The answer is A. Winter.
As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.
Please help im not the brightest with math
Answer:
12 square in
Step-by-step explanation:
In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.
A = pi*r*r = 3*2*2 = 12 square in
Answer:
12 in^2
Step-by-step explanation:
Since the formula to find the area of a circle is already up, we can use that to solve the question.
In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.
--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.
Now, we can just replace r with 2.
--> A = 4[tex]\pi[/tex]
Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.
--> A = 4 x 3
--> A = 12
We can conclude that the area of the circle is 12 in^2.
if csc(θ)=2 and tan (θ)<0, determine the exact value of cos(θ)
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
What is the exact value of a trigonometric function?
In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:
cos θ = - √[1 - (1 / csc θ)²]
If we know that csc θ = 2, then the exact of the cosine function is:
cos θ = -√[1 - (1 / 2)²]
cos θ = -√(3 / 4)
cos θ = -√3 / 2
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
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ts
The table below represents the concessions sold at the last three basketball games. The
games were held on different days and times.
Friday night
Saturday morning
Tuesday night
Total
Candy Hot Dogs
148
94
78
320
102
27
150
279
Nachos
108
42
97
247
Total
358
163
325
846
What is the approximately probability of a person going to a Saturday morning game and
buying nachos?
The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.
What does approximate mean?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. An estimated result can be obtained by rounding the values in a computation before carrying out the procedures.The word type "approximately" is an adverb.A value that is close to, higher than, as close to, and with the specified level of precision is known as an approximation value by the excess of a number.Approximately symbol ≈.The approximately probability of a person going to a Saturday morning game and buying nachos:
Probabaility= [tex]\frac{150}{846} *100[/tex]
=17.7%
Approximately=18%.
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PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3
How to determine the graph of f(x) + g(x)?The functions are given as:
f(x) = x + 3
g(x) = x
From the above functions, we can see that the function g(x) is the parent function of a linear function.
When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points
(x, y)= (0, b) and (-b, -b)
Where b is the y-intercept of the other function
i.e b = 3 from f(x) = x + 3
So, we have the following points
(0, 3) and (-3, -3)
Next, we draw the points and we connect the points
When the equation of f(x) + g(x) is calculated, we have
f(x) + g(x) = 2x + 3
See attachment for the graph of the functions
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A trapezoid is shown. The lengths of the bases K L and J M are 10 feet and 5 feet. The length of side L M is 6 feet. An altitude is drawn from point K to a point on side J M.
A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?
feet
The given height of this trapezoid is given to be 4.5m
How to solve for the height of the trapezoidWe have to solve for this by making use of the height of a trapezoid. The height is given as
A = (1/2) h (b1 + b2)
The variables here are
h = height
b1 = lenght at base 1
b2 = length at base 2
If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base
b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.
Hence the height would begiven as 4.5 ft
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Answer: 4.5
Step-by-step explanation:
Need help with my math please. Determine the most probable next term in each list of numbers.
Answer:
23. 216
24. 56
25. 52
26. -7
27. 5
Step-by-step explanation:
Question 23Work out the differences between the terms until the differences are the same:
[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]
[tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]
[tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]
As the third differences are the same, the sequence is cubic and will contain an n³ term. The coefficient of n³ is always a sixth of the third difference. Therefore, the coefficient of n³ = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^3[/tex]
So the next term in the sequence is:
[tex]\implies a_6=6^3=216[/tex]
Question 24Work out the differences between the terms until the differences are the same:
[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]
[tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+n[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+7=56[/tex]
Question 25Work out the differences between the terms until the differences are the same:
[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]
[tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+3[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+3=52[/tex]
Question 26Given numbers:
-1, 2, -3, 4, -5, 6
As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]
From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.
Therefore, the rule is:
[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]
[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]
So the next term in the sequence is:
[tex]\implies a_7=-7[/tex]
(since 7 is an odd natural number)
Question 27Given numbers:
5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5
The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:
One 5, followed by a 3Two 5s, followed by a 3Three 5s, followed by a 3Four 5s, followed by a 3Therefore, the next number of 5s will be five. This means the next number in the list will be 5, since there are only four 5s after the last 3.
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Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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The side length of each square is 6 units.
The area of the square A2 is 20 squared units
How to determine the area of A2?The complete question requires that we calculate the area of square A2
The side length of each square is 6 units.
So, the side length (L) of A2 is
L^2 = (2)^2 + (6 - 2)^2
This gives
L^2 = 20
The above represents the area of the square A2
Hence, the area of the square A2 is 20 squared units
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Answer:
Triangle Area = 4 units^2Step-by-step explanation:
assuming you are looking for the area of the triangles, there is no specific question, they are right-angled triangles congruent with the catheti of 2 and 4 units.
Triangle area = 1/2 base x height.
so 1/2 2 * 4 = 4 units^2
A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 3y 4z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ 4 (3y 4z = 1) ⋅ 4 (y z = 6) ⋅ −3 (3y 4z = 1) ⋅ 3
Option C is correct (y + z = 6) ⋅ −3
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
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The complete question is -
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
Paulo wants to buy new carpet for his bedroom. The floor is in the shape of a rectangle. Its length is 16 feet and its width is 11 feet. The carpet he wants costs $9 per square foot. How much will the carpet cost for the floor?
Answer:
11x9=99 16x9=144=243 144+99
The cost of the carpet required for the given rectangular floor is $1584.
A rectangle is a quadrilateral with equal pairs of sides.
Given that:
The shape of the floor is a rectangle.
The length of the floor is 16 feet.
The width of the floor is 11 feet.
So,
The area of the floor = length × breadth
= 16 × 11
= 176 sq feet
The area of the floor is 176 sq feet.
The cost of the carpet for a 1 sq foot floor = $9
The cost of the carpet for a 176 sq feet floor = $9 × 176
= $1584
Thus, the cost of the carpet for a 176 sq feet floor is $1584.
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Nereo and Azeneth start recording video at the same time. Nereo's phone starts with 1,0001{,}0001,0001, comma, 000 megabytes (MB\text{MB}MBstart text, M, B, end text) of free space and uses 7 MB7\,\text{MB}7MB7, start text, M, B, end text of space per second of video. Azeneth's phone has 1,255 MB1{,}255\,\text{MB}1,255MB1, comma, 255, start text, M, B, end text of free space and uses 10 MB10\,\text{MB}10MB10, start text, M, B, end text of space per second of video. How much free space will they have when they first have the same amount of space left?
Using a linear function, it is found that they will have 405 MB of free space when they first have the same amount of space left.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The free space for each of Nereo and Azeneth can be modeled by a linear function, in which the slope is negative with the amount that each second of video takes and the y-intercept is the initial free space. Her the functions for the amount of free space after x seconds are given by:
N(x) = 1000 - 7x.A(x) = 1255 - 10x.They will have the same amount of free space when:
N(x) = A(x)
1000 - 7x = 1255 - 10x
3x = 255
x = 255/3
x = 85.
The space will be of:
N(85) = 1000 - 7 x 85 = 405 MB.
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The rock does 1,000 bicep curl-ups on monday.on tuesday he does 30% more bicep curl-ups. on wednesday he does 45% more. how many more bicep curl-ups does he do on wednesday compared to monday
Answer:
either 885 more or 450 more
Step-by-step explanation:
Monday: 1000
Tuesday: 1000*1.3 = 1300
Wednesday:
I'm assuming 45% more from tuesday?
1300*1.45 = 1885
or if not:
1000*1.45 = 1450
either 885 more or 450 more
you can also just do 1000*1.3*1.45 = 1000*1.885 = 1885 if thats what the question means
1)give your answer in terms of π
2) give your answer using 3.14 for π
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
Volume of a cylinderA cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
The volume of the composite cylinder is expressed as shown below;
V = πr²h
where
r is the radius
h is the height
According to the given diagram;
V = Vl - Vs
V = π(10)²*15 - π(5)²*15
V = 1500π - 375π
V = 1125π cubic inches
If the value of π is 3.14, hence;
V = 1125(3.14) cubic inches
V = 3532.5 cubic inches
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
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What is the slope of (2,-1) and (8,4)
Answer:
5/6
Step-by-step explanation:
slope = 4-(-1)/8-2 = 5/6
If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)?
The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]
Therefore [tex](k o h)(x) = \frac{1}{5 + x}[/tex]
Given that the functions h is defined by h(x)=5+x
and k is defined by k (x) = [tex]\frac{1}{x}[/tex]
To find the composition of k and h that is: (k o h) (x)
Therefore
k (h(x)) = k (5+x)
k (h(x)) = [tex]\frac{1}{5+ x}[/tex]
The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators must have the right amount of inputs in the right places, legal characters for these inputs, a clearly defined order of operations, etc.The syntax requirements must be followed for a string of symbols to be considered a valid mathematical expression.To learn more about Expression with the given link
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Allison is saving money to buy a new phone that costs $600 by selling her graphic designs. She is using an app to manage her sales, but it keeps a fraction of each sale. Her net pay is modeled by the function P(x) = x2 + 18x – 160, where x represents the number of sales. How many sales does Allison to make to earn $600?
Answer:
20
Step-by-step explanation:
x^2+18x-160
If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.
To check you can plug 20 in for x. When you do that, y = 600.
Find the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0).
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and
r(1, 1, 0) is x + y + z = 2 .
According to the question
Let the points
p(0, 1, 1) = (x1,y1,z1)
q(1, 0, 1)= (x2,y2,z2)
r(1, 1, 0)= (x3,y3,z3)
now,
The equation of the plane through the points
i.e
The formula of equation of a plane passing through three non collinear points
[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]
by substituting the values in the formula of equation of a plane
[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]
[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]
x(1) - (y-1)(-1) + (z-1)(1) = 0
x + y - 1 + z - 1 = 0
x + y + z = 2
Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2 .
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PLEASE HELP IM STUCK PLS
Step-by-step explanation:
the general slope-intercept form is
y = ax + b
a is the slope, b is the y-intercept.
we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.
x + 2y = 6
2y = -x + 6
y = -x/2 + 6
A circle is formed using a ribbon which has a radius of 28 cm. If a square has to be formed using the same ribbon, determine the length of the side of the square formed using the ribbon.
The length of the side of the square is [tex]44 cm[/tex].
What is a Circle?A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle.The following are a few examples of circles in daily life: the bicycle's wheel. Dinner dish. Coin.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also the location of points evenly spaced apart from the center. The radius of a circle is measured from the center to the edge.Determine the length of the side of the square:
Radius of circle[tex]=28.[/tex]
Circumference[tex]=2\pi r[/tex]
[tex]2\pi (28)=176[/tex]
Side of the square[tex]=\frac{176}{4} =44cm.[/tex]
The length of the side of the square is [tex]44 cm[/tex].
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HELP PLEASE!!
20 points for grabs
Step-by-step explanation:
....................
How to name a angle in 4 different ways?
First answer and correct answer gets to be brainliest!
Hey there!
4 ways to name angles⇒ Use the vertex as the middle letter, and the point from each side (<ABC or <CBA)
⇒ Use the vertex only (<B)
⇒ Use a number (<1)
Classify angles according to their measure.⇒ Acute angle: less than 90°
⇒ Right angle: exactly 90°
⇒ Obtuse angle: between 90° and 180°
⇒ Straight angle: exactly 180°
Thank you,
Eddie
See the attachment for a visual!
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
The area of the trapezoidal tarp in the hotel is 47.3 square inches.
What is a trapezoid?A trapezoid is a quadrilateral having one pair of parallel opposite sides. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is needed.How do determine the area of the trapezoid?
The area of a trapezoid is calculated using:Area = 0.5 × (Sum of parallel sides) × HeightFrom the complete question, the parallel sides are 10ft and 12ft.
So, Area = 0.5 × (10 + 12) × hEvaluate,
Area = 11 × hThe height (h) is computed using the cosine function shown below:
cos(120 - 90) = h/5This gives
cos(30) = h/5Make h the subject:
h = 5cos(30)Evaluate:
h = 4.3So, we get:
Area = 11 × 4.3Evaluate:
Area = 47.3Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.
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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?
to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.
Someone help i cant answer this
Answer:
100%, 20%, 60%
Step-by-step explanation:
250/250 = 100/100 = 100%
50/250 = 1/5 = 20/100 = 20%
150/250 = 3/5 = 60/100 = 60%
The slope of the line shown in the graph is __ and the y-intercept of the line __
Answer:
slope
(0, 6) and (-9, 0)
0 - 6 / -9 - 0 = -6/-9 = 2/3
y intercept is when the line intercepts the y axis and x = 0
The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6
Answer:
slope is 2/3
y intercept is 6
Step-by-step explanation:
We can find the slope of the line by using two point
(-9,0) and (0,6)
The slope formula is
m = ( y2-y1)/(x2-x1)
= ( 6 - 0) /( 0 - -9)
= (6-0)/(0+9)
= 6/9
= 2/3
The y intercept is where it crosses the y axis ( the value where x is 0)
The y intercept is 6
C=22°, a = 14 m, b = 8 m find area of ABC to the nearest tenth
Answer:
21.0 m²
Step-by-step explanation:
The formula for the area of a triangle from two sides and the included angle is ...
A = 1/2ab·sin(C)
AreaUsing this formula, we find the area to be ...
A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²
The area of triangle ABC is about 21.0 square meters.
A circle's diameter has endpoints at
(-4,-7) and (5,-2).
a) What is the length of the diameter?
b) What is the length of the radius?
Part (a)
We'll use the distance formula.
[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]
The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.
========================================================
Part (b)
We divide the diameter in half to get the radius.
Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.
A three-digit number has one more ten than it has hundreds, and it also has one more than twice as many units as tens. The sum of the number and that number reversed is 31 less than 10 cubed. Find the reverse number.
15 pts
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
Read more about digits at:
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]x = -7[/tex]
Step-by-step explanation:
Given the equation:
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],
to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]
⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex] [expand brackets]
⇒ [tex]10x + 96 = -44 - 10x[/tex]
⇒ [tex]10x + 10x + 96 = -44[/tex] [add [tex]10x[/tex] to both sides]
⇒ [tex]20x + 96 = -44[/tex]
⇒ [tex]20x = -44 - 96[/tex] [subtract 96 from both sides]
⇒ [tex]20x = -140[/tex]
⇒ [tex]x = \frac{-140}{20}[/tex] [divide both sides by 20]
⇒ [tex]x = \bf-7[/tex]
Answer:
B) x = -7
Step-by-step explanation:
Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]
Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.
[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]
[tex]\implies 10x+100-4=11-10x-55[/tex]
Step 2: Simplify (combine like terms).
[tex]\implies 10x+100-4=11-10x-55[/tex]
[tex]\implies 10x+96=-44-10x[/tex]
Step 3: Add [tex]10x[/tex] to both sides.
[tex]\implies 10x+10x+96=-44-10x+10x[/tex]
[tex]\implies 20x+96=-44[/tex]
Step 4: Subtract [tex]96[/tex] from both sides.
[tex]\implies 20x+96-96=-44-96[/tex]
[tex]\implies 20x=-140[/tex]
Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].
[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]
[tex]\implies \boxed{x=-7}[/tex]
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] ln(x) x
The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] using L'Hospital rule is 0.
According to the given question.
We have to find the limit of ln(x)/x when x approaches to infinity.
If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].
And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.
Therefore, defferentiating numerator ln(x) and x with respect to x.
[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]
So,
[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]
[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]
As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.
Therefore,
[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]
Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.
Find out more information about limit and L'Hospital rule here:
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A line has a slope of -2/5 and passes through the point (10,7) . Write the equation of this line in point-slope form, slope-intercept form, and standard form.
i will give brainliest if you help
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{10})[/tex]
