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Answer: 1008

Step-by-step explanation:

Given

5 small containers of capacity 16,72,12,24, and 56 litres is required to fill a big container.

The volume of big container is the LCM of the 5 given containers

[tex]LCM(16,72,12,24,56)=1008[/tex]

Therefore, the capacity of the bigger container is 1008 litres.

Answer:

Length of hypotenuse is 13 unit or 5 unit

Step-by-step explanation:

Find;

Length of hypotenuse

Computation;

Assume;

Length of hypotenuse = h

Length of longer leg = h - 1

Length of shorter leg = h - 1 - 7

Using Pythagorean theorem

hypotenuse² = longer leg² + shorter leg²  

h² = (h - 1)² + (h - 1 - 7)²  

h² = (h - 1)² + (h - 8)²  

h² = h² - 2h + 1 + h² - 16h + 64  

h² = 2h² - 18h + 65

h² - 18h + 65 = 0

h² - 13h - 5h + 65 = 0

h(h - 13) -5(h - 13)

(h - 13)(h - 5)

So,

Length of hypotenuse is 13 unit or 5 unit

Answer:

[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]

Step-by-step explanation:

Given

The fractions are:

[tex]\frac{3}{12},\ \frac{1}{6},\ \frac{1}{3}[/tex]

Required

How the fractions can be rewritten

The fractions can be rewritten by taking the LCM of the denominators.

The [tex]LCM[/tex] of [tex]12; 6\ and\ 3[/tex] is [tex]12[/tex]

So, we have:

[tex]\frac{3}{12},\ \frac{2*1}{12},\ \frac{4*1}{12}[/tex]

Simplify the numerators

[tex]\frac{3}{12},\ \frac{2}{12},\ \frac{4}{12}[/tex]

Now, the fractions can be ordered based on the numerators

[tex]\frac{2}{12},\ \frac{3}{12},\ \frac{4}{12}[/tex]

Return to original form

[tex]\frac{1}{6},\ \frac{3}{12},\ \frac{1}{3}[/tex]

Answer:

The third one.

Step-by-step explanation:

Answer:

[tex] \sin(c) = \frac{ab}{ac} \\ \sin(c) = \frac{36}{45} \\ \sin(c) = \ \frac{4}{5} [/tex]

Answer:

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Answer:

18 = 4(3)+6

12 + 6

Step-by-step explanation:

the answer is 18 = 4(3)+6

because y is 18

Answer:

x=3

Step-by-step explanation:

[tex]18 = 4x + 6[/tex]

subtract 6 on both sides

[tex]12 = 4x[/tex]

divide both sides by 4

[tex]3 = x[/tex]

Answer:

[tex](7y^2x^3)^2[/tex]

Step-by-step explanation:

Find the GCF then factor out all the numbers

Answer:

C

Step-by-step explanation:

"grow or develop in a healthy or vigorous way, especially as the result of a particularly favorable environment."

Answer:

C.

hope this helps

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Step-by-step explanation:

Answer:

Step-by-step explanation:

12 D + M = 3.50

3*12 D +4M = 11.80

the pair of equations are

12 D + M = 3.50

36 D +4M = 11.80

Answer:

I need points lol 2=yx thank you for letting me spam

Answer:

C. y = -6

Step-by-step explanation:

3x – 6y = 9

–3x + 3y = 9

-3y = 18

y = -6

Answer:

area=1÷2×diagonal(H1+H2)

=1÷2×8(2+2)

=16m2

Answer:

16 m squared,

Step-by-step explanation:

Thre are two triangles. triangle area formula = 1/2 bh

plug in numbers but there's another rectangle so times 2

1/2 8*2 = 8*2=16

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Answer:

4x+6y

Step-by-step explanation:

distribute and add like terms

Answer:

[tex]4x + 6y[/tex]

Step-by-step explanation:

Collect like terms:

[tex]2(2x + 3y)[/tex]

Distribute 2 through the parentheses:

[tex]4x + 6y[/tex]

Therefore, the answer will be 4x + 6y.

Answer:

44.4

Step-by-step explanation:

sin(40)= x/69

x=69(sin40)

x= 44.4

Answer:

B) Angle 5 and angle 4

Step-by-step explanation:

Given

See attachment for sketch

See comment for options

Required

The alternate interior angles

Interior angles are such that they are located between the given parallel lines.

In the attached sketch, the interior angles are: 3, 4, 5 and 6

Alternate angles are at the opposite sides of the transversal

Hence:

4 and 5 are alternate interior

3 and 5 are also alternate interior

Answer:

54

Step-by-step explanation:

55+71=126

180-126=54

Answer:

the simplified expression of this is -23/2h + 3/2 or -11 1/2h + 1 1/2.

Step-by-step explanation:

7/2h - 3(5h - 1/2)

3(5h - 1/2)

First, we need to use the distributive property to distribute the expression which requires multiplication or division. We take 3 and multiply it by both values in the parentheses which gives us 15h - 1/2. However, since there is subtraction, we need to do the opposite of that which would be 15h +  1 1/2 or 15h + 3/2. Now we can't forget 7/2h at the beginning of the expression. Here is the remaining expression :

7/2h - 15h + 3/2 or 7/2h - 15h + 3/2

Now, we need to combine like terms which requires values to have the same variable. 7/2h and 15h have the same variable so combine like terms. We do subtraction.

7/2h - 15h

We subtract this and get a result of -23/2 or -11 1/2 but don't forget the variable.

-23/2h

1/2 doesn't have a variable so we no longer can combine like terms. Therefore, it would just be -23/2h + 3/2 or -23/h + 1 1/2.

Answer:

The height of the second cylinder is 30mm

Step-by-step explanation:

Given

Cylinder 1:

[tex]R = 15mm[/tex]

[tex]H = 45mm[/tex]

Cylinder 2

[tex]r = 10mm[/tex]

See attachment

Required

Determine h, the height of the small one

To do this, we make use of the following equivalent ratios;

[tex]R : H = r : h[/tex]

This gives:

[tex]15 : 45 = 10 : h[/tex]

Express as fraction

[tex]\frac{15 }{ 45 }= \frac{10 }{ h}[/tex]

Simplify

[tex]\frac{1 }{ 3}= \frac{10 }{ h}[/tex]

Cross multiply

[tex]h *1 = 3 * 10[/tex]

[tex]h = 30[/tex]

Given:

The system of inequalities:

[tex]x>3[/tex]

[tex]y<2x-5[/tex]

To find:

The point that represents a solution to the system by using the graph.

Solution:

We have,

[tex]x>3[/tex]

[tex]y<2x-5[/tex]

The related equations of these inequalities are:

[tex]x=3[/tex]

[tex]y=2x-5[/tex]

The line [tex]x=3[/tex] is a vertical line that intersect the x-axis at 3.

The table of values for [tex]y=2x-5[/tex] is:

x         y

0       -5

1        -3

Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.

The boundary lines are dotted lines because the points on the lines are not included in the solution set.

Check the inequalities for (0,0).

First inequality: [tex]0>3[/tex]           ( False)

Second inequality: [tex]0<2(0)-5[/tex]

                               [tex]0<-5[/tex]     (False)

Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).

Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.

From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

[tex]\sqrt{3[/tex] *2[tex]\sqrt{30[/tex]

2[tex]\sqrt{30*3}[/tex]

2[tex]\sqrt{3*3*2*5}[/tex]

2*3[tex]\sqrt{2*5}[/tex]

6[tex]\sqrt{10}[/tex]

Answer:

458 cm²

Step-by-step explanation:

5 × 5 × 2 + 5 × 18 × 4 = 50 + 360 = 410

2 × 2 × 4 × 3 = 48

410 + 48 = 458

Answer:

We have:

x = t^2 + 2*t

y = -t

where:

–4 ≤ t ≤ 1

Isolating t in the "y" equation, we get:

t = -y

Now we can use the limits of t, to find similar limits for y.

When t = -4

-4 = -y

4 = y

when t = 1

1 = -y

-1 = y

Then the limits for y are:

-1 < y < 4

Now, knowing that t = -y

we can replace that in the "x" equation:

x = t^2 + 2*t

x = (-y)^2 + 2*(-y)

x = y^2 - 2*y

Then the graph of the parametric equation is the one defined by:

x = y^2 - 2*y

in the range

-1 < y < 4

The graph of this can be seen below, where the two black dots are the points where the graph should start/end.

The graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.

An approach to determine the possible graph consists in eliminating [tex]t[/tex] and simplify the resulting expression of the form [tex]f(x)[/tex]:

[tex]x = t^{2}+2\cdot t[/tex] (1)

[tex]y = -t[/tex] (2)

By (2):

[tex]t = -y[/tex]

(2) in (1):

[tex]x = (-y)^{2} + 2\cdot (-y)[/tex]

[tex]x = y^{2}-2\cdot y[/tex]

In a nutshell, the graph that represents the parametric equations is a parabola with an axis of symmetry is parallel to the x-axis.

To learn more on parametric equations, we kindly invite to check this verified question: https://brainly.com/question/9056657

The requried simplified value of 4a is 16. Option C is correct.

Simplification is the process of reducing a mathematical expression to its simplest form by combining like terms, using the distributive property, and performing other algebraic operations.

If b=3, then substituting in the first equation, we get:

a + 3 = 7

Solving for a:

a = 4

Now, 4a = 4 x 4 = 16.

Therefore, the answer is C. 16.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ3

Answer:

you will pay back $4,984 in total and you will owe 984 in interest alone just in case you need that too.

Answer:

12 feet

Step-by-step explanation:

48 divided by 4 is 12 and 48 is the total area

Answer:

12 sq. ft.

Step-by-step explanation:

To find the area of a square (or rectangle) you multiply the length by the width.

To find the length of one side, when you have the area and one side, you divide the area by the side you have.

48 divided by 4 equals 12.

Hope this helps :)