Given the trinomial 5x2 - 2x - 3, predict the type of solutions.

Two rational solutions
One rational solution
Two irrational solutions
Two complex solutions

To calculate the height of a sail that is four times as high as it is wide and made from 32 square meters of material, we use the area formula for a triangle and find that the height is 16 meters.

The student's question concerns the height of a sail in the shape of a right triangle, where the sail's height is four times its width and the total area of the sail is 32 square meters. To find the height, we can let the width be x meters, which makes the height 4x meters due to the given ratio.

Using the formula for the area of a triangle, A = bh/2, where b is the base and h is the height, we can write an equation for the area in terms of x: 32 m² = x × (4x) / 2.

Simplifying this, we get 32 = 2x2, which can be further simplified to x² = 16. Taking the square root of both sides gives us x = 4. Therefore, the height of the sail, being four times the width, is 16 meters.

Answer:

Simultaneous Equation

Step-by-step explanation:

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

To get the number of dimes and the number of quarters q will definitely have to be by simultaneous equation

let the number of dimes be d

let the number of quarters be q

let the cost of quarters/ one  be Q

let the cost of dime/one be  D

q+d=18--------------1

Qq+Dd=2.85.........2

from equation 1

q=18-d

substituting the value of q into equation 2

Q(18-d)+Dd=2.85

if cost of quarters/ one  is given and the cost of dime/one is also given we can go ahead to find

q and d

In this mathematical problem involving a system of equations, we use the information provided about the total number of coins and their total value to form two equations: q + d = 18 and 0.25q + 0.10d = 2.85.

The subject of this question is Mathematics, specifically dealing with a system of equations. Given the problem, the system of equations can be formulated from the conditions that the student has 18 coins in total and their combined value is $2.85. These conditions give us two equations:

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Answer:

A. 90° clockwise rotation around point A of pre-image JKL

Step-by-step explanation:

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Finding the rate of change in something with respect to something is known as differentiation. For Example, Change in y with respect to x is known as the derivative of y with respect to x.

(a) [tex]9{x}^2-{y}^2 = 1[/tex]

Differentiating equation with respect to x :

[tex]9*2x - 2y\frac{dy}{dx} = 0\\ 18x = 2y\frac{dy}{dx}\\9\frac{x}{y} =\frac{dy}{dx}[/tex]

(b)

[tex]9{x}^2-{y}^2 = 1\\9{x}^2-1 = {y}^2 \\\sqrt[2]{9{x}^2-1} = y\\[/tex]

differentiating with respect to x gives:

[tex]\frac{1}{2\sqrt{9{x}^2-1} } *(18x) = \frac{dy}{dx}\\\frac{1}{\sqrt{9{x}^2-1} } *(9x) = \frac{dy}{dx}[/tex]

(c) [tex]9\frac{x}{y} =\frac{dy}{dx}[/tex]

substituting value of y

[tex]\sqrt[2]{9{x}^2-1} = y\\\\\frac{9x}{\sqrt[2]{9{x}^2-1}} = \frac{dy}{dx}[/tex]

Hence the solution is consistent.

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Answer:

can confirm that the answer above is correct

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Step-by-step explanation:

Answer:

[tex]h(x)=2x^2+14x-60[/tex]

Step-by-step explanation:

This question can be solved by two methods

Method 1: Substitute x=3 and x=-10 in all the equations and determine which equals to zero (ie., check h(3)=0 and h(-10)=0 for all the equations)

Equation 1

[tex]h(x)=x^2-13x-30[/tex]

[tex]h(3)=3^2-13(3)-30[/tex]

[tex]h(3)=-60[/tex]

As h(3)≠0, Equation 1 is discounted

Equation 2

[tex]h(x)=x^2-7x-30[/tex]

[tex]h(3)=3^2-7(3)-30[/tex]

[tex]h(3)=-42[/tex]

As h(3)≠0, Equation 2 is discounted

Equation 3

[tex]h(x)=2x^2+26x-60[/tex]

[tex]h(3)=2(3)^2+26(3)-60[/tex]

[tex]h(3)=36[/tex]

As h(3)≠0, Equation 3 is discounted

Equation 4

[tex]h(x)=2x^2+14x-60[/tex]

[tex]h(3)=2(3)^2+14(3)-60[/tex]

[tex]h(3)=0[/tex]

[tex]h(x)=2x^2+14x-60[/tex]

[tex]h(-10)=2(-10)^2+14(-10)-60[/tex]

[tex]h(-10)=0[/tex]

As h(3)=0 and h(-10)=0, Equation 4 represents h(x)

Method 2: Solve to find the roots of each equation where h(x)=0 using the quadratic formula. Roots should be x=3,x=-10

The quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

where a, b and c are as below

[tex]h(x)=ax^2+bx+c=0[/tex]

Equation 1

[tex]h(x)=x^2-13x-30=0[/tex]

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{13\±\sqrt{(-13)^2-4(1)(-30)}}{2(1)}[/tex]

[tex]x=15,x=-2[/tex]

As roots are not x=3 and x=-10, Equation 1 is discounted

Equation 2

[tex]h(x)=x^2-7x-30[/tex]

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-30)}}{2(1)}[/tex]

[tex]x=10,x=-3[/tex]

As roots are not x=3 and x=-10, Equation 2 is discounted

Equation 3

[tex]h(x)=2x^2+26x-60[/tex]

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(26)\±\sqrt{(26)^2-4(2)(-60)}}{2(2)}[/tex]

[tex]x=2,x=-15[/tex]

As roots are not x=3 and x=-10, Equation 3 is discounted

Equation 4

[tex]h(x)=2x^2+14x-60[/tex]

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(14)\±\sqrt{(14)^2-4(2)(-60)}}{2(2)}[/tex]

[tex]x=3,x=-10[/tex]

As roots are x=3 and x=-10, Equation 4 represents h(x)

To solve the equation 15-28i=3l+(4m)i, separate the real and imaginary parts of the equation and solve for l and m separately.

To solve the equation 15-28i=3l+(4m)i, we can separate the real and imaginary parts of the equation. The real part is 15, and the imaginary part is -28. Similarly, the real part of the right side is 3l and the imaginary part is 4m. Equating the real parts and imaginary parts separately, we get two equations: 15 = 3l and -28 = 4m. Solving these equations will give us the values of l and m.

In the first equation, dividing both sides by 3 gives us l = 5. In the second equation, dividing both sides by 4 gives us m = -7.

Therefore, the solution to the equation 15-28i=3l+(4m)i is l = 5 and m = -7.

Answer:

false

Step-by-step explanation:

Answer:

The correct answer is D. The simplified form of the expression 7^4 is 2,401.

Step-by-step explanation:

7 ^ 4, that is, the exponentiation of 7 to the fourth power, implies the continuous multiplication of the number 7 for 4 times. Therefore, this number will appear 4 times in a multiplication, whose result will be said number exposed to the fourth power.

Simplified, this operation translates into 7x7x7x7, whose result is 2,401.

Final answer:

To calculate the value of the car in 8 years with a constant yearly depreciation rate of 5.1%, we can use the formula for compound interest.

Explanation:

To calculate the value of the car in 8 years, we can use the formula for compound interest: A = P(1 - r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial amount is $9,250, the interest rate is 5.1%, and the number of times interest is compounded per year is 1. Plugging these values into the formula, we get:

A = 9250(1 - 0.051/1)^(1*8) = $6630.27

Therefore, the car will be worth approximately $6,630.27 in 8 years.

The numerical value of cosh(ln5) is 2.55, obtained by using the hyperbolic cosine function definition and the properties of exponential and logarithmic functions.

The question asks you to find the numerical value of cosh (ln5). This involves using hyperbolic trigonometry functions, specifically the hyperbolic cosine function.

The hyperbolic cosine, represented by 'cosh', is a mathematical function whose definition is similar to the ordinary trigonometric cosine function. However, it is defined using exponential functions rather than angular measure. The general definition is cosh(x) = (e^x + e^(-x))/2.

Using this formula and substituting ln5 for x results in cosh(ln5) = (e^(ln5) + e^(-ln5))/2.

The expression e^(ln5) simplifies to 5 since e and ln are inverse functions.

For the second term, e^(-ln5), we can use the fact that a negative exponent signifies taking the reciprocal, so this simplifies to 1/5.

Therefore, cosh(ln5) = (5 + 1/5)/2 = 5.1/2 = 2.55.

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The solution to cosh (ln5) is obtained by substituting ln5 in the formula of hyperbolic cosine function, which simplifies it to (5 + 1/5)/2 yielding a result of 2.6.

To find the numerical value of cosh (ln5), we need to know the definition of cosh. It is a hyperbolic function defined as cosh(x) = (e^x + e^-x)/2 where e is Euler's number (approximately 2.71828).

So, to find cosh (ln5), we substitute ln5 in place of x in the formula cosh(x) = (e^x + e^-x)/2.

This gives us cosh(ln5) = (e^ln5 + e^-ln5)/2. However, e and ln are inverse functions, so e^ln5 simplifies to 5. Similarly, for e^-ln5, we need to use the property a^-b = 1/a^b to simplify it to 1/5.

Then we just add and divide, yielding cosh(ln5) = (5 + 1/5)/2 = 2.6.

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There are 840 seats in total in Cinema Hall.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given:

First term, [tex]a_1[/tex] = 22

second row = 22 + 3 = 25

Third row = 25 + 3 = 28

So, the Recursive Formula is

[tex]a_n[/tex] = a + (n-1)d

[tex]a_n[/tex] = 10 + (n-1)3

[tex]a_n[/tex] = 10 + 3n - 3

[tex]a_n[/tex] = 7 + 3n

In 21th rows the seats are

= 7 +3 (21)

= 7 + 63 = 70

Now, to find the number of seats in hall we have to find the sum of seats from row 1 to row 21 using Formula

= n×([tex]a_1[/tex]+ [tex]a_n[/tex])/2

= 21 x (10 + 70) /2

= 21 x 80 /2

= 21 x 40

= 840

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Answer:

50

Step-by-step explanation:

10=20/100*50/1=1000/100=10

Using the normal distribution, it is found that:

a) [tex]Z_0 = -1.75[/tex].

b) [tex]Z_0 = 1.96[/tex].

c) [tex]Z_0 = 1.645[/tex].

d) [tex]Z_0 = -0.83[/tex].

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

This is Z with a p-value of 0.0401, thus [tex]Z_0 = -1.75[/tex].

Item b:

Item c:

Same logic as b, just middle 90%, thus [tex]Z_0 = 1.645[/tex].

Item d:

This is Z with a p-value of 1 - 0.2967 = 0.2033, thus [tex]Z_0 = -0.83[/tex].

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Final answer:

The value of the standard normal random variable Z that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

Explanation:

The z-score that corresponds to the area 0.90 under the standard normal distribution can be found using a z-table or a calculator.

Therefore, the value of the standard normal random variable Z, denoted as Z0, that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

The absolute maximum occurs at x = -1, where y = 5. The absolute minimum occurs at x = 1, where y = 1.

To find the absolute extrema of a function on a closed interval, we first need to find the critical points of the function within that interval. The critical points occur where the derivative of the function is equal to zero or does not exist.

In this case, the function is y = 3x^(2/3) - 2x, and the closed interval is [-1, 1].

We can find the derivative of the function:

y' = 2x^(-1/3) - 2

Setting the derivative equal to zero and solving for x:

2x^(-1/3) - 2 = 0

x^(-1/3) = 1

Raising both sides to the power of -3 gives:

x = 1

We found one critical point at x = 1. Now we need to check the endpoints of the closed interval, which are -1 and 1. Evaluating the function at these points:

y(-1) = 3(-1)^(2/3) - 2(-1) = 5

y(1) = 3(1)^(2/3) - 2(1) = 1

Therefore, the absolute maximum of the function occurs at x = -1, where y = 5, and the absolute minimum occurs at x = 1, where y = 1.

The correct answer is:C. 1,092 people per square mile

To calculate the population density of a state, we divide the total population by the total area. In this case, the state has 1,627,260 people living within 1,490 square miles. We perform the following calculation:

Population Density = Total Population / Total Area

Population Density = 1,627,260 people / 1,490 square miles

When we perform the division, we get approximately 1092.12 people per square mile. Rounding to the nearest whole number, we get a population density of 1,092 people per square mile.

Therefore, the correct answer is:C. 1,092 people per square mile

In the given sets, the concept AB + BC = AC is used to create equations in terms of x. After each equation is solved, you can find the lengths of AB and BC by substituting the value of x into their respective original equations.

For this mathematics problem, you have to make use of the concept that the sum of the parts equals the whole. Specifically, this concept translates to the equation AB + BC = AC, as AC is the entire segment that encompasses both parts AB and BC.

For each of the sets you provided:

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Answer:

b

Step-by-step explanation:

Answer:

D) Group D

Step-by-step explanation:

A range: 38

B range: 48

C range: 40

D range: 51