Use the graph to determine
(a) open intervals on which the function is increasing, if any.
(b) open intervals on which the function is decreasing, if any.
(c) open intervals on which the function is constant, if any.

Answer:

The investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Step-by-step explanation:

The compound interest formula is:

A = P * (1 + (r/n))^(nt)

where

A is the amount of the investment after t years,

P is the principal amount (9070),

r is the annual interest rate (3.3%),

n is the number of times the interest is compounded per year (2),

t is the number of years (17).

Using the formula:

A = 9070 * (1 + (0.033/2))^(2 * 17)

A = 9070 * (1.0165)^34

A = 9070 * 1.882611

A = 16898.67 to the nearest cent.

So the investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Answer: $3660.96 or $3661.0

Step-by-step explanation:

Answer: One way that Olivia might have found a combination of two transformations to move figure ABCDE onto figure A'B'C'D'E' is by using a combination of translations and rotations.

A translation is a type of transformation that moves a figure a certain distance in a specified direction, without changing its size or orientation. A rotation is a type of transformation that turns a figure about a fixed point, called the center of rotation, by a certain angle.

Olivia might have first translated figure ABCDE to a new location and then rotated it about a point to match the orientation of A'B'C'D'E'. For example, she could have translated figure ABCDE so that one vertex coincides with a corresponding vertex in A'B'C'D'E', and then rotated it about that common vertex so that the sides match up.

Alternatively, Olivia might have first rotated figure ABCDE to a new orientation and then translated it to the final position. The sequence of transformations could have been different, but the end result would still be figure ABCDE matching the orientation and position of A'B'C'D'E'.

Step-by-step explanation:

The features of the sine function in this problem are given as follows:

The equation is given as follows:

y = 2sin(2πx/3) - 4.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:

2A = 4.

A = 2.

Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:

D = -4.

The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:

2π/B = 3

B = 2π/3.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 2sin(2πx/3) - 4.

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Answer:

The difference between the vertical intercept is a ratio of 20$ so the difference in intercepts is about 2.50$ or 20 spaces.

Hope this helps

The values of x for which gh(x) = f(x) are -1 and -4.

As a result, we have gh(x) = g(h(x)) = g(x + 2). ² = x² + 4x + 4 f(x) = -x

The equation must be solved in order to determine the range of x values for which gh(x) = f(x):

x² + 4x + 4 = -x

When all the phrases are moved to the left, we obtain:

x² + 5x + 4 = 0

This quadratic equation has the following factors:

(x + 1)(x + 4) = 0

Thus, either x + 1 = 0 or x + 4 = 0 is the answer.

We obtain x = -1 or x = -4 after solving for x.

Hence, -1 and -4 are the values of x for which gh(x) = f(x).

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Answer:

By Thales' Rule (aka "the angle in a semicircle is a right angle"), since PR is a diameter,angle PQR is 90 degrees, i.e. PQ is perpendicular to QR, so their gradients multiply to -1.Thus 8/12 * -6/(a-9) = -1, so 12(a-9) = 48, so a-9 = 4, so a=13, as required.

Step-by-step explanation:

( 4x + 1 ) ° = ( 3x + 4 )°

Opposite side of parallelogram are always equal ...

4x + 1° = 3x + 4°

4x - 3x = 4° - 1°

x = 3°

The measure of angle R from the given parallelogram TPRS is 101°.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, TPRS is a parallelogram.

Here, ∠T=(4x+1)° and ∠S=(3x+4)°

The sum of adjacent angles of a parallelogram is 180°.

∠T+∠S=180°

(4x+1)°+(3x+4)°=180°

7x+5=180

7x=175

x=175/7

x=25°

So, ∠T=(4x+1)°=4×25+1=101°

∠T=∠R=101° (Opposite angles of parallelogram are equal)

Therefore, the measure of angle R is 101°.

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Answer:

The line has a slope of - 3/4.

The line has a slope of 3/4.

Step-by-step explanation:

To determine the slope of a line passing through two points, you can use the formula:

Slope = (y2 - y1) / (x2 - x1)

Using the points (-6, 8) and (-3, 4), the slope would be:

Slope = (4 - 8) / (-3 - (-6)) = -4 / 3 = -4/3

So, the line has a slope of -4/3. The other statements in the list are not necessarily true based on the given information.

Answer:

Below

Step-by-step explanation:

distance / rate = time

1 mi / (45 mi/hr)  = 1/45 hr = .02222 hr = 1 1/3 min

11.3 min

...............

Answer:

23

Step-by-step explanation:

We can think of (f o g)(-4) as f(g(-4)).

As you can see, we start with the inner function and the output of the inner function becomes the output of the outer function.

So we'll plug in -4 for x in g(x) and then the output of this becomes the input of f(x):

[tex]f(x)=2x-1\\g(x)=x^2-4\\f(g(-4))\\\\g(-4)=(-4)^2-4=12\\\\f(12)=2(12)-1=23[/tex]

The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides are given as,

YX / XV = ZX / XW

3 / 9 = 2 / 8

1 / 3 ≠ 1 / 4

The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.

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Answer:

If HM = 37, then ML = 37 as the diagonals of EFGH intersect at point M.

Step-by-step explanation:

To solve the diagonals of EFGH intersecting at point M, if HM = 37, first graph the points on a coordinate grid and draw the diagonals. Then use the Pythagorean Theorem to calculate the length of HM. Finally, use trigonometry to calculate the angle measure of FHG.

1) The perimeter of the composite figure is 31.9

2) The area of the composite figure is 64.25

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

There are 2 shapes: half circle and right triangle

diameter of half circle ,d=10

radius, r=d/2 = 10/2 = 5

Perimeter of half circle = π r = 3.14 * 5 = 15.7

In the right triangle,

base = 5, line perpendicular to  base = 10

hypotenuse² = squares of  other 2 sides  added

                       = 5² + 10²

                       = 25 +100

                       = 125

hypotenuse = ± √125 = ±11.18

consider positive for length

hypotenuse = 11.18

The perimeter of the composite figure

= Perimeter of half circle +base of  right triangle + hypotenuse of  right triangle

=15.7 + 5 +  11.18

= 31.9

Area of  half circle = 0.5*π *r² = 0.5*3.14*5² = 39.25

Area of  right triangle = 0.5*base * height

                                     = 0.5*5*10

                                     =  25

The area of the composite figure

=Area of  half circle + Area of  right triangle

=  39.25 +   25

= 64.25

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Answer: 10777678

ywyw

Answer:

36089.66

Step-by-step explanation:

First you have to change the percent to a decimal (0.271) then you multiply the number by $28,394.70 and get (7,694.96) last you add ($7,694.96)+  ($28,394.70) to get your answer

The smallest angle is 5° when each of those angles was divided into 5 equal parts.

In Geometry, an angle is a figure which is produced by two rays, which share a common point called a vertex. The two rays stand in for the angle's two sides. The Roman word "Angulus," which means "corner," is where the term "angle" originates. The intersection of two curves in this plane results in the angles. Angles of several kinds can be generated on a planar surface. As follows:

Acute Angle

Obtuse Angle

Right Angle

Reflex Angle

Straight Angle

Full Angle

An angle greater than 90° but less than 180°  is referred to as a "obtuse angle."  An obtuse angle is between a right angle and a straight angle.

Now in this question,

Starting with an obtuse angle of 150°, bisecting it gives two angles of 75° each.

Trisecting each of these angles gives three angles of 25° each.

Dividing each of these angles into 5 equal parts gives angles of 5° each.

Therefore, the smallest angle is 5°.

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The discount can be found by subtracting the sale price from the original price:

$25.40 - $16.51 = $8.89

So the discount was $8.89.

To find the percent discount, we can divide the discount by the original price and multiply by 100:

$8.89 / $25.40 * 100% = 35%

Therefore, the percent discount from the coupon was 35%.

Fractions of smallest to largest

Smallest to largest: 1/4, 1/3, 2/5, 2/3, 3/4

Smallest to largest: 1/5, 2/7, 3/5, 5/7, 31/35

Smallest to largest:  31/30, 23/20, 6/5, 13/10, 7/5

Smallest to largest:   13/10, 13/6, 11/5, 25/6, 21/5

An element of a whole is a fraction. The number is mathematically expressed as just a fraction, where the numerator and denominator are split. Both are integers in a simple fraction. A simple fraction contains a fraction in either the numerator or the denominator. A fraction consists of two components. The numerator seems to be the number which goes just at top of the line. 

Smallest to largest: 0.25, 0.33, 0.4, 0.67, 0.75

Smallest to largest: 0.2, 0.29, 0.6, 0.71, 0.89

Smallest to largest:  1.03, 1.15, 1.2, 1.3, 1.4

Smallest to largest:  1.3, 2.16, 2.2, 4.17, 4.2

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Answer:is his brother 4 or 8

Step-by-step explanation:

I don't know for sure

Answer:

1.2 x [tex]10^{14}[/tex]

Step-by-step explanation:

Scientific notation OR standard form:

This is expressed in powers of 10 (i.e [tex]10^{x}[/tex])

If the decimal point cannot be visibly seen, you can deduce that the decimal point is currently located after the last digit (i.e ‘0’).

For the number to be expressed in scientific notation, the decimal point has to be placed right after the first digit (which is NOT a zero) in the left most direction.

For this number, the decimal point has to be placed right after the ‘1’.  Therefore, the decimal point will be moving 14 places to the left. In addition, this 14 is considered as the positive power of 10.

Answer:

1.2 × 10¹⁴

Step-by-step explanation:

Scientific notation is written in the form [tex]a \times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one non-zero digit to the left of the decimal point.

The number of times you have moved the decimal point is the power of 10 (the value of n).

Therefore, to convert 120,000,000,000,000 to scientific notation, move the decimal point 14 places to the left so that [tex]a[/tex] is 1.2.

As the decimal point has been moved 14 places the left, we need to multiply 1.2 by 10¹⁴.

Therefore,  120,000,000,000,000 = 1.2 × 10¹⁴.

Answer:

x = 3

Step-by-step explanation:

A vertical line is drawn on a graph paper, which passes through points (3, 3) and (3, -3).  For a vertical line, slope or gradient is undefined.
Therefore, the equation of vertical line is the common x-coordinate of the points along the line. In this case, the common x-coordinate is 3

∴Equation of line

        x = 3

Answer:

325888899998898897879

Answer:

To find the cost of a standard membership, we need to subtract the $15 premium from the monthly premium membership cost of $40.

$40 - $15 = $25

Therefore, the cost of a standard membership is $25 per month.

X(t) = 2-t, Y(t) = 5-t, and Z(t) = 0 are the parametric equations for the line passing through (2, 5, 0) and being perpendicular to both i+j and j k. The line has symmetric equations x+2 = -(y + 5) and z = 0, or x+2 = -(y + 5) = z.

As x(t) = 2-t, y(t) = 5-t, and z(t) = 0, the parametric equations of the line passing through (2, 5, 0) and perpendicular to both i+j and j k can be written. The x, y, and z coordinates of the line are defined by these equations in terms of the parameter t. It is possible to write the line's symmetric equations as x+2 = -(y + 5) and z = 0, or as x+2 = -(y + 5) = z. These equations define the line as the collection of all points (x, y, and z) that concurrently meet both equations. The line goes through the point and is perpendicular to both i+j and j k. (2, 5, 0).

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The sum of cubes expression is a^3 + 8

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

The list of options

A sum of cube expression can be represented as

a^3 + b^3

From the list of options, we have

a^3 + 8

This can be expressed as

a^3 + 2^3

Hence, teh expression is a^3 + 8

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Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

In algebra, ratios display how infrequently one figure is contained in another. For instance, if there are 8- oranges and 6 citrus in a fruit dish, the percentage of oranges to oranges is 8 to 6. In a similar vein, lemons to whole fruit ratio is 8 to 1, whereas lemons to oranges rate is 6 to 8. A ratio is a non-zero ordered pair of numbers, x and y b, that is stated as a / b. A ratio is really an equation that joins two ratio. The ratio can be written as 1:3, signifying that if there 1 boy and (3) girls (she has 3 girls for every boy), 3/4 of the population is female and 1/4 is male.

given

the ratio of sans , gravel and sand is 6:3:2

total pounds needed = 3300

so 6x + 3x + 2x = 3300

11x = 3300

x = 300

6x = 6 * 300 = 1800

3x = 3* 300 = 900

2x = 2* 300 = 600

Consequently, when 3300 pounds are utilized, sand, gravel, and cement weigh 1800, 900, and 600 pounds, respectively.

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The scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1: 168 and 1: 1080 respectively.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

For the ratio 1 in : 14 feet, we convert to the same unit in inches:

1 foot = 12 inches

14 feet = 12 × 14 inches

14 feet = 168 inches

1 in = 168 in

1 : 168

For the ratio 1 in : 30 yards, we convert to the same unit in inches:

1 yard = 36 inches

30 yards = 36 × 30 inches

30 yards = 1080 inches

1 in = 1080 in

1 : 1080

Therefore, the scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1 : 168 and 1 : 1080 respectively.

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