which absolute value function defines this graph

Answer:

5, 12, 19, 26, 33

Step-by-step explanation:

Using the recursive rule and a₁ = 5 , then

a₂ = a₁ + 7 = 5 + 7 = 12

a₃ = a₂ + 7 = 12 + 7 = 19

a₄ = a₃ + 7 = 19 + 7 = 26

a₅ = a₄ + 7 = 26 + 7 = 33

The first 5 terms are 5, 12, 19, 26, 33

Answer:

see explanation

Step-by-step explanation:

Consider the left side

[tex]\frac{cosA}{1-sinA}[/tex] + [tex]\frac{cosA}{1+sinA}[/tex]

= [tex]\frac{cosA(1+sinA)+cosA(1-sinA)}{(1-sinA)(1+sinA)}[/tex]

= [tex]\frac{cosA+cosAsinA+cosA-cosAsinA}{1-sin^2A}[/tex]

= [tex]\frac{2cosA}{cos^2A}[/tex] ← cancel cosA on numerator/ denominator

= 2 × [tex]\frac{1}{cosA}[/tex]

= 2secA

= right side, thus proven

Answer:

You are currently 40 years old

Step-by-step explanation:

Let's say the current age is represented by the variable x.

x = current age

The question says that "if you take half my age and add 7, you get my age 13 years ago"

This can be represented like this:

1/2(x) + 7 = x - 13

Now we solve for x using basic algebra:

1/2(x) = x - 20

-1/2(x) = -20

x = 40

To check if this is correct, plug it back into the equation and see if both sides equal each other:

1/2(40) + 7 = (40) - 13

20 + 7 = 27

27 = 27

Hope this helps (●'◡'●)

Answer:

y = -1/4x +2

Step-by-step explanation:

First find the slope using two point

(0,2) and (4,1)

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

   = (1-2)/(4-0)

   = -1/4

The y intercept is 2

The slope intercept form of a line is

y= mx+b where m is the slope and b is the y intercept

y = -1/4x +2

Answer:

the equation of the line is y = -1/4x +2

Step-by-step explanation:

The first step is to see where the line intercepts on the y-axis, which is 2. The next step is to see what the slope is so because it goes down 1 right 4, you find out that the slope of the line is -1/4.

Hope this helps!

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

The rational function is:

f(x) = x/ (x - 2)(x + 5).

The correct option is D.

As the function approaches a certain value—typically infinity or negative infinity—as the input approaches positive or negative infinity, this is known as a horizontal asymptote.

When the vertical asymptotes are x = 2 and x = -5, this means that the denominator of the rational expression must contain the factors (x - 2) and (x + 5), but not (x - a) or (x + b) for any other values of a and b.

When the horizontal asymptote is x = 0, this means that the degree of the numerator and denominator must be the same, and the leading coefficients must be equal.

Let's start by setting up the denominator:

denominator = (x - 2)(x + 5)

To satisfy the horizontal asymptote at x = 0, the numerator must also have a factor of x, so we can write:

numerator = kx

where k is a constant to be determined.

To ensure that the rational expression has the desired vertical asymptotes, we need to add any necessary linear or quadratic factors to the numerator.

Since the denominator already has linear factors, we only need to add a quadratic factor.

We can choose any quadratic factor that doesn't affect the horizontal asymptote or the other vertical asymptote.

For example, we can choose:

numerator = kx(x + 7)

Putting it all together, the rational expression is:

f(x) = kx / (x - 2)(x + 5)

To determine the value of k, we can use the fact that the leading coefficients of the numerator and denominator must be equal. The leading term of the numerator is kx², and the leading term of the denominator is x².

Therefore:

k = 1

So the final rational expression is:

f(x) = x / (x - 2)(x + 5)

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Hello!

a) (t - 2)(t - 2) = (t - 2)² = t² - 4t + 4

b) (3y - 2z)(3y + 2z) = (3y)² - (2z)² = 9y² - 4z²

c) 105 × 98 = 10290

Good luck! :)

Answer:

Step-by-step explanation:

a) Identity : (a- b)² = a²- 2ab +  b²

(t - 2)(t -2) = (t-2)²            {a = t & b =2}

                 = t² -2*t*2 + 2²

                 = t² - 4t + 4

b) (a + b)(a - b) = a² - b²

a = 3y   & y = 2z

(3y - 2z) (3y +2z)  = (3y)² - (2z)²

                             = 3²y² - 2²z²

                              = 9y² - 4z²

c) (x + a)(x + b) =x² + (a+b)x + ab

105 * 98 = (100 + 5) (100 - 2)  {here, x = 100 ; a = 5 ; b = -2}

              = 100² + (5 +(-2) ) *100 + (5)*(-2)

              = 10000 + (3)*100 - 10

              = 10000 + 300 - 10

              = 10290

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]

Divide through by 2

[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]

Complete the square by adding the square of the half of the coefficient of x to both sides:

[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]

[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]

Take the square root of both sides

[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]

Hence the value of x is 6.58m

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so,  when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.[tex]\sum(x - \bar x) = 0[/tex]

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

Answer:

-3/5

Step-by-step explanation:

Pythagorean formula :

x^2 + y^2 = r^2

(-8)^2 + (-6)^2 = r^2

64 + 36 = 100

r^2 = 100

r= 10

sin is the y coordinate over the radius :

-6/10

-3/5

Answer:

the last one: x^3 + 5x^2 - 9x - 45 = 0

Step-by-step explanation:

You can solve all the other ones by simple factoring and/or calculator.

Since the last one has more than 3 terms, it's likely that you'll have to use group factoring to solve it.

Answer:

1 = 35p

6 = 35p×6

= 240p

Therefore, 6 bagels cost 240 p

The momentum of a variable is represented by the rate of change. The average rate of change in the area as the radius changes from 2.5 to 5.5 feet is 25.1327ft² per ft.

The momentum of a variable is represented by the rate of change, which is used to quantitatively express the percentage change in value over a specific period of time.

The area of the circle when the radius of the circle is 2.5 feet is,

Area of circle = π × (2.5 feet)²

                      = 19.635 ft²

The area of the circle when the radius of the circle is 5.5 feet is,

Area of circle = π × (5.5 feet)²

                      = 95.0332 ft²

Now, the average rate of change in the area as the radius changes from 2.5 to 5.5 feet is,

Average rate of change = (Change in the area)/(Change in radius)

                                         = (95.0332 ft² - 19.635 ft²) / (5.5 ft - 2.5 ft)

                                         = 25.1327ft² per ft

Hence, the average rate of change in the area as the radius changes from 2.5 to 5.5 feet is 25.1327ft² per ft.

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Answer:

a = 10

b = 15

Hope this is correct!!

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Answer:

divide by 2

Step-by-step explanation:

to find x you must divide 8 by 2.

Answer:

you divide 8 by 2

Step-by-step explanation:

To isolate the variable, x you need to divide by 2 on both sides so it cancels out the 2 on 2x and will divide 8 by 2=4

Answer:

AB is longer FD

Step-by-step explanation:

Given

See attachment for triangles ABC and FDE

Required

Compare line segments AB and FD

From the attachment, we have:

[tex]AC = FE[/tex] --- equal line segments

The measure of angles will then be used to compare the line segments;

[tex]\angle C = 72^o[/tex]

[tex]\angle F = 65^o[/tex]

The longer the angle of depression, the shorter the required line segment

[tex]72 > 65[/tex] implies that AB is longer

Answer:

C 3dge

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because line AB divided the triangle into two equal halves

Answer:

[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]

Answer:

[tex]8\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]

 [tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]

[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]

[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]

            [tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]

Use the height of the cone and the radius of the base to form a right triangle. Then, use the Pythagorean theorem to find the slant height.

Given:

The given equation is:

[tex]-3t^2+24t=h[/tex]

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

[tex]-3t^2+24t=h[/tex]

The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].

[tex]-3t^2+24t\geq 36[/tex]

[tex]-3t^2+24t-36\geq 0[/tex]

[tex]-3(t^2-8t+12)\geq 0[/tex]

Splitting the middle term, we get

[tex]-3(t^2-6t-2t+12)\geq 0[/tex]

[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]

[tex]-3(t-2)(t-6)\geq 0[/tex]

The critical points are:

[tex]-3(t-2)(t-6)=0[/tex]

[tex]t=2,6[/tex]

These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].

Intervals      Check point           [tex]-3(t-2)(t-6)\geq 0[/tex]           Result

[tex](-\infty,2)[/tex]               0                       [tex](-)(-)(-)=(-)<0[/tex]         False

[tex](2,6)[/tex]                    4                       [tex](-)(+)(-)=+>0[/tex]            True

[tex](6,\infty)[/tex]                  8                        [tex](-)(+)(+)=(-)<0[/tex]        False

The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.

[tex]6-2=4[/tex]

Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.

Answer:

7

Step-by-step explanation:

Using the definition

n[tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]

where n! = n(n - 1)(n - 2)..... 3 × 2 × 1

Then

7[tex]P_{1}[/tex] = [tex]\frac{7!}{(7-1)!}[/tex] = [tex]\frac{7!}{6!}[/tex] ← cancel out the multiples 6 ×5 × 4 × 3 × 2 × 1 , then

7[tex]P_{1}[/tex] = 7

Answer:

7 slices

Step-by-step explanation:

1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.

Answer:

0

Step-by-step explanation:

To calculate the slope or gradient we use this formula:

Slope = y2-y1/x2-x1

(-3,2) = (x1, y1)

(4,2) =  (x2, y2)

Slope = 2-2/4-(-3) = 0

Answer from Gauthmath

Answer:

[tex]we \: know \: that \: slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{2 - 2}{4 - - 3} \\ = \frac{0}{7} = 0 \\ slope \: = 0 \\ thank \: you[/tex]

Answer:

The probability that Aaron goes to the gym on exactly one of the two days is 0.74

Step-by-step explanation:

Let P(Aaron goes to the gym on exactly one of the two days) be the probability that Aaron goes to the gym on exactly one of the two days.

Then

P(Aaron goes to the gym on exactly one of the two days) =

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) +

P(Aaron doesn't go to the gym on Saturday and goes on Sunday)

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) =

P(the probability that Aaron goes to the gym on Saturday)×P(If Aaron goes to the gym on Saturday the probability that he does not go on Sunday)=

0.8×0.7=0.56

Thus, P(Aaron doesn't go to the gym on Saturday and goes on Sunday) = P(The probability that Aaron doesn't go to the gym on Saturday)×P(if Aaron does not go to the gym on Saturday the probability he goes on Sunday)

=0.2×0.9=0.18

Then

P(Aaron goes to the gym on exactly one of the two days) =0.56 + 0.18 =0.74

Answer:

10 digress when converted to nearest digree

9514 1404 393

Answer:

  22.09 ft²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr² . . . . where r is the radius, half the diameter

The slice, at 45°, is 1/8 of the circle, so the area of the slice is ...

  A = (1/8)π(15 ft/2)² = 225π/32 ft² ≈ 22.09 ft²