Answers
I'm basing this off the points (0,-4) and (3,-3)
Related Questions
Alyosha and Ivan are standing between two buildings they know to be equal height. The buildings are 500 feet apart. Looking up at the westernmost building, they form a 30 degree angle. Looking to the northeastern building, they form a 45 degree angle.
A) Ivan guesses they are halfway between the buildings. Why is this a bad guess?
B) How far away from each building are they?
Answers
h = height of each building
x = distance from the left building
y = distance from the right building
Because the distance between the buildings is 500 feet, therefore
x + y = 500 (1)
By definition,
tan 45° = h/y = 1
y = h (2)
Also,
tan 30° = h/x = 1/√3
x = h√3 (3)
Part (a)
If Alyosha and Ivan were halfway between the building, then x = y.
Because x ≠ y, they are not halfway between the buildings.
Part (b)
From (1), (2) and (3), obtain
h + h√3 = 500
h(1+√3) = 500
2.732h = 500
h = 183.0 ft
Therefore
x = 183.0 ft
y = 500 - x = 317.0 ft
Answer:
Alyosha and Ivan are 183 feet from the left building, and 317 feet from the right building.
A quadratic equation is shown below:
9x2 − 16x + 60 = 0
Describe the solution(s) to the equation by just determining the radicand. Show your work.
: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
Answers
hello :
help :
the discriminat of each quadratic equation :
ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x =
(-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
A certain bag of potting soil is 1/4 peat moss,and the rest is dirt. What part is dirt?
Answers
4/4-1/4
3/4
So 3/4 bag is dirt.
The part of the bag that consist of dirt is:
3/4
Step-by-step explanation:It is given that the amount of peat moss that is present in a bag of potting soil is:
1/4
Hence, the remaining space that is left in the bag consist of dirt.
Remaining space is calculated as :
[tex]1-\dfrac{1}{4}\\\\\\=\dfrac{3}{4}[/tex]
( Since we subtract 1/4 from a whole of a bag)
Hence, the part that is dirt in the bag of potting soil is:
3/4
Diana can earn money for the tickets she sells. Which of the following statements describes the variables in this situation correctly?
Answers
The variables in this situation are the price of the tickets and the quantity of tickets sold. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand. Diana should lower the price if demand is elastic, raise the price if demand is inelastic, and can maintain the same revenue if demand has unitary elasticity.
Explanation:The variables in this situation are the price of the tickets and the quantity of tickets sold. These two variables directly affect the total revenue generated by Diana from ticket sales. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand.
If demand for tickets is elastic, Diana should lower the price to increase total revenue. A decrease in price will result in a larger percentage increase in the quantity sold, leading to a higher total revenue. On the other hand, if demand is inelastic, Diana should raise the price to increase revenue. A certain percentage increase in price will result in a smaller percentage decrease in quantity sold, ultimately raising total revenue.
If demand has unitary elasticity, an equal percentage change in quantity will offset a moderate percentage change in price. In this case, Diana can earn the same revenue regardless of a moderate increase or decrease in ticket price.
How many cubes with 5 inches side Will completely fill a cube that is 10 inches on each side
Answers
how many times does 125 go into 1000? that many will fill it up.
Determine whether the cost for ordering multiple items that will be delivered is sometimes, always, or never proportional. Explain your reasoning.
Answers
Anthony was tracking the increasing number of animals in the zoo. at 9
a.m., there were 56 animals. at 11
a.m., there were 60 animals. if anthony made the function f(x) = 2x − 38, what would the 2 represent? the number of animals at midnight the rate at which the number of animals was increasing the length of time he recorded for the total change in the number of animals
Answers
It’s a little surprising that this question didn’t come up earlier. Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2). A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.
Answer:
2 would represent the rate at which the animals were increasing
Step-by-step explanation: This all comes back to the slope intercept form:
y = mx + b
2x is the slope, and the slope is the rate of which a point will increase or decrease.
HELP ROUND 604703.472883 TO THE NEAREST HUNDRED
Answers
Answer:
The required number is 604703
Step-by-step explanation:
Consider the provided number 604703.472883
The rule for rounding a number is:
If the number on the right side of rounding digit is 0, 1, 2, 3, 4 then no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
If the number on the right side of rounding digit is 5, 6, 7, 8, 9 then rounding digit rounds up by one number and change the rest of the digit right to rounding digit with 0.
The number on the hundred place is 7 and the number on right side is 0.
Thus, no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
Hence, the required number is 604703
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
Answers
For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range. The vertex is (3, –1), the domain is all real numbers, and the range is y ≥ –1. The vertex is (3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≤ –1. The vertex is (–3, –1), the domain is all real numbers, and the range is y ≥ –1.
Answers
we have
[tex]f(x)=-2(x+3)^{2}-1[/tex]
we know that
the equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
[tex](h,k)[/tex] is the vertex
If [tex]a > 0[/tex] ------> then the parabola open upward (vertex is a minimum)
If [tex]a < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
In this problem
the vertex is the point [tex](-3,-1)[/tex]
[tex]a=-2[/tex]
so
[tex]-2 < 0[/tex] ------> then the parabola open downward (vertex is a maximum)
The domain is the interval-------> (-∞,∞)
that means------> all real numbers
The range is the interval--------> (-∞, -1]
[tex]y\leq-1[/tex]
that means
all real numbers less than or equal to [tex]-1[/tex]
therefore
the answer is
a) the vertex is the point [tex](-3,-1)[/tex]
b) the domain is all real numbers
c) the range is [tex]y\leq-1[/tex]
see the attached figure to better understand the problem
What do the parallel lines shown on segment BD and segment DC represent?
Answers
it means both sections are equal.
so BD = 18 and DC = 18
How many ways can we put 7 adults and 3 kids in line (where order matters) so that no two kids are next to each other?
Answers
7P3
=210
There are more than 210 ways we can do this.
We generally report a measurement by recording all of the certain digits plus ______ uncertain digit(s).
Answers
We generally report a measurement by recording all of the certain digits plus one uncertain digit.
What are significant figures?In positional nomenclature, a number's real numbers are its dependable and essential digits for indicating how much of something there is.
If a measurement's result is expressed by a number with more digits than the measurement resolution permits, only those digits up to the measuring resolution's maximum are trustworthy, and only those digits could be significant figures.
Typically, we record all the confirmed digits of measurement together with one questionable digit.
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Evaluate f(x)= -x^2+1 for x=-3
A.4
B.-4
C.-8
D.-9
Answers
then
f(-3) = -(-3)^2+1 = -9 + 1 = -8
answer
C.-8
-(-3)^2+1
First apply the exponent.
-3^2=9
-(9)+1
Then add.
-9+1=-8
Final answer:C
Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?
Answers
a(n)=ar^(n-1) we are told that the fifth term is 1/4 and the common ratio is 1/2 so:
1/4=a(1/2)^(5-1)
1/4=a(1/2)^4
1/4=a/16 multiply both sides by 16
16/4=a
4=a, so this sequence is:
a(n)=4(1/2)^(n-1)
Use Gauss-Jordan elimination to solve the following linear system.
x – 2z = 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
A. (–5,–3,0)
B. (3,2,–3)
C. (5,3,–5)
D. (3,6,–4)
Answers
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
multiply (1st) equation by 5 and (2nd) equation by 2
-10y + 35z = - 125
10y - 14z = 62
-----------------------add
21z = - 63
z = -3
substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
answer
B. (3, 2, –3)
By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.
What is Gauss-Jordan's elimination method?
In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.
x – 2z = 9 so x = 2z + 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
Multiply (1st) equation by 5 and (2nd) equation by 2.
-10y + 35z = - 125
10y - 14z = 62
21z = - 63
z = -3
Substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
Substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.
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A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. if x represents the length, then the length can be found by solving the equation: x(x−3)=54x(x-3)=54 what is the length, x, of the garden? the length is _____ feet.
Answers
Area = Length x Width
where length = x ft
width = x - 3 ft
area = 54 ft^2
54 ft^2 = x ft (x -3) ft
54 ft^2 = x^2 - 3x ft^2
Solving for the value of x, we will have two values which are
x = -6 ft ( NOTE: this value can't be the answer since we cannot have a negative value for the length)
x = 9 ft = length
Answer
Length of rectangular garden = x feet
As, Width is 3 feet less than Length.
Width = (x-3 ) feet
Area of Rectangle = Length × Breadth
Area = 54 square feet
→54 = x × (x-3)
→ x²-3 x-54=0
Splitting the Middle term
→x² - 9 x + 6 x- 54=0
→x × (x-9)+6 × (x-9)=0
→ (x+6)(x-9)=0
→x+6=0 ∧ x-9=0
x≠-6, as length can't be negative.
So, x=9
Length of Rectangular garden = 9 feet
4x-5=4x+10 solve for x
Answers
The equation 4x - 5 = 4x + 10 has no solution because subtracting 4x from both sides yields -5 = 10, which is a contradiction.
Explanation:The equation 4x - 5 = 4x + 10 cannot be solved for x in the usual way because attempting to isolate x on one side will result in a contradiction. If we subtract 4x from both sides of the equation, we get -5 = 10, which is not true for any value of x. Therefore, this equation has no solution.
How do you complete the square using fractions
Answers
we will complete the squaer for ax²+bx+c=0 regardless of the values of a,b, or c
we will factor it into a(x-h)²=r
so
first group x terms
(ax²+bx)+c=0
factor out a
[tex]a(x^2+\frac{b}{a}x)+c=0[/tex]
take 1/2 of the linear coefinet and squaer it
[tex]\frac{1}{2} \space\ of \space\ \frac{b}{a}=\frac{b}{2a}[/tex] square it to get [tex]\frac{b^2}{4a^2}[/tex]
add positive and negative of that inside parntheasees
[tex]a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2})+c=0[/tex]
factor perfect square
[tex]a((x+\frac{b}{2a})^2-\frac{b^2}{4a^2})+c=0[/tex]
expand
[tex]a(x+\frac{b}{2a})^2-\frac{b^2}{4a}+c=0[/tex]
and that's how you complete the square, just move the constants over to the left when you're done then divide both sides by a then square root both sides, remembering to take the positive and negative roots
Completing the square with fractions involves transforming the quadratic equation into a perfect square trinomial by adding the square of half the coefficient of x to both sides. This enables solving the equation more easily by then taking the square root of both sides and isolating x.
Completing the square using fractions involves a few steps tailored to work with fractional coefficients. To make it understandable, let's explain the process step by step:
Start with the quadratic equation and ensure it is in the form ax2 + bx + c = 0.Divide all terms by 'a' (the coefficient of x2) if 'a' is not equal to 1, to make the coefficient of x2 equal to 1.Rearrange the equation so that the constant 'c' is on the other side of the equation.Take half of the coefficient of x, which is now 'b/a', and square it. This value is added both sides of the equation to form a perfect square on one side.Rewrite the left side of the equation as a squared binomial.Finally, solve for x by taking the square root of both sides and then add or subtract the constant term.For example, let's complete the square for the equation x2 + (3/2)x = 4. We take half of the coefficient of x, (3/2)/2 or 3/4, and square it to get 9/16. Adding 9/16 to both sides gives us (x + 3/4)2 = 4 + 9/16. Simplify the right side to get a single fraction, and then proceed to solve for x. Additionally, in some scenarios, we might need to multiply both the numerator and denominator by a skillfully chosen factor, such as 1/2, to facilitate simplifying or cancelling out terms.
8/3 , 2.28, 10/12 , 0.199 what number in the list above has the greatest value?
Answers
2.28
10/12 = 0.833
0.199
greatest value is : 8/3
Answer:
[tex]\frac{8}{3}[/tex] is the greatest value.
Step-by-step explanation:
The given numbers are [tex]\frac{8}{3}[/tex], 2.28, [tex]\frac{10}{12}[/tex], 0.199
In this question we have to find out greatest value.
So, first we convert all the values in decimals.
To convert [tex]\frac{8}{3}[/tex] in decimal form, we divide 8 by 3. The answer would be 2.67
2.28
[tex]\frac{10}{12}[/tex] = 0.83
0.199
Now we arrange these numbers in the increasing order.
0.199 < 0.83 < 2.28 < 2.67
So the greatest number is 2.67 that is [tex]\frac{8}{3}[/tex].
I I'm not good with math
Answers
a) total cost = 499 + 49.99x
b) x = 5 games
total cost = 499 + 49.99(5) = 499 + 249.95 = 748.95
Evaluate the function rule for the given value. Y=6*4^x for x=-3
Answers
you change x in the equation for -3
y= 6 x 4^ -3
if you do it in the calculator, remember to put parenthesis in between -3
y = 6 x 1/64
y = 3/32 or 0.09375
Answer:
[tex]y = \frac{3}{32}[/tex]
Step-by-step explanation:
Using the exponent rule:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Given the function:
[tex]y = 6 \cdot (4)^x[/tex] ......[1]
To evaluate the function rule for x = -3.
Substitute x = -3 in [1] we have;
[tex]y = 6 \cdot (4)^{-3}[/tex]
⇒[tex]y = 6 \cdot \frac{1}{4^3} = 6 \cdot \frac{1}{64}=\frac{3}{32}[/tex]
Therefore, the function rule for the given value when x = -3 is:
[tex]y = \frac{3}{32}[/tex]
Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, vertex B' has coordinates (5, ?).
Answers
Let OB be the radius of circle with center O.
Let B' be the image of B after the described rotation
OB and OB' are sides of the equilateral triangle OBB'.
The x coordinate of B' is the midpoint of OB, that is 5.
In the right triangle B', point (5, 0) and B:
Distance point (5, 0) to B is 5
|B'B|=|OB|=10
so by the pythagorean theorem:
[tex]a= \sqrt{ 10^{2} - 5^{2} } = \sqrt{ 2^{2} *5^{2} - 5^{2} }= \sqrt{5^{2}(4-1)}=5 \sqrt{3} [/tex] units
Answer: [tex]5 \sqrt{3}[/tex]
How to determine if a series has a sum?
Answers
It can be written mathematically, such that there exists a term k for which the sum from k to infinity is bounded, but you may not need all the jargon.
Again, make sure there was not an assumption about a specific type of series, like geometric, which is the one considered in the other answer
A line with a slope of 4 passes through (6, 11). Which choice is an equation of this line?
Answers
Use the equation y = mx + c
11 = 4(6) + c
11 = 24 + c
c = (11 - 24) = -13
Therefore the equation is y = 4x - 13
Hope it helped!
Answer:PLEASE MARK AS BRAINIEST
y – 11 = 4(x – 6)
A soccer team has won 1/2 of the games they played. they won 12 games. how many games did they play? Show your working/calculations
Answers
they won 1/2 of their games and won 12 games
1/2 = 50% , multiply by 2 to make 100%
so 12 x 2 = 24 games were played
To calculate the number of games played by the soccer team, multiply the number of games they won (12) by 2, because winning 12 games represents winning [tex]\frac{1}{2}[/tex] of all games played. The soccer team thus played a total of 24 games.
To find how many games the soccer team played in total, we can set up a proportion using the information that they won [tex]\frac{1}{2}[/tex] of their games. This means for every game they won, they played two (since [tex]\frac{1}{2}[/tex] represents one out of two games). If the team won 12 games, and that represents [tex]\frac{1}{2}[/tex] of the total games, we can use a simple equation to solve for the total number of games (T).
The proportion is as follows: [tex]\frac{1}{2}[/tex] = [tex]\frac{12}{T}[/tex], where 12 is the number of games won, and T is the total number of games played.
To solve for T, we multiply both sides of the equation by T to get rid of the fraction: [tex]\frac{T}{2}[/tex] = 12. To find T, we then multiply both sides of the equation by 2 to isolate T on one side of the equation: T = 12 * 2.
Therefore, the team played a total of T = 24 games.
Step by step on how to solve that equation
Answers
Add 5 to both sides
(1/4)x=13
Multiply both sides by 4
x=52
Final answer: x=52
x/4 -5 = 8
Common denominator 4
[(x) - (5)(4)]/4 = (8).(4)/4 → (x-20)/4 = (8).(4)/4
multiply both sides by 4:
x -20= 32 →→ x = 52
A data set has the following characteristics: Mean: 4.9 Median: 6 Mode: 6 Variance: 4 The z-score is the number of
Answers
Answer:
Standard deviations and mean
Step-by-step explanation:
Answer:
I.
standard deviations
mean
II.
-1.95
0.05
0.8
Step-by-step explanation:
I.
The z-score is the number of standard deviations a data value is away from the mean.
II.
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
A Sporting good store charges $30 for 12 cans of tennis balls. The tennis coach orders 100 cans of tennis balls for the tennis team. How much were the coach pay for the tennis balls?
Answers
= 30/12 x 100
= $250
Kris wanted to understand whether studentstudents at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
In favor
Opposed
Undecided
Grade 9
6
4
8
Grade 10
10
11
9
Grade 11
12
15
11
Grade 12
15
6
14
If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?
Answers
Answer:
The probability that the student is opposed to extending the school day is 0.3666 or 36.67% approx.
Step-by-step explanation:
Arranging the table properly and adding a column of total students.
In favor Opposed Undecided Total students
Grade 9 6 4 8 18
Grade 10 10 11 9 30
Grade 11 12 15 11 38
Grade 12 15 6 14 35
If the principal randomly selects a student in grade 10 from this survey, this means we will only consider grade 10 students.
The probability that the student is opposed to extending the school day is = [tex]\frac{number of opposed students}{total number of students}[/tex]
There are 11 students who are opposed and total students in grade 10 are 30.
So, probability is : [tex]\frac{11}{30}= 0.3666[/tex] or 36.67% approx.