since W is the midpoint, that simply means that both halves are twins, so
[tex]V\stackrel{9x+7}{\rule[0.35em]{10em}{0.25pt}} W\stackrel{16x - 28}{\rule[0.35em]{10em}{0.25pt}} Y \\\\\\ \stackrel{VW}{9x+7}~~ = ~~\stackrel{WY}{16x-28}\implies 7=7x-28\implies 35=7x\implies \cfrac{35}{7}=x \\\\\\ \boxed{5=x}\hspace{5em}\stackrel{VW}{9(5)+7\implies 52}\hspace{5em}\underset{52~~ + ~~52}{\stackrel{\textit{\LARGE VY}}{104}}[/tex]
The length of segment VY, represented by "a," is 25x - 21.
How to find the length of the segmentTo find the length of segment VY, we can use the fact that W is the midpoint of VY. The midpoint of a line segment divides it into two equal parts. Therefore, the length of VW plus the length of WY equals the length of VY.
Let VY be represented by "a." Then, according to the midpoint property:
VW + WY = VY
Substitute the given expressions for VW and WY:
(9x + 7) + (16x - 28) = a
Now, combine like terms:
25x - 21 = a
So, the length of segment VY, represented by "a," is 25x - 21.
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Aviva's pay stub shows gross earnings of $662.30 for a week. Her regular rate of pay is $10.80 per hour for a 35 hour week and overtime is paid time and a half regular pay. How many Hours did she work
Number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of $10.80 per hour for 35 hour week and 1.5 of regular pay for overtime is 52.6hours.
Given,
Gross earning for week=$662.30
Regular rate per hour for 35hour week=$10.80
Overtime rate=1.5×(10.80)
For 'h' number of hours
(10.80×35)+(10.80×1.5) h=$662.30
⇒378 +16.20h=662.30
⇒h=284.30/16.20
⇒h≈17.6hours
Number of hours Aviva's work=35 +17.6
=52.6hours
Therefore, number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of pay $10.80 per hour for a 35 hour week and 1.5 of regular pay for overtime is 52.6hours.
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Can someone PLEASEE help me
PLEASE SOLVE THIS FOR ME. I ONLY KNOW THAT THE ANSWER WILL HAVE AN X IN IT
Answer: [tex]\boxed{\sqrt{12x-1}}[/tex]
Step-by-step explanation:
[tex]\sqrt{2(6x-3)+5}\\ \\\sqrt{(12x-6)+5} \\\\\boxed{\sqrt{12x-1}} \\\\This\ is\ as\ far\ as\ you\ can\ simplify\ this[/tex]
Chris is studying a type of coral that grows at a constant rate. They measured the age and height of 3
pieces of the coral. Here's what they found:
The equation is; y = 7/2x
What is the equation?We know that we could be able to obtain the equation by the use of the equation is a straight line. The general form of the equation of a straight line is given as y = mx +c
The first thing that we must do is to obtain the slope of the graph from;
m = y2 - y1/x2 x1
m = 45 - 15/6 - 2
m = 7/2
The graph begins at origin hence c = 0
y = 7/2x
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Brainliest, 30 pts, thanks, 5 star guarantee.
The triangle ΔXYZ is congruent to the triangle ΔX'Y'Z'. And the intersection of ZZ' and AB form a right angle.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
The reflection does not change the shape and size of the geometry. But flipped the image.
The triangle ΔXYZ is reflected across the line AB to get the tringle ΔX'Y'Z'.
The diagram is given below.
A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersects the line of reflection at a right angle.
Thus, the triangle ΔXYZ is congruent to the triangle ΔX'Y'Z'. And the intersection of ZZ' and AB form a right angle.
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9. A submarine is 140 ft
below sea level. It rose 30 ft.
What integer describes the
new depth of the submarine?
Answer:
it's easy if you set your mind to it, think about it angain
writing linear equations: two points or graph worksheet, please help
Answer:
Q3
Slope = 5
Standard= y=5X+15
Q5
Slop =-4
Standard= y=-4x+4
Step-by-step explanation:
m=-5-5/-4+2=-10/-2= 5
y-5=5(x+2)
y-5=5x+10
y=5x+15
What is the answer to -5 - 7.
Answer:
it is negative 12
Step-by-step explanation:
-12
Answer:
-12
Step-by-step explanation:
The distance between two places of interest is 2/3km. I go 1/4 of this distance on foot. How far is still to go?
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
Step-by-step explanation:
If I have traveled 1/4th of the distance between two places, I still have 1 - 1/4 = 3/4th of the distance yet to cover
If the distance between the two places is d, distance left =(3/4) . d
In this case, d = 2/3 km
So distance left to cover = [tex]\dfrac{2}{3}\cdot \dfrac{3}{4}[/tex]
We can cross-cancel the 3 which appears as the denominator in the first fraction and the numerator in the second fraction
[tex]\dfrac{2}{\cancel{3}}\cdot\dfrac{{\cancel{3}}}{4}=\dfrac{2}{4}[/tex]
Dividing both numerator and denominator by 2 gives us
[tex]\dfrac{2\div2}{4\div2}=\dfrac{1}{2}[/tex]
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
A person can order a new car with a choice of 12 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
Answer:
96
Step-by-step explanation:
12 colors times 2 possibilities of with or without air conditioning is 24.
24 times two possibilities of with or without automatic transmission is 48.
48 times two possibilities of with or power windows is 96.
96 times two possibilities of with or CD player is 192.
12. Determine if the following equation has one solution, no solution, or infinite
solutions: 3(4x + 6) = 2(6x + 9).
Answer:
Infinite Solutions
Step-by-step explanation:
3(4x + 6) = 2(6x + 9)
Distribute coefficients
12x + 18 = 12x +18
Same equations which means infinite solutions
reflection across y = -1
Please I need help ASP I will mark you brainless please
Answer:
See picture below.
Step-by-step explanation:
Esteban bought a desk lamp at a sale price of $20.25. The original price of the lamp was $45. What was the discount rate of the desk lamp?
Answer:
55%
Step-by-step explanation:
Ans
65.25 Step-by-step explanation:
8,370 divided by 62 with remainder
Answer:
8370/ 62: 135
62/8370: 0.007
Step-by-step explanation:
Under her cell phone plan, Morgan pays a flat cost of $54 per month and $5 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $70 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
Answer: She can use 4 gigabyte while remaining in her budget.
Step-by-step explanation:
You would first subtract 54 from 70 which leaves you with 16,
Then you would divide 16 by 4 to find how many gigabytes she could use which gives you 4
So she can use 4 gigabyte while remaining in her budget.
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Answer: Answer is 3
Step-by-step explanation:
let the maximum number of gigabytes of data is x
total budget is $70
then, flat cost is $54 and $5per gigabyte
we get:
54 +5 × x= 70
5x =70 - 54
x = [tex]\frac{16}{5}[/tex] = 3.2 ≈ 3
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There are five questions listed below. Each question includes the quantity 43. Match the 43 in each question on
the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer
options on the right will be used more than once.
What number is 15% of 43?
43% of 300 is what number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
percent
base
amount
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
What number is 15% of 43?
43 here is the base43% of 300 is what number?
Here 43 is the percent12% of what number is 43?
43 is used here as amount43 is what percent of 106?
43 is used here as amountWhat percent of 43 is 6?
43 here is the baseWhat is base?The base as used in the question refers to the main number that is a=to say the number on which other calculation are focused on.
What is percent?Percent is a term used in mathematics to refer to a fraction with a denominator of one hundred. Numbers in percent is accompanied with the percent symbol which is %. Any number having that symbol means that the number is a fraction with a denominator of one hundred.
What is amount?The term amount as used refers to the result gotten when some mathematical operation is being done on the base.
The calculations to the questions asked are below:
What number is 15% of 43?
= 15/100 x 43
= 6.45
43% of 300 is what number?
= 43/100 x 300
= 129
12% of what number is 43?
= 12/100 x 43
= 5.16
43 is what percent of 106
= 43/106 * 100
= 40.56%
What percent of 43 is 6
= 6/43 x 100
= 13.95%
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for each table, find the constant of proportionality. use decimal notation if neccescry
Step-by-step explanation:
the constant k of proportionality is defined by
y = kx
or in our case
b = ka
so, let's see
14 = k×2
k = 14/2 = 7
this also works for the other data pairs :
7×5 = 35
7×9 = 63
7 × 1/3 = 7/3
perfect.
so, the constant of proportionality is 7.
how many zeros will be in the product of 5 x 105 the 105 is the 10 of the power of 5
Answer: this equation has 5 zeroes.
Step-by-step explanation:
The number of zeroes in any number can be found by,
we have expression as
[tex]5*10^{5}[/tex]
now ;
10*10 has 2 zeroes;
10*10*10 has 3 zeroes;
similarly ;
this equation has 5 zeroes.
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Answer:
none
Step-by-step explanation: 105×5=525
Mike took a loan of $20,000 from a bank on 4 February 2009 at the rate of 8% p.a and paid back the same on 6th July 2009. Find the total amount paid by Mike
A. N20,666.30
B. N21,777.40
C. N22,888.50
D. N24,999.60
Como puedo resolver estas funciones y saber su tipo?
15% of the students in the 6th grade wear glasses. If 12 students wear glasses, how can you determine the number of students in the 6th grade? Explain your reasoning.
Answer: There are 80 people in the 6th grade
Step-by-step explanation:
For positive integer n, defined
[tex] \rm f(n) = n + \frac{16 + 5n - 3 {n}^{2} }{4n + 3 {n}^{2} } + \frac{32 + n - 3 {n}^{2} }{8n + {3n}^{2} } + \frac{48 - 3n - 3 {n}^{2} }{1 2n+3 {n}^{2} } + \cdots + \frac{25 {n} - 7n^{2} }{7 {n}^{2} } [/tex]
Then, the value of [tex] \displaystyle\rm\lim_{n \to \infty } [/tex] is equal to
Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by
[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]
That is,
[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]
[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]
and so on, up to
[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]
We then have
[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]
Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.
[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]
Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].
[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]
Any help would be appreciated.
What is that for?
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TOOIS
Question 3
A pipe is leaking at a rate of 8 fluid ounces per minute. How many gallons per hour will leak from the pipe?
0.02 gal/hr
A
B
C
D
3.75 gal/hr
17.07 gal/hr
3,840 gal/hr
If a pipe is leaking at a rate of 8 US fluid ounces per minute, then 3.75 US liquid gallons of the fluid will leak from the pipe in an hour.
As per the question statement, a pipe is leaking at a rate of 8 US fluid ounces per minute and we are required to calculate the amount of leak that will occur at the same rate of leakage, in an hour, in the units of US liquid gallons.
To solve this question, we need to know to know about two basic mathematical conversions, i.e.,
1 US Liquid Ounce = 0.00781 US Liquid Gallons, and
1 hour = 60 minutes.
Therefore, amount of leak that will occur at the rate of 8 US fluid ounces per minute, in an hour = [tex](8 * 60)=480[/tex] US fluid ounces.
And 480 US fluid ounces = [tex](0.00781 * 480)=3.75[/tex] US Liquid Gallons.
Hence, 3.75 US Liquid Gallons of fluid will leak from the pipe in an hour.
Fluid Ounce: It is an unit of volume, used for measuring liquids. "The British Imperial" and the "United States customary" fluid ounce are the only two that are still in use. The US Fluid ounce is an unit of capacity equal to one-sixteenth of a US pint (approximately 0.03 liter), while the British Imperial fluid ounce a unit of capacity equal to one twentieth of a pint (approximately 0.028 liter).Liquid Gallons: In the United States, Liquid Gallon is an unit of liquid capacity equal to four quarts or 231 cubic inches or 3.785 liters, while in the Great Britain, also known as the "Imperial Gallon", it is an unit of liquid and dry capacity equal to four quarts or 277.42 cubic inches or 4.544 liters.To learn more about Fluid Ounces and Liquid gallons, click on the klink below.
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name a fraction between 6/7 and 1
Answer:7/8, 8/9, 9/10, 10/11, etc.
what is (8^5)^4 (answer must include an exponent )
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]
A rectangular ballroom is being carpeted and measures 32‘ x 24‘. Carpet cost $3.60 per square foot. What is the cost to carpet this room?
The cost to carpet this room area is $2764.8.
What is the area?
The area is the volume that expresses the extent of a region on the plane or on a twisted face. The area of a plane region or plane area refers to the area of a shape or planar lamella, while face area refers to the area of an open face or the boundary of a three-dimensional object.The area can be understood as the quantum of material with a given consistency that would be necessary to fashion a model of the shape.Area of room = 32*24 (product is equal to the area of carpet)
Cost of carpet per square foot = $3.6 (three. six)
Cost of carpet = Area of carpet * Cost of carpet per square foot (product)
= 32 x 24 x 3.6
= 2764.8
The cost to carpet this room area is $2764.8.
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6 mm
4 mm
h
12 mm
8.5 mm
Kiyana's grandmother has a collection of hats for special occasions. Each hat is in a cube-shaped box with edges 1 ft long. She stores the boxes in a rectangular closet with the dimensions shown. Length = 6 ft N Height = 9 ft Width= 5 ft 3 4 5 > 2 of 5 Completed What is the maximum number of boxes that Kiyana's grandmother can fit inside the closet? Choose one option from each drop-down menu to answe the question. Kiyana's grandmother can fit a maximum of [ ] boxes along the length,[. ] boxes along the wide and [ ]boxes along the height of the closet. This means she can fit a maximum of [ ]boxes inside the closet
The maximum number of cubical boxes of side 1 feet that can be placed in a rectangular closet of length 6 feet, height 9 feet and breadth 5 feet is 270 boxes. Maximum number of boxes that can be placed along the length, height and breadth will be 168 boxes, 198 boxes and 150 boxes respectively.
Since the cube shaped boxes of length 1 feet are to be placed in the rectangular closet, the maximum number of boxes that will fit completely would be given as a comparison of volume of rectangular closet being equal to product of number of boxes and volume of 1 cubical box.
Volume of rectangular closet = Number of boxes * Volume of 1 cubical box
6 * 9 * 5 = n * (1*1*1)
Therefore, n = 270 boxes.
To calculate maximum number of boxes that will fit along the length would be calculated as product of length and breadth along 2 faces of closet and length and height along another 2 faces of closet.
Thus, [(9*6) + (9*6) + (6*5) + (6*5)] = 168 boxes along the length.
Similarly, to calculate maximum number of boxes that will fit along the height would be calculated as product of height and breadth along 2 faces of closet and length and height along another 2 faces of closet.
Thus, [(9*6) + (9*6) + (9*5) + (9*5)] = 198 boxes along the height
Similarly, to calculate maximum number of boxes that will fit along the breadth would be calculated as product of height and breadth along 2 faces of closet and length and breadth along another 2 faces of closet.
Thus, [(5*6) + (5*6) + (9*5) + (9*5)] = 150 boxes along the breadth.
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Triangle ABC has coordinates A(0, 6), B(3, 0), and C(4, 3). Triangle ABC is reflected across the x-axis. What are the coordinates of C’?
Answer:
Step-by-step explanation:
create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)