Answer:
15.8
Step-by-step explanation:
To round to nearest tenth we only go so far as the first decimal place. If the second decimal digit is less than 5 we leave that number as it is otherwise we increase it by 1
In 15.839, the second decimal digit is 3 so we get 15.8
(If it had been 15.864 then it would be 15.9)
Solve each system.
2m = -4n - 4 , 3m + 5n = -3
After solving each system, 2m = -4n - 4, 3m + 5n = -3, the values of m and n are calculated to be 4 and -3 respectively.
The two given equations, 2m = -4n - 4, and 3m + 5n = -3 are considered to be linear equations since the highest power of the variables in these equations is one.
By rearranging the second equation, the value of m is calculated to be,
3m + 5n = -3
3m = -3 - 5n
m = -3 - 5n / 3
Putting the calculated value of m in the first equation,
2m = -4n - 4
2(-3 - 5n / 3) = -4n - 4
-6 - 10n / 3 = -4n - 4
-6 - 10n = 3(-4n - 4)
-6 - 10n = -12n - 12
-10n + 12n = -12 + 6
2n = -6
n = -6/2
n = -3
To solve for m, put n = -3 in the first equation as follows,
2m = -4n - 4
2m = -4(-3) - 4
2m = 12 - 4
m = 8 / 2
m = 4
Thus the value of m and n in these systems are calculated to be 4 and -3 respectively.
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For a fundraiser, a school club is selling raffle tickets for $2 each and healthy snacks for $1.50 each. What is the cost of:
Answer:
g) 10 tickets and 8 snacks = 32
h) 7 tickets and 5 snacks = 21.5
i) x tickets and y snacks = 53.5
Step-by-step explanation:
Each ticket cost $2 and the snacks, cost $1.50 so we multiply them by the number of tickets and snacks.
g) 10 tickets and 8 snacks = 32
Explanation: 10x2=20 , 8x1.50 = 32
h) 7 tickets and 5 snacks = 21.5
Explanation:7x2=14 , 5x1.50 = 21.5
i) x tickets and y snacks = 53.5
Explanation: x=17 and y=13
You add the number of tickets for (Question g,h - tickets, and snacks so
the total cost is $53.5
But the question says you do not use the unit $ so don´t use it.
Sorry If I got it wrong
Answer: G. $20 for tickets and $12 for snacks
H.$14 for tickets and $7.50 for snacks
I. Probably $2 for ticket and $1.50 for snack
Step-by-step explanation: G is $20 and $12 because you first have to multiply 10 tickets by $2 to get the cost of 10 tickets and then multiply $1.50 by 8 snacks to get the cost of 8 snacks.
H is $14 and $7.50 because you also have to multiply 7 tickets by $2 to get the cost of 7 tickets and multiply $1.50 by 5 snacks to get the cost of 5 snacks.
I is probably $2 and $1.50 because the variables x and y are unknown so you would have to put how much each raffle tickets and snacks cost for x and y. Hope this makes sense!
Name the missing coordinates of an isosceles right triangle ABC.
The coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles right triangle, the two legs of the triangle are congruent and intersect at right angles and their opposite angles are also equal.
The vertice C lies on the x-axis, then the coordinate of point C will be (a, 0).
The vertice A lies on the y-axis, then the coordinate of point C will be (0, a).
Then the coordinate of B will be at the origin which is (0, 0).
Thus, the coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.
The diagram is attached below.
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Write a glide reflection or composition of transformations that can be used to transform ΔABC to ΔDEF.
[tex]r_{y = 2} r_{y - axis}[/tex] is a glide reflection or composition of transformations that can be used to transform ΔABC to ΔDEF.
A glide translation is what?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.When a figure is subjected to one transformation before another is applied?
A(n) example of this is when a transformation is applied to a figure, and then a different transformation is applied to its image (composition of transformations, order of symmetries). SOLUTION: Composition of transformations; the number of times a figure maps to itself when rotated is determined by the order of symmetries. 2.Learn more about glide reflection
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The circular ride described at the beginning of the lesson has a diameter of 44 feet. What are the radius and circumference of the ride? Round to the nearest hundredth, if necessary.
The circumference is the perimeter of a circle or ellipse in geometry.
The circumference of the ride is about 138.23 feet.
What is meant by the circumference of a circle?The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure.
The radius is half the diameter.
So, the radius of the circular ride is 22 feet.
Circumference of a circle = [tex]\pi[/tex] d
Where the value of d = 44, then
substitute the value of d in the above equation
Circumference of a circle = [tex]\pi[/tex] d
Circumference of a circle = [tex]\pi[/tex]44
Circumference of a circle = 138.33
Therefore, the circumference of the ride is about 138.23 feet.
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Find the equation of the line tangent to the graph of f(x) = (In x)² at x = 2.
Answer:
[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient of a curve.
At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
Differentiate the given function using the chain rule:
[tex]\begin{aligned}f(x) & = \left(\ln x\right)^2\\\implies f'(x)& = 2\left(\ln x\right)^{2-1} \cdot \dfrac{\text{d}}{\text{d}x} \ln x\\& = 2\left(\ln x\right)^{1} \cdot \dfrac{1}{x}\\& = \dfrac{2}{x} \ln x \end{aligned}[/tex]
To find the gradient of the function at x = 2, substitute x = 2 into the differentiated function:
[tex]\implies f'(2) = \dfrac{2}{2} \ln 2 = \ln 2[/tex]
Therefore, the gradient of the function at x = 2 is ln(2).
Substitute x = 2 into the function to find the y-value of the point on the curve when x = 2:
[tex]\implies f(2)= \left( \ln 2\right)^2[/tex]
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Substitute the point (2, (ln 2)²) and the found gradient into the slope-intercept formula and solve for b:
[tex]\begin{aligned} y & = mx+b\\\implies \left(\ln 2 \right)^2 & = \ln 2 \cdot 2 + b\\\left(\ln 2 \right)^2 & =2\ln 2 +b\\b & = \left(\ln 2 \right)^2-2 \ln 2\end{aligned}[/tex]
Therefore, the tangent has the equation:
[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]
Describe the transformations of f(x) that produce g(x) .
f(x) = x/2 ; g(x)=-2 x+4
A compound function is when the output of one function is used as the input of another function. If we have a function ff and another function gg, the function fg(x)fg(x) is called "ff of gg of xx" or "fgfg of xx" and is a composition of the two functions.
The order in which functions are applied is important. Find the function of the function. If you have two or more functions, there can be many different permutations of those functions, giving you many different composite functions.
fg(x)fg (x) can be written f[g(x)] f[g(x)] to indicate that the inner function should be applied before the outer function.
Solution:
Your problem → f(x)=x/2, g(x)=-2x+4, Find f(g(x))
f(x)=x2, g(x)=-2x+4, fog(x)=?
g(x)=-2x+4, f(x)=x2
fog(x)=f(g(x))
=f(-2x+4)
=-2x+42
=-x+2
fog(x)=-x+2
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I need this answered please
Answer:
Perimeter = 9x+4x+18x+16
Perimeter = 31x+16
Give Brainliest please :)
HELP ASP SHOW UR WORK WILL GET BRAINILEST AND 10 points
Elena bikes 20 minutes each day for exercise.
Write an equation to describe the relationship between her distance in miles, D, and her biking speed, in miles per hour, when she bikes:
at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes
D = M/12 + N/4 represents the relationship between Elena's distance in miles, D, and her biking speed.
Speed = distance/ time
Here, we are given that Elena bikes 20 minutes each day for exercise. She bikes at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes.
Therefore, distance covered by her in the first 5 minutes = speed x time
time = 5 minutes = 5/60 hours
= 1/12 hours
Thus, distance = M(1/12)
= M/12
Now, similarly, distance covered by her in the last 15 minutes = N(15/60)
=N/4
Thus, the total distance in miles, D, covered by her in the last 15 minutes = N(15/60)
= N/4
Thus, the total distance in miles, D, covered by her is D = M/12 + N/4
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Ayuda por favor, no recuerdo mucho sobre las fracciones
Answer:
1 25/ 26
2 3/4
3 35/24
6 9/2
8 2/5
Step-by-step explanation:
I will AWARD BRAINLIST! Help I think I am wrong I am confused its a Math problem
Thank you !! have good day!
Answer: 55
Step-by-step explanation
[tex]\sqrt{a^{2} + b^{2}}=c -- Pythagorean theorem[/tex]
[tex]\sqrt{14^{2} + 20^{2}}=c[/tex] ≈24.41 rounding up to whole number = 24
∠θ = [tex]tan^{-1} (opposite/adjacent) = tan^{-1} (20/14) = 55[/tex]
therefore, ∠θ = 55
CCSS ARGUMENTS Write a coordinate proof for each statement.The segments joining the base vertices to the midpoints of the legs of an isosceles triangle are congruent.
The segments joining the base vertices to the midpoints of the legs of an isosceles triangle will split into two equal triangles so they will be congruent.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
ΔABC is isosceles where AB = AC
Now,
Line segment AD is intersecting at the midpoint of BC.
Now,
In ΔABD and ΔACD
AB = AC,AD = AD and BD = DC
Since all sides are equal so by SSS congruent property both will be congruent.
Hence "The segments joining the base vertices to the midpoints of the legs of an isosceles triangle will split into two equal triangles so they will be congruent".
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Write a recursive formula for each sequence. 1,5,14,30, . . . . . . .
The recursive formula for the given sequence: 1,5,14,30, . . . is a(n) = a(n-1) + n². It can also be expressed as a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4), with a(1) = 1.
A recursive formula of a sequence tells us how to find the nth term, a(n), from the preceding terms, a(n-1), a(n-2), ....
The sequence is:
1,5,14,30, . . . .
Here:
a(1) = 1, a(2) = 5, a(3) = 14, and a(4) = 30.
Let us write:
a(1) = 1
a(2) = 1 + 4 = a(1) + 2²
a(3) = 5 + 9 = 5 + 3² = a(2) + 3²
a(4) = 14 + 16 = 14 + 4² = = a(3) + 4²
So we can conclude the recursive formula is:
a(n) = a(n-1) + n²
However, we can find another recursive formula.
We have:
a(n) = a(n-1) + n² ........ (1)
For n -1 this becomes:
a(n-1) = a(n-2) + (n-1)²
a(n-1) = a(n-2) + n² - 2n + 1 ........ (2)
Subtract (1) - (2):
a(n) - a(n-1) = a(n-1) + n² - a(n-2) - n² + 2n - 1
a(n) - a(n-1) = a(n-1) -a(n-2) + 2n - 1
⇒ a(n) = 2a(n-1) -a(n-2) + 2n - 1 ...(3)
Equation (3) applies for any n, therefore for n -1, eq.(30 becomes:
a(n-1) = 2a(n-2) -a(n-3) + 2(n-1) - 1 ....(4)
Subtract Eq.(3) - Eq.(4).
a(n) - a(n-1) = 2a(n-1) -a(n-2) + 2n - 1 - (2a(n-2) -a(n-3) + 2n - 3)
a(n) - a(n-1) = 2a(n-1) - 3a(n-2) + a(n-3) + 2
⇒ a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + 2 ....(5)
Substitute for n-1 again into Eq.(5):
a(n-1) = 3a(n-2) - 3a(n-3) + a(n-4) + 2 ..... (6)
Subtract Eq.(6) - Eq.(5)
a(n) - a(n-1) = 3a(n-1) -3a(n-2) +a(n-3) +2 -3a(n-2) +3a(n-3) -a(n-4) -2
a(n) - a(n-1) = 3a(n-1) -6a(n-2) +4a(n-3) -a(n-4)
⇒ a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4)
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Bob went for a drive in his new car. He drove for 127.5 miles at a speed of 51 miles per hour. For how many hours did he drive?
Answer: 2.5 Hours. I hope I'm not sure but I think you just divide Miles Driven by MPH
A concert is attended by
26,493 people. To the nearest
thousand, about how many people
attended the concert?
Answer: 26,000
Step-by-step explanation:
26 000
See the pictures attached
Step1: Underline the place value spot you are rounding off to
Step2:circle the next door neighbour
Step3: if the number you circled is bigger than 5 it will stay the same. if it is smaller than 5 it will become a 0 and so will all the numbers that follow
Position and label the following triangle on the coordinate plane.
Right ΔX Y Z with hypotenuse YZ, the length of XY is b units long, and the length of XZ is three times the length of XY
The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
Given the right-angle triangle ΔX Y Z
XY = b(base) and XZ = 3b(perpendicular).
By Pythagoras theorem,
Hyp² = Base² + Perp²
Hyp² = b² + (3b)²
Hyp² = 10b²
Hyp = 3.16b
Hence "The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted".
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Which angles are complementary to each other?
Answer:
3 and 4
Step-by-step explanation:
Since complementary angles add up to 90,
and 1 is a right angle while 3 and 4 are vertical angles
find the area of a circle(im in a test rn so please hurry
Answer: Area= 804.248
Step-by-step explanation:
Find the slope of the line.
b. the line containing (8,-3) and
(-6,-2)
The slope of the line containing (8,-3) and (-6,-2) is (1/14).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -2 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -6 , and [tex]x_{1}[/tex] = 8 .
On substituting the values of variables in equation1, we will get
m = ( (-2)-(-3) ) / ( (-6)-(8) ) = (1/14).
As the slope of a line is (1/14), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (8,-3) and (-6,-2) is (1/14).
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how to round the number 19 to the nearest tenth in a percent
Answer:
Step-by-step explanation:
Determine the two consecutive multiples of 10 that bracket 19.
19 is between 10 and 20.
15 is the midpoint between 10 and 20.
As illustrated on the number line, 19 is greater than the midpoint (15)
Therefore, 19 rounded to the nearest is 20
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A tennis club charges players a $ 20 court fee, plus a $ 10 hourly charge with a 5 -hour maximum. A posted list of the total charges for 1,2,3,4 , or 5 hours forms an arithmetic sequence. What is the first term and what is the common difference?
The first term of the arithmetic sequence so formed is $20 and the common difference is $10.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Initial fee charged by players = $20.Hourly charge = $10Maximum number of hours = $5To find: The first term and common difference of the arithmetic progression so formed.
Finding:
As the initial charge charged by the players is $20, it can be taken as the first term of the arithmetic sequence, at 0 hours; a₁ = 20
Now, since the hourly charge is $10, the given arithmetic sequence of the money charged will increase by $10 per hour; thus d = 10
The arithmetic sequence holds true for 5 hours maximum.
Thus the sequence so formed => [tex]a_n = 20 + (n - 1)10[/tex], 1 ≤ n ≤ 5.
Hence, The first term of the arithmetic sequence so formed is $20 and the common difference is $10.
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If K is the midpoint of JL, JK=8x + 11 and
KL=14x-
- 1, find JI
The measure of JL from the given parameters is 54
Midpoint of a lineThe midpoint of a line is the line that divides the line into two equal parts. If K is the midpoint of JL, then the measure of KK is equivalent to the measure of JK. Mathematically;
JK = KL
JK + KL = JL
Given the following parameters
JK=8x + 11 and
KL=14x- 1
Equate
8x+11 = 14x-1
-6x = -12
x = 2
Determine JL
JL = 2(8x+11)
JL = 2(16+11)
JL = 54
Hence the measure of JL from the given parameters is 54
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Determine whether each list is a sequence or a series and finite or infinite. 1,0.5,0.25,0.125,0.0625
From the list of numbers presented ( 1,0.5,0.25,0.125,0.0625) we can determine that this is a finite sequence.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
1, 0.5, 0.25, 0.125, 0.0625
1 ÷ 2 = 0.50.5 ÷ 2 = 0.250.25 ÷ 2 = 0.1250.125 ÷ 2 = 0.06251/2ⁿ
We can clearly notice that we have a limit number and it is 0.0625, as we know the beginning of the sequence and the exact end we can know that we are in the presence of a finite sequence.
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Read question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Two similar trapezoids have a scale factor of 3: 2 . The perimeter of the larger trapezoid is 21 yards. What is the perimeter of the smaller trapezoid?
A. 14 yd
B. 17.5 yd
C. 28 yd
D. 31.5yd
The perimeter of the smaller of the two similar trapezoids is 14 yards.
Similar polygons are polygons that have equal corresponding angles and proportional corresponding sides.
The ratio of one side of a polygon to the corresponding side of the other is called the scale factor.
The ratio of the perimeters is the same as the scale ratio, while the ratio of the areas is the square of its scale ratio.
If two similar trapezoids have a scale factor of 3 : 2, then the ratio of their perimeters is also 3 : 2.
If the perimeter of the larger trapezoid is 21 yards, solve for the perimeter of the smaller trapezoid using the ratio for the perimeter.
3 : 2 = 21 yards : perimeter of the smaller trapezoid
perimeter of the smaller trapezoid = 2(21 yards)/3
perimeter of the smaller trapezoid = 14 yards
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Given: a₁ = 23 and a5 = -5 a1 Find: a22
Using Arithmetic progression(A.P.), the value of a22 will be 107
The formula to calculate A.P. is a + (n-1)d
The value of a5 = 5a1
a1 = 23
a5 = -5a1
a5 = 5 (23)
a5 = 115
a22 = a + (n-1)d
a22 = 23 + (22-1)d
a22 = 23 + 21d ................(1)
a5 = 115
115 = a + (n-1)d
115 = 23 + (4)d ...................(2)
from (1) and (2)
a5 = a + 4d
d = 23
a22 = 107
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In the past year, Dantae watched 18 movies that he thought were very good. He watched 45 movies over the whole year. Of the movie sea watch, what percentage did he think was very good?
Answer:
40%
Step-by-step explanation:
To start off, we are going to place the number of movies he thought were very good, over the movies he watched over the entire year into a fraction (or a certain number over the total amount)!
18/45 or [tex]\frac{18}{45}[/tex]
Next, we are going to place this into our calculator and will get a decimal value.
18/45 → 0.40
Last, we are going to change this number into a percentage, by multiplying our decimal by 100.
0.40 → 40%
Hope this Helps! :)
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Question
Use the follow step as a guide to solve the following equation. Write out your work for all steps to solve the equation.
2x - 5 = 3(4x + 5)
Answer:
x = -2
Step-by-step explanation:
2x -5 = 3(4x + 5) step 1
2x - 5 = 12x + 15 step 2
2x - 12x -5 = 15 Step 3
2x - 12x = 15 +5 simplify
-10x/-10 = 20/-10 step 4
x = -2
Hank is working in a silver mine 10 feet below the surface. He descends until he reaches a point 57 feet below the surface. How many feet does Hank descend?
Answer:
he descends only 57 feet ,as the mine is 10 feet below the surface befor descending
Answer:
he descends only 57 feet ,as the mine is 10 feet below the surface befor descending
Use an explicit formula to find the 10 th term of each geometric sequence. -3,6,-12,24, . . .
The formula to calculate the 10th term of a Geometric Progression is :
=> [tex]a_{10} = a.r^{9}[/tex]
The formula to calculate [tex]n^{th\\}[/tex] term in a given Geometric progression is
=> [tex]a_{n} = a.r^{n-1}[/tex]
Where a1 = a, r is a common ratio defined by the ratio of any two successive terms r = a2/a1, and n is the term to be found.
In the given sequence, we have the first term i.e. a = -3, n = 10,
common ratio => r = a2/a1 => r = -2
Calculating using the G.P. formula for the 10th term
=> [tex]a_{10} = a.r^{9}[/tex]
=> [tex]a_{10} = (-3).(-2)^{(10-1)}[/tex]
=> [tex]a_{10\\}[/tex] = (-3)(-512) = 1536
The 10th term for this sequence will be 1536.
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