Answers
The value of x in given diagram is x=3;
The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.
Area of triangle SXY = 1/2 × SX × (x-2);
Area of triangle STR = 1/2 × ST × (x+3);
Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;
Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;
SX × (x-2) = ST × (x+3) - (2x + 1) × XT;
As; SX = TX = ST/2;
(x-2)/2 = (x+3) - (2x+1)/2;
x - 2 = 2x + 6 -2x -1
x = 3;
A triangle is a closed figure that has three vertices, three sides, and three angles. It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.
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Related Questions
evaluate 3^2018 + 3^2015 / 3^2017 + 3^2016
Answers
The simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
How to evaluate the expression?The expression is given as:
3^2018 + 3^2015 / 3^2017 + 3^2016
Factor out 3^2015 in the expression
So, we have
3^2015(3^3 + 1)/3^2015(3^2 + 3)
Cancel out the common factor
(3^3 + 1)/(3^2 + 3)
Evaluate the exponents
(27 + 1)/(9 + 3)
This gives
28/12
Simplify
7/3
Hence, the simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
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(b) If you put $7750 in the ATM each day, what percent of the days in a month should you expect to run out of cash?
Answers
The percent of the days in month that the cash will run out is given as: 23.33%. See the computation below.
What is the explanation that justified the above answer?Money put in ATM per day=$7750
We have to find the percent of days in a month you should expect to run out of cash.
From the given information
There are 7 days in which you run out cash more than $7750
Assuming that the total number of days in a month = 30
Hence, we can arrive at the above value by saying:
(Corresponding days/Total number of Days) * 100
From we above we state:
(7/30) * 100
= 23.33%
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The US government spent
$2500 billion. If 21% was
spent for Social Security, how
much was that
Answers
Answer:
If your number was 250,000,000,000
The amount of social security would be 52,000,000,000
Step-by-step explanation:
is 7 1/2 equal to 1/10, 1/5 or 4/5?
Answers
7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified line, 7y+2=3x-5, is the next step.
To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.
Check for (2,-1/7)
Connect it to 7y+2=3x–5.
7(-1/7)+2=3(2)-5
-1+2=6-5
1=1
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (3,-2/7)
Connect it to 7y+2=3x–5.
7(-2/7)+2=3(3)-5
-2+2=09-5
1=4
Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.
Connect it to 7y+2=3x–5.
7(-1)+2=3(0)-5
-7+2=0-5
-5=-5
Which is correct; as a result, this point is on the line 7y+2=3x-5.
Verify (1, -4, 7)
Connect it to 7y+2=3x–5.
7(-4/7)+2=3(1)-5
-4+2=3-5
-2=-2
This is why I'm making this point
lies on the line 7y+2=3x-5 that is presented.
Verify (-1, -10/7)
Connect it to 7y+2=3x–5.
7(-10/7)+2=3(-1)-5
-10+2=-3-5
-8=-8
Which is correct; as a result, this point is on the line 7y+2=3x-5.
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please help
maths geometry
(you can’t use congruency)
Answers
Step-by-step explanation:
ok, let's try this again. we need to explain congruence then in its details as an implicit part of the proof, as everything boils down to that.
due to AE = FC we also know that ED = BF.
because as ABCD is a parallelogram, it means AD = BC (and AB = DC).
and AD || BC, AB || DC.
as AD = AE + ED and BC = BF + FC, it means that
AE + ED = BF + FC
with AE = FC we can then simplify to
ED = BF.
as AD || BC, so is also ED || BF.
since the distance from E to D is the same as for B to F, it means that EB and DF must be equidistant to each other, and that means they are parallel.
and because ED || BF, that also means that both line segments are equidistant from each other, and that means that the connections between their end points (EB and DF) must have the same lengths.
therefore, the shape is a quadrilateral with 2 pairs of parallel and equally long line segments. and that is the definition of a parallelogram.
so, BEDF is a parallelogram.
AP Calculus ab question: what is the derivative function, f'(x), using the definition of derivative for : f(x) = 3X^2 + 1. Please show your work with the method shown below:
f'(x)= lim (h->0) [f(x+h) - f(x)] /h
Answers
Answer: f'(x)=6x
Step-by-step explanation:
f'(x)= lim (h->0) [f(x+h) - f(x)] /h
f'(x)= lim (h->0) [3(x+h)^2 + 1 - (3x^2 + 1)] /h
f'(x)= lim (h->0) [3(x^2+2hx+h^2) + 1 - 3x^2 - 1] /h
f'(x)= lim (h->0) [3x^2+6hx+3h^2 - 3x^2] /h
f'(x)= lim (h->0) [6hx+3h^2] /h
f'(x)= lim (h->0) [6x+3h]
f'(x)= [6x+3(0)]
f'(x)=6x
5. Explain how to determine which operation to complete first when simplifying the expression (15 ÷ 5+4²) − [4³ − |(13² + 2) ÷ (4 − 1)]. Be specific.
Answers
Answer: Parentheses
Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.
NO LINKS!! Please help me with these problems. Part 9a1
Answers
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range: [0, ∞)Continuity: Point discontinuity (hole) at x = 3.Infinite discontinuity (vertical asymptote) at x = -1.NoneDecreasing function: (-∞, -1) ∪ (-1, ∞)Symmetry: Neither
Step-by-step explanation:
Given function:
[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]
DomainThe domain is the set of all possible input values (x-values).
Factor the denominator of the function:
[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]
The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.
Therefore, the function is undefined when x = -1 and x = 3.
Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).
RangeThe range is the set of all possible output values (y-values).
As the domain is restricted, the range is also restricted.
Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.
Therefore, there is a point discontinuity at x = 3.
Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.
Therefore, there is an infinite discontinuity at x = -1.
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]
Therefore, there are no stationary points and no minimum/maximum points.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]
[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]
[tex]\implies x+1 < 0 \implies x < -1[/tex]
[tex]\implies x+1 > 0 \implies x > -1[/tex]
Combine the intervals:
(-∞, -1) ∪ (-1, ∞)
Therefore:
The function is decreasing in the interval (-∞, -1) ∪ (-1, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: [0, ∞)
Continuity: Point discontinuity (hole) at x = 3.
Infinite discontinuity (vertical asymptote) at x = -1.
None
Decreasing function: (-∞, -1) ∪ (-1, ∞)
Symmetry: Neither
please refer to the image
Answers
Brief The Question Please, Thank You
b. 40 gallons
What is the quotient of negative 210 over negative 15?
Answers
The quotient of A = - 210 and B = - 15 is 14.
What is Euclid's Division Lemma ?The Euclid's Division Lemma says when a number 'a' is divided by a number 'b' gives the quotient to be 'q' and the remainder to be 'r' then the following relation -> a = bq + r exists, where 0 ≤ r < b.
Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]
Given two numbers A = - 210 and B = - 15
The resultant quotient when A is divided by B can be calculated using Euclid's division lemma. Initially, we will assume remainder [r] = 0.
If the quotient is in decimals, we will change the remainder according to it else if the quotient is a whole number, the remainder will remain 0.
Using Euclid's division lemma -
Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]
- 210 = - 15 x q + 0
- 210 = - 15 x q
q = - 210 / - 15 = 14
Since, the quotient is a whole number, the remainder will remain zero.
Therefore, the quotient of A = - 210 and B = - 15 is 14.
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Sue has a 8 cups of flour and needs to fill it equally in containers that hold 3/4 of a cup each. How many containers can she fill?
Answers
Answer: Sue fills 32/3 (Decimal form = 10.6667 containers)
Step-by-step explanation: 8 divided by 3/4 equals 32/3. If you need it in decimal form it's 10.6667
Please heart this or rate it :)
Answer:
10 2/3 containers BUT can only fully fill 10 containers
Step-by-step explanation:
to solve this equation you need to divide 8 by 3/4
8 / 3/4
that is
8/1 / 3/4
when dividing fractions you must flip the second number and multiply both numbers together
8/1 * 4/3
32/3 is your answer
or
10 2/3
she can fully fill 10 containers
100 more than 365 is equal to 65more then
Answers
Answer:
x = 400Step-by-step explanation:
100 more than 365 is equal to 65more then
we can solve with an equation
100 + 365 = 65 + x
100 + 365 - 65 = x
465 - 65 = x
400 = x
------------
check
100 + 365 = 65 + 400
465 = 465
the answer is good
A line passes through ( - 1, - 1) and ( - 3, 5).
What is the equation of the line in slope-intercept form?
Answers
Answer:
y= -3x-4.
Step-by-step explanation:
1) the slope-interception form is:
y=slope*x+i, where i - interception;
2) using the given two points it is possible to calculate the slope:
[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]
then the required equation has the form:
y=-3x+i;
3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:
-1=-3*(-1)+i; ⇒ i=-4.
4) finally, the required equation is:
y=-3x-4.
P.S. the suggested way is not the shortest one.
The population of deer in a national forest has consistently increased by 5% each year. This year, the population of deer is 5,000. If the population increases at the same rate, what number of deer is expected to be in the national forest next year?
Select the correct answer below:
4,750
5,025
5,250
5,263
5,512
Answers
Answer:
5250.
Step-by-step explanation:
Consistent = Population of deer increases 5% each year.
This year = 5000
105% of 5000 = 5250
What would the Median of 112 113 116 118 119 124 be?
Answers
Check out the attached photo
Financial Goals: Tutorial
Part C
? Question
Diego's cash flow is the difference of his monthly income, $3,000, and his total expenses, $2,715. Which equation
correctly represents Diego's cash flow?
O cash flow = $2,715 - $3,000
O cash flow = $3,000-$2,715
O $3,000 = $2,715 - cash flow
$3,000 = cash flow-$2,715
Submit
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Answers
The equation that represents Diego's cash flow is cash flow = $3,000-$2,715.
What is the cash flow?Cash flow is the difference between cash inflows and cash outflows. Cash inflow are additions to the cash flow. An example of cash inflow is monthly income. Cash outflow would reduce the cash flow. An example of cash inflow is expenses.
Cash inflow = income - expense
$3,000 - $2,715
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A universitys freshman class has 7600 studends. 73% of those students are najoring in computer science. How many students in freshman clsss are computer science majors?
Answers
There are 5548 students majoring in computer science.
This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.
Given that the total number of students in the university class is =7600
Also 73% of students are majoring in computer science.
Number of students majoring in computer science is = (73/100) of 7600
= 73×76
= 5548 students
So, the total number of students majoring in computer science is 5548.
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Can you please help me
Answers
Find the perimeter of the rectangle.
X+1
2.5x - 4
Answers
Answer: 7x-6
Step-by-step explanation:
P=perimeter. L=length. W=width
P=2L+2W
P=2(x+1)+2(2.5x-4)
P=2x+2+5x-8
P=2x+5x+2-8
P=7x-6
Solve P = 2L+ 2W for L.
Question content area bottom
L= ?
Answers
PLEASE HELP DUE TODAY, WILLGIVE LOTS OF POINTS. On a map with a scale 1:100,000 the distance between two cities is 12cm. what would be the distance between these two cities on a different map with a scale 1:300,000?
Answers
Answer:
4cm
Step-by-step explanation:
the ratio of the two scales is 100,000:300,000 which simplifies to 1/3
1/3 x 12 =4
Given: 2 ( x + 3)-8=10
Prove: x = 6
Answers
Answer:
x=6
Step-by-step explanation:
2(x+3)-8=10
use 2 to multiply the one in the bracket
(2x+6)-8=10
group like terms
2x-2=10
send all constant terms to one side of the equation
2x=10+2
2x=12
divide both side by the coefficient of x
2x/2=12/2
x=6
2x= 10-6+8
2x= 12
X = 12\2
X= 6
The curve is the graph of function f. Use the graph to find the value of the function for the following values of x: -2,-.5,0,2.5, and 6.
Answers
Answer:
1, 0.75, 1.25, 3, 0
Step-by-step explanation:
To find the value of the function, we find the y coordinate of the point with the given x value.
The graph of a normal curve is given. Use the graph to identify the value of and . μ sigma
Answers
From the given graph the value of μ is 530 and the value of σ is 15.
In the Normal Curve the value at which the shape of the graph is highest is called it's mean(μ) and the value on the left of mean is μ-σ and the value on the right of the mean is μ + σ .
In the Given question
the shape of the graph is highest at 530,
hence the value of mean(μ) = 530. ....(i)
we know that the value on the left of mean is μ-σ .....(ii)
From the graph the value to the left of mean(μ) is 515. ...(iii)
Equating equation (ii) and (iii) we get ,
μ-σ = 515
Substituting the value of μ from equation (i) we get ,
530 - σ = 515
σ = 530 - 515
σ = 15
Therefore , From the graph the value of μ is 530 and the value of σ is 15.
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How can you decompose one number to subtract? Why did you
choose that way? 696-275
Answers
The minuend and the subtrahend of 696 - 275 can be decomposed to give;
600 + 90 + 6
-
200 + 70 + 5
400 + 20 + 1
The decomposition into place values is chosen because of ease of reinforcing knowledge.
What is the decomposition method of subtraction?The decomposition method of subtraction involves decomposing the subtrahend, which is the smaller number and the place value of the numbers can be simply subtracted from the minuend.
In the subtraction, 696 - 275, the minuend is 696, while the subtrahend is 275.
Decomposing the subtrahend, gives;
275 = 200 + 70 + 5
Decomposing the minuend, gives;
696 = 600 + 90 + 6
The subtraction expression in the question, 696 - 275 gives;
696
-275
The above can therefore be decomposed as follows;
600 + 90 + 6
-
200 + 70 + 5
400 + 20 + 1
400 + 20 + 1 = 421
Therefore;
696 - 275 = 421
The reason the decomposition into place values of each digit is chosen is so as to make use of the easier understanding of subtracting numbers that are multiples of 10.
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Fill in the blanks. (5 x 3) x __) a b 4x( x 9) = 72 C 7x (2x __) = 42 d (_____________× 5) x 5 = 75 x __) = 27 e (3 x 3) x = 60
Answers
The solution to each division problem is;
1) 4
2) 2
3) 3
4) 3
5) 3
1) We are given the expression;
(5 * 3) * ___ = 60
To get the blank answer, we will divide both sides by (5 * 3) to get;
60/(5 * 3) = 4
2) We are given the expression;
4 *( ___ * 9) = 72
To get the blank answer, we will divide both sides by (4 * 9) to get;
72/(4 * 9) = 2
3) We are given the expression;
7 * (2 * ___) = 42
To get the blank answer, we will divide both sides by (7 * 2) to get;
42/(7 * 2) = 3
4) We are given the expression;
(___ * 5) * 5 = 75
To get the blank answer, we will divide both sides by (5 * 5) to get;
75/(5 * 5) = 3
5) We are given the expression;
(3 * 3) * ___ = 27
To get the blank answer, we will divide both sides by (3 * 3) to get;
27/(3 * 3) = 3
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Exit Ticket
A plumber charges a one-time surcharge fee of $50 for
emergency calls plus a rate of $65 per hour. Write a function
using function notation to determine the total amount charged
for an emergency service call. Then find f(4.5), and explain the
real-world interpretation of f(4.5).
Answers
Answer:
f(x) = $65x + $50
f(4.5) = $342.5
The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.
Step-by-step explanation:
We will write a function where x is the hours. Since you pay $65 for every hour, we will multiply $65 by x. Next, there is a fee of $50 so we will add that onto the end.
f(x) = $65x + $50
Now, we will plug 4.5 into the function for x and solve.
f(x) = $65x + $50
f(4.5) = $65(4.5) + $50
f(4.5) = $292.5 + $50
f(4.5) = $342.5
The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.
A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 12 feet less than 3 times the height. Find the width and the height if the carpenter
expects to use 22 feet of lumber to make it.
Width:
feet
Height:
feet
Answers
Answer:
The width is 3 feet and the height is 6 feet.
Step-by-step explanation:
Steven has a rope that is 6ft long. He cuts it into 9 pieces. How many are in each piece
Answers
Answer:2/3
Step-by-step explanation:
what is 6561413+1000000=?
Answers
Answer:
7561413
Step-by-step explanation:
6561413+1000000= Equals Calculator Answer/////7561413
Answer:
7561413
Step-by-step explanation:
The calculator it equals 7561413