be linearly independent if T(x) = Ax is one-to-one.
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Find the surface area of a cube with a side measuring 1.9 in. (Round your answer to one decimal place.)
in²
Answer:
21.7 in^2
Step-by-step explanation:
A = 6a^2 =6 · 1.9^2 = 21.66in²
Round: 21.7 in^2