If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.
How to find the original triangle?Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.
To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:
3 + 2 = 5
So there are 5 small triangles in the third row.
To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:
5 + 2 = 7
So there are 7 small triangles in the fourth row.
To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:
n = (last term - first term) / common difference + 1
n = (7 - 1) / 2 + 1
n = 4
So there are 4 rows in the triangle.
Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:
sum = (n / 2) * (first term + last term)
sum = (4 / 2) * (1 + 7)
sum = 4 * 4
sum = 16
So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:
area = 16 * (1/2)
area = 8
Therefore, the original triangle has an area of 8 square units.
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HELPPP PLS thank you pls
The piecewise function is defined as follows:
y = x² + 4, x < 2.y = -x + 4, x ≥ 2.How to define the piecewise function?A piece-wise function is a function that has different definitions, based on values of the input x of the function.
For this problem, the intervals are given as follows:
x < 2. -> left of x = 2.x ≥ 2. -> right of x = 2.For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence:
y = x² + 4, x < 2.
For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:
y = -x + 4, x ≥ 2.
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Calculate the value of the expression(-7+3)(4-5×2)=
For the function
f
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x
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=
5
x
2
+
3
x
, evaluate and simplify.
f
(
x
+
h
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-
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h
=
In respοnse tο the query, we can state that Therefοre, the simplified equatiοn expressiοn fοr f(x+h) - f(x)/h is: 10x + 5h + 3
What is equatiοn?In a math equatiοn, twο assertiοns are cοnnected by the equals sign (=), which denοtes equivalence. A mathematical assertiοn used in algebraic equatiοns establishes the equivalence οf twο mathematical statements. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. Tο cοmprehend the relatiοnship between the twο sentences written οn οppοsing sides οf a letter, utilise a mathematical fοrmula. The lοgο and the specific prοgramme typically cοrrespοnd. An illustratiοn wοuld be 2x - 4 = 2.
functiοn f(x) intο the fοrmula fοr f(x+h) - f(x)/h, and then simplify the resulting expressiοn algebraically.
f (x + h) — f (x)
= [5(x + h)² + 3(x + 10] — [5x² + 3x]
= [5(x² + 2xh + h²) + 3x + 314 — [5x² + ax]
= [5x² + 10xh + 5k² + 3x + 3h] — [5x² + 3x]
= 10xh + 5h² + 3h f(x+h) - 1(x) h
= 10x + 5k + 3
Therefοre, the simplified expressiοn fοr f(x+h) - f(x)/h is:
10x + 5h + 3
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Is 3/4 greater then 2/10
Answer:yes
Step-by-step explanation:
Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water. What is the height, in inches, of the water in the tank after 5 minutes?
The height of the water in the tank after 5 minutes is approximately 732.6 inches.
What is the equation for a cylinder's volume?V = πr²h, where V is a cylinder's volume, r is its radius, and h is its height, is the formula for calculating a cylinder's volume. The formula is created by first determining the area of the cylinder's base, which equals r2, and then multiplying that area by the cylinder's height to determine the volume. The volume of tanks, pipelines, and other cylindrical objects may be calculated using this formula, among many other uses.
The volume of a cylinder, which is:
V = πr²h
Given that, diameter is 15 feet, so the radius is 7.5 feet.
Also,
2 feet per second = 2 * 12 * 60 inches per minute = 1440 inches per minute
V = πr²h
Substituting the values:
V = π(7.5)^2(14405)
Here, 14405 is the amount of water that flows into the tank in 5 minutes.
Divide the volume of water by the area of the base of the cylinder
V/A = h
2,044,123/(π(7.5)^2) ≈ 732.6 inches
Hence, the height of the water in the tank after 5 minutes is approximately 732.6 inches.
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Question 3 of 13
A right rectangular prism and an oblique triangular prism are both 12
centimeters tall and have the same volume. What statement must be true
about the two solids?
A. The cross-sections of the prisms are the same shape.
• B. The area of the cross-sections of the prisms are multiples of each
other.
c. The vertical cross-sections of the prisms at the same width must
have the same area.
• D. The horizontal cross-sections of the prisms at the same height
must have the same area.
Horizontal cross-sections of the prisms at the same height have the same area.
Option D.
What statement must be true about the two solids?A right rectangular prism is a three-dimensional shape with six faces which are all rectangles. It has twelve edges and eight vertices.
An oblique triangular prism is a prism with 2 congruent triangular faces and 3 rectangular faces at an angle to the triangular faces.
This is the volume of solid figures concept.
The volume of a prism is obtained by multiplying the area of its base to its height. If the two given solid figures have the same volume and the same height then, the areas of their bases are also equal.
In this case, the height of the right rectangular prism and the oblique triangular prism are 12 cm and both prisms have the same volume, we can conclude that:
Horizontal cross-sections of the prisms at the same height have the same area.
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Assignment 2: Please use the IQ data below and assess whether any of the IQ scores are statistically significantly high or low. Please provide corresponding z-score and percent of scores below from the table in the book. That is, you will need to provide the percent of all scores that falls BELOW the z-score you calculate (see z table in back of book gives you this percent). This is often referred to as the percentile rank.
Also, you will need to discuss whether each z- score meets the criteria of “statistically significant” and why. Please use your book to help with this part. While "statistical significance" is determined by an arbitrary score on the z-table, there is a score one must cross to be considered significant (.05 percent for example).
IQ Scores: 100, 90, 110, 160, 90, 85, 65, 100, 95, 98
The statistical significance does not necessarily imply practical significance. In this case, while the IQ score of 160 is statistically significant, it may not necessarily be practically
What is corresponding z-score and percent of scoreTo assess whether any of the IQ scores are statistically significantly high or low, we need to calculate the z-score for each score. The formula for calculating the z-score is:
z = (x - μ) / σ
Where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
First, we need to calculate the mean and standard deviation of the IQ scores:
Mean = (100 + 90 + 110 + 160 + 90 + 85 + 65 + 100 + 95 + 98) / 10 = 99.3
Standard deviation = √[((100-99.3)² + (90-99.3)² + (110-99.3)² + (160-99.3)² + (90-99.3)² + (85-99.3)² + (65-99.3)² + (100-99.3)² + (95-99.3)² + (98-99.3)²) / 10] = 39.77
Now we can calculate the z-score for each IQ score:
z1 = (100 - 99.3) / 39.77 = 0.018
z2 = (90 - 99.3) / 39.77 = -0.233
z3 = (110 - 99.3) / 39.77 = 0.27
z4 = (160 - 99.3) / 39.77 = 1.53
z5 = (90 - 99.3) / 39.77 = -0.23
z6 = (85 - 99.3) / 39.77 = -0.36
z7 = (65 - 99.3) / 39.77 = -0.86
z8 = (100 - 99.3) / 39.77 = 0.017
z9 = (95 - 99.3) / 39.77 = -0.108
z10 = (98 - 99.3) / 39.77 = 0.032
Using the z-table, we can find the percent of scores below each z-score:
z1 = 0.018 or 70.01%
z2 = -0.233 or 34.67%
z3 = 0.27 or 75.01%
z4 = 1.53 or 83.68%
z5 = -0.23 or 34.67%
z6 = -0.36 or 37.47%
z7 = -0.86 or 45.16%
z8 = 0.017 or 70.01%
z9 = -0.108 or 31.80%
z10 = 0.032 or 69.15%
To determine whether each z-score is statistically significant, we need to compare it to a predetermined level of significance, typically α = 0.05. If the probability associated with the z-score (i.e., the percent of scores below it) is less than or equal to α, we consider the score statistically significant.
Based on this criterion, the only score that is statistically significant is the IQ score of 160 (z-score = 2.29, percent of scores below = 83.68%). All other scores have a probability greater than α, and therefore are not statistically significant.
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Use the box-and-whisker plot.
A box and whisker plot. The whisker ranges from 5 to 50. The box ranges from 25 to 40 with the vertical bar inside the box at 35.
About what percent of the data fall between 5 and 35?
Enter your answer in the blank.
We know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35). So the answer is: 50%.
Describe Median?The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses. In addition to the median, other measures of central tendency include the mean and mode. Each measure has its own strengths and weaknesses, and the appropriate measure to use depends on the nature of the dataset and the research question being asked.
To answer this question, we need to determine the position of the lower whisker and the vertical bar relative to the range of the data.
The lower whisker extends to 5, which is the minimum value in the dataset. The vertical bar inside the box is located at 35, which represents the median of the dataset.
Therefore, we know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35).
So the answer is: 50%.
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What is the variable, coefficient, constant of 11 Y +4.5?
Answer: variable Y, coefficient 11, Constant 4.5
Step-by-step explanation:
variable: Y
coefficient: 11
Constant: 4.5
graph y ≤ 2 on a number line
graph x < -3 on a number line
A square with side s has area s to the 2nd power. Brandon uses a square mat when he practices karate. The mat is 11 feet on each side.
Answer:
Step-by-step explanation:
i assume you mean that the mat is 11 feet on each side so
area = s*s(or S^2)
so 11*11=121feet sq
Need help solving this problem.
Option A is correct, 162 is the greatest number of caps she can buy.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Let x be the number of caps.
We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.
We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges (6x+25).
Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000.
We can represent this information in an equation as:
6x+25≤1000
Let us solve for x
Subtract 25 from both sides
6x≤1000-25
6x≤975
Divide both sides by 6
x≤162.5
Hence, Option A is correct, 162 is the greatest number of caps she can buy.
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Pat says that 4-(p+p+p) is the same as 4-p+p+p. 6 a By replacing p by 3 in both expressions, show that Pat is wrong. b Simplify each expression algebraically.
The required, two expressions are not equivalent, and Pat's claim is false.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
a) To show that Pat is wrong, we can substitute p = 3 into both expressions and compare the results:
4 - (p + p + p) = 4 - (3 + 3 + 3) = 4 - 9 = -5
4 - p + p + p = 4 - 3 + 3 + 3 = 7
Since the two expressions have different values when p = 3, Pat's claim is false.
b) Simplifying each expression algebraically, we have:
4 - (p + p + p) = 4 - 3p
4 - p + p + p = 4 + p
Therefore, the two expressions are not equivalent, and Pat's claim is false.
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Suppose the population of a small town is 567 she has a lot of the population decreases the rate of 1.5%. Every year will be the population of a town thousand 20 Round your answer to the nearest whole number.
Answer:
Assuming "she" in the question is a typo and it should be "if", here's the solution:
If the population of a small town is 567, and it decreases at a rate of 1.5% per year, we can find the population after 20 years using the formula:
P = 567 * (1 - 0.015)^20
where P is the population after 20 years.
Simplifying this expression, we get:
P = 567 * 0.742 = 420.414
Rounding this to the nearest whole number, we get:
P ≈ 420
Therefore, after 20 years, the population of the small town would be approximately 420.
Help please due tonight
What is this equation
Answer:
x = 8
Step-by-step explanation:
[tex]15 + x = 23[/tex]
[tex]x = 23 - 15[/tex]
∴[tex]x = 8[/tex]
HELPPPP MEEEE
I NEED TO TURN IN THIS LATE MATH HOMEWORK
Answer:
I think is D
Step-by-step explanation:
because
R:622 and Y:410
Robert is tiling the bathroom floor. Each
square-shaped tile has an area of 120.5
square inches. Which measurement is
closest to the side length of a square tile
in inches?
A. 9 in.
B.11 in.
c. 13 in.
D. 15 in.
The measurement that, in inches, comes closest toward the length equal of a square tile is: 11 in.
Define the properties of the square?A square is a shape that we frequently encounter in our daily lives. Illustrations of square shapes that are frequently used include chess pieces, clock hands, picture frames, pizza boxes, coasters, computer keys, etc.
The square's four sides are equal to one another.A square's diagonals are parallel to one another.The square is split into 2 congruent triangles by each diagonal.Each diagonal in a square is the same length.In the bathroom, Robert is paving the floor.
The area of each square-shaped tile is 120.5 square inches.
Area = side²
side = √Area
side = √120.5
side = 10.97 in
side = 11 in (approx)
The measurement that, in inches, comes closest toward the length equal of a square tile is: 11 in.
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Choose the correct statement.
O-2<-3
05>6
4>-4
O 0<-6
Step-by-step explanation:
here,
[tex] 4 > - 4[/tex]so the correct answer is this
A parallelogram has vertices at (1, 3) , (1, 7) , and (4, 6) as shown. What is the point of the fourth vertex?
Answer:
(4,2)
Step-by-step explanation:
b. What is the distance between points K and L? Show your work.
c. Is JKL an equilateral triangle? Explain.
b. The distance between points K and L is 10 units.
c. ΔJKL is not an equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
Given points as:
J (-5,-3)
K (1,5),
L (7,-3)
b. To determine the distance between points K and L, we can use the distance formula:
distance = √(x₂ – x₁)² + (y₂ – y₁)²
Substituting the coordinates of K and L, we get:
distance = √((7 - 1)² + (-3 - 5)²)
distance = √(36 + 64)
distance = √(100)
distance = 10
Therefore, the distance between points K and L is 10 units.
c. To determine if JKL is an equilateral triangle, we need to check if all three sides have the same length.
We can find the lengths of each side using the distance formula:
JK = √((1 - (-5))² + (5 - (-3))²) = √(6^2 + 8²) = 10
KL = 10 (as we found in part b)
LJ = √((-5 - 7)² + (-3 - (-3))²) = √((-12)²) = 12
Since all three sides have different lengths (JK and KL are 10 units, while LJ is 12 units), JKL is not an equilateral triangle.
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75x+30y=1500. Solve for x and y
For the equation 75x+30y=1500, x is (100 - 2y) / 5 and y is (100 - 5x) / 2.
Describe Equation?An equation is a mathematical statement that uses symbols and numbers to express a relationship between two or more variables. It states that two expressions are equal to each other.
We can solve for x and y in the equation 75x + 30y = 1500 by using algebraic manipulation.
First, we can simplify the equation by dividing both sides by the greatest common factor of 75 and 30, which is 15:
(75x + 30y) / 15 = 1500 / 15
Simplifying the left side gives:
5x + 2y = 100
Next, we can isolate one of the variables. Let's isolate y by subtracting 5x from both sides:
5x + 2y - 5x = 100 - 5x
Simplifying the left side gives:
2y = 100 - 5x
by dividing both sides by 2:
y = (100 - 5x) / 2
This is the equation for y in terms of x. We can use this equation to solve for y given a value of x, or we can substitute it back into the original equation to solve for x in terms of y.
Let's solve for x in terms of y by isolating x in the equation 5x + 2y = 100:
5x = 100 - 2y
Dividing both sides by 5 gives:
x = (100 - 2y) / 5
This is the equation for x in terms of y. We can use this equation to solve for x given a value of y, or we can substitute it back into the original equation to solve for y in terms of x.
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Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals. Determine the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament is 20.
What is a linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0.
In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
Here, we have
Given: Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals.
we have to determine the number of players the team can bring to the tournament.
So to make an equation, the bus charge would be the y-intercept (If no member went, they still paid for the bus fee) and the meals would be the slope (since it is dependent on how many members ride the bus.)
The total would add up to be 2412.50, so the equation would be:
2412.50 = 67x+1072.50
where x = the number of players the team can bring to the tournament without going outside of their budget.
After solving this, we get
2412.50 = 67x+1072.50
2412.50 - 1072.50 = 67x
1340 = 67x
x = 20
Hence, the number of players the team can bring to the tournament is 20.
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Another brand of sheets is on sale 30% off with a regular price of $18.00 per sheet. Which is a better deal, the previous example or this one? Explain.
The sale price per sheet in this example is $12.60.
What is the discount?
A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. It is a form of incentive that is used to encourage customers to purchase goods or services, often by making them more affordable or attractive.
To compare the two deals, we need to calculate the sale price per sheet for each deal.
In the previous example, the sale price per sheet was $15.00 after a 20% discount off the regular price of $18.00.
In this example, the sale price per sheet is 30% off the regular price of $18.00, so we can calculate the sale price per sheet as:
Sale price per sheet = Regular price per sheet - Discount amount
Sale price per sheet = $18.00 - (30% x $18.00)
Sale price per sheet = $18.00 - $5.40
Sale price per sheet = $12.60
Comparing the two deals, we can see that the sale price per sheet in this example is lower than the sale price per sheet in the previous example. Therefore, the better deal is the 30% discount off the regular price of $18.00, which results in a sale price per sheet of $12.60.
Therefore, the sale price per sheet in this example is $12.60.
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What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?
Answer:
Step-by-step explanation:
90 degrees is the answer because there is no movement
What is the surface area of this shape.
I will give brainliest
If you can please explain
The total surface area of the given solid is 256 inch²
Surface area:Surface area is the measure of the total area that the surface of an object occupies. It is usually expressed in square units, such as square meters, square centimeters, or square feet.
Here in this problem take the surface of the solid as the number of faces and calculate the area of each face as shown below.
Here we have
Solid box with dimensions 4 in, 5 in, and 8 in
The surface of the given solid can be divided as given in the picture
The surface area of the shape = Sum of areas of [ 1 to 12 faces ]
Area of (1, 2, 3, 7, 8, 9 faces ) = 6 (4 × 4 )= 96 inch²
Area of (4, 5, 6, 10, 11, 12 faces ) = 6 (5 × 4) = 120 inch²
Area of bottom = (8 × 5) = 40 inch²
Total Surface area = [ 96 + 120 + 40 ] = 256 inch²
Therefore,
The total surface area of the given solid is 256 inch²
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A trapezoidal flower garden is shown below. what is the area of the garden
The area of the trapezoidal flower garden from the dimensions is 123.5 square meters
What is the area of the gardenThe trapezoidal flower garden represents the given parameter, where we have the following readings
Parallel sides = 9 m and 10 m
Height = 13 m
Using the above dimensions, we have the area to be
Area = 1/2 * Sum of parallel sides * Height
When the dimensions are substituted, we have
Area = 1/2 * (9 + 10) * 13
Evaluate the products
Area = 123.5
HEnce, the area is 123.5 square meters
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The equation y equals 4 times 3 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 600
Answer: 8.2 weeks.
Step-by-step explanation: If y = 4*3^t, then 600 = 4*3^t. Therefore, t = log3 (600/4), which is approximately 8.2 weeks.
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Based on the information in the graph, we can infer that the length of Main St between 5th Ave. and 6th Ave. is 0.24km.
How to find the value of Main St between 5th Ave. and 6th Ave?To find the value of Main St. between 5th Ave. and 6th Ave we must perform the following mathematical procedure:
0.4 / x = 0.5 / 0.30.12 = 0.5 * xx = 0.24kmIn accordance with the above, what we did was a relationship between the fractions that represent the length of each street. In this case we had to clear the x that represented Main St. between 5th Ave. and 6th Ave.
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5. In each of the following figures, AB// CD. Find the value of the unknown.
Note: Don't give wrong answer. Give answer by step by step explanation
The values of the unknown in the figures are a = 40, b = 32 and c = 275
How to determine the values of the unknownFigure (a)
A quadrilateral has a total angle measure of 360 degrees.
So, we have
90 - a + 92 + 128 + 90 = 360
Evaluate the like terms
-a = 360 - 400
So, we have
a = 40
Figure (b)
The total measure of angles on a line is 180 degrees.
So, we have the following
4b - 10 + 2b - 2 = 180
Evaluate the like terms
6b = 192
So, we have
b = 32
Figure (c)
The total measure of angles at a point is 360 degrees
So, we have the following
c + 19 + (94 - 28) = 360
Evaluate the like terms
c = 275
Hence, the value of c is 275 degrees
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