A triangle has vertex coordinates (0,0) and (a, 0) . If the coordinates of the third vertex are in terms of at, and the triangle is isosceles, identify the coordinates and position the triangle on the coordinate plane.
Answers
The coordinate of another point will be (a/2,y) where y can be any value.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
An isosceles triangle is a triangle whose two sides are equal.
Let's say AB = AC
So,
Distance associate to AB = Distance associate to AC
(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²
x² + y² = (x - a)² + y²
x = a/2
So the coordinate of the third vertex is (a/2,y)
Hence "The coordinate of another point will be (a/2,y) where y can be any value".
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Related Questions
Which expression is equivalent to (3x^−4y^5) ^−2?
A: -9^8y^10
B: x^8/ 9y^10
C: -9x^8/ y^10
D: 1/ 9x^8y^10
(x's are variables not multiplication) (dashes resemble fractions) (^ resembles powers)
Answers
The equivalent expression to the given one is x^8/(9*y^10)
So the correct option is B.
Which expression is equivalent to (3x^−4y^5) ^−2?Here we just need to operate with the exponent properties that we know and love.
Remember that:
(a^n)^m = a^(n*m)
Then if we apply that to our case we will get:
(3x^−4y^5) ^−2 = (3^(-2)*x^(-4*-2)*y^(5*-2))
= (3^(-2)*x^8*y^(-10)
Now remember that negative exponents just "move" the number to the denominator position, this means that:
3^-2 = 1/3^2 = 1/9
Then we can rewrite our expression as:
(3^(-2)*x^8*y^(-10) = x^8/(9*y^10)
That is the equivalent expression to the given one.
The correct option is B.
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Geometry: fill in the blanks (ASAP!)
Answers
Shelia starts with $50 in her checking account. She spends $45, deposits $32, spends $14, and finally desposits $30. What is her ending balance?
Answers
(3x + 4)(x + 2x + 3)
Answers
Answer:
9x^2 + 21x + 12
Step-by-step explanation:
(3x+4)(x+2x+3)
Combine x and 2x to get 3x.
(3x+4)(3x+3)
Apply the distributive property by multiplying each term of 3x+4 by each term of 3x+3.
9x^2 + 9x + 12x + 12
Combine 9x and 12x to get 21x.
9x^2 + 21x + 12
w+1/7z=4
z=3w-2 using substitution
Answers
Answer:
w = - 2/7 + 4
w = z/3 + 2/3
Step-by-step explanation:
Write an equation in slope-intercept form for each line.
(-5,-3) and (10,-6)
Answers
A slope-intercept equation for each line (-5,-3) and (10,-6)
y = (3/5)x + 3.
How do you calculate the intercept form?The slope-intercept form of the line's equation is y = MX + b, where the material has deposited the slope and b symbolizes the y-intercept. We can see from our equation, y = 7 x + 4, that the y-intercept of the line is 4.
According to the given data:To begin, are using the slope formula to figure out the average slope between two points here.
Let:
x1 = -5
y1 = -3
x2 = 10
y2 = -6
m = (y2-y1)/(x2-x1)
= (-6 - (-3))/ (-10-(-5))
= -3/(-5)
= 3/5
So the slope is 3/5.
We must now find the y-intercept. This will be performed by translating one of the points and the slope into to the point-slope form of a linear equation. y2-y1 = m(x2-x1).
Let’s plug in the point (10,-5).
So we get y-(-3) = (3/5)(x-(-5)) ⇒ y+3
= (3/5)x + 3 ⇒ y
= (3/5)x + 3.
So y = (3/5)x + 3.
a slope-intercept equation for each line (-5,-3) and (10,-6)
y = (3/5)x + 3.
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what equation can represent 27 divided by 6 to represent the unknown quantity
Answers
Answer:
27÷6=? Answer is 4.5
Step-by-step explanation:
All you have to do is do 27/6 and the answer (unknown quantity) is 4.5.
Connor has a biased dice. The
probability of it landing on a
three is 0.8. Connor is going to
throw the dice 120 times.
Work out an estimate for the
number of times the dice will
land on a three.
Answers
Step-by-step explanation:
120×0.8
120/10)×8
=12×8
=96
The estimated number of times the dice will land on a three in 120 throws is 96 times.
We have,
To estimate the number of times the biased dice will land on a three, we can use the probability of getting a three in a single throw and multiply it by the total number of throws.
Probability of landing on a three in a single throw = 0.8
Total number of throws = 120
Estimated number of times the dice will land on a three
= Probability of landing on a three × Total number of throws
Estimated number of times = 0.8 × 120
Estimated number of times = 96
So, based on the biased dice with a probability of 0.8 for landing on a three, the estimated number of times the dice will land on a three in 120 throws is 96 times.
Thus,
The estimated number of times the dice will land on a three in 120 throws is 96 times.
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The battery power available to operate a deep space probe is given by the formula P=42 e°.°°5t , where P is power in watts and t is time in years. For how many years can the probe run if it requires 35 watts? Round the answer to the nearest tenth year.
Answers
The life of the battery is about 36.5 years, if it requires 35 watts.
What is termed as logarithmic functions?A logarithmic term is a number expressed in logarithmic form. Some other name for it is a log term.
A number could also be the sum of two or more numbers. As a result, a term can be the product of two or even more quantities, at least one of which should be in logarithmic form. These same terms are recognised as log terms in such cases.A quantity can also be described as the variation between two quantities. However, if a term contains a quotient of quantities, or if at least one of the amounts can also be conveyed in log form, the term is referred to as a log term.Consider some formulas used in log.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the given question,
The function is written as;
P = 42e∧(-0.005t).
The value of the power P is mentioned in the question; (P = 35 watt).
Thus, substitute the value of the P in teh equation;
35 = 42e∧(-0.005t).
Now, divide both sides by 42.
0.8333 = e∧(-0.005t)
Taking natural log on both side;
㏒0.8333 = ㏒e∧(-0.005t)
㏒0.8333 = -0.005t
Solve the value of the log by using calculator,
-0.182 = -0.005t
t = 36.5
Therefore, the the life for which the battery will run is 36.5 years.
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CCSS ARGUMENTS Write a coordinate proof for each statement.The three segments joining the midpoints of the sides of an isosceles triangle form another isosceles triangle.
Answers
The triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
An isosceles triangle XYZ is been made as shown below. Now, for the ΔXYZ, the midpoints of the line segment XY, YZ, and ZX are A, B, and C, respectively.
Further, the length of the sides of the ΔABC can be written as,
AB = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 1)² + (1 - 1)²]
= √4
= 2
BC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 2)² + (1 - 0)²]
= √2
AC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(1 - 2)² + (1 - 0)²]
= √2
Since, the length of the two sides is the same, while the length of the third side is different, thus, the triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
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need working out pls
Answers
As shown in the above figure:
AB = 4m, AD = 8m, AC = 3m, DE = 12m
Problem A:Ratio of the length AB to the length AD
[tex] →\frac{AB}{AD} = \frac{4}{8} = \frac{1}{2} [/tex]
Ratio = 1:2
Problem B:The length AE
[tex] \frac{AB}{AD} = \frac{AC}{AE} → \frac{4}{8} = \frac{3}{AE} [/tex]
Cross multiply the above.
[tex]4AE = 24[/tex]
Divide both sides by 4
[tex]AE = 6m[/tex]
Problem C:The length BC
[tex] \frac{AB}{AD} = \frac{BC}{DE} → \frac{4}{8} = \frac{BC} {12} [/tex]
Cross multiply the above
[tex]8BC = 48[/tex]
Divide both sides by 8
[tex]BC = 6m[/tex]
Please mark my answer brainliest
Joshua decides to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches then throws back into the water. After plotting all his data, he draws a line of best fit. What is the meaning of the x-value on the line when y=29?
Answers
The x value when y = 29 implies that the length in inches when the weight of the specie is 29
What is the meaning of the x-value on the line when y =29?The given parameters are:
The plot is about the relationship between the length in inches and the weight of a certain species of catfish
This implies that
x represents the length in inches y represents the weight of the speciesWhen the graph is plotted, the x value when y = 29 implies that the length in inches when the weight of the specie is 29
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Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=11 x-11 for x=-11
Answers
f(-11) = -132 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= 11 x-11
Put x = -11 ⇒ 11 * - 11 - 11
⇒ - 121 - 11
⇒ -132
Therefore f (-11) = -132
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Simone calculates the volume of a cube with side length 2.3 cm to be 6.9 cm3. Meiki says the volume is 12.167 cm3. Who is correct, and why?
Answers
Step-by-step explanation:
Philipp Heinrich Scheidemann was a German politician of the Social Democratic Party of Germany. In the first quarter of the 20th century he played a leading role in both his party and in the young Weimar Republic. Wikipedia
Born: July 26, 1865, Kassel, Germany
Died: November 29, 1939, Copenhagen, Denmark
Party: Social Democratic Party of Germany
Spouse: Johanna Dibbern (m. 1889–1926)
Previous offices: Mayor of Kassel (1919–1925), Chancellor of the German Reich (1919–1919), More
Books: The Making of New Germany: The Memoirs of Philipp Scheidemann
Nationality: German, Weimar
Which equation is parallel to 4x- 2y = 6 and passes through (0, 1)
Answers
The equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
How to determine the linear equation?The given parameters are
4x - 2y = 6
Divide through by 2
So, we have
2x - y = 3
Make y the subject of formula
So, we have
y = 2x + 3
A linear equation is represented as
y = mx + c
Where
Slope = m
This means that
m = 2
Parallel lines have equal slopes
So, the slope of the other line is
m = 2
The point on the line is given as (0, 1)
The equation is then calculated as
y = m(x- x1) + y1
So, we have
y = 2(x - 0) + 1
Evaluate
y = 2x + 1
Hence, the equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
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Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=4 x(7-2 x)
Answers
The given function
f(x) = y = 4x(7 - 2x) , is a Quadratic function
where its quadratic term is -8x².
Its linear term is 28x
Constant 0
What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:
f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.
4x (7 - 2x) we apply the distributive property
28x - 8x² is a quadratic function
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Type the correct answer in the box. round your answer to the nearest whole number. dylan has two cubes of iron. the larger cube has twice the mass of the smaller cube. he measures the smaller cube. its mass is 20 grams, and its density is 7.87 g/cm3. what’s the larger cube’s volume? the larger cube’s volume is about cm3.
Answers
The larger cube's volume is 5.08 cm³.
As per the given information, expressing the relation between the mass of iron cubes -
Mass of large iron cube = 2×mass of small cube
Mass of large iron cube = 2×20
Performing multiplication to find the mass
Mass of large iron cube = 40 grams
Now calculating the volume of large iron -
Density = mass ÷ volume
Keep the values in formula to find the volume of cube -
Volume = mass ÷ density
Volume = 40 ÷ 7.87
Performing division to find the volume of cube -
Volume = 5.08 cm³
Hence, the volume of larger iron cube is 5.08 cm³.
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The midpoint of CD is M(–9, –8). One endpoint is D(–9, –7). Find the coordinates of the other endpoint C
Answers
Use the link below to answer your question:
https://www.omnicalculator.com/math/endpoint
Hope this helps!
Write an equation of a circle with the given center and radius. Check your answers.
center (-1.5,-3) , radius 2
Answers
The equation of the circle with radius 2 and center at (-1.5 , -3) is (x + 1.5)^2 + (y + 3)^2 = 4.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-1.5 , -3)
r = 2
(x - -1.5)^2 + (y - -3)^2 = 2^2
(x + 1.5)^2 + (y + 3)^2 = 4
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Can someone help me on this question and explain the process?
Solve for x. The triangles in each pair are similar.
Answers
Answer:
x = 10
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{TS}{TB}[/tex] = [tex]\frac{TR}{TC}[/tex] ( substitute values )
[tex]\frac{10x+17}{65}[/tex] = [tex]\frac{90}{50}[/tex] ( cross- multiply )
50(10x + 17) = 90 × 65 = 5850 ( divide both sides by 50 )
10x + 17 = 117 ( subtract 17 from both sides )
10x = 100 ( divide both sides by 10 )
x = 10
What is the slope of the line passing through the following points? (2,4) and (4,2)
Answers
The slope of the line passing through the points (2,4) and (4,2) is -1
How do you determine a line's slope?
Determine the coordinates of two locations along the line that you choose. Find the difference between these two locations' y-coordinates (rise). Find the difference between these two locations' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Formula to determine the slope is - y₂ - y₁ / x₂ - x₁
Given are the points -
(2,4) and (4,2)
slope of the line = 2 - 4 / 4 - 2
= -2 / 2
= -1
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Find the distance between the points (-5, -4) and (7, -4).
Answers
Answer:
12
Step-by-step explanation:
the distance would be 12 because if you see the y values they are both -4 so they dont have any distance between them. Now if u look in the x values you will see different values -5 and 7 what u have to do now is do the equation 7 - - 5 which will be 12 because minus and minus will be plus so 7 plus 5 is 12, the distance between those points is 12.
Hope this answers ur question.
find the area of the polygon
7 ft, 22 ft, 10 ft.
what is the area of the polygon?
Answers
Answer:1540
Step-by-step explanation: I hope this helps
Is it possible for an inconsistent linear system to contain two lines with the same y -intercept? Explain.
Answers
If they have the same slope and different intercepts then they are parallel and there is no solution to the system.
If the two lines have different slopes, the system has exactly one solution (whether the lines have the same intercept or different intercepts).
If they have the same slope and the same intercept they are the same line, so there are infinitely many solutions to the system.
If they have the same slope and different intercepts then they are parallel and there is no solution to the system.
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18/12 pls??? Someone help
Answers
Answer:
3/2
Step-by-step explanation:
[tex]\frac{18}{12}=\frac{6(3)}{6(2)}=\frac{3}{2}[/tex]
Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above
Answers
The answer is 93.28
Step-by-step explanation:
The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get 93.28
|-a2|, given a = 5, b = -3, and c = -2.
10
25
-10
-25
Answers
|-10|
The answer is positive 10.
9. Writing to Explain Explain why you do not have to do any
computing to solve 15 X 0 X (13 + 7).
Answers
Answer:
because the answers 0 -
Explanation:
15 x 0 x (13+7)
= 15 x 0 x 20
= 0 x 20
= 0
Need help asap!!
Which of the following lists is in order from least to greatest?
√5 , 4, 3 2, -2
-2,√5 , 4, 3 2
-2, 4, 3 2, √5
-2, 3 2, 4, √5
Thanks!
Answers
The numbers in the second option is from the least to the greatest.
How to find the list from least to greatest?The numbers can be list from least to greatest as follows:
√5 , 4, 32, -2
32 is greater than -2.
Therefore, the numbers in first option is not from the least to the greatest.
-2,√5 , 4, 32
The number increases.
Therefore, the numbers in the second option is from the least to the greatest.
-2, 4, 32, √5
32 is greater than √5.
Therefore, the numbers in third option is not from the least to the greatest.
-2, 3 / 2, 4, √5
4 is greater than √5.
Therefore, the numbers in fourth option is not from the least to the greatest.
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PROOF Write a flow proof.
Given: MJ ≅ ML ; K is the midpoint of JL .
Prove: Δ M J K ≅ ΔM L K
Answers
Corresponding angles of congruent must be equal .
What exactly do you mean by congruent?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.Given , L is mid point of JL .
JL = LN Mid point
L is mid point of KM .
KL = LM Mid point
JM = NK Given
Δle JLM ≅ Δ le KLN ( SSS)
∠MJL ≅ ∠ KNL
Corresponding angles of congruent must be equal .
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