The dimensions of the school yard is 58 m and 89 m.
What is rectangle ?A rectangle is a polygon with four sides , It has opposite sides parallel and equal.
It is given that
A rectangular school yard has a perimeter of 294 meters
Perimeter of a rectangle is given by
P = 2(Length +Breadth)
294 = 2( L+B)
147 = L+B
Area of a rectangle is given by
L*B = 5162
B = 5162/L
L + 5162/L =147
L² -147L +5162 = 0
L² -58L - 89L+5162 = 0
L(L-58) -89(L-58)
L = 58 , 89
The dimensions of the school yard is 58 m and 89 m.
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What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?
(6, 31)
(−6, 31)
(6, −31)
(−6, −31)
Answer: (6, -31)
Explanation: See attachment
From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.
Answer:
a) 182.90 m
b) 203.85 m
Step-by-step explanation:
The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.
__
a)The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...
Tan = Opposite/Adjacent
Solving for the adjacent side, we have ...
BF = (90 m)/tan(26.2°) ≈ 182.90 m
The boat is about 182.90 meters from the foot of the cliff.
__
b)The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...
Sin = Opposite/Hypotenuse
BC = (90 m)/sin(26.2°) ≈ 203.85 m
The boat is about 203.85 meters from the top of the cliff.
What is the value of x
Enter your answer in the box
X=_
Answer:
25
Step-by-step explanation:
This is an equilateral triangle so all of its angle measures, and side lengths likewise, are equal.
To find x we can use the following equation:
3x - 5 = 2x + 20 export like terms to the same side of the equation
3x - 2x = 20 + 5 (notice how terms change from "+" to "-" and vice versa)
add/subtract like terms
x = 25
Which of the following statements is false?
In quadrilateral PQRS, ∠P and ∠S are opposite angles.
A polynomial f(x) has the given zeros of 7-1, and-3
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form Show all necessary calculations (3 points)
Part B: Divide the polynomial f (x) by (x²-x-2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote (4 points)
Part C: List all locations and types of discontinuities of the function g(x) (3 points)
The polynomial f(x) in expanded form is [tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
The polynomial f(x)The polynomial zeros are given as:
x = 7, x = -1 and x = -3
Rewrite as:
x - 7 = 0, x + 1 = 0 and x + 3 = 0
Multiply the zeros
f(x) = (x - 7)(x + 1)(x + 3)
Expand
[tex]f(x) = (x - 7)(x^2 + 4x + 3)[/tex]
Further, expand
[tex]f(x) = x^3 + 4x^2 - 7x^2 + 3x - 28x - 21[/tex]
Evaluate
[tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
Hence, the polynomial f(x) in expanded form is [tex]f(x) = x^3 - 3x^2 - 25x - 21[/tex]
Rational function g(x)We have:
[tex]g(x) = \frac{f(x)}{x^2 - x- 2}[/tex]
This gives
[tex]g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}[/tex]
Expand the numerator
[tex]g(x) = \frac{x^3 - x^2 - 2x^2 - 2x + 2x - 25x + 4 - 25}{x^2 - x - 2}[/tex]
Rewrite as:
[tex]g(x) = \frac{x^3 - x^2 - 2x - 2x^2 + 2x + 4 - 25x - 25}{x^2 - x - 2}[/tex]
Factorize
[tex]g(x) = \frac{(x - 2)(x^2 - x- 2) - 25x - 25}{x^2 - x- 2}[/tex]
Evaluate the quotient
[tex]g(x) = x - 2 - \frac{25x + 25}{x^2 - x- 2}[/tex]
The slant asymptote is the quotient i.e. x - 2
Hence, the slant asymptote of the function g(x) is x - 2
The discontinuities of g(x)In (b), we have:
[tex]g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}[/tex]
Set the denominator to 0
[tex]x^2 - x - 2 = 0[/tex]
Expand
[tex]x^2 + x - 2x - 2 = 0[/tex]
Factorize
x(x + 1) - 2(x + 1) = 0
Factor our x + 1
(x - 2)(x + 1) = 0
Solve for x
x = 2 or x = -1
2 is greater than -1.
So, the discontinuities and their types are:
Essential discontinuity at x = 2Removable discontinuity at x = -1Read more about polynomials at:
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What is the domain of the function shown in the
mapping?
Ox|x=-5, -3, 1, 2, 6}
O lyly=-9, -6, 0, 2, 4)
O {x|x=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Oyly=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Domain is the set of values for which the given function is defined. The correct option is A.
What is domain and range of a function?Domain is the set of values for which the given function is defined, therefore the are values that the function can take.
Range is the set of all values which the given function can produce an output.
Domain of a function is the range of the inputs which the function can take, therefore, the domain of the function shown in the mapping is,
x|x= -5, -3, 1, 2, 6}
Hence, the correct option is A.
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The figure below is a right rectangular prism.
X
W
४
M
N
x
Y
N
O
12
2x
T
Which expression represents the volume of the prism?
01x³
O
O
(+)
0 (x)
Answer:
1/2x^3
Step-by-step explanation:
The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).
Just plug the numbers (or in this case variables) into the formula:
v = x times x times 1/2x
v = 1/2 times x^3
v = 1/2x^3
Volume
LBH1/2x(x)(x)1/2(x)³Option A
Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
Can someone help with question 3? I would like to see the working and answer on paper, I’m in a hurry
Answer:
Step-by-step explanation:
so...
on your new sheet of paper, draw a straight horizonal line label one end Y the other Z ( Y will be your vertex, point of angle )
then on original figure, use a compass and put the in B and measure to A
on new sheet put the pin in Y and draw an arc ( lightly )
now back to orig and put pin in C and measure up to A
on new put pin onthe line so that when you draw an arc it will bisect the one you did previously. will will create a point . join the point to Y
hope that makes some sort of sense.
Vertical lines m and n are intersected by lines k and j. At the intersection of lines m and k, the bottom right angle is (x minus 30) degrees. At the intersection of m and j, the uppercase right angle is y. At the intersection of lines k and n, the bottom left angle is (x + 50) degrees.
Find the values of x and y that make k || j and
m || n.
x =? °
y = ?°
Using the same-side interior angles theorem, the values of x and y are:
x = 80
y = 130
What is the Same-side Interior Angles Theorem?The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.
(x - 30) and (x + 50) are same-side interior angles, therefore:
(x - 30) + (x + 50) = 180
Solve for x
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80
(x - 30) + y = 180
Plug in the value of x
(80 - 30) + y = 180
50 + y = 180
y = 180 - 50
y = 130
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Answer:
X= 80
Y= 130
Step-by-step explanation:
do you trust me???
Please help if you can
MATHHH. Probability section!!! HELP!
please give the right answer.
Answer:
10% or 1 /10
Step-by-step explanation:
'Fish' is on the spinner in one slot out of 10 slots
one out of 10 = 1/10 = 10%
Answer:
10%
Step-by-step explanation:
There are 10 possible areas to land on fish is only shown once meaning there is a 1/10 chance which is = to 10%
If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?
Answer:
26
Step-by-step explanation:
Define the variables:
2n = first even number2n + 2 = consecutive even numberGiven information:
2 times the sum of two consecutive even numbers is greater than 94Create an inequality from the defined variables and the given information:
⇒ 2(2n + 2n + 2) > 94
Solve the inequality:
⇒ 2(4n + 2) > 94
⇒ 8n + 4 > 94
⇒ 8n > 90
⇒ n > 11.25
Therefore:
2n > 22.52n + 2 > 24.5As 2n and 2n+2 are even numbers:
smaller number (2n) ≥ 24larger number (2n + 2) ≥ 26Therefore, the smallest possible value of the larger number is 26.
)If 18th February, 2030 falls on Monday then what will be the day on 18th February, 2040
Who ever answers this quickly with explanation I will make then brainliest
The Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
18th February 2030 falls on Monday
To find what will be the day on 18th February 2040
Calculate the expression:
= Given date + Month code + (difference between years) + Numbe of leap year
Leap year = difference between years/4
= (2040-2030)/4
= 10/4 = 2.5 ≈2
= 18 + 3 + (2040-2030) + 2
= 33
Divide 33 by 7 the remainder will be 5
Day code = given day code + remainder
= 1 + 5
= 6 (saturday from the table attahced)
Thus, Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday.
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Girl runs across Across a rectangle field diagonal covering a distance of 120m if the length of the field is 100m calculate the width of the field to the nearest metre
Answer:
66m
Step-by-step explanation:
Answer:
66 m
Step-by-step explanation:
ok so if you think about it, when she runs diagonal she's creating a triangle where she is running along the hypotenuse. we can now use the Pythagorean Theorem a^2 + b^2 = c^2 to solve for the other side with two of them being known.
plug values in
100^2 + w^2 = 120^2
square known values
10,000 = w^2 = 14,400
subtract 10,000 from both sides
w^2 = 4400
take the square root
w = 66 (rounded to the nearest whole number)
Which of the following triangles are right triangles? Select all that apply.
Triangle A:
101
20
Triangle A
Triangle B
Triangle C
89
15
Triangle B:
113
110
20
Triangle C:
29
21
B
So there is a possibility I read it wrong, or you typed it wrong. but from what I see, there are NO right triangles.
Step-by-step explanation:
a right triangle has a 90 degree angle. none of these have one.
Use the following information for problems 5-8.
f(2, 33) = 5.5, p < 0.01
1) how many groups were in this study?
a) 34
b)33
c) 3
d) 2
how many participants were in this study?
a) 36
b) 33
c) 3
d) 2
what is the f ratio?
a) 5.5
b) 2
c) 33
d) 0.01
The number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
f(2, 33) = 5.5, p < 0.01
From the above details, we can find the number of groups:
5) Number of groups = df for groups + 1
Number of groups = 2+ 1 = 3
Option (c) is correct.
6) Number of participants =2 + 33 + 1 = 36
Option (a) is correct.
7) f ratio = 5.5
Option (a) is correct.
8) True; as the p-value is less than the 0.01 level.
Thus, the number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
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If you apply the changes below to the quadratic parent function, f(x) = x²,
which of these is the equation of the new function? Shift 1 unit left.
Vertically stretch by a factor of 5.
Reflect over the x-axis.
A. g(x) = -5(x-1)²
B. g(x) = -5x² - 1
C. g(x) = -5(x + 1)²
D. g(x) = (-5x + 1)²
Answer:
Step-by-step explanation:
Comment
Do the most mechanical part first. Moving 1 unit left will mean that x becomes (x + 1). It is anti intuative, but that is the correct answer.
So far what you have is y = a(x + 1)^2
The reason that you want to do it this way is any answer with a minus sign is wrong which eliminates A and B
When you stretch the parabola, a becomes 5 so now you have another part of the puzzle. and the equation becomes
y = 5(x + 1)^2
The 5 goes on the outside of the brackets which eliminates D
When you reflect this over the x axis, you invert the parabola which means you turn it upside down. The sign in front of the 5 becomes a minus.
Answer
y = - 5(x + 1)^2 or C.
Part 1 - Application Pick one of the two graphs below. Describe a situation which could be modeled by this polynomial graph. Be sure to label the x and y axis with what each will represent in your real life graph. Sample labels could include time, temperature, speed, distance and more. Be sure to add numbers to your axes as well and explain how you came up with your situation.
One good example of a situation that can be modeled by this Polynomial Graph is the price-time relationship between currency pairs being traded on the Foreign Exchange Market.
What is a Polynomial Graph?A polynomial parameter graph is essentially a smooth continuous curve.
Although the forex graph attached has sharp undulations, when regressed and viewed via Polynomial Regression Indicators, they exhibit strong polynomial qualities that meet the requirements of the definition above.
It is to be noted that the Y-Axis is indicative of the price of the currency pairs (which could be any currency against another) and the X-Axis expresses time. See the attached graphs for a better picture.
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Each staple is made from 0.21 g of metal.
How many staples can be made from 1 kg of metal?
Answer:
4762
Step-by-step explanation:
0.21g x 10,000= 2100
0.21 x 5,000= 1050
0.21 x 4,000= 840
0.21 x 4700 = 987
0.21 x 4760 = 999.6
0.21 x 4762= 1000.02
( how much it's made from x the quantity = the grams or kg)
This table represents a quadratic function with a vertex at (1, 1). What is the
average rate of change for the interval from x = 5 to x = 6?
OA. 26
OB. 13
O C. 7
OD. 9
1
2
3
4
5
X
1
2
LO
5
10
17
y
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
How to find the average rate of change on the interval?
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
[tex]r = \frac{f(6) - f(5)}{6 - 5}[/tex]
[tex]f(x) = a*x^2 + b*x + c[/tex]
I we look at the table we see that:
[tex]f(1) = 1 = a + b + c[/tex]
[tex]f(2) =2 = 4a + 2b + c[/tex]
[tex]f(3) = 5 = 9a + 3b + c[/tex]
This is a system of equations.
If we subtract the second and first functions, we get:
[tex]2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c[/tex]
From that we take two relations:
[tex]1 - 3a = b\\2a = c[/tex]
Now we can replace these two in the last equations so we get:
[tex]5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1[/tex]
Now that we know the value of a:
[tex]c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2[/tex]
The quadratic equation is:
[tex]f(x) = x^2 - 2x + 2[/tex]
Evaluating this in x = 6 we get:
[tex]f(6) = 6^2 - 2*6 + 2 = 26[/tex]
And from the table we know that f(5) = 17, then the average rate of change is:
[tex]r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9[/tex]
The correct option is D.
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10. A In the adjoining Figure, ab is perpendicular to bc and ed is to cd while bc=cd . prove i) triangle abc is corresponding to triangle edc
ii)ab = cd
Part (i)
1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)
2) Angles ABC and CDE are right angles (perpendicular lines form right angles)
3) Angles ABC and CDE are equal (all right angles are equal)
4) Angles ACB and DCE are equal (vertical angles are equal)
5) Triangles ABC and EDC are congruent (ASA)
Part (ii)
6) AB = DE (corresponding parts of congruent triangles are equal)
The graph of f(x)=x2 is shown. Use the parabola tool to graph the function g(x)=(12x)2. To graph a parabola, first plot the vertex then plot another point on the parabola.
Answer:
Pease check my assumptions.
Step-by-step explanation:
I will assume that f(x)=x2 is actually f(x) = x^2.
Same for g(x)=(12x)^2 [Is it g(x)=12x^2 ???]
See the attached image.
Note that (12x)^2 results in a narrower, steeper graph. That's because (12x)^2 can be rewritten as 144x^2, so every value is multiplied by 144, compared to just x^2.
The time series pattern that reflects a gradual shift or movement to a relatively higher or lower level over a longer time period is called the _____.
Answer:
Trend pattern
x = √3 + √2/ √3 - √2
y = √3 - √2/ √3 + √2
Find x² + y²
Answer: 98
Given following:
[tex]\Longrightarrow \sf x = \dfrac{\sqrt{3} +\sqrt{2} }{\sqrt{3} - \sqrt{2} }[/tex]
[tex]\Longrightarrow \sf y = \dfrac{\sqrt{3} -\sqrt{2} }{\sqrt{3} + \sqrt{2} }[/tex]
Solve for x² + y²:
[tex]\rightarrow \sf \left(\:\dfrac{\sqrt{3}\:+\sqrt{2}\:\:}{\sqrt{3}\:-\:\sqrt{2}\:}\right)^2\:+\:\left(\dfrac{\sqrt{3}\:\:-\sqrt{2}\:\:}{\sqrt{3}\:+\:\sqrt{2}\:\:}\:\right)^2[/tex]
simplify following
[tex]\rightarrow \sf 49+20\sqrt{6}+49-20\sqrt{6}[/tex]
add/subtract similar terms
[tex]\rightarrow \sf 98[/tex]
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
2nd box, 4th box and 5th box
Step-by-step explanation:
can someone please help mee(10 points)
Answer:
(2,-3)
Step-by-step explanation:
Thats where the parabola is the lowest at
Rewrite in simplest terms: (4x+5)+(−5x−1) pls help
Answer:
-x + 4
Step-by-step explanation:
(4x+5)+(−5x−1)
4x+5−5x−1 [Remove the parentheses]
-x + 4 [Combine Like Terms]
Answer:
-x+4
Step-by-step explanation:
Given:
(4x+5)+(−5x−1)
Solution:
To re-write this in it's simplest terms:
4x+5-5x−1Combine like terms:
4x-5x+5-1-x+4Hence the simplest form is -x+4.
Done.
Which term describes the point where the perpendicular bisectors of the three sides of a triangle intersect? OA. Incenter OB. Centroid OC. Circumcenter D. Orthocenter
Answer: Circumcenter (choice C)
Explanation:
The circumcenter is useful to form a circle that passes through all three points of a triangle. It is the smallest circle possible that doesn't go inside the triangle.
The incenter is formed by intersecting at least two angle bisectors, which means we can rule out choice A. The centroid is the result of intersecting two or more medians, which allows us to cross off choice B. Choice D is out because the orthocenter is the intersection of the altitudes.
Answer:
C. Circumcenter
Step-by-step explanation:
Hope this helps.
How many zero pairs must be added to the function
f(x) = x2 – 10x – 4 in order to begin writing the function in vertex form?
4
10
21
25
1 zero pair of 25 was added to bring given function into vertex form.
What is a Zero Pair ?A zero Pair is the set of two numbers which when added together gives 0.
The function given is
f(x) = x² -10x -4
To convert it into the vertex form
y = a(x-h)² +k
f(x) = x² -10x +25 -25 -4
f(x) = x² -10x +5² -25-4
f(x) = (x-5)² -29
Therefore this is the given function's vertex form and
1 zero pair of 25 was added to bring it into that.
Therefore Option D is the answer.
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