The answer is 112 centimeters.
As this problem represents a right triangle, here we need to apply the Pythagorean Theorem.
h = √113² - 15²h = √12769 - 225h = √12544h = 112 centimetersMrs. washington has a small fenced-in, rectangular play area behind her house for her dog. there is 80 feet of fencing around the perimeter of the play area, and the width is 14.8 feet. mrs. washington needs to buy new sod to cover the entire area of play space. if sod costs $1.50 per square foot, how much will it cost mrs. washington to buy enough sod for the entire play area?
Answer:
$1118.88
Step-by-step explanation:
Lets start by finding all sides of the perimeter to get an accurate measure of the area.
We know the width is 14.8 feet, that means the opposite side also equals 14.8 feet.
Now the other two sides must sum to 50.4 (80-(14.8*2)) and be equal, so we can divide 50.4 by two to get 25.2 for the other two sides.
Now we can calculate area by multiplying one from each side:
[tex]14.8*50.4=745.92[/tex]
Now to find the price of required sod, multiply the area by cost per square foot
[tex]745.92*1.50=1118.88[/tex]
Therefore it will cost 1118.88 dollars to cover the entire area in sod.
In the figure, what is the ratio of the area of square KLMN to the area of LOK?
the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
How to determine the ratioFrom the image given, we can deduce the following;
KLMN is a squareLOK is a triangleThe formula for area of a square is
Area = a^2
Where, 'a' is the side
The formula for area of a triangle
Area = 1/ 2 base × height
Now, let's find the ratio
Ratio = area of KLMN/ area of LOK
Ratio = [tex]\frac{a^2}{\frac{1}{2} bh}[/tex]
Ratio = [tex]\frac{a^2}{\frac{bh}{2} }[/tex]
make the expression linear
Ratio = 2a^2/bh
The ratio of the area of square KLMN to the area of LOK is 2a^2/bh
Thus, the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
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28 grams of seeds cost $100 , and 14 grams of seeds cost $60. If you only have $70 and someone gives you $30 to buy 28 grams, how many grams of seeds would you give the person that gave you $30 if you paid $70?
Answer:
8.4 grams
Step-by-step explanation:
We have $70 to start and someone us another $30 for a total of $100. We pay $100 for 28 grams of seeds. If we assume the peron giving us $30 wants a fair share of the seeds, we would calculate an average cost per gram and use that to determine the grams of seeds that the $30 would have covered.
($100/28 grams) = $3.57/gram
($30/$3.57/gram) = 8.4 grams
Answer:
28 grams of seeds
Step-by-step explanation:
(This question is a little tricky)
Note that:
{28 grams of seeds = $100}
----------------------------------------
You have $70 already, and then someone gives you $30.
It means $70 + $30 = $100
So you have $100 now, you can buy 28 grams of seeds and give the person that gave you $30.
Hope this helps :)
Express 60 as a product of its prime factors
Answer:
The actual prime factors of 60 are 2, 3, and 5.
Step-by-step explanation:
Greetings !
Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2² × 3 × 5.
The graph of the function f(x) = –(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The vertex is the . The function is positive . The function is decreasing . The domain of the function is . The range of the function is .
The graph of the function f(x) = -(x+1)^2 shows that the domain of the function f(x) = -(x+1)² is: -∞ < x < ∞. The range of the function is f(x) ≤ 0.
What is the graph of a function?The graph of a function is the arrangement of all ordered pairs of the function. Typically, they are expressed as points in a cartesian coordinate system. The graph of f is the collection of all ordered pairings (x, f(x)) such that x lies inside the domain of f.
The graph of a function might similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.
From the given information: the graph of the function f(x) = -(x+1)² can be determined if the domain, the range, and the vertex of the function are known.
The domain of the function f(x) = -(x+1)² is: -∞ < x < ∞The range of the function is f(x) ≤ 0The x-intercepts and the y-intercepts are (-1,0) and (0, -1) respectivelyThe vertex is maximum at (-1,0)Since the parabola curve from the graph shows that the graph is facing down, then the function is negative and decreasing.
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1.) maximum value
2.) for no values of x
3,) when x > -1
4.) all real numbers
5.) all numbers less than or equal to 0
Kenton watched 2000 adult men and women board a cruise ship. half of the adults were women. if 20$\%$ of the women and 9$\%$ of the men were wearing sunglasses, what was the total number of men and women wearing sunglasses?
Total number of men and women wearing sunglasses = 290
According to the question,
Total number of men and women = 2000
half of the adults were women = 1/2 × 2000
Number of women = 1000
Number of men = (Total adults) - (Number of women )
Number of men = 2000 - 1000
= 1000
given,
20% of women were wearing sunglasses = 20/100 × 1000
= 200
9% of men were wearing sunglasses = 9/100 × 1000
= 90
Total number of adults wearing glasses = 200 + 90
= 290
What is the percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.
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Given MTS and SQP, find sq
The measure of the side SQ from the given diagram is 19/6
Similar shapesSimilar shapes are shapes that has equal length and equal side measures and angles.
From the given diagram, the measure of the sides TSis congruent to SP and the measure of MS is congruent to SQ.
Using the expression below to determine the value of x
MS/ST = SQ/SP
Given the following parameters
MS =30
ST = 10
SQ = 6x-1
SP = 3 - 2x
Substitute the given parameters into the formula to have:
30/10 = 6x-1/3-2x
Cross multiply
10(6x-1) = 30(3-2x)
Expand
60x - 10 = 90 - 60x
60x + 60x = 90 + 10
120x = 100
x = 10/12
x = 5/6
Determine the measure of SQ
SQ = 6x - 1
SQ = 5(5/6) - 1
SQ = 25/6 - 1
SQ = 19/6
Hence the measure of the side SQ from the given diagram is 19/6
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Question
Each square on the grid represents 1 km2.
What is the approximate area of this park?
about 10 km2 to 20 km2
about 10 km 2 to 20 km 2
about 25 km2 to 35 km2
about 25 km 2 to 35 km 2
about 40 km2 to 50 km2
about 40 km 2 to 50 km 2Question
Each square on the grid represents 1 km2.
What is the approximate area of this park?
about 10 km2 to 20 km2
about 10 km 2 to 20 km 2
about 25 km2 to 35 km2
about 25 km 2 to 35 km 2
about 40 km2 to 50 km2
about 40 km 2 to 50 km 2
The approximate area of the park on the grid is: E. about 40 km² to 50 km².
How to Find the Approximate Area on a Coordinate Grid?The number of square on a coordinate grid that is covered determines the area covered. We can make an estimate by counting how many of this square on the coordinate grid that is covered, then find out the area depending on how much square area each grid represents.
In the coordinate plane given, which shows a park, we are told that each of the square on the grid equals 1 k = square kilometer.
The number of each of these squares we can find that is covered by the park on the grid is: 48 squares.
Therefore, the area of 48 squares on the grid = 48 × 1 = 48 km². Since not all squares are fully covered by the park, we can state that the approximate area of the park on the grid is: E. about 40 km² to 50 km².
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A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
Answer:
23 customers on payment plan B
13 customers on plan text B
Probability: 13/23
Step-by-step explanation:
Our of the four runners: Alex, Ben, Curtis, and Dan, the oldest came in second place. Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis. It is also known, that Ben is older than Alex, and Curtis is older than Dan. In what order did the four runners finish?
Considering the situation described, the classification of the runners is given as follows:
Dan - Ben - Alex - Curtis.
What is the classification of the runners?The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.
Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:
Dan - Ben - Alex - Curtis.
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Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5.
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).
What is transformation in math?A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.
The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:
TranslationRotationReflection; and Dilation.What transformations would you use on the blue triangle to get it to match with the red triangle?The type of transformation that will be used here is called reflection.
D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).
Which line segments on the boat are parallel?The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).
Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.
Which line segments on the boat are perpendicular?The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.
The line segments on the boat that have a slope of zero are:
EF, AB AC, BC. A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.
The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.
The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)
Given that:
Y1 = 5
Y2 = 4
X1 = -10
X2 = -11
Hence,
m = (5-4)/(-11 -10)
m = -0.048
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A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
A.
89 feet
B.
141 feet
C.
71 feet
D.
45 feet
The maximum possible side length of the base of the building is; C: 71 feet.
How to determine the maximum side length of a Pyramid?The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:
Base is expressed as b
Slant height (l) is expressed as 5b
The lateral surface area of the square pyramid is calculated from the formula given as;
LSA = 2bl
Thus, the lateral surface area is expressed as;
L = 2 * b * 5b
L = 10b²
The total surface area is calculated using the formula:
T = L + b²
Thus, plugging in the value of 10b² for L gives the total surface area as;
T = 10b² + b²
T = 11b²
The maximum surface area is 50,000 square feet and so we can find b from the following expression;
11b² = 50000
Divide both sides of the equation by 11 to get;
b² = 50000/11
b = √(50000/11)
b = 71 feet to the nearest foot.
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Jessica fills a cube shaped tank that has an edge of 70 cm with water from a tap. Water flows into the tank at a rate of 7L per minute. How long will it take to fill the tank fully?
The volume of the tank is (70 cm)³ = 343,000 cm³.
Now,
1 mL = 1 cm³
1 L = 1000 mL
so we convert the given rate to
[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]
Then the time it will take to fill up the tank is
[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]
Im trying do it on my own just checking my answer
Answer:
Step-by-step explanation:
when the product of 15 and 40 is diveded by the sum of 15 and 45 what is the quotient
Answer:
The answer is 10Step-by-step explanation:
First, you have to multiply. 15x4=60. All you need to do is add a zero to that product. You will get 600. Product means the answer to a multiplication problem. That is why you would have to multiply to get your answer. Your answer to that part is 600. 15*40= 600. Then, you would do 45+15= 60. 600/60= 10. Your answer is 10.
Explain the similarities and differences between the two relationships in this situation.
Lexi needs to hire a carpenter to redo her bathroom. Charlie and Sons charges $1000 for the design fee and $75 per
hour for labor. Home Dreams charges $800 for the design fee plus $80 per hour for the labor.
Find the cost of each service assuming the job will take 100 hours.
Which contractor is more expensive? How do you know?
What is the area of the triangle shown below?
Answer:
5 un^2
Step-by-step explanation:
the liens from (0, 0) to (1, 3) and (1, 3) to (4, 2) are perpendicular meaning that the angle at (1, 3) is a right angle
to find the lengths of the sides we must use the pythagorean theorem
a^2 + b^2 = c^2
for the leftmost side
we have 1^2 + 3^2 = c^2
1 + 9 = 10
c^2 = 10
c = sqrt(10)
for the top side
we have
the same thing
1^2 + 3^2 = c^2
1 + 9 = 10
c^2 = 10
c = sqrt(10)
you must multiple sqrt(10) by sqrt(10) and then by 1/2
sqrt(10) * sqrt(10) is 10
10 * 1/2 is 5
the area is 5 un^2
Factorise 10xy-12+15x-8y
Answer: 10xy-12+15x-8y=(5x-4)*(2y+3).
Step-by-step explanation:
[tex]10xy-12+15x-8y=(10xy-8y)+(15x-12)=\\=2y*(5x-4)+3*(5x-4)=(5x-4)*(2y+3).[/tex]
Solve 2(1 - x) > 2x
Answer:
x < 1/2
Step-by-step explanation:
2(1-x) > 2x
2-2x > 2x
2 > 4x
1/2 > x
Answer:
x<1/2
Step By Step Explanation
Let's solve your inequality step-by-step.
2(1−x)>2x
Step 1: Simplify both sides of the inequality.
−2x+2>2x
Step 2: Subtract 2x from both sides.
−2x+2−2x>2x−2x
−4x+2>0
Step 3: Subtract 2 from both sides.
−4x+2−2>0−2
−4x>−2
Step 4: Divide both sides by -4.
-4x/2>-2/4
x<1/2
PLEASE HELP!!!!!!!!!!!!!!!!!!
Answer:
[tex]\sin\left(x+\frac{\pi}{7} \right)[/tex]
Step-by-step explanation:
[tex]\sin\left(x+\frac{\pi}{7} \right)=\sin \frac{\pi}{7}\cos x +\cos \frac{\pi}{7} \sin x[/tex]
If the first two angles of a triangle measure 45° and 111°, what does the third angle measure?
Answer:
third angle measures 24°
Step-by-step explanation:
triangles are 180°
add up the first two angles and subtract the sum from 180°
45° + 111° = 156°
180 - 156 = 24
URGENT What is the discontinuity and zero of the function f(x)= (x^2 - 4x - 21)/(x + 7)
Answer:
when x=-7
Step-by-step explanation:
if u are solving a function like this, u must not have a division by zero so if we put x=-7 in the function we hav a division by zero
Jeremy likes to paint. he estimates the number of paintings he completes using the function p of w equals one third times w plus four, where w is the number of weeks he spends painting. the function j(y) represents how many weeks per year he spends painting. which composite function would represent how many paintings jeremy completes in a year? p of j of y equals j times the quantity one third times w plus four j of p of w equals one third times j of y plus four p of j of y equals one third times j of y plus four j of p of w equals j times the quantity one third times w plus four
composite function J[P(W)=J(1/3w+4) represent paintings Jeremy completes in a year .
this equation means number of paintings= weeks(rate)
The function P takes a number of weeks as an argument and returns the number of paintings.
The function J takes some argument (unspecified) and returns a number of weeks per year.
The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).
P(J(y)) = 1/3·J(y) +4 .
Looking at the units of the input and output of each of the functions is called "units analysis."
What is Unit analysis?Unit analysis means using the rules of multiplying and reducing fractions to solve problems involving different units.
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Answer:
P[J(y)] = 1/3 (Jy) + 4
Answered the quiz and it's correct.
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.
What is the required number:Here in the question it is given that,
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
By separating them as two parts
sum of -5/6 and -1 3/5 sum of 2 2/3 and -6 2/5⇒ sum of -5/6 and -1 3/5
- 5/6 + - 1 3/5 = - 5/6 + - 8/5 (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)
= (- 25 - 48)/30 (LCM = 30)
= - 73/30
⇒ sum of 2 2/3 and -6 2/5
2 2/3 + -6 2/5 = 8/3 + -32/5
= (40 - 96)/15 (LCM = 15)
= - 56/15
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)
= (- 56/15) - (- 73/30 )
= - 56/15 + 73/30
= - 112/30 + 73/30 (LCM = 30)
= - 39/30
= - 13/10
= - 1.3
Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.
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The tens digit of a two-digit number is 5 greater than the units digit. If you subtract twice the reversed number from the original number, the result is a fourth of the original number. Find the original number
Answer:
The number is 72.
Step-by-step explanation:
Let the number be xy.
x = y + 5
10x + y - 2(10y + x) = 0.25(10x + y)
10x - 2x + y - 20y = 2.5x + 0.25y
5.5x - 19.25y = 0
Substituting for x:
5.5y + 27.5 - 19.25y = 0
-13.75y = -27.5
y = 2.
So x = 2 + 5 = 7.
Which of the following points below is on the line defined by the two parametric equations below?
x(t)=1/2t+4
y(t)=2t−10
Group of answer choices
(5,8)
(6,6)
(0,4)
(4,−10)
Answer:
(d) (4, -10)
Step-by-step explanation:
We are asked to identify the point that falls on a line defined by parametric equations.
Vector form equationThe parametric equation can be written in a number of forms One of these is a vector form, in which some multiple of a vector is added to a known point.
(x(t), y(t)) = (1/2t +4, 2t -10) = (4, -10) +(1/2t, 2t)
(x, y) = (4, -10) +(t/2)(1, 4)
Clearly, when t=0, one point on the line will be (4, -10) — the last of the offered choices.
Other formsAnother form of the equation can be had by solving the x(t) and y(t) equations for t, then equating those values.
x = 1/2t +4 ⇒ 2(x -4) = t
y = 2t -10 ⇒ (y +10)/2 = t
Equating these gives ...
2(x -4) = (y +10)/2 . . . . t = t
4x -16 = y +10 . . . . . . . multiply by 2
4x -y = 26 . . . . . . . . . add 16-y to put in standard form
Dividing by 26 gives intercept form:
x/6.5 +y/(-26) = 1 . . . . . x-intercept: 6.5, y-intercept: -26.
This tells you the value of y will be negative for all x-values less than 6.5. All of the offered points have x-values less than that, so the only viable answer choice is (4, -10).
Answer:
(4.-10)
Step-by-step explanation:
When t = 0:
x(t)=1/2t+4
x(0)=1/2(0)+4
x(0) = 4
-------------------
y(t)=2t−10
y(0)=2(0)−10
y(0) = -10
(x,y) at t = 0 is (4, -10)
what is the equation of 7.2+c=19 ?
7.2 + c = 19
c = 19 - 7.2
c = 11.8
Answer:
Your answer is 5.
Step-by-step explanation:
7.2 + c = 19
or, 14 + c = 19
or, c = 19 - 14
or, c = 5 ans.
Hope its helpful :-)
A honeybee leaves its hive and travels 100 m due west, 200 m due south, and then returns to a position 5 m north of its hive. what is its total displacement?
The total displacement of the honeybee as it travels west, south and north is 219.2 m.
Total displacement of the honeybeeThe total displacement of the honeybee is calculated as follows;
total horizontal displacement, x = 100 m due west
total vertical displacement, y = 200 m - 5 m = 195 m
total displacement, d = √x² + y²
d = √(100² + 195²)
d = 219.2 m
Thus, the total displacement of the honeybee as it travels west, south and north is 219.2 m.
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