Problems 7and 8 50 POINTS

set this up as a ratio

25 ft tree / 15 foot shadow = X ft tree / 6 foot shadow

25/15 = X/6

 cross multiply:

150 / 15x

x = 150/15 = 10

 the tree is 10 feet tall

Step 1: You want to remove the percent sign and then put the number over 100.

Step 2: If the percent is not a whole number then you want to multiply the top and bottom number by 10 but only for every number that comes after the decimal point.

Step 3: Always simplify if possible.

Examples:

43% = [tex]\frac{43}{100}[/tex]

78% = [tex]\frac{78}{100}[/tex] = [tex]\frac{39}{50}[/tex]

0.4% = [tex]\frac{0.4}{100}[/tex] = [tex]\frac{4}{1000}[/tex] = [tex]\frac{1}{250}[/tex]

Converting percents to fractions involves writing the percent as a fraction with a denominator of 100 and then simplifying. For example, 75% is equivalent to 75/100, which simplifies to 3/4. Decimals can be converted to percents by multiplying by 100 and adding the percent sign.

Converting Percents to Fractions

To convert a percent to a fraction, start by writing the percent value as a fraction with a denominator of 100. For example, 75% would be written as 75/100. The next step is to simplify the fraction if possible. To simplify, you find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number. For instance, the GCD of 75 and 100 is 25, so when we divide both the numerator and the denominator by 25, we get 3/4. Hence, 75% as a fraction in simplest terms is 3/4.

When converting to decimals, simply divide the numerator by the denominator. So, 75% becomes 0.75 when turned into a decimal. Conversely, to convert a decimal to a percent, you multiply by 100 and add the percent symbol (%). For instance, converting the decimal 0.75 to a percent, you would calculate 0.75 * 100 which equals 75%, completing the conversion.

Calculating percents is about understanding the ratio or fraction that the percent represents. The term 'percent' literally means 'per hundred', so any percent can be thought of as that number over 100. For example, 3% means 3/100 and 100% represents a whole or 1 as it's equivalent to 100/100.

Final answer:

The system of equations y = -3x - 2 and 4y = -12x - 8 is dependent with an infinite number of solutions because both equations represent the same line.

Explanation:

The system of equations given is:

y = -3x - 2

4y = -12x - 8

If we examine the second equation, we can simplify it by dividing everything by 4, yielding:

y = -3x - 2

Both equations are now identical, which implies that they are the same line graphed on a coordinate plane. The system is considered dependent, and the number of solutions is infinite because every point on the line y = -3x - 2 is a solution to the system.

Answer:

ur final answer will be 5 x (2k^2+3) x (5k-4). its correct i just did the test

Step-by-step explanation:

find common denominator:

6*4 =24, 8*3 = 24

1/6 = 4/24

3/8 = 9/24

4/24 + 9/24 = 13/24

 Answer is D

The Pesos you would get if you exchanged $121.10 using an exchange rate of $3 = 1 Peso, you can set up a proportion and solve for x.

To calculate how many Pesos you would get if you exchanged $121.10 at an exchange rate of $3 = 1 Peso, you can set up a proportion:

$3 / 1 Peso = $121.10 / x Pesos

Cross multiply to solve for x:

$3 * x = $121.10 * 1

x = $363.30

Therefore, you would get 363.30 Pesos if you exchanged $121.10 at the given exchange rate.

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The complete distance Haruka hiked can be calculated by converting the percent to decimal.

The total distance is 14 km Haruka hike in all.

Given:

She hiked in afternoon is [tex]6\: \rm km[/tex].

Let the distance hiked in morning is [tex]x[/tex].

As per the question, 6 kilometers 25% less she had hiked in morning.[tex]\begin{aligned}\left(\dfrac{100\%-25\%}{100}\right)x&=6\\0.75x&=6\\x&=\dfrac{6}{0.75}\\x&=8\\\end[/tex]

Therefore, Haruka hiked [tex]8\:\rm km[/tex] in morning.

Calculate the total distance hiked.

[tex]\rm Total\: distance=8+6=14 \:\rm km[/tex]

Thus, the total distance is 14 Km Haruka hike in all.

Learn more about percent is here:

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Answer:

Step-by-step explanation:

There's a whole family of points.

(x + 1)^2 + (y + 2)^2= 25

The above is an equation that represents a circle.

Three points are marked below 2 of which are easily seen to be 5 units away from the center (-1,-2)

Answer:  Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Answer:

-b) -8/9

Step-by-step explanation:

Answer:

The correct Answer is B.) -8/9

Step-by-step explanation:

HAVE AN AMAZING DAY!!

The number of 3/4 cup servings that are in 1/2 of a cup of milk is [tex]\frac{2}{3}[/tex]

In order to determine the number of 3/4 cup servings that are in 1/2 cup of milk, divide the fraction of the cup of milk by the fraction of cup servings

Cup of milk ÷ Number of cup servings

= [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex]

[tex]\frac{1}{2}[/tex] x [tex]\frac{4}{3}[/tex]

= [tex]\frac{4}{6}[/tex]

In order to express the answer in its simplest form, divide the numerator by two and the denominator by 2. The numerator and the denominator are both divided by two because two is a common factor of 4 and 6

= [tex]\frac{2}{3}[/tex]

Please check here to learn how to divide fractions: https://brainly.com/question/7722714?referrer=searchResults

discount = price times % off

 discount = 22.50 x 0.20

discount = $4.50

Answer:

[tex]\$22.50*0.20=\$4.50[/tex]

Step-by-step explanation:

Let

x-------> original price

y------> percentage of discount

z-----> discount

we know that

[tex]z=xy[/tex]

In this problem we have

[tex]x=\$22.50[/tex]

[tex]y=20\%=\frac{20}{100}=0.20[/tex]

Substitute the values

[tex]z=\$22.50*0.20=\$4.50[/tex]