Roger can run one mile in 10 minutes. jeff can run one mile in 8 minutes. if jeff gives roger a 1 minute head​ start, how long will it take before jeff catches up to​ roger? how far will each have​ run?

Answer:

The Answer is 4

Step-by-step explanation:

2x² - 16x + 32 = 0

we would multiply 2x² and 32

= 64x²

then factorise 64x² such that the sum of the two nos = -16 AND the product of the nos = 64

the only value that satisfies this condition is -8 (-8 + -8 = -16, and -8 * -8 = 64)

0 = 2x² - 8x -8x + 32

0 = (2x² - 8x) (-8x +32)

2x(x - 4) -8(x - 4)

0 = (2x - 8) (x - 4)

0 = 2x - 8 or 0 = x - 4

8 = 2x or 4 = x

x = 8/2 or 4

x = 4 or 4

x = 4

hope it was clear

Answer:

fourth degree trinomial

Step-by-step explanation:

The correct symbol that Ari should write between the two sets of numbers is C. =.

When Ari writes "2 + 4" on the left-hand side of his paper and then writes "6" to the right of the expression, he is indicating that the sum of 2 and 4 is 6. The symbol "=" is used to denote equality, meaning that the value on the left side of the equation is the same as the value on the right side. In this case, the sum of 2 and 4 indeed equals 6, so the complete equation should be written as:

[tex]\[ 2 + 4 = 6 \][/tex]

This shows that the operation of adding 2 and 4 results in the number 6, which is a true statement. Therefore, the correct answer to the question is option C, the equals sign "=".

To determine when Dakota and Madison will run a half marathon on the same week, we calculate the least common multiple of their running intervals, which is 60 weeks.

The question is to find out how many weeks will pass until Dakota and Madison will run a half marathon on the same week.

We need to find the least common multiple (LCM) of their running intervals, which are 6 weeks for Dakota and 15 weeks for Madison.

To find the LCM, you can list the multiples of each number until you find the smallest number that appears in both lists.

Here, we see that the smallest common multiple is 60 weeks.

Therefore, Dakota and Madison will run a half marathon together in 60 weeks.

To find the rate of change for each time interval, calculate the difference in volume for each interval and divide it by the difference in time. Compare the rates of change to determine the time interval with the lowest rate of change.

To find the rate of change for each time interval, we need to calculate the difference in volume for each interval and divide it by the difference in time. Let's assume the time intervals are 12-18 hours, 18-24 hours, and 12-24 hours. The rate of change for each interval can be calculated as follows:

Rate of change for 12-18 hours = (Volume at 18 hours - Volume at 12 hours) / (18 hours - 12 hours)

Rate of change for 18-24 hours = (Volume at 24 hours - Volume at 18 hours) / (24 hours - 18 hours)

Rate of change for 12-24 hours = (Volume at 24 hours - Volume at 12 hours) / (24 hours - 12 hours)

The time interval during which the volume decreased at the greatest rate will be the interval with the lowest rate of change. Compare the rates of change calculated for each interval to find the time interval with the lowest rate of change.

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To find the smallest possible ages for Jose and Robert, set up a system of equations based on the given information. Robert's age is X, and Jose's age is 3X. The sum of their ages is more than 40, so the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

To find the smallest possible ages for Jose and Robert, we need to set up a system of equations based on the given information.

Let's assume Robert's age is x. Since Jose is three times as old as Robert, his age would be 3x.

The sum of their ages is more than 40, so we can write the equation: x + 3x > 40.

Simplifying the equation: 4x > 40.

Dividing both sides of the equation by 4, we get x > 10.

Therefore, the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

The price of the service that was charged before the tip was:

                            $ 35

Let the price of the service be $ x.

Now it is given that:

Talia gave her hairdresser a 20 percent tip, which amounted to $7.

This means that the 20% of total service charge=7

i.e.  20% ×x =7

i.e. 0.20×x=7

i.e. x=7/0.20

i.e. x=35

Hence, the price of the service that was paid before the tip is: $ 35

multiply the current price by the increase

1.39 * 2.4 = $3.34 ( price next year)

The factor of quadratic function 2x²-2x-40 is 2 (x-5) (x+4).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The quadratic function 2x²-2x-40.

To find the factors;

Take common term out,

2(x²-x-20)

= 2 (x²-5x + 4x -20)

= 2 {x (x-5) + 4(x -5)}

= 2 (x-5) (x+4)

Therefore, the factors are 2 (x-5) (x+4).

To learn more about the quadratic function;

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If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.

Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|

Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.

We get the length of AC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]

Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.

The angle of elevation is calculated as:

[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]

The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).

Thus, Margaret statement is false.

Therefore, we get the answers as:

Learn more about Pythagoras theorem here:

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Answer:

[tex]2x-3y+21=0[/tex]

Step-by-step explanation:

We are given that an equation

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

We have to find an equation of line which is perpendicular to given line and passing through the point (3,9).

We know that when two lines of slope [tex]m_1\;and\;m_2[/tex] are perpendicular then

[tex]m_1=-\frac{1}{m_2}[/tex]

By comparing with

[tex]y=mx+b[/tex]

Where m=Slope of line

Slope of given line=[tex]=m_1=\frac{-3}{2}[/tex]

Slope of the line=[tex]-\frac{1}{m_1}=-\frac{1}{\frac{-3}{2}}=\frac{2}{3}[/tex]

Slope of the line=[tex]\frac{2}{3}[/tex]

The equation of line passing through the point (3,9) is given by

[tex]y-y_0=m(x-x_0)[/tex]

Substitute the values

The equation of line which passing through the point (3,9) is given by

[tex]y-9=\frac{2}{3}(x-3)[/tex]

[tex]3y-27=2(x-3)[/tex]

[tex]3y-27=2x-6[/tex]

[tex]3y=2x-6+27[/tex]

[tex]2x-3y+21=0[/tex]

To simplify 2^4\*2^7, you add the exponents because the bases are the same, resulting in 2^11 which equals 2048.

When simplifying the expression 2^4\*2^7, we use the property of exponents that states when multiplying two exponential terms with the same base, you add the exponents. So, the simplified form of the expression would be 2^(4+7) which is 2^11. Since we are adding the exponents, this process is known as the sum of exponents and is a fundamental concept in the squaring of exponentials.

To calculate 2^11, you would multiply 2 by itself 11 times, but for the sake of simplicity, the answer is 2048.

The length of BC is 15 cm and the length of AB is 12.5 cm.

The given parameters;

An equilateral triangle has three equal sides and the length of each side is calculated as;

[tex]|BC| = |BD| = |CD| = \frac{45}{3} = 15 \ cm[/tex]

Thus, the length of BC is 15 cm.

An isosceles triangle has two equal sides and a third side of different length. This third side is usually the base of the triangle.

[tex]|AB| = |AC| =\frac{Perimeter \ - \ |BC|}{2} = \frac{40 - 15}{2} = 12.5 \ cm[/tex]

Thus, the length of AB is 12.5 cm.

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Answer: its horizontal