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   The equation that defines the parabola with vertex at the point (3, 2) and focus at (4, 2) is:

(Y - 2)² = 16(X - 3)

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

  This will depend on its aperture

  In this case we have the vertex of the parabola at the point (3, 2) and the focus at the point (4, 2) this is displaced on the x-axis to the right, so the parabola is of the form X = Y²

(y - 2)² = 4p(x - 3)

Focus

f = (0 + p, 0)

(y - 2)² = 4*4(x - 3)

(Y - 2)² = 16(X - 3)

Y² - 4Y + 4 = 16X - 48
X = Y²/16 - Y/4 + 13/4

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Based on the information given, the area of the trapezoid will be 89.7cm².

It should be noted that the formula for calculating the area of a trapezoid will be:

= (a + b)/2 × h

where a = 8

b = 13

h = 7.8

Area = (13 + 8)/2 × 7.8

= 21/2 × 7.8

= 11.5 × 7.8

= 89.7cm²

Therefore, based on the information given, the area of the trapezoid will be 89.7cm².

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Answer: y = -4x + 13

Step-by-step explanation:

Given points (2, 5) and (3, 1)

First Step find the slope given the two points:

Use the slope formula [tex]m=\frac{y2 - y1}{x2 - x1}[/tex]

[tex]m = \frac{1-5}{3-2} = -4[/tex] (Result)

Slope is equal to -4

Second step plug into y - y1 = m(x - x1) formula (Point Slope Formula)

For this I am using the first coordinate pair given (2, 5)

y - 5 = -4(x-2)

y - 5 = -4x + 8

y = -4x + 13

Answer:

x=3.5

Y=None

Step-by-step explanation:

Answer:

0=-6 (No solution)

Step-by-step explanation:

2(7x-7)=14x-20 - Distribute the 2 to 7x-7

14x -14 = 14x -20 - Subtract +14 from both sides
    + 14          +14

14x = 14x -6

-14x    -14x

0=-6

Answer: 4x^4

Step-by-step explanation:

from the law of indices,

( a^x)^y = a^xy

Now from the question

( 8x^6)^2/3

8^2/3X^6x2/3

From another law of indices,

a^x/y = ( y cube root of a)^x

8^2/3 = 2^2 = 4 ——— 1

Now X^6*2/3

= X^4 ——————-2
Now combine 1 & 2 together gives the answer

= 4x^4

The card with the number 7 was removed.

So,

Therefore, the card with the number 7 was removed.

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Answer: width = 12 inches

length =  28 inches

Step-by-step explanation:

l = 4 + 2w

Perimeter = 2 ( l + w  )

80 = 2 ( 4 + 2w + w )

80 = 2 ( 4 + 3w )

80 = 8 + 6w

80 - 8 = 6w

72 = 6w

w = 72 / 6

width = 12 inches

length = 4 + 2 (12)

= 4 + 24

= 28 inches

checking

Perimeter = 2 ( 28 + 12 )

= 2 (40)

= 80 inches

correct

The actual length, if the length of the model is 10 ft and the scale factor is greater than one is Option(b) 9.5 ft.

The basic formula to find the scale factor of a figure is as:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given:

length of the model = 10 ft

Now we determine which actual length has a scale factor greater than one.

(a) Scale factor = (10/10)

Here, we can see that the scale factor is equal to 1.

(b) Scale factor = (10/9.5) = 1.05

Here, we can see that the scale factor is greater than 1.

(c) Scale factor = (10/12) = 0.83 ( 1 yard = 3 foot)

Here, we can see that the scale factor is less than 1.

Therefore, the actual length is 9.5 ft.

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Answer:

Negative. Because he should run all seven weeks to get positive result.

We conclude that MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

So,

Given: MN ≅ PQ, PQ ≅RS

To Prove: MN ≅ RS

This rule satisfies the above condition.

Therefore, MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

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A scalene triangle has at least two congruent sides is a FALSE statement.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

A scalene triangle is a triangle whose all sides are unequal.

Since congruent sides are the sides that are equal in length but in a scalene triangle, none of the sides are equal to each other.

Hence "A scalene triangle has at least two congruent sides is a FALSE statement".

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Answer:

The statement is true.

Step-by-step explanation:

Let us plug[tex]24=-4(8)-8[/tex] in 8 for [tex]x[/tex] and 24 for [tex]y[/tex] in our equation: [tex]24 =-4 (8) - 8[/tex].

Now we will solve in the order described by PEMDAS.

-4(8)=32

32-8=24

24=24

Thus, our statement is true.

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

Looking at a graph, we have that:

Hence, for the given function:

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Answer:

C

Step-by-step explanation:

a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.

Answer:181/2

Step-by-step explanation:

90.5 as a fraction is 181/2

Answer:

$3.90

Step-by-step explanation:

Expected Value formula

[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]

where:

Given table:

[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]

Substitute the given values into the Expected Value formula:

[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]

Therefore, the expected value is $3.90.

So, on average, you would expect to receive $3.90 in winnings per game.

An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.

First term a=-3.5,

Common difference d=2.25,

Number of terms n=8

Solution:

Here first term a=-3.5,

Common difference d=2.25

We know that,

f(n)=a+(n-1) d

f (8)=-3.5+(8-1)(2.25)

=-3.5+(15.75)

=12.25

We know that,

Sn=n2[2a+(n-1)d]

∴S8=82⋅[2(-3.5)+(8-1)(2.25)]

=4⋅[-7+(15.75)]

=4⋅[8.75]

=35

Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.

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The explicit formula for the given sequence is a(n) = 1 + 4(n - 1).

A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.

The recursive formula for an arithmetic sequence is as follows.

a(1)  = 1 and a(n) = a(n - 1) + 4.

Remember that this formula provides us with two types of data.

Let's look for a formal formula again for sequence.

Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = 1 + 4(n - 1).

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Answer:16

Step-by-step explanation:

The speed of Caroline in miles per hour is 0.5 miles/hour.

Given that, Caroline walks 9 1/2 inches per second.

How to convert inches to miles. To convert an inch measurement to a mile measurement, divide the length by the conversion ratio. The length in miles is equal to the inches divided by 63,360.

Now, 9.5 inches/second

We know that 1 inch/second=0.0568182 miles/hours

So, 9.5 × 0.0568182=0.5397729 miles/hours

≈0.5 miles/hours

Therefore, the speed of Caroline in miles per hour is 0.5 miles/hour.

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Your question is incomplete, probably the complete question/missing part is:

Give the rate in miles per hour. Round to the nearest tenth. Caroline walks 9 1/2 inches per second.

With a rate of $425/day, Sherry McCoy's gross income for the year, working 180 days, is $76,500.

Gross income refers to the total salary or wages and other form of earnings before any deductions or taxes.

If as a tax consultant, Sherry McCoy charges $425 per diem for her services, then her rate is $425/day.

Rate is a ratio that compares two different quantities which have different units.

We will use this rate to find how much earnings she got if she worked for 180 days last year.

gross income = rate x time

gross income = $425/day (180 days)

gross income = $76,500

Hence, working 180 days last year, Mary has a gross income of $76,500.

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Answer:

9-x

Step-by-step explanation:

The image of the point after the translation is (-4, -1)

The point is given as

(1,4)

The translation is given as

Left 5 units and down 5 units

This is represented as

(x, y) = (x - 5, y - 5)

So, we have

(x, y) = (1 - 5, 4 - 5)

Evaluate

(x, y) = (-4, -1)

Hence, the image of the point after the translation is (-4, -1)

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The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

It follows from the task content that the numbers given are rational and irrational numbers.

To order the numbers, they should be converted to decimal numbers as follows;

Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

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The maximum distance up the wall the ladder will reach = 19.4 ft

The total length of the ladder, L = 20 ft

Minimum distance of the base of the ladder to the wall, B = 1/4 x 20 = 5 ft

Now we need to find the maximum distance up the wall the ladder will reach. This is obtained when the base distance is the least.

i.e., when the base = 5 ft.

Now the ladder, the wall and the base distance between wall and ladder constitute a right triangle. In this right triangle, the ladder is the hypotenuse and the height of the wall up to which ladder reach, 'x' is its altitude with base = 5ft.

Then using Pythagoras theorem,

    [tex]L^2 = B^2 +x^2[/tex]

⇒ [tex]x^2 = L^2 - B^2 = 20^2 - 5 ^2[/tex]

⇒ [tex]x^2 = 375[/tex]

⇒ [tex]x=\sqrt{375}[/tex] = 19.3649

When rounded to the nearest tenth, (i.e., only one decimal place),we get,

⇒ x = 19.4 ft

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The equation in slope-intercept form y = 4/3 x + 4/3 contains the points (-1 , 0) and (2 , 4).

An equation of a line in slope-intercept form is given by the formula y = mx+ b, where m is the slope of the line and b is the y- intercept.

If you know two points on a line, you can use them to write the equation of the line in slope-intercept form.

First is to find the slope of the line using the two given points.

let Point 1(-1 , 0) and Point 2(2 , 4)

slope = m = (y2 - y1) / (x2 -x1)

m = (4 - 0) / (2 - -1)

m = 4/3

Next, use the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.

y = mx+ b

y = 4/3 x + b

Using Point 1,

0 = 4/3 (-1) + b

0 = -4/3 + b

b = 4/3

Finally, set up the equation of the line in slope-intercept form.

y = mx+ b

where m = 4/3 and b = 4/3

y = 4/3 x + 4/3

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When P(A | B) = P(A) and P(B ∩ A) = P(B). Then, the given events A and B are independent events.

Independent events are those where the occurrence is unrelated to any other event.

Now, as for the given question.

There are two events given as A and B.

The probability of occurrence of event A is P(A).

The probability of occurrence of event B is P(B).

The occurrence of the event A when B is already happened is denoted by P(A | B).

The intersection of events A and B are given as; P(B ∩ A).

Now, it is given in the question that;

P(A | B) = P(A) and P(B ∩ A) = P(B)

And, we already know that, the formula of the conditional probability for event A when event B has already occurred is;

P(A | B) = P(B ∩ A)/P(B)

This can also be written as;

P(B ∩ A) = P(A | B).P(B)

Now, P(A | B) = P(A), replace in the obtained equation.

P(B ∩ A) = P(A).P(B)

The obtained result is the condition for independent events.

Therefore, the events A and B are found to be independent events.

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Answer:29.3 repeating

Step-by-step explanation:Just use

calculator