The perimeter of a rectangle is 44 inches. If the width of the rectangle is 8 inches, what is the length? OA. 14 inches​

\(4x=-17\) has the same solution as  \(5x+8=x-9\)

Option (E) is correct

"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =."

We have,

\(5x+8=x-9\)

By solving the given equation

⇒\(5x-x=-9-8\)

⇒\(4x=-17\)

Clearly, Option (E) is correct

⇒\(x=\frac{-17}{4}\)

Explanation for other options:

(A) \(4x=-1\)

⇒\(x=\frac{-1}{4}\)

(B) \(4x=17\)

⇒\(x=\frac{17}{4}\)

(C) \(6x=-17\)

⇒\(x=\frac{-17}{6}\)

(D) \(6x=17\)

⇒\(x=\frac{17}{6}\)

∴ \(4x=-17\) has the same solution as \(5x+8=x-9\)

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The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

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

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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Answer: 3/8

Step-by-step explanation:

1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8

The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Answer:

exact form = \(\frac{13}{10}\)

decimal form = 1.3

mixed number form = 1 \(\frac{3}{10}\)

Step-by-step explanation:

2\(\frac{4}{5}\) - 1 \(\frac{1}{2}\) = \(\frac{13}{10}\)

Answer:

you are doing -4. so the first parenthesis -4(x+2x+1) is incorrect.

Step-by-step explanation:

Hope this helps plz hit the crown :D

Answer:

-4(x-4)²+9y(y+4)=0

Step-by-step explanation:

If we put the -64 with the x’s instead of the y’s, we get:

-4x²+32x-64+9y²+36y=0

-4(x²-8x+16)+9y(y+4)=0

-4(x-4)²+9y(y+4)=0

Answer:

34,500

Step-by-step explanation:

34,528 rounds down rather than up because 528 is closer to 500 than 600 so it will round down to 34,500

Answer:

34,500

Step-by-step explanation:

34,528 = 34,500 because when you round the 5 in the hundred place the 2 isn't high enough to make the 5 round up so its 34,500.

5-10 round up 1-4 round down.

Answer:

b=4

Step-by-step explanation:

\(a^{2}+b^{2}=c^{2}\)

\(3^{2}+b^{2}=5^{2}\)

\(9+b^{2}=25\)

\(b^{2}=16\)

\(\sqrt{b^{2}} = \sqrt{16}\)

b=4

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

The correct answer is A

Step-by-step explanation:

Hope this helps

Answer:

670,000

Step-by-step explanation:

because 10 to the 4 power is 10,000 just add the zero of the number and times 67 give you the answer 670,000

9514 1404 393

Answer:

  1. asymptotes: x=-6, x=6, y=0; zero: x=0

  2. 20 blue fish

Step-by-step explanation:

1. The vertical asymptotes are where the denominator is zero. It factors as (x-6)(x+6), so will have zeros at x=-6 and x=6.

The horizontal asymptote is at the limit when x goes to infinity. Here, the ratio of highest-degree terms is 6/x, so the value goes to zero as x gets large.

The zero is where the numerator is zero, at x=0.

In summary:

__

2. 60% are red, so 40% are blue. The difference in percentages is 60%-40% = 20%. The percentage of blue fish (40%) is twice the difference (=2×20%), so the number of blue fish is twice the difference in numbers.

  blue fish = 2×10 = 20 fish

Check

There are then 20+10=30 red fish, so 20+30=50 fish total. Reds are 30/50 = 60% of the total.

Additional comment

I find it often works well to work with ratios, which I can often do in my head. Other folks like to see equations. Here, we could write equations like ...

  r = 60%(r + b) . . . . reds are 60% of the total

  r - b = 10 . . . . . . . . 10 more reds than blues

We want the value of b, so we can eliminate r by substituting for it:

  r = 10 + b . . . . from the second equation above

  (10 +b) = 0.60((10 +b) + b) . . . . substitute for r

  10 +b = 6 + 1.2b . . . simplify

  4 = 0.2b . . . . subtract b+6

  20 = b . . . . . . multiply by 5 (there are 20 blue fish)

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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The problem can be expressed as follows:

20x^2 = 20x

where x is a nonzero number.

To solve for x, we can simplify the equation by dividing both sides by 20:

x^2 = x/1

Now, we can solve for x by subtracting x/1 from both sides of the equation:

x^2 - x/1 = 0

Next, we can factor out x to get:

x(x - 1/1) = 0

This equation can be satisfied if either x = 0 or x - 1 = 0. However, x cannot be equal to 0 since the problem states that x is a nonzero number. Therefore, the only solution is:

x = 1

So, the nonzero number is 1.

Answer:

225 calories

Step-by-step explanation:

1 recipe makes

12 standard sized pancakes

2 pancakes are 1/6 of the recipe

1/6 of the recipe has 150 calories

6 × 150 calories = 900 calories

The full recipe of 12 pancakes has 900 calories

1/2 recipe was made

1/2 recipe has 1/2 × 900 calories = 450 calories

1/2 recipe made 8 pancakes

4 pancakes are half of the half recipe or 1/4 recipe

1/4 × 900 calories = 225 calories

The mode, median, mean ,weighted mean, spread of the set of data are: 125, 190, 278429,  765 respectively

We are asked to find the following

Mode:  This is the highest occurred frequency in a set of data and the mode here is 125

The median is the middle frequency when arranged in an order of magnitude the the set of data is  $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000. the median is 190

The mean is the average of the data that is: ( $125,000,+$125,000+$178,000+$190,000+$216,000+$225,000+$890,000)/7 = 1949000/7 = 279429

the spread is the range which is the highest frequency minus the lowest frequency =  $890,000 -$125,000= 765000

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Answer:

median

Step-by-step explanation:

Answer:

g(6) = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(n) = n + 2

g(6) is n = 2

Step 2: Evaluate

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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6.

(a)

The slope for the side AB is:

The slope for the side BC is:

The slope for the side DC is:

And the slope for AD is:

(b) According to the previous results:

(c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram

Complete Question

Given two independent random samples with the following results:

\(n_2=13\ , \= x_2=171\ s_1=23\)  

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.

Answer:

Step 1 of 3:

    \(\= x_p  =  15\)

Step 2 of 3:

    \(E =7.79\)

Step 3 of 3:

   \( 7.21 < \mu_1 - \mu_2 < 22.79\)

Step-by-step explanation:

Now considering the Step 1 of 3, the  point estimate that should be used in constructing the confidence interval  is mathematically represented as  

        \(\= x_p = \= x_1 - \= x_2\)

=>     \(\= x_p = 186 - 171\)

=>     \(\= x_p = 15\)

Now considering the Step 2 of 3

Given that the confidence level is  90% then the level of significance is mathematically represented as

     \(\alpha = (100-90)\%\)

=>    \(\alpha = 0.10\)

Generally the degree of freedom is mathematically represented as

        \(df = n_1 + n_2 - 2\)

=>    \(df = 13 + 13 - 2\)

=>   \(df = 24\)

From the student t-distribution table the critical value of  \(\frac{\alpha }{2}\) at a degree of freedom of  \(df = 24 \ is \ \ t_{\frac{\alpha }{2} ,df} = 1.711\)

Generally the pooled variance is mathematically represented as    

  \(s_p^2 = \frac{ (13 -1 ) 33^2 + (13 -1 ) 23^2 }{(13 - 1 )(13 - 1)}\)

         \(s_p^2 = 134.83 \)

Generally the margin of error is mathematically represented as

  \(E = t_{\frac{\alpha }{2} ,df } * \sqrt{\frac{s_p^2}{n_1} +\frac{s_p^2}{n_2} }\)

=>     \(E = 1.711* \sqrt{\frac{134.83}{13} +\frac{134.83}{13}}\)

=>     \(E =7.79\)

Now considering the Step 3 of 3

Generally the 90% confidence interval is mathematically represented as

              \(\= x_p -E < \mu_1 - \mu_2 < \= x_p +E\)

=>  \( 15 -7.79 < \mu_1 - \mu_2 < 15 +7.79\)

=>  \( 7.21 < \mu_1 - \mu_2 < 22.79\)

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Answer:

403.3 feet per second

Step-by-step explanation:

please mark brainlest

Answer:

She had a total of 80 throws.

Step-by-step explanation:

4x20 (20x5%=100%) = 80, so she had 80 throws.

Answer:55+52=107 and 55times5s equals 2860

Step-by-step explanation:

The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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