Answer:
Its gotta be (6, 5)
Step-by-step explanation:
If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.
The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.
The sequence goes like this
(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on
Two cities are 145 miles apart. A truck travels this distance in 2.5 hours. A car is 1.5 times as fast as the truck. How long does it take the car and the truck to meet if they leave at the same time and travel toward each other
The time it will take the car and truck to meet is 5hours
What is velocity?Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per seconds but it can also be measured in other units like kilometers per hour and miles per hour.
Velocity = displacement/time
the velocity of the truck is 145/2.5 = 58miles per hour
the car is 1.5 times faster than the truck
this means the velocity of the car is 58× 1.5= 87miles per hour
displacement = velocity×time
total displacement = 145miles
displacement of car = 87t
displacement of truck = 58t
using addition of vectors
145=87t-58t
145= 29t
t = 145/29
t= 5hours
therefore at 5hours the car and the truck will meet
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Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each. Let x represent the number of apples and y represent the number of mangos she can buy.
Problem part 1: Mia has $20 to spend. Which inequality can be used to represent this situation?
Problem part 2: If Mia decided to buy 3 mangos, determine the maximum number of apples that she could buy.
The inequality that can be used to represent this situation is 2x + 1.50y ≤ 20.
The maximum number of apples she can buy is 7 apples.
How to represent inequality?Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each.
where
x = number of applesy = number of mangoesTherefore, let's represent the inequality when Mia has to spend 20 dollars.
2x + 1.50y ≤ 20
If Mia decide to buy 3 mangoes , the maximum number of apples she can buy can be calculated as follows:
2x + 1.50y ≤ 20
2x + 1.50(3) ≤ 20
2x + 4.5 ≤ 20
2x ≤ 20 - 4.5
2x ≤ 15.5
x ≤ 15.5 / 2
x ≤ 7.75
Therefore, the maximum she can buy is 7 apples.
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Please help meee asap please !!!????
Please help, thank you!
Which is an expression for the derivative P(x) = f(x) / —f(x)
the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
given expression p(x)= f(x)/1-f(x)
The derivative of the given expression will be
p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²
Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
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The price of a coat is reduced by 17% in a sale.
The sale price is £78.85.
What was the original price of the coat?
Give your answer in pounds (£).
The required original price of the coat is given as £95.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95
Hence, the cost of the coat before the sale is £95.
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What is the product of the two largest one-digit primes and the largest two-digit prime?
Answer:
see below
Step-by-step explanation:
A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.
The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.
The two largest two digit prime numbers are: 89 and 97.
89×97=8633
Please answer I’m desperate
Answer: x = 3 and y = 4
Step-by-step explanation:
Step: Solve x + y= 7 for x:
x + y = 7
x + y + −y= 7+−y
x = −y + 7
Step: Substitute −y + 7forxinx+2y=11:
x + 2y = 11
−y + 7 + 2y = 11
y + 7 = 11
y + 7 + −7 = 11 + −7
y=4
Step: Substitute 4 for y in x = −y + 7:
x = −y + 7
x = −4 + 7
x = 3
Answer:
x = 3 and y = 4
Hope I did it right
Express cos E as a fraction in simplest terms.
Answer: cos E=
E
10
24
C
0
The trigonometric ratio, cos E of the right triangle is 5 / 13.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
A right triangle is a triangle that has one of its angles as 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;
opposite sideadjacent sidehypotenuse sideTherefore,
cos E = adjacent / hypotenuse
Hence,
let's find the hypotenuse side using Pythagoras theorem,
24² + 10² = c²
c = √576 + 100
c = √676
c = 26
cos E = 10 / 26
Therefore,
cos E = 5 / 13
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It takes 47 pounds of seed to completely plant a 5 -acre field. How many acres can be planted per pound of seed? (b)
Make
p the subject of the formula q - 2p = p + 4
Answer:
p = q - 2p - 4
Step-by-step explanation:
q - 2p = p + 4 ( isolate p on the right by subtracting 4 from both sides )
q - 2p - 4 = p
the population of a city was 250,000 in 1980, and it was 310,000 in 2000. what was the average rate of growth over this period?
Average rate of growth over this period is 0.4%.
Average rate of growth over a period is given by:
A=P[tex]e^{rT}[/tex] where,
A- Population at time T
P- Initial population
r-average rate of growth
T-Time period
Now, P=250,000, A=310,000 and T=21 (2000-1980+1)
therefore, putting values in the equation, we get:
310,000=250,000[tex]e^{21r}[/tex]
⇒ [tex]e^{21r}[/tex] = 1.24
⇒ 21r = log(1.24)
⇒ r = 0.0044 or 0.4%.
so, the average rate of growth over this time period is 0.4%.
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X² + 3x + y = 0
2x+y=5
Solve for x and y by substitution
The square root of a negative number is not a real number, this system of equations has no solution.
What is the system of equations?
A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
To solve for x and y, we can start by solving one of the equations for one of the variables. Let's solve the second equation for y:
2x + y = 5
y = 5 - 2x
Now we can substitute this expression for y in the first equation to get an equation in terms of x:
x² + 3x + (5 - 2x) = 0
x² + 3x + 5 - 2x = 0
x² - x + 5 = 0
We can then solve this equation for x using the quadratic formula:
x = (-3 ± √(9 - 20))/2
x = (-3 ± √(-11))/2
Hence, the square root of a negative number is not a real number, this system of equations has no solution.
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Find the inverse function in slope-intercept form (mx+b):
f(x) = -x + 6
switch the variables
x = -y + 6
x - 6 = -y
-x + 6 = y
Which of the following equations has a solution of −7?(1 point)
4x−23=5
5x+11=−24
−x+3=−4
−3x−8=−29
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 5 ≤ x ≤9.
7
8
9
6
x
4
5
f(x)
4
8
16
32
64
medically explained PAINL X
128
Deltal/ath
The average rate of change, in simplest form, is -2/5.
What is average rate ?
Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.
The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]
Using the coordinate points from the table (0,41) and (15,35)
Substitute the coordinate into the expression:
[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]
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Geometry
It’s a a kite. Looking for x and y
We have to find the values of x and y. We know that one pair of opposite angles of a kite are equal. We know that the sum of all the angles of a quadrilateral is equal to 360 degrees. Therefore, the values of x and y are 80° and 110°.
A kite is a quadrilateral with two pairs of adjacent sides, congruent. A kite also has perpendicular diagonals, where one bisects the other. You can use either of these things to determine if a quadrilateral is a kite.
What is a kite in geometry terms?
The most general definition that is typically used: A kite is a quadrilateral in which one of its diagonals is its axis of symmetry. This definition is equivalent to the following one: A kite is quadrilateral that has two pairs of equal adjacent sides.
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Two of the coordinates representing the corners of Maya's rectangular driveway are (-1, 1) and (1 1\2, -8 1\2
9. Plot the other two coordinates of Maya's rectangular driveway. What are the ordered pairs that you plotted?
Answer:
the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Step-by-step explanation:
To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).
Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.
We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.
We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:
y = -3/17 * x + (-3 3/4)
x = (y - (-3 3/4))/(-3/17)
Substituting the coordinates of the corner we found earlier, we get:
x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3
So, the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Find the vertex of the graph of 7(x) = 10.25x - 0.75|.
The vertex of the function f(x) = 10.25 |x - 0.75| will be at (0.75, 0).
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The absolute function is given as,
f(x) = 10.25 |x - 0.75|
Compare the function f(x) with standard equation, then we have
h = 0.75
k = 0
The vertex of the capability f(x) = 10.25 |x - 0.75| will be at (0.75, 0).
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When solving an equation, Henry gets to the last line of his work and is left with “3 = 3”. What does this mean? * 4 points A. The solution is 3. B. There is only one solution. C. There is no solution. D. There are infinite solutions.
This mean there are infinite solutions.
What does this mean?Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.
Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.
Any value for the Variable would make the equation true, according to infinite solutions.
We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,
such as
3=3 or 3x=3x, then. Finite solutions exist.
This mean there are infinite solutions.
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What is the solution of the equation x2 - 12x = 8?
The solution of the equation is x = 6±2√11.
What is a quadratic equation?
The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
Here, we have
Given: x² - 12x = 8
Now, we factorize the given equation and find the solution.
x² - 12x = 8
x² - 12x - 8 = 0
We apply here the quadratic formula.
= (-b ±√b²-4ac)/2
= (12 ±√12²-4×1×(-8))/2
= (12±√144+32)/2
= (12±√176)/2
= (12±4√11)/2
= 6±2√11
Hence, the solution of the equation x² - 12x = 8 is 6±2√11.
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Translate: "five less than the product of a number and 6 is at least 8"
Answer:
yx6-5= greater than or equal to 8
Step-by-step explanation:
math brain
2 Fractions equivalent to 2/6
The fractions 1/12 and 1/4 are equivalent to 2/6.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Two fractions are equivalent to 2/6.
There can be many fractions which are equal to 2/6.
Let one fraction is 1/12,
And other fraction is x,
So, according to given condition,
x + 1/12 = 2/6
x = 2/6 - 1/12
x = 3/12
x = 1/4
The required fractions are 1/12 and 1/4.
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A sleep specialist wants to know if meditating before bedtime can help people fall asleep. In a study, he asked the subjects to meditate for various lengths of time just before going to bed.
The specialist tracked the subjects' meditation times, x, and how long it took them to fall asleep, y. Both times were recorded in minutes.
Answer:
whats the question?
Step-by-step explanation:
Angela is following this recipe to make biscuits.
Angela uses 0.9 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 10 biscuits
150 g margarine
180 g sugar
225 ml syrup
225 g oats
40 g sultanas
The amount of margarine needed in Kg for making biscuits is 0.6kg
What is proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
How to find the amount of margarine needed in KgThe amount of margarine needed in Kg is calculated using proportions
If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require
0.225 l = 0.15 kg
0.9 l = ?
cross multiplying
0.225 * ? = 0.9 * 0.15
? = 0.135 / 0.225
? = 0.6
Angela will require 0.6 kg of margarine
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52% of 128 is what?
suppose that, of people who undergo routine screening, for every two people who have colon cancer, there are 100 who do not. (that is, 2/102 people have it.) of those who undergo screening and do have colon cancer, all of them will have a positive test. of the people who undergo screening but don't have colon cancer, only 2 percent have a positive test. a random person undergoes routine screening and has a positive test. what is the probability (not odds) that this person has colon cancer? choose the range in which the answer lies.
The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].
Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.
Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)
In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.
We are given that:
p(B|A) = 1 (all people who have colon cancer will have a positive test result)
p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).
We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).
Substituting these values into Bayes' Theorem, we get:
p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))
Simplifying, we get:
p(A|B) = 0.98
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A cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0°F. The temperature in the chamber is dropping 2.5°F every second. Identify an inequality that represents the numbers of seconds $s$ that can pass for the temperature to drop below -20 °F
Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.
Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.
The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.
We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.
Dividing both sides by 2.5, we get the final inequality: $s$ > 7.
Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.
Can anyone solve this proof?
The proof for the Base Angles Theorem is explained below:
What is meant by Base Angles Theorem?A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."
Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.
Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]
Prove: ∠M≅∠N
According to the figure,
Given,
[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]
By the definition of mid-point,
O is the mid-point of [tex]\bar{MN}[/tex]
Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]
Now, Again by the definition of mid-point
[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]
Now, by using reflexive property,
[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]
By SSS rule,
ΔLMO≅ΔLNO
By CPCTC rule,
∠M≅∠N
Hence proved.
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Which diagram shows the rotation Rc, -90 (ABCD) = A'B'C'D'?
The diagram that shows the rotation of rectangle ABCD by -90 degrees is; Option A
What is the translation transformation rule?
When we rotate positive 90 degrees, the rotation is said to be counterclockwise but when we rotate negative 90 degrees, the rotation is said to be clockwise.
Now, we want to find the rotation that correctly describes rotation of the rectangle ABCD by negative 90 degrees.
Thus, looking at the options, the only one that has the negative 90 degrees rotation that is clockwise will be option A because we see that when we rotate to the right which is clockwise, the first point is A which is exactly what is in option A.
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