A square can be divided into two right-angled triangles with one line, but it can't be divided into two obtuse triangles because none of the angles in a square is more than 90 degrees.
Explanation:
No, it is not possible for Kateri to divide the square into two obtuse triangles by drawing just one line. An obtuse triangle is a triangle that has an angle greater than 90 degrees. However, a square is made up of four 90-degree angles. Therefore, when a square is divided into two triangles with one line, the maximum degrees any angle in resulting triangles would get is 90, hence they would be right-angled triangles and not obtuse triangles.
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The formula to find the perimeter of a regular polygon is P = n × s. This means that you multiply the number of sides times the length of each side. Which polygon will have the greatest perimeter? A. a hexagon with each side 3 cm B. a square with each side 5 cm C. a triangle with each side 7 cm D. a pentagon with each side 4 cm
Sum or product of a nonzero rational number and an irrational number is always_____
A. rational,
B. irrational,
C. a repeating decimal,
D. a fraction
A biologist wants to estimate the median width of over 200 oak trees in a forest. Ten trees were selected at random, and their widths, in centimeters, were recorded. 63, 59, 12, 43, 71, 35, 28, 52, 47, 26 What is the estimated median width of all oak trees in the forest? Enter your answer in the box.
Answer:
45
Step-by-step explanation:
The estimated median width of all oak trees in the forest is 45 centimeters.
How to calculate the median width?
To estimate the median width of all oak trees in the forest, we can use the sample of ten trees that were selected at random.
First, we need to order the sample from smallest to largest:
12, 26, 28, 35, 43, 47, 52, 59, 63, 71
The median is the middle value in the ordered list. In this case, there are ten numbers in the list, so the median is the average of the fifth and sixth numbers:
median = (43 + 47) / 2 = 45
Therefore, the estimated median width of all oak trees in the forest is 45 centimeters.
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the expression (x+a)(x+b) cannot be written as
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
What is the distributive property?The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
Using distributive property, we get
x(x+b)+a(x+b)
= x²+bx+ax+ab
= x²+x(a+b)+ab
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The expression (x+a)(x+b) can not be written as
a) a(x+b) + x(x+b)
b) x² + (a+b)x + ab
c) x² + abx + ab
d) x(x+a) + b (x+a)
Which expression best estimates
What value should go in the empty box to complete the calculation for finding the product of 23.456 × 0.86? 23.456 times 0.86 gives two partial products. The first is 140736, and the second is unknown. 1,576,480 1,623,392 1,876,480 1,923,392
The rabbit population in a certain area is 500% of last year's population. There are 900 rabbits this year. How many were there last year?
Answer:
180
Step-by-step explanation:
we got the same qustion and i just got this wrong
The gear ratio describes the ratio of one gear's diameter to another gear in the same chain. The gear ratio between two specific gears is 3 to 2. If the diameter of the larger gear is 18 cm, what is the diameter of the smaller gear?
A. 24 cm B. 18 cm
C. 12 cm D. 6 cm
The perimeter of a quarter circle is 32.13 what is the quarter circles radius
Follow below steps:
The problem involves finding the radius of a quarter circle given its perimeter. The perimeter of a full circle is known as its circumference, represented by the formula C = 2πr for a circle of radius r. However, for a quarter circle, only 1/4 of this circumference plus twice the radius (the straight sides of the quarter circle) constitutes the perimeter. Therefore, the perimeter (P) can be expressed as P = (πr)/2 + 2r.
Given that the perimeter is 32.13, we use the formula to set up the equation 32.13 = (πr)/2 + 2r. To solve for r, combine the like terms to get (2 + π/2)r = 32.13 and then isolate r by dividing both sides of the equation by (2 + π/2). Using the approximate value of π = 3.14159, you continue with the arithmetic to find the exact value of the radius.
Remember that precision is important in mathematics. When providing an answer, consider the number of significant figures supplied in the given data and maintain the same level of precision in the final answer.
The radius of the quarter circle is 20.48 units.
To find the radius of a quarter circle given its perimeter, we can start by understanding the formula for the perimeter of a circle.
The perimeter of a full circle is given by [tex]\( P = 2\pi r \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle. Since we are dealing with a quarter circle, the perimeter would be one-fourth of the perimeter of a full circle.
The radius of the quarter circle as [tex]\( R \)[/tex]. Then, the perimeter of the quarter circle is [tex]\( \frac{1}{4} \times 2\pi R = \frac{\pi R}{2} \)[/tex].
The perimeter of the quarter circle is 32.13 units, we can set up the equation:
[tex]\[ \frac{\pi R}{2} = 32.13 \][/tex]
To solve for [tex]\( R \)[/tex], isolate it by multiplying both sides of the equation by [tex]\( \frac{2}{\pi} \)[/tex]:
[tex]\[ R = 2 \times \frac{32.13}{\pi} \][/tex]
[tex]\[ R \approx 20.48 \][/tex]
Write the slope-intercept form of an equation of the line that passes through (2,-4) and (0,6)
we know that
the equation of the line in the slope-intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope of the line
b is the y-intercept of the line
Let
[tex]A(2,-4)\\B(0,6)[/tex]
Step [tex]1[/tex]
Find the slope of the line AB
the slope between two pints is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
substitute the values
[tex]mAB=\frac{(6+4)}{(0-2)}[/tex]
[tex]mAB=\frac{(10)}{(-2)}[/tex]
[tex]mAB=-5[/tex]
with the slope m and the point B find the value of b
[tex]B(0,6)[/tex]
[tex]6=-5*0+b[/tex]
[tex]b=6[/tex]
Find the equation of the line
[tex]y=mx+b[/tex]
[tex]y=-5x+6[/tex]
therefore
the answer is
[tex]y=-5x+6[/tex]
Anyone please help if u know how to do this
The medicine capsule shown consists of a cylinder with a hemisphere at each end. The total length of the capsule is 15 millimeters. The diameter is 5 millimeters. Which choice is the best approximation of the total surface are of the capsule? Usa 3.14 to approximate pi.
Answer 236 square millimeters
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Rewrite the given expression in the form 2^u where u is a constant or an algebraic expression.
1/2^5 = ? (Put the answer in exponential notation.)
To rewrite 1/2^5 in exponential notation, remember that 1/2^5 is the same as 2^-5. Therefore, 1/2^5 = 2^-5.
Rewrite the given expression in the form 2u where u is a constant or an algebraic expression.
To rewrite 1/25 in exponential notation, we need to understand that 1/25 is the same as (2-1)5. Using the property of exponents, we can rewrite this as 2-5, where -5 is the new exponent.
Therefore, 1/25 = 2-5, where u = -5.
how can you tell if radicals are like radicals
Answer and step-by-step explanation:
Like radicals have the same root (square root, cubed root, etc.) and the same expression under the radical sign.
In order to determine if two radicals are like, simplify both and then check both the root and the expression under the radical sign.
What is the solution to this equation?
–5(s – 30) = –10
If RS//MN ,then the value of a is
Please help me!!! Zoom in on picture to read the other 2 questions. 1 questions if on 2 parts of the collage.
Ferris wheel is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270° about the origin?
Answer:
1. option A is correct i.e., [tex]\(90^{\circ}[/tex].
2. option B is correct.
3. the coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Step-by-step explanation:
1. The angle of rotation is [tex]\(90^{\circ}[/tex].
To calculate the angle of rotation we can use a protractor and measure the angle between two corresponding angles, using point C as a center.
2. Given: ΔPRS with coordinates P(-3,2), R(2,5) and S(0,0) is rotated through an angle of 270°, the new image will be as follows;
The formula for rotation through 270° is: (x,y) → (y,-x)
hence our image will be at point:
P(-3,2)→P'(2,3)
R(2,5)→R'(5,-2)
S(0,0)→S'(0,0)
from the above, the approximate image will be option B.
3. Given: Ferris wheel is drawn on a coordinate plane at the point P(30,0). The coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Because the formula for rotation through 270° is: (x,y) → (y,-x).
So, point P(30,0)→P'(0,-30).
Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck.
How do you calculate the volume of a cone when given the height and diameter? Describe the steps used to solve.
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
Answer:
Step-by-step explanation:
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
In the diagram below, AC is perpendicular to BD. Find X.
Answer: The correct option is
(D) 17.5.
Step-by-step explanation: Given that in the diagram shown, AC is perpendicular to BD, where
[tex]m\angle BEC=(6x-15)^\circ,\\\\m\angle AED=(3y+12)^\circ.[/tex]
We are to find the value of x.
Since AC is perpendicular to BD and they are intersecting each other at the point E.
So, all the four angles made by this intersection are right angles.
That is, angle BEC is also a right angle.
Therefore, we get
[tex]m\angle BEC=90^circ\\\\\Rightarrow (6x-15)^\circ=90^\circ\\\\\Rightarrow 6x-15=90\\\\\Rightarrow 6x=105\\\\\Rightarrow x=\dfrac{105}{6}\\\\\Rightarrow x=17.5.[/tex]
Thus, the required value of x is 17.5.
Option (D) is CORRECT.
Can you Answer the question
A cylinder has a radius of 4 feet and a height of 3 feet. What is the volume of the cylinder to the nearest tenth 3. Use 3.14 to approximate π
Answer:
70Pi ft2
Step-by-step explanation:
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Matt has a quiz every 6th day of class, and Meg has a quiz every 3rd day of class. When will they have a quiz on the same day?
The correct answer is:
The 6th day.
Explanation:
To solve this, we find the least common multiple (LCM) of 3 and 6. We find the prime factorization of each number:
3 = 3×1
6 = 2×3
We multiply the common factor, 3, by the uncommon factors, 2 and 1:
3×2×1 = 6
The LCM is 6; this means they will both have a quiz on the 6th day.
a cylinder is 8 inches high. The circumference of the base 6pi inches. Find the volume
If you work for an hourly wage, your gross pay is a function of the number of hours that you work. If you earn $8 per hour, complete the following table:
Number of Hours
0
3
5
7
10
12
Gross Pay
If you were to plot the ordered pairs on a set of axes, in which quadrant would the domain and range of the function lie?
a.
8, 16, 24, 32, 40, 48; Quadrant I
b.
0, 24, 40, 56, 80, 96; Quadrant II
c.
8, 16, 24, 32, 40, 48; Quadrant II
d.
0, 24, 40, 56, 80, 96; Quadrant I
Answer:
D is the answer
Step-by-step explanation:
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A box is in the shape of a right rectangular prism. The base of the box has an area of 15 square inches. The height of the box is 12 inches. What is the volume in cubic inches, of the box
An equation is shown below: 6(2x - 11) + 15 = 21 Write the steps you will use to solve the equation and explain each step.
The solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a mathematical equation:
6(2x - 11) + 15 = 21
DIstributive property:
12x - 66 + 15 = 21
Subtraction property:
12x -51 = 21
Add 51 on both side:
12x -51 + 51 = 21 + 51
12x = 72 (adding like terms)
x = 6 (divide by 12 on both side)
Thus, the solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.
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lugos and paschal each wrote an equation for the line that passes through (-3,2) and (6,8) lugos says the equation is y=2/3x+4 and paschal says the equation is 2x-3y=-12. who is correct? why do you say so?
I need desperate help
How many sides does a regular polygon have if each exterior angle has a measure of 15 degrees? (Show work!!)