determine the point on the hyperbola 6x2−5y2=106x2−5y2=10 closest to the point (0, -3).

In the previous problem, we had to find a set of positive integers such that no number in the set has a last decimal digit of 7. Now we have to find a positive integer n that has a last decimal digit of 7 and is not in that set S.  Let's say that S is the set of positive integers that do not have a last decimal digit of 7.

We can show that there is a positive integer n that has a last decimal digit of 7 and is not in S. Suppose that there is no such positive integer. Then every positive integer must either have a last decimal digit of 7 or be in S. But this would mean that the union of S and the set of positive integers with a last decimal digit of 7 would be the set of all positive integers, which is impossible. Therefore, there must be a positive integer n that has a last decimal digit of 7 and is not in S.  To prove that n is not in S, we have to show that n has a last decimal digit of 7. If n were in S, it would not have a last decimal digit of 7. Therefore, n is not in S.  In conclusion, we have found a positive integer n that has a last decimal digit of 7 and is not in S. This proves that S is not the set of all positive integers that do not have a last decimal digit of 7, since there is at least one positive integer that has a last decimal digit of 7 and is not in S.

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The required measure of the tangent CN is 7.

As we know, tangents drawn from a point outside the circle have the same or equal length, following this,
CN = AN
AM = BM
CK = BK

The perimeter of triangle KMN is equal to 34.
CN +AN + AM + BM + CK + BK = 34
CN +CN+ AM + AM+ BK+ BK = 34
2[CN + AM + BK] = 34
CN + 6 + 4 = 17

CN = 17 - 10 = 7

Thus, the required measure of the tangent CN is 7.

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Answer: is it A

Step-by-step explanation:

Odd numbers are whole numbers that cannot be divided exactly into pairs. Odd numbers, when divided by 2, leave a remainder of 1. 1, 3, 5, 7, 9, 11, 13, 15 … are sequential odd numbers. Odd numbers have the digits 1, 3, 5, 7, or 9 in their one's place.

Answer: 6,760,000

Step-by-Step Explanation:

The number of tiles needed to cover the floor is 60 tiles.

Given Information,

The floor area of the passage = 2.4 m²

Length of a side of square tile = 200mm

Length of the side is in mm which needs to be converted in its standard form which is meters.

Therefore, the length of side = 200/1000 m

                                                = 0.2 m

Area of the square tile = 0.2 x 0.2

                                      =  0.04 m²

Let the number of tiles be x.

∴ Number of tiles = \(\frac{Area of passage}{Area of each tile}\)

 x = 2.4/0.04

 x = 60

∴ The number of tiles needed to cover the floor is 60 tiles.

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

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 given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

y = -5

o = 35 degrees

Step-by-step explanation:

If you replace y with -5, the statement  7y = 4y - 15 is correct. You get -35 =  -35. Hope this helped!

Answer:

10 square units.

Step-by-step explanation:

It is given that triangle ABC has its vertices A, B, and C on the sides of a rectangle 4 units by 5 units.

Height of triangle = 4 units

Base of triangle = 5 units

We need to find the area of triangle.

Area of triangle \(=\dfrac{1}{2}\times base \times height\)

Substitute base = 5 and height = 4 in the above formula.

Area of triangle \(=\dfrac{1}{2}\times 5\times 4\)

Area of triangle \(=\dfrac{20}{2}\)

Area of triangle \(=10\)

Therefore, the area of triangle ABC is 10 square units.

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

eight thousandths" or "point zero zero eight" or "point oh oh eight." I don't really see the need to pronounce the zero to the left of the decimal point.

Answer:

Picture Below

Step-by-step explanation:

You can simplify it by dividing it into

y = -1.5x-1

Answer:

0

Step-by-step explanation:

because

k  c  r

10 + (-10)

10 - 10=0

Answer:

☛☚um its 0

Step-by-step explanation:

1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

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Answer:

Notice that 99 players need to be eliminated for there to be declared a winner. Notice also that every match eliminates exactly one person. Therefore, 99 matches are needed to eliminate 99 people and therefore declare a winner. The rest of the information is irrelevant. Therefore, the total number of matches is text divisible by 11.

Answer:

210

Step-by-step explanation:

Using compatible numbers, which is the best estimate of (28.5)(7.1)?

Answer: So let's round 28.5 to 29 because 4 and below let it rest. 7.1 is gonna be 7. Now, 29x7= 203 and since 300 and 36 are way off, we find the answer as 210(B)

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\displaystyle\\\frac{1}{2},\ \ \frac{4}{7},\ \ \frac{9}{14},\ \ \frac{5}{7} ,\ \ ... \\\\\frac{1*7}{2*7} ,\ \ \frac{4*2}{7*2} ,\ \ \frac{9}{14}, \ \ \frac{5*2}{7*2} ,\ \ ...\\\\\frac{7}{14},\ \ \frac{8}{14} , \ \ \frac{9}{14},\ \ \frac{10}{14},\ \ \frac{11}{14},\ \ ...,\ \ \frac{6+n}{14} , \ \ n=1,\ 2,\ 3,\ ...\)

In the recent art project, the teacher purchased 94 pieces of red construction paper and 80 pieces of blue construction paper. To determine the exact ratio of red construction paper to blue construction paper, we divide the number of red construction paper pieces by the number of blue construction paper pieces.

The ratio of red construction paper to blue construction paper can be expressed as:94:80

However, we can simplify this ratio by dividing both numbers by their greatest common divisor. In this case, the greatest common divisor of 94 and 80 is 2.

Dividing 94 by 2 gives us 47, and dividing 80 by 2 gives us 40.

Therefore, the exact simplified ratio of red construction paper to blue construction paper is: 47:40

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Answer:

84.85

Step-by-step explanation:

\( {a}^{2} + {b}^{2} = {c}^{2} \)

\( {60}^{2} + {60}^{2} = {c}^{2} \\ 3600 + 3600 = {c}^{2} \\ 7200 = {c}^{2} \)

now we should find the square root of 7200 to find c

\( \sqrt[]{7200} = 85.85.....\)

Answer:

R = 2524 quarts/s

Step-by-step explanation:

Water flows through a pipe at a rate of 8600 cubic meters per hour.

We know that,

1 m³ = 1056.69 quarts

1 hour = 3600 s

Rate of flow of water = 8600 cubic meters per hour

\(R=8600\ \dfrac{m^3}{h}\\\\=8600\times \dfrac{1056.69\ \text{quarts}}{3600\ s}\\\\=2524.311\ \text{quarts/s}\)

or

R = 2524 quarts/s

So, the rate of flow of water is 2524 quarts/s.

Answer: the answer to this is true

The one step transformations of figure p is reflection over the line x = 1.

option D.

A reflection is a mirror image of a shape or figure. An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So from the given figure P, the figure Q is obtained through the reflection of x axis, particular on x = 1.

When reflecting a figure vertically across x = 1, we essentially flip it over like a mirror reflection across this axis.

By doing so, all points in our original image transform into new points positioned symmetrically to this straight line relative to their previous location - e.g., equidistant but on opposite sides, as shown in figure Q.

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The given expression is equivalent to \(\rm -2(x-7)^2+118\)price is $7 option first is correct.

A quadratic expression is a second-degree algebraic expression represented by the:

\(\rm ax^2+bx+c=0\) ........(1)

Where a, b, and c are the constants and  

We have a quadratic expression:

\(\rm f(x)=-2x^2+28x+20\)

Convert it to perfect square by perfect square trinomial:

\(\rm f(x)=-2(x^2+14x)+20\)  

\(\rm f(x)=-2(x^2+14x+49-49)+20\)   (adding and subtracting by 49)

\(\rm f(x)=-2(x-7)^2+2(49)+20\)

\(\rm f(x)=-2(x-7)^2+118\)

Here \(\rm (x-7)^2\) is the positive term and -2 is the negative term so in order to get the highest weekly profit it should be zero, so

\(\rm -2(x-7)^2=0\)

x = $7

Thus, the given expression is equivalent to \(\rm -2(x-7)^2+118\)  and the price is $7.

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Answer:

First option A.  −2(x − 7)^2 + 118; x = $7

Step-by-step explanation:

Took the test and it's correct, trust me :)

Answer:

Its 70º

Step-by-step explanation:

Question :

justinapace7446

Yesterday

Mathematics

High School

+5 pts

Choco pies are cookies made from chocolate (c), sugar (s), and flour (. Chocolate costs $5 per pound, sugar costs

$3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as

sugar

Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put

$1000 more in a 2-year deposit than in a l-year deposit and invest the rest in a 3-year deposit. How much money

should he invest in each deposit?

Number of Years

Rate

2.0%

5.0%

6.0%

Answer:

1-year: $2200, 2-year: $3200, 3-year: $6600

Step-by-step explanation:

Assume y = Amount invested for 1 year.

y + 1000 = investment amount for 2 years

12000 - (y + y + 1000 ) = amount invested for 3 years

11000 - 2y = amount invested for 3 years

Total interest

Multiplying each by its corresponding rate

(0.02 × y) + (0.05 × (y+1000)) + (0.06 × (11000-2y)) = 600

0.02y + 0.05y + 50 + 660 - 0.12y = 600

-0.05y + 710 = 600

-0.05y = 600 - 710

-0.05y = - 110

y = 2200

Therefore first year = y = $2200

Investment for 2 years =y + 1000 = 2200 + 1000 = $3200

Investment for 3 years = 11000 - 2y = (11000 - (2*2200)) = (11000 - 4400) = $6600

Answer:

Step-by-step explanation:

Io

The particular solution is: Xp(t) = (t/4 - 19/16; -t/2 + 7/8). The correct option is b.

The given system of linear differential equations can be written as:

X'(t) = AX + B(t),

where X'(t) is the derivative of X(t), A is the matrix (2 3; 2 1), and B(t) is the column vector (t; 1). To find the particular solution, we can apply the method of undetermined coefficients. We assume a particular solution of the form Xp(t) = (at + b; ct + d), where a, b, c, and d are constants to be determined.

Taking the derivative of Xp(t), we get Xp'(t) = (a; c). Now, we substitute Xp(t) and Xp'(t) into the given equation:

(a; c) = (2 3; 2 1) (at + b; ct + d) + (t; 1).

Multiplying the matrix and vector, we get:

(a; c) = (2(at + b) + 3(ct + d); 2(at + b) + 1(ct + d)) + (t; 1).

Equating the components, we get the following system of linear equations:

a = 2a + 2b + 3c + 3d + 1,
c = 2a + 2b + c + d + 0.

Solving this system, we find a = t/4 - 19/16, b = -t/2 + 7/8. Therefore, the particular solution Xp(t) is:

Xp(t) = (t/4 - 19/16; -t/2 + 7/8),

which corresponds to option b.

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Answer:

4 units

Step-by-step explanation:

The complete question is

BD and AC are chords that intersect at point Y. A circle is shown. Chords B D and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY?

The picture of the question in the attached figure

we know that

The Intersecting Chord Theorem states that:  When two chords intersect each other inside a circle,the products of their segments are equal.

do

In this problem

substitute the given values

solve for x

therefore

The length of segment AY is 4 units

Answer:

D. Closed circle on 8, shading to the right.