The distance between the line segments PQ, RS and TV are √53 respectively
Distance Between Two PointsThe distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.
The formula is given as;
d = √(x₂ - x₁)² + (y₂ - y₁)²
In the first line segment;
P = (0,4), Q = (7, 2)
d = √((7-0)² + (2 - 4)²)
d = √53
b)
R = (-7, 6), S = (-5, -1)
d = √((-1 - 6)² + (-5 --7)²)
d = √53
c)
T = (0, -8), V = (2, -1)
d = √((-1 --8)² + (2 - 0)²)
d = √53
The distance between the lines are all √53 units
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f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41 Over 8 EndFraction,
The inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace {y} with {x} and vice - versa.Step 2 - Rewrite the equation by solving for {y}.Step 3 - Replace {y} with f⁻¹(x).According to the question, the equation given is as follows
y = f(x) = 2x + 5
y = 2x + 5
Replace 'y' with 'x', we get -
x = 2y + 5
Now, solve for y -
2y = x - 5
y = (x/2) - (5/2)
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = (x/2) - (5/2)
Hence, the inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
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p= ?
m∠RTS=?
explain how you find the requested values
The angle of the T in the ΔRST is 100° and the value of p is 11.
Define Triangle.
A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.
i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.
Given:
∠R = 37°; ∠S = 43°; ∠T = 10p-10°
Let's take ∠T = x
In ΔRST,
∠R + ∠S + ∠T = 180°
37 + 43 + x = 180°
x = 180 - 80 ⇒ 100
∴ ∠T = 100°
To find the value of p,
∠T = 100
10p - 10 = 100
10p = 110 ⇒ 11
∴ p = 11
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can you please help me
3. To find the perimeter of a rectangle, use the equation , where P is the perimeter, l is the length and w is the width of the rectangle.
(a) A rectangular garden has a perimeter of 40 yd and a width of 5 yd. Use the equation and the replacement set to find the length of the garden. Show your work.
(b) A rectangular table top has a perimeter of 18.4 ft and a length of 6.75 ft. Use the equation and the replacement set to find the width of the table top. Show your work.
Answer:
a) 15yd
b)2.45ft
Step-by-step explanation:
P = perimeter, l=length and w = width of the rectangle
P = 2l+2w
a) 40 = 2l+2(5)
40 = 2l+10
30=2l
15=l
b) 18.4 = 2(6.75) + 2w
18.4 = 13.5+2w
4.9=2w
2.45=w
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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What is
(6.8) ( - 1.3)
Answer:
-8.84 = 0.
Step-by-step explanation:
.
Determine which choice best shows the distributive property of multiplication.
Question 1 options:
7 × 9 = 9 × 7
7 × (9 + 6) = (7 × 9) + (7 × 6)
7 × (9 × 6) = (7 × 9) × 6
1 × 7 = 7
Answer: Identify and use the commutative properties for addition and multiplication. Here, the same problem is worked by grouping 5 and 6 first, 5 + 6 = 11. The example below shows how the associative property can be used to simplify. The sum is 14. 7 + 2 + (8.5 + (−3.5)). 7 + 2 + 5. 9 + 5. 14. Group 8.5 and –3.5=5
Step-by-step explanation:
Answer:
7 × (9 + 6) = (7 × 9) + (7 × 6)
Step-by-step explanation:
How long would it take to lose 30 pounds if you’re starting weight is 150
Answer:a minimum of 15 weeks to about 30 weeks.
Step-by-step explanation:
Which question is statistical? Responses What number of feet is equivalent to three miles? What number of feet is equivalent to three miles? How many miles did your family drive last week? How many miles did your family drive last week? How many miles are between the library and the post office? How many miles are between the library and the post office? How many miles does each member of the biking club ride each week?
The question that is a statistical question is "How many miles did your family drive last week?"
Which question is a statistical question?A statistical question is a question that requires collecting and analyzing data to answer.
It involves investigating a specific variable or variables and determining patterns, trends, or relationships within the data.
The question "How many miles did your family drive last week?" is statistical, as it involves collecting and analyzing data related to a specific variable (miles driven) over a certain period of time (last week).
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Which shapes have parallel sides? Choose ALL the correct answers.
Answer:
the green one for sure..
Step-by-step explanation:
Please look at the photo! Thank you.
The output value of (g/f)(x) is 9x/(7x + 28).
The domain of g/f is (-∞, -4) U (-4, ∞)..
How to determine the corresponding composite function?In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;
(g/f)(x) = (9/(x + 4)) ÷ 7/x
By rearranging the mathematical expression using the multiplication operation, we have the following:
(g/f)(x) = (9/(x + 4)) × x/7
(g/f)(x) = 9x/(7x + 28)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
7x + 28 ≠ 0
7x ≠ -28
x ≠ -4
Domain = (-∞, -4) U (-4, ∞).
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5m - 12 - 2m + 6 + 3m
Answer:
6(m-1)
Step-by-step explanation:
See Image Below:)
pls help, u dont have to explain that much
Answer:
876763 979.6
Step-by-step explanation:
can someone help PLS? its Surface Area of Composite Shapes
The total surface area of the figure is 315π square feet, or approximately 988.8 square feet if we use a value of 3.14 for π.
Given information:
The cylinder is sitting on the base of the cone.
The diameter of the base is 14 feet.
The slant height of the cone is 9 feet and the height of the cylinder is 11 feet.
To find the total surface area of the figure, we need to find the surface area of the cone and the surface area of the cylinder and add them together.
The surface area of the cone:
The radius of the cone is half of the diameter, which is 7 feet.
The lateral surface area of the cone can be found using the formula:
L = πrs, where r is the radius and s is the slant height.
L = π(7)(9) = 63π square feet
The base of the cone is a circle with a radius of 7 feet, so its area is:
A = πr² = π(7²) = 49π square feet
The surface area of a cylinder:
The radius of the cylinder is also 7 feet since it shares the same base as the cone.
The lateral surface area of the cylinder is:
L = 2πrh, where r is the radius and h is the height.
L = 2π(7)(11) = 154π square feet
The base of the cylinder is another circle with a radius of 7 feet, so its area is:
A = πr² = π(7²) = 49π square feet
Total surface area:
Adding the lateral surface area and the base area of the cone and cylinder, we get:
63π + 49π + 154π + 49π = 315π square feet
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After 2 hours, 36% of a certain element remains. If a sample has an initial amount of 100 grams, how many hours will it take until only 1 gram remains? Provide an answer supported by valid mathematical reasoning and/or calculations.
It will take approximately 12.85 hours until only 1 gram of the element remains.
If after 2 hours, 36% of the initial amount remains, then the remaining amount is 0.36 times 100 grams, which is 36 grams. Let's define the amount of the element remaining after time t in hours as R(t). Since the element is decaying exponentially, we can model it with the equation R(t) = 100\((0.36)^t\).
We want to find how many hours it will take until only 1 gram remains. We can set R(t) equal to 1 gram and solve for t:
1 = 100\((0.36)^t\)
Taking the logarithm of both sides, we get:
ln(1) = ln(100\((0.36)^t\))
0 = ln(100) + t*ln(0.36)
t = -ln(100)/ln(0.36)
Using a calculator, we find that t ≈ 12.85 hours.
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50 POINTS PLZ HELP MEEEE
Answer:
Step-by-step explanation:
It’s c
Answer:
c
Step-by-step explanation:
Shawna reduced the size of a rectangle to a
height of 2 in. What is the new width if it
was originally 24 in wide and 12 in tall?
Answer: 10 in
Step-by-step explanation:
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.
In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.
Order-Preserving Function:
A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.
Increasing Function:
If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).
Isomorphism:
A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:
a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).
b. f is onto (surjective): Every element in Q has a pre-image in P.
When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.
Automorphism:
An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.
These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.
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Brainliest to RIGHT answer
Answer:
It's C
Step-by-step explanation:
hi can you please help me with my work no Link please no Link
Answer: -12
Step-by-step explanation:
4 1/2-5 1/8= -5/8 divided by 7 1/2
= -12
Hope this helped!!<3
Answer:
-12
Step-by-step explanation:
4 4/8 – 5 1/8 = (4 – 5) + (4/8 – 1/8) = -1 + 4 – 1/8 = -1 + 3/8 = -5/8
7 1/2 ÷ 5/8 = 15/2 ÷ -5/8 = 15/2 × 8/-5 = 15 × 8 2 × -5 = 120 -10 = 120/-10 ÷ 10/10= –12
how many cubes of ice does 8 cups need becuase a cup of lemonade takes 12 cubes of ice
Answer:
number of cubes contained in one cup : 12 cubes
number of cubes needed in 8 such cups : 12 * 8 cubes = 96 cubes!
.
.
.
\({\bold{\red{HOPE\:IT\:HELPS!}}}\)
\(\color{yellow}\boxed{\colorbox{black}{MARK\: BRAINLIEST!❤}}\)
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $160 and first class tickets for $1,120. She used her total budget for airfare for the trip, which was $3,520. How many first class tickets did she buy? How many coach tickets did she buy?
Answer:
c + f = 5
120c + 1140f = 2640
f = 5 - c
120c + 1140(5 - c) = 2640
120c + 5700 - 1140c = 2640
1020c = 3060
c = 3 coach tickets
Step-by-step explanation:
PLEASEEEE HELPPP!!!!!!WILL GIVE BRAINLIEST!!!!!!!!!!!! In quadrilateral ABCD, we have AB=3, BC=6, CD=4, and DA=4. If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.
Answer:
AC = { 4, 5, 6, 7 }
Step-by-step explanation:
If you see, the diagonal AC forms two triangles, Δ ABC, and Δ ADC. In Δ ABC, AC = 3 units and BC = 6 units, while AC is yet to be known. Respectively in Δ ADC, AD = 4 units and CD = 4 units, while AC is again yet to be known.
In both triangles the triangle inequality can help find the possible value( s ) of AD, as this inequality only restricts some of the possible values with which AC can take. At the same time AC is shared among the two triangles, so if we can apply the Triangle Inequality to both of these triangles, the value of AC can be " further restricted. "
\(Triangle 1. BC - AB < AC < BC + AB,\\6 - 3 < AC < 6 + 3,\\3 < AC < 9\\\\Triangle2. AD - CD < AC < AD + CD,\\4 - 4 < AC < 4 + 4,\\0 < AC < 8\)
And there we have two inequalities, 3 < AC < 9, and 0 < AC < 8. Combining both inequalities the only possible integer values for AC would be 4, 5, 6, and 7.
Answer:
Its funny how we all cheat AOPS
Step-by-step explanation:
Write a common denominator for 1/4 and 5/6 (PLEASE THIS IS DUE TMRR) Also just an answer
Factor 3xy+21x+9 completely
- 3x(y+7x+6)
- 3(xy+7x+3)
- Prime (Not Factorable)
- xy+2x+3
Answer:
Hence the second option is the correct answerStep-by-step explanation:
In this problem we are required to factor out the given terms as stated in the expression, what is obtainable is that we look for terms(greatest terms) that are common to all the terms in the expression and factor it out.
here is a way to do it
given the following expression
\(3xy+21x+9\)
From the expression above we can see that 3 is common to all the terms of the expression so that we have
\(3(xy+7x+3)\)
hence the second option is the correct answer
Help needed with this asap
Answer:
x = 10
Step-by-step explanation:
RO and OQ are congruent
Since RO = 50, and RQ = 12x - 20,
OQ = 12x - 20 - 50 = RO
50 = 12x - 70
120 = 12x
x = 10
-Chetan K
5) Vanessa and Javier each signed up for new gym memberships. Vanessa pays a monthly fee of $25 and
$2 per group class. Javier pays $6 per class and no monthly fee. How many classes do they have to take to
pay the same monthly rate?
Answer: 6.5 and 6
Step-by-step explanation:
Hi can any one teach me this constant difference
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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Type the correct answer in the box. Use numerals instead of words.
Answer:
2 squared - 7 + -4
Step-by-step explanation:
Question is in the picture, please explain your answer with steps.
Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.
How to find the costs?Let's define the variables:
x = cost of the washer.
y = cost of the dryer.
We know that the cost combined is $1000, then:
x + y = 1000
And the washer cost 3 times the cost of the dryer, then we will get:
x = 3y
So we have a system of equations, we can replace the second equation into the first one, so we will get:
3y + y = 1000
4y = 1000
y = 1000/4
y = 250
The cost of the washer is:
x = 3*250 = 750
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The population of a city decreases by 1.2% per year. If this year's population is
242,000, what will next year's population be, to the nearest individual?
Answer:
Your answer
212960
Mark it as Brainlist answer. Follow me to get more answer
Step-by-step explanation:
Answer: it is actually 239096
Step-by-step explanation: