Which equation correctly describes the relationship between segment lengths in the given figure?
A. (FP)(GP) = (EP)(DP)
B. (FD)(FG) = (EG)(ED)
C. (FP)(FG) = (EP)(ED)
D. (FP)(DP) = (EP)(GP)

To find a line that is parallel to another line and passes through a specific point, you first find the slope of the original line. Then, you use the point-slope form of a line equation to find the equation of the new line. The final equation is y = 5/3x - 10.

In order to find the equation of a line that is parallel to another and passes through a specific point, you first need to find the slope of the original line. The line given in the question is 5x - 3y = 6, which can be rearranged into slope-intercept form (y = mx + b) to become y = 5/3x - 2. The slope (m) of this line is 5/3. Parallel lines share the same slope, so the slope of the line we are trying to find is also 5/3.

Next, we use the point-slope form of a line equation, which is y - y1 = m(x - x1). The point given in the question is (6, -2), so x1 = 6 and y1 = -2. Substituting these into the equation, we find the equation of the line to be y + 2 = 5/3(x - 6).

Simplify this to y = 5/3x - 10, which is the equation of the line parallel to the given line and passing through the point (6, -2).

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To find an equation of a line parallel to a given line that passes through a specific point, you can use the point-slope form of a line. Find the slope of the given line, and use the slope and the given point to determine the equation of the parallel line.

We can find the equation of a line parallel to the given line by using the fact that parallel lines have the same slope. To find the slope of the given line, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope:

5x - 3y = 6 → -3y = -5x + 6 → y = (5/3)x - 2

So, the slope of the given line is 5/3. Thus, any line parallel to this must also have a slope of 5/3.

Since we now have the slope and a point that the line passes through (6, -2), we can use the point-slope form of a line to find the equation:

y - y₁ = m(x - x₁) where (x₁, y₁) is the point given and m is the slope. Substituting the values in, we get:

y - (-2) = (5/3)(x - 6) → y + 2 = (5/3)(x - 6)

Simplifying this equation gives the final answer:

y = (5/3)x - 22/3

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Answer:

-6

Step-by-step explanation:

This means what value can I plug into -3x-8 so that I get output 10.

g(x)=-3x-8

g(a)=-3a-8

So we are going to solve g(a)=10 for a.

g(a)=10

-3a-8=10

Add 8 on both sides:

-3a   =18

Divide both sides by -3:

 a     =-6

Check it!

g(-6)=-3(-6)-8=18-8=10 and it's good! :)

Answer:

The answer Is B.

Step-by-step explanation:

In "A" I believe japanese should be capatalized and in "C" "genji" should be capitalized but In "B" Murasaki Shikibu’s is a name so it should be capitalized.

Answer:

False

Step-by-step explanation:

A point has zero dimension, once two pints are connected then you get one dimension which is a line

B. False

A point is a fundamental concept in geometry and represents a location in space. It is considered zero-dimensional because it has no length, width, or height.

A point is often represented by a dot or a small symbol and is described by its coordinates in a coordinate system.

In a one-dimensional context, you would have a line segment or a line that consists of multiple points.

However, a single point on its own is considered to have no dimension and is therefore not classified as one-dimensional.

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Answer:

The expression is 5⁵-1 (=3124)

Step-by-step explanation:

Answer:

-20x^2 +14x+12

The domain of f*g is all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6.

f*g = (-4x-2) * (5x-6)

FOIL

first -4x*5x = -20x^2

outer -4x*-6 = 24x

inner -2*5x = -10x

last -2 *-6 = 12

Add them together

-20x^2 +24x-10x+12 = -20x^2 +14x+12

The domain of f is all real numbers, the domain of g is all real numbers

The domain of f*g is all real numbers

Answer:

[tex](f*g)(x)=-20x^2+14x+12[/tex]

Domain: All Real Numbers.

Step-by-step explanation:

Given the function f(x):

[tex]f(x) = -4x - 2[/tex]

And the function g(x):

[tex]g(x) = 5x - 6[/tex]

You need to multiply them. Then:

[tex](f*g)(x)=( -4x - 2)( 5x - 6)\\\\(f*g)(x)=-20x^2+24x-10x+12\\\\(f*g)(x)=-20x^2+14x+12[/tex]

Since we know that the domain is the set of all real values of the variable "x" that will give real values for the variable "y", the domain of [tex](f*g)(x)=-20x^2+14x+12[/tex] is ALL REAL NUMBERS.

Answer:

Please look at the different answers. I wasn't 100% sure what your expression was.

Step-by-step explanation:

If you mean 2/(5x-1) then g(x) will take the fraction into account with a constant 2 for the numerator and a variable for the denominator since that is where our variable is so g(x)=2/x.

Now h(x)=5x-1 since if you plug in 5x-1 into 2/x where x is you will get our original expression.

Now if you did mean (2/5)x-1 I would take notice of where the variable is which is in (2/5)x so g(x)=x-1 where h(x)=(2/5)x since if you plug (2/5)x in place of the x in x-1 you will get the original.

Please let me know if I didn't interpret your expression correctly.

The required functions which satisfy the condition [tex]\ h (x) = g (f (x))[/tex] are,

[tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

Used the concept of composition which states that,

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that;

[tex]\ h (x) = g (f (x))[/tex]

Consider the given function as

[tex]f (x) = \dfrac{2}{5} x - 1[/tex]

It is given that [tex]\ f (x) = g (h (x))[/tex] and neither [tex]g (x)[/tex] nor [tex]h (x)[/tex] is solely x.

Let us assume that,

The function h (x) is defined as,

[tex]h (x) = \dfrac{2}{5} x[/tex]

Then we get;

[tex]\ f (x) = g (h (x))[/tex]

= [tex]h (x) - 1[/tex]

Substitute [tex]h (x) = x[/tex] in the above function for the value of function g (x),

[tex]g (x) = x - 1[/tex]

Therefore, the required functions are [tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

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Answer:

Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004  

= 0.59479  

+ 59.5% to one place of decimals

Step-by-step explanation:

P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5  

=15! / (10! * 5!) * (0.70)^10 * (0.30)^5  

= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5  

= 0.20613  

P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4  

= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4  

= 0.21862  

P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3  

= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3  

= 0.17004  

Answer:

D

Step-by-step explanation:

From any point (x, y ) on the parabola the focus and directrix are equidistant

Here the focus = (- 6, 0) and the directrix is x = 6

Using the distance formula

[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is

[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |

Squaring both sides

(x + 6)² + y² = (x - 6)² ← distribute factors on both sides

x² + 12x + 36 + y² = x² - 12x + 36

Subtract x² - 12x + 36 from both sides

24x + y² = 0 ( subtract y² from both sides )

24x = - y² ( divide both sides by 24 )

x = - [tex]\frac{1}{24}[/tex] y² → D

What composite shape? Where is the shape?

Answer:

[tex]\Huge \boxed{\frac{1}{4}}[/tex]

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]

Therefore, the slope is 1/4, and the correct answer is 1/4.

Answer:

C 1/4

Step-by-step explanation:

To find the slope of the line given two points, we use the formula

m = (y2-y1)/(x2-x1)

   = (3-2)/(3--1)

   = (3-2)/(3+1)

   = 1/4

Answer:

[tex]a_n=42n-621[/tex]

Step-by-step explanation:

This is arithmetic sequence so you should go to linear equations in your head.

Think of the question asking you to find the equation of line going through the points:

(14,-33) and (15,9).

First, let's find the slope.

You need to compute y's change over x's change.

The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.

Like this:

(  15  ,   9)

-(  14  ,  -33)

------------------

   1         42

So the slope is 42/1=42.

(The slope is our common difference.)

Now point slope form is:

y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.

So we have m=42 and (x1,y1)=(15,9).  (You could have chose the other point.)

y-9=42(x-15)

I'm going to put in slope-intercept form.  Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

y-9=42(x-15)

Solve for y by adding 9 on both sides:

y=42(x-15)+9

Distribute 42 to terms in the ( ) :

y=42x-42(15)+9

y=42x-630+9

y=42x-621

So we can which back to n now:

[tex]a_n=42n-621[/tex]

Answer:

6 squared cm

Step-by-step explanation:

The height of a triangle is length of the segment that is perpendicular to the base.  So that length is 2cm here.

The base and the height of the triangle should be perpendicular. So the base is 6cm

The area of a triangle is 1/2 * b * h.

1/2 * b  * h

1/2 *6   * 2

    3    *  2

        6

The answer is 6 squared cm

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

In ΔBCD we have b = 6cm, and h = 2cm.

Substitute:

[tex]A_{\triangle BCD}=\dfrac{(6)(2)}{2}=\dfrac{12}{2}=6\ cm^2[/tex]

Answer:

C. Hours

Step-by-step explanation:

It wouldn't take minutes or seconds to travel 2,442 miles so A and B don't make sense.

Also, it wouldn't take days to travel in the same country, it might a day but not days.

So the only answer that would make sense would be C. Hours

Hope This Helps!!

Answer:

-140

Step-by-step explanation:

Plug in -4 for x, and -6 for y, in the expression:

-7(x - 4y) = -7((-4) - 4(-6))

Simplify. First, solve the terms within the parenthesis. Multiply:

-7((-4) (-4 * -6))

-7((-4) (+24))

-7(-4 + 24)

Solve the parenthesis. Add:

-7(20)

Fully simplify.

-7 * 20 = -140

-140 is your answer.

~

Answer:

[tex]cos^{-1}[\frac{6.3}{9.8}][/tex]

[tex]sin^{-1}[\frac{7.5}{9.8}][/tex]

Step-by-step explanation:

step 1

Find the measure of angle ABC using the function cosine

we know that

The function cosine of angle ABC is equal to divide the adjacent side to angle ABC by the hypotenuse of the right triangle

cos(∠ABC)=BC/AB

substitute

cos(∠ABC)=6.3/9.8

[tex]ABC=cos^{-1}[\frac{6.3}{9.8}][/tex]

step 2

Find the measure of angle ABC using the function sine

we know that

The function sine of angle ABC is equal to divide the opposite side to angle ABC by the hypotenuse of the right triangle

sin(∠ABC)=AC/AB

substitute

sin(∠ABC)=7.5/9.8

[tex]ABC=sin^{-1}[\frac{7.5}{9.8}][/tex]

Answer:

[tex]\large\boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, -4) and (3, 0).

Substitute:

[tex]m=\dfrac{0-(-4)}{3-0}=\dfrac{4}{3}[/tex]

Answer:

C

Step-by-step explanation:

So the system is:

5x+13y=232

12x+7y=218

------------------

Let's look at the options to see which will work:

A) Multiply first equation by -13:  -65x-169y=-3016

& second equation by 7           :    84x+49y=1526

There are no opposites in the either one of the variable columns so not this option.

B) Multiply first equation by 7:  35x+91y=1624

& second equation by 13       : 156x+91y=2834

There are no opposites in the either one of the variable columns so this is not option unless we were asked to subtract the equations.

C) Multiply first equation by -12: -60x-156y=-2784

& second equation by 5           :   60x+35y=1090

There is a column that contains opposites here so when you add the equations the x-variable will get eliminated.

Answer:

3rd one

Step-by-step explanation:

Answer:

x = 6 + 3√10

Step-by-step explanation:

Since this is an unfactorable expression, we need to apply the Quadratic Formula, -b ± √b² - 4ac\2a [radical wrapped around b² - 4ac]. Evaluate, then you will end up with the answer above.

I am joyous to assist you anytime.

Answer:

2/3

Step-by-step explanation:

Ah, I see. A 1-6 die.

Probability of one number = 1/6

2 numbers? = 2/6

6/6-2/6=4/6

4/6=2/3

[tex]\huge{\boxed{\frac{2}{3}}}[/tex]

There are [tex]4[/tex] numbers on a number cube that are greater than [tex]2[/tex]. They are [tex]3, 4, 5, 6[/tex].

Write this as a fraction. [tex]\frac{\text{4 favorable outcomes}}{\text{6 total outcomes}}[/tex]

Divide both the numerator and denominator by [tex]2[/tex] to simplify. [tex]\boxed{\frac{2}{3}}[/tex]

Answer:

First part:

Set h(t) = 231and solve for t.

-16t²+ 152t + 9= 231

-16t² + 152t - 222= 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

Answer:

37*20 = 740/4 = 185 -> Spent on new CD's

740 - 185 = $ 555 -> Savings Account

Step-by-step explanation:

Answer:

Amount of money she spend on CDs: $185

Amount of money she is going to be in her savings account: $555

Step-by-step explanation:

She sold 37 pairs of earrings with each of them costing 20 dollars.

That means she made 20(37)=740 dollars.

She is going to use 1/4 of 740 dollars to buy new CDS. This means she is going to use 740/4 =185 dollars on CDs.

So what money is left from 740 dollars after spending 185 dollars?

740-185=555 dollars

She is going to put 555 dollars into savings.

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

[tex]y > -x+4[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dotted line [tex]y=-x+4[/tex]

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

[tex]y \leq -(1/2)^{x} +6[/tex] -----> inequality B

The solution of the inequality B is the shaded area above the solid line [tex]y=-(1/2)^{x} +6[/tex]

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Answer:

A i think

Step-by-step explanation:

Answer:

yes; 4² + 3² = 5²

Step-by-step explanation:

Pythagorean theorem.

In a right triangle the square of the hypotenuse is equal to  the sum of the squares of the other two sides. Hypotenuse is the longest side of the triangle.

4² + 3² = 5²

16 + 9 = 25

25 = 25  

Answer:

12 * 50 = 600

Step-by-step explanation:

We have to multiply 12 by 50

Short cut method for multiplying a number by 50

Step 1: Take the half of the given number

Step 2: Multiply the result by 100

To find the short cut method to multiply 12 by 50

Here the number is 12

Step 1: divide the number by 2

12/2 = 6

Step 2: Multiply 6 by 100 we get 600

Therefore 12 * 50 = 600

Answer:

12 x 50= 600

Step-by-step explanation:

One way you can do is long and short. But the best way is to do it long because than you will get a better score and get the answer still.

Answer:

The percentage of the calls lasted less than 8 min is 16%

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the percentage of the calls lasted less than 8 min, find the

  z-score for the calls lasted

∵ The rule of z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average phone call in a certain town lasted is 9 min

∴ The mean (μ) = 9

- The standard deviation is 1 min

∴ σ = 1

- The calls lasted less than 8 min

∴ x = 8

∵ z = (x - μ)/σ

∴ z = (8 - 9)/1 = -1/1 = -1

∴ P(z < 8) = -1

- Use z-table to find the percentage of x < 8

∴ P(x < 8) = 0.15866 × 100% = 15.87% ≅ 16%

* The percentage of the calls lasted less than 8 min is 16%

Answer:

The percentage of the calls lasted less than 8 min is 16%.

Step-by-step explanation:

We are dealing with a normal distribution with an average phone call of 9 min and a standard deviation of 1 min. Below we can observe the empirical rule applied with a mean of 9 and a standard deviation of 1. The number 8 represents one standard deviation below the mean, so, the percentage of observations below 8 is 16%. Therefore the percentage of the calls lasted less than 8 min is 16%.

Answer:

i think she should eat

I think ??????

Step-by-step explanation:

Answer:

16 mph

Step-by-step explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be=  x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

[tex]=\frac{80}{x}[/tex]

Time taken by Tamara

[tex]=\frac{80}{4+x}[/tex]

Equation for difference in time

[tex]=\frac{80}{x} -\frac{80}{4+x} =1[/tex]

Solve the equation for difference in time to get value of x which is samantha speed

[tex]=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0[/tex]

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

[tex]x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16[/tex]

Samantha speed is 16 mph

Answer:

-$1.9

Step-by-step explanation:

There are 47 pages.

Printing on both sides would divide the number of pages into half.

47/2 = 23.5

2 pages on each side would mean 4 pages on one sheet. Therefore, the number of pages will be further divided by 2.

23.5/2 = 11.75

There cannot be 11.75 pages so we will round it up to 12 pages.

Each page costs $0.25 so 12 pages will cost:

12 x 0.25 = $3

Faithi has $1.1 so new account balance will be:

1.1 - 3 = $-1.9

Therefore, Fathi's balance in his printing account would be negative $1.9.

!!

When Fathi prints a 47-page document using both sides of pages and printing 2 pages on each side, at a cost of $0.25 per sheet, his printing account balance will be -$1.90.

The question asks what will Fathi's balance be in his printing account after printing a document that is 47 pages long, with specific printing constraints. To solve this, we first need to figure out the number of pages he will print per sheet. Given that Fathi prints two pages on each side of a sheet, he will print 4 pages per sheet. As the document is 47 pages, he will need a total of 12 sheets (47 divided by 4 and rounded up to the nearest whole number).

Next, we need to calculate the cost of printing those sheets. As each sheet reduces his printing account by $0.25, and he's using 12 sheets, the cost will be $3.00 (12 multiplied by $0.25).

Finally, to find the balance in his printing account, we subtract the cost of printing from his initial balance. Fathi started with $1.10 in his printing account, so after deducting the cost of printing 12 sheets, his final balance will be $-1.90 (which means he owes this amount to replenish his account back to zero).

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Answer:

Step-by-step explanation:

According to the given statement two pieces are of same length:

If the length of one piece is x,

Then the length of other piece is also x.

And one piece is 2 feet longer than the other two = x+2

Total length of a board = 10 foot

Now make the equation from these terms:

x+x+x+2= 10

This is the equation of the given question.

You can further solve this equation:

x+x+x+2=10

3x+2=10

Now combine the constants:

3x=10-2

3x=8

x=8/3

x=2.67

It means that the length of two pieces of same length is 2.67

And the length of one piece which is longer than the other two = x+2 = 2.67+2 = 4.67 ....

Final answer:

To cut a 10-foot board into three pieces where two are the same length and one is 2 feet longer, denote the shorter length as 'x', create the equation 2x + (x + 2) = 10, and solve for 'x'. The two shorter pieces will each be approximately 2.67 feet and the longer one will be approximately 4.67 feet.

Explanation:

The question involves dividing a 10-foot board into three pieces with one piece being 2 feet longer than the other two equal pieces. To solve this, let's denote the length of the shorter pieces as 'x'. Since there are two of these, we have '2x', and the longer piece would be 'x + 2' feet long. The sum of the lengths of all three pieces is equal to the length of the board, so:

2x + (x + 2) = 10

This simplifies to:

3x + 2 = 10

Subtracting 2 from both sides gives:

3x = 8

Dividing both sides by 3 gives:

x = 8/3 or approximately 2.67 feet.

Therefore, the two shorter pieces are each approximately 2.67 feet long and the longer piece is 2.67 + 2, which is approximately 4.67 feet long.