PLZZ HEPPP A line passes through (−1, 5) and (1, 3). Which answer is the equation of the line? x + 2y = 7 x + y = 4 x + 2y = 5 x + y = 2

Step-by-step explanation:

since PQRT is a rhombus,

URQ=TPU

y=180-90-24=66

x=180-32-90-24=34

Answer:

12.8

Step-by-step explanation:

you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do

Sin(110)x=17sin(45)

and then it turns into 17sin(45)/sin(110)

then put it into desmos with it being in degrees mode

Answer:

13

Step-by-step explanation:

Put -1 and 12 in the absolute value form and add them together. You'll get 13.

Number of  units separate the points is 13 units.

Given that;

Coordinate of first point = (5 , -1)

Coordinate of second point = (5 , 12)

Find:

Number of  units separate the points

Computation:

Number of  units separate the points = √(x1 - x2)² + (y1 - y2)²

Number of  units separate the points = √(5 - 5)² + (-1 - 12)²

Number of  units separate the points = √(-13)²

Number of  units separate the points = 13 units

Find out more information about 'Coordinate'.

https://brainly.com/question/4399730?referrer=searchResults

Answer:

C

Step-by-step explanation:

We can notice that the balance beam has in one side 7 balls and in the other one 5 balls and a square

The balance beam is balenced

Let x be the square mass

The solution is 2

C fits perfectly what we prooved

Answer:

C: x + 5 = 7; x = 2

Step-by-step explanation:

Refer to the given model. On the left-hand side of the balance beam, there are five circles and one square. On the right-hand side of the balance beam, there are seven circles. The balance beam is evenly distributed, so the value on the left-hand side of the balance beam must be the same as the value on the right-hand side of the balance beam.

The square stands for an unknown quantity. In algebra, variables are used to represent unknown quantities, so x will represent the value of the square.

The model shows that the value of x plus five circles is the same as seven circles. Replacing the word "plus" with a plus sign and replacing "is the same as" with an equal sign gives the equation x + 5 = 7.

To solve the equation, subtract 5 from both sides of the equation to isolate x.

Thus, the solution to the equation is x = 2.

Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

There are 15 points on a circle.

We need three points to form a triangle

Therefore the number of triangles = 15 choose 3 ​= 15!/(3!x12!)​ = (15x14x13)/(3x2x1) = 5x7x13 = 455

Hence the number of triangles formed is 455

Answer:

Sequence B, Sequence A, Sequence C

Step-by-step explanation:

Data obtained from the question include the following:

Sequence A: 160, 40, 10, 2.5,

Sequence B: -21, 63, -189, 567, ...

Sequence C: 8, 12, 18, 27

Next, we shall determine the common ratio of each sequence. This is illustrated below:

Common ratio (r) is simply obtained by dividing the 2nd term (T2) by the 1st term (T1) or by dividing the 3rd term (T3) by the 2nd term (T2). Mathematically, it is expressed as:

r = T2/T1 = T3/T2

For sequence A:

160, 40, 10, 2.5

2nd term (T2) = 40

Ist term (T1) = 160

Common ratio (r) =..?

r = T2/T1

r = 40/160

r = 1/4

r = 0.25

Therefore, the common ratio is 0.25.

For sequence B:

-21, 63, -189, 567

2nd term (T2) = 63

Ist term (T1) = -21

Common ratio (r) =..?

r = T2/T1

r = 63/-21

r = - 3

Therefore, the common ratio is - 3.

For Sequence C:

8, 12, 18, 27

2nd term (T2) = 12

Ist term (T1) = 8

Common ratio (r) =..?

r = T2/T1

r = 12/8

r = 3/2

r = 1.5

Therefore, the common ratio is 1.5.

Summary:

Sequence >>>>> Common ratio

A >>>>>>>>>>>>> 0.25

B >>>>>>>>>>>>> - 3

C >>>>>>>>>>>>> 1.5

From the above illustration,

Ordering the sequence from least to greatest common ratio, we have:

Sequence B, Sequence A, Sequence C.

Answer: C) Plane: 235 km/h, Wind: 24 km/h

Step-by-step explanation:

Given that :

Average Speed while flying with a tailwind = 259km/hr

Return trip = 211km/hr

Let the speed of airplane = a, and wind speed = w

Therefore ;

Average Speed while flying with a tailwind = 259km/hr

a + w = 259 - - - (1)

Return trip = 211km/hr

a - w = 211 - - - (2)

From (2)

a = 211 + w

Substitute the value of a into (1)

a + w = 259

211 + w + w = 259

211 + 2w = 259

2w = 259 - 211

2w = 48

w = 48/2

w = 24km = windspeed

Substituting w = 24 into (2)

a - 24 = 211

a = 211 + 24

a = 235km = speed of airplane

Answer:

The explicit formula for the sequence is

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

Hope this helps you

Answer:

[tex]\huge\boxed{a_n=-6n+44}[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

[tex]a_n=a_1+(n-1)(d)[/tex]

Substitute:

[tex]a_1=38;\ d=-6[/tex]

[tex]a_n=38+(n-1)(-6)[/tex]         use the distributive property

[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]

Answer:

Probability of (one club and one heart) = 0.1275 (Approx)

Step-by-step explanation:

Given:

Total number of cards = 52

Each suits = 13

FInd:

Probability of (one club and one heart)

Computation:

Probability of one club = 13 / 52

Probability of one heart = 13 / 51

Probability of (one club and one heart) = 2 [(13/52)(13/51)]

Probability of (one club and one heart) = 0.1275 (Approx)

Answer:

D. 0.1275

Step-by-step explanation:

Justo took the Pre-Test on Edg (2020-2021)!!

Answer:

Because the triangle is isosceles, the base angles are congruent, meaning that the angles that are not right angles are x and x. Since the sum of angles in a triangle is 180°, we can write:

90 + x + x = 180

x + x = 90

2x = 90

x = 45°

Answer:

45 degrees

Step-by-step explanation:

This triangle is "isosceles..." two legs are equal.  Thus, the triangle has two 45 degree angles.  The indicated angle is 45 degreees.

Answer:

$181,432,754

Step-by-step explanation:

We use the formula for compound interest here, to determine the amount

Mathematically, that would be;

A =I (1 + r/n)^nt

where A is the amount which we want to calculate

I is the initial amount which is $90,000

r is the rate = 23.24% = 23.24/100 = 0.2324

n is the number of times per year the interest is compounded = 12 (compounded monthly)

t is the number of years = 2014 - 1981 = 33

Substituting these values, we have;

A = 90,000(1 + 0.2324/12)^(33 * 12)

A = 90,000(1 + 0.0194)^396

A = 90,000(1.0194)^396

A = 181,432,754.27210504

Which is approximately $181,432,754 to the nearest whole dollars

Answer:

1/6

Step-by-step explanation:

Each roll is independent.  So the probability of rolling a six is 1/6, regardless of the previous rolls.

Answer:

Step-by-step explanation:

In order to convert a binary number into a decimal, it is expanded in the power of 2. Then, by simplifying the expanded form of the binary number, we obtain a decimal number.

Let's solve:

[tex]1000110[/tex]

[tex] = 1 \times {2}^{6} + 0 \times {2}^{5} + 0 \times {2}^{4} + 0 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} [/tex]

[tex] = 1 \times 64 + 0 \times 32 + 0 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 \times 0 \times 1[/tex]

[tex] = 64 + 0 + 0 + 0 + 4 + 2 + 0[/tex]

[tex] = 70[/tex]₁₀

Hope I helped!

Best regards!!

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

[tex]P + B = 14[/tex] ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

[tex]130P + 150B = 1920[/tex] --- Equation 2

Make P the subject of formula in equation 1

[tex]P = 14 - B[/tex]

Substitute 14 - B for P in equation 2

[tex]130(14 - B) + 150B = 1920[/tex]

Open Bracket

[tex]1820 - 130B + 150B = 1920[/tex]

[tex]1820 + 20B = 1920[/tex]

Subtract 1820 from both sides

[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]

[tex]20B = 100[/tex]

Divide both sides by 20

[tex]\frac{20B}{20} = \frac{100}{20}[/tex]

[tex]B = 5[/tex]

Substitute 5 for B in [tex]P = 14 - B[/tex]

[tex]P = 14 - 5[/tex]

[tex]P = 9[/tex]

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

Step-by-step explanation:

Hello,

For any function f which has an inverse function we can write

[tex]x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))[/tex]

This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.

Step 1 - The function f(x) can be written as a variable.  [tex]\boxed{y}=f(x)[/tex]

f(x) = y = 5x + 2

Step 2 - switch the variables x <-> y

x = 5y + 2

subtract 2 to both parts of the equation

<=> x - 2 =  5y + 2 - 2 = 5y

divide by 5 both parts of the equation

[tex]<=> y=\dfrac{x-2}{5}[/tex]

It means that the inverse of f is as below.

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

Step 3 - Find the inverse of g(x)

We already found that the inverse of f is g, so the inverse of g is f.

Let's do it again.

[tex]g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }[/tex]

And we found what we already known, meaning f is the inverse of g.

[tex](gof)(x)=(fog)(x)=x[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answers and Step-by-step explanation:

Step 1:

We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.

So, ff(x) must equal y.

Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:

y = 5x + 2

Step 2:

Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:

y = 5x + 2  ⇒  x = 5y + 2

Subtract 2 from both sides:

5y = x - 2

Divide by 5 from both sides:

y = (x - 2)/5

Step 3:

Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):

g(x) = y = (x - 2)/5

Switch the variables:

y = (x - 2)/5  ⇒      x = (y - 2)/5

Multiply by 5 on both sides:

5x = y - 2

Add 2 to both sides:

y = 5x + 2

Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.

=================================================

Explanation:

For choice C, the x values are out of order, so it might be tricky at first. I recommend sorting the x values from smallest to largest to get -2, -1, 0, 1, 2. Do the same for the y values as well. Make sure the correct y values stay with their x value pairs. You should get the list of y values to be 4, 2, 1, 1/2, 1/4

Check out the attached image below for the sorted table I'm referring to

We can see the list of y values is going down as x increases. This is a good sign we have decay. Further proof is that we multiply each term by 1/2 to get the next one

4 times 1/2 = 2

2 times 1/2 = 1

1 times 1/2 = 1/2

1/2 times 1/2 = 1/4

and so on. Effectively we can say the decay rate is 50%

Answer:

(B), in which the first two values are 2 and 10.

Step-by-step explanation:

We can tell that this is a proportional relationship because we can examine the numbers in there.

(2,10)

(4,20)

and (6,30).

If you notice, the x value times 5 gets us the y value for every single point there.

Therefore, B is proportional and it's equation is y = 5x.

Hope this helped!

Answer:

B.

Step-by-step explanation:

B. Is the only one that proportional because,

(2,10)

(4,20)

(6,30)

All these x values multiply by 5 to get the y value.

So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.

Thus,

answer choice B is correct.

Hope this helps :)

Answer:

Whenever a-5<0 or a<5

Step-by-step explanation:

So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.

Answer:

51°

Step-by-step explanation:

A circle has a total of 360 degrees. So,

360 = 62 + 66 + x + 73 + x + 57

Next, combine like terms:

360 = 2x + 258

Next, isolate your variable by subtracting 258 from both sides:

102 = 2x

Finally, divide both sides by 2 to get x:

x = 51

Answer:

x = 51

Step-by-step explanation:

x + 73 + x + 57 + 62 + 66 = 360

2x + 258 = 360

2x = 360 - 258

2x = 102

[tex]\frac{x}{2} =\frac{102}{2}[/tex]

x = 51

Answer:

130

Step-by-step explanation:

just did test on plato/edmentum..it was correct

84 (the answer above) is incorrect

Answer:

Hi sorry for late respond but the answer in 130!!

Step-by-step explanation:

Answer: y = -5*x + b

Step-by-step explanation:

A line is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

IIf we have a line that passes through the points (x1, y1) and (x2, y2) then the slope of the line is:

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

In this case we can see that the line passes through the points:

(0, 2) and (1, - 3)

Then the slope is:

a = (-3 - 2)/(1 - 0) = -5

Then our line is:

y = -5*x + b

And when x = 0, y = 2 then:

y = 2 = -5*0 + b

2 = b

Our line is:

y = -5*x + b

Answer:

The vertex is ( -5,0)

Step-by-step explanation:

The vertex form of a parabola is

y = a( x-h) ^2 +k

where ( h,k) is the vertex

y=2(x+5)^2

y=2(x - -5)^2 +0

The vertex is ( -5,0)

Answer:

vertex = (- 5, 0 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = 2(x + 5)² , that is y = 2(x + 5)² + 0 ← is in vertex form

with (h, k) = (- 5, 0 )

Answer:

432 aquariums

Step-by-step explanation:

To determine the number of aquariums the factory made, find the volume of 1 aquarium, then divide the total volume of water required.

Solution:

Volume of triangular prism aquarium = triangular base area × length of triangular prism

Volume = ½*b*h*l

Where,

b = 8 ft

h = 4 ft

l = 3 ft

Volume = ½*8*4*3 = 4*4*3

Volume = 48 ft³

Number of aquarium made = Volume of water required ÷ volume of 1 aquarium

= 20,736 ÷ 48 = 432 aquariums

Answer:

[tex]\boxed{\sf \ \ YES \ \ }[/tex]

Step-by-step explanation:

Hello

let's say that the price of the book was x

the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x

and this is $72 so we can write that

0.8*x=72

and then divide by 0.8 both parts

x = 72/0.8=90

So the list price value of the book is $90

and we can verify as 90 - 20%*90 = 90 - 18 = 72

Hope this helps

Answer: 19440 minutes

Step-by-step explanation:

Hi there! Hopefully this helps!

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

Answer: There are 19440 minutes in 324 hours.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:

324 x 60 = 19440.

Answer:

100 degrees

Step-by-step explanation:

360-260=100

Answer:

x=100

Step-by-step explanation:

130+130+x=360

260+x=360

x=100

Have a great and magnificent day

Answer: 4^3

(Four cubed or Four to the power of 3)

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Subtracting the given expressions, that is

3b² - 8 - (b(b² + b - 7) ) ← simplify parenthesis

= 3b² - 8 - (b³ + b² - 7b) ← distribute parenthesis by - 1

= 3b² - 8 - b³ - b² + 7b ← collect like terms

= - b³ + 2b² + 7b - 8 ← substitute b = - 3

= - (- 3)³ + 2(- 3)² + 7(- 3) - 8

= - (- 27) + 2(9) - 21 - 8

= 27 + 18 - 21 - 8

= 16

Answer:

Current Bond price = $1155.5116

Step-by-step explanation:

We are given;

Face value; F = $1,000

Coupon payment;C = (7.3% x 1,000)/2 = 36.5 (divided by 2 because of semi annual payments)

Yield to maturity(YTM); r = 5.6%/2 = 2.8% = 0.028 (divided by 2 because of semi annual payments)

Time period;n = 13 x 2 = 26 years (multiplied by 2 because of semi annual payments)

Formula for bond price is;

Bond price = [C × [((1 + r)ⁿ - 1)/(r(r + 1)ⁿ)] + [F/(1 + r)ⁿ]

Plugging in the relevant values, we have;

Bond price = [36.5 × [((1 + 0.028)^(26) - 1)/(0.028(0.028 + 1)^(26))] + [1000/(1 + 0.028)^(26)]

Bond price = (36.5 × 18.2954) + (487.7295)

Bond price = $1155.5116

Step-by-step explanation:

[tex] \sqrt{p} = \sqrt[r]{w - {as}^{2} } [/tex]

Find raise each side of the expression to the power of r

That's

we have

Send w to the left of the equation

Divide both sides by - a

We have

Find the square root of both sides

We have the final answer as

Hope this helps you