Using the concept of similar triangles, the length of the other two sides of triangle B are: 20 cm and 25 cm
How to find the lengths of similar triangles?Similar triangles are defined as triangles that possess the same shape, but then their sizes may very well vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.
Since the shortest side of triangle B is 10cm, it means that it corresponds to the shortest side of triangle A which is 8 cm.
Thus:
Ratio of corresponding sides of B:A = 10/8
Thus:
Second side of triangle B: (10/8) = (x/16)
x = 160/8
x = 20 cm
Third side of triangle B: 10/8 = y/20
y = 200/8
y = 25 cm
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What is the y-intercept of the line of fit?
b=?
m=5
The y-intercept of the line of best fit is: y = 20
What is the y-intercept?The formula for equation of a line of best fit is:
y = mx + c
where:
m is slope
c is y-intercept
Now, the y-intercept is simply defined as the point where the line crosses the y-axis.
In this case, the line crosses the y-axis at y = 20.
Thus, we can conclude that it is the y-intercept
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Here is part of a field.
11m
10m
Does he have enough fence?
You must show all your working.
18m
Diagram NOT
accurately drawn
This part of the field is in the shape of a trapezium.
A farmer wants to put a fence all the way around the edge of this part of the field.
The farmer has 50m of fence.
netflix has a membership plan in which a person pays a flat fee of $10 plus $2 for each movie rented. Non members pay $4.50 for each movie rented. write a system of equations for each plan
A teacher was interested in the cafeteria food that students preferred in a particular school. She gathered data from a random sample of 200 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for her data?
Stem-and-leaf plot
Line plot
Box plot
Answer:
A stem-and-leaf plot is a graphical representation of a dataset where the numbers are separated into two parts: the stem (the leftmost digit or digits) and the leaf (the rightmost digit). The stem values are listed vertically and the corresponding leaf values are listed to the right of the stem in a row. This type of plot allows for quick and easy data analysis, as it shows the distribution of the data and provides information about the frequency and range of the values. It is particularly useful for smaller datasets and can be easily constructed by hand or with software.
find the surface area of the pyramid. round to the nearest whole number. a=20 b=20 c=7 d=7
Answer:
569 square units
Step-by-step explanation:
You want the surface area of the 8-sided shape that has a square "base" 7 units on a side, and a "height" of 20 units.
Slant heightThe slant height of each triangular face is the hypotenuse of a right triangle with legs 7/2 units and 20 units. That height is ...
h = √(3.5² +20²) = √412.25 ≈ 20.304 units
Surface areaThe area of one triangular face is ...
A = 1/2bh
A = 1/2(7)(20.304) . . . one face
There area 8 congruent triangular faces, so the total area is ...
A = 8(1/2)(7)(20.304) = 8(7)√412.25 ≈ 568.51 ≈ 569
The total surface area is about 569 square units.
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Please help I need this asap
The inequality given that the function f is increasing over it s domain
f(x²-2)<f (7x-8), Df = (-∞,2) is: x ∈ (-∞,1) U (6,2).
What is the inequality?We know the values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).
f (x²-2) = f (7x-8)
So,
x²-2 = 7x-8
Simplify and find x
x² - 7x + 6 = 0
(x - 1)(x - 6) = 0
x = 1 or x = 6
The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:
For x < 1:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
For 1 < x < 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) > 0
For x > 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).
Therefore the inequality is x ∈ (-∞,1) U (6,2).
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Please help !!!!!!!!!!!!!!!!
length LD = 6 units
length DF = 9 units
length HF = 6 units
length LH = 9 units
length L'D' = 2 units
length D'F' = 3 units
length H'F' = 2 units
length L'H' = 3 units
What is dilation?Dilation is the scaling of an object, where it gets bigger or smaller.
Scale factor = new dimension/old dimension
length LD = 15-9 = 6units
length DF = 6-(-3) = 9units
length HF = 15-9 = 6 units
length LH = 6-(-3) = 9 units
Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.
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What function is represented in the graph?
Select one:
У = 3(4^x)
y = 4(3^x)
y = 4(.25)^x
y = 2(.25^x)
Answer:
The correct function is y = 4(.25^x).
Determine whether the pairs of vectors is orthogonal
No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.
What is the dot product of the pair of vectors?The dot product will help us to determine if the pair of vectors are orthogonal or not.
If the dot product is equal to zero, then the pair of vectors are orthogonal.
The dot product of the vectors is calculated as follows;
(3i - 8j).(8i - 3j)
= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)
= (24) - (0) - (0) + (24)
= 24 + 24
= 48
So the pairs of vectors are not orthogonal.
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Please help its due soon
The ratio of sec θ is determined as 5/3.
option A.
What is the ratio of secθ?The ratio is sec θ is calculated by applying the following method;
sec θ = 1/cosθ
Given that tanθ = -4/3 = oppo/adjacent
The hypotenuse side is calculated by applying Pythagoras theorem as shown below;
h = √ 4² + 3²
h = 5
The ratio of sec θ is calculated as follows;
sec θ = 1/cosθ
1/cosθ = 1/(3/5)
1/cosθ = 5/3
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Find the area of a circle and use 3.14 for pi
The area of the shaded region of a circle with a 100 degree angle and a radius of 3cm, using pi=3.14, is approximately 25.64 square centimeters.
To find the area of the shaded region of a circle, we need to subtract the area of the sector formed by the shaded region from the area of the whole circle.
The area of the whole circle is given by
A = πr²
where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14 (as given in the question).
Substituting the given values, we get
A = π(3cm)²
A = 28.26 cm² (rounded to two decimal places)
Now, let's find the area of the sector formed by the shaded region.
The angle of the sector is given as 100 degrees. To find the area of the sector, we need to use the formula:
A = (θ/360)πr²
where θ is the angle in degrees, r is the radius of the circle, and π is again approximately equal to 3.14.
Substituting the given values, we get
A = (100/360)π(3cm)²
A = 2.62 cm² (rounded to two decimal places)
Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the whole circle
Shaded area = Area of circle - Area of sector
Shaded area = 28.26 cm² - 2.62 cm²
Shaded area = 25.64 cm² (rounded to two decimal places)
Therefore, the area of the shaded region of the circle is approximately 25.64 square centimeters.
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--The given question is incomplete, the complete question is given
" Find the area of a shaded region of circle and use 3.14 for pi "--
Find the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 4 3 x . Show your work.
The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).
What is the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 43x?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line has a slope of 43.
To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.
So, the slope of the perpendicular line is -1/43.
Using the point-slope form of a line, we can write the equation of the line as:
y - y1 = m(x - x1),
where (x1, y1) = (4, 2) and m = -1/43
Plugging in the values, we get:
y - 2 = (-1/43)(x - 4)
y - 2 = (-1/43)x + (4/43)
y = (-1/43)x + (4/43) + 2
y = (-1/43)x + (90/43)
Therefore, the equation of the line is y = (-1/43)x + (90/43).
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25 pounds each. The small boxes weigh 50 pounds each. There are 105 boxes in all. if the truck is carrying a total of 3,875 pounds in boxes, how many of each type of box is it carrying?
Use the trapezoid shown to new each statement below as true or false, if false rewrite the statement correctly in the space below the statement.
Note that the perimeter of the trapezoid shown is 23 units. Thus, the statement is false.
How so you arrive at that?To derive the perimeter we must know the following:
a = base = 5
b = base = 8
d = side = 4
c is the hypotenuse" = (h x base of the right triangle) = (4x3)/2 = 6
Thus, Perimeter of the trapezoid = a + b + c + d =
5 + 8 + 4 + 6
= 23 units.
Thus, the statement that the perimeter of the trapezoid shown is 22 units is false.
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Full Question>
Use the trapezoid shown to mark each statement below as true or false. if false, please rewrite the statement correctly in the space below the statement!
Q: The perimeter of the trapezoid shown is 22 units.
True false?
I don't get it, pls help!!
The circumference of the circle is 75.4 cm.
What is the circumference of the circle?The circumference of the circle is calculated from the radius of the circle.
Considering the equilateral triangle, each of the interior angle is 60⁰, a line passing the center of any of this angle, divides it into two with each angle 30⁰.
Considering the right triangle inside the equilateral triangle, the hypothenuse is equal to the radius of the circle.
The radius of the circle is calculated as follows;
sin (30) = opp/hypo
sin (30) = 6 cm/r
r = 6 cm / sin (30)
r = 12 cm
The circumference of the circle is calculated as follows;
C = 2πr
C = 2π x (12 cm)
C = 75.4 cm
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The graph below shows a company's profit tox), in dollars, depending on the price of erasers x, in dollars, sold by the company
300+10x)
270
240
210-
180
150
120
90
60
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x-1 tox-4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
How to explain the informationThe function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5
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geometry please help
A graph of triangle CAT is shown below.
A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.
ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (x, -y)
C (-1, 2) → (-1, -(2)) = C' (-1, -2)
A (-1, 4) → (-1, -(4)) = A' (-1, -4)
T (3, 2) → (3, -(2)) = T' (3, -2)
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help me please fr i just need these questions
a) The base area of the cylinder is given as follows: 78.54 ft².
b) The height of the cylinder is given as follows: 2 ft.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The base area is given as follows:
Ab = πr².
Considering the radius of 5 ft, the base area is of:
Ab = 3.1416 x 5²
Ab = 78.54 ft².
Considering the volume of 157.08 ft³, the height of the cylinder is obtained as follows:
78.54h = 157.08
h = 157.08/78.54
h = 2 ft.
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Please help me asap need to get it done MANY POINTS WILL BE GIVEN
Answer:
Step-by-step explanation:
1. The line of best fit must have an equal number of points above and below the line
2. The line of best fit could be used as a predictions showing a trend in data
The line 3x+5y = 10 is dilated by a scale factor of 3. What is the equation of the dialted line
The equation of the dilated line is 9x + 15y = 10.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:
(x, y) → (SFx, SFy)
Where:
x and y represents the data points.SF represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (3x, 3y)
3(3x + 5y) = 10
9x + 15y = 10.
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Michael checked several websites and stores around town for the television he wanted to purchase. He saw eight different prices: $273 $267 $276 $297 $264 $294 $264 $269 What is the mean, median, and mode of this data set?
The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.
Understanding how to calculate mean, median, modeBy definition:
Mean is the sum of all the numbers in the set divided by the total number of numbers.
Median is the middle value in the set when the numbers are arranged in order.
Mode is the number that appears most frequently in the set.
If we re-arrange the data given in ascending order, we have:
264 264 267 269 273 276 294 297
To calculate Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8
Mean = 270.75
To calculate Median:
We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:
Median = (269 + 273) / 2
Median = 271
To calculate Mode:
We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.
Mode = 264 and 294
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
V = π(19.1^2)(11.8) = 13,523.8 cubic mm
V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm
Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
Answer:
The answer should be 1,260
Answer:
75
Step-by-step explanation:
.
PLEASE HELP FAST!
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has an ODD number.
Event B: The marble selected has a number from 3 to 6.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
The possible outcomes for each of the given events are:
A {1, 3, 5, 7}
B {3, 4, 5, 6}
How to identify the outcomes for the events?The possible outcomes for the experiment are {1, 2, 3, 4, 5, 6, 7, 8}.
The two given events are:
A "The marble selected is an odd number"
The outcomes for this event are the odd numbers that are outcomes for the experiment, then the outcomes here are {1, 3, 5, 7}
The second event is:
B "The marble selected has a number from 3 to 6."
The possible outcomes here are {3, 4, 5, 6}
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The diamond suit from a standard deck of cards are taken out. You draw 2 cards from only the diamonds. What are the chances that you draw a king on your first draw and an ace on your second?
Answer:
There are 13 diamonds in a deck of cards, including one king and one ace.
The probability of drawing a king on the first draw is 1/13, since there is one king among 13 diamonds.
Assuming that the king is not replaced, there are now 12 diamonds left, including one ace. The probability of drawing an ace on the second draw is 1/12, since there is one ace among 12 diamonds.
The probability of drawing a king on the first draw and an ace on the second draw is the product of these probabilities:
P(king first, ace second) = P(king first) * P(ace second|king first not replaced)
P(king first, ace second) = (1/13) * (1/12)
P(king first, ace second) = 1/156
Therefore, the chances of drawing a king on your first draw and an ace on your second draw, when drawing 2 cards from only the diamonds, is 1/156.
Step-by-step explanation:
Branliest please
What are the solutions of 3x^2- x +7=0?
O A. x =
о
B. x =
O C. x =
2-9i
2+9i or x = 2-⁹⁰
6
6
1+iv83 or x =
6
-i√/83
6
1+9i
1-9i
¹+9 or x = 1-⁹
O D. x = 2+√83 or x = 2-i√/83
6
6
Answer:
x = (1 +i√83)/6 or x = (1 -i√83)/6
Step-by-step explanation:
You want the solutions to the quadratic equation 3x² -x +7 = 0.
Quadratic formulaThe solutions to the equation ax² +bx +c = 0 are given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The given equation has a=3, b=-1, c=7, so the solutions are ...
[tex]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}[/tex]
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A middle school took all of its 6th-grade students on a field trip to see a play at a theater that has 3260 seats. The students filled 95% of the seats in the theater. How many 6th graders went on the trip?
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
We have,
If 95% of the 3260 seats in the theater were filled by the 6th-grade students,
We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:
Number of 6th graders = 3260 x 0.95
Number of 6th graders = 3097
Therefore,
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
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full method please
4×(2-6)+35÷(-7)
Answer:
-21
Step-by-step explanation:
4×(-4)+35÷(-7)
Plus and minus together makes minus
Multiplication and division goes first
-16-5= - 21
I need help with math!!!
Please answer this question (picture is provided with question) I just need to find the area.
The value of area of the figure is,
⇒ 10√10 units²
We have to given that;
To find the area of figure.
Here, We have to find length of AD and AB for area of figure.
Coordinate of A = (- 2, 2)
Coordinate of B = (- 4, -4)
Coordinate of D = (3, 2)
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, Length of AD;
AD = √ (-2 - 3)² + (2 - 2)²
AD = √25
AD = 5
Length of AB;
AB = √ (- 2 + 4)² + (2 + 4)²
AB = √4 + 36
AB = √40
AB = 2√10
Thus, The value of area of the figure is,
⇒ AD x AB
⇒ 5 × 2√10
⇒ 10√10
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Kendra is doing her math homework. For each problem, she uses 12
1
2
of a sheet of paper. How many sheets of paper will she need to complete 10 problems?
There are 5 sheets of paper will she need to complete 10 problems.
We have to given that;'
Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.
Hence, For complete 10 problems, number of sheets are,
⇒ 1/2 of 10
⇒ 1/2 x 10
⇒ 5
Thus, There are 5 sheets of paper will she need to complete 10 problems.
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