The points that are solutions to the system of inequalities x + y 5 + 2 y > 2 below are (5, 2), (3, 6), (1, 1). Options B, C, A, and D. For is mathematically given as
What are inequalities?Generally, inequalities are simply defined as the relationship between two non-equal expressions using a symbol like "not equal to," "greater than," or "less than."
In conclusion, The points (5, 2), and (2, 5), (1, 1) are the ones that are the solutions to the system of inequalities x + y 5 + 2 y > 2 below (3, 6).
For (5, 2),
5 + 2* 5 + 2 *2 > 2
19>2
For (2, 5)
2 + 5* 5 + 2*5 > 2
37>2
For (3, 6).
3 + 6*5 + 2*6 > 2
45>2
For (1, 1)
1 + 1* 5 + 2*1 > 2
8>2
For (1, -1)
1 + -1* 5 + 2 *-1 > 2
-6<2
For (2, -5)
2 + -5* 5 + 2*-5 > 2
−33<2
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A company receives $198, of which $13 is for sales tax. The journal entry to record the sale would include a
A : debit to Sales Revenue for $198.
B : credit to Sales Taxes Payable for $13.
C : debit to Cash for $180.
D : debit to Sales Tax Expense for $13.
What decimal is equivalent to each fraction?
1/6
help plez
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
The maximum volume of the box is:
1000 cm³
Step-by-step explanation:Let x be the length of the square base
and h be the height(h) of the box.
As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)
As we know that the surface area of box is given by:
[tex]Surface\ Area=2(lw+wh+hl)\\\\\\i.e.\\\\\\Surface\ Area=2(x^2+xh+xh)\\\\\\Surface\ Area=2(x^2+2hx)[/tex]
We are given surface area of box=600 cm²
Hence,
[tex]2(x^2+2hx)=600\\\\i.e.\\\\x^2+2xh=300\\\\i.e.\\\\h=\dfrac{150}{x}-\dfrac{x}{2}[/tex]
The volume of box is given by:
[tex]Volume(V)=l\times w\times h\\\\\\Volume=x^2h\\\\\\Volume=x^2(\dfrac{150}{x}-\dfrac{x}{2})[/tex]
Hence,
[tex]V=150x-\dfrac{x^3}{2}[/tex]
Now, for maxima or minima we have derivative equal to zero.
[tex]i.e.\\\\\\\dfrac{dV}{dx}=0\\\\\\i.e.\\\\\dfrac{d}{dx}(150x-\dfrac{x^3}{2})=0\\\\\\i.e.\\\\\\150-\dfrac{3x^2}{2}=0\\\\\\i.e.\\\\\\150=\dfrac{3}{2}x^2\\\\\\x^2=100\\\\\\i.e.\\\\\\x=\pm 10[/tex]
Now,
[tex]\dfrac{d^2V}{dx^2}=\dfrac{-6x}{2}\\\\\\=-3x[/tex]
Now, as we know if for a given x
[tex]\dfrac{d^2V}{dx^2}<0[/tex]
then that x is a point of maxima.
Hence, when we put x=10 we get: [tex]\dfrac{d^2V}{dx^2}<0[/tex]
Hence, x=10 is a point of maxima
Also, the value of V at x=10 is:
[tex]V=150\times 10-\dfrac{(10)^3}{2}\\\\\\V=1500-\dfrac{1000}{2}\\\\\\V=1500-500\\\\V=1000\ cubic\ cm.[/tex]
Hence, the maximum volume of the box is:
1000 cm³
1. Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
What is the percent of increase as a decimal? Do not round.
2. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
3. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
4. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
5. Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?
2 cups (into mL of water
Answer:
about 473 mL
Step-by-step explanation:
For liquid measure, there are 16 cups in a US gallon, which is exactly 231 cubic inches. Each cubic inch is exactly 2.54³ = 16.387064 cubic centimeters--the same number of mL.
So, the exact conversion from cups to mL is ...
1 cup = (231/16)(16.387064) mL = 236.5882365 mL
Multiplying this by 2 gives ...
2 cups = 473.176473 mL
For many purposes, the nearest mL is sufficiently accurate:
2 cups ≈ 473 mL
.
Are the two triangles below similar?
Triangles ABC and DEF are shown. Angle A measure 30 degrees, angle C measure 65 degrees, side AC measures 14, side AB measures
Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional
Answer:
The correct answer is A. Yes, because there are two pairs of congruent corresponding angles.
Step-by-step explanation:
This is because to prove that two triangles are congruent, you need at least two pairs of corresponding angles.
Also, the degrees 30, 65, and 85 is equal to 180 degrees.
Hope this helps!
A ship sails due west from a harbor for 28 nautical miles. It then sails S68°W for another 17 nautical miles. How far is the ship from the harbor? (Round your answer to two decimal places.)
The ship is approximately 26.16 nautical miles from the harbor after following the described path.
To find the distance of the ship from the harbor after sailing due west for 28 nautical miles and then S68°W for another 17 nautical miles, we can use trigonometry to calculate the resultant displacement.
Let's break down the two legs of the journey:
1. Due west for 28 nautical miles is a straight line.
2. Sailing S68°W for 17 nautical miles forms an angle of 68° with the west direction.
Using trigonometry, we can find the horizontal and vertical components of the second leg:
Horizontal component = 17 * cos(68°)
Vertical component = 17 * sin(68°)
The total horizontal displacement from both legs is:
Horizontal displacement = 28 - (17 * cos(68°))
The total vertical displacement from both legs is:
Vertical displacement = 17 * sin(68°)
To find the distance from the harbor, we use the Pythagorean theorem:
Distance = √(Horizontal displacement² + Vertical displacement²)
Calculating:
Horizontal component = 17 * cos(68°) ≈ 6.93 nautical miles
Vertical component = 17 * sin(68°) ≈ 15.52 nautical miles
Horizontal displacement = 28 - (17 * cos(68°)) ≈ 21.07 nautical miles
Vertical displacement = 17 * sin(68°) ≈ 15.52 nautical miles
Distance = √(21.07² + 15.52²) ≈ √(443.9749 + 240.5504) ≈ √684.5253 ≈ 26.16 nautical miles
Therefore, the ship is approximately 26.16 nautical miles from the harbor after following the described path.
*Need Help??!!
The graph shows the number of each kind of CD in Dante's collection. What is the probability that a randomly chosen CD will be country?
A.) 15%
B.) 20%
C.) 25%
D.) 30%
Photo of the graph is attached.
The probability of getting a country CD out of all the CDs is the number of country CDs divided by the total number of CDs in Dante's Collection.
The total number of CDs in Dante's collection is [tex]6+12+8+4+10=40[/tex].
The total number of country CDs is 12.
So our required probability is [tex]\frac{12}{40}= \frac{3}{10}[/tex].
In percentage this is 3 divided by 10, and then multiply by 100. We get 30%. Answer choice D is correct.
ANSWER: D
Answer: D.) 30%
Step-by-step explanation:
From the given pie chart, we have the number of country CD = 12
The total number of CD's=[tex]12+8+4+6+10=40[/tex]
Now, the probability that a randomly chosen CD will be country is given by :-
[tex]\text{P(country)}=\dfrac{\text{Number of country CD}}{\text{Total CDs}}\\\\=\dfrac{12}{40}=\dfrac{3}{10}=0.3[/tex]
In percent, [tex]0.3\times100=30\%[/tex]
Hence, the probability that a randomly chosen CD will be country is 30%.
Estimate the fraction equal to 19%
The area of a rectangle is 70 square inches and the length of the rectangle is 3 inches longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
3w = 70
w(w+3)=70w(w+3)=70
w + 3 = 70
w + 3w = 70
HELP ME- 15 points
Jaycee is writing a coordinate proof to show that the diagonals of a rectangle bisect each other. She starts by assigning coordinates to a rectangle. Then she uses these coordinates to write the coordinates of the midpoint of each diagonal. She finds that the midpoints of the diagonals have the same coordinates, so the diagonals must bisect each other.
What are the coordinates of the midpoint of the diagonals of the rectangle?
Enter expressions in the box for the coordinates of the midpoint.
(__,__)
The coordinates of the midpoint of the diagonals of a rectangle are found by averaging the x-coordinates and the y-coordinates of the endpoints of the diagonals. Because of the properties of a rectangle, the midpoint will be the same for both diagonals, confirming that the diagonals bisect each other. The midpoint's coordinates are ((x1+x2)/2, (y1+y2)/2).
Explanation:To find the coordinates of the midpoint of the diagonals of a rectangle, you must first know the coordinates of the rectangle's vertices. Suppose the rectangle has vertices at (x1, y1), (x1, y2), (x2, y1), and (x2, y2). Without loss of generality, let (x1, y1) and (x2, y2) be the endpoints of one diagonal and (x1, y2) and (x2, y1) be the endpoints of the other diagonal.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by averaging each of the x-coordinates and the y-coordinates of the endpoints. Thus, the midpoint M1 has coordinates ((x1+x2)/2, (y1+y2)/2). Similarly, the midpoint M2 for the other diagonal has coordinates ((x1+x2)/2, (y2+y1)/2). Because of the properties of a rectangle, these midpoints will be the same, confirming that the diagonals bisect each other.
Therefore, the coordinates of the midpoint of the diagonals of a rectangle are ((x1+x2)/2, (y1+y2)/2).
A circular walkimg path has a diameter of 45 yards. what is the circunference of the walking path
15 POINTS. Find the total area (in terms of K) of the prism. Place "K" last in your formula.
T.A. =
Please tell me what to put in the blanks, how the question asks
Change 5000 meters to kilometers.
a.0.5 kmb)5 kmc)50 kmd)500 km
option b) 5 km
1 km = 1000 m
Divide the number of meters by 1000:
5000 m / 1000
= 5 km
So, 5000 meters is equal to 5 kilometers.
The correct answer is 5 km.
steve has 276 slides in carousels. each carousel holds 75 slides. how many carousels will be completely filled?
Steve can completely fill 3 carousels with his 276 slides as each carousel holds up to 75 slides.
Explanation:Based on the provided data, Steve has 276 slides and each carousel holds up to 75 slides. To find out how many carousels can be completely filled, we have to divide the total number of slides by the number that each carousel holds.
So, the calculation would be: 276 (total slides) divided by 75 (slides each carousel can hold).
276 ÷ 75 equals about 3.68. Since we cannot have a fraction of a carousel, we round the number down to the nearest whole number. Hence, Steve can completely fill 3 carousels with his slides.
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find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.
Final answer:
To find the volume of a regular hexahedron with a face diagonal of 8√2 inches, we first calculate the side length of the cube and then use it to determine the volume, resulting in a volume of 512 cubic inches.
Explanation:
The question asks to find the volume of a regular hexahedron (which is a cube), given the diagonal of one of its faces is 8√2 inches. Since we know the face of a hexahedron is a square, we can use the Pythagorean theorem to find the side of the square. The diagonal (d) of a square relates to its side (s) by the formula d = s√2. Therefore, we can solve for s: s = d / √2 = (8√2) / √2 = 8 inches. Now that we have the length of the side of the cube, we can compute the volume (V) using the formula V = s3. Substituting s = 8 inches, we calculate the volume as V = 83 = 512 cubic inches.
Please (look at the pionts) I really need help if you help me I will help you if I can. 3. The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy. Lola sold $2030 in ads, Ahmed sold $1540, and Tommy sold $1800. (a) What fraction of the total sales did each salesperson sell? (b) A $100 bonus was awarded to the three salespeople, which they had to share. It was awarded so that each salesperson received the same fraction of $100 as he or she sold of the total sales. How much did each person receive? Round to the nearest whole cent.
which fraction is not equivalent to 7/8
a 21/24 b 35/40 c 15/16 d 28/32
Final answer:
Option c, 15/16, is the correct answer because it cannot be simplified to 7/8, making it not equivalent to 7/8, while the other options are equivalent after simplification.
Explanation:
The question asks us to identify which fraction is not equivalent to 7/8. To determine this, we need to compare each option with 7/8:
Option a: 21/24 can be simplified by dividing the numerator and the denominator by 3, which gives us 7/8, so this option is equivalent.Option b: 35/40 can be simplified by dividing the numerator and the denominator by 5, which gives us 7/8, so this option is equivalent as well.Option c: 15/16 cannot be simplified to 7/8 because when we divide both by their greatest common divisor, we do not get 7/8. Therefore, this fraction is not equivalent to 7/8.Option d: 28/32 can be simplified by dividing the numerator and the denominator by 4, which gives us 7/8, so this option is equivalent.Hence, the correct answer is option c, which is not equivalent to 7/8.
Marie uses 2.3 oz of nuts for each bag of trail mix she makes. She uses 27.6 oz of nuts in all. How many bags of trail mix does Marie make?
The leather of marshalls rectangular poster is 2 times its width. if the perimeter is 24 inches, what is the area of the poster
In a ____ the denominator is one unit
For what value of c is the function defined below continuous on (-\infty,\infty)?
f(x) =
{x2−c2,X < 4 ; cx+20,x≥4.
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers [tex](-\infty, +\infty)[/tex]
Simple question! Thank you for the help so far! :D
Answer:
○ [tex]\displaystyle y ≤ -7[/tex]
Step-by-step explanation:
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
I am joyous to assist you anytime.
Find the perimeter of △ABC with vertices A(−4, 3), B(1, −5), and C(−4, −5). Round your answer to the nearest hundredth.
△ABC△ABC is similar to △XYZ△XYZ. Also, side ABside AB measures 6 cm, side BCside BC measures 18 cm, and side XYside XY measures 12 cm.
What is the measure of side YZside YZ ?
Answer:
36
Step-by-step explanation:
Why is it important to start saving for retirement decades before retirement age?
It is important to start saving for retirement decades before retirement age because of compound interest. When you start saving at a younger age, you have more time for your money to compound. In other words, you can start with a smaller amount of money and after 30 years of compounding, it can grow to a larger amount.
Compounding is the formula 1 + r to the n which means interest compounds into more interest over time.
There are 440 students, ratio of male to female students is 6 to 5. Find how many male and female students in a class
AB = BC
Angle BDC = 37½°
CBD =
Answer:
[tex]\angle CBD=105^{\circ}[/tex]
Step-by-step explanation:
We have been given a diagram. We are asked to find the measure of angle CBD using given diagram.
We can see that in triangle ABD two angles measure 60 degree. Using angle sum property of triangle, we can find measure of triangle angle ADB as:
[tex]\angle A+\angle B+\angle D=180^{\circ}[/tex]
[tex]60^{\circ}+60^{\circ}+\angle D=180^{\circ}[/tex]
[tex]120^{\circ}+\angle D=180^{\circ}[/tex]
[tex]120^{\circ}-120^{\circ}+\angle D=180^{\circ}-120^{\circ}[/tex]
[tex]\angle D=60^{\circ}[/tex]
Since all angles of triangle ABD are equal, so it is an equilateral triangle and its all sides will have same measure.
[tex]AB=BD=AD[/tex]
We have been given segment AB is equal to segment BC. Now, we will get:
[tex]AB=BD=AD=BC[/tex]
In triangle BCD sides two sides (BD and BC) are equal, so it is an isosceles triangle.
We know that angles corresponding to equal sides of an isosceles triangle have equal measure, so measure of angle BDC will be equal to angle BCD.
[tex]\angle BDC=\angle BCD=37\frac{1}{2}^{\circ}[/tex]
Now, we will use angle property of triangle to find measure of angle CBD as:
[tex]\angle CBD+\angle BCD+\angle BDC=180^{\circ}[/tex]
[tex]\angle CBD+37\frac{1}{2}^{\circ}+37\frac{1}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{75}{2}^{\circ}+\frac{75}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{150}{2}^{\circ}=180^{\circ}[/tex]
[tex]\angle CBD+\frac{150}{2}^{\circ}-\frac{150}{2}^{\circ}=180^{\circ}-\frac{150}{2}^{\circ}[/tex]
[tex]\angle CBD=\frac{360}{2}^{\circ}-\frac{150}{2}^{\circ}[/tex]
[tex]\angle CBD=\frac{210}{2}^{\circ}[/tex]
[tex]\angle CBD=105^{\circ}[/tex]
Therefore, the measure of angle CBD is 105 degrees.
What is "Centroid of a triangle" and why is it important?
Find a solution with theta in radians (of possible)
1. tan(theta)
3. 3cos(theta)
5. tan(5(theta)+7
...?