Which of the following best describes DG?
E
G. F
D
A. Perpendicular bisector
B. Altitude
C. Angle bisector
D. Median

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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AB=8.7 cm. Work out the length of BC. ... 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... Give your answer correct to 1 decimal place. ton o. Ady ... Ad. POR is a right-angled triangle. PR = 12 cm. OR = 4.5 cm. Angle PRO = 90°. ... AB= 7 cm. BC = 12 cm. Angle BAD= 65°. Calculate the length of AC.

Answer:

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

I just took the quiz.

Answer:

(A) x(3+5)  is an expression. The rest are equations.

Step-by-step explanation:

Answer:

A = 3

B = -1

C = 5

Step-by-step explanation:

y - 7 = 3(x - 4)    Distribute the 3

y - 7 = 3x -12  subtract y from both sides

-7 = 3x -y -12  Add 12 to both sides

5 =3x -y  Flip the equation around the equal sign

3x -y = 5

The 3 is the A, -1 is the B and 5 is the C.

9514 1404 393

Answer:

  y = 3/4x

Step-by-step explanation:

The equation of a proportional relation is ...

  y = kx

The value of k can be found by dividing by x:

  y/x = k

For the given values, we find k to be ...

  k = y/x = (3 ft)/(4 turns) = 3/4 ft/turn

The relationship can be written ...

  y = 3/4x

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer: 7xy + 2x^2t

Step-by-step explanation:

Answer:

Decreased by 19%.

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

Decrease by of x 10% can be shown as a product of x and:

Same applies to the second decrease, then we get a final number:

It represent a one off decrease of:

Hence the answer is 19%.

Answer:

Step-by-step explanation:

100 - 100/10 = 90

90 - 90/10 = 91

100 - 81 = 19%

for a better understanding look at the figure

Answer: 18.18%

Step-by-step explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

\($$SA = 2lw + 2lh + 2wh$$\)

where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.

The approximate solution of the linear system represented by the graph is, (5, 6)

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

A graph in which two lines are intersecting each other,

basically solution of linear system means where both the lines will intersect,

So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,

Therefore, the solution is (5, 6)

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Suppose \(x>0\); then the curves meet when

\(x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12\)

By symmetry, they intersect at \(x=\pm\frac12\).

We also see that \(\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}\) and \(\max\left\{g(x):|x|\le\frac34\right\} = 2\) at \(x=0\). \(f\) and \(g\) are continuous, so it follows that

\(\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}\)

Compute the area \(\alpha\). Taking advantage of symmetry again, we have

\(\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23\)

and it follows that \(9\alpha = \boxed{6}\).

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Answer:

Pythagorean Theorem: a squared + b squared = c squared

Pythagorean Theorem: implies in every single triangle

Step-by-step explanation:

Using it's concept, it is found that due to the lowest Mean Absolute Deviation, his scores were closest together in Math.

Of the four classes, Math was the lower MAD, hence it has the scores that are closest together.

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Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Answer:

please tell me if there iscany sing after 4xy

Answer:

xy-x+y+1

Step-by-step explanation:

(1-x^2)(1-y^2)+4xy=1-y^2-x^2+x^2y^2+4xy

here, 4xy=2xy+2xy

then, -(x^2-2xy+y^2)+(x^2y^2+2xy+1)=-(x-y)^2+(xy+1)^2

by a^2-b^2=(a+b)(a-b)

(xy+1+x-y)(xy+1-x+y)

1-2x+y-x^2y+x^2=-y(x^2-1)+(x^2-2x+1)=-y(x+1)(x-1)+(x-1)^2

=(x-1)(x-1-xy-y)=-(x-1)(xy-x+y+1)

thus, common factor is xy-x+y+1

Hope this helps

Answer:

You have to divide 46 by 6. thats all I know sorry

Step-by-step explanation:

Each student gets 7 pencils.

What are mathematics operations?

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Here, it is given that :

Mr. Rodriguez purchased 46 pencils to give to the students he tutors

and number of students = 6

Therefore, to find number of pencils each student get we divide 46 with 6 :

pencils will each student get = 46/6

pencils will each student get ≈ 7

as each student get equal number of pencils then 4 pencils are left with Mr. Rodriguez after giving 42 pencils to the students.

Therefore, each student gets 7 pencils.

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Answer:

Q = 12 meters

Step-by-step explanation:

Since all angles of the triangles are the same, the two triangles are similar. Therefore, all you need to do is a simple comparison equation like 10/15=8/x and solve.

Cross multiply, 10x=120. Divide and get x = 12.

Hope this helps!

Answer:

x < 3 1/4

See picture below.

Step-by-step explanation:

1/2 x - 3 < -1 3/8

1/2 x < -11/8 + 24/8

1/2 x < 13/8

x < 13/4

x < 3 1/4

Answer:

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

Given  number is 71830.

The last part:  830 is same on both lines.

We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:

It is 11 thousands.

Answer:

11,000 (or) 11 thousands

Step-by-step explanation:

Now we have to,

→ find the missing number.

→ Let the number be x.

Forming the equation,

→ 60,000 + x + 800 + 30 = 71,830

Then the value of x will be,

→ 60,000 + x + 800 + 30 = 71,830

→ x + 60,830 = 71,830

→ x = 71,830 - 60,830

→ [ x = 11,000 ]

Hence, the value of x is 11,000.

The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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Answer:

$19.63 would be the sales tax on this

Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

To calculate Miranda's discretionary income, we need to first add up her expenses:

$60 + $85 + $195 + $55 + $575 = $970

Next, we need to calculate her monthly income.

Since Miranda gets paid semi-monthly, we'll need to multiply her paycheck amount by 24 (the number of pay periods in a year) and divide by 12 (the number of months in a year):

$550 x 24 / 12 = $1,100

Now we can calculate her discretionary income by subtracting her expenses from her income:

$1,100 - $970 = $130

Therefore, Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

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Answer:7 x 10 ^1 is the right answer

Step-by-step explanation:

Hope this helps :)

There is the bacterial cell 7 × 10¹ times smaller than the amoeba cell which is the correct answer would be an option (B).

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

We have been given that a bacterial cell is around 5 × 10⁻⁶ m long, while an amoeba cell is about 3.5 × 10⁻⁴ m long.

To determine the number of times smaller is the bacterial cell than the amoeba cell.

⇒ amoeba cell / bacterial cell

⇒ 3.5 × 10⁻⁴ m / 5 × 10⁻⁶ m

Apply the division operation, and we get

⇒ 0.7 × 10⁻⁴ × 10⁶

Adding the exponents of the above terms

⇒ 0.7 × 10⁻⁴⁺⁶

⇒ 0.7 × 10²

⇒ 7 × 10¹

Hence, there is the bacterial cell 7 × 10¹ times smaller than the amoeba cell.

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