How many inches apart will four bolts be along the circumference of the metal plate shown in the figure to the right

Answer:

Yes this is a parallelogram because opposite sides and angles of this figure are equal

Answer: 8 1/4 feet of ribbon is 99 inches.

Step-by-step explanation: First, convert that fraction into a decimal, which is 8.25. Now that you have that, multiply it by 12 since there are 12 inches in one foot. 8.25 ft  x 12= 99. Therefore, 99 inches is your answer.

The food stand located at the amusement park is located at the centroid, which is the point of concurrency.

The centroid is the point of intersection of the three medians of a triangle. The medians are the lines drawn from each vertex to the midpoint of the opposite side of the triangle.

In this case, the medians are drawn from each of the three attractions to the food stand. The centroid is the point at which all three medians intersect, making it the point of concurrency.

The centroid can be found by taking the mean of the x and y coordinates of each vertex of the triangle.

The centroid is the point at which the sum of the distances from the vertices to the centroid is at its minimum. This is why the food stand is located at the centroid of the triangle formed by the roller coaster, merry-go-round, and go karts.

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Answer:

B.

Step-by-step explanation:

well, since the generic formula for a circle is

(x - h)² + (y - k)² = r²

with (h, k) being the circumstances of the center of the circle, and r being the radius, it is really just a matter of comparing the data :

h = 5

k = -1

r = 16, r² = 16×16 = 256

it has to be therefore

(x - 5)² + (y + 1)² = 256

The equation y = 160x represents the total number of pencils if one box includes 160 pencils.

One box contains 160 pencils, and x indicates how many boxes there are overall. Therefore, the product of x and 160 will yield the equation for the overall number of pencils.

The equation is = x × 160 = 160x

The definition of an algebra equation is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Equation, is a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.

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The missing parts of the triangles are found below.

1) Cos 34 = x/13

x = 13Cos 34

= 12.9

2) Sin 43 = x/19

x = 19Sin 43

= 13

3) Cos 65 = 16/x

x = 16/Cos 65

= 38

4) Cos 47 = x/13

x = 13Cos 47

= 9

5) Sin 57 = 20/x

x = 20/Sin57

x = 24

6) Sin 69 = 11/x

x = 11/Sin 69

= 12

7) Cos 22 = 12/x

x = 12/Cos 22

x = 13

8) Sin 26 = 17/x

x = 12/Sin 26

x = 27

9) Sin 38 = 17/x

x = 17/Sin 38

x = 28

These are the parts that we need to find in the triangles above.

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The zeros of the function y = -16x² + 246x + 100 are x = -0.4 and x = 15.8

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

y=-16x^2+246x+100

Express properly

So, we have

y = -16x² + 246x + 100

Divide through the equation by 2

So, we have

y = -8x² + 123x + 50

We set the value of y to 0, in order to solve the equation

So, we have

-8x² + 123x + 50 = 0

When solved graphically, we have

x = -0.396 and x = 15.771

Approximate

x = -0.4 and x = 15.8

Hence, the x values are x = -0.4 and x = 15.8

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Answer:  x=13

Step-by-step explanation:

cross multiply to get 5(x-9)=2(x-3) then slove for x

The total change to Ahab's funds is -$175, which means he spent more money than he received and is now $175 poorer

To solve this problem, we need to calculate the total amount of money Ahab spent and the total amount of money he received. We can then subtract the total amount spent from the total amount received to get the total change to Ahab's funds.

The total amount spent on tires is 3 x $50 = $150.

When he returned one tire, he received a refund of $50.

He found a five dollar bill, which adds $5 to his funds.

The total amount spent on jackets is 2 x $40 = $80.

Therefore, the total amount spent is $150 + $80 = $230, and the total amount received is $50 + $5 = $55.

To find the total change to Ahab's funds, we subtract the total amount spent from the total amount received:

$55 - $230 = -$175

Therefore, the total change to Ahab's funds is -$175, which means he spent more money than he received and is now $175 poorer.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities or expressions and shows that they are not equal.

To solve the inequality, we can simplify it as follows:

-3(2x – 5) < 5(2 – x)

-6x + 15 < 10 - 5x (distribute the negative sign on the left and the positive sign on the right)

-6x + 5x < 10 - 15 (add 6x and subtract 15 from both sides)

-x < -5 (combine like terms)

x > 5 (multiply both sides by -1 and reverse the inequality)

Therefore, we have x > 5 as the solution to the inequality. The two correct representations of this solution are:

-6x - 5 < 10 - x (simplified from the original inequality)

A number line from 5 to infinity with an open circle at 5 and a bold line pointing to the right. (graphical representation)

Option 2 and 4 are incorrect because they do not accurately represent the solution to the inequality.

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Answer:

f^-1(0) = 4

Step-by-step explanation:

slope = -1/2 => y = -1/2x + 2

=> 1/2x = 2 - y

=> x = -2y + 4

=> f^-1(x) = -2x + 4

f^-1(0) = 4

Answer:

x= 1  2/5

Step-by-step explanation:

4+2 = 6

6(2-x)=3-2(5-x)

6(2-x)=1(5-x)

The correct answer is Akira should buy 12 daffodil bulbs in packages of 3 and save $1.08.

Given that,

Akira can buy Daffodil bulbs in packages of 3 for $5.28 or in packages of 2 for $3.70.

He needs to buy 12 bulbs at a better price.

Money spent by buying bulbs in packs of 3 = 4 × $5.28 = $21.12.

Money spent by buying bulbs in packs of 2 = 6 × $3.70 = $22.2.

so, we get,

Money saved if bought in packs of 3 = $22.2 - $21.12 = $ 1.08.

Thus Akira should buy 12 daffodil bulbs in packages of 3 and save $1.08.

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Answer:

86

Step-by-step explanation:

According to the information, the solution would be: R1 -> R

Question 1:

Using Gaussian Elimination:

2x + y + 2z = 1

4x + 3z = -5

5y + 4z = 13

R1 -> R1/2

x + 1/2y + z = 1/2

4x + 3z = -5

5y + 4z = 13

R2 -> R2-4R1

x + 1/2y + z = 1/2

0x + z = -7

R3 -> R3-5R1

x + 1/2y + z = 1/2

0x + z = -7

-5x + 9/2y - 17/2z = -15/2

R3 -> R3+5/2R2

x + 1/2y + z = 1/2

0x + z = -7

0x + 11/2y - 29/2z = -11/2

R2 -> R2+3R1

x + 1/2y + z = 1/2

0x + z = -7

0x + 11/2y - 29/2z = -11/2

R1 -> R1 - 1/2R2

x + y - 3z = 8

0x + z = -7

0x + 11/2y - 29/2z = -11/2

Using Gauss-Jordan Elimination:

1 1/2 1 | 1/2

4 0 3 | -5

0 5 4 | 13

R1 -> 2R1

2 1 2 | 1

4 0 3 | -5

0 5 4 | 13

R2 -> R2-4R1

2 1 2 | 1

0 -4 -5 | -9

0 5 4 | 13

R2 -> -1/4R2

2 1 2 | 1

0 1 5/4 | 9/4

0 5 4 | 13

R1 -> R1 - 2R2

2 1 -1/2 | -1/2

0 1 5/4 | 9/4

0 5 4 | 13

R3 -> R3 - 5R2

2 1 -1/2 | -1/2

0 1 5/4 | 9/4

0 0 -9/4 | -2/4

R3 -> -4/9R3

2 1 -1/2 | -1/2

0 1 5/4 | 9/4

0 0 1 | 2/9

R2 -> R2 - 5/4R3

2 1 -1/2 | -1/2

0 1 0 | 17/36

0 0 1 | 2/9

R1 -> R

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Answer:

[tex]\text{As x} \to \infty, \text{then } y \to \infty\\\text{As x} \to -\infty, \text{then } y \to \infty[/tex]

Regardless of what direction x goes to, y goes off to infinity.

In other words, it rises to the left and rises to the right

Both endpoints go up forever.

See the graph below.

====================================================

Explanation:

As x gets bigger, x^2 gets even larger.

Examples:

The -4 at the end won't really put much of a dent in the large outputs as x gets really large. So we can say that as x goes to infinity, y also goes to infinity

[tex]\text{As x} \to \infty, \text{then } y \to \infty[/tex]

Similarly,

[tex]\text{As x} \to -\infty, \text{then } y \to \infty[/tex]

Because something like x = -100 leads to x^2 = 10,000. The negatives cancel out when squaring.

This results in both sides going up forever.

We can describe it as: It rises to the left and rises to the right.

The "rises to the left" portion is [tex]\text{As x} \to -\infty, \text{then } y \to \infty[/tex]

The "rises to the right" portion would be [tex]\text{As x} \to \infty, \text{then } y \to \infty[/tex]

The graph is shown below. I used GeoGebra to make the graph.

The nearest hundredth of a mile, the vertical change in elevation is approximately 1.47 miles.

A right triangle is a triangle that has one angle measuring exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Assuming a right triangle formed by the surveyor, the point on the mountain, and the base of the mountain, we can use the tangent function to find the vertical change in elevation.

tan(18°) = opposite/4 miles

Solving for the opposite (vertical change in elevation), we get:

opposite = 4 miles * tan(18°)

opposite ≈ 1.47 miles

Rounding to the nearest hundredth of a mile, the vertical change in elevation is approximately 1.47 miles.

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When x3 + x² + 2kx + 6 is divided by (x - 2), the remainder is 30 and k = ±1.

An equation is a mathematical statement that establishes an equality between two expressions. It consists of two expressions separated by an equal sign (=). The expressions on either side of the equal sign represent the same value and can be used to solve for a desired quantity. Equations can be used to express relationships between variables, calculate unknowns, and describe physical phenomena.

To solve this problem, we can use the Remainder Theorem, which states that when a polynomial is divided by a linear expression, the remainder is equal to the value of the polynomial at the x-intercept of the linear expression.

In this case, when we divide x3 + x² + 2kx + 6 by (x - 2), we get the following:

(x - 2)(Q(x)) + R = x3 + x² + 2kx + 6

Where Q(x) is the quotient and R is the remainder (in this case, 30).

We can use the Remainder Theorem to find k. Since the x-intercept of (x - 2) is x = 2, we can plug this into the equation to find R:

(2 - 2)(Q(2)) + R = 23 + 22 + 2k2 + 6

R = 30

Therefore, we can solve for k:

30 = 23 + 22 + 2k2 + 6

30 - 23 - 22 - 6 = 2k2

k2 = 1

Therefore, k = ±1.

In conclusion, when x3 + x² + 2kx + 6 is divided by (x - 2), the remainder is 30 and k = ±1.

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Answer:

s>-80

Step-by-step explanation:

12> -68 - s

12> -s -68

add 68 to both sides

12+68 > -s -68+68

s> -80

Answer:

y = sin(3x)

Step-by-step explanation:

Amplitude = A = 1

Period = 2π/B = 2π/3

B = 3

Equation of a sine wave:  y = Asin(B(x + C)) + D

There is no phase shift or vertical shift, so C and D are 0 (zero)

Therefore, the equation of the graph is:

y= Asin(Bx) = sin(3x)

The area of the sector is  30. 52 square units

To determine the area of the sector, we need to consider the formula.

The formula for calculating the area of a sector is expressed with the formula;

A = (θ/360º) × πr2

Such that the parameters of the formula are;

From the information given, we have;

Substitute the values

Area = 140/360 × 3.14 × 5²

Find the square value

Area = 140/360 × 3.14 × 15

Multiply the values

Area = 0. 389  × 3.14 × 25

Multiply

Area = 30. 52 square units

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The probability that she selects a blue floss is 14% greater than the probability that she selects an orange floss.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of spools is given as follows:

8 + 5 + 7 + 10 + 3 + 6 + 4 + 7 = 50 spools.

10 are blue, hence the probability is of:

10/50 = 20%.

3 are orange, hence the probability is of:

3/50 = 6%.

The difference is of:

20 - 6 = 14%.

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Answer:

C; 4

Step-by-step explanation:

the distance between two points in the smaller triangle is 2 units.

the distance between the same two points in the dilated triangle is 8 units, so because 2*4=8, the scale factor is 4

Answer:

[tex] \frac{19 + 6 \sqrt{3} }{2} [/tex]

Step-by-step explanation:

[tex]2a - \frac{1}{ \sqrt{a} } + \frac{1}{a} \: \: \: when \: \: a = 4 + 2 \sqrt{3} [/tex]

[tex]2 \times (4 + 2 \sqrt{3} ) - \frac{1}{ \sqrt{4 + 2 \sqrt{3} } } + \frac{1}{4 + 2 \sqrt{3} } [/tex]

Expand the brackets (multiply every term inside the bracket by the term on the outside) and make the denominator the same (4 + 2√3):

[tex] \frac{(8 + 4\sqrt{3} )\times(4 + 2 \sqrt{3} ) }{4 + 2 \sqrt{3} } - \frac{ \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } + \frac{1}{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{32 + 16 \sqrt{3} + 16 \sqrt{3} + 24 - \sqrt{4 + 2 \sqrt{3} } + 1}{4 + 2 \sqrt{3} } [/tex]

Collect like-terms:

[tex] \frac{57+ 32 \sqrt{3} - \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{57 + 32 \sqrt{3} - \sqrt{( {1 + \sqrt{3}) }^{2} } }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{57 + 32 \sqrt{3} - (1 + \sqrt{3} )}{4 + 2 \sqrt{3} } [/tex]

Eliminate the parentheses:

[tex] \frac{57 + 32 \sqrt{3} - 1 - \sqrt{3} }{4 + 2 \sqrt{3} } [/tex]

Collect like terms:

[tex] \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \times \frac{4 - 2 \sqrt{3} }{4 - 2 \sqrt{3} } = \frac{224 - 112 \sqrt{3} + 124 \sqrt{3} - 186}{16 - 4 \times 3} = \frac{38 + 12 \sqrt{3} }{4} [/tex]

[tex] \frac{2(19 + 6 \sqrt{3}) }{4} = \frac{19 + 6 \sqrt{3} }{2} [/tex]

The playhouse consists of a cube and a square pyramid on top of it. The pyramid has a base of 5 feet and a height of 6 feet. The total volume of the playhouse is 135 cubic feet.

To find the volume of the playhouse, we need to find the volume of both the cube and the pyramid and then add them together.

Let's start with the pyramid

The pyramid's volume formula is: V = 1/3 * base * height

We are given that the base of the pyramid is 5 feet and the height is 6 feet, so we can plug in those values and solve for the volume

V = 1/3 * 5 feet * 6 feet

V = 10 cubic feet

Next, let's find the volume of the cube

The cube's volume formula is: V = length * width * height

Since it is a square pyramid on top of a cube, we know that the base of the pyramid has the same length and width as the cube. Let's call the length of each side of the cube "s". Then we have

V = s * s * s

V = s³

We need to find the value of "s". To do that, we can use the fact that the base of the pyramid has a side length of 5 feet. Since the base of the pyramid is the top face of the cube, we know that the side length of the cube is also 5 feet. So

V = 5 feet * 5 feet * 5 feet

V = 125 cubic feet

Now we can add the volumes of the pyramid and the cube to get the total volume of the playhouse

Total volume = pyramid volume + cube volume

Total volume = 10 cubic feet + 125 cubic feet

Total volume = 135 cubic feet

So the playhouse has a volume of 135 cubic feet.

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so hmmm let's simply get the volume of the outer rectangular prism and then get the volume of the inner rectangular prism, and subtract the inner one from the outer one, what's leftover, is the part we didn't subtract, namely, the vase's volume.

[tex]\stackrel{ \textit{\LARGE Volumes} }{\stackrel{ \textit{outer prism} }{(5)(3)(3)}~~ - ~~\stackrel{ \textit{inner prism} }{(4)(1\frac{1}{2})(1\frac{1}{2})}}\implies 45~~ - ~~9\implies \text{\LARGE 36}~in^3[/tex]

The requried quotient of the given rational expression is 4(x-5)/(x+5).

To divide one rational expression by another, we need to multiply the first rational expression by the reciprocal of the second. In this case, we want to divide:

([x²-25] /[x-11]) by ([x²+10x+25]/[4x-44])

So we multiply the first expression by the reciprocal of the second:

([x²-25] /[x-11]) * ([4x-44]/[x²+10x+25])

[x²-25] /[x-11] can be factored as (x+5)(x-5)/(x-11)

[x²+10x+25]/[4x-44] can be factored as (x+5)²/4(x-11)

So, we have:

([x+5][x-5]/[x-11]) * ([4(x-11)]/[x+5]²)

We can now cancel out the common factors in the numerator and denominator:

=([x-5]/1) * (4/[x+5])

=4(x-5)/(x+5)

Therefore, the quotient of the given rational expression is 4(x-5)/(x+5).

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Answer:

The algebraic expression representing the sentence "The quotient of 2 and a number" would be:

2 / x

where x represents the unknown number.

Step-by-step explanation:

A point that is graphed at (9, 0) include the following: C. Point D.

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;

Point A ⇔  (2, 1) → quadrant I.

Point B ⇔  (5, 3) → quadrant I.

Point C ⇔ (8, 8) → quadrant I.

Point D ⇔ (9, 0) → quadrant I.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.