3x+2y=0
x-5y=17
solve in a Solving Systems by Elimination

Answer:

length = 10.64 cm, width = 5.64 cm, and height = 5 cm.

Step-by-step explanation:

Total volume of dice that filled the box = (150 x 2) cm³

                                         = 300 cm³

Let the length, width and height of the box be represented by l, w and h respectively.

So that;

l = (w + 5) cm

w = w

h = 5 cm

volume of the box = length x width x height

                               = (w + 5) x w x 5

                               = (w + 5) x 5w

                               = 5[tex]w^{2}[/tex] + 25w

volume of the box = 5[tex]w^{2}[/tex] + 25w

Since the box was completely filled by 150 dice, then;

total volume of dice = volume of the box

300 = 5[tex]w^{2}[/tex] + 25w

5[tex]w^{2}[/tex] + 25w - 300 = 0

Divide through by 5 to have;

[tex]w^{2}[/tex] + 5w - 60 = 0

Applying the quadratic expression,

w = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) ÷ 2a

where: a = 1, b = 5 and c = -60

(-5 ± [tex]\sqrt{5^{2} - 4(1*-60)}[/tex] ) ÷ 2

(-5 ± [tex]\sqrt{265}[/tex]) ÷ 2

(-5 ± 16.28) ÷ 2

(-5 + 16.28) ÷ 2 OR (-5 - 16.28) ÷ 2

5.64 OR -10.64

Thus, w = 5.64 cm

So that, l = (w + 5) = 10.64 cm

The possible dimensions of the box are: length = 10.64 cm, width = 5.64 cm and height = 5 cm.

Answer:

a, b ,e

Step-by-step explanation:

The solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a value or a set of values, when substituted for the unknowns, the equation becomes true."

For given question,

We have been given the graph of a quadratic function f(x) and an absolute value function g(x).

We need to find the x-values that are approximate solutions to the equation f(x) = g(x).

To solve the equation f(x) = g(x), we look for the points where the graphs of f(x) and g(x) intersect.

The intersection point of f(x) = g(x) appears to be at point which lie in the second quadrant and the x-value lie between -2 and -4.

Also,  the second intersection point lie in the fourth quadrant where x value is in between 4 and 6.

So, the solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

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Answer:

It’s 55

Step-by-step explanation:

180- 125=55

Answer:

This is a same side interior angle. I just learned this in class so don't blame me if your wrong, ur taking advice from a 4th grader dude.

Answer is: x

read the explanation lol

Step-by-step explanation:

So we know angle 3 and 4 is=180

7 and 8 =180

but 4 and 7 ALSO add up to 180, I think you can do this now. It's mental math.

Hint: 125+x=180

Answer:

5 (12+3)

75

Step-by-step explanation:

so you multiply 5 with the inside of paranthesis. So 5 x 12 and 5 x 3

So its 60 + 15 which is 75. Hope this helps!

Answer: the answer is linear

Step-by-step explanation: (not sure what functions it’s talkin about but it is linear)

Answer:

-9n+108

Step-by-step explanation:

-12n+3(n+36)

-12n+3n+108

-9n+108

Answer:

-9n+108

Step-by-step explanation:

distribute then combine like terms

Answer:

3, 11, and 14

Step-by-step explanation:

One side length of a triangle that is selected at random must be smaller than the sum of the other two side lengths and bigger than their difference

one side of this triangle is 4 and the other is 7 so if we call the third side length x

7-3 < x < 7+3 ➡ 4 < x < 11

Answer:

.51

Step-by-step explanation:

P(F)=.55, P(S)= .4

P(F ∩ not S)= .55×.6=.33

P(S ∩ not F)= .4×.45=.18

.33+.18=.51

Answer:

The probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

Step-by-step explanation:

Given information:

A company is considering purchasing materials:

The probability of purchasing mineral rights

Form the first mountain [tex]p_1=0.55\\[/tex]

From the second mountain [tex]p_2=0.4[/tex]

As the decision is made independently

So, P([tex]p_1[/tex]∩ not[tex]p_2[/tex]) [tex]=0.55 \times 0.6\\[/tex]

P([tex]p_1[/tex]∩ not[tex]p_2[/tex]) [tex]= 0.33\\[/tex]

Similarly, the value of

P([tex]p_2[/tex]∩ not[tex]p_1[/tex]) [tex]=0.4 \times 0.45[/tex]

P([tex]p_2[/tex]∩ not[tex]p_1[/tex]) [tex]=0.15[/tex]

Hence , [tex]P=0.33+0.18[/tex]

[tex]P=0.51[/tex]

Hence , the probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

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Answer:

2,784 miles

Step-by-step explanation:

232*12=2,784

Answer:

5

Step-by-step explanation:

252/140=9/X

252x=1260

x=5

Answer:

If there are 13 guests, it would cost Norma $26

Step-by-step explanation:

Since 12 guest equals 24 dollars all you have to do is divide 24/12 which would give you 2dollars. this means that she has to pay 2 dollars per guest. Multiply 13 becuase you want to know how much money it would cost with 13 guests and you get 26 dollars. Hope this helps.

Answer:

It'll cost $26 !

Step-by-step explanation:

if you set it up like this;

[tex]\frac{13}{x}= \frac{12}{24}[/tex]

you can see a few ways of solving this !

one way is cross multiplication .

13 x 24 = 312

312 / 12 = 26

Answer: 8.49

Step-by-step explanation:

i took the test and it was right

Answer:

0.06

Step-by-step explanation:

probability of multiple of 6= 0.2

probability of multiple of 4= 0.3

0.2 * 0.3 = 0.06

Answer:

[tex]length=(\sqrt{40} )m,breadth=\frac{4\sqrt{40} }{5} m[/tex]

Step-by-step explanation:

Answer:

The coordinates of Good after dilation will be (-1/3,1)

Step-by-step explanation:

Here, we want to get the coordinates of the point G after dilation

Mathematically, that would be having 1/3 multiply the coordinates of G

G’ = 1/3 (-1,3)

G’ = (-1/3 , 1)

Answer:

M(-1,7), N(3,6), O(1,1)

Step-by-step explanation:

The coordinates of ΔMNO are M(1, 3),N(5, 2), and O(3, −3).For a translation, 2 units left and 4 units up the correct vertices of the image will be M'(-1,7), N'(3,6), and O'(1,1).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that the coordinates are M(1, 3),N(5, 2), and O(3, −3).

We have to translate 2 units left and 4 units up.

The coordinates obtained after applying the given geometric transformation are M'(-1,7), N'(3,6), O'(1,1)

Thus, the coordinates of ΔMNO are M(1, 3),N(5, 2), and O(3, −3).For a translation, 2 units left and 4 units up the correct vertices of the image will be M'(-1,7), N'(3,6), and O'(1,1).

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Answer:

16.5 pages

Step-by-step explanation:

Number of pages Ingrid types = 3

Number of pages Tanya types = 4.5

The proportion to find how many pages Tanya would have typed (x), if Ingrid typed 11 pages would be as follows:

3 : 4.5 = 11 : x

Thus:

[tex] \frac{3}{4.5} = \frac{11}{x} [/tex]

Cross multiply

[tex] 3*x = 11*4.5 [/tex]

[tex] 3x = 49.5 [/tex]

Divide both sides by 3

x = 16.5 pages

Answer:

Adam's container

Step-by-step explanation:

Adam's: 8.75/ 3.5 = 2.5

Marco's: 9.75/ 3.75 = 2.6

= 2.5

Answer:

133

Step-by-step explanation:

its an obtuse angle

Answer:

x = 25

Step-by-step explanation:

Answer:

x= 25

Step-by-step explanation:

Add 2 given sides then subtract 180

Answer:10.3

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

because of the way this is put the result simplified would be 3x-8x-20

3-8=-5

so the answer is 20-5x

x=0.25 btw

Answer:

59.4

Step-by-step explanation:

Answer:

He walked 59.4 miles in 11 days

Step-by-step explanation:

You take the number of miles he walked in one day,  (5.4), then multiply it by the number of days he walked (11), so the answer is 59.4

Answer:

Number of moles = 41.67 (Approx)

Number of carbon atom = 250.97 x 10²³ (Approx)

Step-by-step explanation:

Given:

Amount of carbon = 500 g

Find:

Number of moles

Number of carbon atom

Computation:

Number of moles = 500 / Atomic number of weight

Number of moles = 500 / 12

Number of moles = 41.67 (Approx)

Number of carbon atom = Number of moles x Avogadro number

Number of carbon atom = 41.67 x 6.023 x 10²³

Number of carbon atom = 250.97 x 10²³ (Approx)

Answer:

its not A just took the test

Step-by-step explanation:

The effect this scale factor has on the volume is that the volume will be 64 times larger. The correct option is B.

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called a scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k².

to get each other corresponding quantities from their similar figures' quantities.

So the area of the first figure = k² × area of the second figure

Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or

The volume of the first figure = k³ × volume of the second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Since the volume is the product of three linear quantities.

Therefore, if the scale factor of 4 is applied to the given prism then the volume of the prism will grow by 4³. Thus, we can write,

The volume of the scaled prism = 4³ ×Volume of the original volume

The volume of the scaled prism = 64 ×Volume of the original volume

Hence, the effect this scale factor has on the volume is that the volume will be 64 times larger.

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Answer:

50?

Step-by-step explanation:

Answer:

x= 106

Step-by-step explanation:

The angle opposite 32 is also 32. Considering 44, the missing angle in that triangle would be 104. The angle to the left of 104 would be 76, and if you consider that angle 30 you are left with the measure of 74. X is the angle next to 74, so it makes sense for it to measure 106 because the values must add to 180, and even if it's not drawn to scale 106 looks accurate