The diameter of a circle is 170 inches. The circle has two chords of length 26 inches. What is the distance from each chord to the center of the circle?

Answer:

(x) = (-19/9)(x + 3)^2 + 5

Step-by-step explanation:f(x) = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola. Given that the vertex is (-3, 5), we can plug in these values into the vertex form equation:

f(x) = a(x - (-3))^2 + 5

which simplifies to:

f(x) = a(x + 3)^2 + 5

Now, we know that the function passes through the point (0, -14). We can plug in these values into the equation and solve for 'a':

-14 = a(0 + 3)^2 + 5

-14 = 9a + 5

Subtracting 5 from both sides:

-19 = 9a

Dividing both sides by 9:

a = -19/9

lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.

Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.

An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.

According to the given information:

If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.

The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.

To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.

So, the equation of line b is y = -x + 3.

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The new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

To rotate a triangle 270 degrees clockwise with the origin as the centre of rotation, you can follow these steps:

Draw the coordinates of the vertices of the triangle. Let's assume that the coordinates of vertex A are (x₁, y₁), the coordinates of vertex B are (x₂, y₂), and the coordinates of vertex C are (x₃, y₃).

To rotate the triangle 270 degrees clockwise, you need to reflect it first over the x-axis, and then over the y-axis.

To reflect the triangle over the x-axis, you need to change the sign of the y-coordinates of each vertex. So the new coordinates of vertex A would be (x₁, -y₁), the new coordinates of vertex B would be (x₂, -y₂), and the new coordinates of vertex C would be (x₃, -y₃).

To reflect the triangle over the y-axis, you need to change the sign of the x-coordinates of each vertex. So the final coordinates of vertex A would be (-y₁, x₁), the final coordinates of vertex B would be (-y₂, x₂), and the final coordinates of vertex C would be (-y₃, x₃).

These final coordinates represent the vertices of the rotated triangle.

So, the new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

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The number that could be expected to have ordered a medium was 64 people.

The number that could be expected to have ordered a small would be 108 people.

The number that could have been expected to have ordered a small, medium, or large was 75 people.

The number that could have been expected to have ordered a medium was :

= 16 / ( 9 + 16 + 5 + 10 ) x 160 people

= 64 people

The number that could have been expected to have ordered a small would be :

= 9 / ( 9 + 16 + 5 + 10 ) x 480 people

= 108 people

The number that could have been expected to have ordered a small, medium, or large was :

= ( 9 + 16 + 5 ) / ( 9 + 16 + 5 + 10 ) x 100

= 75 people

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We can conclude that a quadratic model is appropriate for the given set of points {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}.

To determine which model is appropriate for the given set of points {(-2,4.5),(0,8),(1,10.67),(3,18.96)}, we need to examine the pattern in the data and choose a model that fits the pattern well.

One common approach to fitting a model to data is to use regression analysis. In this case, we can start by plotting the points on a graph and visually examining the pattern.

When we plot the points, we see that they form a curved shape that resembles a quadratic function. To confirm this, we can use regression analysis to fit a quadratic model to the data.

Using a quadratic regression model, we obtain an equation of the form y = ax^2 + bx + c, where a, b, and c are constants to be determined. The regression analysis yields the following coefficients: a = 2.138, b = 1.959, and c = 5.48.

We can now use this quadratic equation to predict y for any given value of x within the range of the data.

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The operations that are performed with the exponents 2 and 3 in order to simplify the expression include the following:

x²x³ = addition.

(x²)³ = multiplication.

x³/x² = subtraction.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the addition, division, and multiplication law of exponents for powers to each of the expressions, we have the following:

x²x³ = x⁽³⁺²⁾ = x⁵ (addition).

(x²)³ = x⁶ (multiplication).

x³/x² = x⁽³⁻²⁾ = x (subtraction).

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Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . , 80. Therefore, 1640 is the sum of first 40 even numbers.......Sep 23, 2018

PLS MARK BRAINLIEST

Step-by-step explanation:

The sums that prove that the wooden boards can create a triangular outline according to triangle inequality rule are:

The triangle inequality rule states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Testing each combination of sides, we get:

Case 1:

Let 5 feet be the third side

Then,

2.5 + 4 > 5

6.5 > 5

Case 2:

Let 2.5 feet be the third side

Then,

4 + 5 > 2.5

9 > 2.5

Case 3:

Let 4 feet be the third side

Then,

5 + 2.5 > 4

7.5 > 4

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a. The length of one side of the cube  shape x ≈ 3.633 ft

b. The length of one side of the cube  shape is roughly 3.633 feet.

c. The case has a more noteworthy surface region than the block by roughly 10.325 square feet.

Let x be the length of one side of the cube. Since the cube has equal length, width, and height, its volume is  = x^3.

The volume of the box  = (4 feet 5 in) * (3 feet 2 in) * (4 feet 3 in),

which can be converted to feet as Volume of box =

(4 + 5/12) * (3 + 2/12) * (4 + 3/12) = 4.3135 * 3.1667 * 4.25 =

55.0448 cubic feet.

Since the cube has the same volume as the box, we can set Volume of cube = Volume of box and

solve for x:

[tex]x^3 = 55.0448\\x = (55.0448)^{1/3}\\[/tex]

x ≈ 3.633 ft

b. The length of one side of the cube is approximately 3.633 feet.

c. We must determine the surface area of each to compare the cube's and box's surfaces. A cube with side length x has the surface area given by

Surface area of cube = [tex]6x^2[/tex], and

Surface area of a box = 2lw + 2lh + 2wh is the formula for the surface area of a box with the dimensions l, w, and h. Based on the box's dimensions, we have:

Surface area of cube = [tex]6(3.633)^2[/tex] ≈ 79.342 sq. feet

Surface area of box = 2(4.4167 * 3.25) + 2(4.4167 * 4.25) + 2(3.25 * 4.25) ≈ 89.667 sq. feet

By about 10.325 square feet, the surface area of the box is greater than that of the cube.

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The ladder should she placed 12 feet from the base of her house

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

Using the above as a guide, we have the following:

We make use of the pythagoras theorem to calculate how far the ladder should be placed

Represent this with x

So we have

x^2 = 20^2 - 16^2

Evaluate

x^2 = 144

So, we have

x = 12

Hence. the ladder should she placed 12 feet from the base of her house

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The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.

To find the time since the rock reached its closure temperature, we can use the following formula

t = t(1/2) * log(N0/Nt)

where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.

Substituting the given values, we get

t = 96.6 * log(5/0.625) ≈ 579.8 years

Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.

To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.

Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.

Therefore, the rock had 4.375 grams of europium-151 when it was discovered.

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Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.

To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:

Scale factor = bigger dimension/smaller dimension.

To create a smaller image;

bigger dimension length AB = 22in

smaller dimension length AB = 17.6in

Scale factor = 22/17.6 = 1.25

To create a bigger image:

Bigger dimension length = 33in

Smaller dimension length = 22in

scale factor = 33/22 = 1.5

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The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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Answer: There is an approximate 10.7% probability that it will snow on Sunday, making it the day with the lowest likelihood of snow.

Step-by-step explanation: Snow is highly likely on Friday with an 80% probability. The likelihood of no snowfall occurring on Friday is 20%, which can be calculated by subtracting 0.8 (or 80%) from 1.

There is a high probability of snowfall on Saturday with a 7 in 9 likelihood. In simpler terms, the probability can be reduced to 7 out of 9 or around 0.78. The likelihood of snowfall on Saturday is 78%, therefore the chance of no snow on that day is 22% which is equivalent to 1 minus 0.78.

There is a high likelihood of snow on Sunday with a probability of 75 out of 100 or 14 out of 19. It is possible to reduce this to a likelihood of 0.7514, or about 0.107. The likelihood of Sunday not having snow is equivalent to subtracting 0.107 from 1, resulting in a 0.893 or 89.3% probability.

Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

18x9=162

18 cubes and 9 layers of the 18 cubes. so thats just eighteen, nine times.

Given statement: Diversification can reduce portfolio risk even when correlations across stock returns equal zero.

Given statement is true.

Because, By diversifying, you spread your investments across various assets, which can help reduce the overall risk of your portfolio. When correlations are zero, it means that the stock returns move independently of each other, further supporting the benefit of diversification in this case.

Diversification can reduce portfolio risk by combining assets with different return patterns, but even when the correlations between the returns are zero, there is still systematic risk (market risk) that cannot be diversified away.

This is because all stocks are subject to macroeconomic factors such as inflation, interest rates, and changes in consumer confidence, which can affect the entire market.

Therefore, even if the correlations across stock returns are zero, diversification cannot completely eliminate portfolio risk.

However, it can still reduce it to a certain extent by spreading the risk across different assets.

The more uncorrelated the assets are in a portfolio, the greater the potential for risk reduction.

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Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.

Here,

Taking the logarithm of both sides of the equation 10ˣ = 23:

log(10ˣ) = log(23)

Using the power rule of logarithms, the left-hand side simplifies to:

x log(10) = x

Since log(10) = 1, we have:

x = log(23)

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The account value after forty (40) years is approximately $2,789,525.

We can use the formula for future value of an annuity to solve this problem:

FV = PMT * ((1 + r)^n - 1) / r

where FV is the future value, PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods (years in this case).

For the first year, the deposit amount is $3,000, so:

FV1 = 3000 * (1 + 0.0835)^40 = $65,470.22

For the subsequent years, the deposit amount increases by $300, so:

PMT = 3000 + 300 + 300 + ... = 3000 + 300 * 39 = $15,300

Using this value for PMT, we can calculate the future value for the remaining 39 years:

FV2 = 15300 * ((1 + 0.0835)^39 - 1) / 0.0835 = $2,724,054.54

Adding the two future values together, we get the total account value after forty years:

FV = FV1 + FV2 = $2,789,524.76

Therefore, the account value after forty years is approximately $2,789,525.

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Answer: B and D.

Step-by-step explanation: We can simplify the expression -3.75+ 2(-4x +6.1) - 3.25x as follows:

-3.75+ 2(-4x +6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.25x + 8.45 (combining like terms)

Now, let's check each expression to see if it is equivalent to -11.25x + 8.45:

A. 7x-2x +8.2

= 5x + 8.2

Not equivalent to -11.25x + 8.45

B. 8.45-8x-3.25x

= 8.45 - 11.25x

Equivalent to -11.25x + 8.45

C. -1.75-7.25x=6.1

This is not an expression, it is an equation. It is not equivalent to -11.25x + 8.45.

D. -11.25x +12.2 - 3.75

= -11.25x + 8.45

Equivalent to -11.25x + 8.45

Therefore, the expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x are B and D.

Answer:

  x ∈ {6, 7, 8, 9, 10}

Step-by-step explanation:

You want possible values of whole number x such that ...

  4 ≤ √3 +√x < 5

We can solve this inequality by first subtracting √3 from all sides:

  4 -√3 < √x < 5 -√3

Squaring these positive numbers does not change their order:

  19 -8√3 < x < 28 -10√3

  5.14 < x < 10.67

The value of x may be any whole number in the range 6–10, inclusive.

Answer:

[tex]x^{2} + y^{2} = 36[/tex]

Step-by-step explanation:

The form of the equation for a circle is [tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex], where [tex](h, k)[/tex] is the center and [tex]r[/tex] is the radius. Here, (h, k) is (0,0) and r is 6, so the equation would just be [tex]x^{2} + y^{2} = 36[/tex].

Answer:

x² + y² = 36 (top right answer)

Formula for the circle:

(x - h)² + (y - k)² = r²

h = X center point  

k = Y center point

the earned interest after 3 years is $1,608.75.

What is simple interest?

Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal (initial amount)

r = interest rate per year (as a decimal)

t = time (in years)

Substituting the given values, we have:

P = $9,750

r = 0.055 (since the interest rate is 5.5%)

t = 3

I = $9,750 * 0.055 * 3

I = $1,608.75

Therefore, the earned interest after 3 years is $1,608.75.

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C) 36 yards   18*6=108

108ft to yards is 36

Answer:C

Step-by-step explanation:

Each jump rope is 6 feet long, so 18 jump ropes would require a total of:

18 x 6 = 108 feet of rope

Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:

108 ÷ 3 = 36 yards

Therefore, the football coach should buy 36 yards of rope. The answer is (C).

Answer: D

Step-by-step explanation:

The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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