Given that (0,1) is the center of a circle and (-4,4) is a point on the circle, find theradius of the circle:

Answer:

x=161/10 =16.100

Step-by-step explanation:

Combine Like Terms

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Answer:

hope it helps..

Step-by-step explanation:

Simplifying

2.1(0.2x + -1.4) = 1.3(0.4x + -3.5)

Reorder the terms:

2.1(-1.4 + 0.2x) = 1.3(0.4x + -3.5)

(-1.4 * 2.1 + 0.2x * 2.1) = 1.3(0.4x + -3.5)

(-2.94 + 0.42x) = 1.3(0.4x + -3.5)

Reorder the terms:

-2.94 + 0.42x = 1.3(-3.5 + 0.4x)

-2.94 + 0.42x = (-3.5 * 1.3 + 0.4x * 1.3)

-2.94 + 0.42x = (-4.55 + 0.52x)

Solving

-2.94 + 0.42x = -4.55 + 0.52x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.52x' to each side of the equation.

-2.94 + 0.42x + -0.52x = -4.55 + 0.52x + -0.52x

Combine like terms: 0.42x + -0.52x = -0.1x

-2.94 + -0.1x = -4.55 + 0.52x + -0.52x

Combine like terms: 0.52x + -0.52x = 0.00

-2.94 + -0.1x = -4.55 + 0.00

-2.94 + -0.1x = -4.55

Add '2.94' to each side of the equation.

-2.94 + 2.94 + -0.1x = -4.55 + 2.94

Combine like terms: -2.94 + 2.94 = 0.00

0.00 + -0.1x = -4.55 + 2.94

-0.1x = -4.55 + 2.94

Combine like terms: -4.55 + 2.94 = -1.61

-0.1x = -1.61

Divide each side by '-0.1'.

x = 16.1

Simplifying

x = 16.1

Answer:

Okay the, 3 of Y by every unit of X. Simple.

Step-by-step explanation:

Answer:  D.  \(g(x) = (x-b)^2\)

Explanation:

If we want to shift the curve some distance b to the right, then we'll need to replace x with x-b. What this effectively does is shift the xy axis itself b units to the left while the curve is fixed in place. This gives the illusion of the curve moving b units to the right.

Put another way: the old input x is updated to the new input x-b which is smaller by b units. This helps explain why the xy axis is shifted to the left this amount.

So that's how we go from \(f(x) = x^2\) to \(g(x) = (x-b)^2\). You can think of it as \(g(x) = f(x-b) = (x-b)^2\)

The amount Chris started with in his savings is $44. option C

1/2x + 10 = 32

1/2x = 32 - 10

1/2x = 22

x = 22 ÷ 1/2

x = 22 × 2/1

x = $44

Therefore, the amount Chris started with in his savings is $44. option C

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Answer:

Step-by-step explanation:

Answer:

Important note: "of" means to multiply!
22% of 150 is 33

Step-by-step explanation:

\(Y = P\% \times X\\Y = 22\% \times 150\\P = 22\%\div100 = 0.22\\Y = 0.22 \times 150\\Y = 33\)

Hope this helps!

Answer:

The answer is B- X= 31/25

Answer:

x = 31/25

Step-by-step explanation:

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

Answer: Congruent by AAS

Step-by-step explanation:

FG and EH are congruent because they are given.

EH is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

FG is perpendicular to EG because of the definition of perpendicular lines. Lines are perpendicular if they create right angles when they intersect.

Angle G is congruent to Angle E because they are both right angles, and right angles are congruent.

Angle EIH and Angle FIG are congruent because of the vertical angles theorem.

Triangle EHI and Triangle GFI are congruent by the Angle-Angle-Side Theorem, or AAS.

Part b) the trick consists of noting that the difference between the investment of any two consecutive years is the same: $1,750. (In general, this kind of table is called an arithmetic sequence). How much does the investment grow every year? Exactly $1,750.

Part c) The idea here is to find the "first term", which is the investment when everything began (first year): $20,000. (this could seem trivial, but it will be important).

Part d) Remember I told you that this kind of table is called arithmetic sequence (a_n). This means that they have the general (generic) form:

By part b and c, our initial value is $20,000 and our growing rate is $1,750. So we get

Comment: You can think that those dates (initial term, and growing rate) are all you need to understand this kind of table.

Part e) This type of question reveals the "power" of the formula we obtained above (now we can make projections regarding the future; namely, beyond the table).

Now, there is a detail to keep in mind; the wording "another 10 years". It means we must find the value of the sequence in 15, not 10.

Part f) Here there is no trick; we just need to calculate the 20th term of the sequence:

The maximum possible number of points where two polygons can intersect is \($n = 4$\). This is achieved when the two polygons are tangent to each other at four points.

There are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:

This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.

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The radius of a circle with circumference of 4π/3 is equal to 2/3

The circumference of a circle is the same as the total length of the circle boundary. It can also be called the perimeter of a circle.

The circle in question have its circumference as

4π/3.

circumference of circle = 2πr

4π/3 = 2πr

divide through by π

4/3 = 2r

r = 4/(3×2) {by cross multiplication}

r = 4/6

radius = 2/3.

Therefore, the radius of a circle with circumference of 4π/3 is equal to 2/3

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The radius of a circle with a circumference of 4π/3 is equal to 2/3 units.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have the following;

Circumference of circle, C = 2πr

4π/3 = 2πr

4π = 6πr

Radius, r = 4/6 = 2/3 units.

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Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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Answer:

hard work lol

Step-by-step explanation:Lol

Answer:

It’s either D as the answer or A

Step-by-step explanation:

Answer: -2, 1, all real numbers, all real numbers

Step-by-step explanation:

g o f(n) is basically g(f(n))

Using the question as an example we can get that f(0) = 1 so

g(f(0)) = g(1) = -2

f(1) = 0 so g(f(1)) = g(0) = 1

The domain of f(x) is all real numbers and the range of g(x) is all real numbers

Given the statement:

If a system of equations has one​ solution, the system is ___ and the equations are ___

The system has one point of solution, the system will be called consistent

Because it will intersect at one point so, it will be independent

So, the answer will be: consistent, independent

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

What is the Linear equation?

An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

y = mx + c

where m denotes the slope.

The y-intercept is represented by the constant c. (Where x is zero)

In our instance, y-intercept equals 60.

The line's equation will therefore be:

y = mx + 60

y = mx + 60

There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.

90 = 4*m + 60

4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is

y = 7.5x + 60.

If Adam's study for 6 hours then his score would be

y = 7.5x + 60.

y = 7.5(6) + 60

y = 105

Hence,

3) The equation of the linear model would be y = 7.5x+60.

4) If Adam studies for 6 hours then his score would be 88.

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Answer:

7/10

Step-by-step explanation:

70% is equal to 0.7 in other words 7/10 is the most simple form.

9514 1404 393

Answer:

  4%

Step-by-step explanation:

We assume the interest earned is simple interest, because that make the numbers come out "nice."

The account balance is given by ...

  A = P(1 +rt) . . . . principal P earns simple interest at annual rate r for t years

  1080 = 1000(1 +r·2) . . . . fill in the given values

  1.08 = 1 +2r . . . . . . . . . . divide by 1000

  0.08 = 2r . . . . . . . . . . . subtract 1

  0.04 = r = 4% . . . . . . . divide by 2

The annual interest rate is 4%.

_____

Additional comment

If interest is compounded annually, the annual rate is about 3.92%. If it is compounded continuously, the rate is about 3.85%.

Answer:

im sorry im not entirely sure but if you use socratic it might help!

h = 0.5d + 35, shows the total amount of hours h, Julia exercised last year if she exercised d days the rest of the year.

Given,

Last year, Julia had already exercised 35 hours prior to May 1.

After that she exercised on some days during the rest of the year.

So,

Number of hours Julia has already exercised before may 1 = 35 hours.

For rest of the years Julia exercised on some days = 0.5 hours .

Hence,

The equation that satisfies the given condition of Julia for rest of the years will be,

h = 0.5d + 35

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Answer:

B

Step-by-step explanation:

y= -24/x²+8

y-int ( 0,-3

To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

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Answer:

It's an Irregular Quadrilateral

Step-by-step explanation:

It has 4 sides and the length of the sides of the Quadrilateral is not equal. This makes it irregular.

Answer:

Irregular Polygons

Step-by-step explanation:

Let's us first learn the definition of a polygon. A polygon is a closed shape figure that has a minimum of three sides and three vertices. The term ‘poly’ means ‘many’ and ‘gon’ means ‘angle’. Thus, polygons have many angles. The perimeter and area of polygon depend upon its types.

The classification of polygons is described based on the numbers of sides and vertices. For example, a polygon as four sides and four angles, then it is quadrilateral. The polygons up to 12 sides are the important ones. We are going to learn here polygon’s types based on the number of sides of the closed figure along with examples and diagrams.

Polygons are classified into various types based on the number of sides and measures of the angles. They are:

In a regular polygon, all the sides of the polygon are equal, and all the interior angles are the same. For example, a regular hexagon has six equal sides, and all its interior angles measure to 120 degrees.

A polygon with an irregular shape. It means the sides and angles of the polygon are not equal.

In a convex polygon, the measure of the interior angle is less than 180 degrees. It is exactly opposite to the concave polygon. The vertices of a convex polygon are always outwards

In a concave polygon, at least one angle measures more than 180 degrees. The vertices of a concave polygon are inwards as well as outwards.

Trigons are polygons who have three sides. They are nothing but triangles. These trigons or triangles are further classified into different categories, such as:

Quadrilateral polygon is also called a four-sided polygon or a quadrangle. The different types of the quadrilateral polygon are square, rectangle, rhombus and parallelogram.

The five-sided polygon is called pentagon polygon. When all the five sides of the polygon are equal in length, then it is called regular pentagon otherwise irregular pentagon.

Another type of polygon is the hexagon which has 6 sides and 6 vertices. A regular hexagon will have equal 6 sides and all its interior and exterior angles also measure equals.

The polygons whose all the sides are equal are called equilateral polygons, for example, an equilateral triangle, a square, etc.

The polygons whose all the interior angles are equal such as a rectangle are called equiangular polygons.

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

Answer:

12.73 Degrees

Step-by-step explanation:

I'm going to assume some things. The height of the truck is not changing, i.e. the distance and length of the ramp are but the height stays the same.

We draw our right triangle, see photo*

We really only care about finding out what side a is so

\(c = \frac{a}{sin(A)} \\12 = \frac{a}{sin(36)} \\12sin(36) = a\\a = 7.05342302750\\sin(x) = (\frac{opp}{hyp} )\\sin(x) = (\frac{7.05342302750}{12} )\\= 35.9999 \:degrees\)

So, since I stated that height did not change, the same process just using 32 for the hypotenuse.

\(sin(x) = (\frac{opp}{hyp} )\\sin(x) = (\frac{7.05342302750}{32} )\\= 12.73367164 \:degrees\)

Answer:

50%

Step-by-step explanation:

2,000 is 2 x more than 1,000. Or, 1,000 is half of 2,000 and half of 100%=50%.

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer: $0.05

Step-by-step explanation:

Mean of a given set of numbers simply means that one should find the average of the numbers. Therefore, the mean change of the stock prices will be:

= ($1.25 + -$0.75 + $1.25 + -$0.75 + -$0.75) / 5

= $0.25 / 5

= $0.05

Therefore, the mean change of the stock prices is $0.05.