Problem 16: (first taught in lesson 12) If line p bisects CT at point D and if CD = 7x - 10 and DT = 5x + 6, then find CT.

Answer:

the answer is :.......

x+x+x

Answer:

x+x+x

Step-by-step explanation:

Answer:

$22.50

Step-by-step explanation:

So if each topping cost 2.50 then just multiply by 9

Step-by-step explanation:

To calculate the acceleration of the frisbee, we can use the formula:

a = (v2 - v1) / t

where v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

Given:

- The frisbee travels over Point A and Point B.

- It flies over Point A at a velocity of 10 m/s.

- It flies over Point B at a velocity of 6 m/s.

- The time taken to go from Point A to Point B is 9 seconds.

We can first calculate the acceleration using the velocities of Point A and Point B:

a = (6 m/s - 10 m/s) / 9 s

Simplifying, we get:

a = -0.44 m/s^2

Note that the negative sign indicates that the frisbee is decelerating, or slowing down.

Therefore, the acceleration of the frisbee is -0.44 m/s^2.

The distance between the points B and C is 12m

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7

therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)

d=√((0)² + 12²)

d=√144

d= 12m

therefore the distance between the points B and C is 12m.

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The value of 2cos² (-22.5°)-1 is 1/√2.

In trigonometry, double angle identities or double angle trig identities are a set of trigonometric identities for angles of form 2θ. There are three double angle identities for each of sine, cosine and tangent ratios.

Given that, 2cos² (-22.5°)-1

2cos²x -1 = cos2x

2cos² (-22.5°)-1 = cos2(-22.5°)

cos(-45°)

∵ cos(-x) = cosx

∴ cos(-45°) = cos(45°)

cos(45°) = 1/√2

Hence, The value of 2cos² (-22.5°)-1 is 1/√2.

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The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = \(\frac{1}{2}\) and passing through    (-7, -7)

   \(y +7 = \frac{1}{2}(x +7)\\\)

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by \(y - y_1 = m(x - x_1)\) , \((x_1, y_1)\) is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  \(y = 3 \times 0 -9\\y = -9\)

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   \(y = -9 \times 0 -68\\y = -68\)

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    \(y = 5 \times 0 + 2\\y = 2\)

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = \(\frac{1}{2}\)

      The line passes through (5, -3)

     Point slope equation

       \(y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\\)

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Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

Answer:

6.93 so in a mixed number is 693/100

Answer:

Step-by-step explanation:

Remark

The value of the y can be found by using the Geometric Mean.  To use the said mean, you must compare parts of one triangle to parts of the second triangle. In this case, the small triangle containing boy 4 and y, must be compared to the triangle use y and 12

Formula

This translates to

4 / y = y/12

Explanation. The two triangles y and 4 and y and 12 are similar. The short side on the small right triangle on the left is 4. The second longest side on the same triangle is y.

In the triangle containing y and 12 The short side is y and the second side length is 12. You have to read this a couple of times to get the meaning of the two ratios.

Solution

4/y = y / 12                    Cross multiply

y^2 = 4 * 12

y^2 = 48                       Take the square root of both sides.

√y^2 = √48

y = √2 * 2 * 2 * 2 * 3

y = 2 * 2 * √3

Answer

y = 4√3  

Answer:

y = 4√3 y = 4√3

Step-by-step explanation:

i hope it's help

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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Answer:

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)

Step-by-step explanation:

uhhhh what do you mean?

Answer:

a)There are 14 teachers in Ryan's sample, and 362 teachers in the population.

Step-by-step explanation:

Population:-

The totality of observations with which we are concerned, whether this number be finite or infinite  is called population.

Given data population is  376 teachers at a university were female'

Sample:-

A sample is a subset of a Population

sample of given data = 14teachers

The percentage of 376 teachers at a university were female, Ryan randomly selected 14 teachers.

\(p = \frac{14}{376} = 0.0372\) = 3.72%

Answer:

There are 14 teachers in Ryan's sample, and 362 teachers in the population.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

d

Answer:

A. Negative correlation

B. Data isn't given

Step-by-step explanation:

A. A positive correlation occurs when variables that are related(not zero correlation)increase together, in other words variable a(independent variable) increases and makes variable b(dependent variable) increase too. There will be a negative correlation if the opposite happens, that is when variables that are related go in opposite directions, one increases while the other decreases. We observe from what we are told that a negative correlation occurs here since death rate from fires has likely(assumed) decreased as smoke detectors have increased.

Answer:

15, 33

(if I'm not wrong, it should work this way)

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Answer:

(13.0 + 0.8)

Step-by-step explanation:

I hope this helps!

The product of the numbers 4.6 and 3 in the expanded form is (13.0 + 0.8)

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given numbers are 4.6 and 3. The product of the two numbers will be done as below:-

4.6 × 3 = 13.8

Write the product in expanded form.

13.8 = (13.0 + 0.8)

Therefore, the product of the numbers 4.6 and 3 in the expanded form is (13.0 + 0.8).

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Answer:

x>-17.2

Step-by-step explanation:

Simplify both sides of the inequality

-0.5x-3.1< 5.5

Add 3.1 to both sides

-0.5x< 8.6

Divided both sides by -0.5

x>-17.2

Hope this helped! :)

You have the correct answer. It is choice B) -1/4

=======================================================

Explanation:

This is because we're adding -1/4 to each term to get the next one. In other words, we're subtracting 1/4 from each term to get the next one.

and so on.

----------

To find the common difference, all we have to do is subtract any term from its previous one.

For example:

d = (term2) - (term1)

d = (1/4) - (1/2)

d = (1/4) - (2/4)

d = (1-2)/4

d = -1/4

The order of subtraction matters, so we cannot say d = term1-term2.

Answer:

it will be choice 3

Step-by-step explanation:

as if you bend each shape of each of them the only choice that will give you a pyramide with a omitted side

Answer:

  A, B, C

Step-by-step explanation:

The variables in a polynomial term are non-negative integers.

  A: x is to 1/2 power (square root) . . . not a polynomial

  B: x is to -2 power . . . not a polynomial

  C: x is to -2 power . . . not a polynomial

  D: x is to powers of 2 and 1 . . . is a polynomial

The choices A, B, and C are not polynomials

Answer:

C and D

multiply the 6 and -3 to the numbers inside the parenthesis

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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