6. A line passes through the points (-2,5) and (6,9). Calculate the gradient of this line.

Answer:

dimensions are 51x91

Step-by-step explanation:

Assuming that the gym is rectangular in shape, then...

l*w=4641

and 2l+2w=284

We have two variables and two equations so to solve this we plug one equation into another.

Solve for one variable:

l*w=4641

w=4641/l

Plug into the other equation...

2l+2(4641/l)=284

Solve

l*(2l+9282/l)=284

2l^2+9282=284l

2l^2-284l+9282=0

Factor the trinomial:

2(l−51)(l−91)=0

l−51=0 or l−91=0(Set factors equal to 0)

l=51 or l=91

now, lets plug it into one of the equations to find w

51*w=4641

w=91, l=51

or...

91*w=4641

w=51, l=91

Answer:

91 ft × 51 ft

Step-by-step explanation:

while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).

and it assumes you can find the right factoring of the expression.

so, I will show you here how to generally solve this, even if you cannot find the right factorization :

l×w = 4,641 ft²

w = 4641/l

2l + 2w = 284

2l + 2(4641/l) = 284

2l + 9282/l = 284

2l² + 9282 = 284l

2l² - 284l + 9282 = 0

to make things easier let's divide everything by 2

l² - 142l + 4641 = 0

the general solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = l

a = 1

b = -142

c = 4641

l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =

= (142 ± sqrt(20,164 - 18,564))/2 =

= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20

l1 = 71 + 20 = 91

l2 = 71 - 20 = 51

w1 = 4641/91 = 51

w2 = 4641/51 = 91

so, they are interchangeable (it does not matter which we call length and which width).

the dimensions are 91 ft × 51 ft

Answer:

55.9 m

Step-by-step explanation:

If you swam from one cornee to the other, you divide the rectangle into 2 right triangles

the diagonal is a common hypothenus of the triangles

applying pytha

C² = A² + B²

C² = 25² + 50²

C² = 625 + 2500

C² = 3125

C = sqrt 3125

C = 55.9 m

Answer:

105 cubic meters

Step-by-step explanation:

Answer:

let the number of persons be " x "

and , let each person get [tex]\frac{9000}{x}\\[/tex]rupees.

______________________________________

let's first see why each person got [tex]\frac{9000}{x}\\[/tex] rupees ,

let us suppose each person gets an amount of " r " rupees.

then ,

[tex]x \times r = amount \: we \: have \: with \: us \\ \dashrightarrow{xr = 9000} \\ \dashrightarrow{ r = \frac{9000}{x}} [/tex]

_____________________________________

According to Question ,

hαd thєrє вєєn 20 mσrє pєrѕσnѕ, єαch pєrѕσn wσuld'vє gσt rupєєѕ 160 lєѕѕ.

hєncє, wє αrє nσw ín α ѕtαtє tσ frαmє αn єquαtíσn whích íѕ αѕ fσllσwѕ -

[tex]\fbox{(x + 20)(r - 160) = 9000}[/tex]

lєt'ѕ nσw plug ín thє vαluє σf r αѕ [tex]\frac{9000}{x}\\[/tex]

[tex](x + 20)( \frac{9000}{x} - 160) = 900 0\\ \\ \cancel{9000} + \frac{180000}{x} - 160x - 3200 =\cancel{ 9000} \\ \\ taking\:LCM, \\ \\ - 160x {}^{2} - 3200x + 180000 = 0 [/tex]

on dividing the complete equation by (- 160)

[tex]x { }^{2} + 20x - 1125 = 0[/tex]

now , use the method of splitting the middle term so that we get the value of x.

[tex]x {}^{2} + 45x - 25x - 1125 = 0 \\ \\ x(x + 45) - 25(x + 45) \\ \\ (x + 45)(x - 25) = 0 \\ \\ \fbox{x = - 45 \: \: or \: \: 25}[/tex]

since number of persons can't be negative. therefore ,

number of persons = x = 25

_____________________________

_____________________________

hope helpful :D

The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:

6= πd and then divide both sides of the equation by π you get that d = 1.90

To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:

1 = 0.9549θ

Answer:

60

Step-by-step explanation:

1/6 x 360

Central angle is equal to measure of intercepted arc.

60 degrees

Answer:

Improper Fraction:
933/100

Mixed Number:
9 33/100

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

Q15: A

Q12: A,C,D

Q13: B

Q14: C

Answer:

1) Left 5, Down 1

2) A, C, D

3) B

4) D

Step-by-step explanation:

Desmos graphing calculator will help you with all of these.

Answer:

Step-by-step explanation:

Volume of the right triangular prism:

Note: V=l*w*h

L=3cm

W=4cm

H=7cm

Then, multiply.

3*4*7=84

84cm³

Therefore, the correct answer is 84cm³.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

Area = 201.1

Cicumference = 50.27

Your answers are correct

Step-by-step explanation:

A = Area = ?

C = Circumference = ?

SInce both the "Area" and "Circumference" are unknown, we use the formula:

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi { d }^{ 2 }}[/tex]

Remember that:

The diameter is the length of the line through the center

and

The radius is half the diameter

Given:

Diameter = 16

Now we substitute "16" for "d" into the formula and solve

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi {( 16) }^{ 2 }}[/tex]

Calculate 16 to the power of 2 and get 256

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi \times 256}[/tex]

Multiply [tex]\frac{1}{4}[/tex] and 256 to get  [tex]\frac{256}{4}[/tex]

[tex]\mathrm{A = \dfrac{ 256 }{ 4 } \pi}[/tex]

Divide 256 by 4 to get 64

[tex]\mathrm{A=64\pi }[/tex]

Multiply 64 and π to get 201.06192983

[tex]\mathrm{A=201.06192983}[/tex]

Round to the nearest tenth and get 201.1

[tex]\mathrm{A=201.1}[/tex]

Next we need to find the "Circumference"

Formula for finding circumference is:

C = πd

Given:

Diameter = 16

Now we substitute "16" for "d" into the formula and solve

C = π(16)

Multiply 16 and π to get 50.265482457

C = 50.265482457

Round to the nearest hundreth and get 50.27

C = 50.27

So, your answers are correct.

The only mistake that could happen is whether you need to round to the nearest hundreth or tenth.

7 in.3 hope it helps

coordinates: (4, 7) and (4, –3)

slope:

[tex]\sf \dfrac{y_2-y_1}{x_2-x_2}[/tex]

find slope:

[tex]\rightarrow \sf \dfrac{-3-7}{4-4}[/tex]

undefined

equation : x = 4

The type of data which would be considered as the qualitative data is the smell of the plant.

The qualitative data is the data which describes the quality or the characteristics of a thing.

Qualitative data can be felt rather than measure. The data of color of hairs of cricket team player is an example of qualitative data.

The options for the problem are listed below.

Thus, the type of data which would be considered as the qualitative data is the smell of the plant.

Learn more about the qualitative data here

https://brainly.com/question/24492737

Answer:

B: Frequency of Foreign-Language Studies by Row

Answer:

x=15 inches

Step-by-step explanation:

Area of ∆ is 27sq inches

Height is 4.5 inches

base is (x-3) inches

Area of ∆= ½×b×h

27= ½×(x-3)×4.5

27=2.25×(x-3)

27=2.25x-6.75

2.25x=27+6.75

2.25x=33.75

x=33.75/2.25

x=15 inches

Answer:

5n=c

Step-by-step explanation:

the equation 5n=c can represent the total cost Hong would have paid for the notebooks because given that each notebook costs $5, you would multiply 5 by the number of notebooks (n) that Hong would be purchasing, which would bring you to the cost (c) of the notebooks all together

sorry for the delay. hope this helps

Answer:

44%

Step-by-step explanation:

25 divided by the eleven students is .44

Answer:

It would be 44%.

Step-by-step explanation:

There are 11 boys and 25 students in total. That would make it 11/25. That is 44 out of 100. Which is 44%.

Answer:

24

Step-by-step explanation:

12 divided by 1/2 = 24

Hope this helped! :)

Answer:

84.2%

Step-by-step explanation:

420 + 380 = 800

800 / 950 = .842

.842 * 100 = 84.2

84.2 = 84.2%

If Rick was to sell $120,000 worth of cars, he would make approximately $14,400. Hope this helps - Have an amazing rest of your day :)

w = won game

l = lost game

w + l = 15

and

w = I + 3

so

l + 3 + l = 15

2l = 12

l = 6

lost = 6

won = 9

Answer:

The ratio of wins to losses is 3 to 1, out of 32 total games. 3:1 has a total of 4 parts (3+1).

Total games divided by total parts is 32/4 = 8.

Now multiplying number of parts to divisor gives us 3x8 : 1x8 or 24:8. Therefore they won 24 games, lost 8.

Step-by-step explanation:

Answer:

please see explanation

Step-by-step explanation:

look at the photo

Answer:

950.331ft^3

Step-by-step explanation:

I hope this is correct...

I believe 22ft would be the diameter of thr circle so to find the radius you divide it by 2 and follow the formula like so.

Answer:

y- intercept = 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{3}{4}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{3}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , then equation of perpendicular line is

y = [tex]\frac{4}{3}[/tex] x + c

to find c substitute (- 3, - 3 ) into the equation

- 3 = - 4 + c ⇒ c = - 3 + 4 = 1

that is the y- intercept of the perpendicular line is c = 1

Answer:

both weigh the same.

Step-by-step explanation:

you have 5kg of steel and 5kg feathers.

The weight is the same so both weigh the same.

Answer:

here my answer

Step-by-step explanation:

hope this helps

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

═════════════════════

[tex] \frac{5}{6}x = 35[/tex]

[tex]x=35\times \left(\frac{6}{5}\right) [/tex]

[tex]x=\frac{35\times 6}{5} [/tex]

[tex]x=\frac{35\times 6}{5} [/tex]

[tex]x=\frac{210}{5} [/tex]

[tex]x=42 [/tex]

══════════════════════

Step-by-step explanation:

#Carry on learning

Answer:

  36.5 square units

Step-by-step explanation:

There are a number of ways to compute the area of a polygon from the coordinates of its vertices. There are algebraic formulas, geometric methods involving decomposing the figure, and an interesting method described by Pick's theorem.

__

The figure can be enclosed by a rectangle that is 7 units high by 9 units wide. The actual figure is obtained by removing the triangular corners of this rectangle. The areas of those are given by the triangle area formula ...

  A = 1/2bh

Working clockwise from lower left, the triangle base (horizontal) and height (vertical) dimensions are 5×6, 7×1, 2×6, 4×1. That means the area of the triangles is ...

  A = 1/2(5×6 +7×1 +2×6 +4×1) = 1/2(30 +7 +12 +4) = 1/2(53) = 26.5

The area of the bounding rectangle is ...

  A = bh = 9×7 = 63

So, the area of the figure is the difference ...

  A = 63 -26.5 = 36.5 . . . square units

__

The other methods of finding the area have been added as attachments.

Answer:

Step-by-step explanation:

f(t)= 20t-5t^2

Answer:

(4,0)

Step-by-step explanation:

I did it on khan and got it right :)

12 shade out of 15 boxes which gives 0.8 chance of picking a shaded one.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

There are 15 sections given

To make the probability of choosing a shaded section randomly 0.8,

So,

0.8 of 15

0.8 is equal to 80%

we need to figure out 80% of the 15

80% of 15

80% × 15

= 12

Hence, we would need to shade 12 out of 15 boxes which gives 0.8 chance of picking a shaded one.

Learn more about probability;

brainly.com/question/795909