use similar triangles to solve. a person who is 5 feet tall is standing 140 ft from the base of a tree and the tree cast a 154 foot shadow. the person's Shadow is 14 ft in length what is the height of the tree

If [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

In the linear equation [tex]\(y = 2x + 1\)[/tex], the coefficient of [tex]\(x\)[/tex] is 2. This means that the slope of the line is 2, and for every one unit increase in [tex]\(x\), \(y\)[/tex] will increase by 2 units.

Given that [tex]\(x\)[/tex] increases by 4 points, the corresponding increase in [tex]\(y\)[/tex] can be found by multiplying the change in [tex]\(x\)[/tex] by the slope:

[tex]\[\Delta y = \text{Slope} \times \Delta x\][/tex]

[tex]\[ \Delta y = 2 \times 4 = 8\][/tex]

Therefore, if [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

Example:

Let's use the given linear equation [tex]\(y = 2x + 1\)[/tex] and demonstrate how an increase in [tex]\(x\)[/tex] by 4 points results in an increase in [tex]\(y\)[/tex] by 8 units.

Given Linear Equation:

[tex]\[y = 2x + 1\][/tex]

Let's consider an initial point on the line where [tex]\(x = 3\)[/tex]. Find the corresponding [tex]\(y\)[/tex]:

[tex]\[y = 2(3) + 1 = 7\][/tex]

So, when [tex]\(x = 3\), \(y = 7\)[/tex].

Now, if [tex]\(x\)[/tex] increases by 4 points, new [tex]\(x\)[/tex] value will be [tex]\(3 + 4 = 7\)[/tex].

Using the same linear equation to find the new [tex]\(y\)[/tex]:

[tex]\[y_{\text{new}} = 2(7) + 1 = 15\][/tex]

Now, calculate the increase in [tex]\(y\)[/tex]:

[tex]\[\Delta y = y_{\text{new}} - y_{\text{initial}} = 15 - 7 = 8\][/tex]

So, in this example, when [tex]\(x\)[/tex] increases by 4 points (from 3 to 7), [tex]\(y\)[/tex] increases by 8 units (from 7 to 15), confirming that the increase in [tex]\(y\)[/tex] is proportional to the increase in [tex]\(x\)[/tex] with a slope of 2.

<R angle of RST has the smallest measure.

The correct option is C.

We have,

RS=11 ,RT=9 and ST=6

Now, from the given lengths it can be seen that the length of ST is shortest and length of RS is longest.

By the definition which states that,

The angle opposite to longest side is largest and the angle oppsite to shortest side is smallest.

From given, <R is opposite to shortest side ST.

Thus, the smallest angle is R.

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Sergio runs at a speed of 4.5 miles per hour. The ratio of his running distance to time is 9/2.

To determine Sergio's speed in miles per hour (mph), we use the equation: speed = distance/time. Sergio runs 2 1/4 miles in 30 minutes. First, we need to convert the fractional distance to a decimal and the time to hours. 2 1/4 miles is equal to 2.25 miles and 30 minutes is equal to 0.5 hours.

Substitute these values into the equation:

speed = 2.25 miles/0.5 hour = 4.5 mph.

Therefore, Sergio's running speed is 4.5 miles per hour. The ratio of distance to time in fractional form would be 9/2.

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Answer:

Bracken has incurred a loss of $37,500

Step-by-step explanation:

People who have registered with Bracken insurance company pays premium of $100. 1,000 people in total have registered with Bracken. In 5 years Bracken would have earned an income of $500,000 [tex]\left ( $100\times1,000\times5)\right[/tex].

25 among the 1,000 registered have undergone surgery. Average surgery expense is $25,000. $3,500 is deductible.  So Bracken's total expense per client is $21,500 (25,000 - 3,500). For 25 patients, it will be $537,500 [tex]($21,500\times25)[/tex].

Since expenses of $537,500 is more than income of $500,000, Bracken incurs a loss of $37,500 (500,000 - 537,500) over 5 years.

Therefore, Bracken's loss over 5 years is $37,500

Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

SP-CP divided by CP multiplying with 100 we get profit percentage.

P= [(SP-CP)/CP ] × 100

Given the following details about Mr. Rashawn.

Mr. Rashawn recently spent = $100 to open a store selling tee-shirts

He purchases plain tee-shirts for = $11 each

Then sells them for = $26 each

Profit on each shirt = $26 - $11 = $15

Profit = $400 -$100= $ 300

Number of t- shirts= $300/15 = 20 T -shirts.

Thus, Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

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An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now,

The equation of the parabola turned to the left is to the negative side of the coordinate system is:

⇒ y² = - 2 p x  

where, p is the parameter of the parabola

The relationship between the parameter and the focus is.

⇒ p = 2 f  

=> p = 2 × 2

⇒ p =  4 cm  

Then, the equation of the parabola is:

y² = - 2 p x

    = - 2 × 4 x

     = - 8 x

Therefore, An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

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Answer:

C. -20 & -20

Step-by-step explanation:

If you substitute x for 3 in the expressions, they will both evaluate to -20.

Thus, the answer is -20

Final answer:

The given dimensions do not match the American flag's customary ratio of 10 to 19. To find the correct dimensions, the numbers must divide to equal approximately 0.5263. None of the provided options are correct.

Explanation:

The American flag is customarily made with its width and length in the ratio of 10 to 19. To ensure the dimensions are correct, we must find a pair of numbers that, when divided, are in the same proportion as 10/19 (approximately 0.5263). Looking at the listed dimensions:

51 H (Height is not a width or length measurement, so we cannot confirm the ratio)

53 x 38 (53/38 = 1.3947 which is not equal to 10/19)

55 x 0.025 (55/0.025 = 2200 which is not equal to 10/19)

57 x (2.93, 3.59) (This does not provide a pair of length and width measurements)

59 (This is not a dimension)

Since none of the provided options has numbers that mirror the 10 to 19 ratio of the flag, none of these dimensions would be correct for an American flag. If we want to find dimensions that are proportional, we have to look for any two numbers that, when divided, equal approximately 0.5263. Hence, an example of a correct dimension following the flag's ratio would be 10 inches by 19 inches or any multiple thereof.

Final answer:

The inequality for Sam's expenditures on grapes and carrots, with grapes costing $4 and carrots costing $2 per pound, is 4 + 2c <= d.

Explanation:

The inequality that represents Sam's spending on grapes and carrots, given that he has d dollars to spend, is 4 + 2c ≤ d. This inequality is derived from the cost of one bag of grapes, which is $4, and the cost of carrots, which is $2 per pound. The variable c represents the number of pounds of carrots Sam wants to buy. The total cost of grapes and carrots must be less than or equal to the amount of money Sam has, which is d dollars.

Answer: 50t+75g=1,500