A Right Triangle must satisfy the Converse of the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
From the given side lengths, let a = 8, b = 15, c = 17 (c cannot be less than a or b)
[tex]a^2 + b^2 = (8)^2 + (15)^2[/tex]
[tex]a^2 + b^2 = 64 + 225 = 289[/tex]
[tex]c^2 = (17)^2 = 289[/tex]
[tex]a^2 + b^2 = c^2 \ (289 = 289)[/tex]
Therefore, a Triangle with side lengths of 8, 15 and 17 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(8, 15, 17) = 1, they are a primitive Pythagorean Triple.
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
How many solutions and what is the solution, as an ordered pair?
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
what is solution ?A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.
given
We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
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Helppppppppppppppppp
8 books cost 19.60 which equation would help determine the cost of 10 books?
Answer: $24.5
Step-by-step explanation:
8 Books = $19.60
1 Book = $19.60/8 = $2.45
10 Books = $2.45 X 10 = $24.5
Answer:
E none of the above
Step-by-step explanation:
a correct equation would be:
8/19.60 = 10/x
or
19.60/8 = x/10
What is the ordered pair that represents the point (-8, 7) after a reflection over the y-axis?
A. (-8, -7)
B. (8,7)
C. (-7,8)
(7,-8) D.
if AC = 57, find the measure of AB
Answer choices:
A. 9
B. 30
C. 6
D. 27
The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event "spin a 4"?The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event "spin a 4"?
Answer:
Answer: 6/25
======================================================
Explanation:
The table shows the spinner lands on "4" exactly 12 times out of the 50 total.
12/50 = (2*6)/(2*25) = 6/25
In decimal form that is 6/25 = 0.24 which converts to 24%
Just number 9 with work
The correct answer is (c) Left 5. The transformation is a horizontal shift to the left by 5 units.
What is equation?An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.
Here,
The given equation is y = 12/(x + 5), which represents a rational function. The parent function for this type of function is y = 1/x, which has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
To transform the parent function represented by y = 1/x into y = 12/(x + 5), we need to apply the following transformations:
Vertical stretch by 12: This means that the y-values of the graph will be multiplied by a factor of 12, causing the graph to become narrower and taller. Horizontal shift left 5 units: This means that the graph will be shifted 5 units to the left, causing the vertical asymptote to move from x = 0 to x = -5.
Therefore, the correct answer is (c) Left 5, since this represents the horizontal shift of 5 units to the left. The other answer choices do not accurately describe the transformation of the parent function into the given equation.
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Let f(x) = -3x - 5
What is the value of f(-5)?
Answer:
I think its 10Step-by-step explanation:
PLEASE HELP ME
Given the following quadratic functions, complete the following:
1. Identify the zeros.
2. Identify the vertex.
3. Write the quadratic equation in factored form for the function that is graphed.
The zeros and vertex of each quadratic equation are:
Case 1: y = 4 · (x + 2) · (x - 2), Roots: - 2, 2, Vertex: (0, - 16)
Case 2: y = (1 / 2) · (x + 5) · (x - 3), Roots: - 5, 3, Vertex: (- 1, - 8)
Case 3: y = - 2 · (x + 4) · (x + 2), Roots: - 4, - 2, Vertex: (- 3, 2)
Case 4: y = - 2 · (x + 6) · (x + 2), Roots: - 6, - 2
Vertex: (- 4, 8)
How to analyze quadratic functions and derive their expressions
Graphically speaking, quadratic functions have the form of the parabola. The zeros are the points of parabola that are on the horizontal axis (x-axis) and the vertex is the only point of the parabola. The factor form of the parabola is:
y = C · (x - r₁) · (x - r₂)
Where:
C - Vertex constantr₁, r₂ - RootsNow we proceed to determine all the features of the quadratic function:
Case 1
Roots: r₁ = - 2, r₂ = 2
Vertex: (h, k) = (0, - 16)
C = y / [(x - r₁) · (x - r₂)]
C = - 16 / [2 · (- 2)]
C = - 16 / (- 4)
C = 4
Factor form: y = 4 · (x + 2) · (x - 2)
Case 2
Roots: r₁ = - 5, r₂ = 3
Vertex: (h, k) = (- 1, - 8)
C = y / [(x - r₁) · (x - r₂)]
C = - 8 / [(- 1 + 5) · (- 1 - 3)]
C = - 8 / [4 · (- 4)]
C = - 8 / (- 16)
C = 1 / 2
Factor form: y = (1 / 2) · (x + 5) · (x - 3)
Case 3
Roots: r₁ = - 4, r₂ = - 2
Vertex: (h, k) = (- 3, 2)
C = y / [(x - r₁) · (x - r₂)]
C = 2 / [(- 3 + 4) · (- 3 + 2)]
C = 2 / [1 · (- 1)]
C = - 2
Factor form: y = - 2 · (x + 4) · (x + 2)
Case 4
Roots: r₁ = - 6, r₂ = - 2
Vertex: (h, k) = (- 4, 8)
C = y / [(x - r₁) · (x - r₂)]
C = 8 / [(- 4 + 6) · (- 4 + 2)]
C = 8 / [2 · (- 2)]
C = 8 / (- 4)
C = - 2
Factor form: y = - 2 · (x + 6) · (x + 2)
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What is the answer to x3 y3 z3 k?
Answer:
The equation x3+y3+z3=k is known as the sum of cubes problem.
Step-by-step explanation:
if 62 miles is equal to 100 kilometers , what is the ratio of miles to one kilometer
Answer:
0.62 to 1
Step-by-step explanation:
62/100
Divide the numerator and denominator by 100.
62/100 = 0.62/1
The ratio is 0.62 to 1.
Answer:
Step-by-step explanation:
1 mile is equal to 1.60934 km
1km is equal to 0.621371 mile
the worlds population hit 8 billion in 2022. suppose the population increases exponentially with doubling time of 60 years. what population can we expect in the year 2100. Answer in billions
The population in the year 2100 will be approximately 18.8 billion.
Determine exponential equation
The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)[tex]^t[/tex], where P(t) is the population in billions and t is the number of years after 2022.
To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.
We can use the formula for exponential growth, P(t) = P0(1 + r[tex])^t[/tex]where P0 is the initial population, r is the growth rate, and t is the number of years.
Substituting the values for [tex]P_0[/tex]and r into the equation, we get:
P(t) = 8(1.011[tex])^t[/tex]
2100-2022=78
This equation can be used to find the population after t years.
For example, to find the population after 5 years, we can substitute t = 78 into the equation and get:
P(5) = 8(1.011[tex])^78[/tex] ≈ 18.8 billion
Therefore, the population in year 2100 will be approximately 18.8 billion.
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In ΔIJK, i = 100 inches, mm∠I=115° and mm∠J=23°. Find the length of j, to the nearest inch.
The measure of the side J of the triangle ΔIJK will be 43 units.
What is the law of sine?The law of sines defines the ratio of triangle sides, and their respective sine angles are equivalent. The law of sines is also known as the sine law, sine rule, and sine formula.
Given that in the triangle i = 100 inches, m∠I=115° and m∠J=23°. The measure of the length J will be calculated as:-
100 / sin115 = J / sin23
J = (100) x sin23 / sin115
J = 100 x 0.43
J = 43 units
The length of side J will be 43 units.
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The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?
Answer: 19 tickets
Step-by-step explanation: $45 - $7 = 38 38 divided by $2 = 19 tickets
Elijah works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commission on top of his base salary equal to 30% of his total sales for the week. How much would Elijah make in a week in which he made $775 in sales? How much would Elijah make in a week if he made
x dollars in sales?
Total earnings when selling $775:
Total earnings when selling $x:
Elijah's total earnings for the week if he made x dollars in sales would be: $500 + 0.3x.
What is sale?
A sale is an event or activity in which goods or services are sold at a reduced or discounted price.
What is discount?
A discount is a reduction in the price of an item or service. It is often offered as a promotion or incentive to encourage customers to buy or use a product or service.
According to given information:Total sales commission earned by Elijah for selling $775 worth of clothing:
30% of $775 = 0.3 x $775 = $232.50
Therefore, Elijah's total earnings for the week would be:
$500 (guaranteed salary) + $232.50 (commission) = $732.50
For selling x dollars worth of clothing, the commission earned by Elijah would be:
0.3x
Therefore, Elijah's total earnings for the week if he made x dollars in sales would be:
$500 (guaranteed salary) + 0.3x (commission) = $500 + 0.3x
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What is m24 if m25 = (2x)° and m24 = (x +9)°?
4
X
5
m24 =
The value of angle m<4 is 66 degrees
What are supplementary angles?The angles on a straight line are supplementary, this means that the angles sum up to 180 degrees.
From the information given, we have that;
m<4 = x + 9 degreesm< 5 = 2x degreesEquate the angles to 180 degrees
We have;
m<4 + m<5 = 180
Substitute the expression for each of the angles , we have;
x + 9 + 2x = 180
collect the like terms
3x = 180 - 9
subtract the values
3x = 171
Divide by the coefficient
x = 57
But m<4 = 57 + 9 = 66 degrees
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(x^2-4x+3) + (3x^2-3x-5) ASAP PLS
Answer:
(x - 2)(4x + 1)
Brendon is building a clubhouse where 1 inch on the plans is equivalent to 8 inches on the actual clubhouse.
If the clubhouse is to be 126 inches wide, what will the width be on the plans?
Round answer to the nearest hundredth if necessary.
Answer:
To find the width of the clubhouse on the plans, we need to use the given scale of 1 inch on the plans being equivalent to 8 inches on the actual clubhouse. Let's assume that "x" inches on the plan correspond to the actual width of 126 inches of the clubhouse.
Using the proportionality of the scale, we can set up the following equation:
1 inch / 8 inches = x inches / 126 inches
Simplifying the equation, we can cross-multiply to get:
8 inches * x inches = 1 inch * 126 inches
8x = 126
x = 15.75
Therefore, the width of the clubhouse on the plans is 15.75 inches.
Pupils in a class were asked how they travel to school. The results were recorded in the table below
Car 13 bus 6 train 5 walk 8
If s pupil in the class was picked at random what is the probability that one of them walked to school as a percentage
Answer:
1/3
Step-by-step explanation:
circumference is 1884, what is the diameter
Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)
you get this from dividing 1884 by 3.14159 (pi)
If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
19 less than a number is 28
Answer: 47
Step-by-step explanation:
28+19=47
47-19=28
2 2/5 as an improper fraction in simplest form
Answer: 12/5
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is 1 and 4 of the given inequality –3(2x – 5) < 5(2 – x)
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x
x < 5
Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.
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The maximum number of grams of fat that should be in a diet vary directly as a persons way a person weighing 126 pounds should have no more than 84 g of fat per day. What is the maximum daily intake for personally and 30
ponds
Adrian eats 2/3's of a pack of gum each
day. How many packs of gum will he
have eaten after 7 days?
10 points given!!
Simplify to create an equivalent expression.
−
4
(
−
11
+
4
n
)
−
3
(
−
2
n
+
9
)
Answer:
Step-by-step explanation:
To simplify this expression, we will distribute the -4 and -3 to the terms inside the parentheses:
-4(-11+4n) - 3(-2n+9)
= 44 - 16n + 6n - 27
= -16n - 17
Therefore, the simplified expression is -16n - 17.
Decide if each statement is true or false and explain.
All rectangles are quadrilaterals.
Answer: True
Step-by-step explanation:
They have four sides
Answer:true.
Step-by-step explanation: All Rectangles are indeed quadrilaterals because all rectangles have 4 sides and quadrilaterals are known as a four sided shape,
The ratio of new car sales to used car sales at the car lot is 3:5. If the total car sales were $287,400 last month, what was the total of the used car sales?
Answer:
Therefore, the total used car sales were $179,625.
Step-by-step explanation:
Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.
The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:
3x + 5x = 8x
So, the total sales can be expressed as:
8x = $287,400
To find the value of x, we need to divide both sides by 8:
x = $35,925
Now, we can calculate the used car sales by multiplying 5x by the value of x:
Used car sales = 5x * x = 5 * $35,925 = $179,625
Therefore, the total used car sales were $179,625.