Find the sum :
3/8 + 22.5

Shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

As given,

Shapes F and G are similar

Perimeter of shape F=180mm

Area of shape F=2196mm²

Perimeter of shape G=300mm

Let xmm²be the area of shape G

Square of ratio of perimeter of similar shape =Ratio of area of similar shape

⇒(180 /300)² =(2196/x)

⇒9/25=2196/x

⇒x=(2196×25)/9

⇒x=6100mm²

Therefore, shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

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It will take 5 seconds for the waste to hit the ground.

We know that the bird releases the waste from a height of 400ft, so the height equation is:

[tex]h(t) = -16t^2 + 400[/tex]

The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:

[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]

Now we can apply the square root in both sides:

[tex]t = \sqrt{25} = 5[/tex]

It will take 5 seconds for the waste to hit the ground.

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Answer:

with a line accross the points

Answer:

The answer is B

Step-by-step explanation:

By proportion , 3 : 2.91 = 2: x . then you write it in fraction

Answer:

197

Step-by-step explanation:

the answers 197 because if an=5n-3 then a40= 197

Answer:

By using the formulas of circle and geometry, we find that ∠CED = 65°.

Step-by-step explanation:

We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so

∠CED = 0.5 × (arc AB + arc CD)

See the attached figure with letters to better understand the problem

arc AB = 82° (by central angle)

arc CD = 48° (by central angle)

Substitute the values in the formula above

∠CED = 0.5 × (82° + 48°)

∠CED = 0.5 × 130°

∠CED = 65°

Therefore the answer is ∠CED = 65°

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Answer:

8.49 × 10⁻³

Explanation:

Standard form of a number: A. × 10ᵇ

(where 'A' is the number, b is the exponent over 10)

For the number "0.00849​", move the decimal point 3 places right so the exponent of 10 is -3.

Standard form: 8.49 × 10⁻³

Other examples of standard/scientific forms are:   standard forms

i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²

ii) 4030, move the decimal point 3 places left = 4.03 × 10³

Answer:

when a number is given in that manner you have to take that decimal between two whole numbers.

and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.

Answer:

so first we have to divide each side by 38

4.5miles=0.1

45miles=1 hour

Hope This Helps!!!

The hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

It should be noted that a hypothesis means a proposed explanation based on reasoning and evidence.

In this case, the hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

The conclusion is that kids who wear braces will have straight teeth.

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Answer:

Area=12x square units;  Perimeter=5x+14 units

Step-by-step explanation:

Recall the formulas for area and perimeter of a triangle:

Area of a triangle is half of the product of a base its corresponding height:

[tex]A=\frac{1}{2}bh[/tex]

Perimeter is the sum of all of the side lengths:

[tex]P=a+b+c[/tex]

In arbitrary triangles ABC, the sides are labeled across from a vertex with a matching lowercase letter.  So, in my diagram, side "b" is the bottom with length "8".  Side "b" is also the base, so the corresponding height is the perpendicular line segment that connects side "b" with vertex "B", which measures "3x"... 3 times some unknown value.

Side "a" is length "4x-3", and side "c" is length "x+9".

In this situation, where the sides have their specific relationship with "x" and the height is exactly triple "x", solving for x (and thus exact numerical values for the Perimeter and Area) involves trying to relate the two equations, possibly done with Heron's formula for area, or with trigonometry.  Ultimately, it involves solving a 4th degree polynomial to get an exact answer, which is not what the question intends, so we'll leave the Area and Perimeter in terms of x (meaning there will still be "x" in our expressions to represent the Area and Perimeter).

Area

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(8)(3x)\\A=12x[/tex]

So the Area of the triangle equals 12x square units.

Perimeter

[tex]P=a+b+c\\P=(4x-3)+(8)+(x+9)\\P=5x+14[/tex]

So the Perimeter of the triangle equals 5x+14 units

Answer:

a) 1

Step-by-step explanation:

added in the picture

The absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

As we know,

The absolute value of a negative account balance is equal to the amount of debt. A balance of $0 on an account means there is no debt. Credit is shown by a positive account balance.

Richard has a debt of $45.

The negative of 45 value represents the debt.

-$45 = debt

Absolute value = |-45| = 45

Thus, the absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.

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( 1, ∞)  is the domain of (b o a)(x)

A function is defined as a relation between a set of inputs having one output each.

According to the question,

[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]

To find the domain of the composite function,

[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]

Therefore,

[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]

Hence , [ 1, ∞ ] is is the domain of (b o a)(x).

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Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.

Let v be the number of visits Tristan makes to the movie theater.

He receives 25 rewards points just for signing up, and he earns 8.5 points for each visit. So, the total rewards points he will have is

25+8.5v.

He needs at least 110 points for a free movie ticket. Therefore, we can write the inequality:

25+8.5v≥110

To solve for v, we can subtract 25 from both sides of the inequality and then divide by 8.5:

8.5v≥85

v≥85/8.5

v≥10

So, Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.

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The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.

The pertinent data are:

Period Fertilizer Sales Number of Mowers Sold

1 1.6 12.0

2 1.3 10.0

3 1.8 13.0

4 2.0 15.0

5 2.2 15.0

6 1.5 11.0

7 1.6 12.0

8 1.4 10.0

9 1.8 13.0

10 1.4 10.0

11 1.9 15.0

12 1.4 11.0

13 1.7 14.0

14 1.4 13.0

To determine the correlation between the two variables

Regression equation ( y ) = a + bx

y = dependent variable ( mower )

x = independent variable ( fertilizer)

a = intercept point ( y-axis and regression line )

b = slope ( regression line )

From the given data;

N = 14 ,    Σ x = 22.8,  

Σy = 131,   Σy^2 = 1269,

Σx^2 = 38.18,      (Σx)^2 = 519.84

Σxy = 219.8,       (Σy)^2 = 17161

Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

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Answer:

30

Step-by-step explanation:

4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons

The answer is 30 gallons.

Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.

Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.

Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.

Hope this helped.

Answer:

Im pretty sure its C which is 5776.2m

Step-by-step explanation:

Answer:

x • (2xt + 7y)

Step-by-step explanation:

1. ((5xy-((x2)•t))+2xy)+(3x2•t)

2. Pull out like factors :

  2x2t + 7xy  =   x • (2xt + 7y)

Final result

x • (2xt + 7y)

Answer:

[tex]7xy + {x}^{2} t[/tex]

Step-by-step explanation:

[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

In this case we have a linear variable x, whose increase is described by the following expression:

y = x · (1 + r/100)     (1)

Where r is the increase rate.

If we square (1), then we find that:

y² = x² · (1 + r/100)² = (1 + r'/100)     (2)

Where r' is the equivalent increase rate.

(1 + r/50 + r²/10000) = (1 + r'/100)

r'/100 = r/50 + r²/10000

r' = r/2 + r²/100

If we know that r = 25, then the equivalent increase rate is:

r' = 25/2 + 25²/100

r' = 18.75

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

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Answer:

298.97 minutes

Step-by-step explanation:

2^x = 1 000 000      where 'x' is the number of 15 minute periods

x = 19.931      15 minute periods = 298.97 minutes

Answer: 1.44

Step-by-step explanation:

(original price) - (1/6 of the original price) = 1.20

If you let x = original price, then the equation is:

x - 1/6 x = 1.20

5/6 x = 1.20

x = 1.44

the original price is £1.44.

Credits to the person who also answered :)

I hope this helps!

Answer:

£1.44

Step-by-step explanation:

Since the original price was reduced by 1/6, that means the new price is 5/6 of the original price.

Let x = original price.

Write an equation and solve it.

5/6 x = £1.20

x = £1.20 × 6/5

x = £1.44

Answer:

A

Step-by-step explanation:

y = - 2x + 5 → (1)

y = x² + 3x + 9 → (2)

substitute y = x² + 3x + 9 into (1)

x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )

x² + 5x + 4 = 0 ← in standard form

(x + 1)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into (1) for corresponding values of y

x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )

x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )

Answer:

8

Step-by-step explanation:

f(x)=2x^4-4x^3-11x^2+3x-6

f(-2)=2(-2)^4-4(-2)^3-11(-2)^2+3(-2)-6

f(-2)=2(16)-4(-8)-11(4)-6-6

f(-2)=32+32-44-12

f(-2)=64-44-12

f(-2)=20-12

f(-2)=8

An equation is formed of two equal expressions. The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given graph is the graph of an exponential function, the general equation of an exponential function is given by the y=aeᵇˣ. To get the function f(x) and g(x), you need to substitute the points in the given function and produce the equation of each function.

The equation for f(x) from the given graph can be written as,

[tex]f(x)=e^{(\ln2)x}-2[/tex]

Now, similarly from the graph the function of g(x) can be written as,

[tex]g(x)=-3e^{(\ln2)x}+6[/tex]

Further, the equation of function g(x) in terms of f(x) can be written as,

g(x) = -3[f(x)]

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Step-by-step explanation: I got it right!

The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].

From the principle of indices we get,

Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]

Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]

Multiplication, [tex]a^{mn}=(a^m)^n[/tex]

negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]

Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

Calculating we get,

[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae

[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]

[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices

[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula

Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].

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Answer:

b

Step-by-step explanation:

edge 23

None of the equations are parallel or perpendicular to the line jk.

The equation of a line can be interpreted as follows:

y = mx + b

where

Therefore,

Parallel lines have the same slope(m).

Perpendicular line follows the principle below:

Therefore, let's find equation of jk

(-5, 5)(1, -5)

m = -5 - 5 / 1 + 5 = -10 / 6 = - 5 / 3

using (1, -5)

-5 = - 5 / 3 (1) + b

b = -5 + 5 / 3 = -15 + 5 / 3 = -10 / 3

Therefore,

y = -5 / 3 x - 10 / 3

m = - 5 / 3

6x + 10y = 11

10y = -6x + 11

y = - 6 / 10 x + 11 / 10

y = - 3 / 5 x + 11 / 10

hence, m = - 3 / 5

5x - 3y = 8

3y = 5x - 8

y = 5 / 3 x - 8/3

m = 5 / 3

The equation

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Answer:

-9

Step-by-step explanation:

-9

The function is called an exponential function became the exponent is a variable.

The function is called an exponential function became the exponent is a variable.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,

So, the whole statement is =

The function is called an exponential function became the exponent is a variable.

The function y = 3ˣ is an exponential function because it is having a power which is a variable.

The graph of the same is attached to the solution.

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Answer:

x = 1

Step-by-step explanation:

Step 1: Combine like terms.

Step 2: Divide both sides by 30.

Step 3: Check if solution is correct.

Therefore, x = 1.

Solution: X=1

[tex]\searrow[/tex]

Detailed explanation:

Here we need to solve for x. x is our unknown. It's what we should find.

[tex]\searrow[/tex]

Note right up front that we can add the x's. This is a process that is known as "Combining Like Terms". We can combine them by adding, like here.

[tex]\twoheadrightarrow\sf 29x+x=30[/tex]

"x" is the same as 1x.

[tex]\twoheadrightarrow\sf 30x=30[/tex]

We're getting closer to finding the value of the unknown!

Now we know that if we multiply 30 times the unknown, we will get 30.

What will we get if we multiply 1 times the unknown? 1 is what we will obtain upon dividing by 30.

So our unknown, or x, is 1.

Voila! There's our answer!

_____________________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

_____________________________