The slope of the line passing through (-3, -1) and (3, 3) is 2/3, which is found using the slope formula that calculates the change in y over the change in x.
To find the slope of the line that contains the points (-3, -1) and (3, 3), we can use the slope formula
slope = (change in y)/(change in x) = (y2 - y1)/(x2 - x1)
Substituting the values of the given points, we get
slope = (3 - (-1))/(3 - (-3))
slope = (3 + 1)/(3 + 3)
slope = 4/6
slope = 2/3
Therefore, the slope of the line that contains the points (-3, -1) and (3, 3) is 2/3.
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The graph shows g(x), which is a translation of
f(x) = = x². Write the function rule for g(x).
-10 -8 -6 -4
-2
104
-8-
-6-
-4-
2-
0
-2-
-4-
-6
-8-
-10₂
2
4
6
8
Write your answer in the form a(x − h)² + k,
where a, h, and k are integers or simplified
fractions.
g(x) =?
The function rule for g(x) is f(x) = (x - 5)² + 0.
How to determine the function rule?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.Since the parent function is represented by f(x) = x², a function rule for g(x) is given by;
f(x) = a(x − h)² + k
f(x) = 1(x - 5)² + 0.
f(x) = (x - 5)² + 0.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Mrs. Singh bought 9 folders and 9 notebooks. the cost of each folder was $2.50. each notebook cost $4.00 Write two equivalent expressions and then find the total cost.
a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:
2.50x4.00y.b) The total cost of the purchase by Mrs. Singh is $58.50.
What are algebraic expressions?Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).
The unit cost of folders = $2.50
The unit cost of notebooks = $4.00
The number of folders bought = 9
The number of notebooks bought = 9
Let the number of folders bought = x
Let the number of notebooks bought = y
Expressions of the Costs:Folders: 2.50x
Notebooks: 4.00y
Total Costs:Folders: 2.50x = $22.50 ($2.50 x 9)
Notebooks: 4.00y = $36.00 ($4 x 9)
Total costs = $58.50
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Find the area of the triangle with vertices A(-3, 2), B(1, - 2). and C(1, 3).
Answer:
10 units squared
Step-by-step explanation:
Main steps
Step 1. Identify which leg to use as a base
Step 2. Calculate the base length
Step 3. Calculate the height
Step 4. Calculate the area
Step 1. Identify which leg to use as a base
We are given that the shape is a triangle. The formula for the area of a triangle is [tex]A_{triangle}=\frac{1}{2}bh[/tex] where b is the "base" of a triangle, and h is the "height".
One common misconception is that the base must be at the bottom (although it is easy to think of it that way). Rotating the shape, any of the three sides could be at the bottom, and thus any of the three sides could be the base.
The "height" of the triangle depends on which leg is being used as a base. The height for a given base is always the shortest distance from the vertex opposite the base to the line that contains the base. This shortest distance always ends up being the line segment that is perpendicular to the base.
In this case, since side BC is along the gridlines, it will be easiest to use side BC as the base, because the perpendicular line for the height will be along gridlines. The height is the distance from A to the side BC (which is a line segment between (-3,2) and (1,2)).
Step 2. Calculate the base length
The base length is the distance between the two endpoints of the line segment. The distance formula is [tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using Point B as Point 1, and Point C as Point 2:
[tex]D=\sqrt{((1)-(1))^2+((3)-(-2))^2}[/tex]
[tex]D=\sqrt{(0)^2+(5)^2}[/tex]
[tex]D=\sqrt{0+25}[/tex]
[tex]D=\sqrt{25}[/tex]
[tex]D=5[/tex] units
So the base length is 5 units
b=5 units
Since these point are on a graph, it can be verified by counting the squares between the two points, however if work needs to be shown, the Distance formula is the "work".
Step 3. Calculate the height
The "height" for the base from step 2 is a line segment between (-3,2) and (1,2). This distance can again be found using the distance formula:
Using Point A as Point 1, and the point (1,2) on BC as Point 2:
[tex]D=\sqrt{((-3)-(1))^2+((2)-(2))^2}[/tex]
[tex]D=\sqrt{(-4)^2+(0)^2}[/tex]
[tex]D=\sqrt{16+0}[/tex]
[tex]D=\sqrt{16}[/tex]
[tex]D=4[/tex] units
So the height for the base from Step 2 is 4 units.
h=4 units
Again, these point are on a graph, so this answer can be verified by counting the squares between the two points.
Step 4. Calculate the area
Using the formula for the area of a triangle discussed in Step 1, the area can be calculated:
[tex]A_{triangle}=\frac{1}{2}(5~\text{units})(4~\text{units})[/tex]
[tex]A_{triangle}=10 \text{ units}^2[/tex]
The area of a circle is 25π square units. Find th
e circumference of it in terms of π or a unit number
Answer:
10π
Step-by-step explanation:
A=25π
25π=πr^2
25=r^2
5=r
C=2πr
=2π5
=10π
how many tissues should a package of tissues contain? researchers have determined that a person uses an average of 61 tissues during a cold. suppose a random sample of 2500 people yiel
According to unitary method, a package of tissues should contain at least 152,500 tissues to meet the needs of 2500 people during a cold.
To determine the number of tissues required in a package, we need to use a unitary method. A unitary method is a mathematical method used to find the value of a single unit when the value of a known number of units is given. In this case, we know that an average person uses 61 tissues during a cold. Therefore, we can use this information to find the number of tissues required in a package.
Suppose we want to find the number of tissues required for 2500 people during a cold. We can use the unitary method as follows:
Number of tissues required for 1 person = 61
Number of people = 2500
To find the number of tissues required for 2500 people, we need to multiply the number of tissues required for one person by the number of people. Therefore,
Number of tissues required for 2500 people = Number of tissues required for 1 person × Number of people
= 61 × 2500
= 152,500
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The circle provided is identical to the one for problem 2. Label each identified point around the circle. Recall that the radius is 5" units" .
What is the length of the arc on a circle of radius r of 33 cm intercepted by a central angle 1.5 radians.
Find the measure of θ in radians given that s (arc length) is 14 and the radius is 11.
The length of the arc on a circle of radius r of 33 cm intercepted by a central angle 1.5 radians is 49.5 cm.
the measure of θ in radians given that s (arc length) is 14 and the radius is 11 is 1.3 radians.
We know that from trigonometric formula, if the arc length of 's' subtends an angle of θ in radian at the center of a circle with radius of 'r' units then the relation between then is given by,
s = rθ
For the first case:
Radius of the circle is (r) = 33 cm.
Central angle is (θ) = 1.5 radian
Then the length of the arc (s) is given by = 33*1.5 = 49.5 cm.
For the second case:
Radius of the circle is (r) = 11 units.
and the arc length of the circle is (s) = 14 units.
So the measure of the central angle (θ) = s/r = 14/11 = 1.3 radians (round to nearest tenth).
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The two lines shown below are perpendicular. If the slope of the red line is 1/2 what is the slope of the green line?
Answer:
B) -2
Step-by-step explanation:
When perpendicular lines accur to find the translated line just flip the numerator and denominator and making the reciprocals negitive
Please help!!!
What is a 3 sided polygon called?
Answer: A three sided polygon is a triangle.
Step-by-step explanation:
Types of these include: isosceles, equilateral, scalene, obtuse, acute, and right triangles. Example:
if a square's area is increased by 21 square units, it becomes 100 square units. what was the original area?
The square's area is increased by 21 square units, it becomes 100 square units and the original area of the square was 79 square units.
To solve this problem, we can use algebra. Let x be the original area of the square. We know that when we increase the area by 21 square units, we get 100 square units. So we can set up an equation:
x + 21 = 100
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 21 from both sides:
x + 21 - 21 = 100 - 21
x = 79
Therefore, the original area of the square was 79 square units. To check our answer, we can plug it back into the original equation:
79 + 21 = 100
This is true, so our answer is correct.
In summary, to find the original area of a square when the area is increased by 21 square units and becomes 100 square units, we can use algebra and set up the equation x + 21 = 100, where x is the original area. Solving for x, we get x = 79. Therefore, the original area of the square was 79 square units.
To find the original area of the square, we need to consider the given information: when the square's area is increased by 21 square units, it becomes 100 square units.
Since the area is increased by 21 square units to reach 100 square units, we can calculate the original area by subtracting 21 from 100:
Original Area = 100 - 21
Original Area = 79 square units
So, the original area of the square was 79 square units.
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the life of light bulbs is distributed normally. the standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for between 557 and 561 hours. round your answer to four decimal places.
The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%
Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:
z = (x - μ) / σ
where x is the bulb lifetime we're fascinated by
, μ is the cruel(mean) lifetime,
and σ is the standard deviation.
For 557 hours:
z1 = (557 - 530) / 15 = 1.8
For 561 hours:
z2 = (561 - 530) / 15 = 2.07
Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:
P(z1 < Z < z2) = P(1.8 < Z < 2.07)
This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.
Employing a standard ordinary dispersion table or a calculator, we discover:
P(1.8 < Z < 2.07) ≈ 0.0382
Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places).
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The managers of an airline analyzed a random sample of flights and found that 95% of the flights arrived on time. The airline has 480 flights scheduled for next week. What is the BEST estimate of the number of these flights that will NOT arrive on time?
Answer:
456
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Si el 40% de las ventas de Juan corresponde a 120 bolsas de papas, ¿cuántas bolsas de papas corresponden a 120%
If 40% of John's sales correspond to 120 bags of potatoes, 300 bags of potatoes correspond to 120%
To solve this problem, we can use a proportion. If 40% of John's sales correspond to 120 bags of potatoes, we can set up the following proportion:
40/100 = 120/x
Here, x represents the number of bags of potatoes that correspond to 120% of John's sales. To solve for x, we can cross-multiply and simplify:
40x = 12000
x = 300
Therefore, 300 bags of potatoes correspond to 120% of John's sales. This means that if John's sales increase by 20% (from 100% to 120%), he would sell 300 bags of potatoes.
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One or more final O's used after the decimal point are always significant. True or flase?
Answer:
False
Step-by-step explanation:
Trailing zeros after the decimal point are not always significant. The number of significant figures after the decimal point is determined by the measurement instrument used to obtain the value.
An inequality is shown.
Answer: 24
Step-by-step explanation:
For inequalities, you would solve for x like you would if it were an equal sign but keep the sign in middle. The only thing that changes the sign is if you multiply or divide by a negative, then the sign flips(this is not so in this case.
[tex]\sqrt{x}[/tex]<5 square both sides to get rid of square root
x<5²
x<25 x is less than 25; it cannot be = to 25 so the largest integer it can be is 24
express in simplified exponential notation.
x^3 •x^5=
The simplified exponential notation of the given expression is x⁸.
Given that, simplified exponential notation, x³·x⁵,
x³·x⁵ we need to simplify it,
We know that,
mᵃ × mᵇ = mᵃ⁺ᵇ
x³·x⁵ = x³⁺⁵
x³·x⁵ = x⁸
Hence, the simplified exponential notation of the given expression is x⁸.
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I'm a number between 17 and 25 i'm a multpile of 3 6 is not mynfactor
The number that fits the given criteria is 21.
The number 21 is between 17 and 25, and it is a multiple of 3. It is not a multiple of 6 because it is not divisible evenly by 6.
The factors of 21 are 1, 3, 7, and 21. Since 6 is not one of its factors, 21 satisfies the given conditions.
To find the answer, we first identify the range of numbers given, which is between 17 and 25.
Next, we look for a number within this range that is a multiple of 3. Multiples of 3 are numbers that can be divided evenly by 3 without leaving a remainder.
Among the numbers in the given range, only 21 satisfies this condition. Lastly, we check if the number is a multiple of 6. A multiple of 6 is a number that can be divided evenly by 6 without leaving a remainder.
Since 21 cannot be divided evenly by 6, it does not meet this criterion. Therefore, 21 is the number that fits all the given conditions.
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i need help on the practice test from ilearn
Answer:
8 inches
Step-by-step explanation:
You want the diameter of a circle that has a circumference between 20 and 27 inches, expressed as an integer number of inches near the high end without going over.
DiameterThe relationship between diameter and circumference of a circle is ...
C = πd
d = C/π
For the given circumference range, the diameter range is ...
20 ≤ πd ≤ 27
20/π ≤ d ≤ 27/π
6.4 ≤ d ≤ 8.5
Integers in this range are 7 and 8. The largest one is 8.
8 inches is the most reasonable diameter of the circular cardboard model.
a code has 4 digits. you remember that the 4 digits are 1, 3, 5, and 7, but you cannot remember the sequence. what is the probability that you guess the code correctly on the first try?
The probability of guessing the 4-digit code correctly on the first try is 1/24.
Since there are 4 unique digits (1, 3, 5, and 7) and the code has 4 digits, there are a total of 4! (4 factorial) possible sequences for the code.
The calculation for 4! is 4 x 3 x 2 x 1 = 24.
Therefore, there are 24 different sequences.
Since you are trying to guess the code correctly on the first try, there is only one correct sequence out of the 24 possible sequences.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes), the number of favorable outcomes is 1 (correct sequence), and the total number of possible outcomes is 24.
So, the probability is 1/24.
Hence, Given the 4 unique digits 1, 3, 5, and 7 in a 4-digit code, there are 24 possible sequences for the code. The probability of guessing the code correctly on the first try is 1/24.
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2. a. The total cost of 60 apples and 100 eggs is €108,000.00. The cost of 72 apples is the same as that of 30 eggs. Find how much 12 apples and 20 eggs will cost.
Use the distributive property to write an equivalent expression.
3(7 p - 3 q + 9)
Answer:
27p - 9q + 27
Step-by-step explanation:
3(7p - 3q + 9) ← multiply each term in the parenthesis by the 3
= 21p - 9q + 27
A water park has pools, slides, and rides that, in total, make use of 8.7 x 105 gallons
of water. They plan to add a ride that would make use of an additional 7.8 x 10³
gallons of water. Use scientific notation to express the total gallons of water made use
of in the park after the new ride is installed.
Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
The form of the container the water is contained in affects how much water is contained inside. You must know the length, breadth, and depth of a square or rectangular vessel in order to calculate its volume using the volume equation V=L*W*D, where L stands for length, W for width, and D for depth. The volume equation in this case reads: V= (r²)Dπ, where r stands for the radius, D for depth, and, or pi, is a constant value that is typically rounded to 3.14. To perform the same volume calculation for a circular vessel, you must know the vessel's depth and diameter or radius.
Given, the water park has water which is 8.6*10⁵ gallons.
We know that 10⁵ = 100000
Thus, 8.6*10⁵ = 860000
The new ride would use an additional 9.1*10⁴ gallons.
Again, 10⁴ = 10000
Thus, 9.1*10⁴ = 91000
Total water that would be required now is equal to the sum of the original water volume and the volume required by the new ride
= (860000+91000) gallons
= 951000 gallons
= 9.51*10⁵ gallons
Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
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While grocery shopping, Dylan bought
some apples for $3.50. He also bought
some grapes that cost $1.25 more than
the apples. The combined cost of the
grapes and apples made up 20% of his
total grocery bill. What was the total
amount of Dylan's grocery bill in dollars
and cents?
Answer:
Dylan's grocery bill was $41.25.
Step-by-step explanation:
Let's call the cost of the grapes "g".
We know that the grapes cost $1.25 more than the apples, so we can write:
g = 3.50 + 1.25 = 4.75
The combined cost of the grapes and apples is 20% of Dylan's total grocery bill, so we can write:
3.50 + 4.75 = 0.20x
where x is the total grocery bill.
We can solve for x by simplifying the equation:
8.25 = 0.20x
x = 8.25 / 0.20
x = 41.25
Therefore, the total amount of Dylan's grocery bill was $41.25.
Answer:
Dylan's total grocery bill was $41.25
Step-by-step explanation:
Let the cost of the apples be a. Then, the cost of the grapes is a + 1.25, since the grapes cost $1.25 more than the apples.
The combined cost of the apples and grapes is a + (a + 1.25) = 2a + 1.25.
We know that the combined cost of the apples and grapes is 20% of Dylan's total grocery bill, so we can set up the following equation:
2a + 1.25 = 0.2x
where x is the total cost of Dylan's grocery bill.
To solve for x, we can isolate x on one side of the equation:
2a + 1.25 = 0.2x
2a = 0.2x - 1.25
a = 0.1x - 0.625
We also know that the cost of the apples is $3.50, so we can set up another equation:
a = 3.5
Substituting this into the equation we just found:
3.5 = 0.1x - 0.625
4.125 = 0.1x
x = 41.25
Therefore, Dylan's total grocery bill was $41.25.
On a coordinate plane, a triangle has points F (3, 4), D (5, negative 3), and E (1, negative 2).
What are the coordinates of the image of vertex D after a reflection across the x-axis?
(5, 3)
(–5, –3)
(–3, 5)
(3, –5)
Answer:
(5, 3)
Step-by-step explanation:
Since we are reflecting by the x-axis, the x-cooridnate would stay the same.
Vertex D is 3 units dow from the x-axis. By reflecting in using the x=0 reference,the y-coordinate would be a positivo 3 now.
Answer:
D. (3, -5) on edge
Step-by-step explanation:
Picture below⬇️, tried two answers and got me wrong… hope I helped :)
what is the rate of this question
Answer:
The rate of change is 2 feet per second.
Find the equation of the straight line passing through the point (3, 3) which is perpendicular to the line y=-\frac{1}{2}x-4
The equation of the straight line passing through the point (3, 3) and perpendicular to the line y = -¹/₂x - 4 is y = 2x - 3.
The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line. The given line is y = -1/2x - 4. We can rewrite this equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Comparing the given equation with the slope-intercept form, we get:
m = -1/2
Therefore, the slope of the given line is -1/2
The point-slope form of the equation of a straight line is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. We know that the line passes through the point (3, 3) and has a slope of 2 (perpendicular to the slope of the given line).
Substituting these values in the point-slope form, we get:
y - 3 = 2(x - 3)
Expanding and simplifying this equation, we get:
y = 2x - 3
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Complete Question:
Find the equation of the straight line passing through the point (3, 3) which is perpendicular to the line y=-1/2x-4
(8x2-3) - (5x - 5 - 8x2)
in a group of 32 children, 25% have blue eyes. how many children do not have blue eyes?
Answer: 24 children
Step-by-step explanation:
Answer:
Step-by-step explanation:
So if 25% have blue eyes, 75% do not.
100% - 25% = 75%
What is 75% of 32?
Change 75% to a decimal by movinf g the decimal two places to the left.
and multiply.
32 × .75 = 24
This is how to calculate the solution.
6.
ind
ke
12Tom earns $100 to start a painting
job and $35 per hour to complete it.
All jobs he accepts earn him at least
$500. If h represents the number of
hours spent painting, which inequality
describes Tom's situation?
A. 100 + 35h > 500
B. 100 + 35h ≥ 500
C. 100 + 35h < 500
D. 100 + 35h ≤ 500
The inequality to represent Tom's situation is 100 + 35h ≥ 500.
How to find the solve inequality?Tom earns $100 to start a painting job and $35 per hour to complete it. All
jobs he accepts earn him at least $500.
h represents the number of hours spent painting . Therefore, the inequality that represent Tom's situation is as follows:
Therefore,
100 + 35h ≥ 500
where
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Work out(−3)2−3×(2×54)÷112
Answer:
-249/28
Step-by-step explanation:
If the odds on a bet are 13:1 against, what is the probability of winning? Express your answer as a fraction.
If the odds on a bet are 13:1 against, then the probability of winning can be found using the formula:
probability of winning = 1 / (odds against + 1)
Substituting the given values, we get:
probability of winning = 1 / (13 + 1) = 1/14
Therefore, the probability of winning is 1/14 as a fraction.
