a. What is an equation of the parabola with vertex at the origin and directrix x=- 5/2 ?

Answer: x=8 ==> A

Step-by-step explanation:

15x-6=114     ==> both angles are congruent angles, so they're equal

15x-6+6=114+6

15x=114+6

15x=120

15x/15=120/15

x=120/15

x=8 ==> A

The value of x in the question is 4

The given parameters are

PQT = 60

PQS = 4x + 14

The line bisects PQT

So, we have

PQS = 1/2 * PQT

This gives

4x + 14 = 1/2 * 60

Evaluate

4x + 14 = 30

Evaluate the like terms

4x = 16

Divide by 4

x = 4

Hence, the value of x in the question is 4

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Land withdrew money in the form of an geometric series and he had $96 in his account in January.

A geometric series in mathematics is made up of an unlimited number of terms with a fixed ratio between them.

Each term is connected to the previous term by a simple ratio.

if the first term of an Geometric series be a, and the common ratio r then the second term is ar, third term is ar² and so on.

the nth term of a  Geometric series is calculated by

[tex]a_n=ar^{n-1}[/tex]

Now here we know that the final term of the Geometric series is $1.50.

So each month Lang withdrew half of his money.

So the common ratio of each terms is [tex]\frac{1}{2}[/tex].

Number of months=6(n=7)

Now we have to find the initial term of the Geometric series.

We know that [tex]a_n=ar^{n-1}\\[/tex]

Given n=7 and r=1/2 and aₙ=1.5

Substituting the values we get:

[tex]1.5=a\times(\frac{1}{2})^{7-1} \\or, 1.5=a \times (\frac{1}{2} )^6\\or, 1.5=a\times \frac{1}{64} \\or,a=96[/tex]

Hence Lang had $96 in his bank account before his first withdrawal.

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Answer:

23x10

Step-by-step explanation:

Its 23x10^3 because its basically because 10 times 10 is a 100 and 100x10 is 10000 and 11x104 will be like 1000 smth (calculate it if u want)

Answer:

Rounding up to 3 decimals = 170.650

Rounding up to Hundreds = 200

Answer:

[tex]\textsf{a)} \quad a_n=3n+15[/tex]

[tex]\textsf{b)} \quad \begin{cases}a_n=a_{n-1}+d\\a_1=18\end{cases}[/tex]

[tex]\textsf{c)} \quad 63[/tex]

[tex]\textsf{d)} \quad 648[/tex]

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

Explicit Formula

[tex]\boxed{a_n=a+(n-1)d}[/tex]

where:

Given information:

Nadia increases the number of push-ups each day by 3.  Therefore:

Substitute the values of a and d into the formula to create an explicit formula to model the number of push-ups Nadia does each day:

[tex]\implies a_n=18+(n-1)3[/tex]

[tex]\implies a_n=18+3n-3[/tex]

[tex]\implies a_n=3n+15[/tex]

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Recursive Formula

[tex]\boxed{a_n=a_{n-1}+d}[/tex]

where:

We already know the common difference from the previous calculations.

Therefore:

[tex]\implies a_n=a_{n-1}+3[/tex]

When giving a recursive rule we have to define the first term of the sequence, as it is not part of the formula.  Therefore, the full recursive rule for the given scenario is:

[tex]\begin{cases}a_n=a_{n-1}+d\\a_1=18\end{cases}[/tex]

To calculate how many push-ups Nadia will do on October 16, substitute n = 16 into the recursive formula from part (a):

[tex]\implies a_{16}=3(16)+15[/tex]

[tex]\implies a_{16}=48+15[/tex]

[tex]\implies a_{16}=63[/tex]

Therefore, Nadia will do 63 push-ups on October 16.

Sum of the first n terms of an arithmetic series:

[tex]\boxed{S_n=\dfrac12n(a+a_n)}[/tex]

To find the total number of push-ups Nadia does from October 1 to October 16, substitute n = 16, a = 18 and a₁₆ = 63 into the formula:

[tex]\implies S_{16}=\dfrac12(16)(18+63)[/tex]

[tex]\implies S_{16}=8(81)[/tex]

[tex]\implies S_{16}=648[/tex]

Therefore, Nadia does a total number of 648 push-ups from October 1 to October 16.

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Answer:

5 1/15

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form:

76

15

Decimal Form:

5.0

¯

6

Mixed Number Form:

5 1/15

Answer: Most likely 0.44444 (The 4 is repeating.)

Step-by-step explanation:

Because first since its in parenthesis, you would do 2/3 which is 0.6666 repeating. Then you do that to the power of 2 which will give you 0.4 repeating!

Hope this works! If not, I apologize.

The exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle

([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8) then m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .

What is meant by Exterior Angle Inequality Theorem?

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle ([tex]\angle[/tex] 2) is larger than either remote interior angle ([tex]\angle[/tex] 6 and [tex]\angle[/tex] 8).

Similarly, the exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle ([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8).

Therefore, m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .

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A model plane would be 57.7 feet high.

In this question,

A model airplane takes off at an angle of elevation of 30°C

We need to find how much the plane will be high after traveling 100 feet horizontally.

Consider the following diagram.

Let angle ACB is the angle of elevation.

∠ACB = 30°

the horizontal distance CB = 100 feet

We need to find the distance AB.

Consider tangent of angle ACB.

⇒ tan(30) = AB / BC

⇒ 0.577 = AB / 100

⇒ AB = 0.577 × 100

⇒ AB = 57.7 feet

Therefore, a model plane would be 57.7 feet high.

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The area of the parallelogram is approximately equal to 59.994 square units.

The area of a parallelogram is equivalent to the sum of the areas of the two triangles by adding a diagonal. Then, the area of each triangle can be found in terms of side terms by Heron's formula. First, find the length of each side:

Side AB

AB = (4, 6) - (- 2, 6)

AB = (6, 0)

AB = √(6² + 0²)

AB = 6

Side CD

CD = (- 1, - 4) - (5, - 4)

CD = (- 6, 0)

CD = √(6² + 0²)

CD = 6

Side AD

AD = (- 1, - 4) - (- 2, 6)

AD = (1, 10)

AD = √(1² + 10²)

AD = √101

Side BC

BC = (5, - 4) - (4, 6)

BC = (1, - 10)

BC = √[1² + (- 10)²]

BC = √101

Side AC

AC = (5, - 4) - (- 2, 6)

AC = (7, - 10)

AC = √[7² + (- 10)²]

AC = √149

Second, determine the areas of the two triangles.

Triangle ABC

s = 0.5 · (AB + BC + AC)

s ≈ 14.128

A = √[s · (s - AB) · (s - BC) · (s - AC)]

A ≈ 29.997

Triangle ACD

s = 0.5 · (AC + CD + AD)

s ≈ 14.128

A = √[s · (s - AC) · (s - CD) · (s - AD)]

A ≈ 29.997

Third, find the area of the parallelogram by adding the two areas calculated in the previous step:

A' = 29.997 + 29.997

A' = 59.994

The area of the parallelogram is approximately equal to 59.994 square units.

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The coordinate points  of g(x) are (-1, 2), (0, 0), (1, 2).

We know that the points (-1, 1), (0, 0), and (1, 1) belong to f(x) graph, where:

f(x) = x^2

Notice that the inputs in these points are x = -1, x = 0, x = 1.

Function g(x) is:

g(x) = 2x^2

Using the given inputs, we have:

g( -1) = 2*(-1)^2 = 2

g(0) = 2*0^2 = 0

g(1) = 2*(1)^2 = 2

Then the coordinate points  of g(x) are (-1, 2), (0, 0), (1, 2).

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Answer:

pomogło dzięki xxxxxxxxxx

Answer:

The solution below is wrong. The correct solution is [tex]x = \frac{-b (+-)\sqrt{73} }{16}[/tex]

Step-by-step explanation:

Rearrange the numerals :

[tex]9x + 2 = 8x^2 + 6x\\8x^2 + 6x - 9x - 2 = 0\\8x^2 - 3x - 2 = 0\\[/tex]

Use quadratic formula :

Solution 1: (Note: the -b"+"....  is actually "±" as the system has some problem of adding "±" symbol)

[tex]x = \frac{-b+\sqrt{b^2 - 4ac}}{2a} \\x = \frac{-(-3)+\sqrt{(-3)^2 - 4(8)(-2)}}{2(8)} \\x= \frac{3+\sqrt{9 + 64 }}{16} \\\\x= \frac{3+\sqrt{73 }}{16} \\\\[/tex]

Hope this helps, it would really help me if u mark me as the brainliest.

If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;

B' = (0, -5)

K' = (-3, 0)

U' = (2, -2)

Y' = (-3, 4)

When a coordinate (x, y) is rotated 90 degrees clockwise around the origin is (-y, x)

Given the coordinates points

B = (5, 0)

K = (0, 3)

U = (2, -2)

Y = (4, 3)

If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;

B' = (0, -5)

K' = (-3, 0)

U' = (2, -2)

Y' = (-3, 4)

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The three measures of the angle are,

Angle 2 = 37°

Angle 3 = 153°

Angle 4 = 37°

When two straight lines or rays intersect at a single endpoint, an angle is created. The intersection of two points is where an angle's vertex is located. The Latin word "angulus," which means "corner," is where the term "angle" originates. The building's corner provided protection, whether it was a projecting portion or a partially covered area. 2a: Dihedral angle and the figure created by two lines that originate from the same point.

I guess refers to two intersecting angle which form 4 angles.

Angles 1 and 2 are supplementary angles whose sum is 180°.

Angle 1 + Angle 2 = 180°

143° + angle 2 = 180°

Angle 2 = 180° - 143°

Angle 2 = 37°

Angles 1 and 3 are vertical angles, therefore treat them as such.

Therefore, it is easy to find their measures because vertical angles are congruent in measures.

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The system of equations that could be used to determine the number of commercials and the number of movies on which Jayden's songs were played is illustrated as 30(x + 4) + 120(x) = 420.

The variable is that the number of times the song was played in movies is represented by x.

From the information, Jayden is a songwriter who collects royalties on his songs whenever they are played in

a commercial or a movie and she will earn $30 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie

Let the number of times the song was played in movies be x.

Jayden's songs were played on 4 more commercials than movies. This will be x+4.

Therefore, the equation to solve the question will be:

30(x + 4) + 120(x) = 420

30x + 120 + 120x = 430

150x + 120 = 430

150x = 430 - 120

150x = 310

x = 310/150

x = 2.1

Number of movies = 2

Number of commercial = x + 4 = 6

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Answer:

Step-by-step explanation:

The electric potential at the origin is 11.9834 ×[tex]10^{9}[/tex] .

V = k (q/r)

V = 8.98755 × [tex]10^{9}[/tex] ×(-4/3)

V= 11.9834 ×[tex]10^{9}[/tex] is the the electric potential at the origin.

The effort required to transfer a unit charge against an electric field from a reference point to a specified spot.

Electric potential difference is the potential created when a charge is moved from one point to another within the field itself, whereas electric potential is the effort done per unit charge to transport the charge from infinity to a point in the electric field.

The amount of work required to move a unit positive charge from infinity to a particular point in an electric field is called the electric potential.

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The number of miles that Maria ran is 25.6 mile.

From the information given, she runs for 4 hours at a speed of 6.4 miles per hour.

It should be noted that distance is calculated as the speed multiplied by the time taken.

In this case,the distance will be:

= Speed × Time

= 6.4 × 4

= 25.6 miles

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Answer: Discrete

Step-by-step explanation: Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting.

                                         Hope this helps!

Answer: 19 ==> 1st option

Step-by-step explanation:

f(x) = 5x + 1

f(-4)=5(-4) + 1

f(-4)=-20 + 1

f(-4)=-19 ==> 1st option

The distance between pair of parallel lines with the following equation

y=x+2 y=x-4  is  [tex]3{\sqrt 2 }[/tex]

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be -1. Check what are the y-intercept of any of the two lines and write the equation of the perpendicular line through it.

The y-intercept of the line y = x − 4 is (0,−4).

So, the equation of a line with slope −1 and a y-intercept of −4 is y = −x −4.

The perpendicular intersects or meets the line y = x - 4 at (0, 4).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations. Solve the right sides & solve for x.

x + 26 = -x - 6

     2x = -6                                       (combine them like terms)

       x = -3                                       (divide both the side by 2)

Find y:

y = -3 - 4

  = -7

So, the point of intersection is (−3,−7).

Use the Distance Formula to find the distance between the points (-3, -7) and (0,−4).

[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]

  [tex]={\sqrt {\left(0-(-3\right)^{2}+\left(-4-(-7\right))^{2}}}[/tex]

  [tex]={\sqrt {3^2 +3^2}}[/tex]

  [tex]=3{\sqrt 2 }[/tex]

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The solutions are (0, - 6) ,(7, 8)

The given system of equations is expressed as

y = x² - 5x - 6- - - - - - - - - - - - (1)

y = 2x - 6- - - - - - - - - - - (2)

We would apply the method of substitution by substituting equation 2 into equation 1. It becomes

x² - 5x - 6 = 2x - 6

x² - 5x - 6 = 2x - 6

x² - 5x - 2x - 6 + 6 = 0

x² - 7x = 0

x(x - 7) = 0

x = 0 or x - 7 = 0

x = 7 or x = 0

Substituting x = 0 into equation 2, it becomes

y = 2 × 0 - 6

y = - 6

Substituting x = 7 into equation 2, it becomes

y = 2 × 7 - 6

y = 14 - 6

y = 8

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By the use of arithmethic, the final temperature in Sudbury is - 1 °C.

In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:

T = T' + ΔT₁ + ΔT₂

T = 4 °C + 5 °C - 10 °C

T = 9 °C - 10 °C

T = - 1 °C

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The congruent segments, [tex] SC \cong HR [/tex] and [tex] HR \cong AB[/tex], according to the substitution property of equality, gives; [tex] SC \cong AB [/tex]

The given parameters are;

Required;

To prove;

[tex] SC \cong AB[/tex]

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

[tex] SC \cong AB [/tex] (Inverse of the definition of congruency)

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Answer:

x = 9

Step-by-step explanation:

Complementary angles equal to 90 degrees.

So add both equations to equal 90 and solve for x.

(2x+5) + (8x-5) = 90  

Combine like terms.

10x = 90

Divide each side by 10.

x = 9

The value of the expression 8 x `1000 is 8000

The expression is given as

8 x `1000

The above expression implies that we multiply 8 by 1000

This can be done directly using a calculator, and it can be solved step by step

The step by step procedure is as follows

Express 1000 as 10 x 100

So, we have

8 x `1000 = 8 x `10 x 100

Evaluate 8 x 10

8 x `1000 = 80 x 100

Evaluate 80 x 100

8 x `1000 = 8000

Hence, the value of the expression 8 x `1000 is 8000

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The problem statement provides information about the Vasquez Family, who pay visits to their grandmother every three weeks and host a neighborhood party every eight weeks.

The number of weeks combined when the Vasquez Family visits their grandmother and hosts the neighborhood party is 24 weeks.

The total number of weeks with all the three events occurring together (visit, neighborhood party, hiking) is 48 weeks.

Now we concluded that the number of weeks is 24 because we know that the Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks.

Therefore,  we will look for a least common factor of both 3 (visit) and 8 (party) and that LCM (least Common Factor) is 24.

Therefore, the number of weeks when the Vasquez family visits their grandmother and hosts the neighborhood party is 24.

Complete Problem Statement:

The Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks. Every 16 weeks, the Vazquez family takes a day to go hiking. After how many weeks will the Vasquez family visit their grandmother and host the neighborhood party? After how many weeks will all three events occur?

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Answer:

hope u get it............