With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.
What is Pythagoras Theorem?According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given:
Sides of a right triangle are 2 and 4 units.
To find: Area of a square that shares a side with the third side of the triangle.
Finding:
There can the following cases:
If 2 and 4 units are the lengths of the perpendicular sides.
Then, by Pythagoras Theorem, -
[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]
Hence, the area of the square = side² = 20 units²
If 4 units is the length of hypotenuse.
Then, by Pythagoras Theorem,
[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]
side of triangle = [tex]\sqrt{12}[/tex]
Hence, the area of the square = side² = 12 units²
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90% of what number is 45?
Answer:
40.5
Step-by-step explanation:
M, N and P are points on a circle, centre O.
MON is the diameter of the circle.
MP = 3.5 cm
PN = 9.7 cm
Angle = 90º
Work out the circumference of the circle.
Give your answer correctly to 3 significant figures.
Step-by-step explanation:
just draw what I have done
Bashir was out at a restaurant for dinner when the bill came. His dinner came to $32.
After adding in a tip, before tax, he paid $39.36. Find the percent tip.
Answer:
23%
Step-by-step explanation:
39.36-32=7.36
7.36/32=.23
23 percent
what trigonometric expression can be used to find the value of x? replace a and b with the correct values.
The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .
Given :
A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .
Trigonometric Formula for Tan θ
tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .
where θ = 25 , perpendicular = 12 , base = x .
Substituting values in above first formula ,
tan 25 = 12 / x
Therefore , x = 12 / tan ( 25 ) .
Hence , a = 12 and b = 25 .
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What are the key features of the quadratic function f(x) = 2(x - 3)2 + 4
The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
The given quadratic function is f(x) = 2(x - 3)² + 4.
We need to find the key features of the given quadratic function.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Now, the key features of the given quadratic function as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3, 4)
Focus: (3, 33/8)
Axis of Symmetry: x=3
Directrix: y=31/8
Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.
Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
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9. Mr. Crowley bought lunch for himself and eight of his employees.
Each had a sandwich platter that costs $5.85 and a drink that
costs $1.25. Five of the employees had dessert that costs $1.50.
Mr. Crowley gave the delivery person $80 and told her to keep
the change as a tip. How much was the delivery person's tip?
Answer:
$8.60
Step-by-step explanation:
Let x = the tip
80 - x = 9(5.85 + 1.25) + 5(1.50)
80 -x = 63.90 + 7.5
80 - x = 71.40 Subtract 80 from both sides
-x = -8.60 Divide both sides by -1
x = 8.60
A company makes a profit of $55 per software program and $45 per video game. The company can produce at most 225 software programs and at most 275 video games per week. Total production cannot exceed 450 items per week. How many items of each kind should be produced per week in order to maximize the profit?
Use linear programming to solve. Show all your work.
Answer:
they should produce 225 software programs and 225 video games per week.
Step-by-step explanation:
limit 450
there are 2 factors the software and video games.
450•2= 225
SOMEONE HELP ME BEFORE I PASS OUT
1. |X|≤8
2. |X|≤27
Answer: 1. [-8, 8]
2. [-27, 27]
Step-by-step explanation:
1. |X|≤8
x≤8 or x>=-8
-8<=x<=8 ==> [-8, 8]
2. |X|≤27
x≤27 or x>=-27
-27<=x<=27 ==> [-27, 27]
lindsay bedford works at the baseball cap shop she is paid $6.50 per hour plus $0.45 for each cap she embroiders how many caps must she embroider to earn at least $85
Lindsay Bedford should embroider 73 caps.
Let us assume the number of number of caps needed to be embroidered for desired earning be x. Now, forming the equation to solve for x, thus, finding the required number of caps.
Equation -
6.50*8 + 0.45*x = 85
Now solving this equation for the value of x.
Performing multiplication of numbers on Left Hand Side
52 + 0.45x = 85
Shifting the product from Left Hand Side to Right Hand Side
0.45x = 85 - 52
Performing subtraction on Right Hand Side to find the value of x
0.45x = 33
Shifting 0.45 to denominator on Right Hand Side
x = 33÷0.45
Performing division to find the value of x
x = 73.3
The number of caps can not be in fraction. So, we will round off the digit to find exact number of caps.
Number of caps = 73
Therefore, Lindsay Bedford needs to embroider 73 caps.
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The complete question is -
Lindsay Bedford works at a baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders. How many caps must she embroider to earn at least $85 in an 8-hour day?
$72 is 4.5% of what amount
$72 is 4.5% of 6.25 amount. 6.25 Percentage of 72 is 4.5.
By considering the given information
[tex]72\times x=4.5\\x=\frac{4.5}{72}\times 100\\ x=6.25[/tex]
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. percent, which is a relative value used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
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$72 is 4.5% = $3.24
Solution :
The percentage is a rate or proportion per hundred,
The percentage is also used more generally to mean any proportion, as in Studies have shown that a large percentage of people love cute animals.
A percent is one one-hundredth (1/100) of something. The percentage refers to the rate or proportion of that one hundred. Usually, you will see the word percentage used in math equations or statistics or when someone is measuring the increase and decrease in rates
$72 is 4.5% =?
$72 is 10% = $7.2
$72 is 5% = $7.2 /2 = $3.6
$72 is 1/2%= $72 * .5/100 = $.72*.5 = $ 0.36
$72 is 4.5% = 5% - .5% = $3.6- $.36 = $3.24
$72 is 4.5% = $3.24
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2(3x-2)-4x+1= 9 solve for x
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 21 girls in the book club, how many boys are in the club?
Answer:
10
Step-by-step explanation:
(21-1)/2
Simplify (24)−1. one over two raised to the power of negative four one over two raised to the fourth power −24 23
The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).
The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
It is given that the expression is (2⁴)⁻¹
Now,
using the integer exponent properties,
=> (2⁴)⁻¹
=> (2)⁴* ⁻¹
=> (2)⁻⁴
=> 1/2⁴
Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.
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will the sum of 5 + (-2) be positive or negative? what is the sum? show your work.
Answer:
positive the answer is 3
Step-by-step explanation:
URGENT 1000 POINTS. BRAINLIEST GIVER...
(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11 in scientific notation. explain step by step!
Answer:
see image.
Step-by-step explanation:
Basically, what's happening here is you are adjusting one of the terms so that they both have the same exponent. Then you can factor out that 10^11 term and just add the two remaining terms.
see image.
The shaded diagram represents a block of land.
What is the area of the block?
By using Heron's formula and standard formula for the area of a triangle, the area of the composite figure is 921006.497 square meters.
What is the area of a composite figure?
In this problem we must determine the area of a composite figure, which consists in subtracting the area of an isosceles triangle from the area of the equilateral triangle:
Big triangle
The area of the big triangle is determined by Heron's formula:
s = [3 · (520 m)] / 2
s = 780 m
A = √[(780 m) · (1560 m - 520 m)³]
A ≈936693.077 m²
Small triangle
H = (520 m) · sin 60°
H ≈ 450.333 m
h = 450.333 m - 390 m
h = 60.333 m
A = 0.5 · (520 m) · (60.333 m)
A = 15686.580 m²
Then, the area of the composite figure is 921006.497 square meters.
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which measurements best approximate the lengths of the legs, to the nearest tenth of a centimeter, of a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg?
The length of the base will be equal to 65.99 centimeters.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. 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.
The formula for the Pythagorean theorem is given below:-
H² = B² + P²
Given that in a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg.
P = 70/ 3 cm
H = 70 cm
The value of the leg will be calculated as:-
H² = B² + P²
70² = B² + (70/3)²
B² = 70² - (70/3)²
B = √4355
B = 65.99 cm
Therefore, the length of the base will be equal to 65.99 centimeters.
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Can someone please help mee (20 points
brainliest!!!)
Answer:
60,000
Step-by-step explanation:
going straight across the line we can see that for $140 the demand in thousands 60
so
you can buy 60,000 units
Answer:
60 because oficial the line goes to 60
The cost c of a shirt is less than $27. 50.
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
Answer:
8 nickels and 14 pennies
Step-by-step explanation:
Let p = number of pennies
Let n = number of nickels
p + n = 22 .01p + .05n =.54
Take the second equation and multiple it through by 100 to clear the decimals.
100(.01p + .05n( = .54(100)
p + 5 n = 54 Multiply this through by -1 so that I can add it to the first equation.
-p -5n = -54
p + n = 22 Add these together
-4n = -32 Divide both sides by -4
n = 8 We have solved for n. We have 8 nickels.
Plug 8 in for n in the first equation and solve for p.
p + n = 22
p + 8 = 22 Subtract both sides by 8
p = 14 There are 14 pennies.
Check:
p + n = 22
14 + 8 = 22
22 = 22 Checks
.01p + .05n = .54
.01(14) + .05(8) = .54
.14 + .40 .54
.54 .54 check
ngozi earns \$24{,}000$24,000dollar sign, 24, comma, 000 in salary in the first year she works as an interpreter. each year, she earns a 3.5\%3.5%3, point, 5, percent raise.
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by [tex]S = 24000 * (1.035)^t[/tex].
What is a function?
A function in mathematics from a set X(ax) to a set Y allocates exactly one element of Y to each element of X(ax). A relation between a collection of inputs and labor is known as a function.You can use the fact that the raise is done on the previous year's salary.
Let the initial salary be P = $24000
After 1 year, her salary increased by R = 3.5% which, thus,
Total salary = P + increment
Similarly going on, we get
[tex]P_t = P(1+ \frac{R}{100})^t = S[/tex] (we can say)
Putting values of P(value of P) and R(value of R), we get
[tex]S = 24000(1 + 0.035)^t = 24000 *(1.035)^t[/tex]
Thus,
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by
[tex]S = 24000 * (1.035)^t[/tex]
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Please Help
Thanks In advance
Answer:
4
Step-by-step explanation:
you do cross multiplication
you do 3x12÷9
The Evans family drives 21 miles in the first miles in the first 20 minutes of their trip. what is their speed in miles per hour during this time? create a representation to show your work.
The measure of the speed during the time is 63. 64 miles per hour
How to determine the speedThe formula for speed is expressed as;
Speed = distance/ time
Given that;
Distance traveled = 21 milesTime = 20 minutesLet's convert the time in minutes to hour
60 minutes = 1 hour
20 minutes = x hour
cross multiply
x = 20/ 60
x = 0. 33 hours
Substitute the values
Speed = 21/ 0. 33
Speed = 63. 64 miles per hour
Thus, the measure of the speed during the time is 63. 64 miles per hour
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5f+2h=100
Solve for F
Solving for the variable gives f = 100 - 2h/5
What is subject of formula?Subject of formula can be defined as the variable that is expressed in terms of other variables in a given expression, function of equation.
It is the variable worked out in an equation and left to stand on its own on one side of the equality sign
Given the equation;
5f+2h = 100
To make 'f' the subject of formula, we take the following steps;
Take '2' over the equality sign
5f = 100 - 2h
Now, let's make 'f' the subject by dividing both sides by its coefficient which is 5
We have;
5f/5 = 100 - 2h/5
Divide through
f = 100 - 2h/5
Thus, solving for the variable gives f = 100 - 2h/5
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What is 80% of 63? Do not round your answer.
Answer:
What is 80% of 63?
50.4 is the right answer
identify the set of values for which will be a real number. the set of values for which will be a real number is
Except for x = 3, the set of x values for that y will become a real number as per Y=8/x-3 contains all real numbers.
What is real number?A real number is any number which can be found with in real world. Numbers can be found all around us.
Natural numbers are used to count objects, rational numbers for fraction representation, irrational numbers for determining the square root of the a number, integers for temperature measurement, and so on. These various types of numbers combine to form a gathering of real numbers.The union of a set of rational numbers (Q) or the set of irrational numbers yields the set of real numbers (R).Now according to the question;
In actuality, the expression Y=8/x-3 stops producing a real numerical value for y when the denominator has become zero.
When the denominator is zero, the y value is undefined and thus not a real number.
As a result, if we set;
x - 3 = 0
x = 3
Therefore, except for x = 3, the set of x values for which y is a real number per the Y=8/x-3 includes all real numbers.
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The complete question is-
Y=8/x-3
Identify the set of values x for which y will be a real number
Quadrilateral ABCD is dilated at center (0, 0) with scale factor to form quadrilateral 1/2; A^ prime B^ prime C^ prime D^ prime . What is the length of overline A^ prime B^ prime ?
The length with scale factor to form quadrilateral 1/2, A'B' is √5 units when AB is √20.
What is distance formula?The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given :
Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.
Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).
So, the points of the quadrilateral ABCD becomes:
A' (0, 2)B' (2, 1)C'( 2, -2)D'(-1 , -1)So, length of A'B'
AB = √(4-0) ² +(2 -4)²
AB = √16 + 4
AB = √20
AB = 2√5
A'B' = 1/2 AB
A'B' = √5
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7+(2x3) 5-6(9 divided by 5)=
Answer:
26.2
Step-by-step explanation:
7 + (2x3) 5-6 (9/5)
7 + 6*5-6*1.8
7 + 30-10.8
37 - 10.8
26.2
Which statement is true?
The Mississippi River in Iowa is at an elevation of 279 and Death Valley, in California is at an elevation of -282 feet. Which statement is true?
A |279| > |-282|
B |279| < |-282|
C 279 = 282
D 279 < -282
Answer:
Step-by-step explanation:
if we consider mod then the negative turns to positive and positive remains positive so it will be
279 < 282 which is l279l < l-282l
I need help asap (Fractions)
Answer:
Step-by-step explanation:
3 3/4 = 15/4
15/4 divided by 3/4 = 5