Type the correct answer in each box. A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is units. The point (-15, ) lies on this circle.

Answer:

Flat 12,885.68

Compound 13,876.90

Step-by-step explanation:

Flat rate (6% of only the amount you invested originally per year (based on investment) -

(8706.54*.06)*8+8706.54=12885.68 (rounded)

Compound interest (6% interest on total money earned per year(based on amount invested previous year).)

(((((((8706.54*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)=13,876.90

The future value of the investment is $13876.90 and the interest earned is $5170.36.

We can use the following formulas:

Future value = [tex]Principal * (1 + Interest rate)^N^u^m^b^e^r ^o^f^ y^e^a^r^s[/tex]

Interest earned = Future value - Principal

Substituting the known values into the formulas, we get:

Future value =[tex]$8706.54 * (1 + 0.06)^8 = $13876.90[/tex]

Interest earned = $13876.90 - $8706.54 = $5170.36

Therefore, the future value of the investment is $13876.90 and the interest earned is $5170.36.

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Answer:

x = 3/5, -3/5

Step-by-step explanation:

Answer:

x = ± [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Given

25x² + 1 = 10 ← subtract 10 from both sides

25x² - 9 = 0 ← in standard form

note that 25x² - 9 is a difference of squares and factors as

(5x - 3)(5x + 3) = 0

Equate each factor to zero and solve for x

5x - 3 = 0 ⇒ 5x = 3 ⇒ x = [tex]\frac{3}{5}[/tex]

5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - [tex]\frac{3}{5}[/tex]

Answer:

35.25

Step-by-step explanation:

There are 4 data:

262, 313, 393, and 323

The formula for MAD (mean absolute deviation) = [tex]\frac{SUM(|x_{i}-XBar|)}{n}[/tex]

Where x_i are the each individual values (stated)

XBar is the average value

n is the number of data

First, let's find XBar, or the average. We add up all the 4 numbers and divide by 4 to get:

XBar = (262+313+393+323)/4=322.75

Now, let's calculate MAD:

MAD = [tex]\frac{|262-322.75|+|313-322.75|+|393-322.75|+|323-322.75|}{4}\\=35.25[/tex]

MAD = 35.25

Answer:

31.5

Step-by-step explanation:

Final answer:

The equation [x-1]=[x] suggests two possible values for x, which are 0 and 0.5. These are specific values rather than a continuous range or a broad set like all integers or all real numbers.

Explanation:

The equation [x-1]=[x] compares the absolute values of two expressions: x-1 and x. Absolute values are always non-negative, leading to two possible scenarios. First, if x is non-negative, x will be equal to x-1, which only happens when x is zero. Second, if x is negative, then -x is equal to x-1, which is true when x = 0.5. No other values of x will satisfy the equation, as the increment on one side of the equation will not match the decrement on the other. Therefore, the correct set of numbers that describes the possible values of x is neither integers, all real numbers, only negatives, nor only fractions. Instead, it includes specific values, which are 0 and 0.5.

Final answer:

The equation [x-1]=[x] is not satisfied by any real value of x since attempts to solve it lead to contradictions. Thus, there are no possible values of x for this equation; none of the provided choices are correct.

Explanation:

To determine which set of numbers best describes the possible values of x in the equation [x-1]=[x], where [] denotes the absolute value, we must consider when the absolute values of two expressions would be equal.

If x is a non-negative number, then [x] = x and [x-1] = x-1. Thus, the equation implies x = x - 1, which is impossible for any real number.

If x is negative, then [x] = -x and [x-1] = 1-x. The equation becomes -x = 1 - x, which simplifies to 0 = 1, which is also impossible.

Therefore, there are no values of x that can satisfy this equation since we always end up with a contradiction when we attempt to solve it. This means the correct answer is that there are no possible values of x that will satisfy the given equation, which isn't one of the provided choices.

Answer:

Step-by-step explanation:

By showing that 0.20 is greater than 0.18 by doing 0.20-0.18 which gives a positive 0.02, thich means that its greater.

0.2 is greater than 0.18.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have to Compare 0.2 and 0.18.

First we have two digits in 0.18 after decimal.

Then, make 0.2 with two digits after decimal as 0.20.

Now, compare the after decimal value

20 > 18

So, 0.2 is greater than 0.18.

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Answer:

The lines intersected by a transversal must be parallel.

y=9.64

—————

cos21=9/y

Cross Multiply

ycos21=9

Divide both sides by cos21 to isolate y

9/cos21 = 9.640304943

y=9.64

Answer:

Step-by-step explanation:

(2+2i)(5+3i)

(2)5+(2)3i=10+6i

(2i)5+(2i)3i=10i+6i^2

10+6i+10i+6i^2

6i^2+6i+10i+10

6i^2+16i+10

To find the product of (2+2i)(5+3i), apply the distributive property to multiply each part. The result is 10 (real*real), 6i (real*imaginary), 10i (imaginary*real), and -6 (imaginary*imaginary, since i^2=-1), which are summed to give 4 + 16i.

The product of two complex numbers, such as (2+2i)(5+3i), can be found by using the distributive property (also known as foil - first, outer, inner, laters). In this case:

Sum these results together: 10 + 6i + 10i - 6. Thus, (2+2i)(5+3i)= 4 + 16i.

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Answer:

x = 127°

Step-by-step explanation:

We are given a polygon which has six sides but all the sides and angles are not equal so it is an irregular hexagon.

We know that the sum of the measures of the interior angles of a polygon with n sides is given by: [tex](n-2)\times180[/tex].

[tex](6-2)\times180 = 112+133+128+100+120+x[/tex]

[tex] 7 2 0 = 5 9 3 + x [/tex]

[tex] x = 7 2 0 - 5 9 3 [/tex]

x = 127°

Answer:

factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

Step-by-step explanation:

We need to find factors of [tex]x^{12}y^{18}+1 can\,\,be\,\, written\,\, as\,\,\\(x^2y^3)^6 + 1\\It\,\, can\,\, be\,\, further\,\, written\,\, as\\((x^2y^3)^2)^3 +1\\Using\,\, the\,\, formula\,\, a^3+b^3 = (a+b)(a^2-ab+b^2)\\Here \,\, a = (x^2y^3)^2 and y = 1\\((x^2y^3)^2)^3 +(1)^3= ((x^2y^3)^2+1) (((x^2y^3)^2)^2 -(x^2y^3)^2 +1)\\= (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

So, factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

ANSWER

The constant of variation is 6.

EXPLANATION

The inverse variation equation is:

[tex]xy = k[/tex]

We want to find the constant of variation, when x=-3 and y=-2.

We substitute the values for x and y to get,

[tex] - 3 \times - 2 = k[/tex]

Multiply out the left hand keeping in mind that negative times negative yields a positive result.

This implies that;

[tex]k= 6[/tex]

Hence the constant of variation is 6.

Answer:

The constant of variation k is 6.

Step-by-step explanation:

Given that there is inverse variation between x and y with equation

[tex]xy=k[/tex]

we have to find the constant of variation k when x=-3 and y=-2

The inverse variation equation is:

[tex]xy = k[/tex]

To find constant of variation we substitute the values of x and y

Put x=-3 and y=-2

[tex](-3)\times (-2)=k[/tex]

Solve LHS by multiplying

This implies

[tex]k= 6[/tex]

Hence the constant of variation is 6.

Answer:

47%

Step-by-step explanation:

you would take the number of palomino horses and divide that by the total number of horses like this:

7 / 15 = 0.46666667

which would be rounded to 0.47

which equals 47%

so the probability of randomly choosing a palomino horse would be about 47%

i hope this helps :)

Answer:

168 units cubed

Step-by-step explanation:

so we know it's base times height right

so like identifying the base doesn't matter as long as you're smart enough to figure how to calculate then whatever lol

so like the base let's just say it's the triangle because that's probably what you're struggling on

so the base of the triangle is like what lol 6 * 8 / 2 = 48 / 2 = 24 so then you have the base multiply by the third dimension

24 * 7 = 140 + 28 = 168 so yeaaaaaaa and it's cubed because it's three dimensional

Answer:

The answer is D

Answer:

The answer is A

Go 6 units in X axis and 1 unit in Y axis and you get V.

Alternative B

Answer:

B, Point V

Step-by-step explanation:

find 6 on the x-axis and go up 1, you will find point V

Answer:

X = 20.6 inches

Step-by-step explanation:

Pythagorean Theorem: [tex]A^{2} =B^{2} +C^{2}[/tex]

A = 41.2 in, while B = 35.7 in and we are solving for C.

[tex]41.2^{2} = 35.7^{2} +C^{2}[/tex]

[tex]1697.44 = 1274.49 + C^{2}[/tex]

Now solve for C

[tex]422.95 = C^{2}[/tex]

Take the square root

[tex]20.5657482237 = C[/tex]

Answer:

ohh tough one let me figure this out

Step-by-step explanation:

brb

afk

Answer:

The domain is all real numbers or (-infinity, +infinity)

The range is all numbers greater than or equal to 4 or (4,+infinity)

Hope this helped! :)

ANSWER

[tex](-∞,+∞)[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 4[/tex]

This is a polynomial function.

Polynomial functions are defined for all real values of x.

For every x-value, there is a corresponding y-value.

Therefore the domain of the given function is all real numbers.

We can rewrite this as:

(-∞,+∞).

Answer:

A = 36.75 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A = 1/2 (b1+b2) *h

where b1 and b2 are the bases and h is the height

A = 1/2 (12+9) *3.5

A = 1/2(21)*3.5

A = 36.75 cm^2

Answer:

Odds are 3 to 7

Step-by-step explanation:

The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

Let's find:

Probability of blue marble = 3/10 [ 3 blue and 10 in total]

Probabilty of NOT blue marble = 7/10 [7 marbles are red and green (not blue) and 10 in total]

Hence,

Odds of drawing a blue marble = [tex]\frac{\frac{3}{10}}{\frac{7}{10}}=\frac{3}{10}*\frac{10}{7}=\frac{3}{7}[/tex]

The odds are 3 to 7

Answer:

a(n) = 64 * (1/4)^(n-1)

Step-by-step explanation:

64/16 = 4

16/4 = 4

and so on

so r = 1/4

Geometric sequence:

a(n) = a1 r^(n-1)

a(n) = 64 * (1/4)^(n-1)

Final answer:

The explicit formula for the geometric sequence 64, 16, 4, 1 is an = 64 times (1/4)(n-1), where 'an' is the nth term of the sequence.

Explanation:

The explicit formula for a geometric sequence is given by an = a1 times r(n-1), where a1 is the first term and r is the common ratio. To find the explicit formula for the geometric sequence 64, 16, 4, 1, we need to firstly identify the common ratio r. We can find this by dividing any term by the previous term, so r = 16 / 64 = 1 / 4. The first term a1 is 64. Thus, the explicit formula for the given sequence would be an = 64 times (1/4)(n-1).

Answer:

B. The price for each student ticket is the same at both theaters

Correct Option is B.

System of Linear equations:

A system of linear equations is a set of equations which are satisfied by the same set of variables.

Ex : 2x - y = 12 , x - 2y = 48

Here,

Let's take adult ticket price in theatre A = x

And the student ticket price in theatre A = y

So, (Given), 3x + 2y = $42.50 (Melanie paid)

=> 2y = $42.50 - 3x --(1)

Also given, 2x + 4y = $47 (Drew paid)

=> 4y = $47 - 2x

2(2y) = $47 - 2x

Now, substitute 2y value from eq-(1), we get

2($42.50 - 3x) = $47 - 2x

$85 - 6x = $47 - 2x

=>  $85 - $47 = 6x - 2x

=> $38 = 4x

=> x = ($38)/4 => 9.5

Substitute x value in eq-(1), we get

2y = $42.50 - 3(9.5) => y = $7.

In the given options only Option B is the correct answer.

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this question is unclear

Answer:

A (0,0)

Step-by-step explanation:

When a function intersects the y-axis then the point of intersection is called y-intercept of the function,

Also, for y-intercept x = 0.

That is, if f(x) is the function then its y-intercept is (0, f(0) )

By the given table for x = 0, f(x) = 0

Hence, the y-intercept of the given function is (0,0),

Option A is correct.

Answer:

A trust

Step-by-step explanation:

Answer:

2 31/32   cups used

Step-by-step explanation:

We have 4 3/8 cups cherries

Change this to an improper fraction

4 3/8 = (8*4+3)/8 = 38/8

We use 5/8 of the cherries

38/8 *5/8

190/64

Change this back to a mixed number

64 goes into 190 2 times

190 - 128 =62  left over

2 62/64

2 31/32   cups used

Answer:

See attached diagram

Step-by-step explanation:

You are given the equation of hyperbola

[tex]\dfrac{(x-1)^2}{49}-\dfrac{(y+3)^2}{9}=1[/tex]

From this equation,

Draw two parallel lines x=1 and y=-3 (they intersect at the center of hyperbola), then on horizontal line match two hyperbola's vertices (7 units to the left and 7 units to the right from the center). Then draw two branches of hyperbola (one in negative direction and one in positive direction).

The arc is equal to the half of circumference.

The formula for circumference is [tex]C=2\pi r=2\pi 11=22\pi\approx69.11[/tex]. Now divide that by 2 and you get [tex]69.11\div2\approx\boxed{34.56}[/tex]

Semicircular arc has a length of approximately 34.56

Hope this helps.

r3t40

Answer:

9.2 kilo grams

Step-by-step explanation:

Answer:

x is less than or equal to 3.5

Step-by-step explanation:

For this you can any variable but let’s use d representing the distance that Jonathan ran.

Hmm

D_>3.5+5

In other words d is less than or equal to 3.5 plus 5

Hope this helped u :)

Rotation is a type of transformation that turns a figure around a given point called the center of rotation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Rotation is a type of transformation that turns a figure around a given point called the center of rotation.

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Final answer:

A rotation is a transformation that involves a figure turning around a fixed point called the center of rotation, with all other points moving in circular paths around this central point.

Explanation:

A rotation is a transformation that turns a figure around a given point called the center of rotation. In geometry, when objects undergo rotation, such as a compact disc (CD) spinning, each point on the object moves along a circular arc. The rotation is planar, meaning the object stays within a single plane as it turns around a central point. The axis of rotation can be thought of as a line passing through this central point, remaining fixed while the rest of the figure rotates around it. For example, Earth's rotation on its imaginary axis, stretching between the North and South Poles, causes the daily cycle of night and day.

When we consider an individual object rotating in a fixed location, the axis of rotation is the line about which the rotation occurs. Points on this axis do not move, and every other point in the object follows a path around this axis. If we were to visualize the motion of a rotating rod, for instance, we would see that a rod rotated around an axis through its center perpendicular to its length exhibits this rotational motion. In all cases, the center of rotation acts as a pivotal point around which the figure rotates.