Solve for x with the given measures

The number of Caroline's textbook is 8

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

Represent the Notebook bought by Bert as q

q = p-5

p-2= 2q

p = 2q +2

substitute 2q +2

q = 2q+2-5

2q-q = 3

q = 3

substitute 3 for q

3 = p-5

p = 5+3

p= 8

Therefore Caroline's number of notebook is 8

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The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).

Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:

Reflection over the y-axis:

(x, y) → (- x, y)

Dilation centered at the origin with a scale factor of 2:

(x, y) → (2 · x, 2 · y)

If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:

Reflection over the y-axis

A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)

Dilation centered at the origin with a scale factor of 2

A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)

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The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:

C. Graph Y.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.

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The percentage of students who are doing their homework regularly is 75%.

A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.

To find the percentage of students who are doing their homework regularly,

We find the total students and this is 75 + 5 = 80 students

The percentage is 60/80 * 100

= 75%

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Answer:

Step-by-step explanation:

a

Answer:

0

Step-by-step explanation:

surface of ocean = sea level = elevation of zero

Answer:

This is a Right Triangle because the last angle is 90 degrees.

Answer:

the answer to this question is 936

Guido can choose his Jolly Rancher in 78,125 different ways over the course of a week.

Guido chooses one sweet per day from a selection of five options; there are a total of five possible selections for a single day. Since there are seven days in a week, the sum of the ways Guido can choose candy over the course of a week equals the sum of the methods for each day.

Using the multiplication principle of counting

Total number of ways = 5 x 5 x 5 x 5 x 5 x 5 x 5

Simplifying this expression gives:

Total number of ways = 5^7

Using a calculator or by hand, we can compute:

Total number of ways = 78,125

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Answer:

x = 32

Step-by-step explanation:

First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.

3/4x = 27-3

Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3

0.75x = 24

Now we can divide 24 by 0.75 to find x

x = 32

x = 32.

[tex]\frac{3}{4} x+3=27[/tex]

[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]

[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]

If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!

[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]

That's correct!

x = 32.

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The Main Street is 1/12 of a mile longer than the Oak Street

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Difference = Main Street - Oak Street

substitute the known values in the above equation, so, we have the following representation

Difference = 1/3 - 1/4

Evaluate the difference

Difference = 1/12

Hence, the difference is 1/12 of a mile

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The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5

We need to find the value of f(5)

Plug x=5 in the above function

f(x) = x⁴ - 7x³ + 2x² + 40x

f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)

=625-875+50+200

=0

Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

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Complete question is below

f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)

Answer:

120°

Step-by-step explanation:

360 / 12

30 X (5-1)

30 X 4= 120°

All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.

The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.

An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.

A line segment serves as the foundation for the following angles and lines in geometry:

The process of creating a line perpendicular to a point on a line.

The creation of a 45-degree angle (45°).

The creation of a 30-degree (30-degree) angle.

Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.

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Answer: The answer to your problem is choice b

The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.

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

Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-

E = 3h(n) + 2g(n)

E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)

E = 12n + 6 + 2n³ + 10 -4n

E = 2n³ + 8n + 6

Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.

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The proof that z lies on the x-axis is shown below

For z to lie on the x-axis, then the coordinate must be represented as (x, 0)

Given that

[tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex]

We start by simplifying the given expression using the definition of the modulus of a complex number:

So, we have

[tex]\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1[/tex]

Where

z = x + yi or z = (x, y)

Squaring both sides of the equation above, we obtain:

[tex]\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1[/tex]

This gives

[tex]\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1[/tex]

By comparison, we have

[tex](y + 5)^2 = (y - 5)^2[/tex]

Set y = 0 to test the equation

So, we have

[tex](0 + 5)^2 = (0 - 5)^2[/tex]

25 = 25 --- true

The equation is true for y = 0

This means that

z = (x, 0)

Hence, z lies on the x-axis

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Answer:

Step-by-step explanation:

In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:

The length of one pair of opposite sides is equal.

The two pairs of opposite sides are parallel.

To show these two conditions, you may need additional segments or points such as:

Perpendicular lines or segments to the sides to help show the sides are parallel.

Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.

By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.

Answer:if their corresponding sides are proportional.

Step-by-step explanation:

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Step-by-step explanation:

[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]

Multiply by 1-sec(a)

[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]

[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]

[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]

[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]

The volume of the parallelopiped is 4

We have to solve this with the use of matrix system in math

PQ, PR, PS where

P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)

we have to find

Q - P

(-1, 6, 5) - (-3, 3, 2)

= (2, 3, 3)

R - P

R(-4, 2, 1) - (-3, 3, 2)

= ( -1 , -1, -1)

S - P

S(3, 1, 4) - (-3, 3, 2)

= (6 , -2, 2)

we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]

the determinant of the matrix is the volume

2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]

= -8 - 12 + 24

= 4

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Answer: Let's assume that the marked price of the watch is M.

The discount amount would be 20% of M, which can be calculated as:

0.2 * M = 0.2M

The selling price after the discount would be:

M - 0.2M = 0.8M

The VAT amount would be 13% of the selling price after the discount, which can be calculated as:

0.13 * 0.8M = 0.104M

Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:

0.2M = 0.104M + 192

0.096M = 192

M = 192 / 0.096 = 2000

So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and  pi times (16/2)^2=201.06.   201.06-78.54 = about 122.52, which is closest to 122.46, or C.

The number of containers needed is given as follows:

3 containers.

The number of containers needed is obtained applying the proportions in the context of this problem.

She has 2 cups, hence the number of fluid ounces that she has is given as follows:

16 fluid ounces.

Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:

16/6 = 3 containers.

(rounding up).

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Answer:B

Step-by-step explanation:

area of triangle is (10*11)/2=55

area of semicircle is

[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]