How many times can 3 go into 9

Answer:

Option B. False

Step-by-step explanation:

If triangle ABC is similar to DEF then for the similarity of these triangles all angles should be similar or same.

In addition to the angles their corresponding sides should be in the same ratio, in other words sides should be dilated by a scale factor.

Therefore the given statement is false.

Option B. False is the answer.

Answer:

-0.64

Step-by-step explanation:

0.4 ÷ ([tex]-\frac{5}{8}[/tex]) = N

[tex]0.4 * -\frac{8}{5} [/tex] = N

N = -0.64

96 fluid ounces is less than 13 cups.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

To compare 96 fluid ounces and 13 cups, we need to convert one of the quantities so that they are in the same units.

One cup is equal to 8 fluid ounces.

So,

13 cups is equal to:

13 cups x 8 fluid ounces/cup

= 104 fluid ounces

Now,

We can compare 96 fluid ounces and 104 fluid ounces.

Since 104 is greater than 96.

Thus,

96 fluid ounces is less than 13 cups.

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Option B is the expression that does NOT answer the question.

An equivalent expression is an expression that has the same value but does not look the same. When you simplify an expression, you're basically trying to write it in the simplest way possible.

For the given situation,

Let the unknown number be x or 1/x

Option A)  2 1/2 divided by 8

If unknown number is x,

then, 8x = 2 1/2

⇒ x = 2 1/2 ÷ 8

So, option A is correct.

Option B) 5/2 x 1/8

⇒ [tex]\frac{(5)(1)}{(2)(8)}[/tex]

⇒ 5/16

So, option B is incorrect.

Option C) 8 divided 2 1/2

If unknown number is 1/x,

then, 8/x = 2 1/2

⇒ x = 8 ÷ 2 1/2

So, option C is correct.

Option D) ? x 8 = 2 1/2

If fraction is not known, it can be replaced by '?'

So, option D is correct.

Hence we can conclude that option B is the expression that does NOT answer the question.

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From our diagram we can see that angle HED equals to angel GED and angle GDE equals to angel HDE.                    

Two triangles are similar if the corresponding angles are equal, so their corresponding sides will be in equal ratio.

Upon setting ratios of corresponding sides of our triangle equal we will get,

[tex]\frac{EG}{GD} =\frac{EH}{HD}[/tex]

[tex]\frac{99.2}{62} =\frac{112}{(x+2)}[/tex]

Now we will use cross multiplication to solve our equation,  

[tex]99.2(x+2)=112\cdot 62[/tex]

[tex]99.2x+198.4=6944[/tex]

[tex]99.2x=6944-198.4[/tex]

[tex]99.2x=6745.6[/tex]    

[tex]x=\frac{6745.6}{99.2}[/tex]

[tex]x=68[/tex]

Therefore, value of x will be 68 ft.

Answer:

251.33cm

Step-by-step explanation:

Answer:

measure of ∠BAC  is  45°

Step-by-step explanation:

We have Square ABCD

we need to find the measure of ∠BAC

Let us take ΔBAC

We know that all the angles in a square is equal to  90°

Therefore ΔBAC is right angled triangle since  ∠ABC= 90°

Sum of angles in a triangle = 180°

∠ABC + ∠BCA + ∠BAC = 180°

90° + ∠BCA + ∠BAC =180°  ( since  ∠ABC= 90°)

∠BCA + ∠BAC =180° -90°  ( subtracting 90° from both sides)

∠BCA + ∠BAC = 90°

sides of square are equal so  AB = BC  and angles opposite to equal sides are equal hence ∠BCA = ∠BAC

so we have

∠BAC+∠BAC = 90°  

2∠BAC = 90°  

∠BAC = 45°   ( divide both sides by 2)

so we have measure of ∠BAC  is  45°  

Answer: Hi!

We know that Bert has $50, but he needs a total of at least $250 for this holiday. The differences between what he needs and what he has is:

$250 - $50 = $200

So he needs another $200.

He gets paid £20 a day and we want to know the number of days that he needs to work in order to obtain the $200.

The first step is to transform the £20 into dollars.

£1 = $1.27

then his daily pay in dollars is: 20*$1.27 = $25.4

Now let's call X the number of days that he needs to work to obtain the $200, we got:

X*$25.4 = $200

X = $200/$25.4 = 7.8

We should round up this result because we want a whole number.

X = 8, this means that Bert needs to work at least 8 days if he wants to have at least $250 for the holidays.

The value of z is 3.2 units.

What is the law of sines?

The law of sine or the sine law states that the proportion of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is additionally known as the sine rule.

For a triangle ABC the law of sine will be,

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

In triangle XYZ given here,

The law of sine can be written as,

[tex]\frac{x}{sinX} =\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

here ∠Y and ∠Z is given so we write

[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

y=2.6

∠Y=51°

∠Z=76°

sin51°≈0.78

sin76°≈0.97

[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

[tex]2.6/0.78=z/0.97[/tex]

[tex]z=3.2 units[/tex]

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Answer:

The answer would be (3, -4)

Step-by-step explanation:

I just took the test and got  it right :)

Answer:

(3, 4)

Step-by-step explanation:

The volume of the iron cube is 1000 cm³ and its density is 7.9 g/cm³.

1. Volume of the iron cube:

The volume of a cube is calculated by multiplying the length, width, and height. In this case, all three sides are 10cm, so the volume is:

Volume = 10 cm × 10 cm × 10 cm = 1000 cm³

Therefore, the volume of the iron cube is 1000 cubic centimeters.

2. Density of the iron cube:

Density is defined as mass divided by volume. We know the volume from the previous calculation and the mass is given as 7.9 kg.

However, we need to convert the mass to grams because the volume is in cubic centimeters. There are 1000 grams in 1 kg, so:

Mass in grams = 7.9 kg × 1000 g/kg = 7900 g

Now, we can calculate the density:

Density = Mass / Volume = 7900 g / 1000 cm³ = 7.9 g/cm³

Therefore, the density of the iron cube is 7.9 grams per cubic centimeter.