How much paneling needs to be removed?

f(x) = abˣ

"A scientist begins with 130 milligrams", or we can word it differently.

when x = 0, f(x) = 130, which in short simply means a = 130.

"After 30 hours, 65 mg of the substance remains", worded differently.

when x = 30, f(x) = 65.

[tex]f(x)=ab^x~\hspace{10em}\underline{f(x)=130b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} ~\hfill x&=30\\ f(x)&=65 \end{cases}\qquad \implies 65=130b^{30}\implies \cfrac{65}{130}=b^{30}\implies \cfrac{1}{2}=b^{30}[/tex]

[tex]\sqrt[30]{\cfrac{1}{2}}=b\implies \cfrac{\sqrt[30]{1}}{\sqrt[30]{2}}=b\implies \cfrac{1}{\sqrt[30]{2}}=b~\hfill \underline{f(x)=130\left( \cfrac{1}{\sqrt[30]{2}} \right)^x} \\\\[-0.35em] ~\dotfill\\\\ \textit{when x = 56, what is f(x)?}\qquad f(x)=130\left( \cfrac{1}{\sqrt[30]{2}} \right)^{56}\implies f(x)\approx 35.647[/tex]

Given, A + B = 90°

Putting values, we get

7x + 4 + 4x + 9 = 90°

11x + 13 = 90°

11x = 90 - 13 = 77°

x = 7°

Now, m<A = 7x + 4

= 7(7) + 4 = 53°

Hope this helps :)

Answer:

m∠A = 53°

Explanation:

complement angle: : two angles that add up to 90 degrees.

solve:

7x + 4 + 4x + 9 = 90

7x + 4x = 90 - 9 - 4

11x = 77

x = 7

Find m∠A:

7x + 4

7(7) + 4

49 + 4

53°

Explanation:

Any time Alyssa is increasing her speed, the graph will move uphill when going from left to right.

If she slows down, then the graph will move downhill when going left to right.

Always move from left to right when reading a graph because this is how the time axis is set up.

Any flat part represents portions where her speed is constant, i.e. doesn't change.

With all that in mind, the answer is choice D because

Formula:

[tex] \frac{5000}{2000} [/tex]

[tex] = > \frac{5}{2} [/tex]

[tex] = > 2.5[/tex]

Hence, 5000 Pound is equal to 2.5 Ton.

Step-by-step explanation:

The unit of weight in the avoirdupois system equal to 2,000 pounds in the United States and 2,240 pounds in Britain. The metric ton used in most other countries is 1,000 kg, equivalent to 2,204.6 pounds.

Answer: 2 1/2

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

hope this helps :)

Answer:

4

Step-by-step explanation:

Exponential functions are written in the form  [tex]f(x)=ab^x[/tex]

[tex]a[/tex] is the initial value of an exponential function and is found by substituting [tex]x=0[/tex] into the function as [tex]b^0=1[/tex]

Therefore, as y = 4 when x = 0, the initial value is 4

Answer:

First one
2x+3

Step-by-step explanation:

We can factorise the area:

6x²+9x-4x-6

3x(2x+3)-2(2x+3)

(3x-2)(2x+3)

So the width is 2x+3

Answer:

48.2° (1 d.p.)

Step-by-step explanation:

Start by labelling the given sides on the triangle.

The side in which the angle of interest and the right angle sits on is the adjacent side, while the side facing the right angle is the hypotenuse side (denoted by hyp).

[tex]\boxed{ \cosθ = \frac{adj}{hyp} }[/tex]

[tex]\cosθ = \frac{6}{9} [/tex]

[tex]θ = \cos^{ - 1} ( \frac{6}{9} )[/tex]

θ= 48.2° (1 d.p.)

Answer:

y = 2

Step-by-step explanation:

Kindly view the attached image to see the rules when looking for the horizontal asymptote.

In this situation we have 2x² / x²

The powers of both are equal to each other therefore the horizontal asymptote will be at the coefficient of the numerator divided by the coefficient of the denominator.

In other words the horizontal asymptote is at y = 2/1 or just 2

Answer: m<XVY = 82°

Step-by-step explanation: The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

Since the measures of the intercepted arcs are 86° and 78°,

we can setup the equation m<XVY = 1/2(86 + 78).

So we get m<XVY = 1/2(164) or m<XVY = 82°

[tex]ax^2+bx+c=a(x-x_1)(x-x_2)=>\\\text{Ans:} (x-3)(x+2)[/tex]

Answer: 6+2x

Step-by-step explanation:

6 is the fixed cost so you add six regardless of how many kilos you travel. You add the 2x because they charge 2 dollars for every extra kilometer. The x is kilometers(which you don’t know how many you travel.) so you add 6+2x to get the cost.

Linear equation is equation in which each term has at max one degree. The formula for the cost of the journey is y = $6 + $2(x).

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form,

y = mx + c

Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.

The given condition can be modelled using a linear relationship.

It is given that there is a fixed charge of $6 and an additional charge of $2 per kilometre. Therefore, the total charge,y can be modeled as,

y = $6 + $2(x)

where x represents the number of kilometres

The formula for the cost of the journey in Words​ is 6 plus two times of x, where x represents the number of kilometres.

Hence, the formula for the cost of the journey is y = $6 + $2(x).

Learn more about Linear equations:

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Answer:associative property of addition

Step-by-step explanation:The associative property of addition says that changing the grouping of the addends does not change the sum.

Answer:

x = 1

y = 2

Step-by-step explanation:

for the first one it is that because 4 * 1 = 4 and then 2 * 2 equals 4 so 4 + 4 = 8

For the second one it is that because 8 * 1 = 8 and then 4 * 2 = 8 so 8 + 8 = 16!

If this helped you please mark brainliest!

Answer:

x = 1

y = 2

Step-by-step explanation:

cuz that is the answer i found

Value of [tex]x[/tex]is [tex] - 12[/tex].

Final Answer is [tex]480[/tex]

Step-by-step explanation:

Assume that:

First number = x

Second number = 20 - x

Putting the given conditions,

[tex]2x^{2} + 3(20 - x)^{2} [/tex]

Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,

[tex]2 {x}^{2} + 3(20^{2} - 2 \times 20 \times x + {x}^{2})[/tex]

[tex] = > 2 {x}^{2} + 3(400 - 40x + x^{2})[/tex]

Opening the brackets,

[tex]2 {x}^{2} + 3 \times 400 - 3 \times 40x + 3 \times {x}^{2} [/tex]

[tex] = > 2 {x}^{2} - 1200 - 120x + 3{x}^{2}[/tex]

[tex] = > (2x^{2} + 3 {x}^{2}) - 120x + 1200[/tex]

[tex] = > 5 {x}^{2} - 120x + 1200[/tex]

[tex]As \: x= - \frac{b}{2a}[/tex]

[tex] = > - \frac{120}{2 \times 5}[/tex]

[tex] = > - \frac{120}{10} [/tex]

[tex] = > - 12[/tex]

Now substituting the value of x in 5x²-120x+1200,

[tex] = > (5 \times {12}^{2} )-(120 \times 12)+1200[/tex]

[tex] = > (5 \times 144)-(1440)+1200[/tex]

[tex] = > 720 - 1440 + 1200[/tex]

[tex] = > 720 - (1440 - 1200)[/tex]

[tex] = > 720 - 240[/tex]

[tex] = > 480[/tex]

Answer:

$5 for a flashlight and $22.90 fir a sleeping bag

Answer:

(8, 5): No

(8, 0): Yes

(4, -2): Yes

(-6, -4) No

Step-by-step explanation:

For this question, it is very easy, you just substitute the values under (x,y) into the equation above

The equation is: 3x - 7y > 10

And the x and y values are

(x, y)

(8, 5)

(8, 0)

(4, -2)

(-6, -4)

x values: 8, 8, 4, -6

y values: 5, 0, -2, -4

An ordered pair tells you the location of a point by relating the point's location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair). In an ordered pair, such as (x, y), the first value is called the x-coordinate and the second value is the y-coordinate.

Now that we know everything, we set up the equation to see if the ordered pair is a solution or not

3x - 7y > 10

Let's substitute (8, 5) into the equation

3(8) - 7(5) > 10

Multiply the numbers

3(8) becomes 24 and -7(5) becomes -35

24 - 35 > 10

-11 > 10

False

So the ordered pair (8,5) is not a solution to the equation

Now for the next ordered pair: (8, 0)

3x - 7y > 10

Let's substitute (8, 0) into the equation

3(8) - 7(0) > 10

3(8) becomes 24 and -7(0) becomes 0

24 - 0 > 10

24 > 10

True

So the ordered pair (8, 0) is a solution to the equation

Now for the next ordered pair: (4, -2)

3x - 7y > 10

Let's substitute (4, -2) into the equation

3(4) - 7(-2) > 10

3(4) becomes 12 and -7(-2) becomes a positive 14, and remember that a negative times a negative becomes a positive

12 + 14 > 10

26 > 10

True

So the ordered pair (4, -2) is a solution to the equation

Now for the next ordered pair: (-6, -4)

3x - 7y > 10

Let's substitute (-6, -4) into the equation

3(-6) - 7(-4) > 10

3(-6) becomes -18 and -7(-4) becomes a positive 28

-18 + 28 > 10

10 > 10

False

Since they are the same number, they should be equal to

So the ordered pair (-6, -4) is not a solution to the equation

Answer:

f(5) = 17

Step-by-step explanation:

Using the recursive rule and f(1) = 5 , then

f(2) = f(1) + 3 = 5 + 3 = 8

f(3) = f(2) + 3 = 8 + 3 = 11

f(4) = f(3) + 3 = 11 + 3 = 14

f(5) = f(4) + 3 = 14 + 3 = 17

Answer:

0.00355514147

Step-by-step explanation:

Do Long Division

Answer:

-3/8

Step-by-step explanation:

(-2/3)³ / x = (9/8) -²

-2³/3³ = (2³/3²)²x

-2³/3³ = (2^6/3^4)x

-2³ × 3^-3 × 3^4 × 2^-6 = x

-2^-3 × 3 = x

x = -3/8

Answer:

y < 8 and D is my answer

Step-by-step explanation:

-8y > -64

-8. -8

when we reach at this stage, like terms cancel each other to make y subject of the formula

thus

And because y is becoming a postive value, the sign wI'll change to <

y < 8

Answer:

Step-by-step explanation:

The cost per kilogram is found by dividing cost by kilograms:

honeydew:

  ($4)/(2 kg) = $2/kg

Honeydew costs $2 per kilogram.

__

watermelon:

Let w represent the cost per kg of watermelon. The total value of the second purchase was ...

  (1 kg honeydew)×($2/kg) +(2 kg watermelon)×(w) = $3

  $2 +2w = $3

  2w = $1 . . . . . . . . . . . . subtract $2

  w = $1/2 = $0.50 . . . . divide by 2

The watermelon cost $0.50 per kilogram.

The first one is 1:4 and the second is 4:1.

All there is to do is simple division (or simplifying). In the first set of two numbers side length is 6 and perimeter is 24. So if it's side length to perimeter then 6 to 24 which can be simplified to 1 to 4 and just switch the numbers with perimeter to side length.

Answer:

1. Side length to perimeter = 1:4

2. Perimeter to side length = 4:1

Step-by-step explanation:

Ok, so ratios are basically a way to compare two things.

For example, if someone askes the ratio of boys to girls in Mrs. White's class. Say there are 12 boys and 9 girls.

boys to girls = 12 to 9

That's a ratio!

Ratios are typically written like "12 to 9" (with the word "to") or "12:9" (with a colon) but there are also other ways.

In THIS question, you have to find the ratio of side length to perimeter and then vice versa. So, we see that the first number listed for side length is 6, and the first number for perimeter is 24. As we look down the chart, we should notice a pattern- the perimeter is 4 times as much as the side length! Therefore, the ratio of side length to perimeter is 1:4. To find the ratio of perimeter to side length, we just switch the order of the numbers. Now it's 4:1.

There! It's pretty simple! You just are finding the unit ratio!

If you need any more help, let me know! :)

Answer:

Find the volume of the rectangular prism and

divide by the volume of the cube.

Volume of cube = side measure ^3

Cube = (1/8)3 = 1/512

Volume of prism = Ixwxh

Prism (1/4)(1/2)(3/8) =3/64

3/64/1/512

3/64 x 512/1

3x 512/64

1536/64

24

Answer:

x=6, y=3

Step-by-step explanation:

6x +2y=42------(1)

8x-4y=36-------(2)

We can actually simplify it, this makes it easier to do and can avoid alot of careless mistakes

3x+y=21---(1)

2x-y=9----(2)

next, we can see that y can be eliminated

(1)+(2),

5x=21 +9

x = 30/5

x=6

substitute x=6 into (2),

2(6)-y=9

y=3

Lastly ,make a conclusion

Thus, x=6, y= 3

[tex] 6x + 2y = 42 \\ 8x - 4y = 36[/tex]

Simplify the first equation

[tex]y = 18 \\ 8x - 4y = 36[/tex]

Multiply both sides of second equation by 1/4

[tex]y = 18 \\ 2x - y = 9[/tex]

Sum the equations vertically to eliminate at least one variable

[tex]x = \frac{27}{2} [/tex]

The possible solution of the system is the ordered pair (x,y)

[tex] (x,y) = ( \frac{27}{8} , 18)[/tex]

Answer:

9

Step-by-step explanation:

3 times 3 is 9

Answer:

9in.²

Step-by-step explanation:

just multiply the length n height = 3 × 3

= answer

Scale drawing takes scaled versions of original lengths. The actual length of the swing set area of the park is 25 ft long and 100 ft wide

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

For the given case, it is given that

Real dimension of a rectangular park : 600 ft by 1000 ft

In drawing, it was of 12 inches by 20 inches.

Let the scale that the drawing is using be k feet to s inches, then

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

Since it is given that 600 ft : 12 inches and 1000 ft : 20 inches, thus, we get:

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.\\\\600 \: ft = \dfrac{600\times s}{k} \: in. = 12 \: in.\\\\\dfrac{600 \times s}{k} = 12\\\\\dfrac{s}{k} = \dfrac{12}{600} = 0.02[/tex]

Thus, every feet is reduced 0.02 times in drawing.

Now,

it is given that in drawing, the rectangular area for swing sets is 0.5 inch to 2 inch.

Let its real length was L and real width was W. Then we have:
[tex]\rm L \times 0.02 = 0.5 \\\\L = \dfrac{0.5}{0.02} = 25 \:\\\\W \times 0.02 = 2 \\W = \dfrac{2}{0.02} = 100[/tex]

Since these are only magnitudes, and unit was converted from feet to inches, so we have L = 25 feet and W = 100 feet

Thus,

The actual length of the swing set area of the park is 25 ft long and 100 ft wide

Learn more about scaling here:
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Answer:

the answer is 20

Step-by-step explanation:

w = 55

y = 55

X = 125

z = 125

Step-by-step explanation:

Angles with in a cube add up to 360 degrees

Answer:

w = 55 (vertical to 55)

y = 55 (corresponding to 55)

x = 125

z = 125

Step-by-step explanation:

55+55=110

a parallelogram = 360

360-110=250

x+z=250

x=z

250/2=125