(04.07A) Two quantities are related, as shown in the table below: x y 2 10 4 9 6 8 8 7 Which equation best represents the relationship? y = 1 over 2x + 11 y = negative 1 over 2x + 11 y = 2x + 10 y = 2x + 11

Answer:

The first one

Step-by-step explanation:

Let a and b be the two numbers. Then

a + b = -4

a b = -2

Solve the second equation for b :

b = -2/a

Substitute this into the first equation:

a - 2/a = -4

Multiply both sides by a :

a² - 2 = -4a

Move 4a to the left side:

a² + 4a - 2 = 0

Use the quadratic formula to solve for a :

a = (-4 ± √(4² - 4(-2))) / 2

a = -2 ± √6

If a = -2 + √6, then

-2 + √6 + b = -4

b = -2 - √6

In the other case, we end up with the same numbers, but a and b are swapped.

Answer: 36

Step-by-step explanation:

Given:  Sapphire shelves 12 books at a time, whereas Abe shelves 18 at a time.

If they end up shelving the same number of books, what is the smallest number of books each could have shelved = LCM (12,18)

12 = 2 x 2 x 3

18 = 2 x 3 x 3

LCM (12, 18) = 2 x 2 x 3 x 3 = 36

Hence, the smallest number of books each could have shelved = 36

Answer:

36

Step-by-step explanation:

nrly

Answer: C {48,65,80}

Step-by-step explanation:

In order for it to be a right triangle it would have to be {48,64,85}

Hope this helps

Answer:

u say which but don't even give us options.

Answer:

6.9 ft

Step-by-step explanation:

The Pythagorean Theorem. :)

a^2 + b^2 = c^2

4^2 + b^2 = 8^2

16 + b^2 = 64

b^2 = 48

D = 6.928

<3 Enjoy,

    Dea

The length of the stake needs to be from the middle of her tent will be 6.9 feet. Then the correct option is D.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long.

Then the length of the stake needs to be from the middle of her tent will be

We have

P = 4 ft

H = 8 ft

Then the base is given by the Pythagoras theorem.

B² = H² - P²

B² = 8² - 4²

B² = 64 - 16

B² = 48

B = 6.9 ft

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

Answer:

49

Step-by-step explanation:

28-21=7

7 to the power of two is the same as 7(7)

7(7)=49

Given:

Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1).

To find:

The coordinates of point P.

Solution:

Section formula: If a point divide a line segment in m:n, then the coordinates of point are

[tex]\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]

Point P divides the line segment AB in 5:3 where A(-6,9) and B(2,1). Using section formula, we get

[tex]P=\left(\dfrac{5(2)+3(-6)}{5+3},\dfrac{5(1)+3(9)}{5+3}\right)[/tex]

[tex]P=\left(\dfrac{10-18}{8},\dfrac{5+27}{8}\right)[/tex]

[tex]P=\left(\dfrac{-8}{8},\dfrac{32}{8}\right)[/tex]

[tex]P=\left(-1,4\right)[/tex]

Therefore, the coordinates of point P are (-1,4).

Given:

In isosceles triangle ABC, consider AB=BC and the segment BD with D a point on AC is the median to the base AC.

Perimeter of ABC is 50m and the perimeter of ABD is 40m.

To find:

The length of BD.

Solution:

In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC.

[tex]AB=BC[/tex]           ...(i)

[tex]AD=CD[/tex]

[tex]AC=2AD[/tex]         ...(ii)

Perimeter of ABC is 50m.

[tex]AB+BC+AC=50[/tex]

[tex]AB+AB+2AD=50[/tex]      [Using (i) and (ii)]

[tex]2AB+2AD=50[/tex]

[tex]2(AB+AD)=50[/tex]

Divide both sides by 2.

[tex]AB+AD=25[/tex]        ...(iii)

Now, perimeter of ABD is 40m.

[tex]AB+AD+BD=40[/tex]

[tex]25+BD=40[/tex]         [Using (iii)]

[tex]BD=40-25[/tex]

[tex]BD=15[/tex]

Therefore, the length of BD is 15m.

Answer:

Step-by-Step Explanation:

Area of the base = length × breadth

= (4x + 5) (x + 3)

= 4x(x + 3) + 5(x + 3)

= 4x² + 12x + 5x + 15

= 4x² + 17x + 15

_____________________________________

Volume = length × breadth × height

8x³ + 30x² + 13x - 15 = (4x + 5)(x + 3) × h

[tex] \frac{ 8x³ + 30x² + 13x - 15 }{(4x + 5)(x + 3)} = h[/tex]

Answer:

A Plus Plumbing

Step-by-step explanation:

60(2)+80 = 120+80 = 200 < 250

Answer:

A- plus plumbing

Step-by-step explanation:

hope this helps

Answer:

a = (b - bc)/d

Answer:

ad=b-bc

a=b-bc/d or  a=b-bc

                        --------

                            d

*everything is divided by d on the other side...so b-bc is all divided by d

Answer:

A!

Step-by-step explanation:

Answer:

You need to show the graph.

Step-by-step explanation:

Answer:

4000

Step-by-step explanation:

Answer:

slope of st is -0.25

slope of tu is 1

slope of us is -0.25

slope of sv is 1 so it is a parallelogram. the slope of the parallel lines needs to be the same to be a parallelogram. to find the slope, you need to find the change from the points of the referenced line, for example, slope of st you would label each point as x1, y1 and x2,y2. it does not matter which one you label and you can change them for each different line. you would then find the difference by subtracting (y2-y1) divided by (x2-x1) so 4-3=1 and 1-5 is -4. you then divide 1/-4 is -0.25. you the follow the steps for each line. is the parallel lines have the same slope, it is a parallelogram

Answer:

y=-3x+8

Step-by-step explanation:

y=mx+b

(m=slope and b=y-intercept)

Answer:

Step-by-step explanation:

let’s use this equation y = mx + b

where m = slope

and b = y intercept

since slope is -3, m = -3

and since y intercept is 8, b = 8

so the equation is

y = -3x +8

Answer:

12cm

Step-by-step explanation:

You can draw a triangle with hypotenusa 13, height h and base 5 (the difference between the radius 9 and 4). Then pythagoras tells us that

13² = h² + 5²

so

h = 13² - 5² = √144 = 12

Answer:

2625

Step-by-step explanation:

Simple Interest Formula

P*R*T

1250*1.05*2=2625

Answer:

After two years, there will be a total of $1,375 paid and $125 paid in interest.

Step-by-step explanation:

Since, 5 x 2 = 10, first we should find 10% of $1,250.

1,250 x 0.10 = 125

$1,250 + $125 = $1375

Therefore, after two years, there will be a total of $1,375 paid and $125 paid in interest.

Hope this helps! :D

Answer:

c(4) = -76

Step-by-step explanation:

c(x) x=4 so plug 4 in for x

-5(4)² + (4)

Do parentheses first so... 4² = 16

-5(16) + 4

-5(16) = -80

-80+4 = -76

c(4) = -76

Answer:

Perimeter is 80cm

Step-by-step explanation:

A rectangle's area is calculated by multiplying the length by the width. If we are given the area of the rectangle and the length then we would simply need to solve for the width of the rectangle using the area formula we just mentioned...

A = l * w

336[tex]cm^{2}[/tex] = 12cm * w  ... divide both sides by 12cm

28cm = w

Now we can see that the width of this rectangle is 28cm. To find the perimeter we need to add all four sides together, since we know that a rectangle's opposite sides are the same then we add the length and the width twice to calculate the perimeter (P)

P = 12cm + 12cm + 28cm + 28cm

P = 80cm

Answer:

x=4

Step-by-step explanation:

In triangle MLK

Now come to triangle MKJ

MK=5

Hence

[tex]\longrightarrow\sf MJ=5 [/tex]

[tex]\longrightarrow\sf x+1=5[/tex]

[tex]\longrightarrow\sf x=5-1 [/tex]

[tex]\longrightarrow\sf x=4 [/tex]

Answer:

b = 23/3

Step-by-step explanation:

5 = -2/3(4) + b

5 = -8/3 + b

5 + 8/3 = b

b = 23/3

Answer:

d ≈ 6.41

Step-by-step explanation:

Given that F is inversely proportional to d² then the equation relating them is

F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion

To find k use the condition when F = 8, d = 6 , then

8 = [tex]\frac{k}{6^2}[/tex] = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )

288 = k

F = [tex]\frac{288}{d^2}[/tex] ← equation of proportion

When F = 7 , then

7 = [tex]\frac{288}{d^2}[/tex] ( multiply both sides by d² )

d² × 7 = 288 ( divide both sides by 7 )

d² = [tex]\frac{288}{7}[/tex] ( take the square root of both sides )

d = ± [tex]\sqrt{\frac{288}{7} }[/tex] ≈ ± 6.41

The positive value of d is 6.41 ( to 2 dec. places )

Answer:

when F = 7, d = 6.41

Step-by-step explanation:

We know that when 'y' varies inversely with 'x', we get the equation

y ∝ 1/x

y = k/x

where 'k' is called the constant of proportionality

Given that F is inversely proportional to d.

F ∝ 1/d

F = k /d²

When F = 8, d = 6, we need to find k

k = Fd²

k = 8×(6)²=288

Now, we need to find d when F = 7

so substitute k = 288, F = 7 in the equation

F = k /d²

d² = k/F

d² = 288/7

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}[/tex]

but, we need to take the positive value of d, so

[tex]d=\sqrt{\frac{288}{7}}[/tex]

[tex]d=6.41[/tex]

Therefore,

when F = 7, d = 6.41

Answer:

isosceles right triangle

Answer:

The first one is

5x * 10

(x is the variable) TIMES 10

Step-by-step explanation:

Answer: In an ordinary year, if you were to count all the days in a calendar from January to December, you'd count 365 days. But approximately every four years, February has 29 days instead of 28. So, there are 366 days in the year. This is called a leap year.

Step-by-step explanation: