Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8
and AD 4, what is the length of AC ? (Note: the figure is not drawn to scale. )
Answers
The required length of the side AC of the given right triangle is 32 units.
What is the right triangle?A right triangle is a triangle with one right angle or two perpendicular sides.
It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle.
The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.
A triangle is referred to be a right triangle when one of the interior angles is 90 degrees or a right angle.
So, using the hypotenuse AC as the point of convergence for the right triangle ABC,
AB is 8 and AD is 2.
Verify whether the triangle ΔABD resembles ΔACB.
∠ BCA = ∠ DBA (90 - ∠ DBC)
∠ A = ∠ A
As a result, ΔABD and ΔACB share an AAS resemblance.
Utilize the similarity property to determine the length of AC.
AC/AB = AB/AD
x / 8 = 8 / 2
x = 32
Therefore, the required length of the side AC of the given right triangle is 32 units.
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Correct question:
Given a right triangle, ABC with altitude BD drawn to hypotenuse AC. If AB = 8 and AD = 2, what is the length of AC?
Related Questions
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame? (Type your answer in factored form. Type an exact answer in terms of pi.
The area of the frame is __ square units
Answers
The area of the frame is 196.73 x²
What is area ?
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.
(15x)^2 = 225x^2
Area of the frame
= π (3x)²
= 28.27 x²
Metal area surrounding the frame
225 x² - 28.27 x²
= 196.73 x²
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Write −0.39¯¯¯¯¯ as a fraction in simplest form.
Answers
Answer:
-0.3999... = -⅖
-0.393939... = -13/33
Step-by-step explanation:
Only ones I could think of.
Answer:
-39/100
Step-by-step explanation:
Can a/the variable in a algebraic expression be a base?
Answers
Answer:
yes
Step-by-step explanation:
yes
yes
yes
yes
yeyed
yes
How many times would you expect to roll a 5 if you rolled a fair die 1,300 times? Round your answer, if needed.
A.
0.1667
B.
1,083
C.
217
D.
95
Answers
Answer: C, 217
Step-by-step explanation:
What is the domain and range of √ X 2?
Answers
The domain of √ X 2 is X ≥ 4. The range is all real numbers.
Here is the proof, In order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the radicand is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all values of X that are greater than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any non-negative value is a real number.
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An approximate solution to an equation is found using this iterative process.
(x, Jº-1
X,+1
and x, = -1
4
Answers
The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
What is iteration ?
iteration can be defined as the repeating itself to perform a particular task.
Given
X2 is when n=1
X2 = X1+1 = X1 ^ 3 - 5/10
because X1 = -1
so X2 = -1-5/10 = -6/10 = -0.6
X3 is when n=2
X3 = X2+1
= X2 ^ 3 -5/10
because X2 = -3/5
so X3 could be
X3 = (-0.6*-0.6*-0.6) - 5 / 10
X3 = -0.041600
Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.
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Are 5x and 5 like terms?
Answers
The statement given here is true as 5x and 5 are like terms.
This is because like terms have the variables of same degree . Therefore, 5x and x are like terms as both of them have x to the power 1 , which means both are of degree 1.
Like terms differs from the unlike terms only in case of numerical component. By summing the coefficients of like terms , similar phrases can be regrouped. Like terms in a polynomial equation are those terms that have the same variables and these variables have the same powers, but with different coefficients.
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Which is the product of [tex]\frac{7}{9\\}[/tex] and 6?
( 100 POINTS )
Answers
Answer:
[tex] \sf \: \frac{14}{3} [/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]
[tex] \sf \rightarrow \: \frac{(7 \times 6)}{9} [/tex]
[tex] \sf \rightarrow \: \frac{42}{9} [/tex]
[tex] \sf \rightarrow \: \frac{14}{3} [/tex]
Hence, the product is 14/3.
what is the value of x?
Answers
Answer:119
Step-by-step explanation:
because it's on oppisite sides on the outside
Answer:
C) 119°------------------------------
The two given two angles are alternate exterior angles and therefore congruent according to alternate exterior angles theorem:
x = 119°Definition:
Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.560Steve can paint his greenhouse in four hours working alone; his ten-year-old son can paint the greenhouse alone in nine hours. Working together, how long, to the nearest minute, would it take them
Answers
By working together, they can make the work done in two hours and forty-six minutes.
How do you calculate work done together?The equation below may be used to compute work: Work is equal to force times distance. The Newton metre is the SI unit of work (N m). When an item is moved across a distance of 1 m with 1 N of force, one joule is equal to the amount of work that is accomplished.Every time a force pushes anything over a distance, work is done. By multiplying the force by the distance travelled in the direction of the force, you may determine the amount of energy transferred, or work done.Therefore, the formula for work is W = F d s, which stands for work done equal to force times displacement.Given data :
Think of these work rates as "greenhouses per hour", not "hours per greenhouse". Then Steve's work rate is one fourth of a greenhouse per hour, and his son's is one ninth of a greenhouse per hour. Now, multiply each rate by the time t to get the portion of the greenhouse each paints, and add the products up to get one greenhouse. The work equation becomes:
1 / 4 t + 1 / 9 t = 1
9 / 36 . t + 4 / 36 t = 1
13 / 36 t = 1
36 / 13. 13 / 36 t = 36 / 13 .1
t = 36 / 13 hrs
or 36 / 13. 60 = 166 min
This is two hours and forty-six minutes.
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please help: solve for x
Answers
Answer:
x=3
Step-by-step explanation:
Since the altitude of this triangle is at the midpoint of the base,
It is a isosceles triangle making MJ=MK
9x-18=3x
6x-18=0
6x=18
x=3
From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]
Answers
Back with the braids.
Work out the area of this shape. Give your answer
in cm².
4 cm
4 cm
10 cm
Answers
Answer:
48cm^2
Step-by-step explanation:
Rectangle=LxW
Triangle=bh/2
Rectangle: 10x4=40cm^2
Triangle: 4x4=16/2=8cm^2
40+8=48cm^2
Hope this helps :)
Which expression is equivalent to (x^2-2x-37)\(x^2-3x-40)
Answers
Therefore , the solution of the given problem of equation comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).
Describe equation.An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Here,
Given :([tex]x^{2}[/tex]-2x-37)/([tex]x^{2}[/tex]-3x-40)
[tex]x^{2}[/tex]-3x-40
Factor[tex]x^{2}[/tex]-2x-37
[tex]x^{2}[/tex]-2x-37/(x-8) (x+5)
Thus ,
the factors comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5)
Therefore , the solution of the given problem of equation comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).
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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school.
Answers
If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.
If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.
0.48 + 0.3 = 0.78.
In other words, there is a 78% probability of her not being late.
When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.
Answers
When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.
What is the rotation?In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.
Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.
There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).
Here two times rotation means 180 degrees that means no change in the final image.
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Can u please help? .
Answers
Answer:
x= 43
Step-by-step explanation:
The angles are corresponding angles which mean that they are equal to each other.
3x + 5 = 134 Subtract 5 from both sides
3x + 5 - 5 = 134 - 5
3x = 129 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{129}{3}[/tex]
x = 43
What is the degree of the polynomial 2x² 3xy 5y² 2?
Answers
The degree of the given polynomial is 2 because the highest exponent is 2 present in terms 2x^2 or 5y^2.
First, try to understand what is polynomial.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x^2+ 3x - 5 is an illustration of a polynomial with a single variable. There are three terms in this example: x^2, 3x, and -5.
The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases."
Now let's talk about the degree of the polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.
The terms of a given polynomial is 2x^2, 3xy, 5y^2, and 2 Highest exponent is 2 in 2x^2 or 5y^2.
So the degree of the polynomial is 2.
The given Question is an incomplete complete question here.
[tex]2x^2 + 3xy + 5y^2 +2[/tex].
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there are 32 students who studied maths and 28 geography and 26 social science if there are total 40 students in school if they all studies one subject atleast then find maximum number of students who studied all subjects
Answers
Because you add 3+3 more if you do so you can add it. So when you get that question just add or multiply the number you are given.
The maximum number of students who studied all subjects is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total students = 40
Number of students who studied maths = 32
Number of students who studied geography = 28
Number of students who studied social science = 26
The maximum number of students who studied all subjects.
= Highest number of students who studied one subject - Least number of students who studied a subject
= 32 - 26
= 6
Thus,
6 is the maximum number of students who studied all subjects.
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Is polynomial Y^4+4Y^2+5 have zeroes or not?
Answers
Yes, polynomial Y^4+4Y^2+5 has zeroes. Its zeroes can be found by factoring or using the quadratic formula: Y = -2 +/- sqrt(4-5) / 2 = -1 +/- sqrt(-1) / 2 = -1 +/- i/2.
[tex]Y^4+4Y^2+5[/tex]
=[tex](Y^2+1)²-3[/tex]
=([tex]\sqrt{Y^2+1-sqrt3}[/tex])([tex]\sqrt{Y^2+1+sqrt3}[/tex])
=(Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1)
=(Y+ sqrt3)(Y-sqrt3)(Y²-1)
=(Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1)
=0
Therefore the zeroes are Y=-√3, Y=1, Y=√3, Y=-1
Polynomial Y^4+4Y^2+5 is a fourth degree polynomial equation and can be solved by factoring or using the quadratic formula. To solve this equation by factoring, we need to use the difference of squares method. First, we rewrite the equation as (Y^2+1)²-3. Then we factor out the square of the binomial (Y^2+1): (Y^2+1-sqrt3)(Y^2+1+sqrt3). Next, we expand the first binomial to get (Y+ sqrt3)(Y-sqrt3)(Y+1)(Y-1). Then, we factor out the second binomial from the first two terms to get (Y+ sqrt3)(Y-sqrt3)(Y²-1). Finally, we expand the last binomial to get (Y+ sqrt3)(Y-sqrt3)(Y-1)(Y+1). This results in a product of zero, which means the equation has zeroes. The zeroes are Y=-√3, Y=1, Y=√3, and Y=-1.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
y = 3x+4 ← equation of linear function.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have,
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = y_2-y_1/x_2-x_1
with (x₁, y₁ ) = (- 3, - 5) and (x₂, y₂ ) = (1, 7) ← 2 ordered pairs from the table
m = 7+5/1+3
=12/4
= 3 ,
So, y = 3x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (1, 7 ), we get,
7= 3 + c
⇒ c = 7-3
= 4
Hence, y = 3x+4 ← equation of linear function
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Solve for the missing side length in this triangle
Answers
Answer: C= 30
Step-by-step explanation:
A^2+B^2=C^2
C= √(B²+A²)
C= √(18²+24²)
C=30
18=b
x=h
then we know that
h^=p^+b^
x^=18^+24^
x^=324+576
x^=900
x=30
so x=30#
If the original price is 125 pesos and the rate of discount is 25%, how much is the discount? with solution
Answers
Answer:
31.25
Step-by-step explanation:
25% * 125 = 25/100 * 125 = 1/4 * 125 = 31.25
Josefina wants to prove that figures d and d are similar.
What seguence of transformation could Josefina perform to prove the figures are similar?
Answers
The left shift required to translate from D to D" is 6 units and scale factor for dilation of D" from D' is 2.5.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Compare the corresponding vertex of the given figures.
It is given as,
(-5, 0) → (1, 0)
It can be concluded that the graph of D is shifted (1 - (-5)) = 6 units towards left.
The scale factor is given as,
Length of side of D" ÷ Length of side of D'
⇒ 10 ÷ 4 = 2.5
Hence, the required shift and the scale factor are obtained as 6 units and 2.5 respectively.
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Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
20q ^10 - 10q⁹+ 30q^8 + 20q^7
Answers
The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
What is the greatest common factor?The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).
The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.
the factor of 20q¹⁰ is 2*2*5*q*q*q*q*q*q*q*q*q*q
the factor of 10q⁹ is 2*5*q*q*q*q*q*q*q*q*q
the factor of 30q⁸ is 2*3*5*q*q*q*q*q*q*q*q
the factor of 20q⁷ is 2*2*5*q*q*q*q*q*q*q
So that the common factor of all the above terms is 2*5*q*q*q*q*q*q*q
the common factor of all the above terms= 10q⁷
So that the greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
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What is the x-coordinate of the solution to the system shown?
3x - y = 6
3x + y = 34
Answers
Answer:
6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
In this equation I will do the elimination method.
3x-y=6
3x+y=34
6x=40
Simplify
x=6[tex]\frac{2}{3}[/tex].
Check:
3(6.666...)-y=6
20-y=6
-20 from 6
-y=-14
y=14
20-14=6
6=6
3x(6.666...)+y=34
20+14=34
34=34
3x - y = 6 → y = 3x - 6
3x + y = 34 → y = -3x + 34
Next, we plug it in to become an equation with variables on both sides:
3x - 6 = -3x + 34
→ 6x - 6 = 34
→ 6x = 40
→ x = 6 2/3 OR 6.66666
solve for x. each figure is a parallelogram
Answers
9) x = 6
10) x = 1
11) x = 0
12) x = 6
This can be solved from the property of parallelogram.
What is parallelogram?A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.
Properties are:
The opposing sides are equally spaced and parallel.Angles on either side are equal.The angles that are consecutive or contiguous are supplementary.All of the angles will be at right angles if any one of them is a right angle.The two diagonals cut across one another.9) As we know, from the property of parallelogram,
SR = TQ and ST = RQ
Now, 4 + 2x = 3x - 2
or, x = 6
10) As we know, from the property of parallelogram,
EF = DC and ED = FC
17x + 1 = 18x
or, x = 1
11) As we know, from the property of parallelogram,
YZ = XW and YX = ZW
2x + 9 = 9
2x = 0
x = 0
12) As we know, from the property of parallelogram,
TU = SV and TS = UV
6 + 2x = 4x - 6
or, 2x = 12
or, x = 6
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I NEED HELP PLEASEEE!!!
Answers
If the radius is quadrupled, then the area of the new area to the old area will be 4:1
What is quadrupled?You should be aware that the quadrupled of a circle is four times the area of the old one.
In this case the area of the circle is denoted by
Area = πr²
Where r= radius=6 cm
The area of the old circle is 22/7 * 6 * 6
Area of the circle is = 113.1cm²
To this effect, the area of the new circle is 4(area of the old one)
Area = 4*22/7 * 6 * 6
Area = 3167/7
Area is = 452.6
This implies that 4(113.2) =452.6
In conclusion, you will discover that four times the area of the new circle is the old circle
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What are the 3 steps to solving an equation?
Answers
Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.
2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.
3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.
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Peggy completed 5/6 of the math homework and Al completed 4/5 of the homework. Did Peggy or Al complete more hoof the math homework?
Answers
Peggy completed more of the math homework than Al
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
we know that
In order to be able to compare fractions more easily it is recommended that both have the same denominator
Peggy
5/6 x 5 = 25/30
Al
4/5 x 6 = 24/30
Peggy completed more of the math homework
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