Answers
The x1 is[tex]\frac{9}{5}[/tex] and the x2 is [tex]\frac{12}{5}[/tex] and the x3 is [tex]\frac{16}{5}[/tex] using Pythagoras's theorem.
What is Pythagoras's Theorem?According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC2 = AB2 + AC2 is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.
Calculation:The given triangle is a right angled triangle so applying Pythagoras's theorem for ABC triangle we get x1+x2 as [tex]\sqrt{3^{2}+ 4^{2} } = 5[/tex]
The area of ΔABC is [tex]\frac{1}{2}[/tex]×b×h = [tex]\frac{1}{2}[/tex]×3×4=6
Now taking CD as height and AB as base we get [tex]\frac{1}{2}[/tex]×5× x2 = 6 ⇒ x2 = [tex]\frac{12}{5}[/tex].
Now applying Pythagoras's theorem to triangle ACD we get x1 as [tex]\sqrt{3^{2}-\frac{9}{5} ^{2} } = \frac{9}{5}[/tex]
Now substituting x1 in x1 + x3 = 5 we get x3 as [tex]\frac{16}{5}[/tex].
The x1 is [tex]\frac{9}{5}[/tex] and the x2 is [tex]\frac{12}{5}[/tex] and the x3 is [tex]\frac{16}{5}[/tex] using Pythagoras's theorem.
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Related Questions
The endpoints of AB are A(-8, 1) and B(4, -7).
What are the coordinates of point Con AB that is
34
the distance from point A to point B?
∞
6
4
Answers
The Co-ordinates of the point C that divides the line in the ratio of 3:4 is (-20/7, -17/7)
What is Section Formula?
The Section formula is used in coordinate geometry to compute the ratio of a line segment split by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle. It is used in physics to determine the centre of mass of systems, equilibrium locations, and so on.
Solution:
A(-8, 1) and B(4, -7)
Ratio is 3:4
Section Formula is (mx2 + nx1/ m + n), (my2 + ny1/ m + n)
m = 3 and n = 4
Co-ordinates of C are (3*4 + 4*(-8)/ 3+4), (3*(-7) + 4*1 / 3+4)
= (12 - 32 / 7), (-21 + 4 / 7)
= (-20/7, -17/7)
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Given f(x) = x² + 4x, find the average rate of change of f(x) on the interval [4, 4+h]. Your answer will
be an expression involving h.
Answers
Step-by-step explanation:
please refer to the attached sketch for the answer.
which expression in the simplest form of
Answers
The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.
What is simplest form?Expressions are rewritten in a compact and unlike terms-free manner when they are simplified. Expressions are simplified by combining like phrases, resolving any provided brackets, and only leaving unlike terms that cannot be further reduced in the final simplified expression.
The given expression is -(2x³+x²)+3(x³-4x²)
Simplify the given expression as follows
-2x³-x²+3x³-12x²
= x³-13x²
The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.
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A triangle has angle measures of 45 degrees, 45 degrees, and 90 degrees. Which statement is true about the lengths of the sides? Each side has a different length. Two sides have the same length, which is less than the length of the third side. The three sides have the same length. The sum of the lengths of two sides is equal to the length of the third side.
Answers
The sum of the lengths of two sides is equal to the length of the third side is 45°.
What is Triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.As we discussed in the introduction, a triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides. This is one of the important parts of geometry. Some major concepts, such as Pythagoras theorem and trigonometry, are dependent on triangle properties. A triangle has different types based on its angles and sides.To learn more about vertex of the triangle refer to:
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When Landon overdrafts from his checking account, his bank moves $50 from his savings account into his bank account and charges him $5 (from his checking account) as a penalty each time it happens. If Landon had $75.32 in his checking account and he wrote a check for $113.85, how much money would he have in his checking account after the check is cashed and the bank handles his overdraft?
Answers
Answer:
Landon would have -$43.53 in his checking account after the check is cashed and the bank handles his overdraft.
Step-by-step explanation:
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game.
How many points did Carlos score?
Answers
The number of points that Carlos score based on the information is 19 points.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
In this.case, Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos.
Let Carlos point = x
Fabio point will be = 2x - 7
The equation will be:
2x - 7 = 31
2x = 31 + 7.
2x = 38
Divide
x = 19
Carlos had 19 points
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based on this data, what is a reasonable estimate of the probability that todd runs more than 15\text{ km}15 km15, start text, space, k, m, end text tomorrow?
Answers
The reasonable estimate of the probability that Todd runs 5/13.
We know that,
Experimental probability = Number of favorable outcomes/total number of outcomes.
Experimental probability, also called empirical probability, is based on real experiments and rational records of what happened. A series of real-world experiments are conducted to determine the occurrence of events. Experiments with undetermined results are called random experiments. The results of such experiments are uncertain. Repeat the random experiment several times to determine its probability. Experiments are repeated a specified number of times, and each repetition is called a trial. Mathematically, the formula for experimental probability is defined as:
Probability of event P(E) =
frequency of occurrence of event / total number of trials.
According to the question:
The number of favorable outcomes are 5.
The total number of outcomes are 2 + 3 + 3 + 5 = 13.
Therefore, the reasonable estimate of the probability that Todd runs is 5/13.
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At what y points on the curve xy = 25 is the tangent line parallel to 5x + y = 0?
Answers
The point at which =the curve xy = 25 is the tangent line parallel to 5x + y = 0 is y = ± 5√5 so, option A is correct.
What is line?
A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.
Given:
the curve xy = 25 and the equation of the line is 5x + y = 0,
The equation of line parallel to line 5x + y = 0 will be,
y = mx + c
y = -5x + c (y = -5x)
The line will be in the curve as it is tangent, so,
xy = 25 and y = -5x + c line have a solution,
Solve the above equation as shown below,
y = ± 5√5
Thus, the point y = ± 5√5 the line is tangent to the curve.
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a boy owns 1 pairs of pants, 6 shirts, 3 ties, and 6 jackets. how many different outfits can he wear to school if he must wear one of each item?
Answers
A boy owns 1 pair of pants, 6 shirts, 3 ties and 6 jackets then, the number of different outfits the boy can wear to school if he must wear one of each item is 108.
Given:
a boy owns 1 pairs of pants,
6 shirts,
3 ties,
and 6 jackets.
how many different outfits can he wear to school if he must wear one of each item = ?
Combinations here:
1 × 6 × 3 × 6
= 108
hence the boy can wear 108 different outfits.
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what is equilvalent to the square root of -2.
Answers
Answer:
1.4142135623730951i
Step-by-step explanation:
Did it help pls make me the brainliest and you can round your answer to how you want it and if not that's you answer thank you.
find the value of y² when y=-9
Answers
Answer:
81
Step-by-step explanation:
y = -9
y² = (-9)² = 81
Multiple
Solution
Y=-81
Mark Brainly pls
PLEASE PLEASE PLEASE help, I will mark brainliest, this is for my final. In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ
Answers
Answer:
EL/EF
OS/OJ
Step-by-step explanation:
Tangent is equal to opposite/adjacent
Division of Polynomials
1). 2x^3 - x^2 + 3x - 4 / x + 5
2). X^4 - 8x^2 + 2x + 7 / x+5
3). 2x^3 + x^2 - 8x + 15 / x^2 + 2x - 1
Answers
Division of Polynomials is [tex]$$2 x^2-11 x+58-\frac{294}{x+5}$$[/tex] , [tex]$$x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex], [tex]2 x-3+\frac{12}{x^2+2 x-1}[/tex].
What is Polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
1). [tex]\frac{2 x^3-x^2+3 x-4}{x+5}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{2 x^3-x^2+3 x-4}{x+5}: \quad \frac{2 x^3-x^2+3 x-4}{x+5}=2 x^2+\frac{-11 x^2+3 x-4}{x+5} \\& =2 x^2+\frac{-11 x^2+3 x-4}{x+5}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{-11 x^2+3 x-4}{x+5}: \frac{-11 x^2+3 x-4}{x+5}=-11 x+\frac{58 x-4}{x+5} \\& =2 x^2-11 x+\frac{58 x-4}{x+5}\end{aligned}$$[/tex]
Divide [tex]$\frac{58 x-4}{x+5}: \quad \frac{58 x-4}{x+5}=58+\frac{-294}{x+5}$[/tex]
[tex]$$=2 x^2-11 x+58+\frac{-294}{x+5}$$[/tex]
Simplify
[tex]$$=2 x^2-11 x+58-\frac{294}{x+5}$$[/tex]
2.[tex]\frac{x^4-8 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{x^4-8 x^2+2 x+7}{x+5}: \quad \frac{x^4-8 x^2+2 x+7}{x+5}=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$[/tex]
[tex]=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{-5 x^3-8 x^2+2 x+7}{x+5}: \frac{-5 x^3-8 x^2+2 x+7}{x+5}=-5 x^2+\frac{17 x^2+2 x+7}{x+5}$[/tex]
[tex]=x^3-5 x^2+\frac{17 x^2+2 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{17 x^2+2 x+7}{x+5}: \quad \frac{17 x^2+2 x+7}{x+5}=17 x+\frac{-83 x+7}{x+5}$[/tex]
[tex]$$=x^3-5 x^2+17 x+\frac{-83 x+7}{x+5}$$[/tex]
Divide [tex]$\frac{-83 x+7}{x+5}: \quad \frac{-83 x+7}{x+5}=-83+\frac{422}{x+5}$[/tex]
[tex]$$=x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex]
3.
[tex]\begin{aligned}& \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}: \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}=2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& =2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{-3 x^2-6 x+15}{x^2+2 x-1}: \frac{-3 x^2-6 x+15}{x^2+2 x-1}=-3+\frac{12}{x^2+2 x-1} \\& =2 x-3+\frac{12}{x^2+2 x-1}\end{aligned}[/tex]
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Solve the Cryptarithm,
BIRD
FOOD
+GRID
which equals GRAIN.
Also note that food is a multiple of 1279 and that it is a prime number.
Answers
Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378==13674.
What is a cryptarithmetic problem?Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.
What is reverse cryptarithm?A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.
since the digits used are 0 to 9.
first letter can't be zero.
and we can't repeat the same digit for same different alphabets.
Using these rules with the condition that food is multiple of 1279.
The answer is : 9738+2558+1378==13674
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Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378 =13674.
What is a cryptarithmetic problem?
Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.
What is reverse cryptarithm?
A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.
since the digits used are 0 to 9.
first letter can't be zero.
and we can't repeat the same digit for same different alphabets.
Using these rules with the condition that food is multiple of 1279.
The answer is : 9738+2558+1378 = 13674
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Help meee !!??? Please
Answers
The value of [tex]15\sqrt{1513}[/tex] = 585
According to the given information
What is Square Root ?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol [tex]\sqrt{}[/tex]square root of, end square root. The opposite of squaring an integer is finding its square root.
We need to find the value of [tex]15\sqrt{1513}[/tex]
Firstly
The value of square root of 1513
The amount that becomes 1513 when it is multiplied by itself twice is its square root. In other words, this number is equal to 1513 when multiplied by 2.
So
Value of square root of 1513 = 38.8973006776
Hence
Value of [tex]15\sqrt{1513}[/tex] = 15 × 38.8973006776
= 15 × 39
= 585
The value of [tex]15\sqrt{1513}[/tex] = 585
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A bag contains 12 red marbles, 14 yellow marbles, and 3 green marbles.
If I marble is chosen at random, which is the probability that it will be a blue marble?
Answers
Answer:1/3
Step-by-step theexplanation:1/3 is the probablility of the marbles
Calculator
For what value of x is line a parallel to line b?
Enter your answer in the box.
X =
a
b
(5x + 15)°
115°
65°
Answers
Explanation:
If the corresponding angles 5x+15 and 115 are congruent, then line 'a' is parallel to line 'b'.
5x+15 = 115
5x = 115-15
5x = 100
x = 100/5
x = 20
There is a line whose y-intercept is 10 and whose slope is 0. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in
simplest form.
Answers
Answer:
Below
Step-by-step explanation:
A line with slope = 0 is a horizontal line
for y = mx + b form this would be
y = (0)* x + 10
y = 10
Noah is putting together a 27-minute radio show. How many 21-min interviews can he include, and how much time will be left over after the last interview?
Answers
Answer:
One interview, with 6 minutes spare.
Step-by-step explanation:
27/21 is 1 with a remainder of 6
associative analyses cannot determine whether stable relationships exist between two variables. true false
Answers
Associative analyses cannot determine whether stable relationships exist between two variables.
The statement is False
Now, According to the question:
There are statistical analyses beyond simple descriptive measures, statistical inference, and differences tests including associative analyses which determine whether a stable relationship exists between two variables.
Associative analysis is an approach that is used to analyses the peoples mental representation , focusing on meaning and similarities and differences across the culture. It determined that relationship that is hidden in the large data set. It determine the relationship in between two variable as well.
Hence, Associative analyses cannot determine whether stable relationships exist between two variables.
The statement is False
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NEED HELP ASAP!!! please help!!!
Answers
Answer:
x=21
Step-by-step explanation:
rs= 6(x-9)
rt=2(2x-6)
rs=rt
6(x-9)=2(2x-6)
6x-54=4x-12
2x=42
x=21
5. A student surveyed 100 adults who took either vitamin C, zinc, or echinacea
supplements to prevent getting a cold. The adults were asked if they had a cold or no
cold in the last 30 days. The results are shown in the table.
vitamin C
zinc
no cold cold
41
echinacea
total
12
21
74
15
5
6
total
26
56
17
27
100
a. What proportion of adults in the survey took echinacea?
b. What proportion of adults who took vitamin C reported having a cold in the last
30 days?
c. What proportion of adults who reported having a cold took zinc?
Answers
The proportions for this problem are given as follows:
a) Took echinacea: 0.27.
b) Having a cold in the last 30 days, of those who took Vitamin C: 0.2679.
c) Took zinc, of those having a cold: 0.1923.
How to calculate the proportions?The proportions are calculated as the division of the number of desired outcomes by the number of total outcomes.
The survey is composed by 100 adults, and of those, 27 took echinacea, hence the proportion is of:
27/100 = 0.27.
56 adults took vitamin C, and of those, 15 reported a cold in the last 30 days, hence the proportion is of:
15/56 = 0.2679.
26 students had a cold in the last 30 days, and of those, 5 took zinc, hence the proportion is calculated as follows:
5/26 = 0.1923.
Missing InformationThe table is given by the image shown at the end of the answer.
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Which of the following statement is false? a. all isosceles triangles are similar b. all quadrilateral triangle are similar c. all circle are similar
d. none of the above
Answers
The statement that is false is A.. all isosceles triangles are similar
What is an isosceles triangles?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
An isosceles triangle has two of its three sides with equal lengths, and its two base angles are also equal. Although two isosceles triangles can have two sides that are equal on their own, they may not be similar because their sides may be of a different measurement.
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?
What is an equation of the line that passes through the point (8, -7) and is parallel
to the line x + 2y = 18?
Parallel/Perpendicular Through Point
Answers
The equation of the line that passes through point (8, -7) and parallel to the line x + 2y = 18 is
y = -x/2 - 3How to find the equation of the lineA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable
y = output variable
m = slope
x = input variable
c = y intercept
x + 2y = 18
rewriting gives : y = -x/2 + 9
when the line is parallel the slope is equal hence the slope of the line is -1/2.
using the point slope formula for point (8, -7) which is
(y - y') = m(x - x')
(y + 7) = -1/2(x - 8)
y + 7 = -x/2 + 4
y = -x/2 - 3
the equation of the line is y = -x/2 - 3
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a man imported a machine at shillings 600,000 and sold it for shillings 1,080, does 000 find the percentage profit if he spent shillings 60,000clearing the machine from the port and futher shillings 40,000 for shipping
Answers
Answer:
The man made a profit of 63.333% from selling the machine.
Step-by-step explanation:
To find the percentage profit, you will need to first calculate the total profit the man made from selling the machine. To do this, you need to subtract the cost of importing the machine and the other costs associated with clearing and shipping it from the selling price.
Here's the calculation:
Total profit = Selling price - (Import cost + Clearing cost + Shipping cost)Substituting the values you provided, we get:Total profit = 1,080,000 - (600,000 + 60,000 + 40,000)
Total profit = 1,080,000 - 700,000Total profit = 380,000
Next, we need to divide the total profit by the import cost, and multiply the result by 100 to express the profit as a percentage. Here's the calculation:
Percentage profit = (Total profit / Import cost) * 100Substituting the values we calculated above, we get:Percentage profit = (380,000 / 600,000) * 100Percentage profit = 63.333%
Therefore, the man made a profit of 63.333% from selling the machine.
Answer:
Step-by-step explanation:
on his trip to work each day, brady pays the same toll, using either all quarters or all dimes. if the number of dimes needed for the toll is 3 more than the number of quarters, what is the toll?
Answers
Answer:
50 cents
Step-by-step explanation:
25x2=2 quarters
5x10=5 dimes
3 more dimes than quarters
In the figure below, m ABD=100, and m<1 is four times m<2. Find m<2.
Answers
The unknown angle in the intersecting lines is as follows:
m∠2 = 20 degrees
How to find the angles when line intersect?In the figure m∠ABD is 100 degrees and m∠1 is four times m∠2. Therefore, let's find the angle m∠2.
From the diagram, the sum of angle ABC and angle CBD is equals to angle ABD.
Therefore,
m∠ABD = 100 degrees
m∠ABC = m∠2
m∠CBD = m∠1
Therefore,
let
x = m∠2
m∠1 = 4x
Hence,
100 = 4x + x
5x = 100
divide both sides by 5
x = 100 / 5
x = 20 degrees
Therefore,
m∠2 = 20 degrees
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What is the solution to the system of equations graphed below ?
Answers
Answer: (6, -1)
Step-by-step explanation:
<3
suppose you build a model of a concert hall using a scale factor of 18. how will the surface area of the actual concert hall compare to the surface area of the scale model? what about the volume?
Answers
The Surface area of the actual concert hall is 324 times as great as the surface area of scale model A
Given that,
Imagine creating a music hall model with a scale factor of 18.
To find : How will the scale model's surface area and the real music hall's surface area compare? Considering the volume
A new concert hall using a scale factor is 18.
then,
Scale = Dimension on module / Actual dimension
Area =k²
Where
K = Scale factor
Surface area of actual concert hall = (18)²
= 324
Thus, the Surface area of the actual concert hall is 324 times as great as the surface area of scale model A.
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what is the square root of 1476
Answers
Answer : 6√41
