The width of the rectangle is: 33m, by Pythagoras theorem.
What is Pythagoras Theorem?The Pythagorean Theorem describes a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Now,
given:
Length of rectangle = 56m (say, l)Diagonal = 65m (say, d)TO find: Width of rectangle = ? (say, w)
Finding:
BY Pythagoras theorem, in the rectangle ABCD,
For l = AB, w = BC and d = AC,
=> l² + w² = d²
Ob substituting the values, we get: 56² + w² = 65²
=> w² = 65² - 56²
=> w² = 4225 - 3136
=> w² = 1089
=> w = 33m
Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.
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is the number 875 evenly divisible by the number 10
Answer:
no
Step-by-step explanation:
it would be 87.5
a vertical translation 3 units down, a vertical shrink by a factor of 1/4, a horizontal translation one unit right
( - 1.5 , -5 ) is a horizontal translation one unit right.
What is the formula for a vertical shrink?
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
Describe the transformation of the parent graph
f(x)=x^2 represented by g.
g(x)= -(2x+3)^2 - 5
Graph represents ( - 1.5 , -5 )
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X g(x)
10 -16
11 -17
12-18
13 -19
We get the equation for the points of the data as x y + 6 = 0
We are given the data as:
X g(x)
10 - 16
11 - 17
12 - 18
13 - 19
We need to find the equation for the data.
Slope = ( - 17 + 16 ) / ( 11 - 10)
m = - 1 / 1 = - 1
Now, the equation will be:
y - y₁ = m (x - x₁)
Substituting the values, we get that:
y + 16 = - 1( x - 10)
y + 16 = - x + 10
x + y + 16 - 10 = 0
x + y + 6 = 0
Therefore, we get the equation for the points of the data as x y + 6 = 0
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to find the ratio of 7
Answer:
Ratios compare two numbers, usually by dividing them If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10
Step-by-step explanation:
hope this helps u :) have a good day! ^-^
HELP URGENTLY PLEASE
here's the coordinates
b'= (4,5)
c'= (5,3)
The cost of 3 paninis and 2 drinks is £12 The cost of 7 paninis and 2 drinks is £20. how much does panini and drinks cost
Answer:
£23
Step-by-step explanation:
£12 + £20 = £23
or
£20 - £12 = £8 difference.
5. in an experiment that tested how adding variable quantities of sugar to flowers in a vase made the flowers last longer, the dependent variable would be the
Aileen is a salesperson at Lopez Sporting Goods. She is paid a monthly commission on all Little League uniforms she sells. She receives 10% of her first $2,000 in sales and 12% of the balance of her sales. Last week she earned $231.20. What was the total value of the uniforms she sold?
The total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.
Given,
Let us assume the all little League uniform = x
Aileen first commission 10% of 2000$ in sales.
Aileen Second Commission 12% of (x-2000)$
Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)
231.2 = 0.1× 2000 + 0.12× (x-2000)
231.2 = 200 + (0.12x - 240 )
231.2 = 200 + 0.12x - 240
After Transformation, we get
0.12x = 231.2 - 200 +240
0.12x = 271.2
x = 271.2/.12
x = 2260
Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.
So the final Answer is x = 2260$.
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Cost ($)
Rocko paid $12.50 for 25 game tickets.
Louisa paid $17.50 for 35 game tickets. What
is the constant of proportionality?
The constant of proportionality is $0.50.
A mathematical constant is a significant integer whose value is determined by an explicit definition. It is frequently denoted by a symbol or by the names of mathematicians to make it easier to use in a variety of mathematical situations.
The amount paid by Rocko is $12.50 for 25 game tickets.
The amount paid by Rocko is $17.50 for 35 game tickets.
A proportional relation can be written as:
y = k × x
where k is a constant, y is the cost, and x represents the number of tickets purchased in this instance.
Substituting the values, for Rocko
$12.50 = k × 25
Therefore
k = $12.50 / 25
k = $0.50
For Louisa,
$17.50 = K × 35
K = $17.50 / 35
K = $0.50
Now, k = K
So we have the same value of the constant in both cases, which means that the constant of proportionality is k = $0.50.
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To maintain a healthy weight a dog requires 30 calories of food per pound of body weight. if a certain dog weighs 38.45 ibs how many calories would they require
Step-by-step explanation:
30 cal for 1 lb
x cal for 38.45 lbs
x = 38.45lbs × 30 cals
x = 1153.5 cals
Each year, Jennifer's school hosts a student vs. teacher basketball tournament to raise money for charity. This year, there are eight teams participating in the tournament. During the first round, each team plays all of the other teams.
(a) How many games will be played in the first round?
The number of games that will be played in the first round will be 14 games.
How to calculate the value?It should be noted that the appropriate function to use in this scenario will be:
= (n - 1) × 2
where n = total number of people participating.
Therefore, this will be:
= (n - 1) × 2
= (8 - 1) × 2
= 7 × 2
= 14
Therefore, the number of games that will be played in the first round will be 14 games.
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Simplify
(2m^3n^2)^5
[tex] \large \bf \implies{32 {m}^{15} {n}^{10} }[/tex]
Step-by-step explanation:[tex]\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} [/tex]
Note : We have used the two exponent rules:
[tex](1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}[/tex]
[tex](2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}[/tex]
Eight more than twice a number is less than negative eighteen. Solve the inequality for the unknown number.
The answer is
.....
(Simplify your answer. Type an inequality using x as the variable.)
The Equation representing the following inequality will be 2x + 8 < -18
In the given question, it is stated that a number is 8 more than twice a number that is less than -18.
Let the number be x.
The twice of a number = 2x
A number eight more than twice a number = 2x +8
With the following statements, we get the Number = (2x+8). Also, we have a condition that this new number is lesser than -18. So we get our equation,
=> 2x + 8 < -18
Hence, This 2x + 8 < -18 represents the inequality mentioned in the question stating that a two number is created in which it is lesser than -18.
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solve the equation 3x = 21
Answer:
x = 7
Step-by-step explanation:
3x = 21 ( isolate x by dividing both sides by 3 )
x = 7
2. On an average day, Americans spend $1958904.00 buying video games. Of this total $1167123.00 is spent on Sony Playstation games. In one week how much do Americans spend on Sony Playstation Games. How much do they spend on other video games in a week?
Answer:
5,000
Step-by-step explanation:
Answer:
Money spent on playstation games per week: =$8169861
Money spent on other video games per week: = $5542467
Step-by-step explanation:
Hi to answer this first, we have to calculate how much Americans spend on non Playstation video games. So, we have to subtract the money spent on Sony Playstation games to the total money spent:
$1958904.00-$1167123.00= 791781 on other video games per day
Now, since each week has 7 days. We have to multiply each daily amount by 7.
Money spent on playstation games per week: $1167123.00 x 7=8169861
Money spent on other video games per week: $791781 x 7= 5542467
The cross country team left school and trotted to the duck pond at 3mph then ran back to the school at 7mph if the total trip took ten hours how far was the duck pond
Answer:
hey thank you it's I don't know lol thanks
I dont get it pls helpppp ihave ten min left it a test HELP
Answer:
d. p+1
a negative 1 point something decimal plus one negative decimal.
gl sh awty
please help need the answer fast
Answer:
n=7
Step-by-step explanation:
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please show your work after you answer,if you dont.... that's okay too!
Answer: 980.17691.
Step-by-step explanation:
Answer:
980.5714286 ft² or 979.68 ft²
Round this number to the
nearest hundredth.
0.7456
Answer:
0.75
Step-by-step explanation:
it goes tenths hundredths thousandths....
Answer:
0.75
Step-by-step explanation:
4 is the hundredth in this number. The number after 4 is 5. The rule is if its 5 and over you round up and if not, you round down. In this case the number is 5 so we round up. So the number becomes 0.75 instead of 0.74
The school newspaper wants to find the opinions of students on availability of campus parking. They send a staff member to stand outside a busy dorm and interview students as they walk in or out of the building. What type of sampling process did the paper use?.
Answer: single random sample
Step-by-step explanation:
Calculate the unknown angle of x
Answer: x = 50°
Step-by-step explanation:
As you can see in the triangle, the two sides are congruent. One of the angles next to the congruent side is 50 degrees. Therefore the other angle also has to be 50 degrees.
Answer:
X=50°
Step-by-step explanation:
This is because the triangle is an isocele triangle and as we all know an isocele triangle is a triangle with 2 sides equal.
1. A parabola has an axis of symmetry y =3 and passes through the point (2, 1). Find
another point that lies on the graph of the parabola. Explain your reasoning.
A parabola has an axis of symmetry y =3 and passes through the point (2, 1), another point that lies on the graph of the parabola is (2,5).
Axis of symmetry:
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.
Given,
Axis of Symmetry y = 3.
One point = (2,1)
Here we need to find the another point that lies on the graph of the parabola.
Use the axis of symmetry.
Point given (2,1) is 2 units away from that axis, lower.
=> 1 + 2 = 3
Take two units higher,
=> 3 + 2 = 5
and is the another point (2,5), on the same parabola.
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HELPPPPPPPPPPPPPPP ILL MARK AS BRAINLIST HELPP
The graphs of the equations can be obtained by finding the intercepts, and drawing a line through the intercepts.
1. Please find attached the graph of 2•x - y - 6 = 0
2. Please find attached the graph of 4•x + 2•y + 8 = 0
How can a graph be drawn using the intercepts?The graph of the linear equations using the x and y intercepts are found as follows;
1. 2•x - y - 6 = 0
Therefore;
2•x - y - 6 = 0
y = 2•x - 6
The y-intercept is given by the point where x = 0
The y-intercept is therefore;
y = 2×0 - 6 = -6
The y-intercept is y = -6The x-intercept is given by the point where y = 0
Therefore;
0 = 2•x - 6
x = 6/2 = 3
The x-intercept is at x = 3Please find attached the graph of 2•x - y - 6 = 0, created using the x and y-intercept.
2. 4•x + 2•y + 8 = 0
Therefore;
4•x + 2•y + 8 = 0
y = -(4•x + 8)/2 = -2•x - 4
y = -2•x - 4
The y-intercept is therefore;
y = -2×0 - 4 = -4
The y-intercept is y = -4
The x-intercept is therefore;
0 = -2•x - 4
x = -4/2 = -2
The x-intercept is at x = -2
Please find attached the graph of 4•x + 2•y + 8 = 0, created using the x and y-intercept.
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Find a vector function that represents the curve of intersection of the two surfaces. the cylinder x 2 y 2 = 4 and the surface z = xy. r(t) = 2cos(t) i j k
Let [tex]x=2\cos(t)[/tex] and [tex]y=2\sin(t)[/tex], so that
[tex]x^2 + y^2 = 4\cos^2(t) + 4\sin^2(t) = 4[/tex]
is preserved. Then from the surface equation, we get
[tex]z = xy = 4\cos(t)\sin(t) = 2\sin(2t)[/tex]
The curve of intersection is then given by the vector function
[tex]\vec r(t) = 2\cos(t) \, \vec\imath + 2\sin(t)\,\vec\jmath + 2\sin(2t)\,\vec k[/tex]
Postal Clerks weigh each piece of mail to find a mailing cost. It costs $0.45 per ounce to mail an item. If Sara mails two items having weights of 7 ounces and 6 3/5 ounces, how much does she pay?
we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.
Sara has 2 items:
Weight of 1st item = 7 ounces.
Weight of second item = 6 3/5 ounces = 33 / 5 ounces.
Total Weight of items to be mailed = 7 ounces + 33 / 5 ounces
Total Weight = 35 + 33 / 5 ounces = 68 / 5 ounces.
Now, cost of mailing 1 ounce per mail = $ 0.45
Cost of mailing 68 / 5 ounce of mails = 68 / 5 × $ 0.45
Total cost = $ 6.12
Therefore, we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.
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which inquality best represents the domain of the function shown on the graph?G, 3
Which flaw most accurately illustrates the graphed function's domain?
The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.
Domain here refers to the x change. The values of with regard to function should be the domain in this case. Additionally, we need to pay attention to the blank line that starts at -9 to 2 in x values.
Since 9 should not be filled however 2 should be.
Therefore, The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.
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if a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function.
It is true that if a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function.
What do you mean by the term matrix?Without further explanation, matrices represent linear maps and enable explicit computations in linear algebra. In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or a property of such an object. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.
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Laura runs during her lunch break.
The average speed S, in kilometers per hour, at which Laura runs depends on the temperature t, in degrees Celsius (°C), at the start of her run and can be modeled by the function S(t) = 6 + 0.2(25 - t).
The distance, D, in kilometers, that she can run in 30 minutes given that her average speed is a kilometers per hour can be modeled by the function D(x) = 0.5x.
Which expression models the distance that Laura runs in 30 minutes given that it is t°C outside at the start of her run?
A. 5.5 - 0.2t
B. 11 - 0.1t
C. 11 - 0.5t
D. 5.5 - 0.1t
Using composite functions, the expression that models the distance that she runs is:
D. 5.5 - 0.1t.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by:
(f ∘ g)(x) = f(g(x)).
In this problem, we have that:
The velocity as a function of the temperature is: S(t) = 6 + 0.2(25 - t) = 11 - 0.2t.The distance as a function of the velocity is: D(x) = 0.5x.Hence the distance as a function of the temperature is given as follows:
(D ∘ S)(t) = D(S(t)) = 0.5(11 - 0.2t) = 5.5 - 0.1t.
Which means that option D is correct.
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Solve for n.
-3=18m+6n
Answer: n= -1/2 -3m
Step-by-step explanation: