the pair of points (−6, y) and (4, 8) (−6, y) and (4, 8) lie on a line with a slope of 5252. set up and solve for the missing y-value using the slope formula. show all work to receive credit.

The value of a can be either 13.11 cm or 3.33 cm. However, we need to round off the answer to the nearest tenth, which is one decimal place. So, the answer for the value of a is 13.1 cm.

In the given triangle ABC, we are supposed to find the value of a when b=13.7cm. We have been given that the measure of angle A is 53 degrees and the length of side c is 7 cm.

We know that the law of cosines states that c^2=a^2+b^2-2abcos(C)where C is the angle opposite to side c.

So, we can write 7^2 = a^2 + 13.7^2 - 2*13.7*a*cos(53) By solving this equation, we can find the value of a.

To solve the equation, we can first simplify it by using the value of cosine 53 degrees. cos(53) = 0.6

Now, substituting the value of cos(53) in the equation, we get49 = a^2 + 187.69 - 16.44a By bringing all the terms to one side, we get a^2 - 16.44a + 138.69 = 0

To find the value of a, we can use the quadratic formula. a = (-b ± √(b^2-4ac))/(2a)where a = 1, b = -16.44 and c = 138.69

Substituting the values in the formula, we geta = (16.44 ± √(16.44^2 - 4*1*138.69))/2*1a = (16.44 ± 9.78)/2a = 13.11 or a = 3.33

The value of a can be either 13.11 cm or 3.33 cm. However, we need to round off the answer to the nearest tenth, which is one decimal place.

So, the answer for the value of a is 13.1 cm.

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Answer:

-45/7

-7/7

-4/7

0/7

6/7

9/7

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

Answer:

subtract 2x on both sides

Step-by-step explanation:

Answer:

x= -3

Step-by-step explanation:

Move The Terms:

8x -2x =3 = -15

Collect like terms and calculate:

6x = -15-3

Divide both sides of the equation by 6:

x = -3

Final answer:

x= -3

Hope this helped have a good day

The number of years that it will take for the account balance to accumulate to the value of the car would be = 19 years.

The principal amount of money Sally deposits = $1,200

The interest rate for each year = 7%

The time = 1 year

Simple interest = principal×time × rate/100

= 1,200×1×7/100

= $84

In a year the money would be = 1200+84 = $1284

X years = $24,168.77

make X the subject of formula;

X = 24,168.77/1284

= 18.8 = 19 years

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Step-by-step explanation:

BBC sport football r madhava warrier the same the same the

Answer:

your answer will be option B) 5

Step-by-step explanation:

have a nice day!!

Answer:

Below

Step-by-step explanation:

y ( 5.98x - 5.81) - 2.19 y =

5.98xy - 5.81y      - 2.19 y

5.98xy + ( - 5.81y - 2.19 y)

5.98xy + ( - 8y )

5.98xy - 8y       or   y ( 5.98x-8)

Answer:

1.23

0.067

25.34

Step-by-step explanation:

10^2 = 100

The point moves two places towards the right

Using the formula of Confidence interval, a 90% one-sided upper confidence interval for mean SBP is 121.873.

Standard Deviation(s) = 9.9 mm HG

Sample Size(n) = 14

Sample Mean(m) = 118.3 mm HG

We have to construct a 90% one-sided upper confidence interval for mean SBP.

α = 1 - 90%

α = 1 - 0.90

α = 0.1

df = n - 1

df = 14 - 1

df = 13

One sided 90% upper confidence interval is given by

CI = m + tₐ × s/√n

CI = 118.3 + 1.3502 × 9.9/√14

CI = 118.3 + 1.3502 × 9.9/3.742

CI = 118.3 + 1.3502 × 2.646

CI = 118.3 + 3.573

CI = 121.873

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Answer:

x^3-4x^2+25x-100

Step-by-step explanation:

We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root

Combining the roots into a polynomial gives us:

(x+5i)(x-5i)(x-4)

Expand:

(x^2 + 25)(x-4)

x^3-4x^2+25x-100

If this year the population of the bear increased by 20% then the new population of bear in the preserve is 114 .

In the question ,

it is given that ,

there are bears in a nature preserve ,

the number of bears present in the nature preserve last year is = 95 ;

the percent increase in the population of the bear is = 20% ;

So , the new population is = 95 + 20% of 95

= 95 + 0.20×95     ....because 20% = 0.20

Simplifying further ,

we get ;

= 95 + 19  

= 114 bears .

Therefore , the new population of bear in the preserve is 114 .

The given question is incomplete , the complete question is

The population of bear on a nature preserve was 95 last year. This year , the population increased by 20%. What is the new bear population on the preserve ?

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Answer:

D.

Step-by-step explanation:

If ABC is congruent to DEC 4x - 1 = x + 2

3x = 3

x = 1

The inequality that shows the maximum number of hours Penelope can rent is 35 + 4x ≤ 75

An equation shows how two or more numbers and variables are related to each other.

Let x represent the number of hours to rent

There is a fixed $35 fee and an hourly fee of $4. Hence:

Total cost = 4x + 35

Penelope has a budget of $75. hence:

35 + 4x ≤ 75

The inequality is 35 + 4x ≤ 75

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The required percentage increase is given as 40% as per the given conditions.

Given that,
A visit to the zoo cost $80 per family last year and $112 this year. The percent of the increase in its price is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Last year cost = $80
Current year cost = $112
Percentage change = 112 - 80 / 80 = 0.4 or 40%

Thus, the required percentage increase is given as 40% as per the given conditions.

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Answer:

A. 4.5

Step-by-step explanation:

According to my graphing calculator, e^1.5=4.5 which is rounded to the nearest tenth.

Answer: e^1.5 = 4.482

Step-by-step explanation:

Given:  

We need to find the value of function at x=1.5

Put x=1.5 into f(x)

Now we will verify the result using graph.

First we draw the graph of f(x) and a vertical line x=1.5

Please see the attachment for graph.

Hence, The value of  

Answer:

x ≤ 2

Step-by-step explanation:

Expand

3x - 6 + x ≤ 2

Rearrange

4x ≤ 8

x ≤ 2

Answer:

x ≤ 2

Step-by-step explanation:

Step 1: Write inequality

3(x - 2) + x ≤ 2

Step 2: Solve for x

Here we see that any number less than or equal to 2 will work.

Answer:

64

Step-by-step explanation: 7^4=2401   4^4=256     2401/256= 64

Answer:

18cm

if it takes 12cm to wrap 6 presents, it means it takes 2cm to wrap one present.

9 individual presents will take 2 wraps, so Dwayne needs 18cm of wrapping paper.

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Answer:

higher than that. undeterminable without more variables

There are no sign changes in the first column of the Routh array, therefore the system is stable.

Given: Characteristic equation for system `(a)`: 12s⁵ + 4s⁴ + 6s³ + 2s² + 6s + 4 = 0

Characteristic equation for system `(b)`: 12s⁵ + 8s⁴ + 18s³ + 12s² + 9s + 6 = 0

To determine the stability of the systems with the given characteristic equations, we need to find out the roots of the given polynomial equations and check their stability using Routh-Hurwitz criteria.

To find out the stability of the system with given characteristic equation, we have to check the conditions of Routh-Hurwitz criteria.

Let's discuss these conditions:1. For the system to be stable, the coefficient of the first column of the Routh array must be greater than 0.2.

The number of sign changes in the first column of the Routh array represents the number of roots of the characteristic equation in the right-half of the s-plane.

This should be equal to zero for the system to be stable.

There should be no row in the Routh array which has all elements as zero.

If any such row exists, then the system is either unstable or marginally stable.

(a) Let's calculate Routh-Hurwitz array for the polynomial `12s⁵ + 4s⁴ + 6s³ + 2s² + 6s + 4 = 0`0: 12 6 42: 4 2.66733: 5.6667 2.22224: 2.2963.5 0.48149

Since, there are 2 sign changes in the first column of the Routh array, therefore the system is unstable.

(b) Let's calculate Routh-Hurwitz array for the polynomial `12s⁵ + 8s⁴ + 18s³ + 12s² + 9s + 6 = 0`0: 12 18 62: 8 12 03: 5.3333 0 04: 2 0 05: 6 0 0

Since there are no sign changes in the first column of the Routh array, therefore the system is stable.

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If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), then the following statements must be true: Option (b) f'(-1) = 0 and Option (d) the graph of f has a horizontal tangent line at x = 3

Explanation: The relative maximum of a function is the highest point in a particular set, and the relative minimum is the lowest point. If a function f is continuous for all x and has a relative maximum at (-1, 4) and a relative minimum at (3, -2), then the following statements must be true. The value of the derivative will be equal to zero at relative maximum and relative minimum points of the function. In other words, f'(-1) = 0 and f'(3) = 0. Thus, the option (b) is correct. The graph of f has a horizontal tangent line at the relative minimum and maximum points of the function. This implies that the graph of f has a horizontal tangent line at x = -1 and x = 3. Therefore, the option (d) is correct. The graph of f may or may not intersect both axes. There is no proof that the function f will intersect both axes. Therefore, option (e) is incorrect. The point of inflection is a point on a curve where the concavity of the function changes. Since the function f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), there is no certainty that the graph of f has a point of inflection between x = -1 and x = 3. As a result, option (a) is incorrect. Thus, the correct options are (b) f'(-1) = 0 and (d) The graph of f has a horizontal tangent line at x = 3.

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The first term will be 3 and the sum of the first 9 terms will be 81.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Given,

Six terms as 10.5

So,

a₆ = 10.5

Common difference(d) = 1.5

The nth term of an AP is given by

\(a_{n}\) = a + (n-1)d

So,

a₆ = a + (6-1)d

10.5 = a + 5(1.5)

a = 3

Now,

The Sum of n terms is given by

S = n/2[2a + (n-1)d]

S = 9/2[6 + 8(1.5)]

S = 81

Hence the first term will be 3 and the sum of 9 terms will be 81.

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The length of the ladder is - \(\sqrt{2x^{2} - 16x +64}\) . Option(D) is the correct answer.

According to the question,

The distance along the wall from the ground to the top of the ladder =x

The base of the ladder to the wall  = x - 8

The length of the ladder = L(x)

Using the Pythagorean theorem;

      L(x)² = (x - 8)² + x²

⇒ L(x)² = x² - 16x +64 + x² ( using (a-b)² formula)

⇒  L(x)² = 2x² - 16x +64

 ⇒ L(x) =\(\sqrt{2x^{2} - 16x +64}\)

∴ The length of the ladder is - \(\sqrt{2x^{2} - 16x +64}\) . Option(D) is the correct answer.

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The complete question is:

A ladder is leaning against a wall. Paul has measured and determined that the distance along the ground from the base of the ladder to the wall is eight inches less than the distance along the wall from the ground to the top of the ladder. Which of the following functions describes the length of the ladder in terms of x, the distance along the wall from the ground to the top of the ladder?

A. L(x) = \(\sqrt{2x - 8}\)

B. L(x) = \(\sqrt{2x^{2} - 64}\)

C. L(x) = \(\sqrt{2x^{2} + 16x +64}\)

D. L(x) = \(\sqrt{2x^{2} - 16x +64}\)

Answer:

A: Adjacent angles

Answer:

A. adjacent

Step-by-step explanation:

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

s

SO, LAST IS CORRECT

?ARK ME AS BRAILIEST

The expected value of the total return rate for the firm's clients in three types of equity investments is 7.4%.

The expected value of the total return rate for the firm's clients can be calculated by multiplying the rate of return for each equity investment type by the percentage of clients who invest in that type, and then summing up these values.

For A, multiply the rate of return (10%) by the percentage of clients who invest in A (30%).

= 0.10 * 0.30

= 0.03.

For B, multiply the rate of return (6%) by the percentage of clients who invest in B (50%).

= 0.06 * 0.50

= 0.03.

For C, multiply the rate of return (7%) by the percentage of clients who invest in C (20%).

= 0.07 * 0.20

= 0.014.

Sum up the results from steps 1, 2, and 3:

= 0.03 + 0.03 + 0.014

= 0.074.

Therefore, the expected value of the total return rate for the firm's clients is 7.4%.

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Answer:

8.6

Step-by-step explanation:

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The square root of the value 74 will be calculated as below:-

D = √74

D = 8.602325267

D = 8.6

Therefore, the square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

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The required greatest common factor in the given expression is 3x²y.

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

here,
Given expression,
= 18x⁴y+3x³y²-39x²y³+12x²y⁴
Taking common 3x²y from every term,
= 3x²y(6x² + xy - 13y² + 4y³)
Where 3x²y id the greatest common factor,

Thus, In terms of the given expression 3x²y is the greatest common factor.

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The volume of the stump is approximately 73316.6 cubic inches.

A right cylinder is a three-dimensional solid geometric shape that has a circular base and straight, parallel sides that form a curved surface.

The volume of a cylinder, which is given by:

                                V = πr²h

where V is the volume, r is the radius, and h is the height of the cylinder. Additionally, unit conversion from feet to inches is also used.

Here we have

The volume of a tree stump can be modeled by considering it as a right cylinder. Shaniece measures its height as 1. 5 ft and its radius as 36 in.

First, we need to convert the height and radius to the same units.

Let's convert the height to inches:

1.5 ft × 12 in/ft = 18 in

Hence, height h = 18 in and radius r = 36 in

Using the formula, the volume of a right cylinder (V) = πr²h

V = π(36)²(18) = 73316.57 in³

Rounding to the nearest tenth, we get:

V = 73316.6 in³

Therefore,

The volume of the stump is approximately 73316.6 cubic inches.

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