Write 45 in lowest terms.
47

Answer:

1.3 m

Step-by-step explanation:

Given dimensions of rectangle ABCD:

[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\\\implies \sf Area\:of\:ABCD& = x(x+4)\\& = x^2+4x \end{aligned}[/tex]

Given dimensions of isosceles triangle ADE:

[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of $\triangle$ADE}& = \dfrac{1}{2} \cdot x \cdot x\\& = \dfrac{1}{2}x^2\end{aligned}[/tex]

As the area of the portion remaining when ADE is cut off from ABCE is 6 m²:

[tex]\begin{aligned}\sf ABCD-ADE & = 6\\\implies x^2+4x-\dfrac{1}{2}x^2 & = 6\\2x^2+8x-x^2 & = 12\\x^2+8x & = 12\\x^2+8x-12 & = 0\end{aligned}[/tex]

Solve the found quadratic equation by completing the square.

Move the constant to the right side of the equation:

[tex]\implies x^2+8x-12+12=0+12[/tex]

[tex]\implies x^2+8x=12[/tex]

Add the square of half the coefficient of x to both sides:

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=12+\left(\dfrac{8}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+8x+4^2=12+4^2[/tex]

[tex]\implies x^2+8x+16=12+16[/tex]

[tex]\implies x^2+8x+16=28[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (x+4)^2=28[/tex]

Square root both sides:

[tex]\implies \sqrt{(x+4)^2}=\sqrt{28}[/tex]

[tex]\implies x+4=\pm \sqrt{28}[/tex]

[tex]\implies x+4=\pm \sqrt{4 \cdot 7}[/tex]

[tex]\implies x+4=\pm \sqrt{4}\sqrt{7}[/tex]

[tex]\implies x+4=\pm 2\sqrt{7}[/tex]

Subtract 4 from both sides:

[tex]\implies x=-4\pm 2\sqrt{7}[/tex]

As length is positive:

[tex]\implies x=-4+ 2\sqrt{7}\:\:\sf only[/tex]

Taking the value of √7 = 2.65:

[tex]\implies x \approx -4+ 2(2.65)[/tex]

[tex]\implies x \approx -4+5.3[/tex]

[tex]\implies x \approx 1.3[/tex]

Therefore, the width of the sheet is 1.3 m.

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Answer:

Step-by-step explanation: Let x be the smaller and y be the largest number.

Since x+y=13, we deduce y=13-x

Now, for the translation: "two more than the larger number" is y+2 , while "twice the smaller" is 2x

Their sum is y+2+2x

And since we know that y=13-x, we have y+2+2x=13-x+2+2=15+x

Answer:-5

Step-by-step explanation:

5*5*5=125

-5*-5=25

25*-5= -125

or

3√-125

The values of x, y, and z. The diagram is not to scale.

This is further explained below.

Generally, Angle in a triangle is 180^{\circ}

Therefore

45+68+x=180

x=180-(45+68)

x=67

The angle on a line is also 180^{\circ}

x+z =180

67+z =180

z =180-67

z =113

In conclusion

180=113+12+y

-180-(113+12)=y

y=55

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We get that the value of  (f + g​)(x​) is 3 x² - 2 x - 10 and (f + g​)(6​) is 86.

We are given the two functions:

f(x) = 3 x² - x - 6

g(x) = x - 4

We need to find:

(f + g​)(x​)

= f(x) +g(x)

= 3 x² - x - 6 + x - 4

= 3 x² - 2 x - 10

Now we have to find:

(f + g​)(6​).

Put x = 6, we get that:

= 3 (6)² - 2 (6) - 10

= 108 - 12 - 10

= 108 - 22

= 86

Therefore, we get that the value of  (f + g​)(x​) is 3 x² - 2 x - 10 and (f + g​)(6​) is 86.

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The number which represents the third change made to the account according to the task content is; -60.

According to the task content, the second change was the opposite of the first, -60.

Hence, the second change is; +60 which is the additive inverse.

Ultimately, since the third change was the opposite of the second, it follows that the third change is; -60.

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Answer:

Step-by-step explanation:

An addition equation for calculating volume is = 12 units cube.

The fundamental addition formula, sometimes known as the mathematical equation of addition, is as follows. The addends are 5 and 3, and the sum is 8. It should be noted that an addition fact can have many addends. For instance, 5 + 7 + 9 + 3 = 24.

Volume refers to the amount of space occupied by a 3D shape. The volume of a shape can be calculated by multiplying its height, breadth, and depth. If somehow the shape is made using cubic cm blocks, the volume can be calculated by counting the cubes.

Total no. of cubes  = 12

length of the one cube = 1 unit

So,

volume of the given prism = l x b x h

volume of one prism = 1 unit^3

There are 12 cube are present on adding all the units we get

volume of total cubes are  = 12 unit cube.

So,

The volume is  = 12 unit cube.

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Answer:30

Step-by-step explanation:because 30 is a multiple and factor of 30.

The equivalent expression is,

''Negative two over fifteen times x plus two''

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

We have to given the expression as;

''One fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x''

Now, Write in mathematical expression as,

⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]

We can solve it as,

⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]

⇒ [tex]\frac{3}{5} x + \frac{10}{5} - \frac{11}{15} x[/tex]

⇒ [tex]\frac{3}{5} x - \frac{11}{15} x+ 2[/tex]

⇒ [tex]\frac{-2}{15} x + 2[/tex]

Hence, It can be written as;

⇒ Negative two over fifteen times x plus two.

Therefore, The equivalent expression is,

''Negative two over fifteen times x plus two''.

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Answer:

x-6

Step-by-step explanation:

Answer:

4 × 10^6

Because 10^6 = 100,000

Answer:

4×10^6

Step-by-step explanation:

you write a non zero digit which is 4 placing your decimal after the first non zero digit ..then you count the no. of digits you need to move the beginning decimal to get to where your decimal is ...or to use a scientific calculator to make it simple

Answer:

6

Step-by-step explanation:

If there are 4 in each tank, that means there are 2 tanks. 4-2 = 2. 8-2 = 6.

Answer:

There 30 fish left at the store

Step-by-step explanation:

There are 8 tanks

If there are 4 fish in each tank, the total would be 32 fish. If Dalia buys 2 fish, you would do 32 - 2 = 30 fish.

Hope this helped!! ( >ᴗ<) xx

Answer:

The answer is this sequence has 18 terms

Step-by-step explanation:

As you can see, the term-to-term rule of the sequence is +2

We can use that to calculate the amount of terms.

First, calculate the distance between the first and last terms

53 - 19 = 34

Then, use this and divide the term-to-term rule.

34/ 2 = 17

Remember to add 1 at the end :)

17 + 1 = 18

There are 18 terms in this sequence.

If you don't trust me, you can check it yourself :D

Answer:

Step-by-step explanation:

D.16

Answer: D': (-7, -1)

E': (-6, -1)

F': (-6, -10)

G': (-7, -10)

Step-by-step explanation:

In a 90 degree clockwise rotation about the origin for this rectangle, the x and y coordinates of the rectangle's edges are swapped, but the y-coordinates are negated. This is because the transformation is happening to the 3rd quadrant, where both the x and y values will be negative.

D: (1, -7) ==> (-7, 1) ==> D': (-7, -1)

E: (1, -6) ==> (-6, 1) ==> E': (-6, -1)

F: (10, -6) ==> (-6, 10) ==> F': (-6, -10)

G: (10, -7) ==> (-7, 10) ==> G': (-7, -10)

The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

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Answer:

Step-by-step explanation:

the answer is 23.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Variance = 25

Step-by-step explanation:

I'm smart

Answer:

Are there options you forgot to put on the question?

Step-by-step explanation:

Answer:20.4

Step-by-step explanation:

Change the divisor 1.2 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

Answer: 247 miles.

Step-by-step explanation: First, we need to convert the 45 minutes into hours. we know that 1 hour = 60 minutes. Dividing any number of minutes by sixty gives us the number of hours along with the remaining minutes if there are any. so 45/60 simplifies to 3/4. Now for the miles, it's given that the speed is 52 mph. So we can put into the expression 52(4+3/4)= total miles. Once we distribute 52, we get 208 + 39, which equals to 247.

Answer:

247

Step-by-step explanation:

52÷60 mins x 45= 39 miles for 45 mins

45 mins + 4 x 52 =247

The number of vehicle administered by department A only = 18

The number of vehicle administered by department B only = 8

The number of vehicle administered by department C only = 1

Given data

50 vehicles belong to an enterprise that has three departments, A, B and C

6 vehicles are available for the use of all three departments

2 vehicles give service to neither of the departments

24 vehicles are administrated by department B

16 of the 24 used by B are also used by the others departments

There are twice as many vehicles in department A as there are in department C.

equal numbers of vehicles are allocated when used by any two departments

number of vehicles on department A = 2 * number of vehicles in department C.

say A = 2C

B = 24

let x represent the number of vehicles used by any two departments

16 of the 24 used by B are also used by the others departments and equal numbers of vehicles are allocated when used by any two departments hence

16 = 2x + 6

2x = 16 - 6

2x = 10

x = 5

B only = 24 - 2x - 6 = 18 - 2x = 18 - 10 = 8

A only = A - 2x - 6 = 2C - 10 - 6 = 2C - 16

C only = C - 2x - 6 = C - 10 - 6 = C - 16

adding up all the vehicles as allocated to get to the sum of 50

24 - 2x - 6 + A - 2x - 6 + C - 2x - 6 + x + x + x + 6 + 2 = 50

24 - 6 - 6 - 6 + 6 + 2 - 2x - 2x - 2x + x + x + x + A + C = 50

24 - 10 - 6x + 3x + 2C + C = 50

14 - 3x + 3C = 50

3C - 3X = 50 - 14

3C - 3(5) = 36

3C - 15 = 36

3C = 36 + 15 = 51

C = 17

C only

C only = C - 16

C only = 17 - 16

C only = 1

A only
A only = 2C - 16

A only = 2 * 17 - 16 = 34 - 16 = 18

The number of vehicle administered by department A only = 18

The number of vehicle administered by department B only = 8

The number of vehicle administered by department C only = 1

The number of vehicle administered by department A = 2C = 34

The number of vehicle administered by department B = 24

The number of vehicle administered by department C = 17

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So, we are to solve for x in:

[tex] \frac{x + k}{m} = r[/tex]

Cross multiply the above to solve for x

[tex]x + k = mr[/tex]

Now, collect like terms to find x

Therefore: [tex]x = mr - k[/tex]

the maximum number of candy kisses that each person could have received is 4.

We know that each person receives the same number of candy.

Then the quotients between the number of candy and the number of people should give the same value:

20/K = 52/N

Let's find the common factors between 20 and 52, to do so, we need to rewrite the two numbers as a product of prime factors:

20 = 2*10 = 2*2*5

52 = 2*26 = 2*2*13

The greatest common factor between 20 and 52 is (2*2) = 4

Then, if each person receives 4 candy:

The group that receives 20 candy:

20/K = 4

20/4 = k = 5

That group has 5 people.

The group that receives 52 candy:

52/N = 4

52/4 = N = 13

This group has 13 people.

Then the maximum number of candy kisses that each person could have received is 4.

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The vertical distance of helicopter from the ground is equal to 2000 / 3 m.

Let the distance between the two planes A and B be x.

In △ ADC, we get that:

tan 60° = 2000 / y

√3 = 2000 / y  ...(1)

Now, in △ BCD, we get that:

tan 30° = 2000 - x / y

1 / √3 = (2000 - x) / y    ... (2)

Divide (1) from (2):

3 = 2000 / (2000 - x)

6000 - 3 x = 2000

3 x = 6000 - 2000

3 x = 4000

x = 4000 / 3

(2000 - x) = 2000 - 4000/3 = 2000 / 3

Therefore, the vertical distance of helicopter from the ground is equal to 2000 / 3 m.

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