AB is perpendicular to CD how many 90 degrees angles are formed by the intersection

Answer:

The y-intercept is where the line crosses the y-axis, and the x-axis is where the line crosses the x-axis. For example, the y-intercept for Line A is 2 because it crosses the y-axis at (0,2) on the coordinate plane.

Step-by-step explanation:

Answer: y= 12 and x= is a value

Step-by-step explanation:

x=2+7=x

y= 7+5=y which is 12

Given :

A line 2x + 1 =0 .

To Find :

The slope of the given line .

Solution :

We know , slope of line is given by the tangent of the angle between the x-axis and the line .

Now, for line 2x + 1 =0 i.e \(x=\dfrac{-1}{2}\) .

The line is perpendicular to x-axis and cuts the x-axis at \(\dfrac{-1}{2}\) .

Therefore , the angle between the line and x-axis is \(90^o\) .

So , slope \(m=\tan\ 90^o\) i.e undefined .

Therefore , the slope of given line is not defined .

Hence , this is the required solution .

The length of AB can be found to be 9. 85 units .

To find the length of AB, we can use the distance formula which is:

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

The vertices for AB are:

A - ( 1, 7 )

B - ( 10, 3 )

When the values are plugged into the formula, we get :

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

d = √ ( ( 10 - 1 )^ 2 + ( 3  - 7) ^2 )

d = √ ( 81 + 16 )

d = √ 97

d = 9. 85 units

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Answer:

the answer would be 11.75

Step-by-step explanation:

A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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Answer:

Step-by-step explanation:

\((1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i\)

Answer:

-m^2 - 9m + 3 (the third one)

Step-by-step explanation:

separate the terms and group them with their equivalents (integers:inetgers, variables: variables, etc.) like so:

4m^2   &   -5m^2    = -m^2

-8m      &   -m          = -9m

12         &    -9          = 3

add them all together to get the expression -m^2-9m+3

Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          \(\frac{8}{2}\)              :                \(\frac{2}{2}\)

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         \(\frac{16}{4}\)             :               \(\frac{4}{4}\)

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer:

base 1 + base 2 times height times half (basically dividing by 2) is the formula of a trapezoid. 25 + 35 = 60 x 21 = 1260 divided by 2 is 630

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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Answer:

ju4n bakes some j16s

Step-by-step explanation:

so, if \(\neq \sqrt{x} x^{2}\) is a dozen roll, then he has 3 3/4 left to sell

C. 3 3/4

Answer:

3 3/4

Step-by-step explanation:

let me know if im wrong or not ok?

Answer:

He needs to add approximately $ 426.63 to his account to reach the desired balance of  $7000.

Step-by-step explanation:

Here, the principal amount, P = $ 3000,

Semiannual rate of interest, r = 8 %

Time, t = 10 years,

Hence, the amount after 10 years, which is compounded with the semiannual rate of 8% for 10 years,

Thus, the amount, need to add in the balance to reach the amount of $ 7000 = 7000 - 6573.3694291 = 426.6305709 ≈ $ 426.63

⇒ He needs to add approximately $ 426.63 to his account to reach the desired balance of  $7000

Answer:

Step-by-step explanation:

oh nice,  SOH CAH TOA   :P

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

SOH CAH TOA is really helpful,  it also reminds me of south pacific for some reason  :D  

Anyway back to math

we want to find an angle and we have the Hyp and the adj sides

to that angle soooo

let's pick CAH since it's got   Adj / Hyp , which we know and will find that unknown angle for us..  :)

Cos(Ф) = Adj / Hyp

Ф = arcCos( adj / Hyp)

Ф = arcCos( 14 /28 )

Ф = arcCos(.5)    ( if you happen to be good with trig functions you can already tell what it's going to be :P  w/o using the calculator)

Ф = 60 °

1a = 60 °

for 1b we know the opp and they hyp and want to find the angle. So let's use SOH  

sin = Opp / Hyp

sin(Ф) = 5/20

Ф = arcSin(5 /20)

Ф = arcSin ( 1/4)

Ф = 14.4775 °

1b = 14 °  ( rounded to nearest degree )

Answer:

B. 61

Step-by-step explanation:

Given that ∆PQR and PQS are congruent, it follows that their corresponding sides are of the same length.

Therefore,

\( RQ = SQ \)

\( 3x + 16 = 7x - 24 \)

Collect like terms

\( 16 + 24 = 7x - 3x \)

\( 40 = 4x \)

Divide both sides by 4

\( \frac{40}{4} = \frac{4x}{4} \)

\( 10 = x \)

\( x = 10 \)

Find PQ:

\( PQ = 2x + 41 \)

substitute x = 10 into the equation

\( PQ = 2(10) + 41 \)

\( PQ = 20 + 41 \)

\( PQ = 61 \)

Answer:

.7845

Step-by-step explanation:

Answer:

if there were 1600 frogs shaking their butts on lily pads and 199 of them leave, 1401 frogs will still be shaking their butts.

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The fraction of 1 pizza to be shared with 4 friends are 3/8

Division is breaking a number up into an equal number of parts.

Given that, there are pizzas 1\(\frac{1}{2}\) to be shared between 4 friends,

1\(\frac{1}{2}\) = 3/2

For sharing = 3/2÷4 = 3/8

Hence, The fraction of 1 pizza to be shared with 4 friends are 3/8

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The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

The dimensions for this problem are given as follows:

5 m, 12 m and 9 m.

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

Sum= 5000005

Difference= 4999995

Step-by-step explanation:

The place value of 5 in the number 35086941 is 5000000

The face value is 5

The sum between the face value and place value can be calculated as follows

°= 5000000+5

= 5000005

The difference can be calculated as follows

= 5000000-5

= 4999995

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Step-by-step explanation:

Rectangle: A quadrilateral with four right angles; a rectangle is a type of parallelogram. Square: A quadrilateral with four congruent sides and four right angles; a square is both a rhombus and a rectangle. Trapezoid: A quadrilateral with exactly one pair of parallel sides (the parallel sides are called bases)

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

Answer:

A. a = -3, b = 2

Step-by-step explanation:

I calculated it logically

Using the distance formula, the length of segment PQ is:

C. √68 units

The distance formula is given as:

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Segment PQ has the following endpoints:

P(-2, 3)

Q(6, 1)

To find the length of segment PQ using the distance formula, we can apply the formula, where:

\((x_1, y_1)\)are the coordinates of point P

\((x_2, y_2)\) are the coordinates of point Q.

Given:

P(-2, 3) = \((x_1, y_1)\)

Q(6, 1) = \((x_2, y_2)\)

Let's substitute the values into the formula:

PQ = √[(6 - (-2))² + (1 - 3)²]

PQ = √[(8)² + (-2)²)

PQ = √(64 + 4)

length of segment PQ = √68 units

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