A tree shadow is 95 cm long. At the same time of the day Samantha stands next to the tree in measures her shadow to be 30 cm long. Samantha is 150 cm tall. What is the height of tree in centimeters

One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7

Solution:

Given that one number is 7 less than a second number.

Twice the second number is 1 less than 5 times the first.

Need to determine two numbers.

Let assume first number be represented by variable x and second number be represented by variable y.

As first number is 7 less than a second number, adding 7 to first number will give us second number

=> x + 7 = y   ------ (1)

[tex]\begin{array}{l}{\text { Twice of second number }=2 \times \text { second number }=2 \times y=2 y} \\\\ {\text { 5 times the first number }=5 \times \text { first number }=5 \times x=5 x}\end{array}[/tex]

As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,

=> 2y + 1 = 5x     ------ (2)

On substituting value of y as x + 7 from equation 1 into equation 2 , we get

2(x + 7) + 1 = 5x      

=> 2x + 14 + 1 = 5x

=> 2x – 5x = -15

=> -3x = -15

x = 5

Substituting x = 5 in equation (1) to get value of y  

=> y = 5 + 7 = 12

Hence first number is 5 and second number is 12

For this case we have the following inequality:

[tex]-5y \leq-15[/tex]

To solve, we follow the steps below:

We divide between 5 on both sides of the inequality:

[tex]-y \leq \frac {-15} {5}\\-y \leq-3[/tex]

We multiply by -1 on both sides taking into account that the sense of inequality changes:

[tex]y \geq3[/tex]

Thus, the solution is given by all values of "y" greater than or equal to 3.

Answer:

[tex]y \geq3[/tex]

See attached image

The vertical axis represents the "y" axis

Each side of garden measures 13.2 feet.

Step-by-step explanation:

Given,

Area of Kaitlyn's garden = 175 square feet

As the garden is in square shape, each side will have equal length.

Let,

a be the length of each side.

Area of square garden = A = a²

[tex]a^2=175[/tex]

Taking square roots on both sides

[tex]\sqrt{a^2}= \sqrt{175} \\a=13.22 \ feet[/tex]

Rounding off to nearest tenth,

Length of each side = 13.2 feet

Each side of garden measures 13.2 feet.

Keywords: area, square root

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Answer:

13/15

Step-by-step explanation:

Hope it is correct

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The nearest ten million is 4,480,000,000.

It takes 1 painter 24 hours to paint two class rooms

Step-by-step explanation:

When some worker do a job together, then

∵ It takes three painters 4 hours to paint 1 classroom

∵ It takes 1 painter x hours to paint 1 class room

- Equate 3 × 4 by 1 × x because they will do the same job

∴ 3 × 4 = 1 × x

∴ 12 = x

∴ It takes 1 painter 12 hours to paint 1 class room

We need to find it takes 1 painter to paint two class room

∵ The painter will paint 2 class rooms

∵ He takes 12 hours to paint 1 class room

- Multiply his time in one class room by 2

∵ 12 × 2 = 24

∴ It takes 1 painter 24 hours to paint 2 class rooms

It takes 1 painter 24 hours to paint two class rooms

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For this case we must solve the following equation:

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

We follow the steps below:

Multiplying by 3 on both sides of the equation we have:

[tex]x + 4 = 3 * 2\\x + 4 = 6[/tex]

Subtracting 4 from both sides of the equation:

[tex]x = 6-4\\x = 2[/tex]

Thus, the solution of the equation is[tex]x = 2[/tex]

Answer:

[tex]x = 2[/tex]

Answer:

He is correct

Step-by-step explanation:

multiplication and division are inverse operations so lets divide to see if he is correct

40.7/10=4.07

he is correct

Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.

According to Ethan, he assumed that the product of  10 and 4.07 is 40.7, we are to check if the calculation of Ethan is correct.

To do that, we will have to multiply 10 with 4.07 as shown below:

[tex]= 10 \times 4.07 \\= 10 \times \frac{407}{100}\\=\frac{4070}{100} \\=40.70[/tex]

Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.

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Answer:

4.8sq. yards

Step-by-step explanation:

Answer: -8.8n + 7.8

Step-by-step explanation:

2.8 - 5.8n - 3n + 5

Add -5.8n and -3n to get -8.8n

Add 2.8 and 5 together to get 7.8

Answer:

Step-by-step explanation:

7.8-8.8n

Answer:

width = 5

length = 15

Step-by-step explanation:

width: x

length : 3x

x + 3x + x + 3x = 40

8x = 40

x = 5

width = 5

length = 15

Answer:

x< (-6)

Step-by-step explanation:

If you have any questions about the way I solved it,don't hesitate to ask

Answer:

the answer is type 2

Step-by-step explanation:

ok so you first have to find the ratio of all of them and for type 1 it is 40 to 1 for type 2 it is 50 to 1 type 3 is 25 to 1 and type 4 is 30 to 1 so there for type two has the biggest ratio of fragrance to wax

The required table that has a higher ratio of fragrance to wax is type 2.

As given in the question, a company makes four different types of candles. The ratio of fragrance to wax for each type of candle is shown in the tables.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
For Type 1
The ratio of Fragrance to wax.
= 20 / 0.5 = 40 / 1

For Type 2
The ratio of Fragrance to wax.
= 150 / 3 = 50 / 1

For Type 3
The ratio of Fragrance to wax.
= 250 / 10 = 25

For Type 4
The ratio of Fragrance to wax.
= 30 / 1

Now,
50 > 40 > 30 > 25
Type 2 > type 1 > type 3 > type 4

Thus, the required table that has a higher ratio of fragrance to wax is type 2.

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Answer:

solutions

Step-by-step explanation:

use the quotient property to rewrite the expression.

write the difference of logs as the quotient log((d+1)/d).

substitute 1 for d to get log(2).

since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.

Answer:

Use the quotient property to rewrite the expression.

Write the difference of logs as the quotient log((d+1)/d).

Substitute 1 for d to get log(2).

Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.

Step-by-step explanation:

the answer is 9:10 hope it helps

Final answer:

Katie was a quarter of an hour, or 15 minutes, late to school which starts at 8:55 AM. So, she arrived at 9:10 AM.

Explanation:

If school starts at 8:55 AM and Katie was a quarter of an hour late, that means she was 15 minutes late because a quarter of an hour is 15 minutes (60 minutes divided by 4 equals 15 minutes).

To find out what time Katie arrived, we need to add 15 minutes to the starting time of school:

School starts: 8:55 AM

Time late: + 15 minutes

Time of arrival: 9:10 AM

So, Katie arrived at school at 9:10 AM.

Answer:

whats the question?

Step-by-step explanation:

Answer:

Theory

Step-by-step explanation:

A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is  0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

$3 donated_____$120 spent

$1,000 donated__X=$40,000 spent

(1,000*120)/3= 40,000

Answer: The Customers have to spend $4000 in order to raise $1000 for the pet rescue program.

Step-by-step explanation:

Hi, to answer this question we have to write a proportion.

Proportion = money spent / money raised for the pet rescue program

For every $120 that customers spend, $3: 120/3

To raise $100 : x / 100

Where x is the money that customers spent to raise $100 for the pet rescue program.

Solving for x:

120/3 = x /100

(120/3)100=x

x =$4000

Answer:

Δ MNO ≅ Δ PQR by ASA postulate

Step-by-step explanation:

Δ MNO and Δ PQR are congruents because:

1. Their included sides MN and PR are equal (22 units = 22 units)

2. Their angles ∠M and ∠P are equal  (100° = 100°)

3. Their angles ∠N and ∠Q are equal  (35° = 35°)

Now, we can conclude that Δ MNO ≅ Δ PQR by ASA postulate.

The percent equation showing the fiction books is y = 0.65x showing that among the 4,000 books in the library, 2,600 are fiction.

An equation is a mathematical representation of the equality of two expressions.

The number of books in the town's library = 4,000

The number of fiction books = 2,600

The number of nonfiction books = 1,400 (4,000 - 2,600)

The percentage of fiction books to the total number of books = 65% (2,600/4,000 x 100)

Let the total number of books in the library = x

Let the number of fiction books = y

Equation:

y = 0.65x

y = 2,600 (0.65 x 4,000)

The length of basketball court is 32 meters and width is 13 meters.

Step-by-step explanation:

Perimeter = 90 meters

Let w be the width

Length = l = 2w + 6

As basketball court are in rectangular shapes, therefore,

Perimeter = 2(length+width)

[tex]90=2(2w+6+w)\\90=2(3w+6)\\90=6w+12\\90-12=6w\\6w=78[/tex]

Dividing both sides by 6;

[tex]\frac{6w}{6}=\frac{78}{6}\\w=13\ meters[/tex]

Length = 2w+6

[tex]l=2(13)+6\\l=26+6\\l=32\ meters[/tex]

The length of basketball court is 32 meters and width is 13 meters.

Keywords: perimeter, rectangles

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Answer:

21 divided by 14 is 1.5

and

1.5 x 4 = 21

The calculated division of the numbers 21 divided by 14 is 3/2

From the question, we have the following parameters that can be used in our computation:

21 divided by 14

When represented as an equation, we have

21 divided by 14 = 21/14

Divide 21 by 14

So, we have the following result

21 divided by 14 = 3/2

Using the above as a guide, we have the following:

the result is 3/2

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Answer:

what is the problem?

Step-by-step explanation:

Answer:

What work do you need help with tag a photo or write it out.

Final answer:

An absolute value inequality that includes 3 and -6 as solutions is |x + 1.5| ≤ 4.5. Both numbers satisfy the inequality when substituted for x.

Explanation:

To write an absolute value inequality that has 3 and -6 as two of its solutions, we must find an inequality such that both of these numbers satisfy the condition when their absolute values are considered. One such inequality is |x + 1.5| ≤ 4.5.

Let's verify the solutions:

For x = 3: |3 + 1.5| = |4.5| = 4.5, which is less than or equal to 4.5.

For x = -6: |-6 + 1.5| = |-4.5| = 4.5, which is also less than or equal to 4.5.

Therefore, the inequality |x + 1.5| ≤ 4.5 is a valid inequality that includes 3 and -6 as solutions.

Answer:

d = 49

Step-by-step explanation:

Given that the expression is a perfect square of the form

(ay - b)² = a²y² - 2aby + b²

Then comparing like terms

a²y² = 25y², that is

a² = 25 ⇒ a = 5

and -2aby = - 70y, thus

2ab = 70, that is

2(5)b = 70

10b = 70 ⇒ b = 7

b² = 7² = 49

Hence

25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49

Thus d = 49

Answer:

We should invest 9600 .

Step-by-step explanation:

Interest received in Two and a half year = 1,200

So, Interest that should be received in a year = 1200×[tex]\frac{2}{5}[/tex]

                                                                            = 480

Interest rate = 5%.

Let we had invested  amount X.

Thus 5 % of X we will get in a year as interest

Which is [tex]\frac{5}{100}[/tex]×X = [tex]\frac{X}{20}[/tex].

It is also equal to 480 as calculated above,

So. X = 480×20 = 9600.

Thus,

We should invest 9600 .

Answer:

.06 rounded to nearest hundreth

Step-by-step explanation:

Answer:

17 I think

Step-by-step explanation:

Answer:

2(7y+19)

Step-by-step explanation:

14y+38=2(7y+19)

Answer:

8000

Step-by-step explanation:

you multiply 20 and 400

Answer: He could read at most 8000 pages this year.