ABC and D are four towns
B is 25km due east of A
C is 25km due north of A
D is 45km due south of A

work out the bearing of B from C ​

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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Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation:

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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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

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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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

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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The solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is a = -1

In this question, we have been given an equation.

[tex]\frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}[/tex]

We need to find the solution of given equation.

[tex]\Rightarrow \frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}\\\\\Rightarrow \frac{2(2a+1)+6a}{12}=\frac{a-1}{3}\\\\\Rightarrow \frac{4a+2+6a}{12}=\frac{a-1}{3}\\\\ \Rightarrow \frac{10a+2}{4}=a-1\\\\\Rightarrow 10a+2=4a-4\\\\\Rightarrow 6a=-6\\\\\Rightarrow a=-1[/tex]

We need to check above solution.

Substitute a = -1 in LHS of given equation.

2a + 1 / 6 + a/2

= [2(-1) + 1 / 6] + [-1/2]

= (-1/6 - 1/2)

= -(4/6)

= -2/3

Substitute a = -1 in RHS of given equation.

a-1/3

= (-1 - 1)/3

= - 2/3

So, LHS = RHS

Therefore, the solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is      a = -1

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Answer:

Step-by-step explanation:

Differences are 3 less then 2 less.

So, the next term would be 4-1 = 3.

Answer: 6,7,8

Step-by-step explanation:

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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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: 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: C

Step-by-step explanation:

Should be C because the other choices seem false

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.

B

Step-by-step explanation:

just did this one and got a 100%

Athlete swam at a constant rate, his speed in m/s is 2.343 m/s

The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.

The formula for speed is as straightforward as dividing a distance by a time. We may define speed as the rate of change of position of an item in any direction by taking the distance traveled and dividing it by the time.

Given,

the distance covered = 50m

total time taken = 21.34s

Speed = distance / Time

speed = 50/ 21.34

speed = 2.343 m/s

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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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By using distributive property 15(3 + 8) 15 11 = 165 both approaches yield the same conclusion.

Distrubutive Property Formula : a(b+c)=a b+a c

The distributive property is also known as the distributive law of multiplication over addition and subtraction. By its very name, the procedure implies that something will be divided or distributed.  According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC. Subtraction also belongs to the scope of this distributive law, which is expressed as A (B - C) = AB - AC. The distribution of operand A among the other two operands is seen from this.

A (B + C) = AB + AC represents the distributive property of multiplication over addition.

15(3+8) = (15.3) + (15.8)

15.11 = 45 + 120

165 = 165

Using the law of BODMAS, we can now attempt to solve the expression. The solution is as follows. We will first add the figures in brackets, and then we will multiply this total by the figure outside of the brackets.

Hence, using distributive property, it follows that 15(3 + 8) x 15 = 165. As a result, both approaches yield the same conclusion.

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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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Answer: quadrant 4 (IV)

Step-by-step explanation:

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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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 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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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