HELP ME ON THIS QUESTION PLZ!!!

Integration is the process of combining the quantitative and qualitative data collecting and analysis strands of a mixed methods study for comparison and analysis, or for one strand to inform the other.

Let, 1 + x = t

differentiate the assumption

dx = dt

Substitute the values

=> ∫dt/t

=> ln t

In terms of x

=> ln(1 + x)²

Let, x = tan A

differentiate the assumption

dx = sec²A dA

Substitute the values

=>∫(sec²A dA)/(1 + tan²A)

=> ∫ dA

=> A

In terms of x

=> tan⁻¹x

Let, 1 + x² = t

differentiate the assumption

2xdx = dt

Substitute the values

=> ∫dt/2t

=> ln 2t²

In terms of x

=> ln(1 + x²)²

=> ∫(x² +1 - 1)dx/(1 + x²)

=> ∫dx + ∫dx/(1 + x²)

Now we can solve this as problem 2

= ∫sin x.(1 - cos²x) dx

= ∫sin x dx - ∫sin x. cos²x dx --- (1)

= I₁ - I₂ , where I₁ = ∫sin x dx and I₂ = ∫sin x. cos²x dx

Now, I₁ = ∫sin x dx = -cos x + C₁, where C₁ is the constant of integration ---- (2)

For I₂ = ∫sin x. cos²x dx, assume cos x = u ⇒ -sin x dx = du ⇒ sin x dx = -du

I₂ = ∫sin x. cos²x dx

= ∫u² (-du)

= - ∫u² du

= - u³/3 + C₂, where C₂ is the constant of integration

= (-1/3) cos³x + C2 ---- (3)

Substitute the values from (2) and (3) in (1),

∫sin³x dx = (-cos x + C₁) - ((-1/3) cos³x + C₂)

= -cos x + (1/3) cos³x + C₁ - C₂

= -cos x + (1/3) cos³x + C, where C = C₁ - C₂

⇒ ∫sin³x dx = -cos x + (1/3) cos³x + C

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1 gallon = 4 quarts.

2 gallons = 4 x2 = 8 quarts

She needs 8 quarts total and has 3 quarts.

8-3 = 5

She needs 5 more quarts.

Answer:

\((x-(3+\sqrt5))\) or \((x-3-\sqrt5)\) is a factor of the given polynomial.

Step-by-step explanation:

Let us learn the concept with an example first.

Let the polynomial be a quadratic function \(g(x)\).

\(g(x) = x^{2} -5x+6\)

The roots of \(g(x)\) are 2 and 3.

Putting \(x= 2\ in \ g(x)\)

\(2^2-5\times 2+6 = 4-10+6 =0\)

Putting \(x= 3\ in \ g(x)\)

\(3^2-5\times 3+6 = 9-15+6 =0\)

Putting x = 2 or x = 3, g(x) = 0 \(\therefore\) The roots of equation g(x) are 2 and 3.

Now, let us try to factorize g(x):

\(x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)\)

so, the equation can be written as:

\(g(x) = x^{2} -5x+6=(x-3)(x-2)\) where 3 and 2 are the roots of equation.

The factors are (x-3) and (x-2).

\(\therefore\) for the polynomial f(x) which has roots \(3+\sqrt5\ and\ -6\) will have a factor:

\((x-(3+\sqrt5))\) or \((x-3-\sqrt5)\)

Answer:

-539.25

Step-by-step explanation:

(w^2x−3)÷10⋅z

w=−9, x = 2.7, and z=−25

((-9)^2*2.7−3)÷10⋅(-25)

Parentheses first

The exponent in the parentheses

(81*2.7−3)÷10⋅(-25)

Then multiply

(218.7−3)÷10⋅(-25)

Then subtract

(215.7)÷10⋅(-25)

Now multiply and divide from left to right

21.57*(-25)

-539.25

Answer: It's -1 2/25.

Step-by-step explanation:

the area of a rectangle is

length × width

the perimeter of a rectangle is

2×length + 2×width

so,

length×width = 48 cm²

2×length + 2×width = 28 cm

length + width = 14 cm

length = 14 - width

we use this in the first equation :

(14 - width) × width = 48

14×width - width² = 48

-width² + 14×width - 48 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = -1

b = 14

c = -48

width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =

= (-14 ± sqrt(196 - 192))/-2 =

= (-14 ± sqrt(4))/-2 =

= (-14 ± 2)/-2 =

= 7 ± 1

width1 = 7 + 1 = 8 cm

width2 = 7 - 1 = 6 cm

length1 = 14 - width1 = 14 - 8 = 6 cm

length2 = 14 - width2 = 14 - 6 = 8 cm

so, we see, one of them must be 8 cm, and the other 6 cm.

let's length be the longer side, so

length = 8 cm

width = 6 cm

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

The angles marked 1 and 2 share the vertical line as a common side, so they are "adjacent" angles. Each is the sum of an acute angle and a right angle, so is "obtuse."

None of the other descriptors apply.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Looking at the graph, we can see that there is a point on the graph that lies on the vertical line x = 4 and has a corresponding y-value of 3. This point is the point (4, 3). So, the value of f(4) is 3.

In mathematics, a function is a relation between two sets of objects in which each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).

To find f(4) from the given graph, we need to locate the point on the graph that corresponds to x = 4 and read off the corresponding value of y.

The graph shows that there is a point (4, 3) on the graph of the function y = f(x). This means that when x = 4, the value of y (or f(x)) is 3. Therefore, f(4) = 3.

In general, to evaluate a function at a given point, we need to substitute that point's value for the independent variable (in this case, x) in the function expression and simplify the resulting expression.

However, in this case, we are given the value of x and simply need to read off the value of y from the graph.

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The complete question is given below.

Answer:

The given equation is

\(y=4x+3\)

To graph this equation, we need to create a table for all the coordinates pairs.

 X      Y

 0      3

-3/4    0

So, we have two points, (0,3) and (-3/4, 0). Now, we graph them to draw a straight line as the image attached shows.

To find the slope, we use those points.

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{0-3}{-\frac{3}{4} -0} =\frac{-3}{-\frac{3}{4} }\\ m=4\)

So, the slope is 4.

The angle of inclination is found by the formula

\(tan \theta = m\)

Where \(\theta\) is the angle and \(m\) is the slope.

\(\theta = tan^{-1}(4) \approx 76\°\)

Therefore, the angle of inclination is 76°, approximately.

Since the adjustable-rate mortgage is more expensive than the fixed-rate mortgage, the answer is $158,184 rounded to the nearest dollar.

To calculate the total cost of the adjustable-rate mortgage, we need to add up all the payments for the 30-year term:

Total cost = 5 years of payments at 4% + 10 years of payments at 6% + 10 years of payments at 8% + 5 years of payments at 10%

Total cost = (5 x 12 x $2,506.43) + (10 x 12 x $3,059.46) + (10 x 12 x $3,464.78) + (5 x 12 x $3,630.65)

Total cost = $150,385.80 + $367,135.20 + $415,773.60 + $217,839.00

Total cost = $1,151,133.60

To calculate the total cost of the fixed-rate mortgage, we can use a mortgage calculator or formula:

Total cost = Monthly payment x Number of payments

Total cost = $2,763.35 x 360

Total cost = $993,606

The difference in total cost between the two mortgages is:

Difference = Fixed-rate mortgage cost - Adjustable-rate mortgage cost

Difference = $993,606 - $1,151,133.60

Difference = -$157,527.60

Thus, the answer is $158,184 rounded to the nearest dollar. Therefore, the correct option is C.

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Answer:

12 miles

Step-by-step explanation:

3 miles per 1 hour pace

3 × 4 = 12 miles

Answer:

x = 12 miles

Step-by-step explanation:

Sarah can walk 3 miles in 1 hour.

At this pace how many miles will Sarah walk in 4 hours​?

Write and solve an equation of ratios:

 3 mi        1 hr

---------  =  --------

    x           4 hr

Cross-multiplying yields x = 12 miles.  

Sarah can walk 12 miles in 4 hours

Given the model:

Where x is the number of years after 1980 and p is the percentage of college freshmen who had an average grade of A in high school.

a.

From the definition of x, in 2010 we have:

Using the formula for p:

From the graph, in 2010 we have 47%, so the model overestimates the actual value by 2%.

Therefore, the value of x in the right triangle is 24 cm.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.

Here,

In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.

Using the Pythagorean Theorem, we can find the missing length x:

a² + b² = c²

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

In this case, a = 7 cm, b = x, and c = 25 cm.

Substituting these values into the Pythagorean Theorem, we get:

7² + x² = 25²

49 + x² = 625

x² = 625 - 49

x² = 576

x = √576

x = 24

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Step-by-step explanation:

All I did was minus 16 from 37 to get 21, then divided that by 3.

The value of x is 32.

A rectangle is a quadrilateral (a four-sided polygon) with four right angles (90-degree angles) and opposite sides that are parallel and congruent (the same length). The opposite sides of a rectangle are also perpendicular to each other, meaning they intersect at a 90-degree angle.

The rectangle is a special case of a parallelogram, where all the angles are right angles. A square is also a special type of rectangle, where all the sides are congruent.

We can use the formula for the area of a rectangle, which is:

Area = Length x Width

Substituting the given values, we get:

40 = (5/8)x + 5 x 4

Simplifying, we get:

40 = (5/8)x + 20

Subtracting 20 from both sides, we get:

20 = (5/8)x

Multiplying both sides by 8/5, we get:

x = 32

Therefore, the value of x is 32.

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The correct graph that represents the solution set of the system of inequalities is in Option(b).

Inequality is a  statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.

The given system of inequalities are,

y < -3x - 2

y ≤ x - 2

We have to select the graph that represents the solution set of the system of inequalities.

y < -3x - 2

Let, y = -3x - 2

Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).

y ≤ x - 2

Let, y = x - 2

Now, plot the graph of the line y = x - 2 on the graph.

The area between the two lines of inequalities on the graph represent the solution set.

Upon comparison with the graphs in the options, the correct graph is present in Option(b).

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Answer:

4c^2+7c-5=0

4c^2+7c=5

4c^2+7c=5

4c^2+7c-5=0\quad :\quad c=\frac{-7+\sqrt{129}}{8},\:c=\frac{-7-\sqrt{129}}{8}\quad \left(\mathrm{Decimal}:\quad c=0.54472\dots ,\:c=-2.29472\dots \right)

Hope This Helps!!!

Answer:

C) c = -7 ± √129 / 8

Step-by-step explanation:

x = (-b ± √ (b² – 4ac) ) / 2a

[quadratic formula]

where ax² + bx + c = 0.

[quadratic / square trinomial]

given 4c² + 7c – 5 = 0,

↓ ↓ ↓

a b c

where c = x,

c = (-b ± √ (b² – 4ac) ) / 2a.

c = (-(7) ± √ ((7)² – (4)(4)(-5)) ) / 2(4)

c = (-7 ± √ (49 – (-80)) ) / 8

c = (-7 ± √ (129) ) / 8

c = -7 ± √129 / 8

Answer:

the correct answer is A. 25 sandwiches.

Step-by-step explanation:

Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.

Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.

So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.

Therefore, the correct answer is A. 25 sandwiches.

Answer: 25

Step-by-step explanation:

We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.

2+2...=50

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

Step-by-step explanation:

180-123 = 57 G = 57

6x -1 + 5x +14 +57 = 180

11x = 110

x = 10

H = 6(10) - 1 = 59

Answer:

59°

Step-by-step explanation:

Use the equation:

( 6x - 1 )° + ( 5x + 14 )° = 123°

Combine like terms

6x + 5x = 11x         -1 + 14 = 13

New simplified equation:

11x + 13 = 123

Subtract 13 from both sides of the equation

11x + 13 = 123

       -13    -13

We are subtracting because the opposite of addition is subtraction and we are using PEMDAS backwards to isolate the variable 'x' on one side of the equation.

Equation now:

11x = 110

Divide both sides of the equation by 11

\(\frac{11x}{11}\) = \(\frac{110}{11}\)

Solve

x = 10

Solve for the measure of angle H

Plug in the variable

6(10) - 1

60 - 1 = 59

measure of angle H is 59°

Answer:

x= 381.56

Step-by-step explanation:

.......................

Answer:

\(\sqrt {45}\)

Step-by-step explanation:

Distance between two points, (x1, y1) and (x2, y2)  in a 2D cartesian coordinate is given by
\(d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

here the points are (6, - 2) and (3, 4)

We get

\(d = \sqrt {(3 - 6)^2 + (4 - (-2))^2}\\\\d = \sqrt {(-3)^2 + (6)^2}\\\\d = \sqrt {{9} + {36}}\\\\d = \sqrt {45}\)

Answer:

The slope of -1.2 means that for each cup of antioxidant a person consumes per day, it's BMI decreases by 1.2.

The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.

Step-by-step explanation:

Line of best fit:

\(y = -1.2x + 26\)

Slope:

The slope is the number that multiplies x, that is, -1.2. The slope of -1.2 means that for each cup of antioxidant food a person consumes per day, it's BMI decreases by 1.2.

Intercept:

Value of y when x = 0, that is, 26. The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.

Answer:

the slope is -1.2 and the intercept is 26.

Step-by-step explanation:

our line's equation is y= -1.2x + 26

In the equation y = mx + b, m is the slope and b is the y-intercept. So in this equation, look for where the numbers are placed and that it what you get.

Answer:

3. Yes, because 160 / 4 = 40 and 120 / 3 = 40.

4. 10, because 24 / 12 = 2 and 20 / 2 = 10

Answer:

3. David and Aryana use their phones at the same rate.

4.10 parts of water to 20 parts of cornstarch.

Step-by-step explanation:

3. First, you have Aryana who uses 160 mins in 4 days. Then there is David who has 120 minutes in 3 days. You want to divide the minutes by days to see  how many minutes per day they use their phone. 160/4=40 120/3=40. David and Aryana use their phones at the same rate.

4. First, you have 24c to 12w (c is cornstarch and w is water). If you want to find 20c and what w is, you need to make c into a smaller number. What I mean is that you need to divide the equation as low as it can go, this one happening to be 12. So you do 24 to 12/12 = 2c to 1w. You then multiply the number back up to twenty. so 2*10 = 20 1*10=10. Your final answer is 10 parts of water to 20 parts of cornstarch.

Answer:

No

Step-by-step explanation:

If you are just seeking answers, you are basically cheating and trying to get someone to do your work...which will not help you learn the material ....sad.

Answer: YOU SHOULD DIVIDE ALL OF THEM TO GET YOUR ANSWER

Answer:

Hello!

Here are the coordinates and a picture example!

Original coordinates: -3, -5

New coordinates: 3, -5

Hope that helps!

Answer:

\(\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }\)

Step-by-step explanation:

Hello, let's note v the rate of the boat and r the rate of the current. We can write the following

\(\dfrac{135}{v-r}=3=\dfrac{183}{v+r}\)

It means that

\(135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}\)

But we can as well use the second equation:

\(3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}\)

and then

\(\boxed{v=\dfrac{159*8}{24}=53}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The expression √36 - 2² is equivalent to the expression 2. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ √36 - 2²

Simplify the expression, then the value of the expression will be

⇒ √36 - 2²

⇒ 6 - 4

⇒ 2

The expression √36 - 2² is equivalent to the expression 2. Then the correct option is A.

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Answer: The answer is 2

Step-by-step explanation: