Answer:
n × 0.77
Step-by-step explanation:
Decreasing a number by 23% is the same as multiplying that number by 0.77, so n number of animals decreased by 23% is:
n × 0.77
Find the area in square centimeters of the composite shape shown
below. Enter only a number as your answer.
A
E
13 cm
D
11 cm
7 cm
B
18 cm
C
Answer:
73cm²
Step-by-step explanation:
Area of rectangle=½ length×width
=½×18×7
=63cm²
Area of triangle=½b×h
base=18-13= 5cm
height=11-7 =4cm
½×b×h
½×5×4
=10cm²
Area of total=63+10
73cm²
Answer: 73c2
Step-by-step explanation:
Find the distance between the points (0, 10) and (–9, 1).
The distance between the points (0, 10) and (–9, 1) is 12.73 units.
Given the following data;
Points ([tex]x_1, x_2[/tex]) = 0, -9
Points ([tex]y_1, y_2[/tex]) = 10, 1
To find the distance between the points;
In Mathematics, the distance between two points on a plane is calculated by using the formula;
[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }[/tex]
Substituting the points into the formula, we have;
[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]
Distance = 12.73 units
Therefore, the distance between the points is 12.73 units.
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Solve the system of equations: y=x^2+3x-6 y=2x-6
here's your answer in the given attachment
Answer:
Solution: {(-1,-8), (0,-6)}
Step-by-step explanation:
y=x^2+3x-6 ............(1)
y=2x-6 ....................(2)
Solution:
by comparison, the right-hand sides of both equations are equal (to y)
x^2+3x-6 = 2x - 6
Transpose and simplify
x^2 -x = 0
x = -1 or x=0
Substitute x = -1 in (2)
y = 2(-1) -6 = -8 ..............(-1,-8)
substitute x = 0 in (2)
y = 2(0) -6 = -6 ...............(0,-6)
So there are two solutions, corresponding to the intersection of the quadratic and the straight line.
How many terms are in the arithmetic sequence 7, 0, –7, …,–175?
Answer:
27 terms
Step-by-step explanation:
a1 = 7
nth term is -175
common difference d= 0-7 = -7 or -7 - 0 = -7
nth term = first term + ( n-1) * common difference
-175 = 7 + ( n - 1 ) * (- 7)
-175 = 7 - 7n + 7
-175 = 14 - 7n
-175-14 = -7n
-189 = - 7n
n= -189 /-7
n=27
someone plz help !
A town currently has a population of 1,000,000, and the population is increasing 6 percent every year. Write a recursive function in now-next form to predict the population at any year in the future.
Answer:
Y=x(t)(0.06) + x
Y =predicted population
X= population currently
t= number of years
Y= 60000(t) + 1000000
Step-by-step explanation:
Let the current population be x
X= 1000000
The rate of increase= 6% each year
Let the the predicted population= y
If the population is to increase by 6% each year the function predicting the population at the future will be
Y=x(t)(0.06) + x
The only changing value in the above formula is the time.
Y= 1000000(0.06)(t) +1000000
Y= 60000(t) + 1000000
Answer: The actual answer is:
next = now x 1.06, starting at 1,000,000
A cylindrical container with a radius of 5 cm and a height of 14 cm is completely filled with liquid. Some of the liquid from the cylindrical container is poured into a cone–shaped container with a radius of 6 cm and a height of 20 cm until the cone–shaped container is completely full. How much liquid remains in the cylindrical container? (1 cm3 = 1 ml)
Answer:
Volume left in the cylinder if all the cone is made full:
[tex]\bold{345.72 \ ml }[/tex]
Step-by-step explanation:
Given
Radius of cylinder = 5 cm
Height of cylinder = 14 cm
Radius of cone = 6 cm
Height of cone = 20 cm
To find:
Liquid remaining in the cylinder if cone is made full from cylinder's liquid.
Solution:
We need to find the volumes of both the containers and find their difference.
Volume of cylinder is given by:
[tex]V_{cyl} = \pi r^2h[/tex]
We have r = 5 cm and
h = 14 cm
[tex]V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3[/tex]
Volume of a cone is given by:
[tex]V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3[/tex]
Volume left in the cylinder if all the cone is made full:
[tex]1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }[/tex]
8x + 5y=-22
-3x - 5y = 2
Answer:
(-4, 2).
Step-by-step explanation:
8x + 5y=-22
-3x - 5y = 2 Adding the 2 equations:
5x = -20
x = -4.
Substitute x = -4 in the first equation:
8(-4) + 5y = -22
5y = -22 + 32
5y = 10
y = 2.
Answer:
[tex]x=-4,\:\\y=2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\[/tex]
[tex]\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2[/tex]
Maria rotated the triangle 90 degrees clockwise about the origin. What is the new triangle?
Answer:
A’B’C’
Step-by-step explanation:
Well if triangle ABC is rotated 90 degrees clockwise around the origin it will turn right to create triangle A’B’C’.
Given: Circle k(O), diameter US , m RU=50°, m UT=30° Find: m∠RUS, m∠STU
Answer:
[tex]\boxed{m<RUS = 65 \ degrees}\\\boxed{m<STU = 90 \ degrees}[/tex]
Step-by-step explanation:
Finding m∠RUS:Given that RU = 50°, So Central Angle ROU = 50° too because the measure of arc is equal to its central angle
Now, Let's assume a triangle ROU. It is an isosceles triangle since RO = RU (Radii of the same circle)
So,
∠ORU ≅ ∠OUR (Angles opposite to equal sides are equal)
So, we can write them as 2(∠RUO)
So,
2(∠RUO)+50 = 180 (Interior angles of a triangle add up to 180)
2(∠RUO) = 180-50
2(∠RUO) = 130
Dividing both sides by 2
∠RUO = 130/2
∠RUO = 65 degrees
m∠RUS = 65 degrees (Both are the same)
Finding m∠STU now:In a semi circle (Given that SU is a diameter) , there must be a 90 degrees angle sin it opposite to the diameter.
So,
m∠STU = 90 degrees
From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°
CircleGiven that:
m RU = m∠ROU = 50°, m UT = m∠UOT =30°m∠ORU = m∠OUR (isosceles triangle)
m∠ORU + m∠OUR + m∠ROU = 180° (angle in triangle)
50 + 2 * m∠OUR = 180
m∠OUR = 65°
m∠OUR = m∠RUS = 65°
m∠STU = 90° (angle subtended at circumference by semicircle).
From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°
Find out more on circle theorems at: https://brainly.com/question/17023621
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate in standard form the equation of the line through the given points. P(0, -4), Q(5, 1)
Answer:
x -y =4
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
= (1- -4)/(5 - 0)
= (1+4)/(5-0)
5/5
= 1
Then we can use slope intercept form
The slope is 1 and the y intercept is -4
y = mx+b
y = 1x-4
We want it in standard form
Ax + By = C where A is a positive integer
Subtract x from each side
-x +y = -4
Multiply by -1
x -y =4
Answer:
x -y =4
Step-by-step explanation:
Scarlett bought an ant farm with 80 ants. Frond the following week forward, the ant population tripled every week. Let g(n) be the number on ants in scarletts farm in the nth week since she got it. G is a sequence. What kind is it? Write an explicit formula for the sequence starting with g(n)=? Need help really bad
Answer:
g(n)=80*3^(n-1)
Step-by-step explanation:
Scarlett started with 80 ants
That is, first term (a)=80
The ant population tripled every week.
First week: 80×3=240
Second week=240×3=720
Common ratio=720/240=3
Or
240/80=3
Therefore, r=3
G is a geometric sequence
Geometric sequence is given by
g(n)=a*r^(n-1)
Substitute a=80 and r=3 into the equation
g(n)=a*r^(n-1)
g(n)=80*3^(n-1)
The explicit formula for the sequence is
g(n)=80*3^(n-1)
If we increase the number 100 by 10% and then reduce the resulting number by 20% what would the answer be plz show how u did it and I will mark brainliest for the best explanation
Answer:
88
Step-by-step explanation:
The original number ⇒ 100
100 is increased by 10%
The result is 20% reduced.
Calculate increase.
100 × (1 + 10%)
100 × (1.1)
= 110
Calculate decrease.
110 × (1 - 20%)
110 × 0.8
= 88
which one of the following equals the difference between the total surface area and base area of any three-dimensional figure?A. Lateral area, B,altitude, C,perimeter, D,slant height PLEASE NEED ANSWERS
Answer:
lateral area
Step-by-step explanation:
examble a cube if you remove the base and the top you remain with the vertical faces and lateral means vertical(we remove the top because it has potential to be a base if you turn it) it applies to any side touching the ground e.g in a cuboid
Answer:
A. Lateral area
Step-by-step explanation:
The lateral surface area is the area of the lateral (vertical) surfaces, it excludes the area of the base and top of a 3D shape.
first correct answer gets best marks and it doesn't have to be long just a quick answer that's it
Answer:
see below
Step-by-step explanation:
-3.55 g≤ -28.4
Divide each side by -3.55, remembering to flip the inequality
-3.55 g/-3.55≥ -28.4/-3.55
g≥8
Closed circle at 8 and the line goes to the right
Point P has coordinates P(-3,5).
What are the coordinates of the image P" after I translate point P: 2
units to the right 3 units up and then I reflect its image across the x-
axis?
P starts at (-3,5)
Move to the right 2 units and you'll get to (-1,5). We add 2 to the x coordinate here.
Then shift the point up three units to get to (-1,8). We add 3 to the y coordinate.
Finally, reflect over the x axis to get the answer (-1, -8)
Note how the y coordinate flipped in sign but the x coordinate stays the same
The area of a rectangular dining room is 20 square meters. It is 5 meters long. How wide is it?
Answer:
4 meters
Step-by-step explanation:
To do this you would need to know what the area of a rectangle is, it is base times width. So you already know the area so you would just divide it by 5 and you would get the width, which is 4 meters
7 (42 ÷ 3) + 4 (72 + 53) + 8 (-3) 4
Answer:
Step-by-step explanation:
7(42 ÷ 3) + 4 (72 + 53) + 8 (-3)4
7(14) + 4(125) + 8(-12)
98 + 500 - 96
598 - 96
502
Answer:
502Step-by-step explanation:
[tex]7(42 \div 3) + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]
Divide the numbers
[tex] = 7 \times 14 + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]
Add the numbers
[tex] = 7 \times 14 - 4 \times 125 + 8 \times ( - 3) \times 4[/tex]
Calculate the product
[tex] = 7 \times 14 + 4 \times 125 - 96[/tex]
Multiply the numbers
[tex] = 98 + 500 - 96[/tex]
Add the numbers
[tex] = 598 - 96[/tex]
Subtract the numbers
[tex] = 502[/tex]
Hope this helps..
Best regards!!
PLEASEEE HELP JUST THE ANSWER I don’t to explain !!!
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.
The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713
Given that:
[tex]Entrance\ Fee = \$18[/tex]
[tex]Rate = \$0.08[/tex] per ball
Let:
[tex]B \to Balls[/tex]
The amount (A) Carolina can spend on B balls is:
A = Entrance Fee + Rate * B
This gives:
[tex]A = 18 + 0.08 * B[/tex]
[tex]A = 18 + 0.08B[/tex]
To get $10, Carolina must spend $75 or more.
This means:
[tex]A \ge 75[/tex]
So, the inequality is:
[tex]18 + 0.08B \ge 75[/tex]
The smallest number of balls is calculated as follows:
[tex]18 + 0.08B \ge 75[/tex]
Collect like terms
[tex]0.08B \ge 75 - 18[/tex]
[tex]0.08B \ge 57[/tex]
Divide both sides by 0.08
[tex]B \ge 712.5[/tex]
Round up
[tex]B \ge 713[/tex]
Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713
Learn more about inequalities at:
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Using a linear function, it is found that:
1. [tex]18 + 0.08B \geq 75[/tex], given by option B.2. She has to buy at least 713 paintballs.-----------
The linear function for the cost of B paintballs has the following format:
[tex]C(B) = C(0) + aB[/tex]
In which
C(0) is the fixed cost.a is the cost per paintball.-----------
Question 1:
Entrance fee of $18, thus [tex]C(0) = 18[/tex].Cost of $0.08 per ball, thus, [tex]a = 0.08[/tex]Thus:
[tex]C(B) = 18 + 0.08B[/tex]
The promotion is valid if the cost is of at least 75, thus:[tex]C(B) \geq 75[/tex]
[tex]18 + 0.08B \geq 75[/tex], given by option B.
-----------
Question 2:
The smallest number is the solution of the inequality for B, thus:[tex]18 + 0.08B \geq 75[/tex]
[tex]0.08B \geq 57[/tex]
[tex]B \geq \frac{57}{0.08}[/tex]
[tex]B \geq 712.5[/tex]
Rounding up, she has to buy at least 713 paintballs.
A similar problem is given at https://brainly.com/question/24583430
A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number. cubic inches
Answer:
927 cubic inches
Step-by-step explanation:
The area of the octagonal base is ...
A = (1/2)Pa
where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...
A = (1/2)(8·4)(4.83) = 77.28 . . . square inches
The volume of the prism is given by ...
V = Bh
where B represents the area of the base, and h is the height.
V = (77.28 in^2)(12 in) = 927.36 in^3
The volume of the prism is about 927 cubic inches.
the answer on edg is 927
Please answer this question now
Answer:
397.7 m²
Step-by-step Explanation:
Step 1: find m < W
W = 180 - (33+113) (sum of ∆)
W = 34°
Step 2: find side UV using the law of sines
[tex] \frac{UV}{sin(W)} = \frac{VW}{sin(U)} [/tex]
[tex] \frac{UV}{sin(34)} = \frac{29}{sin(33)} [/tex]
Multiply both sides by sin(34)
[tex] \frac{UV}{sin(34)}*sin(34) = \frac{29}{sin(33)}*sin(34) [/tex]
[tex] UV = \frac{29*sin(34)}{sin(33)} [/tex]
[tex] UV = 29.8 m [/tex] (approximated)
Step 3: find the area using the formula, ½*UV*VW*sin(V)
area = ½*29.8*29*sin(113)
Area = 397.7 m² (rounded to the nearest tenth.
find the coordinates of the point whose ordinate is -7 and lies on y axis
Answer:
(0,-7)
Step-by-step explanation:
If nay point is form (x,y)
x is abscissa can be also called x axis coordinate
y is ordinate can be also called y axis coordinate
ordiantes are points lying on y axis.
For any point lying on y axis, its x-axis coordinate will be 0
given that ordinate is -7. it means that value of y coordinate is -7
Thus, coordinates of the point is (0,-7)
Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil
Answer:
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
Step-by-step explanation:
Given;
Total Months = 14
Total Words = 1920
Required
Find the time spent in Portugal and time spent in Brazil
Let P represent Portugal and B represent Brazil; This implies that
[tex]P + B = 14[/tex] ---- Equation 1
Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that
[tex]130P + 150B = 1920[/tex] --- Equation 2
Make P the subject of formula in equation 1
[tex]P = 14 - B[/tex]
Substitute 14 - B for P in equation 2
[tex]130(14 - B) + 150B = 1920[/tex]
Open Bracket
[tex]1820 - 130B + 150B = 1920[/tex]
[tex]1820 + 20B = 1920[/tex]
Subtract 1820 from both sides
[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]
[tex]20B = 100[/tex]
Divide both sides by 20
[tex]\frac{20B}{20} = \frac{100}{20}[/tex]
[tex]B = 5[/tex]
Substitute 5 for B in [tex]P = 14 - B[/tex]
[tex]P = 14 - 5[/tex]
[tex]P = 9[/tex]
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
A body is projected at an angle of 30degrees to the horizontal with a speed of 30m/s. What will be the angle with the horizontal after 1.5sec. Take g as 10m/s^2
Given Information:
Launch angle of projectile = 30°
Initial velocity = V₀ = 30 m/s
Acceleration due to gravity = g = 10 m/s²
Required Information:
Angle with the horizontal after 1.5 sec = ?
Answer:
The angle of the projectile to the horizontal after t = 1.5 seconds is 0°
Step-by-step explanation:
The horizontal component of the velocity is given by
[tex]Vx = V_0 \cos(\theta)[/tex]
Where V₀ is the initial velocity and θ is the launch angle
The vertical component of the velocity is given by
[tex]Vy = V_0 \sin(\theta) - gt[/tex]
Where V₀ is the initial velocity, θ is the launch angle, g is the acceleration due to gravity and t is the time.
So after t = 1.5 sec
The horizontal component of the velocity is
[tex]Vx = V_0 \cos(\theta) \\\\Vx = 30 \cos(\30) \\\\Vx = 30 \times 0.866\\\\Vx = 25.981 \: m/s[/tex]
And the vertical component of the velocity is
[tex]Vy = V_0 \sin(\theta) - gt \\\\Vy = 30 \sin(30) - 10 \times 1.5 \\\\Vy = 30(0.5) - 10 \times 1.5 \\\\Vy = 15 - 15 \\\\Vy = 0 \: m/s \\\\[/tex]
The angel is
[tex]\tan(\theta) = \frac{0}{25.981} \\\\\theta= \tan^{-1}( \frac{0}{25.981}) \\\\\theta= 0[/tex]
Therefore, the angle of the projectile to the horizontal after t = 1.5 seconds is 0°
Which two features of igneous rocks are determined by their cooling rate?
color and shininess
shininess and hardness
hardness and crystal size
crystal size and rock texture
Answer:
crystal size and rock texture D
Step-by-step explanation:
:)
Hence, the option (D) is the correct answer i.e., crystal size and rock texture.
What is the texture?
The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.
The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.
Hence, the option (D) is the correct answer i.e., crystal size and rock texture.
To know more about the texture
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A walking path across a park is represented by the equation y=-3x - 3.A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3,6). Identify the equation that represents the new path.
Answer:
y -6 = 1/3(x +3) or y = 1/3x +7
Step-by-step explanation:
The slope of the line describing the given path is the x-coefficient, -3. The slope of the perpendicular line will be the negative reciprocal of that:
m = -1/(-3) = 1/3
The point-slope form of the equation for a line can be used to write the equation for the new path:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
For m=1/3 and (h, k) = (-3, 6), the new path can be represented by ...
y -6 = 1/3(x +3) . . . . point-slope form
y = (1/3)x +7 . . . . . . slope-intercept form
As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below: As Devine rides her bike, she picks up a nail in her front tire. The height, h, of the nail from the ground as she rides her bike over time, t, in seconds, is modelled by the equation below:
f(x)=-14 cos(720(t-10))+14
Using the equation, determine the following. Show your work for part marks.
a) What is the diameter of the bike wheel?
b) How long does it take the tire to rotate 3 times?
c) What is the minimum height of the nail? Does this height make sense? Why?
Answer:
a) 28 units
b) 0.0262 seconds
c) Minimum height of the nail = 1.923 units
Step-by-step explanation:
a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)
Where:
d = The mid line
a = The amplitude
The period = 2π/b
c/b = The shift
Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28
b) Given that three revolution = 6×π, we have;
At t = 0
cos(720(t-10) = cos(720(0-10)) = cos(7200) = 1
Therefore, for three revolutions, we have
720(t - 10) = 720t - 7200
b = 720
The period = 2π/b = 6·π/720 = 0.0262 seconds
c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;
f(x) = -14×cos(720(t - 10)) + 14
At t = 0 gives;
f(x) = -14×cos(720(0 - 10)) + 14
Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923
Minimum height of the nail = 1.923
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flat screen TV makes. Each sound bar and TV must be processed by cutting machine (A), A fitting machine (B), and a polishing machine (C). each sound bar must be processed on machine A for one hour, Machine B for one hour machine C for four hours. each TV must be processed on machine A for two hours, machine B for one hour, machine C for one hour. Machine A is available for 16 hours, machine B for nine, machine C for 24. Using the information in the problem, right the constraints. Let X represent the number of sound bars made, and Y represent the number of TVs
Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]
Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C
Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C
So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]
Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]
Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]
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Use the elimination method to solve the ststem of equations.choose the correct ordered pair 10x+2y=22 3x-4y=-21
Answer:
x=1 and y=6
Step-by-step explanation:
10x+2y=22
3x-4y=-21
First at all, you have to multiply both sides of this equation of 10x+2y=22, like this,
2(10x+2y)=2*22
*Put the 2 for the both sides.
Then, expand them.
20x+4y=44
When we have 20x+4y=44, we can eliminate with another equation.
20x+4y=44
3x-4y=-21
So, the first equation has +4y and the second equation has -4y, so we can use elimination method to eliminate one variable.
This time we can sum these equation to get one variable to get the answer easily. Like this...
20x+4y=44
3x-4y=-21
to become...
23x=23
x=23/23
x=1
When we get the equation like this, we can divide 23 by 23, so we can get the value of x. So, the value of x is 1.
When we know x is equal to 1, we can do the last part substitute x=1 into the second equation which is 3x-4y=-21.
The following steps is like this:
Substitute x=1 into 3x-4y=-21,
3(1)-4y= -21
3-4y= -21
Move the 3 to the another side, like this;
-4y= -21-3
-4y= -24
y= -24/ -4
y=6
*Be careful! When you calculate -24/-4 , you have to know how to eliminate the negative sign. (-) / (-) = +
Negative number divided by negative number is equal to positive number.
So, here we go! the value of x is 1 and the value of y is 6.
That is my solution and explanation from me. I hope you can understand. Bye!
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
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