What is Orthocentre?

Answer:

Take away the equal sign , track the graph ( solid or dotted ) , determine the inequality sign by seeing the direction in graph are the few steps to be known while writing an inequality

Step-by-step explanation:

Linear inequalities are two mathematical expressions that are compared using the inequality symbol. The expression could be either just one or both numerical and algebraic.

Few steps which we need to know while writing an inequality

1. Identify the line's equation. Once we take away the equal sign, this gives us the fundamental shape of our inequality.

2. Keep track of whether the line is solid or dotted. Remember that in an inequality, solid lines denote ≤ or ≥ and dotted lines denote < or >.

3. Determine which direction your inequality sign will face by using the shading on the graph.

Take away the equal sign , track the graph ( solid or dotted ) , determine the inequality sign by seeing the direction in graph are the few steps to be known while writing an inequality

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The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

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Answer:

x=6, y=9

Step-by-step explanation:

1.) Since you are substituting, you plug 6 (X) in wherever you have X in the other equation. You will get y = 2*6 -3.
2.) Simplify. By simplification, you will get y=12-3=9. Therefore, x=6, y=9.

Answer:

Volume of a pyramid with a sqaure base is 14.5 ft³.

The perimeter of a form represents the gap around it, the vicinity of a form is the surface or flat area that the shape covers (in 2D) even as the quantity of a form is the distance it occupies in actual lifestyles (in 3D).

The perimeter of the base is 8.7ft

The length of the side of the base is:

8.7÷4=2.175 ft

The area of the base

S=(2.175)² =4.730625 ft²

The volume of the rectangular pyramid =

V= 1/3 × area of its base ×area of heights

V = 1/3 × 4.730625 ×9.2

V≅ 14.3 ft³

Hence, the volume of a square base is 14.3 ft³.

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The center of the circle is (-9, -6).

What is the center of the circle?

A circle's center is the point from which all of the distances to the other points on the circle are equal. The radius of the circle is the measurement at issue.

Here, we have

The equation of a circle is written as:

(x - h)² + (y - k)² = a²

Where (h, k) is the center and a is the radius of the circle.

Where (h, k) is the center and a is the radius of the circle.

(x + 9)² + (y + 6)² = 10² (Given)

From the equation, the center of the circle is (-9, -6)

The radius of the circle is 10.

In general form, the equation can be written as

x² + 18x + 81 + y² + 12y + 36 = 100

x² + y² + 18x + 12y + 17 = 0

Hence, the center of the circle is (-9, -6).

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The slope of the line, using two points (2, 2) and (-2, -3), is calculated as: 5/4.

Using two points on a line, the slope of a line can be calculated by applying the slope formula below:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Pick two points on the line in the graph given to find the slope of the line. The two points that are marked on the line are:

(2, 2) = [tex](x_1, y_1)[/tex]

(-2, -3) = [tex](x_2, y_2)[/tex]

Substitute the values into the slope formula:

Slope (m) = (-3 - 2) / (-2 - 2)

Slope (m) = -5/-4 = 5/4

The slope of the line is: 5/4.

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The domain and the range of this function shown in the graph are;

Domain = -5 ≤ x < 1

Range = -4 ≤ y < 7

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent -1 unit.

By critically observing the graph of this function shown, we can reasonably and logically deduce the following:

Domain = -5 ≤ x < 1 or [-5, 1].

Range = -4 ≤ y < 7 or [-4, 7].

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Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

Answering its the 2 one on the left

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve complex fractions addition the steps are elaborated below

Basically, a complex fraction is a rational expression that has a fraction in its denominator,  numerator or both, or we can simply state that there is at least one least fraction within the overall fraction.To solve complex fractions addition, the steps are first to convert the  denominators  and numerators  into single fractions and then simplify them, the next step is  to add the fractions with  the like denominators, then Simplify it again, then the step is to   Divide the complex fractions by multiplying the numerator by the reciprocal of the denominator.

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Answer: 96

Step-by-step explanation:

Simplify: [tex]5x^4 + 35x^3y -30x^2y^2[/tex]

I used distributive property to mulitply.

ie. [tex]5x^2*x^2[/tex]

The ratio of 240 to 160 is part to part ratio.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The votes for Tigers outnumbered the votes for Lions by a ratio of 240 to 160.

⇒ 240 : 160.

Now,

We know that,

The ratio of part to part will be two different objects.

And, The ratio of part to whole will be the ratio of object to whole object.

Here, The ratio is given as;

⇒ 240 to 160.

⇒ 240 : 160

And, 240 > 160

So, The ratio is part to part ratio.

Thus, The ratio of 240 to 160 is part to part ratio.

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The concurrency point for medians of a triangle is known as centroid.

A median is a line drawn from one of the vertices of a triangle that bisects the side opposite to the vertex. Since there are 3 vertices in a triangle, there are also 3 medians in a triangle. A median divides the triangle into 2 equal halves.

The 3 medians of a triangle intersect at a point inside the triangle. This point is known as the centroid of the triangle. It is the center point of a triangle and divides the medians in the ratio of 2 : 1.

Thus, the name of concurrency for medians of a triangle is centroid.

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The angles m∠ABC = (3·x - 2)° and m∠ABD formed by the ray [tex]\overrightarrow{BA}[/tex], which is an angle bisector of angle m∠CBD = (5·x + 18)°, indicates that m∠ABD is 64°

An angle bisector is a line, segment or ray that divides an angle into two congruent angles.

The information in the question are;

The ray that bisects ∠CBD = [tex]\overrightarrow{BA}[/tex]

The measure of angle, m∠CBD = (5·x + 18)°

The measure of angle, m∠ABC = (3·x - 2)°

Therefore;

(5·x + 18)° = 2 × (3·x - 2)° (definition of angle formed by an angle bisector)

(5·x + 18)° = (6·x - 4)°

(6·x - 5·x)° = (18 + 4)°

x = 22°

m∠CBD = m∠ABD + m∠ABC  (angle addition postulate)

m∠ABD = m∠ABC (angles formed by angle bisector [tex]\overrightarrow{BA}[/tex])

m∠ABC = (3·x - 2)°

Therefore; m∠ABC = (3 × 22 - 2)° = 64°

m∠ABD = m∠ABC = 64°

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The length of the line segment will be 4 units. Then the correct option is A.

The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,

D² = (2 - 2)² + (2 + 2)²

Simplify the equation, then we have

D² = (2 - 2)² + (2 + 2)²

D² = (4)²

D = 4 units

The length of the line segment will be 4 units. Then the correct option is A.

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The missing diagram is attached below.

The equation of the demand function is D(x) = 1400√(25-x²) + 11400

From the question, we have the following parameters that can be used in our computation:

Marginal demand function, D'(x) = -1400x÷√25-x²

Also, we have

D = 17000, when the value of x = 3

To start with, we need to integrate the marginal demand function, D'(x)

So, we have the following representation

D(x) = 1400√(25-x²) + C

Recall that

D = 17000 at x = 3

So, we have

17000 = 1400√(25-3²) + C

Evaluate

17000 = 5600 + C

Solve for C

C = 17000 - 5600

So, we have

C = 11400

Substitute C = 11400 in D(x) = 1400√(25-x²) + C

D(x) = 1400√(25-x²) + 11400

Hence, the function is D(x) = 1400√(25-x²) + 11400

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Y = 1x – 2 is the equation for linear regression.

A linear regression line is represented by the equation Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of a line, b, is equal to the intercept of that line, which is the value of y when x = 0.

Based on the value of another variable, linear regression analysis can be used to predict the value of a variable. You want to be able to predict the dependent variable. You create a forecast about the value of the other variable using the independent variable.

A positive linear relationship exists if the slope of the line is positive, meaning that when one rises, the other rises as well.

Y = -2 -1 x

Y= -2 -1x

Y = 1x - 2

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Answer: Lenny = 12.5%

Leo = 15%

Candice = 10%

Josie = 20%

Step-by-step explanation:

Lenny = (18-16)/16 = 0.125

Leo = (11.5-10)/10 = 0.15

Candice = (13.2-12)/ 12 =0.1

Josie = (24-20)/20 = 0.2

For percentage, multiply each number by 100

Using the compound interest formula, if the account compounds at 4.8% monthly and he withdraws $500 monthly, it will take Steve 33 years, 7 months (403 months) to reduce $100,000 to a balance (future value) of $0.

The future value is the compounded present value, while the present value is the discounted future value.

However, with periodic withdrawals, a present value that compounds at an interest rate into the future can become $0 (future value) after some periods.

The time (period) Steve reduces his inheritance to $0 can be computed using an online finance calculator as follows:

I/Y (Interest per year) = 4.8%

PV (Present Value) = $100,000

PMT (Periodic Payment) = $-500

FV (Future Value) = $0

Results:

N (# of periods) = 403.164

Sum of all periodic payments = $-201,581.83

Total Interest $101,581.83

Thus, after 403 monthly withdrawals, Steve's inheritance will be reduced to a $0 future value.

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The sale price is $13.5 and discount is $1.5.

A price that is lower than the usual price.

Given that, a store sells a shirt at $15, and there is a discount of 10%.

Price reduced after discount = 10% of 15 = $1.5

Selling price = 15 - 1.5 = $13.5

Hence, The sale price is $13.5 and discount is $1.5.

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Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answer: 36 cm= 8, 112 cm=1.25, 183.75 cm= 12.25

The pressure is 38.5 Newton per square meter (N/m²)

Temperature can be defined as the quantity that is used to measure the degree of hotness or coldness of a body in °Kelvin or ° Celsius.

When the pressure of a glass varies directly with the temperature, this means that once there is an increase in temperature there should be an increase in pressure of the medium too.

To calculate the new pressure the gas formula is used;

Where,

P1 = 18.9N/m²

T1 = 90k

V1 = 20m³

T2 = 110k

V2 = 12m³

P2 = X

P1V1/T1 = P2V2/T2

Make P2 the subject of formula;

P2 = P1V1T2/T1V2

P2 = 18.9×20×110/90×12

P2 = 41580/1080

P2 = 38.5 N/m²

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The value of the solution is 6.6%

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation might be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

According to the above question :-

= (3 × 4)C3 × (52 — 3 × 4)C(5 — 3) / 52C5

= 12C3 × 40C2 / 52C5

= 12! × 40! × 47! × 5! / (52! × 9! × 3! × 38! × 2!)

= 12!/9! × 40!/38! × 47!/52! × 5!/(3!2!)

= ((10 × 11 × 12) × (39 × 40) / (48 × 49 × 50 × 51 × 52)) × (5 × 4 / 2)

= 10 × (1 × 11 × 1 × 3 × 40) / (4 × 49 × 5 × 51 × 4)

= (10 × 40 / (4 × 5 × 4)) × (11 × 1 / (49 × 17))

= 5 × 11 / (49 × 17)

= 55 / (17 × (50 — 1))

= 55 / (850 — 17)

= 55 / 833

≈ 6.6%

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From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|

What is graph of a function?

The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.

Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.

Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|

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1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

[tex]a^2+b^2=c^2[/tex]

Making substitutions and applying the math results in:

[tex]15^2 + 36^2= 39^2[/tex]

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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A. Congruence means the same.

B. Angle addition postulate states that two angles side by side sum the measure of the two angles.

C. Linear pair theorem states that linear pair angles add up to 180 degrees.

D. Vertical angles theorem states that vertical angles are congruent.

Congruence in angles simply means the same or equals to.  Two angles are congruent when they are the same.

The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.

The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value

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Answer:

It will cost Marley £7.20 to paint the toy box. This is calculated by taking the total surface area of the toy box (180000 cm²) and dividing it by the area covered by each tin of paint (7500 cm²). This equals 24, so Marley will need 24 tins of paint. Twenty-four tins multiplied by the cost of each tin (£8.99) equals £215.76, which is the total cost of the paint.

Step-by-step explanation:

The most general interpretation of the linear equation 11 - y = 3 is:

"The difference between 11 and a number is equal to 3"

Here we have the following linear equation:

11 - y = 3

Which only depends on the variable y, that we assume it can take any real number as its value.

The linear equation says that if we subtract the number y from eleven, the outcome is 3.

Or we can use other words, like: "The difference between 11 and a number is equal to 3"

Where subtraction and difference are words that reffer to the same operation, which is the subtraction: A - B.

So that is the correct (and more general) interpretation of the linear equation.

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