f (x) = 8 (1.25) ^ -2.5

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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AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

Two expressions with equal sign is called as Equation.

Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven= 60+1.50x

Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven=30+2.50x.

60+1.50x=30+2.50x

60-30=2.50x-1.50x

30=x

Therefore, AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

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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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By applying the triangle midpoint theorem to the triangle, the value of x is equal to: D. 12.

In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the triangle, we have:

8x = 2(2x + 24)

8x = 4x + 48

8x - 4x = 48

4x = 48

x = 48/4

x = 12.

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The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

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 (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .

Therefore, the correct answer is ∠ 7 and ∠ 8.

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Answer: Small box has the lowest amount when divided, that box has the best value.

Step-by-step explanation:

Given data,

Big box = 500 g

It cost is $8.00

Small box = 300 g

It cost is $ 5.40

First switch the box that's in kilograms into grams.

One kilogram=1000 grams.

Then,    Big box = 500 g = $ 8.00

            Small box = 300 g = $ 5.40

Next divide the amount in each box by the cost of each box.

           Big box = 500/8

           Big box  = 62.5

           Small box = 300/540

           Small box  = 0.5555

Therefore,

So, since small box has the lowest amount when divided, that box has the best value.

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The value of x is 15.

(3 - x/2) - (1 - x/3) = 7 - (x - x/2)

(6 - x/2) - (3 - x/3)  = 7 - (2x - x/2)

(6 - x/2) - (3 - x/3) =14 - 2x +x /2

by solving these equations we get ,

18 - x -6 = 42 - 3x

12 - 42 = - 2x

where, x = 15 .

therefore the value of x is 15.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

examples of equation and expression.

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When both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.

It should be noted that one will pay for an excess luggage when the luggage is heavier than the allowance when the person checks in.

It should be noted that every airline has a restriction on how heavy the luggage can be.

Therefore, when both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.

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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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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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Answer:

m = 6

Step-by-step explanation:

➟ m² = 36

in order to find the value of m take square root from both side

➟ [tex] \sf \: \sqrt{ {m}^{2} } = \sqrt{36} [/tex]

Calculate the values

➟ m = 6

∴ the value of m is 6

The value of f(x)= (x-3).g(x)+8

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division.

dividend= divisor x quotient+ remainder

given that, f(x) has remainder 8 and divided by x-3

as per division algorithm we can say that

dividend= divisor x quotient+ remainder

f(x)= (x-3).g(x)+ 8

if we need to find f(3) then put 3 in the place of x

that gives you f(3) = (3-3).g(x)+ 8

                        f(3)= 8

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The answer to f(x)= (x-3). g(x)+8

An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm.

Dividend equals Divisor x Quotient plus Remainder.

Given that, f(x) is divided by x-3 and has a remainder of 8.

The division algorithm allows us to state that

Dividend equals Divisor x Quotient plus Remainder.

f(x)= (x-3) (x-3).

g(x)+ 8

If we need to find f(3), we should substitute 3 for x.

giving you f(3) = (3-3).

g(x)+ 8

f(3)= 8

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The following set of numbers, 15, 36, and 39, can be the measures of the sides of a right triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 15, b = 36, and c = 39

a + b > c     15 + 36 > 39     51 > 39     True

a + c > b     15 + 39 > 36     54 > 36     True

b + c > a     36 + 39 > 15     75 > 15     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

15^2 + 36^2 = 1521

2. Compare it to the square of the largest side.

39^2 = 1521

1521 = 1521

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 15, 36, and 39 can be the measure of the sides of a right triangle.

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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 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:

[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Step-by-step explanation:

In triangle ABD,

[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]

In triangle BCD,

∠CBD=34° (isosceles triangle)

∠DCB=116° (sum of angles in a triangle)

[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Answer:

4.59 cm to nearest hundredth.

Step-by-step explanation:

Consider triangle ABD.

sin 72 = DB / 8

DB = 8 sin 72

      = 7.608 cm.

Imagine a line from point C perpendicular to DB at point E.

As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2

so, DE = 1/2 * 7.608 = 3.804.

Now consider triangle DCE which is a right-angled triangle at E.

cos 34 = 3.804 / DC

DC = 3.804 / cos 34

      = 4.588 cm

BC = DC = 4.588.

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]

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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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Answer:

5(2.47y−2.03)

Use the distributive property to multiply 5 by 2.47y−2.03.

12.35y−10.15

Step-by-step explanation:

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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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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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

Answer:

A=h(b+c) solve for c

First, multiply h to b and c

A = hb + hc

Then, transfer hb to the other side and change its sign from positive to negative.

A – hb = hc

To get c, Divide both sides by h

(A – hb)/h = hc/h

(A - hb)/h = c  OR c = (A – hb)/h

Example. Let us assume the following. A = 500 ; h= 10;b= 20; c= ?

c = (A – hb)/h

c = (500 – (10*20))/10

c = (500 – 200)/10

c =  300/10

c = 30

To check; use the original equation given.

A = h(b+c)

A = 10(20+30)

A = 200 + 300

A = 500. same as the figure given in the example.

[tex]\displaystyle\\Answer:\ b=\frac{A-hc}{h}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A=h(b+c)\\A=hb+hc\\A-hc=hb+hc-hc\\A-hc=hb\\Divide\ both\ parts\ of\ the\ equation\ by\ h(h\neq 0):\\\frac{A-hc}{h}=b\\ Hence,\\b=\frac{A-hc}{h}[/tex]

Answer:

x+6/4=13

Step-by-step explanation:

the result is 11.5

Step-by-step explanation:

this is the solution above

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 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 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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