Answers
[tex]y \leq 2x-2[/tex]
[tex]y +2 \leq 2x[/tex]
[tex] \frac{y+2}{2} = x [/tex]
Plug that into the second equation for x:
[tex]y \leq ( \frac{y+2}{2})^2-3(\frac{y+2}{2})[/tex]
[tex]\frac{y^2+4y+4}{4}- \frac{3y-2}{2} = \frac{y^2+4y+4}{4}- \frac{6y-4}{4} [/tex]
[tex]y \leq\frac{y^2-2y}{4} [/tex]
[tex]0 \leq y^2-2y-4y[/tex]
[tex]0 \leq y(y-6) [/tex]
[tex]6 \leq y[/tex]
Now, plug this back into the first equation to solve for x:
[tex]6 \leq 2x-2[/tex]
[tex]8 \leq 2x[/tex]
[tex]4 \leq x[/tex]
So, the solution to that system is (4, 6) which looks like the D.
Related Questions
A right rectangular prism has a square base and a height of 9 feet. its volume, v, is 144 cubic feet. what is the length of s, the sides of the base?
Answers
Given that the volume is 144 ft³ and height is 9 ft
volume = base area x height
144 = base area x 9
base area = 144 ÷ 9
base area = 16 ft²
The base is a square which means both sides are of the same length
area = length x length
16 = length²
length = √16
length = 4 ft
s, the side of the base is 4 ft
The length of the sides of the base of a rectangular prism is 4 feet.
Given that, a right rectangular prism has a square base and a height of 9 feet.
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
Volume of a rectangular prism = Area of a base × Height.
Here, the volume of a rectangular prism = 144 cubic feet
Area of base = Area of a square = s²
So, 144 = s² × 9
⇒ s² = 16
⇒ s = 4 feet
Therefore, the length of the sides of the base of a rectangular prism is 4 feet.
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A room's length is 3 feet less than twice its width. The area of the room is 135 square feet. What are the room's dimensions?
Answers
Hope this helps:
A= L x W
135 = (2w-3)(W)
135 = (2w squared - 3W)
135 = 2w^2-3w
2w^2-3w-135 = 0
-----
Use the quadratic formula to get:
w = [3 +- sqrt(9 - 4*2*-135)]/4
Positive solution:
w = [3 + sqrt(1089)/4
w = [3 + 33]/4
w = 9 ft
L = 2W-3 = 2*9-3 = 15 ft.
If the width is w, the length is l = 2w-3.
The total area is length x width = w*(2w-3)
Solve
w*(2w-3)=135 to find w.
2w^2-3w-135=0
w = (3 +/- sqrt ( 9 +8*135))/4
The positive solution is
w = ( 3 + 33) /4 = 9 and then l = 15.
The dimensions of room are: Length = 15 feet and Width = 9 feet.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
we have,
A room's length is 3 feet less than twice its width.
The area of the room is 135 square feet.
let the width be x then length = 2x - 3.
So, Area of Room
135 = l w
135 = x (2x- 3)
2x² - 3x - 135= 0
2x² + 15x - 18x - 135 = 0
x (2x+ 15) - 9 (2x- 15)= 0
(2x+ 15)(x- 9)=0
x= -15/2 or x= 9.
Thus, the dimensions of room are:
Length = 2(9)-3 = 15 feet
Width = 9 feet
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In a drawing of the solar system, the scale is 1 mm = 500 km. for a planet with a diameter of 6,000 km, what should be the diameter of the drawing of the planet?
12 mm
120 mm
6,000 mm
3,000,000 mm
Answers
Multiply the above equation by 12 to get
12 mm : 6000 km
The 1st selection is appropriate.
Sonya has four straws of different lengths: 2cm,8cm,14cm,and 16cm. How many triangles can she make using the straws?
Answers
You can make a triangle with 6, 14 and 16 straws.
The answer is one triangle
Im assuming you are not allowed to stick together any of the straws
There is no way to make a triangle with numbers 2,8,14, nor 2,8,16, nor 2,14, and 16. Using 6, 14, and 16 straws, you can form a triangle.
I'm guessing you're not supposed to stick any one of the straws together. Kindly see the accompanying document for more information. As a result, B is represented by one triangle. All two sides add up to more than the third side. As a result, the difference between the two sides is less than the difference between the first and third sides.Therefore, the final answer is "one triangle".
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Company A can produce 100 CPUs in 3 days while Company B can produce 150 CPUs in 4 days. If the two companies join forces, how many days would it take them to produce 1000 CPUs?
Answers
Hope this helped!
Answer: They would need 15 days
Step-by-step explanation:
The data is:
Company A produce 100 CPUs in 3 days, so the rate per day is:
Ra = 100/3 CPUs per day: 33.33 CPUs per day.
Company B produce 150 CPUs in 4 days, then it produces:
Rb = 150/4 = 37.5 CPUs per day.
Then, if both companies work toggeter, they produce
Ra + Rb = 33.33 + 37.5 CPUs per day = 70.83 CPUs per day.
We want to know the number X of days needed to make 1000 CPUs, then we need to solve:
70.83*X = 1000
X = 1000/70.83 = 14.11 days, we could round it up to 15 days if we want to have a whole number.
Please Help!!!
(x-3)^2/64 + (y+5)^2/100 = 1
a. Identify the coordinates of the center of the ellipse.
b. Find the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. Label the center and foci.,
Answers
[tex]\frac{(x - xc)^{2} }{ a^{2} } + \frac{(y - yc)^{2} }{ b^{2} } = 1[/tex]
Indeed, you have:
[tex]\frac{(x-3)^{2} }{64} + \frac{(y+5)^{2} }{100} = 1[/tex]
Therefore you can easily find:
a) the coordinates of the center:
in your case xc = 3 and yc = -5
hence C(3 , -5)
b) lenght of the major and minor axis:
in your case a² < b²:
a² = 64 ⇒ a = 8 (ATTENTION! This is the semi-minor axis)
b² = 100 ⇒ b = 10 (again, this is the semi-major axis)
Therefore,
minor axis 2a = 16 and major axis 2b = 20
c) coordinates of the foci:
Since you have a² < b², foci have the generic coordinates F₁₂ (xc , yc+/-c)
where c = √(b² - a²)
Let's compute c = √(100 - 64) = √36 = 6
yf₁ = -5 - 6 = -11
yf₂ = -5 + 6 = -1
Therefore:
F₁ (3, -11) and F₂(3, +1)
d) the graph is in the picture attached
10 POINTS + BRAINLIEST ANSWER!!!
65x + y = 455
A grocery store receives a shipment of oranges and consistently sells the same number of oranges each day. The equation above models the number of oranges, y, that remain x days after the shipment is received. What does it mean that (7, 0) is a solution to the equation?
A. It takes 7 days after the shipment until none of the oranges are remaining.
B. There are 7 oranges in the shipment.
C. It takes 7 days for orange to be sold to 455 customers.
D. After the shipment, 7 oranges are sold each day.
Answers
A bicycle store costs $1700 per month to operate. The store pays an average of $75 per month. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Answers
The formula in computing the break-even point is:
Break-even = fixed cost / contribution margin
The fixed cost is already given which is $1700 per month. To compute for the contribution margin, you have to deduct the average cost per month ($75) to the selling price of each bicycle ($95). The contribution margin is $20 ($95 - $75).
Substituting the amounts to the formula:
Break-even = $1,700/$20
= 85
Therefore, the store must sell 85 bicycles each month to break even.
the diameter of a bike is 90cm. How far would it travel after 5 revolutions?
Answers
[length of a circumference]=2*pi*r
diameter=90 cm-------------> r=d/2--------> r=45 cm
[length of a circumference]=2*pi*45----------> 90*pi cm
with 1 revolution will go the length of the wheel
if 1 revolution is-------------------> 90*pi cm
5 revolution is--------------------> X
X=5*90*pi----------> 1413 cm
the answer is 1413 cm
Two sides of a triangle have lengths 5 in. and 16 in. Describe the possible lengths of the third side.
5 < x < 21
5 < x < 16
16 < x < 21
11 < x < 21
Can you construct a triangle that has side lengths 11 cm, 12 cm, and 15 cm?
no
yes
Answers
Answer:
11 < x < 21
Yes
If PQRS is a parallelogram, what is the value of Y
Answers
y = 13 * 4
y = 52
answer
C. 52
Answer:
52
Step-by-step explanation:
did the question
how many 1020 flats can fit on (2) 8'x4' tables?
Answers
The dimensions of each 1020 flat is 11" by 22". We will convert the measurements of the table to inches. 8(12) = 96". 4(12) = 48". If we lay the longest edge of the flat side along the long edge of the table, 4 flats will fit along it with 8 inches left over. This would put the smaller edge of the flat along the smaller edge of the table, which would allow for 4 rows of 4, or 16 flats on each table. 16*2=32 flats between both tables.
This works out the same if we turn the flats around. Let the smaller edge of the flat, 11", be along the longer edge of the table, 96". This would allow for 8 flats. This puts the longer edge of the flat, 22", along the shorter edge of the table, 48"; this puts 2 rows of 8, which would be 16 flats on each table, for a total of 32 flats.
helppppppppppppppppppppppppp
Answers
x = 10 units
Explanation:
First, let's consider the smaller triangle.:
It is a right-angled triangle, therefore, we can use the special trig functions.
tan θ = opposite / adjacent
tan 45 = opposite / 5
opposite = 5
Now, for the larger triangle:
It is also a right angled triangle which means that we can use the special trig functions.
sin θ = opposite / hypotenuse
sin (30) = 5 / x
x = 10 units
Hope this helps :)
A graphic artist earns $22 an hour, and she works 44 hours a week. What is her weekly wage?
A. $154
B. $308
C. $66
D. $968
Answers
Answer:
The answer is option D. The weekly wage is $968.
Step-by-step explanation:
The weekly salary can be found multiplying the earned money per hour and the amount of hours worked in the week:
[tex] Wweek=22\ \$/hr* 44\ hr/week[/tex]
[tex] Wweek=968\ \$/week[/tex]
What is the measure of angle S?
Answers
helppppppppppppppppppppppppp
Answers
[tex] \frac{y2-y1}{x2-x1} [/tex]
[tex] \frac{5-1}{-2-3} [/tex]
[tex] \frac{4}{-5} [/tex]
So -4/5 is the right answer.
Hope this helps :)
please help asap! 54 points
Answers
a)
point slope intercept
y + 2 = 4/3(x - 3)
standard form
y + 2 = 4/3(x - 3)
3y + 6 = 4x - 12
- 4x + 3y = -18 ..........this is standard form
Answer is C
y + 2 = 4/3(x - 3); -4x + 3y = -18
point-slope from is
y - (-2) = (4/3)(x - 3)
y + 2 = (4/3) (x - 3) is the equation in point slope form
Standard form is -4x + 3y = -18
The answer is C
Please show me the steps on how to do this.
Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
I'm learning about vectors right now.
Options:
o 54 degrees
o 36 degrees
o 46 degrees
o 44 degrees,
Answers
In this case, the angle α can be easily found with trigonometry:
tan α = (opposite side / adjacent side)
Therefore:
α = tan⁻¹ (tree / shadow) = tan⁻¹ (10 / 14) = 35°
NOTE:
tan⁻¹ is sometimes found written as arctan.
A sign standing 6 feet tall is situated 18 feet away from a flag pole. at a certain time of day the sign's shadow is 3 feet long and the flagpole's shadow is 24 feet long. how tall is the flagpole?
Answers
On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft
When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.
We can apply trigonometry rules to find height of flagpole.
From small triangle containing sign we can find tangens function:
[tex]tan \alpha = \frac{C}{D} [/tex]
Similarly we can do for large triangle containing flagpole:
[tex]tan \alpha = \frac{A}{B} [/tex]
We see that these two equations have same left sides. This means that their right sides must also be same:
[tex]\frac{C}{D} = \frac{A}{B}[/tex]
We can solve for A:
[tex]CB=AD \\ A= \frac{CB}{D} \\ A= \frac{6*24}{3} \\ A=48 ft[/tex]
Height of flagpole is 48 feet.
f(x) = x3 - 3x2 + 4 = 0 For the equation given, 2 has a multiplicity of? 1, 2, 3
Answers
a certain solution to the function.
In this case, we are finding out how many times 2 appears in the function, meaning you’ll have to solve for it when it equals 0. You may use a calculator or use the rational roots method. I will simply derive the answer from the calculator. If you’d like to know about the rational roots method, comment.
x^3 - 3x^2 + 4 = 0 // Given
0 = (x + 1)(x - 2)(x - 2) // Calculator skills
0 = (x + 1)(x - 2)^2 // Simplify
Therefore, 2 has a multiplicity of 2
1. 16y + 0 = 16y
Associate Property of Addition
Zero Property of Multiplication
Commutative Property of Addition
Identity Property of Addition
2. d • r = r • d
Commutative Property of Multiplication
Identity Property of Multiplication
Zero Property of Multiplication
Commutative Property of Addition
3. 27a • 0 = 0
Associative Property of Multiplication
Commutative Property of Multiplication
Zero Property of Multiplication
Identity Property of Multiplication
4. 16x + 5y = 5y + 16x
Commutative Property of Addition
Zero Property of Addition
Ident
Answers
2) Commutative Property of Multiplication
3) Zero property of multiplication
4) Commutative property of addition
Hope this helps!
Juliana and Maria logged a total of 90 hours working for their dad. Juliana worked 2 hours more than three times as much as Maria. How many hours did Juliana work?
Answers
Juliana worked 68 hours
Explanation:
Assume the hours logged by Juliana is x
Assume the hours logged by Maria is y
We are given that:
1- Total hours logged by both is 90. This means that:
x + y = 90
This equation can be rewritten as:
x = 90 - y ...........> equation I
2- Juliana worked 2 hours more than 3 times as much as Maria. This means that:
x = 3y + 2 ...........> equation II
Substitute with equation I in equation II and solve for y as follows:
x = 3y + 2
90 - y = 3y + 2
88 = 4y
y = 22
Substitute with y in equation I to get x as follows:
x = 90 - y
x = 90 - 22
x = 68
Based on the above:
Hours logged by Juliana = x = 68 hours
Hours logged by Maria = y = 22 hours
Hope this helps :)
Let
x---------> the hours logged by Juliana
y---------> the hours logged by Maria
we know that
[tex]x+y=90[/tex] ---------> equation [tex]1[/tex]
[tex]x=3y+2[/tex] ---------> equation [tex]2[/tex]
Substitute equation [tex]2[/tex] in equation [tex]1[/tex]
[tex](3y+2)+y=90[/tex]
[tex]4y+2=90[/tex]
[tex]4y=90-2[/tex]
[tex]4y=88[/tex]
[tex]y=88/4[/tex]
[tex]y=22\ hours[/tex]
Find the value of x
[tex]x=3y+2[/tex]
[tex]x=3*22+2[/tex]
[tex]x=68\ hours[/tex]
therefore
the answer is
Juliana worked [tex]68\ hours[/tex]
If a fictional shrinking man shrinks proportionately to 1/10 his original height, his weight will be multiplied by
Answers
The final weight will be reduced by 1/10 of its original weight.
What is equation modelling? What is a mathematical equation and expression?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is a fictional shrinking man shrinks proportionately to 1/10 his original height.
Assume the weight to be [W]. Then -
W = mg
m = ρV {ρ is density}
Then -
W = ρVg
Assume the body to be cylinder of radius [r] and height [h], we can write-
W = πr²ρgh
Than, the initial weight will be -
W = πr²ρgh
After Shrinking -
W' = πr²ρgh/10
Then -
W'/W = {πr²ρgh/10}/{πr²ρgh}
W'/W = πr²ρgh/10 x 1/πr²ρgh
W'/W = 1/10
W' = W/10
Therefore, the final weight will be reduced by 1/10 of its original weight.
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The area of a rectangular hotel room is 209 square feet. the perimeter is 60 feet. what are the dimensions of the room?
Answers
B) 2x + 2y = 60
A) y = 209 / x putting this into equation B
B) 2x + (2 * 209 / x) = 60
2x + 418 / x = 60 multiplying by x
2x^2 + 418 = 60x
2x^2 -60x + 418 = 0
Solving by quadratic formula
x = 19
y = 11
Write the expression as either the sine, cosine, or tangent of a single angle
Answers
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
where in this case,
x = pi/3
y = pi/5
So,
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(pi/3-pi/5) = cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(pi/3-pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(5pi/15-3pi/15)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(2pi/15)
------------------------------------------------------------
The answer is cos(2pi/15) which can be written as [tex]\cos\left(\frac{2\pi}{15}\right)[/tex]
which equation has (2, -1) as a solution?
A. y = 2x - 1
B. y = x + 3
C. y = x - 3
D. y = -2x + 1
If someone could explain this to me it would be greatly appreciated. Thank you.
Answers
A. 2(2)-1 = 3 <>-1
B. 2+3 = 5<>-1
C. 2-3 = -1 = y
so C has (2,-1) as a solution
In the United States the speed limit signs are in miles per hour. Unfortunately, your speedometer only reads in km/hour. How fast are you allowed to go if the speed sign says 70 mph (rounded to the nearest hundredth)
Answers
Answer:
The speed limit will be 112.65 kph.
Step-by-step explanation:
In order to find how fast one can go when speed sign says 70mph and the speedometer reads in km per hour we convert mph to kmph.
The conversion unit is 1mph= 1.609344kph
So 70mph = 70x1.609344=112.6541kph
Or 70mph=112.65 kph
One can travel at 112.65 kph.
The measures of exterior angles of a regular polygon with n numbers of sides ______ as n increases.
increases
decreases
remains the same,
Answers
answer asap Malia created a correct function table using the equation g = 4f.
Which table could be Malia's?
A.
B.
C.
Answers
hope I helped
Marge orders the following items and would like to leave a 20 percent tip based on her bill. There is no tax on her meal. What is the total cost of her dinner including gratuity? Item Amount Soup $3.75 Shrimp scampi $15.00 Iced tea $2.60 Dessert $4.25.
Answers
Answer:
The total cost of her dinner including tip would be $30.72
Step-by-step explanation:
Marge orders the following items on her meal.
Soup = $3.75
Shrimp scampi = $15.00
Iced tea = $2.60
Dessert = $4.25
The total cost of her dinner including gratuity is
3.75 + 15.00 + 2.60 + 4.25 = $25.60
She would like to leave a 20% tip based on her bill
Therefore, 20% of $25.60
= 0.20 × 25.60 = $5.12
Now add this tip amount to the bill amount.
$25.60 + $5.12 = $30.72
The total cost of her dinner including tip would be $30.72