-
4. Which shows the solution to the
inequality? 6(x-2) +21 <39

The volume of 3 of shipping containers 267.75 cubic yards.

We need to find the volume of one shipping container and then multiply it by 3 to find the volume of three shipping containers.
Find the volume of one shipping container.
Volume = Base Area × Height
Volume = 25.5 square yards × 3.5 yards
Calculate the volume.
Volume = 89.25 cubic yards
Find the volume of three shipping containers.
Total Volume = Volume × Number of Containers
Total Volume = 89.25 cubic yards × 3
Calculate the total volume.
Total Volume = 267.75 cubic yards.

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Answer:

(3,2)

Step-by-step explanation:

Setting up equation so we can use substitution method

x - y = 1 , x + 3y = 9

step 1 set first equation equal to x by adding y to both sides so we can use the substitution method to solve the system of equations.

x = y + 1 , x + 3y = 9

now we can plug in ( or substitute hence substitution method ) the first equation into the second

Solving for y using the substitution method

x + 3y = 9

plug in x = y + 1

y + 1 + 3y = 9

combine like terms

4y + 1 = 9

subtract 1 from both sides

4y = 8

divide both sides by 4

y = 2

Now to find the value of x we plug in the value of y into one of the equations and solve for x.

Solving for x

x - y = 1

y = 2

x - 2 = 1

add 2 to both sides

x = 3

The solution would be (3,2)

Answer:

x = 3 and y = 2 or (3,2) in coordinate form

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Solve by elimination of x-terms by multiplying either one of equations with -1:

For this, I choose to multiply -1 in first equation:

[tex]\displaystyle \large{\begin{cases} -1(x-y=1) \\ x+3y=9 \end{cases}}\\\displaystyle \large{\begin{cases} -x+y=-1 \\ x+3y=9 \end{cases}}[/tex]

Then add both equations:

[tex]\displaystyle \large{-x+x+y+3y=-1+9}\\\displaystyle \large{4y=8}[/tex]

Divide both sides:

[tex]\displaystyle \large{\dfrac{4y}{4} = \dfrac{8}{4}}\\\displaystyle \large{y=2}[/tex]

Next, substitute y = 2 in one of equations to solve for x:

For this, I choose to substitute y = 2 in the first equation:

[tex]\displaystyle \large{x-y=1}[/tex]

Substitute y = 2 in:

[tex]\displaystyle \large{x-2=1}[/tex]

Add both sides by 2:

[tex]\displaystyle \large{x-2+2=1+2}\\\displaystyle \large{x=3}[/tex]

Hence, the solution is x = 3 and y = 2 or you can write as in coordinate form (3,2)

__________________________________________________________

First method is elimination method, I’ll demonstrate another method which is by using matrices to find the solutions.

Given:

[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]

Write the system of equations in matrices form:

[tex]\displaystyle \large{\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Let:

[tex]\displaystyle \large{A=\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] }\\\displaystyle \large{X=\left[\begin{array}{ccc}x\\y\end{array}\right] \\\displaystyle \large{B = \left[\begin{array}{ccc}1\\9\end{array}\right] }[/tex]

From [tex]\displaystyle \large{AX=B \to X=A^{-1}B}[/tex] where:

[tex]\displaystyle \large{A^{-1}=\dfrac{1}{\det A} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] = \dfrac{1}{ad-bc} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] }[/tex]

Find [tex]\displaystyle \large{\det A}[/tex]:

[tex]\displaystyle \large{\det A = ad-bc = 3+1=4}[/tex]

Therefore:

[tex]\displaystyle \large{A^{-1} = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right]}\\\therefore \displaystyle \large{X = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right] \left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]

Evaluate the matrices:

[tex]\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3(1)+1(9)\\-1(1)+1(9)\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3+9\\-1+9\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}12\\8\end{array}\right]}\\\displaystyle \large{X= \left[\begin{array}{ccc}3\\2\end{array}\right] }\\\therefore \displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}3\\2\end{array}\right]}[/tex]

Therefore, the solution is x = 3 and y = 2

Answer:

13πr/60 units

Step-by-step explanation:

Formula

Solving

q=w/ 3-7

q(3-7)= w

hope this helps :)

Answer:

w = 3q + 21

Step-by-step explanation:

assuming you mean

q = [tex]\frac{w}{3}[/tex] - 7 ( add 7 to both sides )

q + 7 = [tex]\frac{w}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

3(q + 7) = w , that is

w = 3q + 21

Answer: 12

Step-by-step explanation:

Start with 90/10 which gets you 9

Then add 3 and 9 which is 12

Answer:

12

Step-by-step explanation:

Order of operations says to do the division first

90/10 = 9

Then add the rest

9+3 = 12

Answer:

I got you with Question 3 and 4 my guy.

3) He would need 12 and it would cost 50k

4) 9% payments: $563.24, 7% payments: $494.75. Monthly savings: $69.49, 9% total repaid: $2022,764.90 , 7% total repaid: $148,423.63 , Savings: $54,341.27

The Tom will need to bring to the closing $54,341.27

He would need 12 and it would cost 50k.

We have given that,

Tom buys a condominium for $42,600.

He makes a down payment of 15% and pays these closing costs to survey $225.

The meaning down payment is a part of the full price paid at the time of purchase or delivery with the balance to be paid later.

Inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286

9% payments: $563.24

7% payments: $494.75.

Monthly savings: $69.49

9% total repaid: $2022,764.90  

7% total repaid: $148,423.63

Savings: $54,341.27

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Answer:

y = [tex]\frac{3}{2}[/tex] x + 7

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 8 = - [tex]\frac{2}{3}[/tex] (x + 5) ← is in point- slope form

with m = - [tex]\frac{2}{3}[/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{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex]

the equation of a line in slope- intercept form is

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

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 6, - 2 ) into the partial equation

- 2 = - 9 + c ⇒ c = - 2 + 9 = 7

y = [tex]\frac{3}{2}[/tex] x + 7 ← equation of line K

The equation of the perpendicular line in the slope-intercept form will be y = (3/2)x + 7.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y - 8 = -2/3(x+5)

The equation of the line that is perpendicular to the line y - 8 = -2/3(x+5) is given as,

y = 3/2x + c

The line is passing through (-6, -2), then we have

-2 = 3/2(-6) + c

-2 = -9 + c

c = 7

The equation of the perpendicular line in the slope-intercept form will be y = (3/2)x + 7.

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Answer:

-8

Step-by-step explanation:

Hey there!

(1/2)(10) - (-12) - 25

= 1/2(10) - (-12) - 25

= 5 - (-12) - 25

= 5 + 12 - 25

= 17 - 25

= -8

Therefore, your answer is: -8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

This is hard

Step-by-step explanation:

I'm so sorry I can't do it

Answer:

[tex]\frac{69}{20}[/tex]

Step-by-step explanation:

[tex]\frac{3}{7} -\frac{11}{4} +\frac{16}{5} +\frac{18}{7}[/tex]

= [tex]\frac{3}{7} +\frac{18}{7}-\frac{11}{4} +\frac{16}{5}[/tex]

= [tex]\frac{21}{7} -\frac{11}{4} +\frac{16}{5}[/tex] As both denominators have 7 you can add their numerators

=[tex]\frac{21}{7} -(-\frac{9}{20})[/tex]     L.C.M

=[tex]\frac{21}{7} +\frac{9}{20}[/tex]   L.C.M

=[tex]\frac{69}{20}[/tex]

The proportional relationship between (0,0) and (4,11) represents a direct variation

The equation that represents the graph is  y = 11x/4

The points on the graph are given as:

(x,y) = (0,0) and (4,11)

The equation of the graph is then calculated using:

y = (y₁/x₁) * x

This gives

y = (11/4) * x

Evaluate

y = 11x/4

Hence, the equation that represents the graph is  y = 11x/4

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Answer:

Ray.

Step-by-step explanation:

Lines have no endpoints, while rays have 1 endpoint (:

Answer:

1.9998 inches = radius

Step-by-step explanation:

V=(4/3)πr³

33.5 = (4/3)πx³

33.5 * 3/4 = (4/3)πx³(3/4)

25.125 / π = (πx³) / π

[tex]\sqrt[3]{7.998}[/tex] = [tex]\sqrt[3]{x^3}[/tex]

1.9998 = x

Answer:

  19

Step-by-step explanation:

The triangle inequality tells you the possible values of x are ...

  24 -10 < x < 24 +10

  14 < x < 34

There are 19 integer values of x in this range.

Length: 44 metre

Here given,

length = L

breadth = 12 metre

perimeter = 112 metre

Answer:

$292.00

Step-by-step explanation:

Total amount collected= number of people×amount per each person

total amount= 73×$4.00

Total amount collected=$292.00

Answer:

$292

Step-by-step explanation:

its really easy, you just multiply 73 to 4

     You commented that part of the instruction included "If the theorem cannot be applied, explain the reason."

     The theorem cannot be applied. Since this is not a right triangle, we cannot solve using the Pythagorean Theorem unless we are given a height. If we have the height of this triangle, then we can break it into two different right triangles and solve.

What is a right triangle? A right triangle is a triangle that has an angle measurement of 90 degrees.

       In summary, this is an isosceles triangle and the Pythagorean Theorem only applies to right triangles.

Answer:

5.735

pythagorian theorem is a^2 + B^2 = c^2

C is the longest side of the right triangle

Hello there!

In order to solve this inequality, we should first use the distributive property:-

3(a-4)≥4(a+5)

3a-12≥4a+20

Now, add 12 to both sides:-

3a≥4a+32

Subtract 4a from both sides:-

3a-4a≥32

-a≥32

Divide both sides by -1:-

a≤-32

The inequality sign changed because we divided both sides by a negative number.

[tex]\mathcal{NOTE:-}[/tex]

I hope everything is clear; however, if you need any explanation or clarification, don't hesitate to let me know, and I will comment or edit my answer. Good luck and have a great rest of your day! :)

Answer:

A

Step-by-step explanation:

my brain says so?

Answer:

its 10

Step-by-step explanation:

The reason its 10 is because it shows more 10 then any number

Answer:

x = 5

Step-by-step explanation:

Tangents from a specific point are equal in length.

3x - 7 = 18 - 2x

5x - 7 = 18

5x = 25

x = 5

Answer:

90 degrees

Step-by-step explanation:

a triangles angles add up to 180

this means that you can add all the angles together and get 180

you can first add 30 and 60 and then subtract the sum from 180

30 + 60 = 90

180 - 90 = 90

the last angle is 90 degrees

Hey ! there

Answer:

Step-by-step explanation:

In the question we are given with two angles of the triangles that are 30° and 60° . And we are asked to find the third angle of triangle .

For solving this question we must have knowledge of angle sum property which says that the sum of all the angles which are present inside the triangle ( interior angles ) is equal to 180°.

Solution : -

As we know that ,

So ,

[tex] \longmapsto \qquad \: 30° + 60° + x° = 180°[/tex]

Step 1 : Adding 30° and 60° :

[tex] \longmapsto \qquad \:90° + x° = 180° [/tex]

Step 2 : Subtracting 90° from both sides :

[tex] \longmapsto \qquad \: \cancel{90°} - \cancel{90 ° } + x° = 180° - 90° \: [/tex]

On further calculations , We get :

[tex] \longmapsto \qquad \: \blue{\underline{\boxed{\frak{x° = 90°}}}}[/tex]

Verifying : -

Now we are verifying our answer by adding all the angles of triangle and equating them with 180° because of angle sum property. So ,

Therefore, our solution is correct .

Answer:

The zeros are -5, -1, 0, 4, 5.

Step-by-step explanation:

x(x2 – 25)(x2 – 3x – 4) = 0

x(x - 5)(x + 5)(x + 1)(x - 4) = 0

so either x or the other 4 factors can be 0 :

x = 0, x - 5 = 0, x + 5 = 0, x + 1 = 0 or x - 4= 0, giving:-

x = 0, 5, -5, -1, 4.

just more and more of these.

⇒ ANSWER :   x = 0, x = 5, x = -5, x = 4 and x = -1

EQUATION GIVEN: g(x) = x(x2 – 25)(x2 – 3x – 4)

1) factorize the equation

g(x)=x(x-5)(x+5)(x²-3x-4)

2) expand the equation

g(x)=x(x-5)(x+5)(x²+x-4x-4)

3) factorize

g(x)=x(x-5)(x+5)(x(x+1)-4(x+1))

4) factor out x+1

g(x)=x(x-5)(x+5)(x-4)(x-1)

5) equate to 0

x(x-5)(x+5)(x-4)(x+1)=0

6) solve for x

x = 0, x = 5, x = -5, x = 4, x = -1

Pain.

Answer:

204, there is no remainder.

Step-by-step explanation:

Answer: 204 Rem 2

Step-by-step explanation: Use long division

Answer:

71.98

[tex]d=2\sqrt{ \frac{A}{\pi }} = 2 * \sqrt{\frac{4069.44}{\pi }}[/tex] ≈ 71.98175 rounded to hundred-thousandths

Answer:

97 1/3 or 97.3333

Step-by-step explanation:

multiply 2 2/3 by 36 1/2

:)

The number of rotations for the new wheel will be  1,056 rotations

Let the initial circumference be 50 rotations  (assumed)

If the number of rotations of the circumference of the tires were increased by 20%, then the new circumference will be:

Ne circumference = 1.2 * 50 = 60

number of rotations for the new wheel = 63360/60
number of rotations for the new wheel = 1,056 rotations

Hence the number of rotations for the new wheel will be  1,056 rotations

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