The circumstance of a circle is 9pie cm. What is the diameter?
Describe the composition of an atom.
The atom consists of a tiny nucleus surrounded by moving electrons. The nucleus contains protons, which have a positive charge equal in magnitude to the electron's negative charge.
Jake bought the pizza shown above for lunch, which was cut into four equal slices. What percentage of the pizza did Jake eat if he had three slices?
A) 25%
B) 50%
C) 67%
D) 75%
the pic is below
What is the first step of rationalizing the denominator of 7√11√?
Final answer:
The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and denominator by the conjugate of the denominator.
Explanation:
The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of √11 is -√11. Therefore, we multiply both the numerator and denominator by -√11 to get:
7√11 * -√11 = -77
√11 * -√11 = -11
So, the rationalized denominator is -11. The denominator becomes -11, and the simplified expression is:
-77 / -11 = 7
Convert each unit of weight....5,500 Ib = ____T
Andrea wants to estimate the answer to this problem to see if her answer is reasonable. 7457 – 3908 Which expression shows these numbers correctly rounded to the nearest hundred? A. 7400 – 3900 B. 7500 – 3900 C. 7400 – 4000 D. 7500 – 4000
Glenn Andrews recently bought a new motorbike for $3,950. If he had to pay 6 percent sales tax on the bike, what was the total cost of the bike?
Anyone know this please and thank you
Translate this sentence into an equation.
33 is the product of Jenny's height and 3
Use the variable
to represent Jenny's height.
I WILL GIVE BRAINLIEST!!!!
Question 16 Unsaved
Which of the following statements is true?
Question 16 options:
-4.5 < -5.8
-3.4 > -4.2
0 < -8.5
3.9 < 1.3
What’s equivalent to 4/7 X 5/9? 5/9X4/7, 4/7 X 5/9, 4/9 X 5/7, 4/7 X 9/5 X=times
Find the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 if interest is compounded quarterly for five years
Final answer:
After rearranging the formula and solving for the interest rate, the required rate is found to be approximately 4.7%.
Explanation:
The subject of this question is finding the required annual interest rate that will grow a principal amount of $5,200 to $6,500 when compounded quarterly over five years. To solve this, we shall use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We are given:
A = $6,500
P = $5,200
n = 4 (since interest is compounded quarterly)
t = 5 years
We need to solve for r. First, we rearrange the formula to isolate r:
(1 + r/n) = (A/P)[tex]^({1/(nt))}[/tex]
Then we can insert our known values and solve for r:
(1 + r/4) = ($6,500/$5,200)^(1/(4*5))
Calculate the right-hand side:
(1 + r/4) = (1.25)[tex]^({1/20)}[/tex]
Find the 20th root of 1.25:
(1 + r/4) ≈ 1.01168
Subtract 1 from both sides:
r/4 ≈ 0.01168
Multiply both sides by 4:
r ≈ 0.04672
Convert the decimal to a percentage:
r ≈ 4.672%
Round to the nearest tenth of a percent:
r ≈ 4.7%
Therefore, the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 with interest compounded quarterly for five years is approximately 4.7%.
A high-speed elevator can rise 480 feet in 30 seconds. Which expression represents the rate, in feet per minute, of the elevator?
a- 480 × 30
b- 480 ÷ 30
c- 480 × 0.2
d- 480 ÷ 1/2
Please help me with this
Simplify this expression:
3 2/3x-4/5(x-3 3/4)
What the answer to simplifying( 6 to the power of negative 2) by (3 to the power of negative 3) and (3•6) to the power of 4
ABC is congruent to FGH, AB=8.3, BC=10.4, and CA=4.2. What is the measure of segment GH?
For a better understanding of the explanation provided here please go through the diagram in the attachment given below.
As we can see from the diagram of the congruent triangles ABC and FGH, the vertices A,B,C of [tex] \Delta ABC [/tex] correspond to the vertices F,G,H of [tex] \Delta FGH [/tex], so the corresponding sides must correspond too. Thus, AB corresponds to FG, BC corresponds to GH and CA corresponds to GF.
Now, we know that BC=10.4. Therefore, it's corresponding side GH must be 10.4 too because they are corresponding sides of a congruent triangle.
Thus, GH=10.4 is the correct answer.
the long leg of a 30-60-90 triangle is 11√3. what is the length of the hypotenuse?
A town doubles its size every 22 years. If the population is currently 4,500, what will the population be in 88 years?
two triangles are similar, and the ratio of the lengths of each pair of corresponding sides is 2:1. which statement regarding the two triangles is NOT True?
A- Their corresponding angles have a ratio of 2:!
B- Their areas have a ratio of 4:1
C- Their perimeters have a ratio of 2:!
D- Their altitudes have a ratio of 2:!
All statements are true. Ratio of corresponding angles, areas, perimeters, and altitudes is 2:1. No false statement exists.
To determine which statement regarding the two triangles is NOT true, let's analyze each option step by step.
Given:
- Two triangles are similar.
- The ratio of the lengths of each pair of corresponding sides is 2:1.
Let's denote the lengths of corresponding sides in the first triangle as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], and in the second triangle as [tex]\( 2a \)[/tex], [tex]\( 2b \)[/tex], and [tex]\( 2c \),[/tex] respectively.
A. Their corresponding angles have a ratio of 2:1.
- This statement is true because corresponding angles in similar triangles are congruent, so their ratios would indeed be 2:1.
B. Their areas have a ratio of 4:1.
- The area of a triangle is proportional to the square of the length of its sides. So if the ratio of the lengths of corresponding sides is 2:1, the ratio of their areas would be [tex]\( (2:1)^2 = 4:1 \)[/tex]. Hence, this statement is also true.
C. Their perimeters have a ratio of 2:1.
- The perimeters of triangles are directly proportional to the lengths of their sides. Since the ratio of the lengths of corresponding sides is 2:1, the ratio of their perimeters would indeed be 2:1. So, this statement is also true.
D. Their altitudes have a ratio of 2:1.
- The ratio of the altitudes of two similar triangles is equal to the ratio of their corresponding sides. So, if the ratio of corresponding sides is 2:1, the ratio of their altitudes would also be 2:1. Therefore, this statement is true.
Since all the statements are true, the correct answer is NONE.
How to make a box and whisker plot for 21,21,22,20,13,13,27,24
What is the slope of a line that is parallel to y=5x+3
What is 4,321,109,432 rounded to the nearest ten million?
A. 4,000,000,000
B. 4,320,000,000
C. 4,321,000,000
D. 4,322,000,000
Final answer:
The number 4,321,109,432 rounded to the nearest ten million is 4,320,000,000,hence the correct option is B.
Explanation:
To round the number 4,321,109,432 to the nearest ten million, we need to look at the digit in the ten million's place and the digit to the right of it, which are 3 and 1, respectively. The rule for rounding is that if the digit to the right is 5 or greater, we round up.
In this case, the digit is 1, so we do not round up and the ten million's place remains unchanged.
Therefore, the answer is 4,320,000,000 (Option B), as every digit after the ten million's place is replaced with zero.
A triangle has two sides that are perpendicular. Could the triangle be isosceles equilateral or scalene? Explain
Final answer:
A triangle with two perpendicular sides could be scalene or isosceles if the non-perpendicular sides are unequal or equal, respectively. It cannot be equilateral because equilateral triangles have no right angles.
Explanation:
If a triangle has two sides that are perpendicular to each other, it could potentially be a scalene or isosceles triangle, but it cannot be equilateral. When two sides of a triangle are perpendicular, they form a right angle. Thus, if a triangle has a right angle, it is a right triangle by definition. According to Theorem 2, if two angles of a triangle are equal, the opposite sides are equal, and the triangle is isosceles.
In our case, this theorem would apply if the two non-perpendicular sides are of equal length, resulting in an isosceles right triangle. On the other hand, Theorem 3 states that in a triangle with unequal angles, the side opposite the greater of the angles is greater than the side opposite the smaller. Therefore, if the sides forming the right angle are of different lengths, the triangle would be scalene.
I think the answer is C but I’m not sure. Plz help me out
Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, how much longer is the second rectangle's perimeter? 3 times as long 6 times as long 9 times as long 6 inches longer
Answer:
Option a.
Step-by-step explanation:
Two rectangles are similar. Height of one rectangle is 3 inches and height of second rectangle is 9 inches.
Let width of rectangles are x inches and y inches.
Then width of the second rectangle will be in the same ratio as of their heights.
[tex]\frac{x}{y} =\frac{3}{9}[/tex]
[tex]\frac{x}{y} =\frac{1}{3}[/tex] ⇒ x = [tex]\frac{y}{3}[/tex]
Now perimeter of first rectangle P₁ = 3 + 3 + x + x = 2x + 6
Perimeter of second rectangle P₂ = 9 + 9 + y + y = 18 + 2y
Ratio of P₁ and P₂ = [tex]\frac{2x+6}{18+2y}[/tex]
= [tex]\frac{2(\frac{y}{3})+6}{18+2y}[/tex] [as [tex]x=\frac{y}{3}[/tex]]
= [tex]\frac{\frac{(2y+18)}{3} }{(18+2y)}[/tex]
= [tex]\frac{2y+18}{3(18+2y)}[/tex]
Ratio of P₁ and P₂ = ([tex]\frac{1}{3}[/tex]) ⇒ P₂ = 3P₁
Therefore, Option a is the answer.
name each angle in four ways. then classify each angle as acute, right, obtuse, or straight.
In this geometric scenario, angles are named and classified. Angle 1 is a right angle, angle 3 is a straight angle, angles 2 and 6 are obtuse, while angles 4 and 5 are acute.
Let's name each angle in four ways and classify them:
Angle ABC (B is 90 degrees):
1 (as labeled)
∠ABC (using the vertex B)
∠CBA (using the vertex C)
∠1 (angle 1)
Classification: Right angle
Angle DEF (E is also labeled as 2):
2 (as labeled)
∠DEF (using the vertex E)
∠FED (using the vertex F)
∠2 (angle 2)
Classification: Obtuse angle
On line LN with point M (labeled as 3):
3 (as labeled)
∠LNM (using the vertex N)
∠MNL (using the vertex M)
∠3 (angle 3)
Classification: Straight angle
Angle XYZ (Y is also labeled as 4):
4 (as labeled)
∠XYZ (using the vertex Y)
∠ZYX (using the vertex Z)
∠4 (angle 4)
Classification: Acute angle
Angle KLM (L is also labeled as 5):
5 (as labeled)
∠KLM (using the vertex L)
∠MLK (using the vertex M)
∠5 (angle 5)
Classification: Acute angle
Angle RSP (S is also labeled as 6):
6 (as labeled)
∠RSP (using the vertex S)
∠PSR (using the vertex P)
∠6 (angle 6)
Classification: Obtuse angle
So, to summarize:
Right angle: 1
Obtuse angles: 2, 6
Straight angle: 3
Acute angles: 4, 5
To know more about angle:
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the midpoint od EF is point P at (-6 -2). If point E is at (2,-4), what are the coordinates of point F
a rectangular deck has a area of 320 ft squared. the length of the desk is 4 feet longer than the width. find the dimensions of the desk. Solve by completing the square.
The price of oil recently went from $7.80 to$10.40 per case of quarts. Find the ratio of the increase in price to the original price.
what formulas could be used to determine the surface area of a cylinder sandwiched between one cone and half of a sphere?
To find the surface area of a cylinder sandwiched between one cone and half of a sphere, use the sum of the cylinder's lateral surface area, the cone's lateral surface area, and half the sphere's surface area. The formula is 2πrh + πrl + 2πr², excluding the base areas where the shapes intersect.
To determine the surface area of a cylinder sandwiched between one cone and half of a sphere, you should first consider the formulas for the surface area of these individual shapes. The shapes consist of simple geometrical forms: a cylinder, a cone, and a sphere. The surface area of these shapes can be described with established formulas within the geometry:
Cylinder: The surface area of a cylinder (excluding the ends) is calculated by multiplying the perimeter of the base circle (which is 2πr, where r is the radius) by the height h of the cylinder plus the area of the two circles (2πr²). This gives: 2πrh + 2πr².Cone: The surface area of a cone is the sum of the area of its base (πr²) and the lateral surface area, which is πr times the slant height. However, if the cone is placed on one end of the cylinder and they share a base, you do not need to calculate the area of the base since it is covered by the cylinder. You would just need the lateral surface area of the cone (πrl, where l is the slant height).Sphere: Half of the surface area of a sphere is 2πr² since the full surface area is 4πr².Therefore, the final formula to calculate the total surface area of the described complex shape is the sum of the surface area of the lateral side of the cylinder, the lateral surface area of the cone, and half of the surface area of the sphere. This could be written as:
Total Surface Area = 2πrh + πrl + 2πr².
Note that you would omit the area of the circle that is common between the cylinder and the cone, as well as the area that is common between the cylinder and the half-sphere, since they are internall and not part of the external surface area.