Answer:
The side length of the square region is about 181,166 kilometres.
Step-by-step explanation:
population density = no. of people / area of region
given
population = 200,000
population density = 1650 people per square kilometers
1650 = 200,000/area of region
=> area of region = 1650*200,000 = 330,000,000
given that region is square in shape
area of square = side^2
side^2 = 330,000,000
side = [tex]\sqrt{ 330,000,000} = 181165,90[/tex]
The side length of the square region is about 181,166 kilometres.
Examine the graph. Which statements are true about the function represented by the graph? Select all that apply.
The function is negative over the interval (−16,0).
The function is negative over the interval (−5,3).
The function is positive over the interval (3,∞).
The function is positive over the interval (−∞,−5).
The function is positive over the interval (−5,3).
The function is negative over the interval (−∞,−5).
====================================================
Explanation:
The portion below the x axis is when f(x) is negative. This happens on the interval [tex]-5 < x < 3[/tex]. Note how -5 and 3 are the x intercepts or roots. So because f(x) is negative when [tex]-5 < x < 3[/tex] we can say f(x) is negative over the interval (-5, 3). This is interval notation and not ordered pair notation.
----------
The function f(x) is positive in two places. When x < -5 and when x > 3. This is where the purple parabola is above the x axis.
The x < -5 portion converts to the interval notation (−∞,−5)
The x > 3 portion converts to the interval notation (3,∞)
The function is positive over the interval (3,∞) and interval (−∞,−5) while negative over interval (−5,3) so options (B),(C), and (D) will be correct.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
After that, we need to substitute the values of x's and y's into the coordinate geometry.
If we look at the graph
The value of graph is positive after x = 3 and it is positive before x = -5
Let's say the graph is going infinitely in both directions.
Then the function is positive over the interval (3,∞) and interval (−∞,−5).
The function is negative from x = -5 to 3 so it will be negative over that.
Hence "The function is positive over the interval (3,∞) and interval (−∞,−5) while negative over interval (−5,3)".
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1.find the sum. (3^3+5x^2+3x-7)+(8x-6x^2+6)
2. Find the Difference: (8x-4x^2+3\)-(x^3+7x^2+3x-8)
1.
[tex](3^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=27\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=-x^2+11x+26[/tex]
or if you mean (3x^3+5x^2+3x-7)+(8x-6x^2+6):
[tex](3x^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=3x^3\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=3x^3-x^2+11x-1[/tex]
2.
[tex](8x-4x^2+3)-(x^3+7x^2+3x-8)=\\\\=\underline{8x}\ \underline{\underline{-\ 4x^2}}+3-x^3\ \underline{\underline{-\,7x^2}}\ \underline{-\,3x}+8=\\\\=-x^3-11x^2+5x+10[/tex]
Preview: 5 People fit comfortably in a 2 foot by 2 foot area. Use this value to estimate the size of a
crowd that is 4 feet deep on both sides of the street along a 1-mile section of a parade route.
Answer:
The estimate size of the crowd is 52800 people
Step-by-step explanation:
The given information are;
The number of people that fit comfortably in a 2 by 2 foot area = 5
Therefore, we have;
The area occupied by the 5 people = 2 × 2
The crowd ratio = 5/(2 × 2) = 5/4
The area occupied by the crowd = 4 feet deep, and 1 mile long on both sides of the street
By conversion factors, 1 mile = 5,280 feet
Therefore, the area occupied by the crowd = 4 × 5280 × 2 = 42240 ft²
The number of people in the crowd = Crowd ratio × The area occupied by the crowd
The number of people in the crowd = 5/4 × 42240 = 52800 people
Therefore, The estimated size of the crowd = 52800 people.
an angle is 14 degrees more than complementary angle find the measure
Answer:
[tex]\Huge \boxed{\mathrm{52\°}}[/tex]
Step-by-step explanation:
Complementary angles add up to 90 degrees.
There are two angles in this case.
Let the first angle be x.
Let the second angle be x+14.
The sum of these two angles is 90.
x + x + 14 = 90
Combine like terms.
2x + 14 = 90
Subtract 14 from both sides.
2x = 76
Divide both sides by 2.
x = 38
Let x = 38 for the second angle.
38 + 14 = 52
The two angles are 52 degrees and 38 degrees.
52 degrees is 14 degrees more than complementary angle.
Answer:
[tex]\huge\boxed{ Angle = 52\ degrees}[/tex]
Step-by-step explanation:
Complementary angles add up to 90 degrees
So, Let the first angle be x then the second angle will be x + 14
Given condition is:
x + x + 14 = 90
2x + 14 = 90
Subtracting 14 to both sides
2x = 90 - 14
2x = 76
Dividing both sides by 2
x = 38
So, the second angle that is 14 degrees more than 38
=> Second Angle = 38 + 14
=> Second Angle = 52 degrees
Which slope is steepest?
A.-8
B.-1/15
C.5
D.0.9
Answer:
A.-8
Step-by-step explanation:
The greater the slope the steeper the line.
In order to determine which line is closer to vertical, we have to consider the absolute values, because the slope can be positive or negative.
Therefore, the steepest is -8.
How can you tell from the graph of Molly’s garden on the previous slide that it represents a proportional relationship?
Answer:
The graph of a proportional relationship has the same unit rate, is a straight line, and starts at the origin.
Step-by-step explanation:
this the answer
The graph of a proportional relationship is a straight line.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have a graph of Molly’s garden.
Since, the graph is not given, i will write the condition for proportional relationship. The graph of a proportional relationship is a straight line whose equation is given by -
y = mx + c
Therefore, the graph of a proportional relationship is a straight line.
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(x²+10x+7)(2x-1) = 2x³+19x²+4x-7 show the steps
Joshua has 11 baskets of apples. In total he has 88 apples. How many are there in 1 basket?
Answer:
8
Step-by-step explanation:
We know Joshua has 11 baskets of apples with a total of 88 apple, it can be written down to something like this:
88 ÷ 11
We know that 88 divided by 11 is 8, therefore, there are 8 apples in each basket.
Don't believe me? Checked work:
11 x 8 = 88
8 apples per basket
PLEASE HELP AND EXPLAIN SO I CAN LEARN. THANKS. Indicate whether each item described contains parallel lines or perpendicular lines. a. The back and side edge of a filing cabinet b. Two walls facing each other in a square room c. The hands of the clock at 3:00 d. Two straight telephone poles on flat ground e. The hands of the clock at 9:00
Answer:
Hey! I think I can help.
Parallel lines are lines that can't meet.Perpendicular lines are lines that can meet.
e.)Since the line at 12 and the line at 9 meets then it is a perpendicular line.
c.)Perpendicular line.
a.)Perpendicular line.
b.)Parallel line.
d.)Depending on how they are faced if the ends of the telephone wire meets the second one then it is perpendicular but if not then it is parallel that's if they are in different directions which they can not meet.Thank you for the question
Help me please!!!!!!
Answer: see both proofs below
Step-by-step explanation:
Use Difference Identity: tan (A - B) = (tan A - tan B)/(1 + tanA · tanB)
Use Unit Circle to evaluate: tan (π/4) = 1
Use Tangent Identity: tanA = (sinA)/(cosA)
Use Half-Angle Identities:
[tex]\cos \dfrac{A}{2}=\sqrt{\dfrac{1+\cos A}{2}}\\\\\\\sin \dfrac{A}{2}=\sqrt{\dfrac{1-\cos A}{2}}[/tex]
Part 1 Proof LHS → Middle
LHS: [tex]\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)[/tex]
Difference Identity: [tex]\dfrac{\tan (\frac{\pi}{4})-\tan(\frac{A}{2})}{1+\tan(\frac{\pi}{4})\cdot \tan(\frac{A}{2})}[/tex]
Unit Circle: [tex]\dfrac{1-\tan(\frac{A}{2})}{1+ \tan(\frac{A}{2})}[/tex]
[tex]\text{Tangent Identity:}\qquad \qquad \dfrac{\frac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}}}{\frac{\cos\frac{A}{2}+\sin\frac{A}{2}}{\cos\frac{A}{2}}}[/tex]
Simplify: [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]
LHS = Middle: [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}=\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}\qquad \checkmark[/tex]
Part 2 Proof Middle → RHS
Middle: [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]
[tex]\text{Half-Angle Identity:}\qquad \qquad \dfrac{\sqrt{\frac{1+\cos A}{2}}-\sqrt{\frac{1-\cos A}{2}}}{\sqrt{\frac{1+\cos A}{2}}+\sqrt{\frac{1-\cos A}{2}}}[/tex]
Simplify: [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}[/tex]
Rationalize Denominator: [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}\bigg(\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}-\sqrt{1-\cos A}}\bigg)[/tex]
[tex]=\dfrac{1+\cos A-2\sqrt{1-\cos^2 A}+1-\cos A}{1+\cos A-(1-\cos A)}[/tex]
Simplify: [tex]\dfrac{2-2\sqrt{1-\cos^2 A}}{2\cos A}[/tex]
[tex]=\dfrac{2-2\sqrt{sin^2 A}}{2\cos A}[/tex]
[tex]= \dfrac{2-2\sin A}{2\cos A}[/tex]
Factor: [tex]\dfrac{2(1-\sin A)}{2(\cos A)}[/tex]
Simplify: [tex]\dfrac{1-\sin A}{\cos A}[/tex]
Expand: [tex]\dfrac{1-\sin A}{\cos A}\bigg(\dfrac{1+\sin A}{1+\sin A}\bigg)[/tex]
[tex]=\dfrac{1-\sin^2 A}{\cos A(1+\sin A)}[/tex]
Simplify: [tex]\dfrac{\cos^2 A}{\cos A(1+\sin A)}[/tex]
[tex]=\dfrac{\cos A}{1+\sin A}[/tex]
Middle = RHS: [tex]\dfrac{\cos A}{1+\sin A}=\dfrac{\cos A}{1+\sin A}\qquad \checkmark[/tex]
pleasee nn tyyy yall i rlly need help
You need to find the GCF (greatest common factor) of 96 and 36. The GCF of 96 and 36 is 12.
12 times what gets you 36?
12 times 3 gets you 36.
12 times what gets you 96?
12 times 8 gets you 96.
So the third answer has 12 as the GCF.
The answer is 12(8+3) = 96+36 = 132
♡ Hope this helped! ♡
❀ 0ranges ❀
Alicia had $-11 in her checking account. She did a few chores and made $44.50. She
decided to pay for her and a friend to go to the movies, and each ticket cost $6.25. How
much money does she have left in her checking account?
Answer:
she would have 21 dollars left
Step-by-step explanation:
44.50-11
33.50-12.50
Answer:
[tex]\Huge \boxed{\$ \ 21}[/tex]
Step-by-step explanation:
She had $-11 initially and gained $44.50.
-11 + 44.5 = 33.5
She has $33.5 in her account.
She buys two tickets for $6.25 each.
33.5 - (2)6.25 = 21
She has $21 left in her account.
How would you explain a number system to someone who had never seen numbers before?
We have that in teach number system to someone who had never seen numbers before you have to give a clear and understand explanation on numbers and number systems to in a language they can understand.
Firstly we have to understand what number are
Numbers
A number or numbers are just words or expressions or drawings or even symbols use to represent(Represent being a key word) a particular quantity or used to calculate.
With the definition above every one must have come across number but in a different way from other
Therefore
its just left for you to open their eyes to what the have already encountered
Firstly you have to give the person a Generally knowledge on NumbersSecondly you have to teach the person the different branches of number system which are Decimals Binary Octal Hexadecimal And the various basesFinally you give a test to ensure the person has understood you.In conclusion
You have to give a clear and understand explanation on numbers and number systems to in a language they can understand
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A number system is a mathematical system for representing numbers, that is, quantities.
Thus, the numbers are writing symbols that allow a mental representation of a certain quantity, as well as the different mathematical operations that arise from said quantities.
Otherwise, that is, if the numbers did not exist, the representation of quantities would be very limited.
It also would only abstain from the existence or nonexistence of a certain thing or situation.
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Choose the rate of change (slope) to match the line.
What is the product of complex conjugates? The product of complex conjugates is a difference of two squares and is always a real number. The product of complex conjugates is the same as the product of opposites. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.
Answer:
Last given option is the correct answer:
"The product of complex conjugates is a sum of two squares and is always a real number."
Step-by-step explanation:
The product of two conjugates can be described and solved like this:
[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]
so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.
Answer:
(a + bi)(a – bi) = a2 – (bi)2 = a2 + b2
The product of a complex number and its complex conjugate is
✔ always
a real number.
1. Marcar con rojo los pares de ángulos que sean complementarios y con verde los que sean suplementarios. A. 25º B. 155º C. 65º D. 30º E. 150º F. 15º G. 28º 2. Averiguar el valor de los ángulos a. ¿Cuál es el complemento de un ángulo a=39º? b. Se sabe la amplitud del ángulo R=143º pero se desconoce la del ángulo m, ¿Cuánto medirá m?
Answer:
A y C → complementarios
A Y B → suplementarios
D Y E → suplementarios
El complemento de un ángulo de 39°, mide 51°
La amplitud de m, como suplemento es de 36°
Si lo tomamos como ángulo conjugado, es de 217°
Step-by-step explanation:
Ángulos completarios → Aquellos que sumados, me dan 90°
Ángulos complementarios → Aquellos que sumados, me dan 180°
Angulos complementarios entonces, son:
A y C (sumados, dan 90° → 25 + 65)
Angulos suplementarios entonces, son:
A y B (sumados, dan 180° → 25 + 155)
D y E (sumados, dan 180° → 30 + 150)
Complemento de un ángulo de 39° → Ya vimos que su suma debe dar 90°, por lo que el complemento mide: 90 - 39 = 51°
Si la amplitud del ángulo R es 143°, la del ángulo m, será 37°. Sería el ángulo suplementario a R.
No podríamos tener un complemento porque estamos en valores a 90°, pero también se podría obtener otro ángulo cuya amplitud sea de 217°, en este caso ambos ángulos suman 360°, se los llama angulos conjugados.
Find the measure of c. A. 10 B. 280 C. 100 D. 140
Answer:
63°
Step-by-step explanation:
a = 27°
b = 180° - (a + 27°)
b = 180° - (27° + 27°)
b = 180° - 54°
b = 126°
By inscribed angle theorem:
c = 1/2 b = 1/2 * 126°
c = 63°
How to get the answer
Answer:
2*x^4*z^3
Step-by-step explanation:
To answer this kind of question, you first start rearranging the terms in the numerator and denominator, so you don't get confused.
3x^3 * 4x^3 * z^4 / 2x * x * 3z
Now you multiply like parts in the numerator and denominator to keep it simple.
(3x^3 * 4x^3) * z^4 / (2x * x) * 3z
3x^3 * 4x^3 = 12x^6
2x * x = 2x^2
12x^6 * z^4 / 2x^2 * 3z
Now divide like terms that are in the numerator and denominator so multiplying later will be easier.
12x^6 / 2x ^ 2 * z^4 / 3z
12x^6 / 2x^2 = 6x^4
z^4/3z = z^3 / 3
Now you multiply both terms,
6x^4 * z^3/3
2*x^4*z^3
Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
Answer:
1/7
Step-by-step explanation:
From the above question, we have the following values:
White socks = 2
Brown socks = 4
Black socks = 2
Total number of socks = 8
We are told in the question that:
You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot.
From above question, we can see that this is a probability with dependent events. This means have a white sock on your left foot and brown sock on your right are events that depend on each other, hence, the probability will occur with replacement.
The probability ( having a white sock on your left foot and brown sock on right) =
2/8 × 4/7
= 8/56
= 1/7
Therefore, the probability of this occuring is 1/7
solve √3+√48/√6.....
Answer:8.26402
Step-by-step explanation:
Mr. Garcia and his 30 students are collecting soup labels to help buy classroom equipment. The total number of labels collected can be found evaluating the expression 30/ + 15. If / = 5, what is the value of the expression?
Answer: C 165
Step-by-step explanation:
30(5)+15= 165
Which is the best estimate of the product of 13 and 49?
Answer:
if you round the 13 to fifteen and the 49 to 50, your best estimate answer would be 750. Hope this is what you were looking for and that it helps!
Step-by-step explanation:
The best estimate of the product of 13 and 49 is 600.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The two given numbers are 13 and 49.
The product of 13 and 49 is
13×49 =637
So, 637 is estimated to 600
Therefore, the best estimate of the product of 13 and 49 is 600.
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Your annual salary is $61,061.83 what is your semimonthly salary
On three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to
achieve an average score of 95%?
Answer:
97%
Step-by-step explanation:
89%+98%+96%+?=95×4
283+?=380
?=380-283
?=97%
The lowest score Olivia can get on her fourth test is 97%.
The average score can be determined by dividing the sum of the four scores by the total number of tests taken.
The first step is to determine the sum of the three scores Olivia already has.
Sum of scores = 89 + 98 + 96 = 283%
The second step is to multiply 95 x 4. 95% x 4 = 380%
The third step is to subtract 283% by 380%. 380% - 283% = 97%
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Find the value of x. A. 51 B. 76.25 C. 129 D. 25.25
Answer:
[tex]\Huge \boxed{\mathrm{C. \ 129 }}[/tex]
Step-by-step explanation:
Apply : Angles of Intersecting Chords Theorem
m∠x is half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
m∠x = 1/2(54+204)
Add numbers in brackets.
m∠x = 1/2(258)
Expand brackets.
m∠x = 129
which is a function? {(8,9),(−2,9),(7,5),(−4,−7)} {(−5,−7),(−5,4),(−2,−8),(3,5)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}
Answer:
All but the second {(8,9),(−2,9),(7,5),(−4,−7)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}Step-by-step explanation:
Function means that for each x we get y, and no no x gives two different y-es
{(−5,−7),(−5,4),(−2,−8),(3,5)} for x = -5 we have two different y-es therefore its not function
Board 1
C
(3x + 16)°
7
(5x - 54)
Board 2
Enter the measure of ZC.
Answer:
59°
Step-by-step explanation:
From the question given, we obtained the following:
C + (3x + 16) = 180 (sum of angle on a straight line)
5x – 54 = 3x + 16 (Altanate angles are equal)
Next, we shall determine the value of x.
This can be obtained as follow:
5x – 54 = 3x + 16
Collect like terms
5x – 3x = 16 + 54
2x = 70
Divide both side by the coefficient of x i.e 2
x = 70/2
x = 35
Finally, we shall determine the value of C as shown below:
C + 3x + 16 = 180
But, x = 35
C + 3(35) + 16 = 180
C + 105 + 16 = 180
C + 121 = 180
Collect like terms
C = 180 – 121
C = 59°
Therefore, the value of C is 59°
-6/11 + (-5/11) =? HELP ASAP ps the dash means that there a fraction
Answer:
-1
Step-by-step explanation:
Since the denominators are the same, then we add the numerators
-6+-5/11
-11/11
-1
Step-by-step explanation:
-6/11 - 5/11 = -11/11
1. The fraction of -5/11 stays negative because -*+ = -. So the fraction stays negative.
2. Then, you can add the two fractions because they are both the same sign and also have the same denomination.
The answer is -1 or -11/11.
Hope this helped,
Kavitha
Without simplifying Select all the expressions that represent a rational number( someone helppppppp)
Answer:
The correct options are;
[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex]
[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]
Step-by-step explanation:
We note that a rational number is one that can be expressed as a ratio of two integers a and b
An irrational number is one that cannot be expressed as a ratio of two integers. Example of an irrational number is √3
Also an irrational number divided by a rational number is an irrational number, therefore, we have, the expressions without irrational numbers, which are;
[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex] = [tex]\dfrac{53}{12}[/tex]
and
[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]
solve 5u– 5(1–u)=u+8
Answer:
u= -3
Step-by-step explanation:Solve for
u by simplifying both sides of the equation, then isolating the variable.
Answer : 5u– 5(1–u)=u+8
5u - 5+ 5u = u+ 8
10u -5 = u+ 8
9u = 13
u = 1.44