Lines r , s , and t are parallel. That means they have the same slope. Each of these lines has a slope of - 2 . Enter numbers to complete an equation for each line.

Answer:

We can conclude that Δ XYZ ≅ Δ RST by AAS postulate

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by AAS postulate because:

1. Their non-included sides YZ and ST are equal (10 units = 10 units).

2. Their angles ∠Y and ∠S are equal.

3. Their angles ∠X and ∠R are equal.

4.Their non-included sides XZ and RT are equal.

Now, we can conclude that Δ XYZ ≅ Δ RST by AAS postulate.

Answer:

√8 + √50

= 2√2 + 5√2

=√2(2+5)

= 7√2

Hope this helps!

Answer:

[tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex]. This is the solution.

Step-by-step explanation:

The homogeneous differential equation is given by  

[tex]\frac{dy}{dx} = \frac{x^{2} + y^{2} }{2xy}[/tex]

⇒ [tex]\frac{dy}{dx} = \frac{1 + (\frac{y}{x} )^{2} }{2(\frac{y}{x} )}[/tex] ........ (1)

Now to solve this differential equation we assume that y = vx where v is another variable.

So, differentiating with respect to x we get [tex]\frac{dy}{dx} = v + x \frac{dv}{dx}[/tex]

Therefore, the above equation (1) becomes

[tex]v + x \frac{dv}{dx} = \frac{1 + v^{2} }{2v}[/tex] {Since [tex]v = \frac{y}{x}[/tex]}

⇒ [tex]x\frac{dv}{dx} = \frac{1 + v^{2} - 2v^{2}  }{2v}[/tex]

⇒ [tex]x\frac{dv}{dx} = \frac{1 - v^{2}}{2v}[/tex]

⇒ [tex]\frac{2v}{1 - v^{2} } dv = \frac{dx}{x}[/tex] {By separation of variables}

Now, integrating both sides we get,

[tex]\int {\frac{2v}{ 1- v^{2}}} \, dv = \int {\frac{dx}{x} } \, dx[/tex]

⇒ [tex]- \int {\frac{d(1 - v^{2} )}{1 - v^{2}}}  = \int {\frac{dx}{x} }[/tex]

⇒ [tex]- ln (1 - v^{2}) = ln x + c[/tex] {Where c is the integration constant}

⇒ [tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex] (Answer)

Answer:

11i

Step-by-step explanation:

first you have to get a postive root.

[tex]\sqrt{-121} \\ \sqrt{-1}  \sqrt{121} \\[/tex]

then you solve the square roots from there, keeping in mind the imaginary number answer to the square root of -1, i.

[tex]\sqrt{-1} = i\\ \sqrt{121} =11\\ 11i[/tex]

The circumference of a circle whose radius is given would be =200.96cm.

How to calculate the circumference of a given circle?

To calculate the circumference of a given circle whose radius is given, the following steps should be taken as follows:

The formula for circumference = 2πr

where;

radius = 32cm

Circumference = 2× 3.14× 32

= 200.96cm.

Answer:

100 hours

Step-by-step explanation:

Monthly salary = monthly bonus + total wage based on hours worked

Monthly salary = monthly bonus + (dollars per hour x number of hours worked)

Given, monthly salary = $2000

MOnthly bonus = $400

dollars per hour = $16/hr

let h = number of hours worked

hence, equation becomes

2000 = 400 + (16 x h)

2000 = 400 + 16h   (subtract 400 from each side and rearrange)

16h = 2000 - 400

16h = 1600  (divide both sides by 16)

h = 1600 / 16 = 100 hours

Answer:

[tex]K=-2J+28[/tex]

Step-by-step explanation:

For the given trend line, we need to find the y-intercept and slope of the line for determining its equation.

Equation of a line is of the form [tex]y=mx+b[/tex]

Where, 'm' is the slope and 'b' is the y-intercept.

Here, the variables are 'J' and 'K'.

The y-intercept is the point where the 'J' value is 0. From the graph, when 'J' is 0, then the 'K' value is 28. Therefore, the y-intercept is 28.

Slope is given as the ratio of change in 'K' and change in 'J'

The overall change in 'K' is 0 - 28 = -28.

The overall change in 'J' is 14 - 0 = 14

Therefore, the slope is given as:

[tex]m=\frac{\Delta K}{\Delta J}=\frac{-28}{14}=-2[/tex]

Therefore, the equation of trend line is given as:

[tex]K=-2J+28[/tex]

Answer:

Option B

Step-by-step explanation:

On the first row of the Punnett square, the offspring inherits IA from one parent and IB from another parent hence the resulting genotype is IAIB.

Answer:

(1)

Donna = Pounds 180

Kyra = Pounds 240

(2)

Kelly = Pounds 225

Nelly = Pounds 175

Step-by-step explanation:

(1)

Donna = x

Kyra = x + 60

If Donna spends 1/3 of her money she is left with 2/3 of her money;

2/3 x

Kyra now has twice as much money as Donna can be represented as;

X + 60 = 2 * 2/3 x

X + 60 = 4/3 x

(x + 60)3 = 4x

3x + 180 = 4x

180 = 4x – 3x

180 = x

Donna = 180

Kyra = 180 + 60 = 240

(2)

Kelly = x

Ned = y

Kelly spends 40% of her money. Therefore he is left with 60%;

60/100 x

Nelly spends Euros 40 of his money. Therefore he is left with;

y- 40

If they now have the same amount of money;

60/100 x = y – 40

3/5 x = y – 40

3x = 5y – 200

3x – 5y = -200

Remember Kelly & Ned has Euros 400 in total;

x + y = 400

Now we can solve the simultaneous equation by substitution;

x + y= 400

3x – 5y = -200

3x + 3y = 1200

-

3x – 5y = - 200

=

8y = 1400

Y = 175

X = 225

Kelly = 225

Nelly = 175

Learn More:

https://brainly.com/question/2273184

https://brainly.com/question/11876335

#LearnWithBrainly

Answer:

3. £60

4. Ned had £175

Step-by-step explanation:

3. 3 segments of Donna plus £60 is the money that Kyra has. Ater Donna spend 1/3 of her money, Kyra has twice as much money as Danna. This means that  2 segments of Donna are equal to 1 segment plus £60, so 1 segment is equal to £60. Donna spend 1 segment of her money, that is, £60.

4. Let's define x the money of Kelly, and y the money of Ned.

Kelly and Ned have £400 in total:

x + y = 400 (eq. 1)

Kelly spends 40% of her money (so she conserves the other 60%), Ned spends £40, They now have the same amount of money:

0.6*y = x - 40 (eq. 2)

From equation 1:

y = 400 - x

Replacing into equation 2:

0.6*(400 - x) = x - 40

240 - 0.6*x = x - 40

- 0.6*x - x = - 40 - 240

-1.6*x = -280

x = -280/-1.6

x = £175

Answer:

Equation:  2x + 10y = 98

y-intercept:  (0, 9.8)

Step-by-step explanation:

The easiest possible way to solve thios problem follows:

Keep the form of the given line 2x + 10y = 7, replacing the '7' with the constant 'c:'

2x + 10y = c

Now take the coordinates of the given point (4, 9) and substitute them into the above equation, to find c:

2(4) + 10(9) = c

Then 8 + 90 = c, and c = 98

Then the desired equation is 2x + 10y = 98

To find the y-intercept, let x = 0 and solve for y.  We get

10y = 98, so that y = 9.8.  The y-intercept is thus (0, 9.8).

The y-intercept of the line parallel to 2x + 10y = 7 and containing the point (4, 9) is 8.6.

The y-intercept of a parallel line can be found using the equation y = mx + b, where m is the slope and b is the y-intercept. Since the given line 2x + 10y = 7 is in the form Ax + By = C, we need to rearrange it to the slope-intercept form. Therefore, the equation becomes: 10y = -2x + 7 → y = (-2/10)x + 7/10. The slope of the given line is -2/10, which means any line parallel to it will also have a slope of -2/10. Now we can use the point-slope form to find the equation of the parallel line that passes through the point (4, 9):

y - y1 = m(x - x1) → y - 9 = (-2/10)(x - 4)

Expanding and simplifying the equation, we get:

y - 9 = (-2/10)x + 8/10 → y = (-2/10)x + 8/10 + 9 → y = (-2/10)x + 86/10

Therefore, the equation of the parallel line that contains the point (4, 9) is y = (-2/10)x + 86/10. The y-intercept of this line is 86/10 or 8.6.

https://brainly.com/question/30097515

#SPJ2

Answer:

Yes

Step-by-step explanation:

2a+6=12

2a=12-6

2a=6

a=6/2

a=3

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

a+3=6

a=6-3

a=3

----------

Yes, the two equations are equivalent.

Answer:

The Number is 8.

Step-by-step explanation:

Let the number be x.

Given:

1/2 is subtracted from four times the reciprocal of a number, the result is 0.

Hence the equation will become like;

[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]

Now Solving the equation we get.

[tex]\frac{4}{x} -\frac{1}{2}=0\\\\\frac{4}{x} = \frac{1}{2}\\\\x= 4\times 2\\x=8[/tex]

Now the we can see the number is 8, when 1/2 is subtracted from 4 times the reciprocal of number means 4/8 which becomes 1/2 and hence when 1/2 is subtracted from 1/2 it equals to 0.

Hence the number is 8.

Correct Answer: A. Scatter plot A

Explanation: The line y=x slopes upward from the lower left corner of the graph to the upper right corner, at a 45-degree angle. The scatter plot whose points most closely match that trend is scatter plot A.

Answer:

Step-by-step explanation:

We need to find the scatter plot that is closest to y = x.

First of all, you must know the behaviour of y = x. That equation represents a straight line that passes through the origin of the coordinate system.

So, the right scatter plot must have the majority of points on this line that passes through the origin.

Notice that the Scatter plot A has this beahivour, if you draw a straight line through the origin and the points, you'll observe that the line best fits.

On the other hand, the other scatter plots are not following this linear behaviour.

Therefore, the right answer is A.

The quotient is: 4a-5

The remainder is: 0

Step-by-step explanation:

We need to divide -40a^6+50a^5 by -10a^5

The division is shown in figure attached.

The quotient is: 4a-5

The remainder is: 0

Keywords: Division of polynomials

Learn more about Division of polynomials at:

#learnwithBrainly

Answer:

[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]

Step-by-step explanation:

Solving trigonometric equations.

We are given a condition and we must find all angles who meet it in the provided interval. Our equation is

[tex]cos5x=-\frac{1}{2}[/tex]

Solving for 5x:

[tex]5x=\frac{2\pi}{3}+2n\pi[/tex]

[tex]5x=\frac{4\pi}{3}+2n\pi[/tex]

The values for x will be

[tex]x=\frac{\frac{2\pi}{3}+2n\pi}{5}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+2n\pi}{5}[/tex]

To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval [tex](0,2\pi)[/tex]

For n=0

[tex]x=\frac{\frac{2\pi}{3}}{5}=\frac{2\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}}{5}=\frac{4\pi}{15}[/tex]

For n=1

[tex]x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+2\pi}{5}=\frac{2\pi}{3}[/tex]

For n=2

[tex]x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}[/tex]

For n=3

[tex]x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+6\pi}{5}=\frac{22\pi}{15}[/tex]

For n=4

[tex]x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+8\pi}{5}=\frac{28\pi}{15}[/tex]

For n=5 we would find values such as  

[tex]x=\frac{\frac{2\pi}{3}+10\pi}{5}=\frac{32\pi}{15}[/tex]

[tex]x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}[/tex]

which don't lie in the interval [tex](0,2\pi)[/tex]

The whole set of results is

[tex]\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}[/tex]

Answer:

0

Step-by-step explanation:

If the answer is between 0 to 0.49, the best estimate is 0.

If the answer is between 0.5-1.49, the best estimate is 1.

If the answer is 1.5 or greater, the best estimate is 2.

Without giving the fractions 1/10 and 1/12 a common denominator, we know the answer is between 2/12 and 2/10.

2/12 is less than 2/10. 2/10 is 0.2, which is less than 0.5.

Since the final answer is less than 0.5, the best estimate is 0.

Answer:

The answer is A.

Step-by-step explanation:

Just took the test. You are welcome.

Answer:

The length of the farm is 310 yards and the width is 105 yards

Step-by-step explanation:

The correct question is

The Williams have a farm that is in a rectangular shape. The length of the farm is one hundred yards more than twice the width. The whole perimeter of the farm is 830 yards

Find the dimensions of the farm

Let

x ----> the length of the rectangular farm

y ----> the width of the rectangular farm

we know that

The perimeter of the farm (rectangle) is equal to

[tex]P=2(x+y)[/tex]

we have

[tex]P=830/ yd[/tex]

so

[tex]830=2(x+y)[/tex]

simplify

[tex]415=(x+y)[/tex] -----> equation A

[tex]x=2y+100[/tex] ----> equation B

substitute equation B in equation A

[tex]415=(2y+100+y)[/tex]

solve for y

[tex]415=(3y+100)[/tex]

[tex]3y=415-100[/tex]

[tex]3y=315[/tex]

[tex]y=105\ yd[/tex]

Find the value of x

[tex]x=2y+100[/tex]

[tex]x=2(105)+100=310\ yd[/tex]

therefore

The length of the farm is 310 yards and the width is 105 yards

Answer:

x=7 and x=(3/4)

Step-by-step explanation:

Answer:

n = 36

Step-by-step explanation:

1. Let's find the value of n for the expression: (9^3)^12 =9^n

(9^3)^12 =9^n

(9³) ¹² = 9 ⁿ

Let's remember that the power rule tells us that to raise a power to a power, we multiply the exponents. Here you see that 9³ is raised to the 12th power is equal to 36 (3 * 12)

9 ³⁶ = 9 ⁿ

n = 36

Answer:

PLEASE PROVIDE MORE INFORMATION

Step-by-step explanation:

Multiply the current price by 1 + percentage of increase.

3.50 x 1.11 = 3.89

The new price will be $3.89

Answer:

The answer is C.

Step-by-step explanation:

Very easy question.

Answer:

its a or c

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

8 x n + m = ?

8 x 7 + 6

8 x 7 = 56

56 + 6 = 62

Answer: 62

Step-by-step explanation:

solution here m=6,n=7,and 8n+m=? now 8n+m =8×7+6 =56+6 =62

Answer:

D: All of the above.

Step-by-step explanation:

A. All simple machines are useful in some way, weather that be making it easier to lift heavy objects, activating other machines, or something else.

B. Any simple machine must be, well, simple. i. e. have few moving parts.

Take the lever, for example. It has only one moving part, yet it is still very useful.  

C. They can be used to do work. Simple machines can be put together to make something that can do work.

Imagine a windmill that generates power, which then is taken by a motor attached to an Archimedes screw. All of these machines are simple, yet they are still used to do work.

HERE IS THE ANSWER 85

Answer:

33

Step-by-step explanation:

substitute 4 in the place of x.

multiply 4 by 7 then add 5 and your answer is 33.

You roll a 6-sided die. The probability of getting prime is 50%.

Solution:

Given, that we have rolled a 6 – sided die.

We have to find the P(prime) as percentage.

Now, It means that we have to find the probability of getting a prime number on the face.

On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6

Number of possible outcomes = 6

We have to get a prime number on rolling a die

The prime numbers in possible outcomes are 2, 3, 5

So number of favorable outcomes = 3

[tex]\text {Probability of an event as percentage }=\frac{\text { favourable number of outcomes }}{\text { total number of outcomes }} \times 100[/tex]

[tex]\text {Probability of getting prime number on face of die }=\frac{3}{6} \times 100[/tex]

[tex]\begin{array}{l}{\text { P(prime) }=\frac{1}{2} \times 100} \\\\ {\text { P(prime) }=50 \%}\end{array}[/tex]

Hence, probability of getting prime is 50%.

Answer:

Either x  = + i/2 or  x = i/2 is the solution for the given quadratic equation.

Step-by-step explanation:

Here, the given quadratic equation is:[tex]4x^2 + 1 = 0[/tex]

Now, comparing the given equation with standard Quadratic Form, [tex]ax^2 + bx + c = 0[/tex]

we get,a  = 4, b =0 and c = 1

Now, the Quadratic Formula is given as:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

So, here the solution for the given expression is:

[tex]x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies  x = \frac{0 \pm4i}{8}\\\implies x  =  \frac{0 + 4i}{8} = \frac{i}{2} \\or,  x  =  \frac{0 - 4i}{8} = \frac{-i}{2}[/tex]

Hence, either x  = + i/2 or  x = i/2 is the solution for the givenquadratic equation.

Answer:

3h-9/2

Step-by-step explanation:

3/4(4h-6)=3h-18/4

simplify

3h-9/2

Answer:

3(3h-3/2) in its simplified form.

Step-by-step explanation:

Given the equation 3/4(4h-6),

First we will open the bracket up by multiplying through by 3/4 to have;

3h - 9/2

Since 3 is common at both sides of the resulting equation, we will factor it out to have;

3(h-3/2).

Since we cannot simplify further, then the expression 3/4(4h-6) is also equivalent to 3(h-3/2).