Answers
The integral of the given function is determined as (4²ˣ) / ln4 + C.
option B.
What is the integral of the function?The integral of the function is calculated by applying exponent rule of integration as follows;
The given integration ∫ 4²ˣ4⁻⁴
The given integral function is simplified as follows;
4²ˣ4⁻⁴ = ( 4² )ˣ 4⁻⁴ = 16ˣ4⁻⁴
The simplified expression is integrated as follows;
∫16ˣ4⁻⁴ = [ 16ˣ / ln 4 ] + C
where;
C is the constant of integrationThe integral of the given function is determined as;
∫ 4²ˣ4⁻⁴ = [ 16ˣ / ln 4 ] + C = (4²ˣ) / ln4 + C
so option B is the correct answer.
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Related Questions
IXL S.10…Pls Explain Down Below
Answers
Step-by-step explanation:
it says in the headline here : "college".
really ???
this is basic triangle calculation.
the yellow (shaded) area is the total area of the large triangle minus the area of the small (white) triangle.
both area right-angled triangles, so their areas are simple :
leg1 × leg2 / 2
the area of the full large yellow triangle is therefore
31.6 × 33.1 / 2 = 522.98 in²
the area of the small white triangle is
17.1 × 17.9 / 2 = 153.045 in²
that means the shaded area alone is
522.98 - 153.045 = 369.935 in² ≈ 369.94 in²
find the value of k, if X=3 ,y=2 is a solution of the equation X+3y=k
Answers
[tex]6 + 3 = 9 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
jannele drove 60 km in 5/6 hour and bernie drove 54 km 2/3 hour who drove faster and how many times fast
Answers
Bonjour,
v1 = 60/(5/6) = 60 x 6/5 = 360/5 = 72km/h
v2 = 54/(2/3) = 54 x 3/2 = 162/2 = 81km/h
it's Bernie
z=(2-i)^2+((7-4i)/(2+i))-8
(i is for imaginary numbers)
Answers
After the mathematical calculations, we can see that the value of z = 5 - 15i.
How to solveTo simplify, let's square the complex number (2 - i):
[tex](2 - i)^2 = 2^2 - 2i + 2i - i^2 = 4 - 4i - 1 = 3 - 4i.[/tex]
Divide the complex number (7 - 4i) by (2 + i):
The approach we will take involves multiplying the top and bottom of the equation by the complex conjugate of the denominator.
[tex](7 - 4i) * (2 - i) / (2 + i) * (2 - i) = (14 - 7i - 8i + 4i^2) / (4 + 1) = (14 - 15i + 4(-1)) / 5[/tex]
= (10 - 15i) / 5
= 2 - 3i.
We have to minus 8i:
[tex](3 - 4i) + (2 - 3i) - 8i = 5 - 7i - 8i = 5 - 15i.[/tex]
Therefore, z = 5 - 15i.
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Evaluate the step function for f(1.4).
Answers
The step function evaluated in x = 1.4 gives the outcome y = 1, thus, the correct option is the first one.
How to evaluate the step function?The step function, written as:
f(x) = [x]
Is a function that rounds down the value of x to the nearest whole number.
So, for any input that we give to that function, the output will be equal to the number before the decimal point.
If we evaluate this function in x = 1.4, then we will round to the number before the decimal point, thus the outcome is y = 1.
Then we will get:
f(1.4) = [1.4] = 1
The correct option will be the first one.
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how many odd integers are between 15 and 344
Answers
Answer: 149
Step-by-step explanation: 15 17 19 21
23 25 27 29 31 33 35 37 39 41
43 45 47 49 51 53 55 57 59 61
63 65 67 69 71 73 75 77 79 81
83 85 87 89 91 93 95 97 99 101
103 105 107 109 111 113 115 117 119 121
123 125 127 129 131 133 135 137 139 141
143 145 147 149 151 153 155 157 159 161
163 165 167 169 171 173 175 177 179 181
183 185 187 189 191 193 195 197 199 201
203 205 207 209 211 213 215 217 219 221
223 225 227 229 231 233 235 237 239 241
243 245 247 249 251 253 255 257 259 261
263 265 267 269 271 273 275 277 279 281
283 285 287 289 291 293 295 297 299 301
303 305 307 309 311 313 315 317 319 321
323 325 327 329 331 333
Number of odd integers = (difference between endpoints) / 2 rounded up
Number of odd integers = 329 / 2 rounded up
Number of odd integers = 165
Therefore, there are 165 odd integers between 15 and 344.
Adrian wants to purchase an electric keyboard. The price of the keyboard at Macelli’s, with tax, is $2,400. He can save $150 per month. How long will it take him to save for the keyboard? (round to a full month).
Answers
It will take Adrian 16 full months to save enough money for the electric keyboard.
- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.
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what percent of 75 is 57?
Answers
Answer:
76%
Step-by-step explanation:
57/75
(57 X 100)/ 75
5700/75
1900/25
76/1
76
Guys please help, which one of this is and what is the x and y
Answers
The given matrix has no solution. Therefore, option A is the correct answer.
From the given matrix,
[tex]\left[\begin{array}{ccc}1&1&-4\\-2&-1&6\\-5&-3&16\end{array}\right]\left[\begin{array}{ccc}x\\y\\x\end{array}\right] = \left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x+y-4z\\-2x-y+6z\\-5x-3y+16z\end{array}\right] =\left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]
x+y-4z=6 -------(i)
-2x-y+6z=-10 ---------(ii)
-5x-3y+16z=-26 ---------(iii)
Multiply equation (i) by 2, we get 2x+2y-8z=12 ---------(iv)
Add equation (ii) and (iv), we get
-2x-y+6z+2x+2y-8z=-10+12
y-2z=2 ---------(v)
Multiply equation (i) by 5, we get
5x+5y-20z=30 ---------(vi)
Add equation (vi) from (iii), we get
5x+5y-20z+(-5x-3y+16z)=30-26
5x+5y-20z-5x-3y+16z=4
2y-4z=4
y-2z=2 ---------(vii)
From equation (vi) and (vii), we understood the matrix has no solution
Therefore, option A is the correct answer.
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The measures of the angles of a triangle are shown in the figure below. Solve for x
48⁰
to
56⁰
*****
Answers
The value of x is given as follows:
x = 76º.
How to obtain the value of x?To obtain the value of x, we must consider that the sum of the internal angle measures of a triangle is of 180º.
The internal angles of the triangle in this problem are given as follows:
48º.56º.x.Considering that the sum of the measures is of 180º, the value of x is obtained as follows:
48 + 56 + x = 180
x = 180 - (48 + 56)
x = 76º.
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A. It represents a function because each x-value corresponds to exactly one y-value.
B. It represents a function because each y-value corresponds to exactly one x-value.
&. It does not represent a function because each x-value corresponds to exactly one -value.
D, It does not represent a function because each y-value does not correspond to exactly one x-value.
Answers
A statement that is true about the mapping shown include the following: A. It represents a function because each x-value corresponds to exactly one y-value.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the mapping diagram below, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).
In this context, we can reasonably infer and logically deduce that the mapping diagram represent a function.
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Complete Question:
Which is true about the mapping shown?
A. It represents a function because each x-value corresponds to exactly one y-value.
B. It represents a function because each y-value corresponds to exactly one x-value.
&. It does not represent a function because each x-value corresponds to exactly one -value.
D, It does not represent a function because each y-value does not correspond to exactly one x-value.
100pts! Please help <3
______________________
Answer each question individually
______________________
A community is developing plans for a pool and hot tub. The community plans to
form a swim team, so the pool must be built to certain dimensions. Answer the
questions to identify possible dimensions of the deck around the pool and hot tub.
Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be
the same width on all sides of the pool. Including the deck, the total pool area
has a length of (x+25) yards, with a width of (x+9) yards.
a.) write an equation, representing the total area of the pool and the pool deck. Use white represent the total area. Hint: the area of a rectangle is the length times width
b.) re-write the area equation in standard form. Hint: use the FOIL method.
c.) re-write the equation from part B in vertex form by completing the Square. Hint: move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate the Y.
d.) what is the vertex of the parabola? What are the X - and Y - intercepts? Hint: use your answer from part a to identify the X – intercepts. Use your answers from part B to identify the Y – intercept. Use your answer from part C to identify the vertex.
e.) grab the para bola. Use the key features of the graph that you identified in part D.
f.) in this problem, only positive values of X makes sense why?
g.) what point on your graph shows a total area that includes the pool but not the pool deck?
h.) the community decided on a pool area that add 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when X=6 yards?
Part ll
A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by X feet of deck on each side. The enclosed space is also square that has an area of 169 ft.². Find the width of the deck the space around the hot tub, x.
Step 1-Ryan equation for the area of the enclosed space in the form Y=(side length)2 hint: don’t forget to add x to each side of the hot tub
Step 2- substitute the area of the enclosed space for y in your equation
Step 3- so if your equation from part B for X
Step 4: what is the width of the deck around the hot tub? Hint : one of the answers from part seat is not reasonable
Answers
a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).
b) The area equation in standard form is A = x² + 34x + 225.
c) The vertex form is A = (x + 17)²- 289
d) The x-intercepts is (-4, 0).
a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).
b) Re-writing the area equation in standard form using the FOIL method:
A = x² + 9x + 25x + 225
A = x² + 34x + 225
c) Re-writing the equation from part b in vertex form by completing the square:
A = (x + 17)²- 289
d) The vertex of the parabola is (-17, -289).
The x-intercepts can be found by setting A = 0:
(x + 17)² - 289 = 0
(x + 17)² = 289
x + 17 = ±17
x = -34, 0 (x-intercepts)
The y-intercept is found by setting x = 0:
A = (0 + 17)² - 289
A = 0 (y-intercept)
e) The graph of the parabola is a downward-opening parabola with vertex (-17, -289).
f) In this problem, only positive values of x make sense because the dimensions of the pool and deck cannot be negative.
g) The point on the graph that shows a total area that includes the pool but not the pool deck is the vertex (-17, -289).
h) When x = 6 yards, the total area of the pool and deck can be calculated by substituting x = 6 into the equation:
A = (6 + 17)² - 289
A = 23² - 289
A = 529 - 289
A = 240 square yards
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Edgardo created a rectangular prism with a square base. The volume of the prism is 45 cubic inches. The dimensions of the prism are all whole numbers. What is the height of the prism
Answers
The calculated height of the prism is 5 inches
How to calculate the height of the prismfrom the question, we have the following parameters that can be used in our computation:
Volume = 45 cubic inches
Base = square
The height of the prism is calculated as
Volume = Base length² * Height
substitute the known values in the above equation, so, we have the following representation
Base length² * Height = 45
So, we have
Base length² * Height = 3² * 5
This means that
Base length = 3
Height = 5
Hence, the height of the prism is 5 inches
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Part A. Write the equation 5=10x−5y in slope-intercept form.
Part B. Identify the y-intercept.
please write both answers
Answers
5 + 5y = 10x
Next, we'll subtract 5 from both sides of the equation:
5y = 10x - 5
Finally, we'll divide both sides of the equation by 5:
y = 2x - 1
Therefore, the equation 5=10x-5y in slope-intercept form is y = 2x - 1.
Part B. The y-intercept is the point where the line crosses the y-axis. In slope-intercept form, the y-intercept is the constant term. In this equation, the constant term is -1. Therefore, the y-intercept is -1.
A student takes a true-false test that has 8 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(5)
Answers
The student's chances of answering all five questions correctly are 7/64.
This is an example of a binomial distribution, where each question has a probability of 1/2 of being answered correctly and there are 8 independent trials.
The probability mass function for a binomial distribution is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, p is the probability of success, and k is the number of successes.
In this case, n = 8, p = 1/2, and we want to find P(X = 5).
P(X = 5) = (8 choose 5) * (1/2)^5 * (1/2)^(8-5)
P(X = 5) = (8 choose 5) * (1/2)^8
Using the formula for combinations, (n choose k) = n! / (k! * (n-k)!) we get:
P(X = 5) = (8! / (5! * 3!)) * (1/2)^8
P(X = 5) = 56 * 1/256
P(X = 5) = 7/64
Therefore, the probability of the student getting 5 questions correct is 7/64.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
Answers
Answer:
quadratic formula, completing the square, factorisation
Step-by-step explanation:
Quadratic formula:
x = (-b ± √(b² - 4ac) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
x = ((-b ± √(b² - 4ac)) ÷ 2a)
= (( -16± √((-16)² - 4(8)(3)) ÷ 2(8))
= ((-16 ± √(256 - 96)) ÷ 16)
= (-16 ± √(160)) ÷ 16
= -1 ± (√10)/4
Completing the square:
divide through by 8
x² + 2x + 3/8 = 0
1) put the x, not ^2, in parenthesis.
(x + ) = 0
2) half the coefficient (2) of x. that is 1. Put that into same parenthesis.
(x + 1) = 0
3) we have (x + 1)
4) square this and multiply out. (x + 1)² = x² + x + x +4 = x² +2x + 1
5) this looks just like the original equation (x² + 2x + 3/8) except for +1. What do we have to do to get back to original? 1 – (3/8) = 5/8. We have to subtract 5/8
6) now we have (x + 1)² – 5/8 =0
7) (x + 1)² = 5/8
8) (x + 1) = ± √(5/8)
9) x = ± √(5/8) - 1
= -1 ± (√10)/4
Factorisation:
(8x (- (2√10)) + 8) = 0,
8x = -8 + (2√10)),
x = -1 + (√10)/4
(x ( + (√10)/4 + 1) = 0
x = -1 - (√10)/4
A box has the shape of a rectangular prism with height 30 cm. If the height is increased
by 0.2 cm, by how much does the surface area of the box increase?
Use pencil and paper. Show your work. Then show a second way to solve the problem.
Explain which way you like better and why.
The surface area increases by
cm².
13 cm
30 cm
8.7 cm
Answers
Answer:
8.68 cm²
Step-by-step explanation:
You want the increase in surface area of a box with length and width 13 cm and 8.7 cm when the height is increased from 30 cm by 0.2 cm.
AreaThe increase in area is effectively the lateral area of the prism whose length and width are the same, but whose height is 0.2 cm. That is ...
A = Ph = 2(L+W)h
A = 2(13 cm +8.7 cm)(0.2 cm) = 8.68 cm²
The surface area increases by 8.68 cm².
Alternate solutionWe can find the total area of the box with the different dimensions, then subtract the original area from the increased area.
A = 2(LW +H(L+W))
A1 = 2(13·8.7 +30(13 +8.7)) = 1528.2 cm²
A2 = 2(13·8.7 +30.2(13 +8.7)) = 1536.88 cm²
The increase in area is 1536.88 -1528.2 = 8.68 cm².
We prefer the first solution, as it requires a lot less arithmetic.
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Veronica is making a large table in the shape of a trapezoid.
twice as long as the table's width. Find the area of the table
Click the icon to view the table.
First find the missing dimension.
The length of the bottom base is x= 16 yd.
(Type an integer or a decimal.)
What is the area of the table?
The area is A = (10.) + 2(28)--[
(Type an integer or a decimal.)
Table
3 yd
Help me solve this View an example Get more help
Print
10 yd
8 yd
X
3 yd
Done
Answers
The area of the trapezoid is 104 square yards
As given a table was made by Veronica which is in the shape of a trapezoid.
twice as long as the table's width
Let us find the area of the trapezoid by the given data and formula of trapezoid
The length of the bottom base is x= 16 yd.
Area A=(a+b)h/2
a=10 yd
b=16 yd
h =8 yd
Substitute the values of a, b and h in the area of trapezoid
Area =1/2(10+16)8
=208/2
=104 square yards
Hence, the area of the trapezoid is 104 square yards
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Hi, can you help solve this problem?
Answers
An exponential equation that best fit the data above is [tex]y = 535.02(1.15)^x[/tex]
a = 535.02
b = 1.15.
How to write the regression equation and determine the correlation coefficient?In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the exponential equation and the correlation coefficient are given by:
[tex]y = 535.02(1.15)^x[/tex]
Correlation coefficient, r = 0.9973006 ≈ 1.0
In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is is greater than 0.7;
0.7＜|r| ≤ 1.0 (strong correlation)
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Determine the values of a, b, and c
Answers
A=52
B=38
C=142
Si la secuencia es 7,12,17,22 y la regla es agregar 5 cuales son los siguentes dos terminos ?
Answers
the next two terms in the sequence would be 12 and 17.
Step-by-step explanation:
The attraction force between two particles is inversely proportional to the square of the distance between them. If the force is F when the distance between them is 2r and the force is kF when the distance is 3r, find the value of k.
Answers
F ∝ 1/d^2
Using proportionality, we can write:
F = k/d^2
where k is a constant of proportionality.
If the distance between the particles is 2r, then we have:
F = k/(2r)^2 = k/4r^2
If the distance between the particles is 3r, then we have:
kF = k/d^2 = k/(3r)^2 = k/9r^2
We can then set these two expressions equal to each other and solve for k:
k/4r^2 = k/9r^2
Multiplying both sides by 36r^2 (the least common multiple of 4r^2 and 9r^2), we get:
9k = 4k
Simplifying, we get:
k = 4/9
Therefore, the value of k is 4/9.
At the start of the day, a painter rested a 3 m ladder against a vertical wall so that the foot of the ladder was 50 cm away from the base of the wall. k to task During the day, the ladder slipped down the wall, causing the foot of the ladder to move 70 cm further away from the base of the wall. How far down the wall, in centimetres, did the ladder slip? Give your answer to the nearest 1 cm.
Answers
Answer:
21cm
Step-by-step explanation:
Pythagoras Theorem for right angled triangle a² = b² + c²
hypotenuse² = opposite ² + adjacent ²
Call vertical height of wall (where ladder meets it) H
call ladder L and call ground distance G
50cm = 0.5m
3² = 0.5² + H², H² = 3² - 0.5² = 9 - 0.25 = 8.75. H = √8.75.
length of ladder is always 3m.
After ladder has slipped, G is now 0.5 + 0.7 = 1.2m.
H² = 3² - 1.2²
= 9 - 1.44
= 7.56
H = √7.56
H has changed from √8.75 to √7.56
It has slipped (√8.75 - √7.56)m
= 0.208m
= 20.8 cm
=21cm to nearest cm.
Find the axis of symmetry.
f(x) = -(x - 2)(x + 4)
a) x = 2
b) y = -1
c) y = 8
d) x = -1
Answers
The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.
What is the axis of symmetry of the function?Given the function in the question:
f(x) = -(x - 2)(x + 4)
To find the axis of symmetry, first expand quadratic function f(x) = -(x - 2)(x + 4).
f(x) = -(x - 2)(x + 4)
f(x) = (-x + 2)(x + 4)
f(x) = -x(x + 4) + 2( x + 4 )
f(x) = -x² - 4x + 2x + 8
Collect and add like terms
f(x) = -x² - 2x + 8
To find the axis of symmetry, we can use the formula:
x = -b/2a
Where a = -1 and b = -2.
Substituting these values, we get:
x = -(-2) / 2(-1)
Simplify
x = 2 / -2
x = -1
Therefore, the the axis of symmetry is x = -1.
Option D) x = -1 is the correct answer.
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9. A farmer wants to construct a fence to create a square horse corral with an area of 10,000 square feet. Fence posts along each side will be 10 feet apart at their center. Including the four corner posts, how many posts are needed to construct the fence?
Answers
the total number of posts needed is, 56
Since, we know that the area of the horse corral is 10,000 square feet.
So, it is a square corral, we can find the length of each side by taking the square root of the area, which is 100 feet.
Now, For the total number of posts needed, we need to calculate the perimeter of the corral.
Since there are four sides of equal length, the perimeter of the corral is 4 times the length of one side.
Therefore, the total perimeter is 400 feet.
Now, we need to find the number of posts needed.
We know that each post is placed 10 feet apart along the sides of the corral.
Since there are 4 sides, we need 3 intervals of 10 ft between each post, which gives us a total of 4 posts for every 30 feet of fencing.
Therefore, the total number of posts needed is,
= (400 / 30) x 4 + 4
= 56 posts.
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100 Points! Algebra question. Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Thank you!
Answers
The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537
What is a function
A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
By substitution:For x = -3;
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3
f(-3) = 243 + 108 + 27 + 15 - 3
f(-3) = 390
For x = 4;
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
f(4) = 3(256) - 4(64) + 3(16) - 20 - 3
f(4) = 768 - 256 + 48 - 20 - 3
f(4) = 537
Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.
At the city museum, child admission is $5.10 and adult admission is $8.20. On Wednesday, 176 tickets were sold for a total sales of $1201.40. How many child tickets were sold that day?
Answers
Answer:
So 98 adult tickets were sold.
Step-by-step explanation:
Let's use a system of equations to solve the problem.
Let x be the number of child tickets sold and y be the number of adult tickets sold. Then we have:
x + y = 176 (equation 1)
5.10x + 8.20y = 1201.40 (equation 2)
We can solve for x by isolating y in equation 1 and substituting into equation 2:
y = 176 - x (from equation 1)
5.10x + 8.20(176 - x) = 1201.40 (substitute into equation 2)
5.10x + 1443.20 - 8.20x = 1201.40
-3.10x = -241.80
x = 78
Therefore, 78 child tickets were sold that day. We can find the number of adult tickets by substituting x into equation 1:
78 + y = 176
y = 98
So 98 adult tickets were sold.
Solve for measure of angle a. 36° a 124° a = [? ]° If two chords intersect inside a circle:
Answers
The value of angle a is 80 degrees.
The two chords intersect angle theorem, also known as the intersecting chords theorem, states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
From two chords intersect angle theorem
∠a=(∠b+∠c)/2
in a given case,
∠b=36°
∠c =124°
So, ∠a=(36+124)/2
∠a= 80°
Therefore, the value of angle a will be 80 degrees.
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Complete question:
alfa bought a brand new box of sugar he wants to transfer it to a new container will there be any sugar left over after filling the new container explain show work
Answers
There will be no sugar left after the transfer.
Given are two containers in the shape of a rectangular prism and the second one is a composite solid of rectangular prism and a triangular prism,
We need to compare the volume of both prisms,
For the volume of the composite solid we will add the volume of both solids = 1/2 × base area × height + length × width × height
= 1/2 × 300 × 8 + 12 × 12 × 25
= 1200 + 3600
= 4800 cm³
Now the volume of the old container (rectangular prism - the blue one) = length × width × height = 30 × 20 × 8 = 4800 cm³
Since the volume of both old and new container is same, so there will be no sugar left after the transfer.
Hence there will be no sugar left after the transfer.
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What influenced Denis to write the first non-objective statement? (You must use one quote from his article the Definition of Neotraditionism)
What factors led Kandinsky to arrive at non-objective painting? (You must give at least one quote from Concerning the Spiritual in Art, and list the page number.
What did Kandinsky write about color? (You must give at least one quote from Concerning the Spiritual in Art - Part II. About Painting, VI: The Language of Form and Color and give the page number.)
Answers
1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself.
2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience.
3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul.
Denis was influenced to write the first non-objective statement because of the limitations of representational art.
1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself, which featured a landscape that was "no longer a transcription of nature, but a creation" (Denis, 1914), influenced him to write the first non-objective statement.
This painting by Denis challenged the traditional notions of art as mere representation of nature, and instead presented a new idea of art as a creative act in its own right.
2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience. He wrote that "the artist must be blind to distinction between 'recognized' or 'unrecognized' conventions of form, deaf to the transitory teaching and demands of his particular age.
He must watch only the trend of the inner need, and hearken to its words alone" (Kandinsky, 1977, p. 8). This suggests that Kandinsky was motivated by a desire to break away from the conventional artistic norms of his time and create something that was more true to his own personal vision and inner creative impulses.
3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul. Color is the keyboard, the eyes are the hammers, the soul is the piano with many strings. The artist is the hand that plays, touching one key or another purposively, to cause vibrations in the soul" (Kandinsky, 1977, p. 72).
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