What is the equation and solution?

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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Answer:

24 square units

Step-by-step explanation:

The formula for computing the area of a trapezoid is shown below:

As we know that

Area of a trapezium is

\(= \frac{1}{2} \times h(a+b)\)

where

h = perpendicular height

The a and b =  length of the parallel sides.

Now,

h = 2 - -2 = 4 units

a = 5 - -3 = 8 units

b = 3 - -1 = 4 units

Now placing these values to the above formula

So, the area of a trapezoid is

\(= \dfrac{1}{2} \times 4(8+4)\)

\(= 2 \times 12\)

= 24 square units.

Hence we applied the above formula so that the area of trapezoid could come

11:59 AM is midday not midnight

Answer:

3.3e+7

Step-by-step explanation:

Answer:

X+8/100x ; X+0.08x

Step-by-step explanation:

Let x = last month's earning

8% =8/100 or 0.08

8/100 of x= 8/100x 008 of x=0.08x

last month + 8/100 of last month:

x+8/100x

last month + 0.08 of last month:

x+0.08x

Those are your two answers. I am sorry if they are wrong. I am not the best at math, but I tried supplying the answers as best as I could.

The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

The only god i know is time and truth! i worship him and whenever i do mistakes i apologise them :)

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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Answer:

93

Explanation:

9x - 3y - 12

9(10) - 3(-5) - 12

= 93

Answer: $34.85

Step-by-step explanation: $41 x 15%= 34.85 before tax

Answer:

I belive its z > -5/2

Step-by-step explanation:

First subtract 10 from both sides.

Then simplify

Then multiply both sides by -1 because you're reversing the inequality

simplify again

Then divide both sides by 4

Finally you simplify to get

z > -5/2

:)

The completed statements and reasons, which can be used to complete the two column table to prove that the triangles ΔRSU and ΔTQU are congruent can be presented as follows;

Statement \({}\)                            Reasons

U is the midpoint of \(\overline{QS}\)      \({}\)    Given

U is the midpoint of \(\overline{QS}\)    \({}\)      Given

\(\overline{QT}\) ≅ \(\overline{RS}\)  \({}\)                                Given

\(\overline{TU}\) ≅ \(\overline{RU}\) \({}\)                                 Definition of midpoint

\(\overline{QU}\) ≅ \(\overline{SU}\)        \({}\)                          Definition of midpoint

ΔRSU ≅ ΔTQU \({}\)                        SSS

Congruent triangles are triangles that have the same shape and size.

The details of the reasons used to prove that the two triangles are congruent can be presented as follows;

Definition of midpoint;

The midpoint of a line is the point that splits the line into two segments that have the same length.

SSS;

The SSS (Side-Side-Side) congruence theorem states that two triangles are congruent if the length of the three sides of one triangle are congruent to the three sides of the other triangle.

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Answer: a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

\((\frac{a}{b^{3} } )^{4}\)

\(a^{4}\)/(\(b^{3}\)\()^{4}\)

\(a^{4}\)/\(b^{12}\)

Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

Answer:

equilateral

Step-by-step explanation:

There are various types of triangles out there, each with its own unique characteristics that distinguish it from others.

One such triangle is called an equilateral triangle. Essentially, like its name suggests, this kind of triangle has all three angles equal (they're actually all equal to 60 degrees). Additionally, this triangle has all three sides that same, as well.

Thus, the answer is equilateral.

Just for future reference, here are a couple more types of triangles:

- Isosceles

These triangles have at least 2 sides equal to each other; in other words, an equilateral triangle is an example of an isosceles triangle. In addition, the two angles of an isosceles triangle opposite to the two equal sides are themselves congruent.

- Scalene

These triangles have all three sides different, which in turn means that all three angles are distinct.

- Acute

These triangles' angles are all less than 90 degrees. That's what "acute" means: less than 90 degrees.

- Obtuse

These triangles have exactly 1 angle that is larger than 90 degrees.

- Right

These triangles have exactly 1 angle that is equal to 90 degrees.

~ an aesthetics lover

Answer: Equilateral triangle

Step-by-step explanation: A triangle with 3 congruent sides is called an equilateral triangle or stated another way, an equilateral triangle is a triangle in which all 3 sides have the same length.

I have attached an example of this below.

The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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Answer:

30.76%

Step-by-step explanation:

subtract 450-650=200

200÷650×100=30.76

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

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x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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Answer:

x=9

Step-by-step explanation:

The angles that measure 13x and 7x make a line. A line is 180°. 13+7 is 20 and 20 x 9 is 180.

Therefore x is 9

Answer:

Remind me if i'm wrong, 2nd, 3rd, 5th are the right answers .

Answer:

Plan A

Step-by-step explanation:

Plan A -

$7 + 2.50(5)

$7 + $12.50

Plan A = $19.50

Plan B-

$4(5) = $20

Plan A is the cheapest, therefore it is the best plan.

Hope this helped! :)

Answer:

  a) 125 different numbers

  b) 60 numbers with different digits

Step-by-step explanation:

You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.

Any of the three dials may be set to any of the five digits, so there are ...

  5 × 5 × 5 = 125

possible three digit combinations.

The number of different 3-digit numbers is 125.

If the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...

  5 × 4 × 3 = 60

possible combinations with different digits.

The number of 3-digit numbers with different digits is 60.

<95141404393>

The chi-squared test statistic will be 3.11. The test statistic is contrasted with a predicted value based on the Chi-square distribution.

Finding the squared difference between the actual and anticipated data values, then dividing that difference by the expected data values, constitutes the test statistic.

The formula for the chi-squared test statistic is;

\(\sum \frac{(O_i-E_i)^2}{E_i } \\\\\)

Where,

\(\rm O_i\) is the observed value

\(\rm E_i\) is the expected value

The chi-square test statics is;

\(\rm( \frac{18-18}{18} )^2 +( \frac{14-18}{18} )^2 + (\frac{24-18}{18} )^2+( \frac{16-18}{18} )^2 \\\\ 0+ \frac{16}{18}+ \frac{36}{18} +\frac{4}{18}\\\\ \frac{56}{18} \\\\ 3.11\)

Hence, the chi-squared test statistic will be 3.11.

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Answer:1000

Step-by-step explanation:

Yes

Answer:

994.74in²

Step-by-step explanation:

Are of circle: 21²×3.12=1384.74

Area of Triangle: 20×39/2=390

Then subtract

Answer:

10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...

Step-by-step explanation:

Subtract 0.25 from each to find the next number

Answer:

8.25

Step-by-step explanation:

If you substract .25 from each number until you get to a8 you will get 8.25

Answer:

Step-by-step explanation:

18