Acquarium workers are making a mixture of salt water. The desired ratio is 90 grams of salt per liter of water. What is the ratio in ounces per gallon?

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Explanation:

If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.

Side note: this type of triangle is an isosceles right triangle.

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You could use the tangent rule to get the same thing

tan(angle) = opposite/adjacent

tan(45) = 100/x

1 = 100/x

1*x = 100

x = 100

In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.

Answer:

[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]

Step-by-step explanation:

The base of the right triangle created is 100 meters.

The angle between the base and the hypotenuse of the right triangle is 45 degrees.

We can use trigonometric functions to solve for the height of the tower.

[tex]\displaystyle \mathrm{tan(\theta) = \frac{opposite }{adjacent} }[/tex]

[tex]\displaystyle \mathrm{tan(45) }= \frac{x }{100}[/tex]

Multiplying both sides by 100.

[tex]\displaystyle \mathrm{100 \cdot tan(45) }= x[/tex]

[tex]\displaystyle \mathrm{100 }= x[/tex]

The height of the tower is 100 meters.

Answer:

11

Step-by-step explanation:

|1 - 12| = |-11| = 11

Answer:

11

Step-by-step explanation:

Answer:

270°

Step-by-step explanation:

For example,

(x, y) is in 1st quadrant (x- coordinate is positive, y - coordinate is positive) , then

(y, - x) is in 4th (x- coordinate is positive, y - coordinate is negative).

x and y changed places, so clockwise is 90°,

and counter-clockwise 360-90= 270°.

Step-by-step explanation:

A playing card is in the form of a rectangle whose perimeter is equal to 28 cm and area is 45 cm².

If l and b are length and breadth of the rectangle.

Area,

[tex]A=lb[/tex]

[tex]45=lb\\\\l=\dfrac{45}{b}\ .....(1)[/tex]

Perimeter,

[tex]P=2(l+b)\\\\28=2(l+b)\\\\14=(l+b)\ ....(2)[/tex]

Put the value of l from equation (1) to equation (2). So,

[tex]14=\dfrac{45}{b}+b\\\\14=\dfrac{45+b^2}{b}\\\\14b=45+b^2\\\\b^2-14b+45=0\\\\b^2-9b-5b+45=0\\\\b(b-9)-5(b-9)=0\\\\b=5\ cm, 9\ cm[/tex]

Put the value of b in equation (1),

If b = 5 cm

[tex]l=\dfrac{45}{5}=9\ cm[/tex]

If b = 9 cm

[tex]l=\dfrac{45}{9}=5\ cm[/tex]

So, the dimensions of the playing card is 9 cm by 5 cm.

Answer: C

Step-by-step explanation: Absolute value means all the values in the | | are positive so make them positive and you will see it’s 3.5, 4.2, and 9 in order from least to greatest.

Answer:

8 x2.20 = Answer

Step-by-step explanation:

Answer:

7d+6q=2.20

Step-by-step explanation:

Answer:

3.33

Step-by-step explanation:

3.45

- 0.12

______

3.33

Answer:

One segment is 8.89 long and the other one is: 11.11 long

Step-by-step explanation:

Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.

In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.

The proportionality indicated by the bisector theorem gives;

[tex]\frac{20-x}{x} =\frac{30}{24}[/tex]

and we can solve for "x":

[tex]\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89[/tex]

Then the other segment is:  20 - 8.89 = 11.11

Answer:

Angle EFG = 104 degrees

Angle GFH = 76 degrees

Step-by-step explanation:

Angle EFG and Angle GFH are a linear pair, which means that they add up to 180 degrees.

Angle EFG = 4n + 20 and Angle GFH = 2n + 34, so 4n + 20 + 2n + 34 = 180.

We can then combine like terms, getting 6n + 54 = 180.

Then, we can subtract both sides by 54, getting 6n = 126.

Lastly, we can divide both sides by 6, getting n = 21.

EDIT - solve for EFG and GFH:

Angle EFG = 4n + 20 = 4(21) + 20 = 104 degrees

Angle GFH = 2n + 34 = 2(21) + 34 = 76 degrees

Answer:

∠EFG = 104°

∠GFH = 76°

Step-by-step explanation:

∠EFG + ∠GFH = 180

(4n + 20) + (2n + 34) = 180

6n + 54 = 180

6n = 180 -54

n = 126 / 6

n = 21

plug in values to ∠EFG

∠EFG = 4(21) + 20

∠EFG = 104°

plug in values to ∠GFH

∠GFH = 2(21) + 34

∠GFH = 76°

Answer:

The percentage increase of the production expectation to 1 decimal place is 178.6%

Step-by-step explanation:

Here in this question, we are interested in finding the percentage increase in the production capacity of the hypothetical company;

We can make or have a formula for this to make our workings easier;

% increase = (new value - old value)/old value * 100%

From the question;

The old value is the former productive capacity which is 1.4 million

The new productive capacity is 3.9 million

Thus;

The percentage increase in the production capacity would be;

(3.9 million - 1.4 million)/1.4 million * 100%

= 2.5 million/1.4 million * 100% = 178.57%

But the question asks we should have our answer in one decimal place;

Thus; 178.57% becomes 178.6%

Answer:

A length of 5 and a perimeter of 20

Step-by-step explanation:

Personally, I'm lactose intolerant so I wouldn't take any Cheez-Its, but oh well.

Everyone wants the most Cheez-its, right? So we need to find the rectangle with the greatest area.

Let's look at the first one, a rectangle with a length of 9 and a perimeter of 22.

The perimeter of a rectangle can be expressed as [tex]2l+2w[/tex], where l is the length and w is the width.

We know the length and area, so let's solve for w (the width).

[tex]2\cdot9+2w=22\\\\18+2w=22\\\\2w=4\\\\w=2[/tex]

So the width is 2. The area of a rectangle is the length times the width.

[tex]9\cdot2=18[/tex]

So the first rectangle has an area of 18.

Using the same concept for the second statement, a length of 5 and a perimeter of 20, we can find the area.

[tex]2l+2w=20\\\\2\cdot5+2w=20\\\\10+2w=20\\\\2w=10\\\\w=5\\\\5\cdot5=25[/tex]

So the area of the second one is 25.

The greatest area is 25, so you'd want this one.

Hope this helped!

Answer:

The second one

Step-by-step explanation:

yaaaaaaaa

Answer:

Step-by-step explanation: all yu need to do is plug in each number option you have to replace in for until you get what it equals aka 4

for ex.

18/3-2=4 so that means 18 is your answer

Answer:

Step-by-step explanation:

In algebra, there is always an orderly progression of steps. Once we get an answer for the value of x, we must test it in the original question to make sure it is correct.

n/3 × 3 = 6 × 3

n = 18

18/3 - 2 = 4

6 - 2 = 4

4 = 4 ✓

Answer: 3/2

Step-by-step explanation:

1 3/4 ÷ 1 1/6

STEP 1. convert into improper fraction

1 3/4=7/4

1 1/6=7/6

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STEP 2. to the operation

 1 3/4 ÷ 1 1/6

=7/4 ÷ 7/6

=7/4 × 6/7

=6/4

=3/2

Hope this helps!! :)

Please let me know if you have any question

Answer:

1.5

Step-by-step explanation:

First find 1 3/4 and 1 1/6 as an improper fraction. 1 3/4 = 7/4 because 1 times 4 plus three. 1 1/6 = 7/6 because 1 times 6 plus 1, so now you have 7/4 divided by 7/6. You change 7/6 to it's reciprocal, which is 6/7. Now it's like multiplication with fractions. 7*6=42. 4*7=28, so it's 42/28.

Now we want to simplify. It can be simplified to 1 1/2, which is also 1.5. Hope this helps.

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

The computation of the fraction of her overall lawn remaining unmowed is shown below:

Let us assume that the back lawn be x

So the front lawn would be

[tex]= \frac{1}{3}\times x\\\\ = \frac{x}{3}[/tex]

So, the total lawn is  ................... (i)

[tex]= x + \frac{x}{3}\\\\ = \frac{4x}{3}[/tex]

The back lawn mowed is [tex]\frac{2x}{3}[/tex]

Front lawn moved is [tex]\frac{x}{6}[/tex]

So, the total mowed is ....................(ii)

[tex]= \frac{2x}{3} + \frac{x}{6}\\\\ = \frac{5x}{6}[/tex]

So, the total unmowed is

[tex]= \frac{4x}{3} - \frac{5x}{6} \\\\= \frac{x}{2}[/tex]

Now the fraction is

[tex]= \frac{x}{2} \times \frac{3}{4x} \\\\ = \frac{3}{8}[/tex]

The fraction of the entire lawn unmoved is 3 / 8

The fraction is defined as the division of the whole part into an equal number of parts. The computation of the fraction of her overall lawn remaining unmowed is shown below:

Let us assume that the back lawn is x

So the front lawn would be

[tex]=\dfrac{1}{3}\times x[/tex]

[tex]=\dfrac{4x}{3}[/tex]

So, the total lawn is  ................... (i)

[tex]=x+\dfrac{x}{3}[/tex]

The back lawn mowed is

The front lawn moved is

So, the total mowed is ....................(ii)

[tex]=\dfrac{2x}{3}+\dfrac{x}{6}[/tex]

[tex]=\dfrac{5x}{6}[/tex]

So, the total unmowed is

[tex]=\dfrac{4x}{3}-\dfrac{5x}{6}[/tex]

[tex]=\dfrac{x}{2}[/tex]

Now the fraction is

[tex]=\dfrac{x}{2}\times \dfrac{3}{4x}[/tex]

[tex]=\dfrac{3}{8}[/tex]

Therefore the fraction of the entire lawn unmoved is 3 / 8

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Answer: Supplementary, 3 and 2, substitution, 2.

Step-by-step explanation: just did it .

The ∠1 is congruent to ∠3 by definition of congruency.

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.

m∠1 + m∠2 = 180°  (given)

m∠2 + m∠3 = 180°  (given)

Hence:

m∠1 + m∠2  = m∠2 + m∠3  (equality property)

Subtract m∠2 from both sides to get:

m∠1  = m∠3

The ∠1 is congruent to ∠3 by definition of congruency.

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Answer

So changing 1/4 by multiplying top and bottom by 9 gives 9/36 and changing 2/9 by multiplying top and bottom by 4/4 gives 8/36 and adding 9/36 to 8/36 gives 17/36 - a rational number.

Step-by-step explanation:

Answer:

[tex] \sqrt{5} [/tex]

Step-by-step explanation:

decimal repeats without a pattern

Answer:

Yes, I think so!

Step-by-step explanation:

3*3=9

4*2=8

So i will be 9/8

Hope this helps!

(pls mark brainiest!)

Answer:

I think the answer is 59

Step-by-step explanation:

6p+5

6(9)+5

54+5=59

Answer:

C with points A and B on the line

The diagram that supports the postulate is line option (c).

Lines and points are both undefined terms in geometry.

The given postulate states that;

Exactly one line exists between any two points.

This means that the line must pass through the two points.

From the given options, Only option (c) is true because the line passes through points A and B.

Hence, the diagram that supports the postulate is line option (c).

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Answer:

154

Step-by-step explanation:

To find the percentage, we can set up a percentage proportion, where x is 7% of 2200.

[tex]\frac{x}{2200} = \frac{7}{100}[/tex].

Now we can cross multiply to find the value of x.

[tex]2200\cdot7=15400\\\\15400\div100=154[/tex]

Hope this helped!

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Explanation:

For now, assume the inequality is true

We can cross multiply to get

2/11 < 5/22

2*22 < 11*5

44 < 55

Since the last inequality is true (44 is smaller than 55), this means the first inequality is also true.

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We could use a calculator to see that

2/11 = 0.1818 approximately

5/22 = 0.2273 approximately

Since 0.1818 is smaller than 0.2273, this means 2/11 is smaller than 5/22.

In other words, 0.1818 < 0.2273 leads to 2/11 < 5/22

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An alternative is to multiply 2/11 by 2/2 to get 4/22

So 2/11 < 5/22 would update to 4/22 < 5/22. Both have the same denominator so we just compare the numerators. Because 4 < 5 is true, this makes 4/22 < 5/22 true, and consequently 2/11 < 5/22 true as well.

Answer:

-1

Step-by-step explanation:

(-1) ^3

This is (-1) multiplied together 3 times

(-1) * (-1) * (-1)

-1

The answer is

2^6(1-3n)×2^4(3n-3)=2^6(-3n-3).

2^(6-18n)×2^(12n-12)=2^(-18n-18).

(6-18n)×(12n-12)=(-18n-18).

6-18n×12n-12=18n-18.

6-12×-18n-12n=18n-18

-6×-30n=18n-18.

-6×18=-18+30

-108=48n.

n= -108/48.

n=-2.25.

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A square is a quadrilateral that has the same length on every side.

The area of the garden is 196 square feet. To find the area of a garden, you have to multiply the length times the width. Since you know that both widths are the same, you can simply just calculate the square root of 196. The square root of 196 is 14. So you know that one side is 14 feet in length.

Now you will need to find the perimeter. The perimeter of any polygon is the lengths of all sides added up. Since there are 4 sides on a square, and each side is the same length, you can just add 14, 4 times. 14+14+14+14 equals 56. So the perimeter of the garden is 56 feet.

Hannah will need 56 feet of fencing.

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she needs to put 56 feet of fencing materials around ground

A quadrilateral which has four equal sides and four equal angles is known as a square.

According to the question,

To find the fencing material means to calculate the length around the square garden, or the perimeter of the square shaped garden.

Area , A is given as 196  square feet.

Formula for Area of a square (A )= Side × side

196 = side × side

This can be written as  

Side × Side  = 196

 [tex]side^{2}[/tex] = 196

Take the square root of both sides,

[tex]\sqrt{side^{2} }[/tex]  = [tex]\sqrt{196}[/tex]

side = 14 feet

The perimeter of a square can be calculated, P = 4(s), because all the four

sides are equal

P = 4 × side

   = 4 × 14

   = 56 feet

Hence, she needs 56 feet of fencing materials.

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