2x + 3y= 7
-2x+4y=14

a) An equation for the circle with centre (0, 0) and point B(5,-12) at circumference is (x)² + (y)² = 13².

b) The point (8,10) lies outside of the circle.

What is equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

The points that lie on the circumference is B(5,-12).

The origin is O(0,0).

The distance from O to B is the radius.

OP² = (x2-x1)² + (y2-y1)²

OP² = (5-0)² + (-12-0)²

OP² = (5)² + (-12)²

OP² = 25 + 144

OP = √169

OP = 13

The radius is 13 units.

The standard equation of a circle is given by -

(x-h)² + (y-k)² = r²

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

So, after substituting all the values the equation will be -

(x)² + (y)² = 13²

To find if (8,10) lies inside the circle or not, substitute x = 8 and y = 10

(8)² + (10)² = 13²

8 + 10 = 13

18 ≠ 13

Therefore, the (8,10) does not lie inside the circle.

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The animal shelter has a number of 35 dogs.

According to the statement, the animal shelter has a total of 65 abandoned cats and dogs and cats to dogs ratio is 6 : 7. We are asked to find the number of abandoned dogs in the shelter:

D = [d / (c + d)] · N

Where:

If we know that d = 7, c = 6 and N = 65, then the number of abandoned dogs is:

D = (7 / 13) · 65

D = 35

There are 35 dogs in the animal shelter.

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Answer:

r90° (P) = (4, -5).

Step-by-step explanation:

The point P is (5, 4). To find the image of P after rotating it 90° counterclockwise, we use the transformation matrix for a 90° counterclockwise rotation:

[[0, -1], [1, 0]]

The coordinates of the image of P after rotating 90° counterclockwise are given by:

[[0, -1], [1, 0]] * [5, 4] = [4, -5]

So, r90° (P) = (4, -5).

The smallest value of 'n' that can be obtained by adding three consecutive numbers is 48.

By using Monte-Carlo simulations,

A large class of computational techniques known as "Monte Carlo procedures" or "Monte Carlo experiments" rely on repeated random sampling to get numerical results. The core idea is to leverage randomness to find solutions to issues that, in theory, may be deterministic.

16    22    10     7    28    13     1    19    25     4

7    10    25    13     4    28    16     1    19    22

16    10    22     7    13    28     1    19    25    4

(remember that the numbers are arranged in a circle, rather than the straight line shown here)

The underline number represent the smallest value for n that can be obtained by the summation of three consecutive numbers.

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The total savings on the men's clothing is not 60% to 65%

To determine if the total savings is 60% to 65%, we need to calculate the original price of the shirts given the final cost and the percentage of savings.

We start by calculating the original price of the shirts before the extra 50% off clearance:

Original = $11.06 / (1 - 0.60) = $27.65 i.e. 60% saved

$16.88 / (1 - 0.65) = $48.23 i.e. 65% saved

Now we need to find the price of the shirts before the extra 50% off clearance

$27.65 / (1-0.5) = $55.30

$48.23 / (1-0.5) = $96.46

The calculated prices of the shirts before the extra 50% off clearance are not between $29.50 to $45.00

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We choose three local banks after comparing the interest rates offered by these 3 banks.

The first gives out things to consider before opening an account. Comparing the interest rates offered by these 3 institutions is the first step. The second thing is to compare the customer service ratings of these three banks.

Checking the historical growth of all banks is the third point. When picking a bank, make sure that the institution offers a competitive effective rate of interest, prioritizes its clients, and responds quickly to their complaints.

Employees of banks should behave well toward customers. The other thing to keep in mind is that the bank should have continued to grow the prior year.

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Answer: Either Likely or  This value is not possible to represent probability of a chance event.

Step-by-step explanation:

So, if P = Chocolate Chip cookies, it is 68%, its more then a 50/50 percentage so most kids would **probably** choose Chocolate Chip cookies so it could be likely.

Hope this helps!

Answer:

0.42

Step-by-step explanation:

- 2.4 = - 12/5

The opposite of the reciprocal of – 2.4 is

+ 5/12 ≈ 0.42

Answer: 5/12

Step-by-step explanation:

if -2.4 in fractions is 12/5 the opposite reciprocal is the fraction and sign fliped which is 5/12

Assume that y = mx+c1 and y = mx+c2 are two parallel lines. D = |(c2-c1)/(1 + m2)| calculates the distance between the lines.

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The size of each exterior angle is given by β = 180° - θ.

To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first.

If the number of sides is n, then the sum of the interior angles is:

S = 180 (n-2)

This formula derives from the fact that if you draw diagonals from one vertex in the polygon, the number of triangles formed will be 2 less than the number of sides. Each triangle has 180°.

This form of the formula derives from drawing triangles in the polygon by drawing lines from a central point to each vertex. In this way the number of triangles is the same as the number of sides, but the angles at the centre are not required, so 360° is subtracted.

Once you have the sum of all the interior angles you divide by the number of sides to find the size of each interior angle.

Each interior angle of a regular polygon with n sides:

θ = 180°(n-2)/n

Each exterior angle of a regular polygon with n sides:

β = 180° - θ

Thus, the size of each exterior angle is given by β = 180° - θ.

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Answer: The term in this expression is D. -3x

A term in an expression is a single mathematical entity, such as a variable or a constant. In the expression -3x - 7(x + 4), -3x is a term on its own, it is the product of -3 and x, and it doesn't have any other mathematical operation.

-7 is a constant, but it is not a term on its own because it has an operation with another term (x + 4)

(x + 4) is a term as well, it is the sum of x and 4.

So the term in this expression is -3x

Step-by-step explanation:

the pairs of ratios that form a true proportion: a and b

An equation proving the equality of two ratios is a genuine proportion. Knowing one ratio in a percentage can be used to determine values in the other equal ratio.

Where x is the number of successes and n is the sample size, p′ = x / n. The variable p′ represents the proportion of the sample and acts as a point estimate for the proportion of the genuine population.

Now, given that -

a. 3:6 and 5:10

= 1:2 and 1:2

Thus, it is a true proportion.

b. 4/12 and 6/18

= 4:12 and 6:18

= 1:3 and 1:3

Thus, it is a true proportion.

c. 20/5 and 10/3

= 20:5 and 10:3

= 4:1 and 10:3

Thus, it is not a true proportion.

d. 24:36 and 8:9

= 2:3 and 8:9

Thus, it is not a true proportion.

So, correct pairs of ratios that form a true proportion is: a and b.

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Answer:

  12 + s

Step-by-step explanation:

You want the total of 6th and 7th graders on the soccer team if there are 12 6th graders and 's' 7th graders on the team.

The sum of 12 and s is written as ...

  12 + s

The inverse equations are F(x)⁻¹ = ( x - 2 ) / 5and F(x)⁻¹ = 5x + 2.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x and y are interchanged, and then the value of y is given an inverse function.

Given that the two equations are y= 1/2X+10 and y= -8X+3. The value of inverse functions will be calculated by replacing the x and y values and solving for y,

f(x)=5x+2

x = 5y + 2

y = ( x - 2 ) / 5

The inverse of the second equation is calculated as,

g(x)=(x-2)/5

x = ( y - 2 ) / 5

y = 5x + 2

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The factors of the given expression 4x² + 28x + 49 is (2x + 7)(2x + 7).

Given polynomial is 4x2 + 28x + 49

Factoring polynomials is done in many ways. The four significant methods of factoring polynomials are as follows.

Method of Common Factors

Grouping Method

Factoring by splitting terms

Factoring Using Algebraic Identities

Let us operate the algebraic identity to factor this.

⇒ 4x² + 28x + 7²

⇒ 4x² + 2(14)(x) + 7²

⇒ (2x)² + 2(2x)(7) + 7²

This is similar to a² + 2ab + b² = (a + b)²

⇒ (2x + 7)²

⇒ (2x + 7)(2x + 7)

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The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expressions are given below.

1/10 of 3 and 1/10 of 0.3

Then the multiplication of the expression is given by putting a cross sign between them. Then we have

⇒ [(1/10) x 3] x [(1/10) x 0.3]

⇒ 0.3 x 0.03

⇒ 0.009

The multiplication of the expression 1/10 of 3 and 1/10 of 0.3 will be 0.009.

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Answer:

She would've traveled 4cm on the map

Step-by-step explanation:

If 1cm=18km in the map and Rashmi drove 72km, we just have to divide 72 by 18 to get the distance she traveled on the map.

72÷18=4

The ratio of the area of circle A to the area of circle B expressed in the common fraction is 4/9.

An arc is a portion of the circumference of a circle. The length of an arc is proportional to the radius of the circle and the measure of the angle formed by the arc and the center of the circle. The formula for the length of an arc is:

Arc Length = (Angle Measure / 360) x (Circumference)

In this problem, we are given that the arc of 55 degrees on circle A has the same length as the arc of 40 degrees on circle B. So we can set up the following equation:

(55/360) x (Circumference of A) = (40/360) x (Circumference of B)

We can simplify this equation by canceling out the common factor of 360:

(5/12) x (Circumference of A) = (2/9) x (Circumference of B)

Now we can use the fact that the circumference of a circle is equal to 2π times the radius:

(5/12) x (2π x radius of A) = (2/9) x (2π x radius of B)

We can cross-multiply and divide by 2π to find the ratio of the radii of the two circles:

(5/12) x (radius of A) = (2/9) x (radius of B)

radius of A / radius of B = (2/9) / (5/12) = 12/18 = 2/3

Since the ratio of the areas of two circles is equal to the square of the ratio of their radii, the ratio of the area of circle A to the area of circle B is:

Area of A / Area of B = (radius of A / radius of B)^2 = (2/3)^2 = 4/9

So the ratio of the area of circle A to the area of circle B is 4/9.

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The angle be 5x - 12 and 3x - 8 then the value of x  = 25.

The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner."

A protractor is a precision tool for measuring angles. Angles are measured in degrees, therefore the term "degree measure." Because one full revolution is equivalent to 360 degrees, it is divided into 360 segments.

Let the two angle be 5x - 12 and 3x - 8

5x + 3x - 12 - 8 = 180

Add similar elements: 5x + 3x = 8x

8x - 12 - 8 = 180

Subtract the numbers: -12 - 8 = -20

8x - 20 = 180

Move 20 to the right side

8x = 200

Divide both sides by 8

= 8x / 8 = 200 / 8

x  = 25

Therefore, the value of x  = 25.

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The scale factor of the dilation transformation of the pre-image triangle ΔDEF to the image ΔD'E'F', with the origin as the center of dilation is 3.

A dilation transformation is one in which the lengths of the sides of the pre-image are scaled up by a common factor to get the lengths of the sides of the image.

The coordinates of the vertices of the triangle ΔDEF are;

D(1, 5), E(1, 2), F(3, 2)

The length of the sides of triangle ΔDEF, making use of the difference between the non equal coordinate points, are;

DE = 5 - 2 = 3

EF = 3 - 1 = 2

The length of the side DF can be found using the formula for the distance between two points on the coordinate plane (a form of the Pythagorean Theorem), which is presented as follows;

DF = √((3 - 1)² + (2 - 5)²) = √(2² + (-3)²) = √(13)

The coordinates of the vertices of triangle ΔD'E'F' are; D'(3, 15), E'(3, 6), F'(9, 6)

Therefore; D'E' = 15 - 6 = 9

E'F' = 9 - 3 = 6

D'F' = √((9 - 3)² + (6 - 15)²) = √(6² + (-9)²) = √(9 × 13) = 3·√(13)

The scale factor, s.f. = The ratio of the corresponding sides of the triangles which is found as follows;

D'E'/DE = 9/3 = 3

E'F'/EF = 6/2 = 3

D'F'/DF = 3·√(13)/√(13) = 3

s.f. = D'E'/DE = E'F'/EF = D'F'/DF = 3

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The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the functions is given below.

Equation  1: f(x) = 2x³ + 24x + 2

Equation 2: f(x) = 4ˣ

The graph of the functions is given below.

From the graph, the intersection of the graph is at (-0.044, 0.9407).

The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

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We can rewrite g(x) = 6(2)ˣ⁺³ and y = 100(5)ˣ⁻² in the form y = a(b)ˣ as g(x) = 48(2)ˣ and y = 4(5)ˣ respectively

An exponential function is a mathematical function in which the input, or the variable, is raised to a power.

The most common form of an exponential function is f(x) = eˣ, where e is the base of the natural logarithm and x is the exponent.

In order rewrite g(x) = 6(2)ˣ⁺³ and y = 100(5)ˣ⁻² in the form y = a(b)ˣ, you need to apply your knowledge of indices.

g(x) = 6(2)ˣ⁺³ can be rewritten as:

g(x) = 6(2)ˣ⁺³

g(x) = 6(2)ˣ × 2³

g(x) = 6(2)ˣ × 8

g(x) = 48(2)ˣ

Also,  y = 100(5)ˣ⁻² can be rewritten as:

y = 100(5)ˣ⁻²

y = 100(5)ˣ × 5⁻²

y = 100(5)ˣ × (1/5²)

y = 100(5)ˣ × 1/25

y = 4(5)ˣ

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Equation represents the value of the collection after 5 years is 350(1.03)³ .

An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

Future value with appreciation can be calculated using the following general formula:

V = P(1+r)ⁿ  where

V = Future value

P = Present value

r = appreciation rate

n = number of years

Given P = $350 , r= 2.8%=0.03 , n = 3

Now we substitute the given values in the equation to get:

V=350(1+0.03)³

or, V= 350(1.03)³

or, V= 381.5 dollars approximately .

Hence the required equation is V= 350(1.03)³ .

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The exact value of the trigonometric cosine function cos 30° is √3/2.

In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. Using the unit circle, we can find the exact values of the trigonometric functions for angles in degrees or radians. One of the most important concepts in trigonometry is the unit circle.

A special triangle is a 30-60-90 triangle, where one angle is 30 degrees, another angle is 60 degrees, and the last angle is 90 degrees. The ratio of the adjacent side to the hypotenuse in this triangle is √3/2. Therefore, the exact value of cos 30° is √3/2. This means that the cosine of 30 degrees is the ratio of the adjacent side (x) to the hypotenuse (1) in the unit circle where x = √3/2.

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Answer: write it out then ill answer

Step-by-step explanation:you could at least write it so i know what im answering cuz that shows nothing

The required evaluation of the given fraction 4/5 of 3/4 is 3/5.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by the addition, subtract, dividing, and multiplying built-in functions.

We have to determine the evaluation of 4/5 of 3/4

As per the question, we have

⇒ 4/5 of 3/4

This can be also rewritten as:

⇒ (4/5) × (3/4)

Apply the multiplication operation,

⇒ 12/20

Reduce the above fraction into the simplest form,

⇒ 3/5

Thus, the required evaluation is 3/5.

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The probability that the horse will not win the race is 0.5. The result is obtained by subtracting the probability of winning from 1.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

While, the probability for the opposite event is

P(not A) = 1 - P(A)

If the probability that a horse will win the race is 2/4, find the probability that the horse won't win the race!

The probability that the horse will win the race is

P = 2/4 = 0.5

The probability that the horse will lose is

P = 1 - P(A) = 1 - 0.5 = 0.5

Hence, the horse will lose with the probability of 0.5.

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Answer:

14.5

Step-by-step explanation:

The area of the rectangle is [tex](5)(6)=30[/tex].

The areas of the three right triangles in the rectangle but not in [tex]\triangle JKL[/tex] are 2.5, 10, and 3.

[tex]\implies [JKL]=30-2.5-10-3=14.5[/tex]