Given
cost of an LCD TV dropped from $800 in 2012 to $700 in 2014
Find out unit rate at which the cost has been decreasing
Proof of (1)
As given in the question
let x denote the number of year and y denote the cost of the LCD TV
Take 2012 as intial year
cost of LCD TV = $800
Thus
x = 0 , y = 800
Take 2014 as the final year.
cost of LCD TV = $700
y = 700
x =2
( as the year changes 2012 to 2014 here exit change of 2 years)
Now find out the unit rate at which the cost is decreasing.
Take two points
( 0, 800) and ( 2, 700)
[tex]unit\ rate=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
putting the above value
we get
[tex]unit\ rate=\frac{700-800}{2-0}\\unit\ rate=\frac{-100}{2}[/tex]
thus
unit rate = -50
unit rate at which the cost has been decreasing is -50.
proof of ( 2)
points are( 0, 800) and ( 2, 700)
The equation is
[tex]\left ( y - y_1 \right ) =\frac{y_2 - y_1}{x_2-x_1}(x-x_1)[/tex]
put the values in the above equation
[tex]\left ( y - 800 \right ) =\frac{700 - 800}{2-0}(x-0)[/tex]
thus the equation becomes
y = -50x+800
Thus y = -50x+800 is the linear model to perdict the cost of LCD TV.
Now find out cost of the LCD TV in 2016
As taken earlier 2012 as the intial year
find the cost of LCD TV in 2016
thus x =4
( year changes 2012 to 2016 here exit the change of 4 years)
put x = 4 in the linear model y = -50x + 800
y = -50× 4 + 800
y = -200 + 800
y = 600
The cost of the LCD TV in 2016 is $600.
Hence proved.
Final answer:
The unit rate at which the cost has been decreasing is $50/year. The predicted cost of an LCD TV in 2016 is $900.
Explanation:
(i) To find the unit rate at which the cost has been decreasing, we can use the formula:
Unit rate = (Change in cost) / (Change in time)
Here, the change in cost is $800 - $700 = $100, and the change in time is 2014 - 2012 = 2 years. Substituting these values into the formula:
Unit rate = $100 / 2 years = $50/year
So, the cost has been decreasing at a rate of $50 per year.
(ii) To construct a linear model, we can use the formula:
Cost = mx + b
Where m is the slope (unit rate) and b is the y-intercept. Substituting the values:
Cost = $50(x - 2012) + $700
Since we want to predict the cost in 2016, we substitute x = 2016:
Cost = $50(2016 - 2012) + $700
Cost = $50(4) + $700
Cost = $200 + $700 = $900
Therefore, the predicted cost of an LCD TV in 2016 is $900.
expand the expression 4(3/2x+5)
Identify and EXPLAIN the ERROR * Show CORRECT WORK and SOLUTION * What STRATEGY did you use for solving this problem *
Which expression is equivalent to the expression 2/3(3 - 1/3)(-1)?
(i'm doing a giveaway worth 25 points if you get the right.)
2/3 (5/3)(-1) = -10/9
Answer:
-7/9
Step-by-step explanation:
2/3(3 - 1/3)(-1) = (1-2/9)(-1) = -1+2/9 = -7/9
a store sells rope by the meter The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long. a. How much does the nylon rope cost per meter. b. How long is a piece of nylon rope that costs $1.00
(a) $0.80
(b) 1.25 m
Step-by-step explanation:(a) Put 1 where L is, and evaluate the equation.
... p = 0.8·1 = 0.8
The cost for 1 meter of rope is $0.80.
(b) Put 1 where p is and solve for L.
... 1 = 0.8L
... 1/0.8 = L = 1.25
The length of rope that costs $1 is 1.25 meters.
Answer:
a. $ 0.8
b. 1.25 meters.
Step-by-step explanation:
Given equation that represents the price p (in dollars) of a piece of nylon rope having length L meters,
[tex]p=0.8L[/tex]
a. If L = 1 meter,
The cost of the rope would be,
[tex]p=0.8(1) = \$ 0.8[/tex]
b. if p = $ 1.00,
[tex]\implies 1 = 0.8L[/tex]
[tex]\implies L=\frac{1}{0.8}=1.25[/tex]
Thus, the length of the rope would be 1.25 meters.
a. Is it possible for a shape to have both reflectional and rotational symmetry? If so, provide an example with a line of symmetry for reflectional rotation and the minimum degree of rotation for rotational symmetry. If not, explain why.
Yes. For example, the shape I will use is the circle.
No matter how you rotate the circle, it will always look the same. If you reflect the circle over any drawen line in which it passes through the middle, the two halves created would be congruent.
~Rise Above the Ordinary, Senpai
In the troposphere, one layer of the Earth's atmosphere, the temperature decreases with increasing altitude from approximately 17°C at Earth’s surface to –51°C at the boundary with the next layer. By how many degrees Celsius does the temperature change in the troposphere?
WILL GIVE BRAINLIEST AND 99 POINTS!!
From the statement select the related given statement.
In a triangle a segment joining the midpoints of two sides is one-half the length of the third side.
A.) Plane R is parallel to plane S; Plane T cuts planes R and S.
B.) △ABC with ∠1 = ∠2.
C.) Point B is between points A and C
D.) Line l; point P not on l.
E.) △ABC with midpoints M and N.
Answer:
E.) △ABC with midpoints M and N.
Step-by-step explanation:
You want a related given statement to the scenario "in a triangle a segment joining the midpoints of two sides is one-half the length of the third side."
ChoicesThe scenario describes a triangle ABC with midpoints designated on two of the sides. There is no "plane R", angles 1 and 2, line l, point P. In triangle ABC, point B will not be between A and C.
These considerations eliminate choices A–D, leaving choice E:
E.) △ABC with midpoints M and N
I need some help with this!
(-x³ +3x +4) -(2x³ +7x² -9) = -x³ +3x +4 -2x³ -7x² +9 . . . . eliminate parentheses
= x³(-1-2) +x²(-7) +x(3) +(4+9)
= -3x³ -7x² +3x +13 . . . matches the second choice.
While riding her bike to the ocean and back home 7 7 times, Corinne timed herself at 52min 52min , 63min 63min , 66min 66min , 60min 60min , 51min 51min , 69min 69min , and 50min 50min . She had set a goal of averaging 59 59 minutes for her rides. How many minutes will she need to spend on her eighth ride to attain her goal?
this is a late assignment, help a girl out hah..
she would need to ride for 61 minutes
Which represents a side length of a square that has an area of 450 square inches? 15 sqrt 2 in. 15 sqrt 3in. 112.5 in. 115.5 in.
15√2
area = s² = 450 ← s is length of side
to find s take the square root of both sides
s = [tex]\sqrt{450}[/tex] = [tex]\sqrt{2(9)(25)}[/tex]
= √2 × √9 × √25 = √2 × 3 × 5 = 15√2
15√2 represents a side length of a square that has an area of 450 square inches.
The answer is option A.
How to find the side length of a square?The area of any quadrilateral can be determined by multiplying the length of its base by its height.
area = s² = 450 ← s is length of side
to find s take the square root of both sides
s = √450 = √2(9)(25)
= √2 × √9 × √25 = √2 × 3 × 5 = 15√2
Since we know the shape here is square, we know that all sides are of equal length. From this, we can work backward by taking the square root of the area to find the length of one side.
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The graph below represents the distance of a dog from a trainer after a command is given.
Which statement could describe the dog’s movement 5 seconds after the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
Answer:
The dog was running towards the trainer to receive a treat
Step-by-step explanation:
At the point on the graph where Time is 5 (seconds), the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer. The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.
Answer:B.The dog was running towards the trainer to receive a treat.
Step-by-step explanation:cuz im right
M is the midpoint of segment AB. A has the coordinates (-5,4) and M is at the origin. Find the coordinates of B
Using geometry:
Since M is the origin, point B is the mirror image of point A with respect to the origin. From the origin to point A, you go 5 units left and 4 units up. For the mirror image, start at the origin, and go 5 units right and 4 units down.
Answer: B(5, -4)
Using the midpoint formula:
[tex] x_m = \dfrac{x_1 + x_2}{2}~~~and~~~y_m = \dfrac{y_1 + y_2}{2} [/tex]
[tex] 0 = \dfrac{-5 + x_2}{2}~~~and~~~0 = \dfrac{4 + x_2}{2} [/tex]
[tex] 0 = -5 + x_2~~~and~~~0 = 4 + x_2 [/tex]
[tex] -x_2 = -5~~~and~~~-4 = x_2 [/tex]
[tex] x_2 = 5~~~and~~~x_2 = -4 [/tex]
Answer: B(5, -4)
As you can see, both methods give you the same answer.
Let x = a + bi and y = c + di and z = f + gi Which statements are true? Check all of the boxes that apply. x + y = y + x (x × y) × z = x × (y × z) x – y = y – x (x + y) + z = x + (y + z) (x – y) – z = x – (y – z)
The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...
x + y = y + x . . . . . . . . . . . . . . . commutative property of addition(x × y) × z = x × (y × z) . . . . . . . . associative property of multiplication(x + y) + z = x + (y + z) . . . . . . . . associative property of additionThe true statements after evaluating the expression based on principle of commutativity and associativity are :
x + y = y + x(x × y) × z = x × (y × z)(x + y) + z = x + (y + z)x = a + bi
y = c + di
z = f + gi
Recall :
Commutative property establishes that, if the ordering of the numbers an addition or multiplication expression, is changed, the result is unchanged : a + b = b + a The Associative property maintains that, the grouping of values in a multiplication operation does not affe t the result of the product. : a × ( b × c) = b × (a × c) = c × (b × a)Evaluating the options :
x + y = y + x ; This is true (Commutative property of addition) (x × y) × z = x × (y × z) (True according to the Associative property) x - y = y - x (False) (x + y) + z = x + (y + z) (True ; Commutative property) (x – y) – z = x – (y – z) (False)Hence, only 3 of the given statements are true, according to the Commutative or Associative rule.
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Find the quotient of 6/8 ÷ 3/-4
Answer:
1
Step-by-step explanation:
The physics scores of 200 students follow a normal distribution with a mean of 75 and a standard deviation of 7. Which conclusion is best supported by this information?
We can say that nearly all of the students got between a 54 and a 96, that 95% got between a 61 and an 89, and about two-thirds got between a 68 and an 82, but there may be other conclusions one may wish to draw.
What is the solution of sqrt2x+4=15
Answer:
x = 126
Step-by-step explanation:
Square both sides of the equation. (sqrt2x+4)^2 = 16^2
2x+4 = 256
Then you should solve for x. (First Subtract 4 from both sides; Then simplify; Next divide both sides by 2; Finally, simplify once more)
This should give you your answer. (x = 126)
Hope this helps! ^-^
Answer:
x = 72
Step-by-step explanation:
sqrt {2x} +4 = 16
sqrt {2x} = 12
2x = 12 ^ 2
x = 144/2
x = 72
If you wanted to write:
sqrt {2x + 4} = 16
2x + 4 = 16 ^ 2
2x + 4 = 256
2x = 252
x = 252/2
x = 126
PLZ HELP ASAP! ILL MARK BRAINLEST!
Factor completely 12x4 + 6x3 + 18x2.
Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)
Factor completely 7x3y +14x2y3 − 7x2y2.
7x2(xy + 2y3 – y2)
7x2y(x + 2y2 – y)
7(x3y +2x2y3 − x2y2)
Prime
What is the Greatest Common Factor of x6 and x3?
x4
x3
x2
x
Question 1.) Factor completely [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex]
Since [tex]6[/tex] divides all the three terms of the equation, so we take [tex]6[/tex] common out from the equation.
i.e., [tex]6(2x^{4}+ 1x^{3}+3x^{2})[/tex]
Now, since [tex]x^{2}[/tex] divides all the three terms of the equation, so we take [tex]x^{2}[/tex] common out from the equation.
i.e., [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Now, this cannot be factored further as [tex]2x^{2}+ 1x+3[/tex] is a quadratic equation and taking out discriminant of it is:
[tex]D = (1)^2 - 4(2)(3)\\ \ \ = 1- 24\\ \ \ = -23<0[/tex]
Since, the discriminant is less than zero. Therefore, the factored form of the given equation : [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex] is : [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Question 2.) [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex]
Since [tex]7[/tex] divides all the three terms of the equation, so we take [tex]7[/tex] common out from the equation.
i.e., [tex]7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})[/tex]
Now, since [tex]x^{2}y[/tex] divides all the three terms of the equation, so we take [tex]x^{2}y[/tex] common out from the equation.
i.e., [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Therefore, the factored form of the given equation : [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex] is : [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Question 3.) What is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex] ?
The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.
Now, for the expressions [tex]x^{6}[/tex] and [tex]x^{3}[/tex]:
Since, [tex]x^{3}[/tex] divides both the expressions completely and it is the biggest expression which divides both the expressions.
Therefore, [tex]x^{3}[/tex] is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex]
Answer:
#2 is definatly B
Step-by-step explanation:
6 divided by 603 is?
Note that both numbers are multiple of 3: you can simplify the ratio as follows
[tex] \dfrac{6}{603} = \dfrac{3\cdot 2}{3\cdot 201} = \dfrac{2}{201} [/tex]
The ratio can't be further simplified because 2 and 201 are coprime. So, the only thing you could do is write down the decimal expansion of the number.
For the record, its period is 33 digits long, and it is
[tex] 0.009950248756218905472636815920398 [/tex]
Answer:
0.00995025
Step-by-step explanation:
I need help with finding X's value.
Please help it's geometry.
See attachment
The marks on the line segments tell you they are the same length, and that the triangle is an equilateral triangle. That tells you the angles are the same size, and all are 60°. This lets you find x and y.
(7x+4)° = 60°
7x = 56 . . . . . . . . divide by °, subtract 4
x = 8 . . . . . . . . . . divide by 7
_____
(8y+12)° = 60°
8y = 48 . . . . . . . . divide by °, subtract 12
y = 6 . . . . . . . . . . divide by 8
A piece of copper weighed 4⁄5 of a kilogram and a piece of nickel weighed 3⁄5 of a kilogram. How much more did the piece of copper weigh?
You find the difference in weight by subtacting the weight of the nickel from the weight of the copper.
... (4/5 kg) - (3/5 kg) = (4 -3)/5 kg = 1/5 kg
The piece of copper weighed 1/5 kg more than the piece of nickel.
Which relation is a function?
the diagram on the top left hand side is a function
For each value of x on the domain (x- axis ) there can only be one corresponding value of y in the range (y- axis)
Apart from the diagram on the top left side, the other 3 all fail this definition
what is the length of the missing side
Answer:
The answers are:
m = 9 and n = 15
Step-by-step explanation:
m/15 = n/25 = 12/20
m/15 = 12/20
m/15 = 3/5
5m = 45
m = 9
n/25 = 12/20
n/25 = 3/5
5n = 75
n = 15
m = 9 and n = 15
Find the length( l ) of the leg in the large right triangle using Pythagoras' identity
l = √(25² - 20²) = √225 = 15
the outer and inner right triangles are similar hence the ratios of corresponding sides are equal
[tex]\frac{25}{n}[/tex] = [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex]
using [tex]\frac{25}{n}[/tex] = [tex]\frac{20}{12}[/tex] (cross-multiply )
20n = 300 ( divide both sides by 20 )
n = 15
using [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex] ( cross-multiply )
20m = 180 ( divide both sides by 20 )
m = 9
A line is drawn so that is passes through the points (-4,0) and (2,3) what is the slope of the line
-1/2
1/2
-2
2
you would use the form y2-y1/x2-x1 so in this case it would be 3-0/2+4 which would be 3/6 but simplify your answer and you get would be 1/2 so your answer is 1/2
slope = [tex]\frac{1}{2}[/tex]
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (2, 3)
m = [tex]\frac{3-0}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
What is the measure of ∠ A in this quadrilateral?
Answer:
30°
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360°. You have 3 angles given, so can find the fourth using that fact. (The double arcs on angles B and C mean those angles are congruent. Same symbols are used to mark same-size angles.)
... 360° = A + B + C + D
... 360° = A + 115° + 115° + 100°
... 360° -330° = A = 30°
the length of the hypotenuse of a right triangle is 13 m. The length of one leg in 5 cm. find the length of the other leg
PLEASE HELP AND FAST!
other leg = 12 cm
using Pythagoras' identity with x as the side to be found, then
x = √(13² - 5² ) = √(169 - 25 ) =√144 = 12
The class has 14 boys, 12 girls, and one teacher. What is the ratio boys to girls?
Final answer:
The ratio of boys to girls in the class is 14:12, which simplifies to 7:6.
Explanation:
The ratio of boys to girls in the class is determined by comparing the number of boys to the number of girls.
Given that there are 14 boys and 12 girls, the ratio of boys to girls is:
14 boys : 12 girls
This can be simplified by dividing both numbers by the greatest common divisor, which is 2 in this case.
Hence, the simplified ratio is:
7 boys : 6 girls
g(x) = 2x − 1 h(x) = 1 − g(x) The functions g and h are defined above. What is the value of h(0)?
Answer:
h(0) is equal to 2.
Step-by-step explanation:
In order to find this, we first put 0 in for x in the g(x) equation.
g(x) = 2x - 1
g(0) = 2(0) - 1
g(0) = -1
Now that we have this, we can stick the answer for g(x) into the f(x) equation.
f(x) = 1 - g(x)
f(x) = 1 - -1
f(x) = 1 + 1
f(x) = 2
The value of [tex]h(0)[/tex] is 2.
It is given that,
[tex]g(x)=2x-1[/tex][tex]h(x)=1-g(x)[/tex]Explanation:
We have,
[tex]h(x)=1-g(x)[/tex]
[tex]h(x)=1-(2x-1)[/tex]
[tex]h(x)=1-2x+1[/tex]
[tex]h(x)=2-2x[/tex]
Substitute [tex]x=0[/tex] in the above function.
[tex]h(0)=2-2(0)[/tex]
[tex]h(0)=2-0[/tex]
[tex]h(0)=2[/tex]
Thus, the value of [tex]h(0)[/tex] is 2.
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what is the sine value of 7pi/6
A. - sqrt 3 over 2
B. Sqrt 3 over 2
C. - 1/2
D. 1/2
Answer:
C. -1/2
Step-by-step explanation:
7π/6 radians is equivalent to (7π/6)(180°/π) = 210°, a 3rd-quadrant angle whose reference angle is 30°. The sine of angles in the 3rd quadrant is negative.
sin(30°) = 1/2
sin(210°) = -sin(30°) = -1/2
_____
In radians mode, your calculator can tell you this result directly.
C - [tex]\frac{1}{2}[/tex]
sin(7π / 6 )
note 7π\6 is in the third quadrant where sin is negative
the related acute angle to 7π/6 is 7π/6 - π = π/6
sin (7π/6) = - sin(π/6) = - [tex]\frac{1}{2}[/tex]
Write an equation of the line passing through each of the following pairs of points. d (5, 0), (−3, 0)
baseball field.....................
Umm. What is the question?
The design and layout of a Baseball Field Design to the game experience by affecting play flow and ensuring visibility, vital for both players and fans. Elements like the diamond infield and the extensive outfield reflect American sports culture, which emphasizes strategy and skill, and has historically fostered community engagement and identity.
The design and layout of a baseball field significantly impact the experience of the game by determining the flow of play and the visibility of actions, which is crucial for player performance and fan engagement.
Specific elements, such as the diamond shape of the infield and the expansive outfield, align with the American sports culture, which values a balance between strategy and physical skill, offering a variety of play styles from power hitting to meticulous base running.
The historical evolution of professional baseball teams and their ballparks reflects a facet of American identity through sports, as communal spaces like Fenway Park and Forbes Field facilitated a collective civic pride and a space for social interaction among diverse groups including immigrants.
Moreover, participation in sports, even at the informal level of pickup games, represents an integral part of cultural dynamics in American society, aligning with the practice of community building and local support within the cultural geography framework.
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The probable question may be:
How does the design and layout of a baseball field contribute to the overall experience of the game, and what specific elements align with the principles of American sports culture as taught in the curriculum?