what is the equation for a parabola with a focus at (2,2) and a directix of x=8

The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.

Answer:

s = 17 units

Step-by-step explanation:

Given f(t) = t³ - 8t² + 27t

Differentiating f(t), we have

f'(t) = 3t² - 16 t + 27

At t = 0

f'(t) = 27

This is the required obtainaible distance, s.

Answer:

The average score of 6 tests is 19.

Step-by-step explanation:

Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :

[tex]let \: x = total \: no. \: of \: scores[/tex]

[tex] \frac{x}{5} = 18[/tex]

[tex]x = 18 \times 5[/tex]

[tex]x = 90[/tex]

We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :

[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]

We need to know how to find the average

☄ For this case, We are gonna find average score...!

[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]

So, Let's proceed further towards solution....

We have,

Finding total score in 5 tests,

⇛ Total score = Avg. score × No. of tests

⇛ Total score = 18 × 5

⇛ Total score = 90

According to question,

⇛ Total score now = 90 + 24 = 114

Finding the average score of 6 tests,

⇛ Avg. score = 114 / 6

⇛ Avg. score = 19 points

☄ Avg. score of lynette in 6 tests = 19

━━━━━━━━━━━━━━━━━━━━

Answer:

The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:

|x - 8| = 2

Step-by-step explanation:

The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:

|x - 8| = 2

The equation is written in the notation of absolute value as required.

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet

Answer:

[tex]\huge\boxed{IQR = 21}[/tex]

Step-by-step explanation:

The data set given is:

57,63,44,29,36,62,48,50,42,34

Arrange in ascending order:

29,34,36,42,44,48,50,57,62,63

Place parenthesis around the number making two equal sets.

(29,34,36,42,44) | (48,50,57,62,63)

            ↑                             ↑

            Q1                          Q3

Q1 = 36 , Q3 = 57

So, IQR = Q3-Q1

IQR = 57-36

IQR = 21

Answer:

[tex]\huge \boxed{\sf A. \ 21}[/tex]

Step-by-step explanation:

The data set is given,

[tex]\sf 57 \ 63 \ 44 \ 29 \ 36 \ 62 \ 48 \ 50 \ 42 \ 34[/tex]

Arrange the data set in ascending order.

[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ 48 \ 50 \ 57 \ 62 \ 63[/tex]

Split the data set into two equal sets.

[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ \ \ 48 \ 50 \ 57 \ 62 \ 63[/tex]

Find the median of the lower half and upper half.

[tex]\sf Median \ of \ lower \ half = 36[/tex]

[tex]\sf Median \ of \ upper \ half = 57[/tex]

Interquartile range = median of upper half - median of lower half

[tex]\sf IQR = 57 - 36[/tex]

[tex]\sf IQR = 21[/tex]

The interquartile range for the number of points scored at ten basketball games is 21.

Answer:

  one car at a time

Step-by-step explanation:

For each car in the shorter train* (A) ...

When there are no more train A cars in front of train B, both trains can continue on their journey.

We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.

_____

* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.

Step-by-step explanation:

1965 round to the nearest tenth is 1970

Answer:

1965.0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)

Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:

Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).

This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:

Bags ≤ 3  

Answer:

2.50 + 5B ≤ 21;

Step-by-step explanation:

Cost of eggs = $2.50

Cost of avocado = $5 (bag of 3)

Total budgeted amount = $21

Bags of avocado = B

Therefore :

(Cost of eggs + cost of avocado) ≤ total budgeted amount

($2.50 + $5(B)) ≤ 21

2.50 + 5B ≤ 21

5B ≤ 21 - 2.50

5B ≤ 18.50

B ≤ 18.50 / 5

B ≤ 3.7

Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)

X/5 -1/2 = x/6

Find the least common denominator of the 3 denominators:5,2,6

The limited is 30

Multiply all 3 fractions by 30:

6x -15 = 5x

Subtract 6x from both sides:

-15 = -x

Multiply both sides by -1:

X = 15

Answer:

the interest is 195dollars

Answer:

Below

Step-by-step explanation:

First triangle)

This triangle is a right one so we will apply the pythagorian theorem.

● 25 is the hypotenus

● 25^2 = b^2 + 24^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Seconde triangle)

Again it's a right triangle

x is the hypotenus.

● x^2 = 12^2 +5^2

● 12^2 = x^2-5^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

This is a right triangle

AC is the hypotenus.

● AC^2 = BC^2 + BA^2

Notice that: BC = BE+EC and BA=BD+DA

● AC^2 = (BE+EC)^2 + (BD+DA)^2

Answer:  2) b = 7       3) x = [tex]\sqrt{119}[/tex]

Step-by-step explanation:

Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²

2) b² + 24² = 25²

   b² + 576 = 625

            b² = 49

         [tex]\sqrt{b^2}=\sqrt{49}[/tex]

            b = 7

3) 5² + x² = 12²

   25 + x² = 144

            x² = 119

        [tex]\sqrt{x^2}=\sqrt{119}[/tex]

           [tex]x=\sqrt{119}[/tex]

Answer:

a) 5[tex]cm^{3}[/tex]

Step-by-step explanation:

Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.

When raising to 3, these dimensions are included and therefore  5[tex]cm^{3}[/tex] is a measure of volume.

Answer:

5cm^3

Step-by-step explanation:

Volume for a form will always be in cubic units.

Area of a shape will always be in squared units.

Length will not be in cubic or squared units.

Hence, the first option is a measure for volume.

The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.

The third option represents a measurement of length, for example the length of a line segment or the height of a figure.

Answer:

x+12=78

Step-by-step explanation:

like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.

Answer:

n + 12 = 78

Step-by-step explanation:

Let n = number.

n + 12 = 78

Answer:

its b and e

Step-by-step explanation:

The statements given in options B and E are   true so options B and E are right options.  

Given some statements we have to determine that which of the following statements are true

The given statements are as follows

A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.

B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.

C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.

D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

We know some facts about each type of geometry

In Euclidean geometry  plane is used to plot the points and line.

In spherical geometry uses the sphere to plot the points and circles

Elliptical geometry is such a geometry where no parallel lines exists.

The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with   and they can be written down in the following points

So from the above observations we can conclude that statements given in options B and E are   true so options B and E are right options.  

For more information please refer to the link given below

https://brainly.com/question/4637858

Answer:

The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Step-by-step explanation:

The distributive property of multiplication is:

[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]

The two polynomials provided are:

[tex](2x+3)\\(x^{2}+x-2)[/tex]

Determine the final expression by multiplying the two polynomials as follows:

[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]

[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]

Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Answer:

Option (G)

Step-by-step explanation:

Let the length of the race = a miles

Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

Time taken to cover 'a' miles with the speed = 12 mph,

Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]

Time taken to cover 'a' miles with the speed = 11 mph,

Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]

Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.

So, [tex]t_2=t_1+\frac{1}{6}[/tex]

[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]

[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]

[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]

a = 22 mi

Therefore, distance of the race = 22 mi

Option (G) is the correct option.

Answer:

3:50 pm

Step-by-step explanation:

Count backwards with the 25 min.

4:15 - 15 min >

25 - 15 = 10 >

4:00 - 10 = 3:50

Answer:

3:50 pm

Step-by-step explanation:

Starting Time + Time Interval = Ending Time

=> Ending Time - Time Interval = Starting Time

Ending Time = 4:15 pm

Time Interval = 25 minutes

Starting Time = x

=> 4:15 - 25 = x

=> 4:15 - 15 - 10 = x

=> (4:15 - 15) - 10 = x

=> 4:00 - 10 = x

=> 3:50 pm = x

So, she needs to leave the house at 3:50 pm to get to the movie theater on time.

Answer:

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Step-by-step explanation:

An augmented matrix is the coefficients of the variables and then the solution in rows

Rewriting the equations

2x -7y +6x = 7

x +3y -4z = 5

x +6y -15z = -6

The matrix is

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Let [tex]\mu[/tex] be the average number of televisions per household in the United States .

As per given ,

[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]

Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.

For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]

T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]

Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]

This means we cannot reject null hypothesis.

We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.

Answer:

17h+1.75m=522 m=40h

Step-by-step explanation:

Let h=  {the number of hours the driver drove}

Let m=  the number of miles driven

The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:

17h+1.75m=522

17h+1.75m=522

Since the driver drove an avearge of 40 miles per hour, if the driver drove  hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:

m=40h

m=40h

Write System of Equations:

​  

17h+1.75m= 522

m=40h

The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

The following are the different costs of the truck that Luke must be pay while running a truck:

Let ' x ' be the total time of driving a truck in hours.

and ' y ' be the total mile distance that is covered by the truck.

Therefore, the system of the equation for the overall running cost for a truck is given below.

[tex]\rm{Cost}=17x+1.75y[/tex]

Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.

Thus,

The total distance traveled by truck is 40x.

That is,

[tex]y=40x[/tex]

Substitute the values and solve them further.

[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]

Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]

To know more about variables, please refer to the link:

https://brainly.com/question/14393109

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

Answer: Hi!

We can simplify this by combining like terms:

-12w + 7w - 3 - 6

-12w + 7w = -5w

-3 - 6 = -9

Out equation now looks like this:

-5w - 9

There's nothing left to simplify, so we're done!

Hope this helps!

Answer:

Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.

Step-by-step explanation:

The given equation is

[tex]-2y=5x+11[/tex]

We need to find three points that solve the equation.

Put x=0,

[tex]-2y=5(0)+11[/tex]

[tex]-2y=11[/tex]

[tex]y=-5.5[/tex]

Put x=-1,

[tex]-2y=5(-1)+11[/tex]

[tex]-2y=6[/tex]

[tex]y=-3[/tex]

Put y=0,

[tex]-2(0)=5x+11[/tex]

[tex]5x=-11[/tex]

[tex]x=-2.2[/tex]

So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.

Plot these points on a coordinate plane and connect them by a straight line as shown below.

Answer: 30 i think 10x3=30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]

Step-by-step explanation:

[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,

499, 498, 497.......7 terms

Since there is a common difference between successive and previous term,

d = 498 - 499 = -1

This sequence is an arithmetic sequence.

Sum of n terms of an arithmetic sequence is,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

where a = first term of the sequence

n = number of term

d = common difference

For the given given sequence,

[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]

    = [tex]\frac{7}{2}[998-6][/tex]

    = [tex]\frac{7}{2}(992)[/tex]

    = 3472

Therefore, sum of seven terms of the given sequence will be 3472.

Answer:

Slope= 1/9

Y-Intercept= 5

Answer:

8

Step-by-step explanation:

f(x)=x²+4 ( find quadratic equation: given vertex)

g(x)=x+2  ( find linear equation : given 2 points)

(f-g)(-2)

(x²+4-x-2)of (-2)

x²-x+2  now find (f-g)(-2)

-2²-(-2)+2=4+2+2=8

Answer:

You would multiply 8.25 by 3 which equals 24.75. Then multiply 1.50 by 8 which is 12.00.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2:3

Step-by-step explanation:

It’s easy

Answer:

2.5

Step-by-step explanation:

i think