factorize -b^2+48c^2+8bc

If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved.

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.

In the given triangle below;

Line segment BC is intersecting at the midpoint of AD and AE.

Now,

Since ΔABC ≈ ΔADE by similarity property.

So,

AB/AD = BC/DE

AB/(AB + BD) = BC/DE

Since AB = BD = AB lets say,

AB/2AB = BC/DE

BC/DE = 1/2

Hence "If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved".

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The number according to the given statement is x<-0.55.

Given the statement is five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​.

A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Five and three-tenths of a number means 5.3x.

And two and seven-tenths means 2.7.

So, five and three-tenths times a number plus two and seven-tenths means 5.3x+2.7.                ......(1)

It is also given that three and three-tenths times a number means is 3.3x.      

And one and six-tenths means 1.6.

So, three and three-tenths times a number plus one and six-tenths​ means 3.3x+1.6         .......(2)

Now, we will substitute equation (1) less than equation (2) according to the given statement is

5.3x+2.7<3.3x+1.6

Further, we will subtract 2.7 from both sides, we get

5.3x+2.7-2.7<3.3x+1.6-2.7

5.3x<3.3x-1.1

Now, we will subtract 3.3x from both sides, we get

5.3x-3.3x<3.3x-1.1-3.3x

2x<-1.1

Now, we will divide both sides by 2, we get

2x/2<-1.1/2

x<-0.55

Hence, the number for the given statement "five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​" is -0.55.

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The value of a for the given equation is a=(r-q)/g.

The given equation is ga+q=r.

We need to find the value of a from the given equation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, ga+q=r can be solved for a as follows:

⇒ga=r-q

⇒a=(r-q)/g

Therefore, the value of a for the given equation is a=(r-q)/g.

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Graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

As given in the question,

Function: f(x)=(3.1)⁴

Here x  is independent variable and f(x) is dependent variable on x.

f(x)=(3.1)⁴ is a constant value and does not have any x variable.

It is shown in the drawn graph.

x =0 , f(x)=(3.1)⁴

x =1 , f(x)=(3.1)⁴

x = 2 , f(x)=(3.1)⁴

x = -1 , f(x)=(3.1)⁴

x = -2 , f(x)=(3.1)⁴ and so on.

Therefore, graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

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The required wood needed to build four vertical sides is 60 inch.

According to the question, the given parameters for the box-shaped drum is as follows:

Length = 18 inch; Breadth = 12 inch; Height = 11 inch

To know the quantity of the wood need to build four vertical sides, calculation of perimeter is required.

Therefore, perimeter of the box = 12 + 18 + 12 + 18 = 60 inch

Hence, the required wood needed to build four vertical sides is 60 inch.

What is perimeter of a shaped box?

Perimeter of a shaped box is the addition of all the sides of a box. It is used for the closed shaped boxes. And it is measured in the linear units like meter, centimeter, etc.

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 The ratio of the height of the larger prism to the smaller prism is a/b = 5.

 To solve this problem we must know what a scale factor is.

  The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.

  If we have as reference the volumes of two hexagonal prisms, with the values of:

  If the reason or scale for the volume is given by

 Let's go for the reason of the length, for this we apply the cubic root.

a³/b³ ⇒ ∛(a³/b³)

∛250/2

a/b = 5

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Answer: quadrant 4 (IV)

Step-by-step explanation:

Answer: h(-1) is equal to -2.

Step-by-step explanation:

We have to find , h(-1).

First you can plot the value of x = -1 in the graph.

Then you can draw a perpendicular line on the down ward direction and intersect to the parabola curve.

What is a parabola curve?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix. Parabola is an integral part of conic section topic and all its concepts parabola are covered here.

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )

Now you can see the point of (-1,-2) in the graph

Where,

                   h(-1) = -2

So, h(-1) is equal to -2.

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Answer:

Below in bold.

Step-by-step explanation:

3n + 4:

The common difference = 3,

First term = 3(1) + 4 = 7

First 4 terms

= 7, 10, 13, 16

10th term = 3(10) + 4 = 34.

4n - 5:

The common difference = 4,

First term = 4(1) - 5 = -1

First 4 terms

= -1, 3, 7, 11

10th term = 4(10) - 5 = 35.

Answer:

The price of a ticket after the team loses 22 games is $26.93

Step-by-step explanation:

Original value = $31.55

value decrease per game lost = $0.21

equation uses C and L

C = 31.55 - 0.21L

22 games lost

C = 31.55 - 0.21(22)

C = 31.55 - 4.62

C = 26.93

C = $26.93

Answer:  the distance is (4,2)

Step-by-step explanation: it takes from 3 to seven 4 1s. and 6 -4 will be 2

hope this helps

In the equation y = -x + 5, the value of y when we substitute -3 for x is 8.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the equation y = -x + 5, if we substitute -3 for x, the equation becomes

y = -(-3) + 5

Performing the arithmetic operations, we can have the value of y.

y = -(-3) + 5

y = 3 + 5

y = 8

Hence, for the equation y = -x + 5, y is 8 when x is -3.

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The expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

The expression is given as:

3(−4.5b − 2.1) − (6b + 0.6)

Open the brackets

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b − 6.3 − 6b - 0.6

Collect the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b  − 6b − 6.3 - 0.6

Evaluate the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -19.5b − 6.9

Hence, the expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

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Answer:

C: -19.5b-6.9

Step-by-step explanation:

Answer: 6,7,8

Step-by-step explanation:

Here no enough information to determine if the triangles are congruent.

Option C is true.

What is Congruent triangle?

Congruent triangle have both the same shape and the same size.

Given that;

Two sides of triangles are 6 and 13.

Now,

Since, Congruent triangles are triangles that have equal corresponding angles and sides.

From the images of the triangles (see attachment),

We can see that the two triangles have 6cm and 13cm as the lengths of their sides.

However, The side lengths of both triangles are not corresponding, and the angle measures are not given.

Hence, There is no enough information to determine if the triangles are congruent.

Option C is true.

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The probabilities from the binomial probability mass function P(x ≤ 2) will be 0.9298.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

q = 1 - p = 1 - 0.10 = 0.90

Let x be a binomial random variable with p = 0.1 and n = 10.

The probabilities from the binomial probability mass function P(x ≤ 2) will be

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x ≤ 2) = ¹⁰C₀ × (0.1)⁰ × (0.9)¹⁰ + ¹⁰C₁ × (0.1) × (0.9)⁹ + ¹⁰C₂ × (0.1)² × (0.9)⁸

P(x ≤ 2) = 0.3487 + 0.3874 + 0.1937

P(x ≤ 2) = 0.9298

Your question was incomplete but the complete question is given below.

Let x be a binomial random variable with p = 0.1 and n = 10. Calculate the probability from the binomial probability mass function less than or equal to 2.

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Answer:

73

Step-by-step explanation:

97 - 2 × (16 - 4) ← evaluate parenthesis

= 97 - 2 × 12 ← evaluate multiplication

= 97 - 24 ← evaluate subtraction

= 73

Answer:

73

Step-by-step explanation:

97 - 2 x (16-4) =

97 - 2 x (12) =

97 - 24 =

73

By the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

From the question, we are to prove that ΔBXA ≅ ΔBYA

From the Hypotenuse Leg theorem which states that "two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side".

From the given information,

BX ⊥ XA.

ΔBXA is right triangle with hypotenuse AB

Also,

BY ⊥ YA.

ΔBYA is right triangle with hypotenuse AB

∴ The hypotenuses of the triangles are congruent

Also, from the given information,

XA is congruent to YA

XA and YA are the legs of the right triangles.

Hence, by the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

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The soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

According to the given question.

We have a linear equation in one variable 4 + x = -52.

Since, we have to solve the above equation for x.

As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the above equation 4 + x = -52 is given by

4 + x = -52

⇒ x = -52 - 4    ( subtract 4 both the sides)

⇒ x = -56

Hence, the soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

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A linear equation that gives the price p they can charge for n shirts is equal to p(n) = -0.07n + 147.

Given the following data:

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope, m = (47 - 26)/(1000 - 4000)

Slope, m = -21/3000

Slope, m = -0.07

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + b ≡ p = mn + b

At point (1000, 47), we have:

47 = -0.07(1000) + b

47 = -70 + b

b = 47 + 70

b = $147

In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is p(n) = -0.07n + 147.

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The quadrilateral is a parallelogram because the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Given:- A quadrilateral ABCD in which AB=CD and AD=BC.

To prove:- AB∥CD and AD∥BC

Construction:- Joi A and C.

Proof:-

In △ABC and △CDA,

AB=CD(Given)

AD=BC(Given)

AC=AC(Common)

∴△ABC≅△CDA(By SSS)

Therefore, by CPCTC,

∠ACD=∠BAC

∠DAC=∠ACB

Since alternate angles are equal, thus the lines are parallel.

Therefore,

AB∥CD and AD∥BC

Since both the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Hence proved.

A quadrilateral in geometry may be a four-sided polygon with four sides and four corners (vertices). The Latin words Quadri, a variation of 4, and latus, meaning "side," are the source of the name. In regard to other polygons, it's also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). Since "gon" is an anagram for "angle," it's also known as a quadrilaterals or 4-angle.

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The function g(3)'s expression is 8, which is

The supplied function is defined by a single expression, as per the query. Calculate the value of the other function using the provided expression.

In light of this, g(r) = -5 + 13 = 8

Additionally, the computed value can also be used as the value of the function expression g(3).

Consequently, the value of the function provided is 8.

The relationship between the dependent and independent variables is explained by the function. For the functions, it has a collection of values that may be connected using the domain technique.

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Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation:

Answer:

yes, it’s proportional

Step-by-step explanation:

Answer:

E= 36 D=102 F=42

Step-by-step explanation:

E= 36 because of the vertical angles theorem, d =102 because of vertical angles theorem, and finally we have f = 42 because all these angles form a straight angle/line which adds up to 180. So before we knew that d=102 and e=36 so we can add those up and we get 138. Then we subtract 132 from the measure of a straight angle (180 degrees), to get f. SO 180-132 =f=42

Answer: C

Step-by-step explanation:

Should be C because the other choices seem false

B

Step-by-step explanation:

just did this one and got a 100%