Martin ha 0. 50 cent Sara ha 10 time a much a Martin Jon ha one tenth a much money a Martin

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

Simon's age is 18.

Step-by-step explanation:

Let Simons age be s and the age of each twin be t.

s + 2t = 48

s - t = 3

Subtract the second equation from the first:

s - s + 2t - (-t) = 45

2t + t = 45

3t = 45

t = 45/3 = 15.

Now we find Simon's age by plugging t = 15 in the second equation:

s - t = 3

s - 15 = 3

s = 3 + 15 = 18.

Answer:

2x - 7 = x + 14

Answer:

(A) 22

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the answer is 24 according to therom 3

The ellipse's equation is [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex] and  [-3, 3] is the ellipse's domain.

The ellipse's equation is (Part A) [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is shown in Part B as [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex]

Part C: [-3, 3] is the ellipse's domain.

The hyperbola's domain lies between [-, -4].

The ellipse and hyperbola's domains do not intersect, hence the system of equations cannot be solved. The origin is the location of the ellipse's centre;8 units make up the vertical main axis. The minor axis equals six units.

Here is a general representation of the ellipse equation:;[tex]$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$[/tex]

a= The semi-major axis, where 8/2 = 4.

The semi-minor axis, b= 6/2 = 3.

Therefore, the ellipse's equation is

[tex]${\frac{-x^2}{3^2}+\frac{y^2}{4^2}=1}$[/tex]

The negative vertex and the domain of the hyperbola are equal.

∴ The hyperbola's domain is [x -4] = [-, -4]

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Answer:

I am positive it is B guys!

Step-by-step explanation:

took da quiz

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into n - 2 triangles.

The sum of a the internal angle measures of a polygon of n sides is given by the equation presented as follows:

S(n) = 180(n - 2).

Hence the sum of the internal angle measures of a triangle, composed of three sides, is given as follows:

180.

Thus the number of triangles on a polygon of n sides is given as follows:

180(n - 2)/180 = n - 2.

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The range of data is calculated by subtracting the lowest value from the highest value.

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Range, which shows statistical dispersion, is the size of the smallest interval in descriptive statistics that encompasses all the data. It is best suited to capturing the dispersion of tiny data sets because it only depends on two observations.

Data is a group of discrete values used to represent information. These discrete values can describe amount, quality, fact, statistics, or other fundamental units of meaning. They can also just be a series of symbols that can be further understood.

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The normal written form of the number given as in the task content is; 0.000101.

It follows from the task content that the normal representation of the given number as in the task content is to be determined.

On this note, since the given number is; 1.01 × 10-⁴, it follows that the given normal representation of the number requires shifting the decimal point 4 spaces to the left so that we have;

= 0.000101.

Ultimately, the required normal representation of the number is; 0.000101.

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The derivation of the surface area of the cuboid,

A  =  2(ab² + bc² + ca²)

The surface area is a total outer layer of the three-dimensional figure. It is defined only for three dimensional shapes.

Suppose,

The length of  sides of the cuboid  are

a,

b,

c

Cuboid has 6 faces, and each face is like a rectangle,

So, If area of each face is calculated,

Then, the sum of area of each face will be equal to surface area of cuboid.

Surface Area =  A₁ + A₂ + A₃ + A₄ + A₅ + A₆

                      =  ab + bc + ca + ab + bc + ca

                      = 2( ab + bc + ca )

Hence, the surface of a cuboid is 2( ab + bc + ca )

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The substance having half-life of 6 seconds and quantity of 50 gm initially will remain 1.5625gm after 30seconds.

What is half-life of a substance?

When we talk about half life, we are talking about the time taken for exactly half of the mass of the radioactive mass in question to have disintegrated.

More like, the amount of time it takes for the radioactive mass to have lost exactly half of its mass.

Now,

Since it is just 5 half lives, we can proceed manually

In the first, we shall have 25g left

in the second, we shall have 12.5g left

In the third, we shall have 6.25g left

In fourth, we shall have have 3.125g left

and finally, in the fifth, we shall have 1.5625g.

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Answer:

To calculate the volume of a triangular pyramid, we can use the formula:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

Since the base of the pyramid is a right-angled triangle, we can use the Pythagorean theorem to find the length of the other two sides, which are the legs of the triangle. The hypotenuse is 6 cm and the angle opposite to the hypotenuse is 30°, so we can use the sine function to find the length of the other leg:

sin(30) = opposite / hypotenuse

opposite = (sin(30) * hypotenuse) = (1/2 * 6) = 3

Now we can use the area formula for a right-angled triangle:

B = (1/2) * base * height = (1/2) * 3 * 6 = 9

To find the height of the pyramid, we can use the fact that all side faces form an angle of 60° with the base. We can use the sine function to find the height of the pyramid:

sin(60) = opposite / hypotenuse

opposite = (sin(60) * hypotenuse) = (√3/2 * 6) = 3√3 cm

Now we can substitute the values of B and h into the volume formula:

V = (1/3) * B * h = (1/3) * 9 * 3√3 = 3√3 cm³

So the exact volume of the triangular pyramid is 3√3 cm³.

Step-by-step explanation:

You can add the same amount to each side, take the same amount away from each side, multiply or divide each side by the same positive amount, and so on when resolving an inequality.

The inequality symbol must be turned around if either side is multiplied or divided by a negative number.

Run the show 1. The imbalance image remains the same whether the same amount is included or subtracted from both sides of an disparity. Run the show 2. The imbalance image remains unaltered when both sides are duplicated or isolated by a positive number.

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Considering triangle HRC, the equations that can be used to solve for the value of w are

The triangle HRC is a right triangle and can be solved by various methods such as: Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

m² = s² + w²

(√125)² = 9² + w²

Applying SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

solving for w using cos, CAH

cos y = w / m

cos y = w / √125

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Answer: -3/2

Step-by-step explanation:

To find the slope of the line perpendicular to the given one, we first need to change the equation to y=mx+b to find the original slope.

[tex]6x-9y=216[/tex]             [subtract both sides by -6x]
[tex]-9y=-6x+216[/tex]        [divide both sides by -9]
[tex]y=\frac{2}{3} x-24[/tex]

Now we know slope is 2/3. The slope of the perpendicular line is the opposite sign and reciprocal of the slope.

Opposite would make it -2/3.

Reciprocal would be -3/2.
So the slope is -3/2.

The property of circumcircle is that the circumcircle always passes through all three vertices of a triangle.

A circumcircle is a circle that traverses a triangle's three vertices. It is also known as a "circumscribed circle." Every triangle's three vertices fall within the circumcircle.

The object's Center is defined as the point at where all of the triangle's perpendicular bisectors intersect. The circumcenter is the name of this Centre. The triangle's triangle might have its  Centre within or outside the circle. The radius of the circumcircle is also known as the triangle's circumradius. In a right triangle, the Centre is located precisely at the midpoint of the hypotenuse, and the hypotenuse is a diameter of the circumcircle.

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The inequality of p is p < 10

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

Total amount = $140

Coupon = $20

Number of people = 12

The inequality of p is then represented as

p < (Total amount - Coupon)/Number of people

Substitute the known values in the above equation, so, we have the following representation

p < (140 -20)/12

Evaluate

p < 10

Hence, the inequality is p < 10

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The scatter plot is the type of graph that is most frequently used to show the relationship between two numerical variables.

The graphs that show the association between two variables in a data set are called scatter plots. It shows data points on a two-dimensional plane or a Cartesian system.

The independent variable or attribute is represented by the X-axis, and the dependent variable is plotted using the Y-axis. To describe these charts, diagrams or graphs are usually employed. An XY graph, scatter chart, or scattergram are other names for a scatter plot. The scatter diagram plots numerical data pairings with one variable on each axis to show the relationship between them.

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Account B has more money than account A. Then account that has the greater principal will be account B.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Dakota procured $10.50 in revenue in Record An and $35.00 in revenue in Record B following 21 months. In the event that the straightforward financing cost is 3% for Record An and 5% for Record B.

Then the account has the greater principal will be given as,

10.50 = [P₁ x 3 x (21/12)] / 100

1050 = 5.25P₁

P₁ = $200

35 = [P₂ x 5 x (21/12)] / 100

3500 = 8.75P₂

P₂ = $400

Account B has more money than account A. Then account that has the greater principal will be account B.

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Correct options are B, E. The point (0, -5) lies on the graph. The function is undefined for x = 1.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The range is made up of all values that the function's output can take.

Given,

the function is y = 2x + 5 / x - 1

⇒ The value of x ≠ -1, as function can become undefined.

⇒ Horizontal Asymptote is 2

the value of y for x = 0,

y = 2x + 5 / x - 1

y = 2(0) + 5 / 0 - 1

y = -5

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After addition, 3/5 + 2/7 can be expressed as a fraction as 31/35.

Math is not complete without fractions. The same fundamental procedures that may be applied to integers also apply to fractions. To solve the given problem, we need to add the given fractions using the common denominator property of fractions.

The Least Common Multiple (LCM) of 5 and 7 is 35. Hence, the common denominator is 35.

So, 3/5 + 2/7 = (3 × 7) / (5 × 7)  + (2 × 5) / (7 × 5)

                    = 21/35 + 10/35

                    = 31/35.

Hence, 3/5 + 2/7 can be represented as 31/35 as a fraction after addition.

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The mirror image of the coordinates is (4, - 20)

The term coordinates is defined are ordered pairs of points that help us locate any point in a 2D plane or 3D space.

Here we have given the coordinates (4, 20).

And we need to find the mirror image of given coordinates.

As per the definition of coordinates the rule of Mirror image of (x , y ) in the x - axis is  written ( x , -y).

Here we have the value of x as 4 and the value of y as 20.

When we apply the rule on the given coordinates then we get the resulting points,

=> (4, 20) = (4, - 20)

Complete Question:

What is the mirror image of the coordinate (4,20)?

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The commutative property applies only to addition and multiplication of real numbers.

What is commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.

so as ask in question that, does the commutative property apply to all real numbers?

The commutative property applies to addition and multiplication of real numbers, meaning that a + b = b + a and a * b = b * a for any real numbers a and b.

However, it does not apply to subtraction or division, meaning that a - b ≠ b - a and a / b ≠ b / a for all real numbers a and b.

Therefore, the commutative property applies only to addition and multiplication of real numbers.

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The value of x for the equation 2x-3=7 is x=5

Given the equation:

2x-3=7

Here, we have to determine the value of  

For that, transposition method should be used.

Now, transpose 3 to the right hand side of the above equation.

2x=7+3

Now, add the terms on the right side of the above equation, we get

2x=10

Now, we have to divide both sides by 2 we get

[tex]\[\frac{{2x}}{2} = \frac{{10}}{2}\][/tex]

Simplify further, we get

x=5

Thus, the required solution is x=5

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Graph behavior as x approaches is referred to be the end behavior of a polynomial function.

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Answer:0 on his road trip playlist

Step-by-step explanation:

Answer:

The equation y=-1.5x+5.5 forms a straight line with a slope of -1.5 and a y-intercept of 5.5. Graphically, the solution can be estimated to be around (3.3, -1.05).

Evaluating the exponential equation:

y = (1/3)*4^x

on x = 3/2 gives y = 8/3.

Here we have the following exponential equation:

y = (1/3)*4^x

And we want to evaluate it on x = 3/2, to do so, we just need to replace the variable on the equation by the given number.

We will get:

y = (1/3)*4^(3/2)

The power part can be rewrite as:

y = (1/3)*√4^3

y = (1/3)*2^3

y = (1/3)*8 = 8/3

That is the value of the equation when evaluated on x = 3/2.

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Answer:

8kg:800g:4000g

1kg=1000g

8kg=8000g

8000:800:4000

80:8:40

10:1:5

Answer:

h

Step-by-step explanation:

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