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. )

Answer:

31.25

Step-by-step explanation:

25% * 125 = 25/100 * 125 = 1/4 * 125 = 31.25

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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If the radius is quadrupled, then the area of the new area to the old area will be 4:1

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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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

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.

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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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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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 :)

The maximum number of students who studied all subjects is 6.

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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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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Answer: C, 217

Step-by-step explanation:

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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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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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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Answer: C= 30

Step-by-step explanation:

A^2+B^2=C^2

C= √(B²+A²)

C= √(18²+24²)

C=30

Answer:119

Step-by-step explanation:

because it's on oppisite sides on the outside

Answer:

------------------------------

The two given two angles are alternate exterior angles and therefore  congruent according to alternate exterior angles theorem:

Definition:

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:

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

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.

y = 3x+4 ← equation of linear function.

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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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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Back with the braids.

Therefore , the solution of the given problem of equation comes out to be  [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).

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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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

Answer:

yes

Step-by-step explanation:

yes

yes

yes

yes

yeyed

yes

9) x = 6

10) x = 1

11) x = 0

12) x = 6

This can be solved from the property of 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:

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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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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When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.

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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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.

The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.

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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By working together, they can make the work done in two hours and forty-six minutes.

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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