Find the slope between the following two points: (-15, -7) and (5,-3) *

The equation of the first parabola with vertex (2, -1), opens upward with a focal width of 16 is (x-2)² = 16*(y+1). The equation of the second parabola with a focus (2, -3) and directrix x = 5 is (x-2)² = -24*(y-5).

1. For a parabola that opens upward with vertex (h, k) and focal width 4p, the equation is given by: (x-h)² = 4p*(y-k). Given the vertex (2, -1) and focal width of 16, we can deduce that 4p = 16, so p = 4. Plug these values into the formula to get the equation of the parabola: (x-2)² = 16*(y+1).

2. For a parabola with a focus (h, p) and directrix x=d, the equation is (x-h)² = 4p*(y-d). Given the focus (2, -3) and directrix x = 5, meaning h = 2, p = -3, and d = 5. This gives us the equation of the parabola: (x-2)² = -24*(y-5).

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The equation of the first parabola described is (y+1) = (x-2)^2. The equation of the second parabola, given the focus at (2,-3) and the directrix at x = 5, is (x-2) = -(1/12)(y+3)^2.

1. The standard form of a parabola that opens upward or downward is (y-k)=(1/4p)(x-h)^2, where (h,k) is the vertex and p is the distance from the vertex to the focus. In this case, h is 2, k is -1 and the focal width is 4p which is given as 16. So p = 16/4 = 4. So, the equation of the parabola is (y+1) = (x-2)^2.

2. The standard form of a parabola that opens to the right or to the left is (x-h)= (1/4p)(y-k)^2. In this case, the focus is (2,-3) and the directrix is x=5. From these, we know h=2, and since the directrix is to the right of the focus, p=h-5 is negative, so p=2-5=-3. The vertex of the parabola is thus (2,-3). So, the equation of the parabola is "(x-2) = -(1/12)(y+3)^2".

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Answer:

f(x) = y

y = 7.50x

To find the inverse, swap x and y

x = 7.50y

Now solve for y

y = x/7.50

f-1(x) = x/7.50

Answer:2nd one

Step-by-step explanation:

Answer:

1/2 and 1/3

Step-by-step explanation:

1/2 can have a denominator of 6 by multiplying by 3

[tex]\frac{1}{2} *\frac{3}{3} =\frac{3}{6}[/tex]

1/3 can have a denominator of 6 by multiplying by 2

[tex]\frac{1}{3} *\frac{2}{2} =\frac{2}{6}[/tex]

Answer:

1250 Students applied.

Step-by-step explanation:

If you set it up as a proportion and then cross multiply, it comes out to 3x=3750 so then you would simplify and get x = 1250 as your answer!

Hope this helps!

1. y = 2/3x - 5

2. 4x - 6y = 30

Divide 2. by 2

3. 2x - 3y = 15

Substitute 1. into 3.

4. 2x - 3(2/3x - 5) = 15

5. 2x - 2x + 15 = 15

6. 15 = 15

False. There are an infinite number of solutions.

Final answer:

The expression log(c) log(20) - log(5) is simplified using the quotient rule for logarithms to log(c) log(4), by subtracting the logs and simplifying the inside expression from 20/5 to 4.

Explanation:

The student's question involves simplifying a logarithmic expression. The initial expression is log(c) log(20) - log(5). To simplify this expression, we can use logarithmic properties, specifically the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b).

Applying this property to the given expression, we combine the two logs that are subtracted:

log(20) - log(5) = log(20/5). Simplifying the division inside the log gives us:

log(4). Therefore, the simplified expression is log(c) log(4).

Answer:

14 hits in 28 games

Step-by-step explanation:

every 2 games there is 1 hit

Answer:

The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072

Step-by-step explanation:

In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:

p(0) = (1 - 0.312)^(12) = 0.688^(12) = 0.01124

We now need to calculate the probability that one child learns to swim before 6 years of age.

p(1) = 12*0.312*(1 - 0.312)^(11) = 3.744*(0.688)^(11)

p(1) = 3.744*0.01634

p(1) = 0.0612

The probability of 1 or less children from that group to learn how to swim before 6 years of age is:

p = p(0) + p(1) = 0.01124 + 0.0612 = 0.07244

The probability that 1 or fewer of the 12 children will learn to swim before age 6 is approximately 0.072 when rounded to three decimal places.

1. Given:

  - Probability that a child will learn to swim before age 6, ( p = 0.312 )

  - Number of children, ( n = 12 )

2. Calculating ( P(X = 0) ):

[tex]\[P(X = 0) = \binom{12}{0} (0.312)^0 (1 - 0.312)^{12}\]\[P(X = 0) = 1 \times 1 \times (0.688)^{12}\]\[P(X = 0) \approx (0.688)^{12}\][/tex]

Using a calculator for [tex]\((0.688)^{12}\)[/tex]:

[tex]\[(0.688)^{12} \approx 0.0088\][/tex]

3. Calculating ( P(X = 1) ):

[tex]\[P(X = 1) = \binom{12}{1} (0.312)^1 (1 - 0.312)^{11}\]\[P(X = 1) = 12 \times 0.312 \times (0.688)^{11}\][/tex]

Using the binomial cumulative distribution function (CDF):

[tex]\[P(X \leq 1) = \sum_{k=0}^{1} \binom{12}{k} (0.312)^k (0.688)^{12-k}\][/tex]

Using the binomial probability tables or calculator, we get:

[tex]\[P(X = 0) \approx 0.0088\]\[P(X = 1) \approx 0.0623\][/tex]

Summing these:

[tex]\[P(X \leq 1) \approx 0.0088 + 0.0623 = 0.0711\][/tex]

Thus, the probability that 1 or fewer of the 12 children will learn to swim before age 6 is approximately 0.0711, which rounds to 0.072.

Answer:

B. Prices increase.

Step-by-step explanation:

When demand for a product is greater than the product's supply, that increases the value of said product, and thus they bring the price up.

When demand exceeds supply, it's referred to as a shortage or excess demand, and generally leads to an increase in prices. Sellers are able to charge more because more consumers are vying for a limited number of goods.

When demand exceeds supply in economic terms, it leads to a situation called excess demand or shortage. In this scenario, more people want a product than the amount of the product available. As a result of this excess demand, prices generally increase. This increase happens due to the basic law of demand and supply. Since more consumers are chasing a limited number of goods, sellers can charge higher prices. This increase in prices can help reduce the demand and bring the market back into equilibrium.

For instance, consider a situation where new smartphones are released, and the demand outstrips the supply. The prices will likely increase because people are willing to pay a higher price to secure one of the limited handsets.

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Answer:Which expression represents the distance between the points (a, 0) and (0, 5) on a coordinate grid? StartRoot a squared + 5 EndRoot StartRoot a squared + 25 EndRoot StartRoot (a minus 25) squared EndRoot StartRoot (a minus 5) squared EndRoot

Step-by-step explanation:

0, 5) on a coordinate grid? StartRoot a squared + 5 EndRoot StartRoot a squared + 25 EndRoot StartRoot (a minus 25) squared EndRoot StartRoot (a minus 5) squared EndRoot

The distance between the two points is given by:

[tex]d = \sqrt{a^2 + 25}[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Then for the given points, that are (a, 0) and (0, 5) the distance is given by:

[tex]d = \sqrt{(0 - a)^2 + (5 - 0)^2} \\\\d = \sqrt{a^2 + 25}[/tex]

Then the correct option is the second one, the square root of the sum between a squared and 25.

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Answer:

The dept of the lake will be 279 ft in 6 weeks

Step-by-step explanation:

We are given that the depth of a lake can be modeled by the function

[tex]y = 323(0.976)^{x}[/tex]

Where x is the number of weeks and y is the depth of lake in feet

The depth of the lake today is (x=0)

[tex]y = 323(0.976)^{0}[/tex]

[tex]y=323[/tex] [tex]ft[/tex]

The depth of the lake after 6 weeks will be (x=6)

[tex]y = 323(0.976)^{6}[/tex]

[tex]y = 323(0.864)[/tex]

[tex]y=279[/tex] [tex]ft[/tex]

Therefore, the dept of the lake will be 279 ft in 6 weeks.

Answer:

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Step-by-step explanation:

Graph (-5,-3) and use the slope, -2, to find another point. -2 can also be written as [tex]-\frac{2}{1}[/tex]

[tex]\frac{rise}{run} =\frac{-2}{1}[/tex] and  [tex]\frac{rise}{run} =\frac{2}{-1}[/tex] **

Use both. This works because either way, they will lie on the same line with the same slope. So, starting at (-5,-3), go down two points (-)* and to the left 1 (+)*, then, starting at (-5,-3) again, go up two points (+)* then to the right 1 point (-)*.

* If the number is negative, you either go down or to the right. If the number is positive, you go up and to the left.

**Rise over run refers to the change in the y-axis and the change in the x-axis: [tex]\frac{rise}{run} =\frac{y-axis}{x-axis}[/tex]. Only one number is negative because, if both were negative, that would make a positive number, but the slope is -2, not 2.

Another way you could do this is by finding points first. All you need to do is turn the slope into a "point". Remember, 2 is the y and 1 is the x:

[tex]-2=-\frac{2}{1} = (1,-2)[/tex] and [tex](-1,2)[/tex]

Then, using (-5,-3) and your new points, add them separately:

[tex](-5,-3)+(1,-2)\\(-5+1,-3+(-2))\\(-5+1,-3-2)\\(-4,-5)[/tex]

(-4,-5) is one point

[tex](-5,-3)+(-1,2)\\(-5+(-1),-3+2)\\(-5-1,-3+2)\\(-6,-1)[/tex]

(-6,-1) is another point. Connect the three points. You can check your work on the graph:

Answer:

B.

Step-by-step explanation:

Answer:

B is the correct answer

Step-by-step explanation:

Answer:

615.75216....

Step-by-step explanation:

The formula is A = π * (ø/ 2)^2

A = Circle area

π = Pi = 3.14

ø = Circle diameter

A= 3.14  (28/2)^2

Answer:

Area = 615.44 inches

Step-by-step explanation:

Diameter = 2 * radius

28 = 2 * radius

Divide both sides of the equation by 2

14 = radius

Find area

A = π r²

A = 3.14 (14)²

A = 3.14 (196)

A = 615.44

Hope this helps :)

The value of c from the given equation is 34.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is x²+19x+c=0

Vieta's Theorem is If f(x) = ax² + bx + c is a quadratic equation with roots α and β then,

Sum of roots = α + β = -b/a

(x + a) (x + b) = x² + (a + b) x + ab

a + b = 19

a - b = 15

a = 17

b = 2

c = ab = 34

Therefore, the value of c from the given equation is 34.

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Using Vieta's Theorem, the difference of the roots was used to set up two equations. Solving them simultaneously gave us the individual roots, which were then multiplied to find the required product, c, which is 34.

To solve for c in the quadratic equation x^2 + 19x + c = 0 using Vieta's Theorem, we need to find the two roots of the equation and their relationship to the coefficients.

According to Vieta's formulas, for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots -b/a and the product of the roots c/a. Since the coefficient a is 1 in our equation (x^2 + 19x + c = 0), the sum of the roots is -19, and the product is c.

We are told the difference of the two roots is 15. Let's denote the larger root as r1 and the smaller one as r2. Thus, r1 - r2 = 15. But we also know that r1 + r2 = -19 (the negative coefficient of x).

We can now set up two equations:

By solving these two equations simultaneously, we add them together to eliminate r2:

2r1 = -4

r1 = -2

Substitute r1 back into one of the original equations to find r2:

r1 + r2 = -19

-2 + r2 = -19

r2 = -17

Now, we use the product of the roots to find c:

c = r1 * r2

c = -2 * -17

c = 34

Therefore, the value of c in the quadratic equation is 34.

The graph of both functions are positive, thus the graph is increasing in the upward direction.

The graph of a quadratic equation.

The graph of a quadratic equation is a parabolic curve or a U-shaped curve. From the given function, the parent function is f(x) = x² and the g(x)  is the transformed function of the original function.

The function of g(x) = 5x² - 2 is vertically stretch by 5 units and  it is shifted vertically downward by 2 units.

Thus, we can say that the graph of g(x) = 5x² - 2 is related to  f(x) = x² because of the vertical stretch and the vertical shift. Also, since both functions are positive, the graph is increasing in the upward direction.

Answer:

a. 4/21

b. 4/7

Step-by-step explanation:

Please kindly check the attached files for explanation.

Answer:

A) 3/12

B)7/12

Step-by-step explanation:

I used a tree diagram to go through this with my daughter, bear in mind the second question asks for the probability of exactly one red counter to be taken from the bag.

Answer:

Yes, there s a vertical shift to the right by 1

Step-by-step explanation:

If you distribute the 2 among the (x+2) you get:

              2x+4-5

Combine like terms:

              2x+1

There fore the line shifts right by one.

Answer:

Yes, the equation shifts down by five.

Step-by-step explanation:

In equations, vertical shifts happen when the ENTIRE equation, or y, is added or subtracted a number.

Horizontal shifts happen when JUST the x value is added or subtracted a number, but this is a little different.

The formula for the equation you gave us is

m(x - h) + k

Since "h" is already negative, we have to flip the sign of the +2, so the horizontal shift would be LEFT two units.

As far as the vertical shift goes, we just have to look at the "+k."

Since k = -5, the equation shifts down five units.

Answer:

1 1/2

Step-by-step explanation:

60/40 = (60 ÷ 20)/(40 ÷ 20) = 3/2; 3 > 2 => improper fraction Rewrite: 3 ÷ 2 = 1 and remainder = 1 => 3/2 = (1 × 2 + 1)/2 = 1 + 1/2 = = 1 1/2, mixed number (mixed fraction)

Hope this helped!

Answer:

1 1/2

Step-by-step explanation:

40 can go into 60 1 time

simplify the rest

Answer:

all work is pictured and shown

Answer:

9 months.

Step-by-step explanation:

225 / 25 = 9

Feel free to let me know if you need more help! :)

Answer:

9

Step-by-step explanation:

225/25 is 9

Answer:

182.12

Step-by-step explanation:

2πr , then substitute the numbers

Answer:

182.12ft

Step-by-step explanation:

Just remember to divide the diameter by two to get the radius.

58/2  = 29

C=2 π r    

C = 2 * 3.14 * 29= 182.12ft

Answer:

The student is correct.

Step-by-step explanation:The circle's circumference is the distance around the circle.  To find out the circle's circumference, you will NEED the radius.  Without the radius OR diameter, there will be no way of telling what the circumference is with just the area.

Answer:

$12

Step-by-step explanation:

30% is 0.3

So 0.3 × 40 = 12

Answer:

The two expressions of an equation are separated by an equal sign. When the statement is given in words, the equal sign is indicated by the word “is” or the words “the same as.”

Step-by-step explanation:

Two expressions of the equation by properly interpreting the words into appropriate signs and digits.

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement. To achieve our goal, we use two principles of equality, the addition principle and the multiplication principle.

A binomial expression is an algebraic expression which is having two terms, which are unlike. Examples of binomial include 5xy + 8, xyz + x3, etc.

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

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Answer:

3 min 12 seconds

Step-by-step explanation:

Using the conversion

1 minute = 60 seconds, then

2 min 6 seconds = (2 × 60) + 6 = 120 + 6 = 126 seconds

Divide 126 by 525 then multiply by 800, that is

time = [tex]\frac{126}{525}[/tex] × 800 = 192 seconds = 3 min 12 seconds

Final answer:

After calculating Tomos's average speed from the 525 m ski race, we use that speed to determine that it should take him approximately 3 minutes and 12 seconds to complete an 800 m race.

Explanation:

To determine how long Tomos should take to complete an 800 m race given his average speed, we start by calculating his speed during the 525 m race. Tomos completed the 525 m ski race in 2 minutes and 6 seconds, which is a total of 126 seconds.

Firstly, we calculate Tomos's average speed:

Average speed (v) = Total distance (d) / Total time (t)

v = 525 m / 126 s

v = 4.1667 m/s (approximately)

Now, to find out how long it will take Tomos to ski 800 m at the same speed, we use the formula:

Time (t) = Distance (d) / Speed (v)

t = 800 m / 4.1667 m/s

t = 192 seconds (approximately)

Finally, we convert the time from seconds to minutes and seconds:

There are 60 seconds in a minute, so:

Time = 192 s = 3 minutes and 12 seconds

Therefore, it should take Tomos approximately 3 minutes and 12 seconds to complete an 800 m race at his average speed.

To draw an integer chips model for the subtraction problem, first draw nine positive chips to represent the grapes Mary took, then draw four negative chips for the grapes she gave back. Subtract the negative from the positive chips to get the final answer.

In this integer subtraction problem, you would first draw 9 positive chips, symbolizing the 9 grapes Mary initially received from Rohin. Positive chips can be represented by circles or squares. You could use different colors, such as blue for positive (or grapes Mary has).

Next, to represent the 4 grapes that Mary returned to Rohin, you would draw 4 negative chips. Negative chips (or the grapes Mary gave back) could be represented by a different color, such as red.

Subtracting 4 from 9, we then remove 4 positive chips from the model, leaving five positive chips, representing the 5 grapes Mary has left after she returned 4 to Rohin.

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To find the missing constant term, we want to think about what two numbers would add up to 2. Of the numbers we've thought of, we want to find the numbers that are the same. In this case, that would be 1 and 1. If we multiply, or square, 1 and 1 together, we get 1. So, the missing constant term in the perfect square given here would be 1.

Hope this helps!! :)

Answer:

solve for y

Step-by-step explanation:

[tex]5x-2y=-10[/tex]

subtract 5x from both sides

[tex]5x-5x-2y=-10-5x[/tex]

[tex]-2y=-10-5x[/tex]

Divide each term in the equation by -2

[tex]\frac{-2y}{-2}=\frac{-10}{-2} -\frac{-5x}{-2}\\\\y=\frac{-10}{-2} +\frac{-5x}{-2} \\\\y=5+\frac{5x}{2}[/tex]

(negative+negative=positive)

re-write in slope-intercept form [tex]y=mx+b[/tex] , where m is the slope and b is the y-intercept

[tex]y=\frac{5}{2}x+5[/tex]

Now you know that the slope is [tex]\frac{5}{2}x[/tex] and the y-intercept is [tex]5[/tex].

Now, to graph, you just need to choose random values for x (like 0,1,2,3 or any other number) and insert into the equation [tex]y=\frac{5}{2}x+5[/tex] to find the points, or you can just use the slope. To find the x-intercept, do the following:

make y equal to 0

[tex]0=\frac{5}{2}x+5[/tex]

Solve for x:

simplify [tex]\frac{5}{2}x[/tex]

[tex]0=\frac{5x}{2} +5[/tex]

Subtract 5 from both sides

[tex]0-5=\frac{5x}{2}+5-5\\ \\-5=\frac{5x}{2}[/tex]

Multiply both sides by 2

[tex]2(-5)=2(\frac{5x}{2})\\\\-10=5x[/tex]

Divide both sides by 5

[tex]\frac{-10}{5}= \frac{5x}{5}\\\\-2=x[/tex]

Flip

[tex]x=-2[/tex]

The x-intercept is -2.

Answer:

14:20 :)

Step-by-step explanation: