Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)?

O Focus (2, -0.5); directrix x = 0
O Focus (2,-0.5); directrix y = -1.5
O Focus (0, -0.5); directrix y = -1.5
O Focus (0, -0.5); directrix x = 0

The equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.

We are given:

The perimeter of the 1 triangle = 24

The perimeter of the 2 triangle = 30

The perimeter of the 3 triangle = 36

As we can see in the given figures two sides with lengths of 9 are fixed and the side with a length of 6 is varying.

So, we can write this as,

P = 6n + 18, where n = number of triangles.

Now, check the equation formed by substituting the values;

Substitute n = 1, and we get;

P = 6(1) + 18

P = 6 +18

P = 24 True.

Substitute n = 2, and we get;

P = 6(2) + 18

P = 12 +18

P = 30 True.

Substitute n = 3, and we get;

P = 6(3) + 18

P = 18 + 18

P = 36, true.

So, it is true for all the figures.

Thus, the equation which relates the number of triangles in figure (n) to the perimeter of the figure (P) is P = 6n + 18. Option A is correct.

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The simplified expression using the commutative property is in the first option :  1/3 + 2/3 + 3/5   = 1 + 3/5 = 1 3/5 .

now the given expression is 1/3 + 2/3 + 3/5 .

Therefore this expression can be simplified using the commutative property where we put the like terms together.

1/3 + 3/5  + 2/3

= 1/3 + 2/3 + 3/5 (here we use commutative property on the second and third terms of the expression)

= 1 + 3/5 (we know that 1/3 +2/3 = 1)

=1 3/5

Hence by using the commutative property we calculate the sum easily.

The commutative property applies to the arithmetic operations of addition and multiplication. This suggests that no matter how the numbers are arranged or placed, the result of adding or multiplying them remains the same.

As an illustration, 1 + 5 = 6 and 5 + 1 = 6. No matter how two numbers are added, the sum is unaffected. Multiplication uses the same principle. The commutative property does not hold for division and subtraction because the results are completely different when the numbers are rearranged.

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Zeros of f(x) = [tex]x^{2} +6x[/tex] is (0,0) and (-6,0).

Given, f(x) = [tex]x^{2} +6x[/tex]

                = x(x+6)

For zeros, function f(x) = 0

x(x+6) = 0

x = 0    x+6 = 0

                x = -6

Putting values of x in equation,

For x = 0

f(x) = [tex]0^{2}+6(0)[/tex]

     = 0

Therefore, (0,0)

For x = -6

f(x) = [tex](-6)^{2}+6(-6)[/tex]

     = 36 - 36

     = 0

Therefore, (-6,0)

Hence, zeroes for f(x) is (0,0) and (-6,0).

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Answer:

Step-by-step explanation:

x=-4 that should be the answer i don't really know how too explain but i did this 2 years ago

Answer:

Step-by-step explanation:

Equation of the line that passes through (7, 10) and is perpendicular to the line y =x-9 is y = -x+17.

Given equation, y = x-9

Slope = m = 1

Slope of line perpendicular to given line = -1/m

                                                                    = -1/1

                                                                    = -1

Let the equation of line be y = mx + c

Passes through A(7,10)

10 = -1(7) + c

10 = -7 + c

c = 10 + 7

  = 17

Hence, equation is y = -x+17

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The formula that is used to calculate the midpoint for the given two point is written as ( (x₁ + x₂)/2 , (y₁ + y₂)/2).

Mid point:

Midpoint refers the point on a line that is at an equal distance from either end.

Given,

Here we have to explain the concept of midpoint in a simple manner.

According to the definition, midpoint refers the central point between the two points.

So, in a simple manner we have said that the mid point is calculated by finding the average of the two given point.

For example, (x₁, y₁) and (x₂, y₂) are the points, then the midpoint (xₙ, yₙ) is calculated by using the formula,

(xₙ, yₙ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)

Similarly, if one point and the midpoint is given, then the another point is calculated by apply the remaining point as (x, y) and solve it accordingly, then we can get the value of it.

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Answer:

34562

Step-by-step explanation:

you add them together

As per the concept of inequality, the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is 15 + 4m ≥ 35

Inequality

Inequality shows a non equal relationship between two numbers or two expressions.

Given,

Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles.

Here we need to determine the inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

Here we know that, his goal for this week is to run a minimum of 35 miles.

For this week, he has already run 15 miles.

In the given inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

=> 15 + 4m ≥ 35

Here we know that, 4m = number of m miles run in 4 days.

Therefore, inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is written as,

=> 15 + 4m ≥ 35

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The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

Below is a polynomial equation that is given:

0 = 3x⁵ − x⁴ − 5x² + 1

Which can also be written as

3x⁵ − x⁴ − 5x² + 1 = 0

A polynomial of degree 5 is used in the accompanying polynomial equation.

Using a graphing application to solve it graphically is the simplest approach.

The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.

Now that we have the graph, we can use it to find the equation's roots.

There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

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The answer should be C.

The range of definition of the cosine function is all real numbers. [tex]R[/tex]

It is also periodic in [tex]2\pi[/tex].

It is an even function. [tex]f(x)=f(-x)[/tex]

It can also be written in this form.

Answer:

a) 190 - 70(2/3) = 430/3 = 143 1/3 degrees

b) 190 - (2/3)x = 120

70 = 2x/3

210 = 2x

Step-by-step explanation:

x = 105 minutes

Answer:

x=59

Step-by-step explanation:

this is a full circle which is 360 degrees

We subtract 296 from 360 first

360-296=64

Then subtract 29 from 64

64-29=35

now we can set x-24 equal to 35

X-24=35

  +24 +24

x=59

Hopes this helps please mark brainliest

Answer:

60

Step-by-step explanation:

I believe two angles should add up to 180 in a parallelogram

Answer: 11 Cents per ounce of Juice

Step-by-step explanation:

The first step here is going to be to find how many ounces are in a gallon. This can be determined as shown using the given information you stated above:

1 gallon * 4 quarts * 2 pints * 2 cups * 8 ounces = 128 ounces in 1 gallon

Step 2 is multiplying 128 ounces by 2 because we have two gallons of juice in the bottle:

128 ounces per gallon* 2 gallons = 256 ounces

Step 3 is dividing the total cost of the juice, which is $28.16, by the number of total number ounces (256)

$28.16 / 256 ounces = .11 dollars per ounce (aka 11 cents per ounce)

I Think thatthe answer is 2

Answer:bgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvddddddddddddddddddddddddddd

Step-by-step explanation:

Answer:

Step-by-step explanation:

well it will be 16 because a square has 4 sides so you multiply by the grams that would be 4. 4*4= 16

Answer:

f ≤ 4

Step-by-step explanation:

f/4 + 6 ≤ 7

f/4 ≤ 7 - 6

f/4 ≤ 1

f ≤ 4

Answer:

 F<4

________

________

The solution is

The Hypotenuse = FD

Side Opposite of ∠F = MD

Side Adjacent of ∠F = MF

Side Opposite of ∠D = MF

Side Adjacent of ∠D = MD

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

The triangle FMD and the ∠M is a right angle

So , ∠M = 90°

From the figure , we can deduce that

The Hypotenuse = FD

Side Opposite of ∠F = MD

Side Adjacent of ∠F = MF

Side Opposite of ∠D = MF

Side Adjacent of ∠D = MD

Hence , the required solution is based on trigonometric relations

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The distance between the cars increasing 2 hours later is 65mph

Let’s say, the velocity in the west is x, the velocity in the south is y, and the distance between them is s at any time t. Since the west and south directions are perpendicular to each other, this will be for a right-angled triangle.

So, we have [tex]x^2 + y^2 = s^2[/tex] --------------(1)  

(please note all of them are changing as t increases.)

So, x=u×t and y=v×t,

so using (1), we can write

[tex][(u\times t)^2 + (v\times t)^2] = s^2[/tex]

[tex]s= \sqrt{(u^2 + v^2)}* t[/tex]

Using the value of u and v,

get [tex]\sqrt{(u^2 + v^2)}[/tex]= 65

So, s= 65 t

ds/dt = 65 mph

There fore the distance between the cars increasing 2 hours later is 65mph

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we know that [tex]r[/tex]

area of the circle is equal to

A=  [tex]\pi[/tex] × [tex]r^{2}[/tex]

solve for [tex]r[/tex]

[tex]r[/tex] = [tex]\sqrt{\frac{A}{\pi } }[/tex]

for A=60cm2

[tex]r[/tex] = [tex]\sqrt{\frac{60}{\pi } cm}[/tex]

we know that

[tex]\sqrt{60\\}[/tex] = [tex]\sqrt{2^{4} }[/tex] × 3 × 5

=2[tex]\sqrt{15}[/tex]

so,

[tex]\sqrt{\frac{60}{\pi } }[/tex] = 2 [tex]\sqrt{\frac{15}{\pi } }[/tex]

2[tex]\sqrt{\frac{15}{\pi } } = 2\frac{\sqrt{15} }{\pi }[/tex]  × [tex]\frac{\sqrt{\pi } }{\sqrt{\pi } }[/tex]

= 2 [tex]\frac{\sqrt{15\pi } }{\pi }[/tex]cm

this means the answer is-

2 [tex]\frac{\sqrt{15\pi } }{\pi } cm[/tex]

The number of bananas Bruce can eat in 4 weeks is 70 bananas

From the question, we are to calculate the number of bananas Bruce can eat in 4 weeks.

From the given information,

Bruce can eat 2 1/2 bananas per day

First, we will determine the number of days there are in 4 weeks

NOTE: There are 7 days in 1 week

If there are 7 days in 1 week

Then,

There are 4 × 7 days in 4 weeks

4 × 7 = 28 days

That is, 4 weeks = 28 days

Now, we will determine the number of bananas Bruce can eat in 28 days

If Bruce can eat 2 1/2 bananas per day

Then,

Bruce can eat 28 × 2 1/2 bananas in 28 days

28 × 2 1/2 = 28 × 5/2

= 14 × 5

= 70

Hence, Bruce can eat 70 bananas in 4 weeks

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Answer:

70

Step-by-step explanation:

Bruse can eat 2 1/2 bananas in one day so:

1day=2 1/2bananas.

if 1wk=7days

4wks=x =28days

1day=2 1/2 bananas

28da

28×2 1/2

=28×5/2=70

answer=70bananas

Answer:

Slope is -48, y-intercept is 432

[tex]y = - 48x + 432[/tex]

Step-by-step explanation:

[tex]m = \frac{432 - 288}{0 - 3} = \frac{144}{ - 3} = - 48[/tex]

[tex]432 = - 48(0) + b[/tex]

[tex]432 = 0 + b[/tex]

[tex]b = 432[/tex]

[tex]y = - 48x + 432[/tex]

The equation of a straight line can be written if its slope and any one point lying on it is given. The  equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3). The correct answer is option B.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given that,

The slope of the line = -1 / 7

The coordinate of the point on the line = (3,3)

The equation of a line having slope m and passing through a point (x₁, y₁) is given as,

(y - y₁) / (x - x₁) = m

Thus, the equation of the line for given slope and point is given as,

(y - 3) / (x - 3) = -1 / 7

=> (y - 3) = -1 / 7 × (x - 3)

Hence, the equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3).

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Answer: t = 5d t = 1/5d

Step-by-step explanation:

The equation that models the amount of time that is left on the cd is 80 - m.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:

= Total minutes - Time used

= 80 - m

This illustrates the equation.

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The apple mean weight's 95% confidence interval is;

CI = (119.14, 125.86) (119.14, 125.86)

The confidence interval above should be understood as;

We have a 95% confidence that each apple's average weight, across all of the apples they send, falls between 119.14 and 125.86 grams.

Ours is given;

12 for the standard deviation.

Sample size: 49; n

x = 122.5 is the indicated mean weight.

The current confidence interval formula is;

CI = x⁻ ± z(σ/√n)

Tables indicate that z = 1.96 at a 95% confidence level.

Thus;

CI = 122.5 ± 1.96(12/√49)

CI = 122.5 ± 3.36

CI = (122.5 - 3.36), (122.5 + 3.36)

CI = (119.14, 125.86)

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