How do I solve this equation?

48 feet long (horizontally) would a ramp need to extend to elevate a person from a height of 2 feet to a height of 6 feet

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.

Given, ADA guidelines mandate a 1:12 ratio of rise to run for wheelchair ramps.

That means to raise a height of 1 foot we need to give a slope of 12 feet.

Since total height to elevate = 6-2

Since total height to elevate = 4 feet

Thus, an increase in elevation that could result in = 4 * 12

an increase in elevation that could result in = 48 feet

Also given, If a ramp extends 30 feet horizontally

The maximum increase in elevation that could result in = 30 /12

therefore, the maximum increase in elevation that could result is 2.5 feet.

Learn more about scale here:

https://brainly.com/question/1287267

#SPJ2

The right-endpoint Riemann sum for the given integral is indeterminate due to the limit (∞ * 0).

To evaluate the integral ∫[2, 0] (3x² + 1) dx using a right-endpoint approximation to generate the Riemann sum, we can divide the interval [2, 0] into subintervals and calculate the sum of the areas of rectangles formed using the right endpoints of these subintervals.

Let's assume we divide the interval into n subintervals, each with a width of Δx. The width of each subinterval is given by Δx = (2-0)/n = 2/n.

Now, we can calculate the right endpoints of these subintervals as follows:

x_i = 2 - iΔx

where i ranges from 1 to n.

Next, we evaluate the function at the right endpoints:

f(x_i) = 3(x_i)² + 1

The Riemann sum is then given by:

R_n = Σ[1 to n] f(x_i)Δx

Substituting the values:

R_n = Σ[1 to n] (3(2-iΔx)² + 1)(2/n)

Simplifying the expression:

R_n = (2/n) * [ Σ[1 to n] 3(4 - 4iΔx + (iΔx)²) + Σ[1 to n] 1 ]

Now, we can evaluate the summations:

Σ[1 to n] 3(4 - 4iΔx + (iΔx)²) = 3Σ[1 to n] (4 - 4iΔx + (iΔx)²)

= 3Σ[1 to n] (4Δx - 4iΔx² + i^2Δx²)

Σ[1 to n] 1 = n

Substituting back into the Riemann sum expression:

R_n = (2/n) * [ 3Σ[1 to n] (4Δx - 4iΔx² + i^2Δx²) + n ]

Simplifying further:

R_n = (2/n) * [ 3(4nΔx - 4(Δx²)Σ[1 to n] i + (Δx²)Σ[1 to n] i²) + n ]

The summations Σ[1 to n] i and Σ[1 to n] i^2 can be evaluated using the formulas:Σ[1 to n] i = n(n + 1)/2

Σ[1 to n] i² = n(n + 1)(2n + 1)/6

Substituting these formulas into the Riemann sum expression:

R_n = (2/n) * [ 3(4nΔx - 4(Δx²)(n(n + 1)/2) + (Δx²)(n(n + 1)(2n + 1)/6) + n ]

Simplifying further:

R_n = (2/n) * [ 3(4nΔx - 2(Δx²)(n^2 + n) + (Δx²)(n² + n)(2n + 1)/3) + n ]

Now, we can substitute Δx = 2/n and simplify the expression:

R_n = (2/n) * [ 3(8n - 4(4/n)(n² + n) + (4/n)(n² + n)(2n + 1)/3) + n ]

R_n = (2/n) * [ 3(8n - 16(n² + n) + (2n² + 2n)(2n + 1)/3) + n ]

R_n = (2/n) * [ 3(8n - 16n² - 16n + (4n² + 4n)(2n + 1)/3) + n ]

R_n = (2/n) * [ 3(8n - 16n² - 16n + (8n^3 + 8n² + 4n² + 4n)/3) + n ]

Simplifying further:

R_n = (2/n) * [ 3(8n - 16n² - 16n + (8n^3 + 12n² + 4n)/3) + n ]

R_n = (2/n) * [ 3(8n - 16n² - 16n + (8n^3 + 12n² + 4n)/3) + n ]

R_n = (2/n) * [ 3(8n - 16n² - 16n + 8n^3/3 + 12n²/3 + 4n/3) + n ]

R_n = (2/n) * [ (24n - 48n² - 48n + 8n^3 + 12n² + 4n)/3 + n ]

R_n = (2/n) * [ (8n^3 - 36n² - 44n + 24n)/3 + n ]

R_n = (2/n) * [ (8n^3 - 36n² - 20n)/3 + n ]

R_n = (2/n) * [ (8n^3 - 36n² - 20n + 3n²)/3 + n ]

R_n = (2/n) * [ (8n^3 - 33n² - 20n)/3 + n ]

Now, we take the limit of the Riemann sum as n approaches infinity:

lim[ n→∞ ] R_n = lim[ n→∞ ] (2/n) * [ (8n³ - 33n^2 - 20n)/3 + n ]

Taking the limit of each term:

lim[ n→∞ ] (2/n) = 0

lim[ n→∞ ] (8n³ - 33n² - 20n)/3 = ∞

lim[ n→∞ ] n = ∞

Therefore, the limit of the Riemann sum as n approaches infinity is indeterminate (∞ * 0), and we cannot directly evaluate the integral using this method.

In summary, using a right-endpoint approximation to generate the Riemann sum, we have derived the expression for the Riemann sum but cannot evaluate it directly as the limit is indeterminate.

Learn more about integral

brainly.com/question/31433890

#SPJ11

Answer:

1) 4, 1.25, 2
2) 12, 5, 3

3) 2, 18, 5

4)5, 8, 12

Step-by-step explanation:

1) You had to either multiply/divide by 4

2)You had to either multiply/divide by 3

3)You had to either multiply/divide by 6

4)You had to either multiply/divide by 5

Solution

- The solution steps are given below;

Question 1

Question 2:

Answer:

we have the width is 8 cm and the diagonal line is 17 cm so to get the length you're going to use Pythagoras theorem so 8 centimetres will be represented by a 17cm will be represented by c then length will be represented by b so b squared is equals to c squared minus a squared say 17 squared - 8 squared 17 squared is 289 while 8 squared is 64 the result will be 225 so b squared is equals to 225 to get b we will get the square root so b is equals to 15 so our length is 15 the area is equals to length x width so 15 * 8 you get 120 square centimetres

120 square centimeters is the area of rectangle FGHK.

Area of a rectangle (A) is the product of its length (l) and width (w).

here, we have,

from the given figure,

we have the width is 8 cm and the diagonal line is 17 cm

so to get the length you're going to use Pythagoras theorem

so 8 centimeters will be represented by a

17cm will be represented by c

then length will be represented by b

so b squared is equals to c squared minus a squared

say 17 squared - 8 squared

17 squared is 289 while 8 squared is 64

the result will be 225

so b squared is equals to 225

to get b we will get the square root

so b is equals to 15

so our length is 15

the area is equals to length x width

so 15 * 8

you get 120 square centimeters.

hence, 120 square centimeters is the area of rectangle FGHK.

To learn more on Area click:

brainly.com/question/20693059

#SPJ2

(a) There are 20 people in the room.

We can simply use the set theory to find the total number of people in the room by following these steps:

1. Start with the number of math majors, which is 10.

2. Add the number of ECE majors, which is 10. However, 2 of them are math-ECE double majors, so we only add 8 new people (10 - 2 = 8).

3. Add the number of CS majors, which is 3. However, 1 of them is a math-CS double major, so we only add 2 new people (3 - 1 = 2). Now, add the numbers from each step: 10 (math majors) + 8 (ECE majors) + 2 (CS majors) = 20 There are 20 people in the room.

The number of 10-letter binary strings that do not contain the pattern "10" as a substring is 6824.Solution.

( c ) 6824 10-letter binary strings do not contain the pattern "10" as a substring.

To determine the number of 10-letter binary strings that do not contain the pattern "10" as a substring, we can use the principle of inclusion-exclusion (PIE).How many 10-letter binary strings do not contain the pattern "10" as a substring?The number of 10-letter binary strings that do not contain the pattern "10" as a substring is 6824.Solution:Let A be the set of all 10-letter binary strings, B be the set of all 10-letter binary strings that contain the pattern "10," and C be the set of all 10-letter binary strings that contain the pattern "010." Then, we want to find the cardinality of A \ B, which is the set of all 10-letter binary strings that do not contain the pattern "10" as a substring.By PIE,|B ∪ C| = |B| + |C| - |B ∩ C|We can count the cardinality of each set as follows:|B| = 2^9 (there are 9 places to put the "10," and the other digits can be either 0 or 1)|C| = 2^8 (there are 8 places to put the "010," and the other digits can be either 0 or 1)|B ∩ C| = 2^7 (there are 7 places to put the "10" and "0," and the other digits can be either 0 or 1)Therefore,|B ∪ C| = |B| + |C| - |B ∩ C| = 2^9 + 2^8 - 2^7 = 640A ∩ (B ∪ C)^c = (A ∩ B^c ∩ C^c)^cby De Morgan's laws.So,A \ B = A ∩ B^c = A ∩ (B ∪ C)^cTherefore,|A \ B| = |A ∩ (B ∪ C)^c| = |A| - |B ∪ C||A| = 2^10, so|A \ B| = 2^10 - |B ∪ C| = 2^10 - (2^9 + 2^8 - 2^7) = 6824Therefore, 6824 10-letter binary strings do not contain the pattern "10" as a substring.

(d) The number of 10-letter binary strings that do not contain the pattern "1010" as a sub-string is 5324.

We can use the principle of Inclusion and Exclusion to answer this question: There are 2^10 binary strings of length 10. However, we cannot allow binary strings that contain the pattern "1010".Let X1 denote the number of binary strings of length 10 that contain 1010 as a sub-string. Let X2 denote the number of binary strings of length 10 that contain 2 copies of 1010 as a sub-string. Let X3 denote the number of binary strings of length 10 that contain 3 copies of 1010 as a sub-string. Let X4 denote the number of binary strings of length 10 that contain 4 copies of 1010 as a sub-string. Then, by the principle of Inclusion and Exclusion, the number of 10-letter binary strings that do not contain the pattern "1010" as a sub-string is:2^10 - X1 + X2 - X3 + X4We need to calculate X1, X2, X3, and X4. Let us consider X1. Let us remove the sub-string 1010 from the binary string. Then we are left with a string of length 6, which can be any binary string. Thus, 2^6 binary strings of length 6 contain 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 4 ways (there are 4 positions where we can insert the sub-string 1010 back in). Thus, X1 = 4*2^6Similarly, we can calculate X2, X3, and X4.X2: Let us remove 2 copies of 1010 from the binary string. Then we are left with a string of length 2, which can be any binary string. Thus, 2^2 binary strings of length 2 contain 2 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 5 ways. Thus, X2 = 5*2^2.X3: Let us remove 3 copies of 1010 from the binary string. Then we are left with a string of length 14, which can be any binary string. Thus, 2^14 binary strings of length 14 contain 3 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 6 ways. Thus, X3 = 6*2^14.X4: Let us remove 4 copies of 1010 from the binary string. Then we are left with a string of length 18, which can be any binary string. Thus, 2^18 binary strings of length 18 contain 4 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 7 ways. Thus, X4 = 7*2^18.Now, we can substitute these values in our formula:2^10 - X1 + X2 - X3 + X4 = 2^10 - 4*2^6 + 5*2^2 - 6*2^14 + 7*2^18= 1024 - 256 + 20 - 98304 + 7340032= 7254416 Thus, 7254416 10-letter binary strings do not contain the pattern "1010" as a sub-string.

#SPJ11

Answer:

Step-by-step explanation:

We need to change the English writing into an inequality.

We know that a number "n" added to 7 is less than or equal to 9.

This can be written as follows:

n + 7 ≤ 9

Now, we will isolate the "n" at one side of the inequality. We will do this by subtracting 7 from both side as follows:

n + 7 - 7 ≤ 9 - 7

n ≤ 2

Answer:

n+7≤9 or n≤2

Step-by-step explanation:

A number= n

plus 7= +7

less than or equal to=≤

9= 9

n+7≤9

n+7-7≤9-7

n≤2

Answer:

k=24

Step-by-step explanation:

The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.

f=-x^2+8x+20

Differentiating both sides:

f'=(-x^2+8x+20)'

By sum rule:

f'=(-x^2)'+(8x)'+(20)'

By constant multiple rule:

f'=-(x^2)'+8(x)'+(20)'

By constant rule:

f'=-(x^2)+8(x)'+0

By power rule:

f'=-2x+8

f' at x=a is -2a+8

This is the slope of any tangent line to the curve f.

The slope of g is 4 if you compare it to slope intercept form y=mx+b.

So we gave -2a+8=4.

Subtracr 8 on both sides: -2a=-4

Divide both sides by -2: a=2

The tangent line to the curve at x=2 is y=4x+k.

To tind y we must first know the y-coordinate of the point of tangency.

If x=2, then

f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32

So the point is (2,32).

g(x)=4x+k and we know g(2)=32.

This gives us:

32=4(2)+k

32=8+k

k=32-8

k=24

From the tangent given, the value of k will be 24.

From the information given, g(x) = 4x + k and this is a tangent to f(x)= -x² +8x + 20.

f(x)= -x² +8x + 20

= f'(x)  = -2x  + 8

The slope of tangent = -2x + 8  at (x , y)

g(x) = 4x  + k  

Hence, slope = 4

-2x + 8 = 4

Collect like terms

-2x = 4 - 8

-2x = - 4

Divide both side by -2

-2x/-2 = -4/-2

x = 2

f(x)= -x² +8x +20

where, x = 2

y = -2² + 8(2) + 20  

y =  32

Hence (2 , 32) lies on g(x)= 4x+k

32 = 4(2) + k

32 = 8 + k

k = 32 - 8

k = 24

In conclusion, the value of k is 24.

Learn more about tangent on:

https://brainly.com/question/13598644

Answer:

7

Step-by-step explanation:

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB. The cosine of angle X in triangle XYZ is given as 2.5/5.59.

When a triangle is dilated by a scale factor, the corresponding sides of the original and dilated triangles are proportional. In this case, triangle XYZ was dilated by a scale factor of 2 to create triangle ACB.

To find the relationship between the corresponding angles of the two triangles, we can use the fact that the corresponding sides are proportional. Since the scale factor is 2, the corresponding sides of triangle ACB are twice the length of the corresponding sides of triangle XYZ.

Now, let's focus on angle X. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. Since we don't have information about the type of triangle XYZ, we cannot determine the exact lengths of the sides. However, given that the cosine of angle X is 2.5/5.59, we can conclude that the ratio of the adjacent side to the hypotenuse in triangle XYZ is the same as the corresponding ratio in triangle ACB, due to the proportional relationship between the sides.

Therefore, the cosine of angle X in triangle ACB will also be 2.5/5.59.

Learn more about angle here:

brainly.com/question/13954458

#SPJ11

Answer:

16

Step-by-step explanation:

You're doing a subtraction problem between (x+5) and (2x+3)

(x+5) - (2x+3) =

**You need to solve for x first then plug it in to find the answer.***

(I had to break the parentheses because that is the only way to solve)

-x +8

x= -8

-8 + 5 - (-16+3)

-3 + 16 + 3

13 + 3 = 16

Answer:

-x+2

Step-by-step explanation:

(x+5)-(2x+3)
distribute
x+5-2x-3
combine like terms
x-2x+5-3
-x+2

Answer:

Step-by-step explanation:

In a triangle, the sides have a ratio of 3:7:10. If the perimeter is 210 feet, what is the length of the longest side in feet? (A) * 10.5 (B) 31.5 (C) (D) 105​

[210 : (3 + 7 + 10)] x 10 = 105 ft (your answer)

Step-by-step explanation:

the ratio tells us into how many units the total amount is split and then distributed among the different parts or members of the ratio.

3:7:10 means there are 3+7+10 = 20 units of length.

210 ft is the total of all lengths.

this is now split into these 20 units.

that means one unit of length for the ratio is

210/20 = 10.5 ft

the longest side is clearly the one with 10 units in the ratio.

so, it has

10×10.5 = 105 ft

Assuming an equal probability of having a girl or a boy for each child, the probability that a couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

If we assume that the probability of having a girl or a boy for each child is equal (which is a simplifying assumption), then the probability of having a girl for each child is 1/2, and the probability of having a boy is also 1/2.

To find the probability that the couple does not have girls for all three children, we need to find the probability of having a boy for each child. Since the gender of each child is independent of the others, we can multiply the probabilities together.

So, the probability of having a boy for the first child is 1/2, for the second child is also 1/2, and for the third child is also 1/2.

Multiplying these probabilities together, we get:

(1/2) * (1/2) * (1/2) = 1/8

Therefore, the probability that the couple does not have girls for all three children is 1/8 or approximately 0.125 (12.5%).

To learn more about probability  Click Here: brainly.com/question/31828911

#SPJ11

The intervals on which the function is increasing is (0, 1). Option D

A polynomial is a type of mathematical expression that has variables that are raised to whole number powers.

Since the factors of 5 are 1 and 5, we'll try to factor the polynomial by assuming that (x-1) and (x-5) are factors.

The product of (x-1) and (x-5) is (x² - 6x + 5), which is the polynomial we're given.

⇒ (x² - 6x + 5) is the factored form of the polynomial.

A polynomial is increasing on the intervals where it's greater than zero. So we just need to look at the sign of (x² - 6x + 5) for values between 1 and 5.

For values between 1 and 5, the function is always positive, so it's increasing on the interval (1, 5). Therefore, the increasing interval is (1, 5).

Learn more about polynomials on https://brainly.com/question/11536910

#SPJ1

Answer:

option 6b):) is correct

Answer:

The Student has 72% out of 100%

Step-by-step explanation:

Its the same thing but with fractions

The system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

To create a system of equations where the solution is (3, -4), we can assign arbitrary values to the coefficients of the equations. Let's use the following values:

Equation 1: 4x + 1y = 8

Equation 2: 2x - 3y = -17

By plugging in the values (3, -4) into these equations, we can find the missing coefficients:

Equation 1: 4(3) + 1(-4) = 12 - 4 = 8

Equation 2: 2(3) - 3(-4) = 6 + 12 = 18 - 17 = -17

Therefore, the system of equations that satisfies the solution (3, -4) is:

4x + 1y = 8

2x - 3y = -17

Learn more about equation at https://brainly.com/question/29174899

#SPJ1

Answer:

3/2 is the slope

Step-by-step explanation:

Answer:

with what

Step-by-step explanation:

Answer:

the Carroll is 1110 kilometer far

60 miles is equal to 96.56 kilometers.

To convert miles to kilometers, you can use the conversion factor of 1 mile  = 1.60934 kilometers. To convert 60 miles to kilometers, you would multiply 60 by 1.60934.

60 miles * 1.60934 kilometers/mile = 96.56 kilometers

Another way to think about it is that 1 mile is about 1.6 kilometers, so 60 miles is about 60 x 1.6 = 96 kilometers

It's important to remember that when measuring distance, the Units of measurement must be consistent. For units of example, if you are measuring the distance between two cities, it would not make sense to use miles for one city and kilometers for the other.

In short, 60 miles is equivalent to 96.56 kilometers, which is a standard unit of measurement used in most of the world.

Know more about Units of Measurement

https://brainly.com/question/777464                                                                            #SPJ11

Answer:

9

Step-by-step explanation:

.9 is bigger than 5 so we can round 8 up to 9

Answer:

x-intercept= (5,0)

y-intercept= (0,-2)

Slope= 2/5

Step-by-step explanation:

The original area can be calculated by dividing by 1,000,000. thus option C is correct.

One kilometer is equal to 1000 times meters. To convert meters into kilometers divide the factor by 1000 meters.

1 km = 1000 m

Beth is trying to convert an area from meters squared to kilometers squared.

She divided the area she had by 1000 and got the wrong answer because we can only convert one unit by dividing with 1000.

The original area can be calculated dividing by 1,000,000.

Learn more about kilometers;

https://brainly.com/question/13987481

#SPJ2

The value of the given integral is \((-1/18)ln|x| - (1/36)ln|6x^2-1|\)+ C, where C is the constant of integration.

To evaluate the integral, we can use integration by substitution. Let u = x² - x, then \(\frac{du}{dx}\) = 2x - 1 and dx = \(\frac{du}{(2x-1)}\). Substituting this in the integral, we get:

We can further simplify this by breaking the integral into partial fractions:

\(\frac{u}{(18x(2x-1))}\) = A/x + B/(2x-1)

u = A(2x-1) + Bx

Equating coefficients, we get A = -1/18 and B = 1/18. Substituting these values, we get:

∫ \(\frac{(x^2 - x)}{(36x^3 - 6x)}\) dx = (-1/18)∫ \(\frac{dx}{x}\) + (1/18)∫ dx/(2x-1)

= \((-1/18)ln|x|\) - (1/36)ln|2x-1| + C

Since the natural logarithm function is only defined for positive values, we need to use absolute values in the final answer to account for negative values of x. Therefore, the answer is  

\((-1/18)ln|x| - (1/36)ln|6x^2-1|\) + C.

Learn more about Integrals:

https://brainly.com/question/22008756

#SPJ4

We have:tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(7/2)

To prove the equation tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) without using a calculator, we can utilize the trigonometric properties and identities to simplify the expression.

Let's start by using the addition formula for the tangent function:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

We can rewrite the given expression as:

tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2)

Using the addition formula, we can combine the first two terms:

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)((1/11 + 5/6) / (1 - (1/11)*(5/6)))

Simplifying further:

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)((11/66 + 55/66) / (1 - 5/66))

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)(66/66 / (61/66))

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)(1)

Using the same approach, we can combine the remaining terms:

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)((1/3 + 1/2) / (1 - (1/3)*(1/2)))

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)((5/6) / (3/2))

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(5/9)

Now, we have:

tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(1) + tan^(-1)(5/9)

Using the addition formula again:

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)((1 + 5/9) / (1 - (1)*(5/9)))

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)((14/9) / (4/9))

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)(14/4)

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)(7/2)

For more such question on tan visit:

https://brainly.com/question/28587485

#SPJ8

In the box plot, most of the data is clustered around 75 - 78 (option A).

A box plot is used to study the distribution and level of a set of numbers. The box plot has two whiskers and a box. The two whiskers represent the minimum value and the maximum value.

The first line on the box is the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile. Majority of the data would lie between the first quartile and the third quartile.

To learn more about box plots, please check: https://brainly.com/question/27215146

#SPJ1

The possible algebraic equations, obtained based on the algebraic expressions in the question are;

1. \(\frac{x}{8} = y\)

2. 15 - n = m

3. 25 + x = y

An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.

What is an algebraic equation?

An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.

The algebraic expressions can be presented as follows;

1. Some number divided by 8

Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question

The equation with x as the number and y as the result can be presented as follows;

2. n less than 15

The expression n less than 15 is; 15 - n

Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;

3. 25 more than a number

Let x represent the number, we get

25 more than a number = 25 + x

The y represent the result or value of the expression 25 + x, we get the following algebraic equation;

Learn more on writing equations here: https://brainly.com/question/1918577

#SPJ1

The set (3,7,9,12) is a part of a solution set for which inequality The inequality that the set (3,7,9,12) is a part of a solution set is not given.

We can find the inequality that contains these numbers by using the following steps. Step 1: Arrange the numbers in increasing order as (3,7,9,12).Step 2: To find the inequality, we need to find the smallest and largest values in the set. Step 3: The smallest value in the set is 3 and the largest value is 12.

We can form the inequality 3 ≤ x ≤ 12, where x is the variable that the inequality relates to.Step 4: Thus, the set (3,7,9,12) is a part of the solution set for the inequality 3 ≤ x ≤ 12, where x is a real number .In conclusion, the inequality containing the set (3,7,9,12) is 3 ≤ x ≤ 12. This means that any value of x that falls between 3 and 12, inclusive, would make the inequality true.

To know more about inequality visit:

https://brainly.com/question/32145656

#SPJ11

Answer:

sin(θ)  =  -6/10  =  -0.60 and tan(θ)  =  -6/8  =  -0.75.

Step-by-step explanation:

Since  cos(θ) = adjacent / hypotenuse  in a right triangle andsince cos(θ) = 0.8  =  8/10   --->   adjacent = 8  and  hypotenuse  =  10.Using the Pythagorean Theorem, opposite = +6  or  -6, depending upon the quadrant.Since tan(θ) < 0, the triangle is found in either the second quadrant or the fourth quadrant.Since cos(θ) > 0, the triangle is found in either the first quadrant or the fourth quadrant.Therefore, it must be in the fourth quadrant.In the fourth quadrant, sin(θ) < 0, making the opposite side -6.--->   sin(θ)  =  -6/10  =  -0.60.--->   tan(θ)  =  -6/8  =  -0.75.