The slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the given containing ordered paid A(2,-5) and B(-2,6) is:
Slope = 6+5/-2-2 = 11/-4
Hence, the slope of the given containing ordered paid A(2,-5) and B(-2,6) is -11/4.
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On a coordinate plane, quadrilateral Q R S T has points (0, 2), (negative 4, 0), (0, negative 3), and (4, 0).
The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is DO,0.5(x, y) → (0.5x, 0.5y).
What are the coordinates of Q', if Q(0, 2)?
(, )
By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).
How to apply rigid transformations on a point
Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:
(x, y) → (k · x, k · y), for k > 0
If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:
Q'(x, y) = (0.5 · 0, 0.5 · 2)
Q'(x, y) = (0, 1)
By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).
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Answer: Q' = (0,1)
Step-by-step explanation: just did it on edge
2.
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table:
Range Number of Values Relative Frequency
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25
What is the relative frequency for the range 16 – 20?
0.4
0.33
0.2
.27
The relative frequency for the range 16 - 20 is 0.27.
What is the frequency of a data set?The frequency of a data set refers to the number of times a data or an event is occurring.
From the given information:
Range Number of values
1 - 5 3
6 - 10 1
11 - 15 4
16 - 20 5
21 - 25 2
Total 15
Relative Frequency = Subgroup frequency/ Total frequency
Relative Frequency for the range 16 - 20:
= 4/15
= 0.27
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Answer:
.27
Step-by-step explanation:
You and a friend go to Tacos Galore for lunch. You order two soft tacos and three burritos, and
your total bill is AED 18. Your friend's bill is AED 20.00 for four soft tacos and two burritos.
How much does a soft taco cost?
Answer:
AED 3
Step-by-step explanation:
Let tacos: t
Let burritos: b
1) Set up equations.
2t + 3b = 18
4t + 2b = 20
2) Solve the system of equations using substitution.
2t = 18 - 3b
t = 18/2 - 3b/2
t = 9 - 3b/2
Substitute this into the second equation and simplify.
4(9 - 3b/2) + 2b = 20
36 - 12b/2 + 2b = 20
36 - 6b + 2b = 20
36 - 4b = 20
-4b = 20 - 36
-4b = -16
b = -16/-4
b = 4
3) Substitute the found answer in any one of the two equations.
2t + 3(4) = 18
2t + 12 = 18
2t = 18 - 12
2t = 6
t = 6/2
t = 3
Therefore, a soft taco costs AED 3.
Members of a baseball team raised $1780.50 to go to a tournament. They rented a
bus for $1151.50 and budgeted $37 per player for meals. Determine the number of
players the team can bring to the tournament.
Answer: 17 players
Step-by-step explanation: 1780.50-1151.50=629, 629/37 = 17
The number of players the team can bring to the tournament is 17.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Budget = $1780.50
Fixed cost (bus rent) = $1151.50
Variable cost = $37 per player.
For n number of players.
Total cost = 1151.50 + 37n
Total cost ≤ total budget
1151.50 + 37n ≤ $1780.50
37n ≤ 629
n ≤ 17
Hence "The number of players the team can bring to the tournament is 17".
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Four friends had dinner togethere.
The total cost was $65.60.
The four friends shared the cost eaually between them.
How much did each person pay
Answer:
Your answer is $16.40
What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%
-0.5244 will separates the highest 70% of the scores in a normal distribution from the lowest 30%
Normal Distribution is bell shaped and symmetrical in nature.
We use standard normal to find probabilities of normal distribution.
Fig 1 represents Graph of standard normal
and Fig 2 is % points Table for standard normal distribution.
From % points Table the value separates the highest 70% of the scores in a normal distribution from the lowest 30% is 0.5244 since 30% lies left side from 0 it will be negative
⇒ value separates the highest 70% of the scores in a normal distribution from the lowest 30% is -0.5244
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for what values of m does the equation mx=5 have a single solution? can m have a value for which the equation does not have any solution? what about an infitnite number of solutions? i know that not any solution is m=0 and for a single one i need it like x<-3 3
The equation has no solutions when m = 0, and when m ≠ 0, the equation has only one solution.
For what values of m we have a single solution?
Here we have the equation:
m*x = 5
If we solve for x, we get:
x = 5/m
So, as long as m is different than zero, we will have one solution.
We can't have m = 0 because we can't divide by zero.
Then:
m > 0 or m < 0.
When we have no solutions?We have no solutions when m = 0, the equation becomes:
0*x = 5
0 = 5
This equation has no solution
And we never can have infinite solutions.
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Use your calculator to estimate the value of
log752.
Click on the correct answer.
1.450
1.653
2.031
The value of the given logarithm using calculator is 2.031
Logarithm functionsLogarithm are inverse of exponential functions. Given the following logarithm expression;
log(7)52
This can also be expressed as:
log(7)52 = log52/log7
log(7)52 = 0.5399/0.9804
log(7)52 = 2.031
Hence the value of the given logarithm using calculator is 2.031
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What is the relationship between the domain and range of a relation and its inverse?
Answer:
the x-values of the relation are the y-values of the inverse.
Two points located on JK are A-1,-9) and K(5,3). What is the slope of JK ?
OA -2
OB. -1/2
OC. 1/2
O D. 2
Answer:
D .2
Step-by-step explanation:
3-(-9)
5-(-1)
=3+9
5+1
12
6
= 2
Fitness Your goal is to take at least 10,000 steps per day. According to your pedometer, you have walked 527 4 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal.
The inequality is x + 5274 ≥ 10,000.
The total number of steps I have to take to reach my goal is 4726.
How many more steps do I have to take?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toNumber of steps I have to take + number of steps I have taken ≥Total steps
X + 5274 + x ≥ 10,000
x ≥ 10,000 - 5274
x ≥ 4726
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Question 3(Multiple Choice Worth 4 points)
(01.05 LC)
Solve for x: 3
06
06>x>9
00
00>x>3
The value of x from the given equation is ±√10
Solving linear equationsLinear equations are equation that has a leading degree of 1. Given the equation below:
Given the equation below;
x² = 10
Take the square root of both sides
√x² = ±√10
x = ±√10
Hence the value of x from the given equation is ±√10
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For the following exercises, solve the inequality and express the solution using interval notation.
71. |3x − 2 | < 7
Answer:
In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].
Step-by-step explanation:
The given absolute value function is |3 x-2|<7.
It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x
Step 1 of 3
Given absolute value equation is |3 x-2|<7.
It can be written as -7<3 x-2<7.
To solve for the equality, 3x-2=7 and
[tex]$$3 x-2=-7$$[/tex]
First, solve the equation 3x-2=7, then add 2 on both sides.
[tex]$$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$$[/tex]
Step 2 of 3
Simplify 3x=9 further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$$[/tex]
Step 3 of 3
Similarly, 3x-2=-7
From the above term 3x-2=-7,
Add 2 on each side.
[tex]$$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$$[/tex]
Simplify $3 x=-5$ further, by dividing each side with 3 .
[tex]$$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$$[/tex]
Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.6 reproductions and the population standard deviation is known to be 2.2. If a sample of 707 was used for the study, construct the 90% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
The confidence interval for the true mean number of reproductions per hour is (7.5,7.7)
Given mean of 7.6 , standard deviation of 2.2, n=707 and 90% confidence level.
We have to find the confidence interval for the true mean number of reproductions per hour for the bacteria.
α=0.90
μ=7.6
σ=2.2
m=707
α/2=0.45
We have to calculate z value for the p value of 0.45 which is z=1.64.
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=1.64*2.2/[tex]\sqrt{707}[/tex]
=0.13
Lower level=mean -m
=7.6-0.13
=7.47
after rounding upto 1 decimal
=7.5
Upper level= mean +m
=7.6+0.13
=7.73
after rounding upto 1 decimal
=7.7
Hence the confidence interval is (7.5,7.7) for the true mean number of reproductions per hour.
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I really need help with this please.
Answer:
y = - 6x + 7.5
Step-by-step explanation:
the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.
calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )
[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6
the midpoint of BC is the average of the x and y coordinates
midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6 , then
y = - 6x + c ← is the partial equation
to find c substitute (1, 1.5 ) into the partial equation
1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5
y = - 6x + 7.5 ← equation of perpendicular bisector of BC
10.one hundred and sixty-seven it students are transported by 3 buses to a workshop. there are 4 more students in the second bus than in the first bus and in the third bus there are 9 more students than in the second one. how many students are in each bus?
inverse of y = 2x squared
The inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
The function given is
y = 2x²
To find the Inverse of a function ,
The x and y are interchanged and the function is again written in terms of x
Here
x = 2y²
y² = x/2
y = [tex]\rm \sqrt {x/2}[/tex]
Therefore the inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].
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AD= in
What is AD?
Help me please, thanks:)
Step-by-step explanation:
ATTACHED IS THE SOLUTION!A 2-column table with 9 rows. The first column is labeled x with entries negative 8, negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries negative 16, negative 8, 0, 8, 16, 32, 64, 128.
Which could be the entire interval over which the function, f(x), is negative?
(–8, –2)
(–8, 0)
(–∞, –6)
(–∞, –4
Answer: (–∞, –6)
Step-by-step explanation:
From the given information, the function is never non-negative over (-8,-6), which is the only subset of the interval that is given.
Today only, a table is being sold for $100.80. This is 24% of its regular price. What was the price yesterday?
Answer:
$420
Step-by-step explanation:
100.80/x = 24/100
with x being the regular price
x = (100.8*100)/24
x = 420
solve for: 3x-91>-87 AND 17x-16>18
a) x>2
b) x>4/3
c) 4/3d) there are no solutions
The correct answers are option an x>2 for inequality 17x-16>18 and option b x>(4/3) for an inequality 3x-91>-87.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Given inequalities are:-
3x-91>-87 AND 17x-16>18The inequalities will be solved as:-
i ) 3x - 91 > -87
3x > -87 + 91
3x > 4
x > ( 4 / 3 )
ii) 17x-16>18
17x > 18 + 16
17x > 34
x > 34 /17
x > 2
Therefore the correct answers are option an x>2 for inequality 17x-16>18 and option b x>(4/3) for an inequality 3x-91>-87.
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What is the coefficient of the last term in the binomial expansion of (x 1)9? 0 1 9 10
The coefficient of the last term in the binomial expansion is 1.
Given term is (x + 1)⁹.
The algebraic expansion of a binomial's powers is expressed by the binomial theorem or binomial expansion. The process of expanding and writing terms that are equal to the natural number exponent of the sum or difference of two terms is known as binomial expansion.
The binomial expansion formula for (a + b)ⁿ= ⁿC₀(aⁿb⁰)+ⁿC₁(aⁿ⁻¹b¹)+ⁿC₂(aⁿ⁻²b²)+ⁿC₃(aⁿ⁻³b³)+...............+ⁿCₙ(a⁰bⁿ)
Here, a = x, b = 1 and n = 9.
Substituting the values in the formula,
⁹C₀(x⁹{1}₀)+⁹C₁(x⁹⁻¹{1}¹)+⁹C₂(x⁹⁻²{1}²)+⁹C₃(x⁹⁻³{1}³)+......+⁹C₉(x⁰{1}⁹)
The last term is ⁹C₉(x⁰{1}⁹)
The coefficient of the last term = ⁹C₉ = 1.
Hence, the coefficient of the last term in the binomial expansion of (x+1)⁹ is 1.
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la mama de fabiana tiene un vivero. En su ultimo pedido compro 5 fresias, una con flores rojas, una con flores blancas, una con flores celestes y otra con flores violetas, 3 rosales, una con flores rojas, otro con flores rosas y otro con flores amarillas y 2 calas, una con flores blancas y otra con flores azules.
Me ayudan porfa.
Les doy puntos y coronita si me ayudan.
Porfa.
The computation shows that the number of flowers will be 10.
How to calculate the value?The information illustrates the flowers that were brought for the nursery.
Based on the information given, the total number of flowers bought for the nursery will be:
= 5 freesias + 3 rosebrushes + 2 calls lilies
= 10
In conclusion, the total number of flowers is 10.
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You have 73 trading cards. Your cousin says that
you have 7 less than half the cards he has. You
say you have 33 more than one-fourth the cards
he has. Can you both be right?
Using proportions, it is found that both can be right, as the amounts found from each operation are the same.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering you have 73 cards, and your cousin says that you have 7 less than half the cards he has, his amount is found as follows:
0.5x - 7 = 73
0.5x = 80
x = 160.
Then, one-fourth of his amount is:
(1/4) x 160 = 40.
33 more than this is:
33 + 40 = 73.
Both operations have results (73,160), hence the both can be right.
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INTEGERS A frog starts at 0 on a number line. It jumps 100 units to the right then jumps 200 units to the left. It then jumps 199 units to the right followed by 198 units to the left, and then 197 units to the right followed by 196 units to the left. The frog continues to move in alternate directions. Each movement is 1 unit less than the previous movement.
Where on the number line is the frog after 10 moves?
On the number line after 10 moves frog is at the integer -96.
Given that, a frog starts at 0 on a number line.
It jumps 100 units to the right then jumps 200 units to the left=+100-200=-100 (2 moves).
It then jumps 199 units to the right followed by 198 units to the left =-100+199-198=-99 (2 moves).
It then jumps 197 units to the right followed by 196 units to the left =-99+197-196=-98 (2 moves).
It then jumps 195 units to the right followed by 194 units to the left =-98+195-194=-97 (2 moves).
It then jumps 193 units to the right followed by 192 units to the left =-97+193-192=-96 (2 moves).
Hence, on the number line after 10 moves frog is at the integer -96.
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What is the value of x? (There should be an image)
Answer:
22
Step-by-step explanation:
Question 5 of 10
Which information would most likely cause a company's stock price to go up?
A. Consumers reduce spending because of a recession.
B. The company releases an innovative car with unique features.
C. The company's charismatic CEO must resign after revelations of
fraud.
D. Congress threatens to break up a large tech company.
SUBMIT
Answer:
B
Step-by-step explanation:
How many solutions does this linear system have?
y = 2/3x+ 2
6x -4y = -10
O one solution: (-0.6, -1.6)
O one solution: (-0.6, 1.6)
no solution
infinite number of solutions?
Which function has a vertex at (2, 6)?
Answer:
A quadratic function
Step-by-step explanation:
Answer:
f(x) = 2|x – 2| + 6
Step-by-step explanation:
On edg 2022
suppose f(x)=x+3 find the graph of f(2x)
Answer:
2x + 3Step-by-step explanation:
f(2x) means that we have to substitute x with 2x
So, the answer is
2x + 3