Convert the angle 3 radians to degrees, rounding to the nearest 10th.

The solution set of the given homogeneous system in parametric vector form is x₁ = 5 = x₂ , x₃ = 1.

What is parametric vector form?

The identity matrix's two columns, which stand in for the two leading coefficients in the row echelon form of the original matrix, are added to create the parametric vector.

We are given set of equations as:

x₁ + 2x₂ - 15x₃ = 0

2x₁ + x₂ - 15x₃ = 0

-x₁ + x₂ = 0

Now, representing this in the matrix form, we get

[tex]\left[\begin{array}{cccc}1&2&-15&0\\2&1&-15&0\\-1&1&0&0\end{array}\right][/tex]

Now, we will reduce the matrix i.e. in row echelon form using elementary operations

From this, we get

[tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&-5&0\\0&0&0&0\end{array}\right][/tex]

So, we get that x₃ is the free variable.

Now, representing this in the parametric vector form, we get

x₁ - 5x₃ = 0

x₂ - 5x₃ = 0

x₃ = x₃

From this, we get

x₁ = 5x₃

x₂ = 5x₃

x₃ = x₃

So, we now get

x = [tex]\left[\begin{array}{c}x_{1} &x_{2} &x_{3} \end{array}\right][/tex]

This is equal to

x = [tex]\left[\begin{array}{c}5x_{3} &5x_{3} &x_{3} \end{array}\right][/tex]

Thus,

x = [tex]\left[\begin{array}{c}5 &5 &1 \end{array}\right][/tex]

Hence, the solution is x₁ = 5 = x₂ , x₃ = 1.

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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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Since both the coordinates of (-2,-3) are negative the point lies in option B: quadrant iii.

What is a quadrant?

A quadrant is an area or section of a cartesian plane that results from the intersection of two axes. It is used to establish a point's location in a plane.

Consider the point A = (x,y) given in the coordinate system, where x and y are arbitrary numbers.

If x and y are positive numbers then point A is in the first quadrant.

If x is negative number and y is positive then point A is in the second quadrant.

If x and y are negative numbers then point A is in the third quadrant.

If x  is positive number and y is negative then point A is in the fourth quadrant.

Now the given point is (-2,-3).

The first coordinate of this point is a negative number, and the second is also negative.

So, the point lies in third quadrant.

Therefore, (-2,-3) is in 3rd quadrant.

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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:

( 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:

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:

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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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

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

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%.

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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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.

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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For the statement "Integer x divisible by 6" the option C is correct.

Either statements are NOT sufficient, but BOTH together are sufficient.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

(1) x + 3 is divisible by 3

This means that x is a multiple of 3.

Hence x + 3 is a multiple of 3.

But x could be 0, 3, 6. If x = 3, x is not divisible by 6.

Otherwise it is.

So, this statement is insufficient.

(2) x + 3 is an odd number

This means that x is an even number.

X can be 6, or 10.

So, this statement is insufficient.

Together -

From (1) it is known that x is a multiple of 3.

Hence X can be 0,3,6,9,12,15,18,21,24,27,30.

From (2) it is known that x is even.

Hence X can be 0,6,12,18,24,30.

Therefore, x is divisible by 6.

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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.

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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The given diagram in the image is dilated by a scale factor of 1.5.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or decrease

The coordinate point of the image is at 2. After dilation, the point will reach the coordinate at 5.

The scale factor of the point will be calculated as:-

Scale factor = 9 / 6

Scale factor = 1.5

Therefore, the scale factor for the given diagram in the image is 1.5.

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$89.1 is the amount paid by Beau to buy skateboard.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Beau buys a skateboard with a price tag of $82.50

The tax rate is 8%

Let us find what 8% of 82.50

Convert 8% to decimal value

8/100=0.08

0.08×82.5=$6.6

Now let us find the amount he paid including tax

$82.50+$6.6

$89.1

Hence, $89.1 is the amount paid by Beau to buy skateboard.

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The value of y is 13√2 (optionB)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos (tetha) = adj/hyp

tan(tetha) = opp/adj

therefore cos 45 = 13/y

1/√2 = 13/y

y = 13√2

therefore the value of y is 13√2

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The Standard deviation of data(5, 13, 9, 10, 5, 12) that represents orders filled per day is 3.4

The sample standard deviation formula looks like this:

s = √Σ(X-x)² / √n-1

Where….

s = sample standard deviation

Σ = sum of…

X = each value

x = sample mean

n = number of values in the sample

We have,

Number of values in the sample, n = 6

sample mean, x = 5+13+9+10+5+2 / 6 = 9

So sample standard deviation, S = √Σ(X-x)² / √n-1

s = √58/√5

s = 7.6/2.2

s = 3.4

Therefore sample standard deviation of data that represents orders filled per day is 3.4

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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:

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]

Answer: 10777678

ywyw

Answer:is his brother 4 or 8

Step-by-step explanation:

I don't know for sure

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

Answer:

Step-by-step explanation:

4:05pm go back 4hours and it’s 12:05, then go back another 2 hours, 10:05, then go back another 20mins and it’s 9:45am

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.

Answer: 16 cats

Step-by-step explanation: how many times does 5 go into 20?? 4 times (5x4) so you multiply 4 by 4

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