Answer:
The maximum area of one square plot is 144 [tex]m^2[/tex]
Step-by-step explanation:
Start by looking at what are the greater common factor of both provided dimensions (840 and 396) to find what the numbers are they both can be divided by evenly:
[tex]840=2^3\,*\,3\,*\.5\,*\,7\\396=2^2\,*\,3^2\,*\,11[/tex]
therefore, both numbers can be divided by [tex]2^2\,*\,3=12[/tex]
Which then gives:
[tex]\frac{840}{12} =70\\\frac{396}{12} =33[/tex]
Then, one can divide the longest side (840 m) into 70 sections of 12 meters each, and the shortest side of the piece of land (396 m) into 33 sections of 12 meters each.
Then we can have a total of 33 * 70 = 2310 smaller lots of 12 m by 12 m
That is smaller plots of a total area 144 square meters
A television set costs $350 cash. When bought on hire purchse, a deposit of $35 is required, followed by 12 monthly payments of $30. How much is saved by paying cash?
Answer:
$45
Step-by-step explanation:
find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395
difference: 395 - 350 = $45
HELP PLEASEEEEEEEEEEEEE! Soup can be packaged in two different containers: a box and a cylinder. The dimensions of the box are 7.5 cm by 4.7 cm by 14.5 cm. The cylinder has a radius of 3.3 cm and a height of 10 cm. Determine which container uses less material to make and find out which container holds more soup. Create a design for each container shape. Be sure to name your soup!
Answer:
Step-by-step explanation:
Use the following formulas:
surface area of rectangular prism: A = 2wl + 2lh + 2hw
volume of rectangular prism: lwh
surface area of cylinder: A=2πrh+2πr^2
volume of cylinder: V=πr^2h
using these formulas, the surface area of the box is 424.3
the volume of the box is about 511.3
the surface area of the cylinder is about 275.77
the volume is 342.12
knowing this, the cylinder uses less material but the box holds more soup.
Which equation represents a line that is perpendicular to line FG? A. y=-1/2x+5 B. y=1/2x+2 C. y=-2x-3 D. y=2x-6
The equation of line which is perpendicular to the line FG is
y = -2x -3.
What is equation of line?
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Formula for finding the equation of line from two points [tex](x_{1} ,y_{1} ) and (x_{2}, y_{2} )[/tex][tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]
What is the slope of two perpendicular lines?If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].
What is the slope intercept form of a line ?The slope intercept form of the line is given by y = mx + b
Where, m is the slope of a line.
According to the given question
We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.
Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]
⇒ The slope of the line which is parallel to line FG is -2
Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .
Hence, the equation of line which is perpendicular to the line FG is
y = -2x -3.
Learn more about the equation of a perpendicular line here:
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Calculate the shaded region
｡☆✼★ ━━━━━━━━━━━━━━ ☾
First find the area of the sector.
For that, use this equation:
area = [tex]\frac{x }{360} * \pi r^{2}[/tex]
where 'x' is the angle and 'r' is the radius
Sub the values in
area = [tex]\frac{56}{360} * \pi15^2[/tex]
Solve:
area = [tex]35\pi[/tex]
It is easier to keep it in terms of pi until the end
Now, calculate the area of the triangle within the sector
area = 1/2 ab x sinC
where 'a' and 'b' are the radius (side lengths) and C is the angle
thus,
area = 1/2(15 x 15) x sin(56)
area = 93.27 (to 2 d.p)
Now subtract the area of the triangle from the area of the sector
[tex]35\pi[/tex] - 93.27 = 16.6857
This would give you a final answer of 16.69 units^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
HELP ME PLEASEEEE! Thank you
Answer:
A. Yes
B. Yes
C. No
Step-by-step explanation:
We can substitute each value in to the equation and see if the sides match up. Let's start with a.
[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]
So, n = 2 works for equation a. Let's try B.
[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]
So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.
[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]
So y = 30 doesn't work for C.
Hope this helped!
Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle exists because the sum of any two side lengths is greater than the length of the third side. This triangle exists because the sum of 4 and 12 is less than 17. This triangle does not exist because the sum of any two side lengths is greater than the length of the third side. This triangle does not exist because the sum of 4 and 12 is less than 17.
Answer:
The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."
Answer:
This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17
Step-by-step explanation:
The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.
Triangle
Sides - 3, 4, 5
3+4=7
Meaning the two smaller sides add up to because greater than 5.
Non-Triangle
Sides - 5, 6, 13
5+6=11
This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.
Gemma’s Triangle
Sides - 4, 12, 17
4+12=16
Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.
What are the solutions of the system? y=−6x−6 and y= x^2 −5x−6
Answer:
(0,-6) and (-1,0)
Step-by-step explanation:
First:
Set both sides equal to each other: -6x-6=x^2-5x-6
Next:
factor -6 our from the first side and write -5x as a difference:
-6(x+1)=x^2+x-6x-6
Then:
factor out x and -6 drom the second side:
-6(x+1)=x(x+1)-6(x-+1)
Then:
Factor out (x+1)
-6(x+1)=(x+1)(x-6)
Next Combine to one side and factor:
-(x+1)(6+x-6)=0
Simplify:
(x+1) (x)=0
find the zero:
x+1=0 --> x=-1
x=0 --> x=0
Substitute into the equations to find y:
y=-6(-1)-6
y=-6(0)-6
Solve:
y=0
y=-6
Answer:
(x1,y1)= (-1,0)
(x2,y2)= (0,-6)
Help please!!!!!!!!!!!
Answer:
B. 2/3
Step-by-step explanation:
To solve this we have to take into account this axioms:
- The total probability is always equal to 1.
- The probability of a randomly selected point being inside the circle is equal to one minus the probability of being outside the circle.
Then, if the probabilities are proportional to the area, we have 1/3 probability of selecting a point inside a circle and (1-1/3)=2/3 probability of selecting a point that is outside the circle.
Then, the probabilty that a random selected point inside the square (the total probability space) and outside the circle is 2/3.
Graph this compound inequality: 2.5 < x < 4.5
-5 4
-3
-2
-1 0
+ ++ +
1 2 3 4 5
o
Drag a point to the number line.
Answer:
Please find the attached the required inequality graph
Step-by-step explanation:
Given that inequality is 2.5 ≤ x ≤ 4.5, we have;
The region in the given inequality is the region between 2.5 and 4.5 inclusive
Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;
A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.
The number of people contacted at each level of a phone tree can be represented by f(x) = 3^x where x represents the level.
What is x when f(x) = 27?
A. X = 2; At level 2, 27 people will be contacted.
B. x = 24; At level 24, 27 people will be contacted.
C. x = 3; At level 3, 27 people will be contacted.
D. x = 9; At level 9,27 people will be contacted.
Answer:
3
Step-by-step explanation:
Answer:
c is the correct answer
Step-by-step explanation:
How many terms are in the expression shown?
2n + 5 – 3p + 4q
1
2
3
4
Step-by-step explanation: A term can be a number, a variable, or a number times one or more variables.
So in this expression, the terms are +2n, +5, -3p, and +4q.
This means that there are 4 terms.
The answer is D - 4 :)
Match each quadratic graph to its respective function
Answer:
f(x) = (x - 3)(x + 1) → Corresponds with the first (raised higher ) ∪ shaped graph
f(x) = -2(x - 1)((x + 3) → Corresponds with the ∩ shaped graph
f(x) = 0.5(x - 6)((x + 2) → Corresponds with the second (lower) ∪ shaped graph
Step-by-step explanation:
For the function f(x) = (x - 3)(x + 1)
We have;
When x = 0, y = -3
When y = 0 x = 3 or -1
Comparing with the graphs, it best suits the first ∪ shaped graph that rises here than the other ∪ shaped graph
For the function;
f(x) = -2(x - 1)((x + 3)
When x = 0, y = 6
When y = 0, x = 1 or -3
Which corresponds with the ∩ shaped graph
For the function;
f(x) = 2(x + 6)((x - 2)
When x = 0, y = -24
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = 0.5(x - 6)((x + 2)
When x = 0, y = -6
When y = 0, x = 6 or -2
Which best suits the second ∪ shaped graph that is lower than the other (first) ∪ shaped graph
For the function;
f(x) = 0.5(x + 6)((x - 2)
When x = 0, y = -6
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = (x + 3)((x - 1)
When x = 0, y = -3
When y = 0, x = -3 or 1
Graph not included
Answer:
The guy above me was right. i accidently put in the answers in the wrong order so i thought it was wrong and rated it 1 star
Step-by-step explanation:
If ABCD is a rectangle, calculate x as a function of α
Answer:
Step-by-step explanation:
The length of this triangle is 10 squares
and the width is 4 squares
The diagonals divide the rectangle into four triangles
These traingles are isoceles
Each two triangles facing each others are identical
<B = 90 degree
B = alpha + Beta
Let Beta be the angle next alpha
The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:
Beta = 2x
Then B = alpha + 2x
90 = alpha +2x
90-alpha = 2x
x = (90-alpha)/2
Answer:
x = 90 - 2α
Step-by-step explanation:
Solution:-
- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".
< BAD > + < ADB > + < ABD > = 180°
< ABD > = 180 - 90° - α
< ABD > = 90° - α
- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".
- We name the foot of the perpendicular bisector as " F ": " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.
< ABD > = < BAE > = 90° - α ... ( Isosceles triangle " BEA " )
Where, sides ( BE = AE ).
- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:
< ABF> + < BFA > + < BAF > = 180°
< ABF > = 180 - (90° - α) - 90°
< ABF > = α
Where, < BAF > = < BAE >
- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE > = x.
< ABD > = < ABE > = < ABF > + x
90° - α = α + x
x = 90 - 2α ... Answer
The text classifies information systems as either operations or management support information systems. Which one of the following would not be classified as an operations support system?
A. Transaction processing systems
B. Process control systems
C. Enterprise collaboration systems
D. Decision support systems
Answer:
D. Decision support systems
Step-by-step explanation:
Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.
It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.
There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:
1. Transaction Processing Systems
2. Process control system
3. Enterprise collaboration system
4. Enterprise Resource
Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
5.8 ft
6.3 ft
27.5 ft
69.1 ft
Answer:
69.1 ft
Step-by-step explanation:
A circle has 360 degrees.
The arc we are finding the length of is 330 degrees.
Its length is 11/12 of the circle's total circumference. (330/360=33/36=11/12)
Let's find the circumference of the entire circle.
Circumference is πd.
The radius of the circle is 12ft.
Diameter is double of radius.
12*2=24
The diameter is 24.
Plug that in.
24π=75.36 when using 3.14 for π
Multiply that by 11/12.
11/12*75.36=69.08
Round 69.08 to nearest tenth.
69.1
Keywords:
Circle
Circumference
Arc
Diameter
Radius
Learn more about arc length here:
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What is 5,000 - 245( 30/2))?
Answer:
1,325
Step-by-step explanation:
30 /2
= 155,000 - 245(15)
= 5,000 - 3,675
= 1,325
Answer:
1,325
Step-by-step explanation:
3. In the diagram, PRST and PQWV are rectangles. Q, V
and U are midpoints of PR, PU and PT respectively.
Find the area of the shaded region.
======================================================
Work Shown:
A = area of trapezoid RSTU
A = height*(base1+base2)/2
A = ST*(UT+RS)/2
A = 14*(5+10)/2
A = 105 square cm
-----------------------
B = area of rectangle PQWV
B = length*width
B = WV*PV
B = 7*2.5
B = 17.5 square cm
If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.
-----------------------
C = total shaded area
C = A + B
C = 105 + 17.5
C = 122.5
According to the rational root theorem, which of the following are possible
roots of the polynomial function below?
F(x) = 6x3 - 7x2 + 2x + 8
Answer:
18- 14+8=3x
4+8=3x
12=3x
12/3=2x/3
x=4
Answer:
2/3, -8, -1/6, 4.
Step-by-step explanation:
Step-by-step explanation:
The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :
Now, from the given options, the possible choices can be :
A, B, C and E
D can be there because after taking any pair the rational root can't be 3
F can't be possible because an does't have 4 in its factors so denominator cannot be 4.
Pls help I'm so dumb
Answer:
C. p > -3
Step-by-step explanation:
We observe the characteristics of the shaded ray on the number line.
It goes to the right, so the inequality must be either greater than or greater than or equal to.
The circle where it starts on is open, so the inequality must not be less than or equal to or greater than or equal to.
Now, without even looking at the numbers themselves, we can find our answer.
There are four different types of inequalities, and we eliminated three of them (<, <=, >=). This leaves only one left (>). The only answer choice that uses the greater than symbol is C, so it must be our answer.
What is the approximate angle between two position vectors if their terminal points are (5, -2) and (7, 3)?
Hi,
Answer:
[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°
Have a good day.
You have a standard number cube. What is the probability of rolling a number less than 3, and then rolling a prime number? A. 1/3 B. 1/2 C. 1/36 D. 1/6
Hey Mate !
Your Answer is given in the snip below !!
Please do mark me as brainliest !!!
(ANSWER= (D) [tex]\frac{1}{6}[/tex] )
Explanation
Answer:
You have a standard number cube.
What is the probability of rolling a number less than 3, and then rolling a prime number?
D. 1/6
Please answer this question now
Answer:
s = 11.4
Step-by-step explanation:
The following data were obtained from the question:
Angle S = 60°
Opposite S = s =?
Opposite U = u = 13
Opposite T = t = 5
Thus, from the data obtained from the question, we can calculate the value of s by using cosine rule as shown below:
s² = u² + t² – 2ut Cos S
s² = 13² + 5² – 2 × 13 × 5 × Cos 60
s² = 169 + 25 – 130 × 0.5
s² = 194 – 65
s² = 129
Take the square root of both side.
s = √129
s = 11.4
Therefore, the value of s is 11.4
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
the length of the unknown side is ____
the perimeter of the triangle is ____
the area of the triangle is ___
Answer/Step-by-step explanation:
a. Unknown side, b, using the Pythagorean theorem is solved as shown below.
[tex] b^2 = c^2 - a^2 [/tex]
[tex] b^2 = 45^2 - 27^2 [/tex]
[tex] b^2 = 1,296 [/tex]
[tex]b = \sqrt{1,296}[/tex]
[tex] b = 36 [/tex]
Unknown side, b, = 36 km
b. Perimeter of the triangle = sum of all the sides of the ∆ = [tex] 36 + 45 + 27 [/tex]
[tex] perimeter = 108 km [/tex]
c. Area of triangle = ½*base*height
where,
Base = 36 km
Height = 27 km
[tex] Area = \frac{1}{2}*36*27 [/tex]
[tex] Area = 18*27 [/tex]
[tex] Area = 486 km^2 [/tex]
Please help me!!!!!! I do not understand...
Answer:
the second one........the shape of the conic section os circle
If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
Answer:
Step-by-step explanation:
REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.
Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by
[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]
this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.
So, in our case since -3+i is a root, then -3-i necessarily is another root.
If -3 + i is a root then -3 - i is too.
Therefore, the answer is -3 - i
Audrey charges a flat fee of $4 for each delivery plus a certain amount,in dollars per mile, for each mile she drives. For a distance of 30 miles, Curtis and Audrey charge the same amount
How many triangles does a=6 b=10 A=33° create?
Answer:
2 triangles are possible.
Step-by-step explanation:
Given
a=6
b=10
[tex]\angle[/tex]A=33°
To find:
Number of triangles possible ?
Solution:
First of all, let us use the sine rule:
As per Sine Rule:
[tex]\dfrac{a}{sinA}=\dfrac{b}{sinB}[/tex]
And let us find the angle B.
[tex]\dfrac{6}{sin33}=\dfrac{10}{sinB}\\sinB = \dfrac{10}{6}\times sin33\\B =sin^{-1}(1.67 \times 0.545)\\B =sin^{-1}(0.9095) =65.44^\circ[/tex]
This value is in the 1st quadrant i.e. acute angle.
One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 = [tex]114.56^\circ[/tex]
For the value of [tex]\angle B = 65.44^\circ[/tex], let us find [tex]\angle C[/tex]:
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+65.44+\angle C = 180\\\Rightarrow \angle C = 180-98.44 = 81.56^\circ[/tex]
Let us find side c using sine rule again:
[tex]\dfrac{6}{sin33}=\dfrac{c}{sin81.56^\circ}\\\Rightarrow c = 11.02 \times sin81.56^\circ = 10.89[/tex]
So, one possible triangle is:
a = 6, b = 10, c = 10.89
[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=65.44°, [tex]\angle[/tex]C=81.56°
For the value of [tex]\angle B =[/tex][tex]114.56^\circ[/tex], let us find [tex]\angle C[/tex]:
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+114.56+\angle C = 180\\\Rightarrow \angle C = 180-147.56 = 32.44^\circ[/tex]
Let us find side c using sine rule again:
[tex]\dfrac{6}{sin33}=\dfrac{c}{sin32.44^\circ}\\\Rightarrow c = 11.02 \times sin32.44^\circ = 5.91[/tex]
So, second possible triangle is:
a = 6, b = 10, c = 5.91
[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=114.56°, [tex]\angle[/tex]C=32.44°
So, answer is : 2 triangles are possible.
This isn’t too difficult of questions and I am pretty sure I know the answers but I just want to make sure. Can someone please help.
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
x = 64Step-by-step explanation:
To find x we use tan
tan∅ = opposite / adjacent
From the question
The adjacent is x
The opposite is 30
So we have
tan 25° = 30/x
x tan 25 = 30
Divide both sides by tan 25
x = 30/tan 25
x = 64.34
x = 64 to the nearest tenth
Hope this helps you
Which store has the lowest delivery charge?
Answer:
Igloo Ice has the lowest delivery charge.
Step-by-step explanation:
Igloo Ice when you plug in 120 for the y you get 25.714 as the x.
Freds freeze at 120 is 20.
And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)
Answer:
Igloo Ice
Step-by-step explanation:
Igloo Ice C(n) = 1.75n + 75
Fred's Freeze C(n) = 2n + 80
Tasty Treats C(n) = 1.25n + 90
75 is the lowest delivery charge
C(n) is total charge including what they are delivering