In ΔDEF, e = 67 inches, ∠F=37° and ∠D=70°. Find the area of ΔDEF, to the nearest 10th of an square inch. ​

There are 6 subgroups of order 7 in Z/28Z. To find them, you need to identify which elements of Z/28Z generate a group of order 7.

These elements are 1, 7, 13, 19, 25, and 27. Each element creates a subgroup of order 7. These subgroups are:

1) {1, 7, 13, 19, 25, 27, 28}
2) {1, 7, 13, 19, 25, 27}
3) {1, 7, 13, 19, 25}
4) {1, 7, 13, 19}
5) {1, 7, 13}
6) {1, 7}

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well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

A

Step-by-step explanation:

The diameter is 2πr or 4032π in this. The arc from B to C counterclockwise is 130° out of 360°. 130/360 multiplied by 4032 is 1456

If the radius of the circular ground be 2016 feet and angle between the radius given is 130 degrees then race car travelled 1456π feet which is option a.

Sector is basically length of that area of circle's arc which is formed by two radius of the circle. The length of sector is Θr where r is radius and Θ is angle made by both radius but in radian form.

We have been given radius equal to 2016 feet and angle 130°. We have to find the distance that race car had travelled by racing from point B to point A. It can be equal to the length of sector of the circular ground.

Sector BAC =130π/180* 2016

=262080π/180

=1456 feet.

Hence if the radius of the circular ground be 2016 feet and angle between the radius given is 130 degrees then race car travelled 1456π which is option a.

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The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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Answer:

in 1 minut he eats 21 and 1/2 of a hotdog

Step-by-step explanation:

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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Step-by-step explanation:

(5/4_3/4)×(_2/27)÷_4

5_3/4

1/4×_2/27÷_4

1/54÷4

=0.004629

The repeating decimal written as an infinite series using powers of 10 and geometric series as a fraction are

The infinite series of the repeating decimal can be using powers of 10 written as follows:

0.13-0.131313 = 0.13 + (-0.0013) + (-0.000013) + ...

This is a geometric series with first term 0.13 and common ratio -0.001. The sum of this series can be found using the formula for a geometric series:

where a = first term

r = common ratio. In this case, a = 0.13 and r = -0.001.

Substituting these values into the formula gives:

S = 0.13/(1-(-0.001))

S = 0.13/1.001

S = 13/100

Therefore the decimal written as an infinite and geometric series are :

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Answer:

$16.90

Step-by-step explanation:

First you need to find how much the markup is in dollars.

Multiply 13(0.3).

This will give you 3.9.

Then you add this to the original cost of the glasses.

13+3.9= 16.9.

So, the final cost of the glasses is $16.90.

It's reasonable to assume the sample distribution's shape would be similar to the population distribution's shape. However, without more information, we cannot confirm the exact shape of the distribution.

The center of the data distribution is represented by the mean. According to the national Census Bureau, the mean number of people in a household for the entire population is 4.66.

The variability of the population distribution is represented by the standard deviation. In this case, the standard deviation provided by the Census Bureau is 1.94.

So, the center of the data distribution is 4.66, and the variability of the population distribution is 1.94.

Since the Census Bureau has used a random sample of 225 homes, the sample mean (4.8) and standard deviation (2.1) could be used to estimate the population mean and standard deviation. However, these sample statistics are not necessarily equal to the population parameters.

As for the shape of the data distribution, it's difficult to predict without more information about the distribution itself. If the data is normally distributed, the shape would be bell-shaped. If the sample is representative of the population, it's reasonable to assume the sample distribution's shape would be similar to the population distribution's shape. However, without more information, we cannot confirm the exact shape of the distribution.

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⇒ n + n - 0.18n

collect terms and add them

⇒ 1.82n

B is the correct choice

\(\sf \rightarrow -\dfrac{1}{3} (6x+15)-3 \ \ = -2x -5-3 \ \ = -2x - 8\)

D is the correct choice.

\(\sf \rightarrow \dfrac{8+4*3}{5} \ = \ \dfrac{8+12}{5} \ = \ \dfrac{20}{5} \ = \ 4\)

There are 24 female over the age of 100.

(3 + 5) + 2 = 2(? + 2)

8 + 2 = 2? + 4

2? = 10 - 4

2? = 6

? = 3

∴ The missing number is 3

Answer:

Step-by-step explanation:

Q1

Combine like terms by taking n as a common factor :

n + n - 0.18n

n (1 + 1 - 0.18)

n (2 - 0.18)

B) 1.82n

Q2

Distribute terms in the parentheses :

-1/3 (6x + 15) - 3

(-1/3)(6x) + (-1/3)(15) - 3

-2x - 5 - 3

Combine like terms :

D) -2x - 8

Q3

Applying PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) :

Let's simplify the numerator first.

8 + 4 × 3 / 5

8 + 12 / 5

20/5

4

Q4

Subtract the number of males from the total to get the number of females :

30 - 6

24

Q5

Simplify the LHS and solve for the missing value in the RHS :

(Remember to apply PEMDAS!)

(3 + 5) + 2 = 2( _ + 2 )

8 + 2 = 2( _ + 2 )

10 = 2 ( _ + 2 )

_ + 2 = 5

_ = 3

Answer:

4 containers orange juice

4 containers pinapple

2 containers cranberry

Step-by-step explanation:

1000 milliliters are in a liter

4 liters orange juice, 4*500 = 2,000

4 liters pinapple, 4*500 = 2,000

2 liters cranberry, 2*500 = 1,000

Total 5 liters

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Emanuel did a mistake in her first step by taking negative sign twice.

Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.

Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.

For instance:

According to question,

= \(\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)\)

Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.

Correct steps are:

Step 1:

\(\frac{(3)(4)(-1)}{(5)(9)(2)}\)

Step 2:

\(\frac{-12}{90}\)

Step 3:

\(-\frac{2}{15}\)

Therefore, the step 1 was miscalculated by Emanuel.

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The complete question is -

Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?

The correct statements about the PACF plot and partial autocorrelations are:

b. The PACF plot starts at Lag 1.

The PACF plot starts at Lag 1. The first value in the PACF plot represents the partial autocorrelation at Lag 1.

c. The partial autocorrelation at lag 1 is the same as the autocorrelation at lag 1.

The partial autocorrelation at lag 1 is the same as the autocorrelation at lag 1. This is because the partial autocorrelation at Lag 1 measures the correlation between the variable and its lag 1 value, which is equivalent to the autocorrelation at Lag 1.

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(a) The total area under the curve is nearly equal to 24.

(b) The area under the curve by evaluating the function at the left-hand endpoints of the subintervals is 24.

(a) To approximate the area under the curve of f(x) = 8x - \(x^2\) from x = 0 to x = 4 using 2 subintervals and evaluating the function at the right-hand endpoints of the subintervals.

We can use the right-endpoint rule for approximating definite integrals:

First, we need to find the width of each subinterval:

Δx = (4-0) / 2 = 2

Then, we can evaluate the function at the right-hand endpoints of the subintervals and multiply by the width of each subinterval to find the area of each rectangle:

f(2) = 8(2) - \(2^2\) = 12

f(4) = 8(4) - \(4^2\) = - 8

Area of the first rectangle = f(2)Δx = 12(2) = 24

Area of the second rectangle = f(4)Δx = -8(2) = -16

The total area under the curve is the sum of the areas of the two rectangles:

Total area ≈ 24 + (-16) = 8

(b) To approximate the area under the curve of f(x) = 8x - \(x^2\) from x = 0 to x = 4 using 2 subintervals and evaluating the function at the left-hand endpoints of the subintervals, we can use the left-endpoint rule for approximating definite integrals:

The width of each subinterval is still Δx = 2.

Now, we evaluate the function at the left-hand endpoints of the subintervals and multiply by the width of each subinterval to find the area of each rectangle:

f(0) = 8(0) - \(0^2\) =0

f(2) = 8(2) - \(2^2\) =12

Area of the first rectangle = f(0)Δx = 0(2) = 0

Area of the second rectangle = f(2)Δx = 12(2) = 24

The total area under the curve is the sum of the areas of the two rectangles:

(a) To approximate the area under the curve of f(x) = 8x - \(x^2\) from x = 0 to x = 4 using 2 subintervals and evaluating the function at the right-hand endpoints of the subintervals, we can use the right-endpoint rule for approximating definite integrals:

First, we need to find the width of each subinterval:

Δx = (4-0)/2 = 2

Then, we can evaluate the function at the right-hand endpoints of the subintervals and multiply by the width of each subinterval to find the area of each rectangle:

f(2) = 8(2) -  \(2^2\) = 12

f(4) = 8(4) - \(4^2\) =-8

Area of the first rectangle = f(2)Δx = 12(2) = 24

Area of the second rectangle = f(4)Δx = -8(2) = -16

The total area under the curve is the sum of the areas of the two rectangles:

Total area ≈ 24 + (-16) = 8

(b) To approximate the area under the curve of f(x) = 8x - \(x^2\) from x = 0 to x = 4 using 2 subintervals and evaluating the function at the left-hand endpoints of the subintervals, we can use the left-endpoint rule for approximating definite integrals:

The width of each subinterval is still Δx = 2.

Now, we evaluate the function at the left-hand endpoints of the subintervals and multiply by the width of each subinterval to find the area of each rectangle:

f(0) = 8(0) -\(0^2\) =0

f(2) = 8(2) - \(2^2\) =12

Area of the first rectangle = f(0)Δx = 0(2) = 0

Area of the second rectangle = f(2)Δx = 12(2) = 24

The total area under the curve is the sum of the areas of the two rectangles:

Total area ≈ 0 + 24 = 24

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The total surface area of the pyramid is  335 square centimeters

The formula for determining the total surface area of a pyramid is expressed as;

TSI = 1/2(PI) + B

Given that;

Now, let's determine the base perimeter

Perimeter = 2( l + w)

Substitute the values

Perimeter = 2 ( 8 + 12)

Perimeter = 40 centimeters

The base area is given as;

Base area =  8(12)

Base area = 96 square centimeters

Substitute the values, we have;

Total surface area = 1/ 2 (40)(12) + 96

Total surface area = 240 + 96

Total surface area = 335 square centimeters

Hence, the value is 335 square centimeters

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The estimated cost of common equity for the high-risk division of Alice Corporations can be calculated using the Capital Asset Pricing Model (CAPM). Hence, the estimated cost of common equity for the high-risk division is 10.2%.

The Capital Asset Pricing Model (CAPM) is commonly used to estimate the cost of equity. It is based on the relationship between the expected return on an investment and its systematic risk (measured by beta). The formula for estimating the cost of equity using CAPM is as follows:

Cost of Equity = Risk-Free Rate + Beta * Market Risk Premium

Since the high-risk division can be financed optimally in line with others in the industry at 25% debt and 75% equity, we can assume that the beta for the division represents the weighted average of the industry's beta. Therefore, the estimated beta for the high-risk division is 1.5.

Plugging in the values into the CAPM formula:

Cost of Equity = 2.7% + 1.5 * 5%

= 2.7% + 7.5%

= 10.2%

Hence, the estimated cost of common equity for the high-risk division is 10.2%. This represents the expected return on equity based on the risk profile of the division as measured by its beta and the overall market conditions.

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Answer:

(C). (t² - p)( \(t^{4}\) + pt² + p²)

Step-by-step explanation:

a³ - b³ = (a - b)(a² + ab + b²)

\(t^{6}\) - p³ = (t²)³ - p³ = (t² - p)( \(t^{4}\) + pt² + p²)

Wronskian of y1 = e^{5x} and y2 = e^{−2x} is -7e^{3x}. General solution to differential equation (d²y/dx²) -10(dy/dx) + 25y = 0 is y(x) = c1e^{5x} + c2e^{-2x} on interval of (-∞, ∞).

To compute the Wronskian of the functions y1 = e^{5x} and y2 = e^{−2x}, we use the formula:

W(y1,y2) = y1*y2' - y1'*y2

where y1' and y2' denote the derivatives of y1 and y2 with respect to x, respectively.

Taking the derivatives, we have:

y1' = 5e^{5x}

y2' = -2e^{-2x}

Substituting these values into the formula, we get:

W(y1,y2) = e^{5x}*(-2e^{-2x}) - (5e^{5x})*e^{-2x}

W(y1,y2) = -2e^{3x}- 5e^{3x}

W(y1,y2) = -7e^{3x}

Therefore, the Wronskian of y1 = e^{5x }and y2 = e^{−2x} is -7e^{3x}.

To find the general solution to the differential equation (d² y)/(dx²) - 10(dy/dx) + 25y = 0, we use the fact that y1 and y2 are linearly independent solutions, and thus the general solution has the form:

y(x) = c1y1(x) + c2y2(x)

Substituting y1 and y2, we get:

y(x) = c1e^{5x} + c2e^{-2x}

This is the general solution on the entire real line (-∞, ∞).

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Answer: 320 miles

Step-by-step explanation:

Let the miles that they drove be represented by x.

Since Sarah drove two-fifths of the miles which is 128 miles, then the total miles would be:

= 2/5 × x = 128

0.4 × x = 128

0.4x = 128

x = 128/0.4

x = 320

The total miles is 320 miles.

The largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) is 15

Divisor of a Number :  

A Divisor is any number that divides a given number completely or with a reminder. Where a factor, is a divisor that divides the number entirely and leaves no remainder.

Here we have,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  

And n is a positive even integer  

For n = 2 ⇒  (2 + 1)(2 + 3)(2 + 5)(2 + 7)(2 + 9) = (3× 5 × 7 × 9 × 11 )    

For n = 4 ⇒   (4 + 1)(4 + 3)(4 + 5)(4 + 7)(4 + 9) = (5× 7 × 9 × 11 × 13 )

and so on.

From the above calculations,

we can say that (n + 1); (n + 3); (n + 5); (n + 7); (n + 9) are 5 consecutive odd numbers  

In every 5 consecutive odd positive integers,

One of them is always divisible by 3

And one of them is always divisible by 5.

Therefore,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

As we know product of 3 and 5 = 15

then (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15

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The complete question is

What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?  

(A) 3         (B)  5        (C)  11          (D) 15             (E)  165    

Based on the provided information, the mean of the area of the circle is 1/3 and the variance is 4/45.

The mean and variance of the area of a circle with a uniformly distributed radius on the interval (0,1) can be found using the expected value and variance formulas for continuous random variables.

The expected value (mean) of a continuous random variable X is given by:

E[X] = ∫xf(x)dx

Where f(x) is the probability density function of X. In this case, since the radius is uniformly distributed on the interval (0,1), the probability density function is f(x) = 1 for 0 ≤ x ≤ 1.

The expected value of the area of the circle is therefore:

E[A] = ∫a*f(a)da = ∫r^2*1dr = (1/3)r^3 for 0 ≤ r ≤ 1 = (1/3)(1)^3 - (1/3)(0)^3 = 1/3

The variance of a continuous random variable X is given by:

Var[X] = E[X^2] - (E[X])^2

The expected value of the square of the area of the circle is:

E[A^2] = ∫a^2*f(a)da = ∫r^4*1dr = (1/5)r^5 for 0 ≤ r ≤ 1 = (1/5)(1)^5 - (1/5)(0)^5 = 1/5

Therefore, the variance of the area of the circle is:

Var[A] = E[A^2] - (E[A])^2 = 1/5 - (1/3)^2 = 4/45

So the mean of the area of the circle is 1/3 and the variance is 4/45.

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Answer:

6.03 seconds

Step-by-step explanation:

Given

\(y = -16t\² + 96t + 3\)

To solve this, we simply set the height to 0.

i.e. \(y = 0\)

So, we have:

\(-16t\² + 96t + 3 = 0\)

Solve using quadratic formula.

\(t = \frac{-b+-\sqrt{b^2 - 4ac}}{2a}\)

Where

\(a = -16\)

\(b = 96\)

\(c = 3\)

\(t = \frac{-96+-\sqrt{96^2 - 4 * -16 * 3}}{2 * -16}\)

\(t = \frac{-96+-\sqrt{9216 +192}}{-32}\)

\(t = \frac{-96+-\sqrt{9408}}{-32}\)

\(t = \frac{-96+-96.9948452239}{-32}\)

\(t = \frac{-96+96.9948452239}{-32}\) or \(t = \frac{-96-96.9948452239}{-32}\)

\(t = \frac{0.9948452239}{-32}\) or \(t = \frac{-192.994845224}{-32}\)

\(t = -0.031088913245535\) or \(t = 6.0310889132455\)

Since time can't be negative, we have:

\(t = 6.0310889132455\)

\(t = 6.03\ seconds\) (approximated)

Answer:

last graph

Step-by-step explanation:

Answer:

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Step-by-step explanation:

Let the numbers be x and 5x.

Since x + 21 is smaller than 5x + 21, therefore according to the question,

21 + 5x = 2(x + 21)

21 + 5x = 2x + 42

Transposing 2x to LHS and 21 to RHS, we obtain

5x - 2x = 42 - 21

3x = 21

Dividing both sides by 3, we obtain

x = 7

First number is x = 7

Second number is 5x = 5 × 7 = 35

Hence, the numbers are 7 and 35 respectively.

Answer:

Step-by-step explanation:

Let the 2 consecutive integers be x and x+1.

x²+(x+1)²=1684

x²+(x+1)(x+1)=1684

x²+x²+x+x+1=1684

2x²+2x-1683=0

Using quadratic formular