The coordinates of the midpoint of AB is (x, 3x+2).
Given:
A line segment has endpoints A(-2x+1,4x-3) and B(4x-1,2x+7) .
Midpoint of AB = (-2x+1+4x-1 / 2 , 4x-3+2x+7 / 2)
= (2x+1-1 / 2 , 6x+7-3 / 2)
= (2x+0 / 2 , 6x+4 / 2)
= (2x/2 , 6x+4 / 2)
= (x, 3x+2).
Therefore the coordinates of the midpoint of AB is (x, 3x+2).
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sin A = 3/5, cos B = 8/17 and A and B are acute angles, determine the exact value of tan A tan B
According to the Pythagoras theorem, the exact value of tan A is 3/4 and the value of tan B is 15/8
Pythagoras Theorem
Pythagoras theorem defines that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
Given,
Here we have the value of sin A = 3/5, cos B = 8/17 and A and B are acute angles.
And we need to find the value of tan A and tan B.
According to the Pythagoras theorem,
If the value of sin A = 3/5, then we have the value of the right angle triangle of hypotenuse and the opposite.
So, the adjacent value is calculated based on the theorem is,
=> 5² = ad² + 3²
=> 25 = ad² + 9
=> ad² = 25 - 9
=> ad = √16
=> ad = 4
Therefore, the value of tan A is written as,
=> tan A = opposite/ adjacent
=> tan A = 3/4
Similarly, the value of tan B is calculated as,
If the value of cos B = 8/17, then we have the value of the right angle triangle of hypotenuse and the adjacent.
So, the opposite value is calculated based on the theorem is,
=> 17² = 8² + op²
=> 289 = 64 + op²
=> op² = 289 - 64
=> op = √225
=> op = 15
Therefore, the value of tan B is written as,
=> tan B = opposite/ adjacent
=> tan B = 15/8
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For two consecutive integers, the result of adding double the smaller integer and triple the larger integer is 153. What are the two integers?.
Based on the information, the two integers are 30 and 31.
Let the first integer be x. The second consecutive integer will be (x + 1).
So, the smaller integer = 2x
The larger integer = 3(x + 1)
Their sum = 153
Forming the equation now -
2x + 3(x + 1) = 153
Performing multiplication on Left Hand Side of the equation
2x + 3x + 3 = 153
Performing addition on Left Hand Side of the equation
5x = 153 - 3
Performing subtraction on Right Hand Side of the equation
5x = 150
x = 150/5
Performing division on Right and Side of the equation
x = 30
Smaller integer = 30
Large integer = 30 + 1
Large integer = 31
Thus, the two integers are 30 and 31.
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Please help I tried multiple times but still can't get it right
Answer:
-3
Step-by-step explanation:
You want the slope of the line through points (1, 2) and (3, -4).
SlopeThe slope of the line is its "rise" divided by its "run." The values of these can be found several ways. Perhaps the easiest is to count the squares on the graph.
The bottom point on the graph is 2 grid squares to the right of the top point, and 6 grid squares below it. The "rise" is -6 (down is negative), and the "run" is 2. The slope is ...
slope = rise/run = -6/2 = -3
You can also use the slope formula with the coordinates of the points.
m = (y2 -y1)/(x2 -x1)
m = (-4 -2)/(3 -1) = -6/2 = -3
The slope of the line is -3.
martin is making four milkshakes if the recipe calls for 2/3 cup of milk how many cups of milk does he need
Answer:
[tex]2\frac{2}{3}[/tex] cups of milk
Step-by-step explanation:
The problem is [tex]\frac{2}{3}[/tex] of a cup per milkshake times 4 milkshakes. Keeping in mind that we can write any number over 1 without changing its value, our math problem is:
[tex]\frac{2}{3}[/tex] × [tex]\frac{4}{1}[/tex]
We multiply numerator times numerator and denominator times denominator to get [tex]\frac{8}{3}[/tex]. If we convert that improper fraction to a mixed number fraction we get [tex]2\frac{2}{3}[/tex].
The number of cups of milk would be 2 2/3 needed in the four milkshakes.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
We have been given that martin is making four milkshakes. The recipe calls for 2/3 cup of milk.
We have to determine the number of cups of milk he needs
Let the number of cups of milk would be x in the four milkshakes.
As per the given situation, we can write the ratio would be as:
1 milkshakes : 2/3 cup of milk = 4 milkshakes : x cup of milk
⇒ 1 / (2/3) = 4/x
Reciprocal the term in the numerator,
⇒ 3/2 = 4/x
Apply the cross-multiplication operation,
⇒ 3x = 8
⇒ x = 8/3
⇒ x = 2 2/3
Thus, the number of cups of milk would be 2 2/3 in the four milkshakes.
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Would someone help me? This is due tomorrow
Answer: Someone already answered this but he said:
True, the product of three positive integers is positive.
What is a positive integer?
A positive integer is a non-negative whole number which belong to real numbers.
Examples of positive integer
1, 2, 3, 4, 5, 6, etc
Product of three positive integers
1 x 2 x 3 = 6
Thus, we can conclude that the product of three positive integers is positive.
The person is this guy: brainly.com/question/1367050
Answer: True
Step-by-step explanation:
If all the integers are positive, the only answer you get when multiplying them all is positive. If one of the three integers is negative, then the product is negative because if you have 2*3*(-1), the answer would be -6. But if you have 2*3*1, the answer is 6. If two of the three integers are negative, then the product is positive given the third integer is positive because a negative times a negative is a positive.
Yoko needs to buy plastic forks. Brand A has a box of 36 forks for $1.54. Brand B has a box of 48 forks for $1.66 .
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Answer:
brand b is the better buy, brand a unit price is 0.0427, and brand b is 0.0346
Step-by-step explanation:
hope it helped :)
If this net were to be folded into a
cube, which number would be
opposite of the number 1?
6
3
5 1
4
2
If the given net was folded into a cube, the number that would be opposite of 1 would be number 6.
How to find the opposite number?If the net was folded into a cube, it would be done such that 1 would be at the bottom of the cube. 4 and 3 would raised to be on the sides of the cube. 2 and 5 would also be raised as well. This would then put 6 on the top of the dice.
With 6 being on top of the dice, this means that it would be the opposite of 1 which is at the bottom. 3 and 4 would be opposites and 5 and 2 would be opposites.
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identify the center and the radius of a circle that has a diameter with endpoints at (5, 8) and (7, 6).
The center of the circle is (6,7) and the radius of the circle is 1.414 units
The diameter with endpoints = (5, 8) and (7, 6)
The mid point of the diameter = The center of the circle
The center of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Substitute the values in the equation
The center of the circle = ( (5+7)/2 , (6+8)/2 )
= (12/2 , 14/2)
= (6, 7)
The radius of the circle = The distance between (6, 7) and (7, 6)
The distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance between (6, 7) and (7, 6) = [tex]\sqrt{(7-6)^2+(6-7)^2}[/tex]
= [tex]\sqrt{1^2+(-1)^2}[/tex]
= [tex]\sqrt{1+1}[/tex]
= [tex]\sqrt{2}[/tex]
= 1.414 units
Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units
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select all that apply. the probability of rolling an even number with a six-sided, equally weighted die is group of answer choices 1/3. 1/2. 1/6. 3/6.
Using the sample space, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.
In the given question we have to find the probability of rolling an even number with a six-sided dice.
The sample space of dice through the experiment is
{1,2,3,4,5,6}
The even numbers is {2,4,6}.
The probability of rolling an even number with a six-sided dice is
P(E)=Total number of even outcome/Total number of outcome
P(E)=3/6
P(E)=1/2
Hence, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.
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Multiply. Write your answer as a fraction or as a whole or mixed number.
7 ×
5
6
Answer: 5 5/6
Step-by-step explanation: make them both into fractions so 7/1 and 5/6 multiply across 7*5=35 and 1*6=6 simplify that down into a mixed number gives you 5 5/6
A fortune wheel has 5 sections of equal size with the colours: red, green and white. The probability to get a red sector if you turn the wheel once is 40% Work out the number of red sectors .
The number of red sectors is given as 2.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
The total number of sectors on the fortune wheel is 5.
And, the probability of getting red colour is 40%.
Which is equivalent to 40/100 = 0.4.
The probability of getting red is given as,
P(red) = Number of red sectors ÷ Total number of sectors
=> 0.4 = Number of red sectors ÷ 5
=> Number of red sectors = 5 × 0.4
= 2
Hence, the number of red sectors are 2.
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suppose we were interested in determining if there were differences in the average prices of items from two local supermarkets. we randomly pick six items to compare at both supermarkets. which statistical procedure would be best to use for this study?
The statistical procedure that would be best to use for this study is the two-sample t test.
We were interested in determining if there were differences in the average prices of items at two local supermarkets. We randomly picked six items to compare at both supermarkets. We need to identify the statistical procedure that would be best to use for this study.
Statistics is the study of data gathering, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
The statistical procedure that would be best to use for this study is the two-sample t test because determining if there were differences in the average prices among two local supermarkets.
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If your job pays you a 10% commission based on your sales, how much
commission would you make if your sales were $20,000?
$200
$2,000
$20,000
$22,000
A boy cycles 12x km in 5 hours. How far can he cycle in 3y hours at the same average speed?
Answer:
Step-by-step explanation:
this is the Answer:
xy/180 km
Step-by-step explanation:
Mathematically, we have it that;
Speed = distance/ time
If he cycles x km in 3 hours
We know that ; 60 minutes = 1 hr
3 hours = 3 * 60 = 180 minutes
So the speed in km per minutes will be;
x km/180 minutes = x/180 km/minute
Recall,
Distance = speed * time
= x/180 * y = xy/180 km
HOPE THIS HELP !!!!!!!!!!!!!!!!!!!!!!!! :D
The stemplot displays 26 students' scores on a 90-point
statistics test.
Which of the following best describes the shape of the distributor test scores
Bimodal and symmetric
Slightly skewed left
Slightly skewed right
Heavily skewed right
Answer:
I think C is correct
Step-by-step explanation:
I am not really sure
Find the missing values for the exponential function represented by the table below.
To find the missing values for the exponential function represented by the table above.
An exponential function is in general form, that is
[tex]f(x) = y = a(b)^{x}[/tex]
Now, given points are (-2,8), (-1,12), (0,18)
First let us consider
f(x) = 8 at x = -2
[tex]f(x) = a(b)^{x}[/tex]
[tex]f(-2) = a(b)^{-2}[/tex] = 8
[tex]\frac{a}{b^{2} } = 8[/tex]
So, [tex]a = 8b^{2}[/tex] lets consider this as equation 1
second let us consider
f(x) = 12 at x = -1
[tex]f(-1) = a(b)^{-1} = 12[/tex]
[tex]\frac{a}{b} = 12[/tex]
a = 12b lets consider this as equation 2
From equations 1 & 2, we have
[tex]8b^{2} = 12b[/tex]
[tex]8b^{2}-12b = 0[/tex]
4b(2b-3) = 0
b = 0 or [tex]\frac{3}{2}[/tex]
This is not possible otherwise function will not remain exponential.
[tex]b = \frac{3}{2} ,[/tex] so putting b in equation 1
we have [tex]a = 12b = 12x\frac{3}{2} = 18[/tex]
therefore a = 18
therefore [tex]f^{n} = f(x) = 18(\frac{3}{2})^{x}[/tex]
1. [tex]f(1) = 18(\frac{3}{2})^{1} = 27\\[/tex]
f(1) = 27
2. [tex]f(2) = 18(\frac{3}{2})^{2} = \frac{81}{2} = 40.5[/tex]
f(2) = 40.5
Hence the answer is the missing values is 27, 40.5
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Communicate and Justify In Example 5, Pedro finds applesauce that comes in packages of 8, but now he finds juice bottles only in packages of 3. Will the LCM change? Explain.
*If answer given on next 3-8 hours will give brainliest.*
Yes, the LCM changed for the two terms. Because there is no common term in the 3 and 8.
What is LCM?It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.
It is given that Pedro finds applesauce that comes in packages of 8, but now he finds juice bottles only in packages of 3.
The factor of 8,
8=2×2×2×1
The factor of 3,
3=3×1
There are no common terms in both the given integers as a result the LCM changes.
Thus, the LCM changed for the two terms. Because there is no common term in the 3 and 8.
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A toy company makes wooden blocks. A carton holds 87 blocks.
How many blocks can 15 cartons hold?
The cartons can hold
blocks.
The cartons hold 1305 blocks.
What are Comparing quantities?
- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.
- One or more quantities with their units will be provided to us, and we will be required to determine the value of the same quantity in other units (i.e. in higher values or in lower values).
We given that,
A carton holds 87 blocks.
It means, 1 carton holds = 87 blocks
So find 15 cartons holds how much of blocks.
15 cartons holds = 15 * 87
= 1305 blocks
Hence, we can say that the cartons hold 1305 blocks.
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A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 6800 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 150-kilogram crates that can be loaded into the shipping container.
The greatest number of 150-kilogram crates that can be loaded into the shipping container are 138
Greatest weight that can be loaded = 27500 kilograms
Weight of each crate = 150 kilogram
Weight of other shipments = 6800 kilograms
Let c be the greatest number of 150 kilogram crates that can be loaded.
The required inequality
27500 ≥ 6800 + 150c
27500 - 6800 ≥ 150c
20700 ≥ 150c
c ≥ 20700/150
c ≥ 138
Hence, the maximum number of crates are 138.
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Question Progress
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Homework Progress
10/29 Marks
The nth term of a sequence is 25 - 3n
a) Work out the first three terms of the sequence.
9
7
b) Work out the value of the first negative term of the sequence.
8
First three terms of sequence are 25,22,19 and first negative term of the sequence is -2.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of a sequence is 25 - 3n
Twenty five minus three times of n.
25 - 3n
the first three terms are
the first term is 25
25-3=22
25-6=19
25-9=16
The first three terms are 25,22,19.
25-3(9)=25-27=-2
The first negative term of the sequence is -2.
Hence, first three terms of sequence are 25,22,19 and first negative term of the sequence is -2.
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PLS HELP I WILL GIVE BRAINIEST TO WHOEVER ANSWERS BOTH OF THESE CORRECTLY
Answer:
Step-by-step explanation:
Problem 2
The metal rim of a magnifying glass is inches around.
What is the area of the surface of the glass inside?
The area of the glass inside the 10 inches metal rim is 25/π square inches
What is the area of a plane shape?The area of a geometric shape or figure is a measure of the flat surface the shape occupies.
The dimension in the question, obtained from a similar question online are;
The length of the metal rim around the magnifying glass = 10 inches around
Required; The surface area of the glass inside the rim
The metal rim around the magnifying glass indicates the circumference of the glass inside;
Therefore;
The circumference of the glass inside the rim = 10 inches
The formula for the circumference of a circle = 2·π·r
Where;
r = The radius of the circle;
Therefore;
r = Circumference ÷ (2×π)
The radius of the glass inside is therefore;
r = 10 inches/(2·π) = 5/π inches
The area of a circle = π × r²
The area of the glass, A = π × (5/π)² = 25/π
The area of the glass inside is A = 25/π square inches
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What is the value of x?
Enter your answer in the box.
X =??
Answer:
x = 9
Step-by-step explanation:
Triangles are similar due to AAA (all angles are congruent due to shared angle and corresponding angles). Thus, the sides are proportional, and we can set up a proportion with corresponding sides:
9/(72 + 9) = (3x - 20)/(3x - 20 + 56)
9/81 = (3x - 20)/(3x + 36)
(1/9) * (3x + 36) = 3x - 20
(3x + 36)/9 = 3x - 20
3x + 36 = (3x - 20)*9
3x + 36 = 27x - 180
36 + 180 = 27x - 3x
216 = 24x
x = 9
Francis heard that a car stereo system was on sale for 30%off. If the sale price was %57.75, what was the original price of the stereo?
Answer:
Original Price = Sale Price / ( 1 - Percent Off / 100 )
= 57.75 / (1 - 30/100)
= 57.75 / (1 - 0.3)
= 57.75 / 0.7
= $82.50
Original price = $82.50
When we are writing in expanded form what digit do we put in the places in front of the digit given?
random signs or 0
When we are writing in expanded form we put zero (0) in the places in front of the digit given.
As we all know, zero (0) doesn't add any value or make any difference in the number while putting in front.
Hence, putting 0 in the front won't make any difference to the number
So, we put 0 in the front.
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Answer: Depends on the number!
Step-by-step explanation:
The digit to put in front of the given digit depends on the number. For example, if the given digit is an 8, then a 0 should be placed in front of it to indicate that it is a two-digit number. If the given digit is a 3, then a 0 should be placed in front of it to indicate that it is a three-digit number.
Does x + 2 = -3(x+1) have exactly one solution?
Answer:
Yes
Step-by-step explanation:
the solution would be -5/4
Answer:
yes have on solution
Step-by-step explanation:
Decimal
=-1.25
Fraction
=[tex]-\frac{5}{4}[/tex]
Mixed fraction
=[tex]-1\frac{1}{4}[/tex]
In the coordinate plane, line p has slope 13 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
In the coordinate plane, line p has slope 13 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin.
Line P
Slope (m) = 13
y intercept is (0,2)
Equation is
y = mx+y
y= 13x+2
Dilated by scale factor of 3 with center at (0,3)
First make the centre at origin (0,0) by shifting the line 3 units downwards.
y = (13x+2)-3
y = 13x-1
In case of dilation, slope remains same only the y-intercept gets multiplied.
New equation is y = 13x-(1x3)
y = 13x-3
Now again take this line 3 units upwards
y = (13x-3)+3
y = 13x+0
Hence line r has slope of 13, y intercept is (0,0)
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15. Which is an equation of the line with slope of that passes through (5,-5)?
3
Ay-5= -²(x+5)
Cy+5=-(x - 5)
By-5=-(x-5)
Dy+5=-x-5
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
What is meant by slope of line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.The equation of a line is given by the expression:
(y-y1)=m(x-x1)
in the given problem the slope is m=1 and the point (x1, y1) is (5, 3), so substituting those values we have:
(y-3)=1(x-5)
simplifying:
y-3=x-5
isolating "y":
y=x-5+3
y=x-2
The complete questions is,
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? A.y = x – 2
B.y = x + 2 C.y = x + 3
D.y = x – 5
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following and propo Out of 250 coins, 50 are in mint condition. What is the ratio of mint condition coins to the total number of coins?
Reason:
We have 50 mint condition coins out of 250 total
This forms the ratio 50:250, in which we divide both parts by the GCF 50 to end up with 1:5
The ratio 1:5 tells us that the total is 5 times that of the number of mint condition.
Complete the table of solutions to this equation: y=6x+1.
The table of solutions to the given Linear Equation, be
x 0 1 2 3 4
y 1 7 13 19 25
Given, a linear equation
y = 6x + 1
the table of solutions to the given equation, be
x 0 1 2 3 4
y 1 7 13 19 25
as, when x = 0,
y = 6(0) + 1
y = 1
when x = 1,
y = 6(1) + 1
y = 7
when x = 2,
y = 6(2) + 1
y = 13
when x = 3,
y = 6(3) + 1
y = 19
when x = 4,
y = 6(4) + 1
y = 25
Hence, the table of solutions to the given Linear Equation, be
x 0 1 2 3 4
y 1 7 13 19 25
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