The simplification of the ratio 1320 feet : 1 mile will be 1:4
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. The term ratio is a straight borrowing from the Latin word ratio. In Latin, ratio could imply everything from "reason" to "calculation" to "proportion," and it was this last meaning that was used to create the mathematical and English ratios.
Given taht we need to simplify the ratio 1320 feet : 1 mile
For simplifying ratios we need to convert the terms in same units
and we know that 1 mile = 5280 feet
So,
1320 feet : 1 mile can be written as 1320 feet : 5280 feet
The simplification wil be 1:4
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what is the volume of a solid with a radius of 12 and a height of 24
The volume of a solid of cylinder with a radius of 12 and a height of 24 is
3456[tex]\pi[/tex].
What is volume?Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.
Given that the cylinder with a radius of 12 and a height of 24.
Volume of a cylinder = [tex]\pi[/tex] r² h
Volume of a cylinder = [tex]\pi[/tex] (12)² × 24
Volume of a cylinder = [tex]\pi[/tex] ( 144 × 24)
Volume of a cylinder = [tex]\pi[/tex] (3456)
Therefore, the volume of cylinder is 3456[tex]\pi[/tex].
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If PS ≅ WX, then PS= WX
F. Reflexive
G. Symmetric
H. Definition of congruent segments
J. Transitive
two sheets of plywood are leaning up against one another, forming a small camping shelter. One sheet of plywood is 7 feet long and makes a 31 degree angle with the ground. The other sheet of plywood is 4 feet long. What is the approximate measure of the angle made between the two pieces of plywood.
The angle made between the two pieces of plywood found using the law of sines is approximately 85°
The law of sines states that the ratio of the sine of an angle to the length of the opposite side is the same for the three angles and sides of the triangle.
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]
The length of one plywood = 7 feet
The angle made by the 7 feet plywood with the ground = 31°
Length of the other sheet of plywood = 4 feet
Using the law of sines, we get;
sin(31)/4 = sin(B)/7
sin(B) = 7 × (sin(31)/4)
∠B = arcsine(7 × (sin(31)/4)) ≈ 64.33°
The angle between the two pieces of wood is therefore;
Angle = 180° - 31° - 64.33° = 85°
The measure of the angle formed between the two plywood is about 85°
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6. Find the area bounded by f(x) and the x-axis on the interval [0,pi]
f(x) = sin x + 1
The area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,pi]
What is a interval?
An interval is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbersGiven that:
x-axis on the interval [0,pi]
f(x) = sin x + 1
= integral 0 - integral π (sin x) dx + integral 0 - integral π (1) dx
= [- cos π + cos 0] + [π - 0]
= [-(-1) + 1 ] + π
= 2 + π
Therefore, the area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,π]
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I’m confused on this question
The adjacents angles are ∠ RTL and ∠ ETL, The obtuse vertical angles are ∠ RTL and ∠ STE, the two supplementary angles are ∠ NTE and
∠ NTR and angles supplementary to ∠ RTS is ∠ RTL
What are angles?The two rays intersecting at a common point makes an angle.
Given is a figure,
Adjacent Angels =
The angles having one arm in common are called adjacent angles.
Here, adjacents angles are ∠ RTL and ∠ ETL
Vertical angles =
A pair of angles that have the same vertex and are on opposite sides of two intersecting rays makes Vertical angles
Here, vertical angles are ∠ RTL and ∠ STE
Supplementary angles =
When the sum of two angles is 180°, then they are supplementary angles.
Here, supplementary angles are ∠ NTE and ∠ NTR
We see that, the angle supplement to ∠ RTS is ∠ RTL
Hence, the correct answers are, adjacents angles = ∠ RTL and ∠ ETL, The obtuse vertical angles = ∠ RTL and ∠ STE, the two supplementary angles = ∠ NTE and ∠ NTR and angles supplementary to ∠ RTS is ∠ RTL
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the ftoli (fundamental theorem of line integrals) says: (select all correct answers) group of answer choices none of these the work done by a gradient vector field is always zero. the work done by any vector field is independent of path. the line integral of a gradient vector field depends only on the initial and terminal points of the path. the work done by a gradient vector field is independent of path.
Fundamental Theorem of Line Integral, also called the Gradient theorem, tells us that line integrals through gradient fields are path independent and depend only on the initial and final values. correct answer is option 4 and 5
What does the Line Integrals Fundamental Theorem teach us?
In general, this theorem, like the Fundamental Theorem of Calculus, states that if we integrate a "derivative-like function" (f′ or f), the outcome depends only on the values of the original function (f) at the endpoints.
It is referred to be a conservative vector field if a vector field F is the gradient of a function, F=f.
The line integral of a gradient vector field depends only on the initial and terminal points of the path.
The workdone by gradient vector field is independent of path..
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A step that has a height of 6 inches. A ramp starts 5 feet away from the base of the step,making a 5.7 angle with ground. what can you say about the angle the ramp would make with the ground if the starts closer to the step?
Considering all the option and the question, We cannot determine anything about the angle is the right answer.
what is angle?An angle is a geometric shape that is formed by two rays that share a common endpoint, called the vertex.
what is vertex?The vertex of an angle is the common endpoint of the two rays that form the angle. The vertex is also sometimes called the "corner" of the angle.
It is not possible to determine whether the angle of the ramp will decrease or increase without more information. The angle of the ramp is determined by the slope of the ramp, which is the change in height divided by the change in distance. If the ramp starts closer to the step, it will have a different slope, and therefore a different angle, than if it starts 5 feet away from the base of the step.
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Find the slope of each line.
66) pls answer
Answer: The slope is 5/6
Answer:
5/6
Step-by-step explanation:
12. An antique painting is purchased in 1980 for $995. The value increases by 3.1% every
year. Determine the increase in value of the painting in the 6th year after it was pur-
(3)
chased. You must include an equation with your solution.
An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02
What is increase in value?Increased Value is the amount obtained after deducting the Base Value from the current assessed value.
Given that,
An antique painting is purchased in 1980 for $995 = P
The value increases by 3.1% every = r
r = 3.1%
r = 3.1/100
r = 0.031
As we know,
Value of painting after t years: [tex]P (1+r)^t[/tex]
So, after 6 years:
f(6) = [tex]995 (1+0.031)^6[/tex]
or, f(6) = [tex]995 (1.031)^6[/tex]
or, f(6) = 1195.0197
or, f(6) = 1195.02
Now, at t = 0, f(0) = 995
Thus, value increased by, f(6) - f(0)
= [1195.02 - 995]
= 200.02
Thus, increase in price since it purchased = $200.02
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Please Hurry
Complete the algebraic proof by identifying the reason for each statement.
In mathematics is an expression which is made up of variables and constants, along with algebraic operations
What is algebra explain with example?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.An algebraic equation is a mathematical sentence, when two algebraic expressions are related with an equality sign (=). For example, 3x+6 = 1 is an algebraic equation.Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.There are many laws which govern the order in which you perform operations in arithmetic and in algebra. The three most widely discussed are the Commutative, Associative, and Distributive Laws.Commutative Rule of Addition.Commutative Rule of Multiplication.Associative Rule of Addition.Associative Rule of Multiplication.Distributive Rule of Multiplication.x = 1
3(5x+1) = 13x + 5
3(5x) + 3(1)
15x + 3 = 13x + 5
-13x -13x
2x + 3 = 5
__-3__-3____
2x = 2
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You are starting a new job and are told that your pay will be $3 on the first day. Each day after that, your pay will double until you reach the amount of $96. Starting from the first day, on what day will you reach $96?
6th day
8th day
4th day
10th day
Answer:
A=3, b=2, t=0 to t=5, covering 6 days. $3, $6, $12, $24, $48, $96.
Step-by-step explanation:
A is the starting amount at t=0. b is the base, two because the amount doubles each day. b would be 3 if it tripled every day. t is the final day number, counting from zero.
Here is a shaded parallelogram inside a rectangle.
2x
5
12
W
The area of the parallelogram is (10x +50) cm².
Work out the length of the base of the parallelogram.
Answer:
8
Step-by-step explanation:
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. Y = x2, y = 5 x2 + 4.
The graph of the equation Y = x² and the 5x² + 4 is attached below.
Equation:
Equation is the combination of variables, numbers and constants.
Given,
Here we have to sketch the region enclosed by the given curves for the equations, Y = x² and Y = 5x² + 4.
Here we have to take some sample value for x to find the value of equations.
And then by using the values, we have to plot the graph through this.
x = -2, -2, 0, 1, 2
Then the corresponding value of y is calculated as,
=> x = -1 => y = 1
=> x = -2 => y = 4
=> x = 0 => y = 0
=> x = 1 => y = 1
=> x = 2 => y = 4
Similarly, the value of Y for the next equation is,
=> x = -2 => y = 24
=> x = -1 => y = 9
=> x = 0 => y = 4
=> x = 1 => y = 9
=> x = 2 => y = 24
Then the graph of the given equation is drawn as.
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If u + t = 5 and u-t=2, what is the value of
(u-t) (u²-1²)?
The value based on the given equation is 22.5
What is an equation?
In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
According to given info.
u + t = 5 ------(1)
u - t = 2 ------(2)
adding equation 1, 2 ;we get
2u = 7
u = 7/2
using value of u in any equation,
7/2 - t = 2
t = 3.5 - 2
t = 1.5
we need to find value of
(u-t) (u²-1²)
(3.5 - 1.5) (3.5² -1²)
2*(12.25 - 1)
2*(11.25)
22.5
Hence the value of the function is 22.5
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Write an expression equivalent to (2/5)x(2/5)x(2/5)x(2/5) using a positive exponent
Answer:
2/5^4
Step-by-step explanation:
2/5 is being multiplied four times
Jared also gathered data from a competing real estate broker's office. The competitor's sales were equal to the average
number of sales 8 months before Jared began gathering data and again 2 and 6 months after he began gathering data.
The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.
Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.
Real estate is any immovable property of this kind that has a stake in a piece of land, a building, or housing in general. It also includes the natural resources on the land, such as water, crops, minerals, and minerals.
How does this occur?
from a company real estate broker's office. The competitor's sales were equal to the average number of sales 8 months before jured began gathering data and again 2 and 6 months after he began gathering data. The relative minimum number of sales was lower than the relative minimum number of sales of Jared's office.
Use the sliders for a, b, c, and d to create a graph that could model the competitor's number of sales.
Graph is given below in Image.
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What color is the condensed water, also called condensation, that collects on the inside of the top cup?
When the coloured water evaporates and condenses on the inside of the top cup, there is no colour in the water on the inside surface of the cup.
As water molecules in the air cool, they slow down and combine into tiny droplets of liquid water. This process is called condensation. This happens when water molecules in the air touch the outside of a cold mug exposed to air.
Water vapour in the air is extracted by several techniques, such as cooling the air below the dew point, exposing the air to a desiccant, using membranes that allow only water vapour to pass, collecting the mist, or pressurizing the air. I can do it.
Common examples are water forming on the outside of a cold mug, or moisture forming on a car window on a cool night.
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Ayana is making 6 scarves that each require 114 yards of purple fabric and a certain amount of blue fabric. She will use 10 yards in all. Which equation can be used to determine how many yards of blue fabric, b, are needed for each scarf?.
each scarf's 0.4166 yards of blue scarf
What is the basic algebraic formula?
This problem can be solved using a straightforward algebraic equation. For each scarf, Ayana requires many yards of blue cloth.
When solving a straightforward equation, visualize the equals symbol (=) as the fulcrum or center of a balance.
What three sorts of equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
In order to answer this question, let's say that each scarf needs x square inches of purple fabric and y square inches of blue fabric.
A total of six scarves are reportedly required. It is assumed that a total of 10 yards of fabric—the combined amount of the purple and the blue fabrics—will be utilized.
So that we may solve this equation.
We use x and y as 6x and 6y as 6 scarves are needed.
10 yards of cloth were used in total (6x + 6y).
Next up It goes without saying that 1 yard of purple cloth is required for each and every scarf.
Therefore, a total of 6 * 1(1/4) yards is required for 6 scarves.
As a result, 6x becomes 6 * 1/4 yards.
This equates to 6 yards of purple material
We now solve for the required amount of blue cloth.
6y = 10 -30/4 = 40-30/4 = 10/4
However, the yards are for six scarves, therefore we need to divide it by six to obtain the amount of material for one scarf.
Each scarf needs 0.4166 yards of blue fabric, or y = (10/4)/6 =10/4 *1/6 =10/24 = 5/12 yards.
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Select the correct answer.
Which statement about the inequality 2 1/5< 2 3/5 is true?
A. On the vertical number line, 2 1/2 is located below 2 3/5
B. On the vertical number line, 2
3/5 is located below 2 1/5 C. On the vertical number line, 2 3/5 and 2 1/5 are located at the same point
D. On the vertical number line, 2 1/5 and 2 3/5 are both located
is located below 0
Answer: A.
Step-by-step explanation: On the vertical number line, 2 1/5 is located below 2 3/5.
To compare the values of 2 1/5 and 2 3/5, you need to first convert them to fractions with a common denominator. For example, you can convert 2 1/5 to a fraction with a denominator of 5 by multiplying the numerator (1) and the denominator (5) by 2: 2 1/5 = (2 * 1)/(2 * 5) = 2/10 = 1/5.
Then, you can add the fractions to get a common denominator: 2 1/5 + 2 3/5 = (2 + 2) + (1/5 + 3/5) = 4 + (4/5) = 4 4/5.
Since 4 4/5 is greater than 4, it follows that 2 3/5 is greater than 2 1/5. Therefore, on the vertical number line, 2 3/5 is located above 2 1/5.
HELP ASAP PLEASE I NEED THIS QUICK
40 POINTS
Answer: 4/25
Step-by-step explanation:
(2/5)^2 or can write as 2/5 times 2/5
2/5 times 2/5 = 4/25
Answer:
0.08
Step-by-step explanation:
2/5 = 0.4 x 0.4
A point at (−3,−2) is transformed in two steps.
It is reflected about y = x.
It is translated 3 units right and 2 units up.
What is the location of the transformed point?
The location of the transformed point will be at the coordinate (0,4).
What is translation?In mathematics, a translation moves a shape left, right, up, or down but does not turn it. The translated (or picture) shapes appear to be the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.
Given that a point at (−3,−2) is transformed in two steps. It is reflected in y = x. It is translated as 3 units right and 2 units up.
The translated point will be,
(−3,−2) ⇒ (-3,2)
Translation of the point,
(-3,2) ⇒ (-3+3, 2+2) ⇒(0,4)
Therefore, the location of the transformed point will be at the coordinate (0,4).
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George i 89. 99 cm tall. Alex i 72. 44 cm tall. How much taller i George than Alex?
George is 17.55 cm taller than Alex. By simply subtracting the heights of the two, we get the required change between them.
How to do decimal subtraction?Decimal subtraction is as similar to normal number subtraction. Here the subtraction starts from the decimals or the digits after the decimal point.
Calculation:It is given that,
The height of George is 89.99 cm and the height of Alex is 72.44 cm.
Since 89.99 cm > 72.44 cm; George is taller than Alex.
To know how much he is taller, we just simply subtract the height of Alex from the height of George.
I.e., 89.99 cm - 72.44 cm = 17.55 cm
Therefore, George is 17.55 cm taller than Alex.
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PLSS HELP! I'LL GIVE BRAINLIEST!!
Answer:
20.625
Step-by-step explanation:
a=− 3263i/24 + 1/12 ≈0.083333333−2.380111459i, b= 165/8 =20.625
Hope this helps
Answer:
1.1
Step-by-step explanation:
Here is the answer. Have a good day!
Find the first five terms of the geometric sequence whose constant ratio is -4 and whose first term is 7.
Answer:
7, - 28 , 112 , - 448 , 1792
Step-by-step explanation:
to obtain a term in the sequence multiply the previous term by r , so
a₁ = 7
a₂ = a₁ × - 4 = 7 × - 4 = - 28
a₃ = a₂ × - 4 = - 28 × - 4 = 112
a₄ = a₃ × - 4 = 112 × - 4 = - 448
a₅ = a₄ × - 4 = - 448 × - 4 = 1792
has one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
What is eigenvalue?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]
and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]
and the roots of this polynomial is:
[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)
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Complete Quetion
The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.
A cyclist travels 24 km from home to the park.
She leaves home at 13:05 and arrives at the park at 13:50.
What is her average speed in km/h?
Which fraction has the same value as 55.5¯%?
Answer: 55.5 as a fraction is 111/2.
Answer:
55.5/100 or 111/200 in its simplest form
Step-by-step explanation:
55.5 (per)cent) - means every 100
55.5/100= 111/200
(y + 1)^5 divided by (y + 1)^2
Answer:
(y+1)³
Step-by-step explanation:
(y+1)⁵/(y+1)²
=(y+1)(y+1)(y+1)(y+1)(y+1)/(y+1)(y+1)
=(y+1)(y+1)(y+1)
=(y+1)³✓✓
help me with this math question
Answer:
c
Step-by-step explanation:
Lin family travels 235 miles to reach her grandmothers.how far have they traveled when they have completed 72% of the trip distance.I’m so stuck I can’t figure out
Answer:
72% of the trip is 169.2 miles
Step-by-step explanation:
[tex]\frac{235}{100} =\frac{y}{72}[/tex]
y · 100 = 235 · 72
100y = 16920
100y ÷ 100 = 16920 ÷ 100
y = 169.2