3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
Given that,
In a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
We have to find how much longer is the longer leg.
We know that,
Let the one side of the triangle be x
The other side we get x-1 and x+2
From Pythagoras theorem,
x²+(x-1)²=(x+2)²
x²+x²-2x+1=x²+4x+4
2x²-2x+1-x²-4x-4=0
x²-6x-3=0
To find the value of x we have a formula that is
x=-b±√(b²-4ac)/2a
Here, a=1, b=-6 c=-3
x=6±√(-6²-4(1)(-3))/2(1)
x=6±√36+12/2
x=6±√48/2
x=6±4√3/2
x=3±2√3
Therefore, 3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
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The italian mathematician fibonacci is known for introducing what mathematical concept?
Which of these fractions is equivalent to the fraction in this image?
1 of 3 slices of pizza
1) 4/12
2) 3/12
3) 2/12
4) None of these is correct.
Answer:
4/12
Step-by-step explanation:
What is the equation of the line that passes through the points − 2 1 and 4/5 in the Cartesian coordinate plane?
The equation of the line that passes through the points (2, 1 ) and (4,5) in the Cartesian coordinate plane is y = (2/3)(x - 4) + 5.
By subtracting the y coordinates [5 - 1] = 4, we get
Subtract the x coordinates in the same order [4 - (-2)] = [4 + 2] = 6
The slope is given by y-coordinate/x-coordinate = 4/6 = 2/3.
Now, just choose one point say (4,5), and substitute the coordinates in this formula-
y - [y-coordinate of our point] - (slope)* [ x - ( the x-coordinate of our point)]
y - 5 = (2/3)(x - 4) ...........(adding 5 to both sides)
y = (2/3)(x - 4) + 5
Hence, the equation of the line in the "slope-intercept" form is y = (2/3)(x - 4) + 5.
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The complete question is -
what is the equation of the line that passes through the points (-2,1) and (4,5) in the cartesian coordinate plane?
What is quadrilateral with two distinct pairs of congruent and adjacent side?? a quadrilateral with two pairs of adjacent, congruent sides. it has perpendicular diagonals and one pair of opposite interior angles that are congruent. if you draw midsegments between adjacent sides of this quadrilateral, you form a parallelogram.
A quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
A quadrilateral is a figure that has 4 sides and edges. Parallelogram, rectangle, square are all examples of quadrilateral.
Different quadrilaterals have different properties. A quadrilateral in which two distinct pairs of adjacent sides are congruent is termed as a kite.
Only kite is a quadrilateral which has the given property.
Some other properties of kite include-
1. diagonals of a kite are perpendicular to each other
2. along its main diagonal, a kite is symmetrical
3. one of the diagonals of the kite bisects the other
Thus, a quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
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What is the y-coordinate of the solution to the following system of equations?
y=2x + 1
x+y = 1
Answer : y coordinate is 1
y = 2x + 1
x + y = 1
solve for y : x + y = 1
-x -x
y = -x + 1
Graph them,
(0,1) (x,y) y value is 1
What is the end behavior of the graph of the polynomial function y 7x12 3x8 9x4?
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
Given,
The polynomial function; y = 7x12 – 3x8 – 9x4
We have to find the nd behavior of the graph of the polynomial function;
End behavior of polynomial function;
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ), the end behavior of a function represents the trend of the graph.
Here,
We examine the polynomial's degree and the sign of the coefficient of the variable with the highest exponent to determine the graph's final behavior.
The degree is even 12.The coefficient, 7, is a positive number.That is,
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
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Kyle buys a mobile phone that weighs 310 g to 2 significant figures.
He puts the phone inside a protective case that weighs 15.6 g to 1 decimal
place.
Work out the smallest possible total weight, in grams (g), of the phone and
case combined.
Answer:
325.6g
Step-by-step explanation:
weight of phone + weight of case
= 310 + 15.6
= 325.6g
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create a birthday polynomial with 10-12-2247
The birthday polynomial with 10-12-2247 is given as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
How to create a birthday polynomial?A birthday polynomial is created attributing each digit of the birthday as a coefficient of the polynomial.
The birthday in this problem is given as follows:
10-12-2247.
Thus the coefficients of each term of the polynomial, in order, are given as follows:
1.0.1.2.2.2.4.7.There are eight coefficients, hence the polynomial is of the seventh degree.
The signs of each coefficient is not important, they can be chosen at random, and thus the birthday polynomial for the date of 10-12-2247 can be defined as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
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Gabriel's salary is £24500.
Next year he is due to get a 9% increase.
What will his new salary be?
Answer:
26,705
Step-by-step explanation:
First find 9% of 24500
24500 x 0.09 = 2205
Second add 2205 + 24500
2205 + 24500 = 26,705
8th grade math help plsssss
members of the fitness club hosted a benefit. They charged $4 for adults and $3 for students. if they earned a total $435 and 120 people attended, how many students were there?
Answer:
101.25
Step-by-step explanation:
To find the number of students, we need to first determine the total amount earned from the students. We can do this by multiplying the number of people by the cost per student: $3/student * 120 people = $<<3*120=360>>360.
Since the total amount earned was $435 and we know that $360 of that came from students, we can find the number of students by subtracting the total earned from students from the total amount earned: $435 total - $360 from students = $75 from adults.
Since the cost per adult was $4, we can divide the total amount earned from adults by the cost per adult to find the number of adults: $75 / $4/adult = <<75/4=18.75>>18.75 adults.
Since there were 120 people in total and 18.75 of them were adults, there must have been 120 people - 18.75 people = <<120-18.75=101.25>>101.25 students
the tunnel under the english channel that connects england and france is actually three separate tunnels built end to end. each is a half-cylinder that is 50,000 meters long and 4 meters high. how many cubic meters of dirt had to be removed to build the tunnel?
Answer: im not exactly sure but i think 600,000m³
Step-by-step explanation: multiply 50,000m by 4 to get 200,000m and then multiply that by 3 (because 200,000 is only one section of the tunnel)
and by doing that you get 600,000m and then add cubed onto the end because it says cubic meters
Can someone pls tell me how many boxes he can afford it’s due at 11:59 tonight!!
Answer:
You have chosen the correct answer
Step-by-step explanation:
He cannot spend more than 55. So the cost of the groceries has to be 55 or less.
He is only buying one package of eggs and the x represents how many packages of sugar he can purchase knowing that each box costs 11.50.
I need to find the measure of the arc or angle indicated and assume that the lines that appear to be tangent are tangent
By using tangent chord angle formula, the measure of angle FGH is 50°.
What is tangent chord angle?
The angle formed by the chord in the alternate segment is equal to the angle formed by the tangent through the point of contact of the tangent for any circle, according to the theorem.
Another name for the tangent-chord theorem is the alternate segment theorem.
We have to find the m ∠FGH.
Since, by tangent - chord angle theorem, the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle.
GH = 2(m ∠FGH)⇒ m ∠FGH = 1/2(GH)
Here GH = 100° ⇒ m ∠FGH = 1/2(100°) m ∠FGH = 50°
Hence, by using tangent chord angle formula, the measure of angle FGH is 50°.
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Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes three times as long as Meredith to edit a textbook. Together, it takes them 15 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
hours
How long does it take Meredith to edit a textbook if she works alone?
The number of hours taken by Meredith to edit a textbook if she works alone is 20 hours and time taken by Phil alone to edit text book is 60 hours..
Given that, Phil and Meredith work for a book publisher editing mathematics textbooks.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let the time taken by Meredith be x.
Phil has less experience and takes three times as long as Meredith to edit a textbook.
So, time taken by Phil be 3x.
Now, 1/x +1/3x =1/15
⇒ (3+1)/3x =1/15
⇒ 4/3x =1/15
⇒ 4/x =1/5
⇒ x=20 hours
So, time taken by Phil =3x =60 hours
Therefore, the number of hours are 60 hours.
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what is 5 3/4 divided by 3 1/2
Step-by-step explanation:
convert, Keep Change Flip, convert back
[tex]\frac{23}{4} * \frac{2}{7}[/tex]
[tex]\frac{46}{28} \\[/tex]
[tex]1\frac{18}{28}[/tex]
3times a number is 4 less than the square of that number find the negative solution
Answer: the answer is -1
50x=10 please help!!!
Answer:
[tex]\boxed{\boxed{\tt x=\frac{1}{5}}\: \bf Or\:\boxed{\tt x=0.2}}[/tex]
Step-by-step explanation:
[tex]\tt 50x=10[/tex]
Divide both sides by 50:-
[tex]\tt \cfrac{50x}{50}=\cfrac{10}{50}[/tex]
Simplify:-
[tex]\tt x=\cfrac{1}{5}[/tex]
_____________________
Hope this helps!
Have a great day!
help.
Find the area of the figure.
the area of the triangle is 7.5
Pre-image ABCD was dilated to produce image A'B'C'D'.
What is the scale factor from the pre-image to the image?
Enter your answer in the box as a fraction in simplest form.
The scale factor from the pre-image to the image is 2/5.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
let the scale factor be m, so that the scale factor multiplied by the dimension of pre-image should give dimension of image.
so that we have,
20 x m = 8
20m = 8
divide both sides by 20
m = 8/20
m = 2/5
In conclusion the dilation factor is 2/5
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I need help can someone help pls?
Answer: B
Step-by-step explanation:
Does dilation change the position?
Yes , Dilation do changes the position
Dilation is the process of changing the size or shape of an object. With the aid of the specified scale factor, it is a transformation that makes the objects smaller or larger.
The pre-image is the original figure before dilation, while the new figure is referred to as the image.
Dilation can be of two types:
Expansion - When the size of an object is increased.Contraction - When the size of an object is decreased.Dilation does not change the shape of the object from preimage to image only size and position are changed.
The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or shrunk but the proportion of each dimension of the shape and the angles remain the same.
Hence , It is true that dilation changes the position
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the serving size for the granola that ted likes to eat for breakfast is 3/4 cup. how many servings are there in a box that holds 13 cups? (what operation should be used here? solve the problem.)
With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.
Given that:
Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.
We need to know how many servings of 3/4 cup can be obtained from 13 cups.
now we need to divide 13 by 3/4
=13 ÷ 3/4
= 13 × 4/3
= 52/3
= 17[tex]\frac{1}{3}[/tex]
With one third of a serving remaining, there are 17 servings total.
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Given the points (-15, 30) and (5, 50). The slope of the line between the two points would be?
Answer:
The slope of the line is 1
Step-by-step explanation:
gradient = difference of y-coordinates / difference of x-coordinates
gradient = (y2-y1) / (x2-x1)
gradient = 50-30 / 5-(-15)
gradient = 20/20
gradient = 1
Select all the statements that are true of the relation.
Answer: A C and D
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling pizza slices and sodas. Each pizza slice sells for $2.50 and each soda sells for $1.25. At the end of the night you made a total of $696.25. You sold a total of 384 pizza slices and sodas combined. You must report the number of pizza slices sold and the number of sodas sold. What equations did you use to solve this where P = the number of pizza slices sold and S = the number of sodas sold?
please help, answers only!!
Answer:
Step-by-step explanation:
Upper right graph meets both of the requirement, the line lays on both (0,9) on the y axis and (3,0) on the x axis
When θ = 28° , which equation can be used to find the distance from point a to point b?
The equation used to represent the distance between two points A and B is AB = x Cos 28°
The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.
As per the given question,
A and B are the points in a triangleΘ = 28Let the hypotenuse be x
The two points A and B are on the base of the triangle so,
Base - length = AB
The distance between the two points is
⇒ cos Θ = base / hypotenuse
where, base = AB
hypotenuse = x
⇒ cos Θ = AB / x
⇒ AB = x cos Θ → 1
Substitute Θ = 28 in 1,
⇒ AB = x cos 28°
Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.
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The complete question is
When θ = 28° , which equation can be used to find the distance from point a to point b?
The circumference of a circular garden is 84 feet. What is the diameter of the garden
Round your answer to the nearest hundredth.
Diameter is 25.46 feet as circumference is 2πr and 2r is d so we just simply divide the circumference with π and get the value as 25.46
Step-by-step explanation:
Answer:
26.727feet
Step-by-step explanation:
Circumference = 22 x diameter
7
7x 84= 22d
d= 588
22
= 26.727feet
Evaluate the expression for the given value of the variables.
0.7g - 2.7h
g= 17, h =2
Answer:
6.5
Step-by-step explanation:
Step 1: Plug in g = 17, h = 2
0.7 * 17 - 2.7 * 2
Step 2: Solve Using PEMDAS
11.9 - 2.7 * 2
11.9 - 5.4
6.5
What does it mean to dilate a rectangle?
To dilate a rectangle means to either expand or contract the size of rectangle without changing it's shape .
Dilation is where the polygon grows or shrinks but keeps the same overall shape.
To dilate a rectangle means to either expanding or contracting the rectangle without changing it's shape .
For example: Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.
Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)
To dilate this rectangle by factor 3 , then every coordinate point of the original triangle will multiplied by the scale factor
Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4, -4)
Therefore, When we dilate a rectangle by scale factor 2 ,
The rectangle has enlarge it's size .
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