I'm having a hard time understanding how
x2+3x=0
then x(x+3)=0
breaks down to x=-3,0

A system of equations can be used to determine whether the paths of the boats cross include the following:

A. y = -1/9(x - 1)² + 10.

    y = 1/8x² - 7

Based on the information provided about the first boat, the x-coordinate of the vertex can be determined as follows;

x = -b/2a

1 = -b/2a

b = -2a

Additionally, the standard form of the equation of a parabola (quadratic function) is given by;

y = a(x - h)² + k.

y = ax² - 2ax + c.

Therefore, the y-coordinate of the vertex is given by:

y = ax² - 2ax + c

10 = a(1)² - 2a(1) + c  

c - a = 10   .......equation 1.

Since the parabola passes through the point (-8, 1), we have:

y = ax² - 2ax + c

1 = a(-8)² - 2a(-8) + c  

80a + c = 1     .......equation 1.

Solving equations 1 and 2 simultaneously, we have:

81a = -9

a = -9/81 = -1/9

b = -2a = -2(-1/9) = 2/9

c = 10 + a = 10 - 1/9 = 89/9

Rewriting the equation for the first boat, we have:

y = -1/9x² + 2/9x + 89/9

y = -1/9(x - 1)² + 10.

For the second boat, the x-coordinate of the vertex can be determined as follows:

y = ax² + bx + c

x = -b/2a

0 = -b/2a

b = 0

Additionally, the y-coordinate of the vertex is given by:

y = ax² + c

-7 = a(0)² + c  

c = -7

Since the parabola passes through the point (-8, 1), we have:

y = ax² + c

1 = a(-8)² - 7

a = -1/8

b = 0

c = -7

Rewriting the equation for the second boat, we have:

y = ax² + c

y = 1/8x² - 7

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Answer: A

Step-by-step explanation:

edge 2023

The derivative for each of the definite integrals using the fundamental theorem of calculus is

a) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt is 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

b)  d/dx ∫ x³(4sin(t³−3))dt is 12(b²sin(b³-3) - a²sin(a³-3))

The fundamental theorem of calculus tells us that the derivative of the definite integral of a function f(x) with respect to x is equal to the function evaluated at the upper limit of integration minus the function evaluated at the lower limit of integration. In other words, if we have an integral of the form ∫f(x)dx evaluated from a to b, then

d/dx ∫f(x)dx = f(b) - f(a)

Let's apply this to the first integral, A).

A) d/dx ∫ 4x(2(6cos(t)+7)⁴)dt

We begin by recognizing that the function inside the integral is a function of t, not x. However, we want to take the derivative with respect to x. This means that we need to use the chain rule to differentiate the integrand with respect to x.

Using the chain rule, we have

d/dx [4x(2(6cos(t)+7)⁴)] = 4(2(6cos(t)+7)⁴)(d/dx [4x])

= 4(2(6cos(t)+7)⁴)(4)

= 32(2(6cos(t)+7)⁴)

Now, we can apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ 4x(2(6cos(t)+7)⁴)dt = [4b(2(6cos(t)+7)⁴)] - [4a(2(6cos(t)+7)⁴)]

= 4(2(6cos(b)+7)⁴) - 4(2(6cos(a)+7)⁴)

This is the final answer for A).

Now, let's move on to integral B).

B) d/dx ∫ x³(4sin(t³−3))dt

Again, we need to use the chain rule to differentiate the integrand with respect to x.

d/dx [x³(4sin(t³−3))] = (d/dx [x³])(4sin(t³−3))

= 3x²(4sin(t³−3))

Now, we apply the fundamental theorem of calculus. Let's say we are evaluating the integral from a to b. Then,

d/dx ∫ x³(4sin(t³−3))dt = [3b²(4sin(t³−3))] - [3a²(4sin(t³−3))]

= 12(b²sin(b³-3) - a²sin(a³-3))

This is the final answer for B).

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Answer: We know that the area of the base of a cylinder is given by the formula:

A = πr²

where A is the area of the base, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the base.

To find the perimeter of the base, we need to know the circumference of the circle that forms the base of the cylinder. The formula for the circumference is:

C = 2πr

where C is the circumference and r is the radius.

To find the radius of the base, we can rearrange the formula for the area:

A = πr²

r² = A/π

r = √(A/π)

Substituting the given value for the area of the base, we get:

r = √(38.5/π) ≈ 3.5 m

Now, we can use the formula for the circumference to find the perimeter of the base:

C = 2πr = 2π(3.5) ≈ 22 m

Therefore, the perimeter of the base is approximately 22 meters.

Step-by-step explanation:

Answer:

We need to find the value of f(g(10)) when k = 3, where f(x) = 6x - 2 and g(x) = 5x - kx + 15.

First, we need to evaluate g(10) when k = 3:

g(x) = 5x - kx + 15

g(10) = 5(10) - 3(10) + 15

g(10) = 50 - 30 + 15

g(10) = 35

Now that we know g(10) = 35, we can evaluate f(g(10)):

f(x) = 6x - 2

f(g(10)) = 6(35) - 2

f(g(10)) = 208

Therefore, when k = 3, f(g(10)) = 208.

The equation x/√16+x² can be rewritten by using x= 4 tan θ as x/4.

The given expression is x/√16+x^2 and we need to rewrite it by using x= 4 tan θ.

We know that 1 + tan2θ = sec2θ ⇒ 1 = sec2θ − tan2θ ... (1)

x = 4tanθ⇒ x/4 = tanθ ... (2)

Let's substitute (2) in (1) and get:

sec2θ − tan2θ = sec2θ − x²/16 ... (3)

Now, let's simplify the denominator and numerator of x/√16+x² using trigonometry.

We have:

x/√16+x²= x/[4sec2θ]

Using (2), we know that x = 4 tanθ, so substituting this in (3) we get:

sec2θ − x²/16 = sec2θ − (4tanθ)2/16= sec2θ − tan2θ= 1 (from equation (1))

Therefore,

x/√16+x²= x/[4sec2θ] = x/[4√(sec2θ − tan2θ)] (from equation (3))= x/[4√1]= x/4

Hence, x= 4 tan as x/4 can be used to rewrite x/16+x².

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The surface area of a cube with a volume of 4913 cubic yards is 972 square yards.

Surface area is the measurement of the total area of a 3D object. It is the sum of all the individual faces of a 3D object, including the area of each side of the object. It is a way to measure the total exposed area of an object, including any protrusions or indentations.

The surface area of a cube is the sum of the areas of the six faces of the cube. The formula for the surface area of a cube is 6 × s2, where s is the length of the side of the cube.

In this case, the volume of the cube is 4913 cubic yards, so the length of the side of the cube is ∛4913 = 17. Therefore, the surface area of the cube is 6 × 172 = 972 square yards.

To find the surface area of a cube, the first step is to determine the length of the side of the cube. This is done by finding the cube root of the volume (in this case, 4913). Once the length of the side is known, the surface area of the cube is simply 6 times the length of the side squared.

In conclusion, the surface area of a cube with a volume of 4913 cubic yards is 972 square yards.

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Answer:

  8.65 g/cm³

Step-by-step explanation:

You want the density of a bronze statue with a volume of 36 cm³ and a mass of 311.4 g.

Density is the ratio of mass to volume:

  ρ = mass/volume = (311.4 g)/(36 cm³) ≈ 8.65 g/cm³

The density of the statue is about 8.65 g/cm³.

The principal mortgage amount is $220,000.

To compute the principal loan amount, we need to apply the compound interest formulation for a loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where M is the monthly reimbursement, P is the primary mortgage amount, i is the month-to-month interest charge, and n is the range of months.

First, we need to calculate the month-to-month interest charge:

i = 2.49% / 12 = 0.02075

Subsequent, we want to calculate the range of months:

n = 30 years x 12 months/year = 360 months

Now we are able to plug in the given values:

$986.50 = P [ 0.02075(1 + 0.02075)^360 ] / [ (1 + 0.02075)^360 – 1]

Solving for P, we get:

P = $221,114.07

Rounding to the nearest ten thousand dollars, the principal mortgage amount is $220,000.

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Answer: -1

Step-by-step explanation:

An easy way to figure out the slop of a linear graph is the formula:

(y1-y2)/(x1-x2)

In order to use this, find two spots on the line that run exactly through a point, in this example (0,20) and (20,0).

Plug in the xs and ys into the formula, which gets you  

(20-0) / (0-20)

When simplified, the result is -1 and that is your slope

Answer:

17:85

Step-by-step explanation:

Answer:

The perimeter of the portrait is $2\times(1+2)=6$ yards.

To find the cost of the frame, we need to calculate the length of the frame needed, which is the same as the perimeter of the portrait. So, the length of the frame needed is 6 yards.

The cost of the frame will be the cost per yard multiplied by the length of the frame:

$6~\text{yards} \times $10.17/\text{yard} = $61.02$

Therefore, the frame will cost $61.02.

The PMF of X+Y is given byP(X + Y = k) = P(X = 0,Y = k) + P(X = 1,Y = k-1) + P(X = 1,Y = k) = (1/2)(1/3)^k + (1/2)(1/3)^(k-1) + (1/2)(1/3)^(k-1)for k = 0, 1, 2.

The CDF of X+Y can be determined as below:P(X + Y = 0) = (1/2)(1/3)^0 = 1/2P(X + Y ≤ 1) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) = 1/2 + (1/2)(1/3) + (1/2)(1/3) = 5/6P(X + Y ≤ 2) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) + P(X = 1,Y = 1) + P(X = 0,Y = 2) = 1/2 + (1/2)(1/3) + (1/2)(1/3) + (1/2)(1/3)(2/3) + (1/2)(1/3)^2 = 11/18P(X + Y ≤ 3) = 1, as the range of X+Y is 0, 1, 2.

The expectation of X+Y can be determined asE(X + Y) = E(X) + E(Y) = 1/2 + 1/3 = 5/6

The variance of X+Y can be determined asVar(X + Y) = Var(X) + Var(Y) = (1/2)(1/2) + (1/3)(2/3) = 7/18

The expectation of X⋅Y can be determined as below: E(X⋅Y) = P(X = 1,Y = 1) = (1/2)(1/3) = 1/6

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A. Differently organized; B. Different rates; C. Inconvenient access; D. Limited membership.

To calculate the interest rate on a loan, you will need to figure out the amount of interest you will need to pay over the life of the loan. First, you will need to determine the loan amount, the interest rate, and the loan term. Then, you will need to calculate the total interest by multiplying the loan amount by the interest rate and the loan term. Finally, you will need to divide the total interest by the loan amount and then multiply that by 100 to get the annual percentage rate (APR). This will give you the interest rate you will need to pay over the life of the loan.

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Answer:

7.5%

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

In order to express 150 mL as a percentage of 2 liters (2000 mL), you need to divide 150 by 2000 and then multiply the result by 100 to get the percentage.

Therefore, 150 mL is 7.5% of 2 liters.

98 Degrees and 82 degrees  are  the measurements of the numbered angles of this circle.

What is a circle?

With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

                           The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The symmetry line of reflection is formed by each line that traverses the circle. Moreover, it possesses rotational symmetry around the center for each angle.

Measure of angle 1 = (33 + 131)/2

                         = 82 degrees

Measure of angle 2 = 180 - 82

                         = 98 Degrees

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well, Not from tips that'd be 100% - 9% = 91%, so 91% of $7000.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{91\% of 7000}}{\left( \cfrac{91}{100} \right)7000}\implies \text{\LARGE 6370}[/tex]

There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.

This hypothesis is either rejected or accepted, depending on whether the population or sample under investigation is viable.

In other words, the null hypothesis is an assertion that the sample observations are the result of chance. It is asserted that surveyors who are interested in the data have made this allegation. It has the prefix H0.

Let p be the proportion of authors who support continuing the system.

Then hypotheses are:

H0: p=0.67

Ha: p>0.67

For calculating the test statistic:

z = p(s)-p/√ [p0(1-p)/N]

where, p(s) = 72/104 ≈ 0.692, p is 0.67 and N is the sample size =104

Then Z ≈ 0.477

The test statistic's p-value is 0.317.

Since 0.317>0.05 and we're assuming a significance level of 0.05, we are unable to reject the null hypothesis.

p-value 0.317 is the likelihood that the sample is chosen from the distribution assumed under null hypothesis, that is where the fraction of authors favouring the new publication scheme is at most 0.67.

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We can say that after answering the offered question The terms in the equation given equation can be streamlined and rearranged to produce the following equation: 23p – 101 = 64p – 40

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Using the equality properties, we can rewrite the preceding equation as follows:

2.3p – 10.1 = 6.5p – 4 – 0.01p

2.3p – 10.1 = 6.49p – 4

We can alter the equations using the equality characteristics to look for equations that have the same solution. The answers to the next two equations are the same as those for the previous one:

2.3p – 10.1 = 6.4p – 4

The following equation can be created by adding 0.09p to both sides of the given equation:

2.3p - 10.1 + 0.09p = 6.5p - 4 - 0.01p + 0.09p

2.39p – 10.1 = 6.4p – 4

23p – 101 = 65p – 40 – p

The terms in the given equation can be streamlined and rearranged to produce the following equation:

23p – 101 = 64p – 40

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The prime factorization of 6 is the expression of 6 as a product of its prime factors.

A prime factor is a prime number that is a factor of the given number. To find the prime factorization of 6, we need to express 6 as a product of its prime factors. Since 6 can be evenly divided by 2 and 3, which are both prime numbers, the prime factorization of 6 is 2 x 3. We can also write this as 2^1 x 3^1, using exponents to show that there is only one 2 and one 3 in the prime factorization of 6. Finally, since 2 and 3 are both prime, we order the factors from least to greatest as 2 x 3.

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Therefore , the solution of the given problem of area comes out to be section has a size of about 164.07 square centimetres.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.

Here,

The following algorithm determines a sector's area:

=> A = (θ/360°) * π * r²

where is the mathematical constant pi, r is the radius, and is the centre angle (approximately 3.14).

If we substitute the numbers provided, we get:

=> A = (30/360) * 3.14 * (12.5)^2

By condensing and computing, we arrive at:

=> A ≈ 164.06

To the closest hundredth, we have the following:

=> A ≈ 164.06 ≈ 164.07

Consequently, the section has a size of about 164.07 square centimetres.

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10. Domain: all real numbers; Vertical Asymptotes: x=14; Horizontal Asymptotes: none
11. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=5x+22
12. Domain: all real numbers; Vertical Asymptotes: x=0 and x=9; Horizontal Asymptotes: none
13. Domain: all real numbers; Vertical Asymptotes: x=-5; Horizontal Asymptotes: y=0
14. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x3
15. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x3-16x3
16. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x2-1
17. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=0
18. Domain: all real numbers; Vertical Asymptotes: x=-6; Horizontal Asymptotes: y=0
19. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=3x-14
20. x-intercepts: -4 and 1; y-intercepts: 5
21. x-intercepts: 0 and 1; y-intercepts: 0
22. x-intercepts: -8 and -3; y-intercepts: 7
23. x-intercepts: -1 and 6; y-intercepts: 0
24. x-intercepts: -2 and 0; y-intercepts: -1294

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We can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb]. This was calculated using a confidence interval formula for the mean.

The confidence interval for the mean concentration of THMs can be calculated using the formula x ± z * (s/√n), where x is the sample mean, z is the z-score for a given confidence level, s is the sample standard deviation and n is the sample size.

In this case, we have x = 3 ppb, s = 0.3 ppb, and n = 200. To calculate the confidence interval at a certain confidence level (e.g. 95%), we need to find the corresponding z-score. For a 95% confidence level, the z-score is approximately 1.96.

Substituting these values into the formula above gives us:

3 ± 1.96 * (0.3/√200) = [2.9584, 3.0416]

So we can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb].

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Answer:

35 Degrees

Step-by-step explanation:

Given in figure.

Happy to help :)

The solution is, the value of the angle ADF = 35° .

Here, we have,

from the given diagram, we get,

ABCD is a trapezium.

EBC is a straight line.

F is the point on AB so that DFE is a straight line.

Angle BEF = 45°

Angle FBC = 100°

now, we have,

angle FBE = 180 - 100

                 = 80 degrees

now, from triangle BEF , we get,

Angle EFB = 55 degrees

again, as AFB is vertically opposite angle,

so, angle AFB = Angle EFB = 55 degrees

finally from triangle ADF , we get,

Angle ADF = 180 - 90 - 55

                  = 90 - 55

                  = 35 degrees

so, the value of the angle ADF = 35° .

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Answer: a. 25.50(h)(25%) >= 160  

b. 26

Step-by-step explanation:

a. Let the number of hours Oliver works be h hours.

25.50(h)(25%) >= 160

b. 25.50(h)(25%) >= 160

h >= 25.1 (cor. to 3 sig. fig)

The minimum number of hours Oliver needs to work is 26 hours.

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

dudjeisosidheis9sjdhxisjdgskkjehud

Answer:

6

Step-by-step explanation:

.

Answer:

6

Step-by-step explanation:

look above

Peter will receive R134,417.50 of the profit.

Investment refers to the purchase of goods that are not consumed today but are used in the future to create wealth. In financial terms, investment typically involves buying assets such as stocks, bonds, real estate or other financial instruments with the expectation of earning a profit or income from them.

Khomo paid R245,000 for the house, so his investment ratio is:

245,000 / 575,000 = 0.426

Peter's investment ratio is:

1 - 0.426 = 0.574

If they share the profit in the same ratio as their respective investment, then Peter will receive:

0.574 x 234,500 = 134,417.5

Therefore, Peter will receive R134,417.50 of the profit.

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The system of equations created from the statements is 3m + 2l = 7 and 4m + l = 6

Let's define the variables:

Using these variables, we can create the following system of equations to represent the given information:

Equation 1: 3m + 2l = 7

Muffy ordered 3 muffins and 2 lattes for $7.

Equation 2: 4m + l = 6

Sammy ordered 4 muffins and a latte for $6.

Hence, the system is 3m + 2l = 7 and 4m + l = 6

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