Given
h
(
x
)
=
−
x
−
4
h(x)=−x−4, find
h
(
−
6
)
h(−6).

The expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{x[/tex]

When the function is stretched horizontally by a factor of 2, the rule is:

f'(x) = f(x/2)

So, we have:

[tex]f'(x) = \sqrt{\frac x2[/tex]

When the function is shifted left by 1 unit, the rule is:

f"(x) = f(x + 1)

So, we have:

[tex]f"'(x) = \sqrt{\frac {x - 1}2[/tex]

When the function is shifted up by 3 units, the rule is:

g(x) = f"(x) + 3

So, we have:

[tex]g(x) = \sqrt{\frac {x - 1}2} + 3[/tex]

Hence, the expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the slope of a line passing through (-2,-7) and (-2,2)

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{6cm} To find the slope, \\ we use the formula below.\end{minipage}}[/tex]

[tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex]   | put in the values

[tex]\bf{\dfrac{2-(-7)}{-2-(-2)}}[/tex] | look what happens when I simplify!

[tex]\bf{\dfrac{2+7}{-2+2}}[/tex] | uh-oh

[tex]\bf{\dfrac{9}{0}}[/tex] ...

The operation above is an operation we can't do.

[tex]\bf{Slope=\;Not\;D e f ined}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=Slope=Not\;De fined}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

The average rate of change is illustrated below.

The average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a).

In this case the interval is [0,2], then a=0, b=2

r=[f(2)-f(0)]/(2-0)

r=[f(2)-f(0)]/2

1) First function: h(x)

r=[h(2)-h(0)]/2

x=2→h(2)=(2)^2+2(2)-6

h(2)=4+4-6

h(2)=2

x=0→h(0)=(0)^2+2(0)-6

h(0)=0+0-6

h(0)=-6

r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(2+6)/2

r=(8)/2

r=4

2) Second function: f(x)

A function, f, has an

x-intercept at (2,0)→x=2, f(2)=0

and a y-intercept at (0,-10)→x=0, f(0)=-10

r=[f(2)-f(0)]/2

r=[0-(-10)]/2

r=(0+10)/2

r=(10)/2

r=5

3) Third function: g(x)

r=[g(2)-g(0)]/2

From the graph:

g(2)=6

g(0)=2

r=(6-2)/2

r=(4)/2

r=2

4) Fourth function: j(x)

r=[j(2)-j(0)]/2

From the table:

x=2→j(2)=-8

x=0→j(0)=4

r=(-8-4)/2

r=(-12)/2

r=-6

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The rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min. Computed using differentiation.

The sand is falling onto a conical pile, thus we get the pile in the shape of a cone, whose volume is given as:

V = (1/3)πr²h,

where V represents the volume of the cone, r represents its radius, and h represents its height.

In the question, we are given that the rate of piling is 16 ft.³/min, which implies that:

dV/dt = 16 ... (i)

We are also given that the diameter is three times the altitude (height), which can be shown as:

2r = 3h,

or, r  = (3/2)h.

Thus, the volume can now be shown as:

V = (1/3)π{(3/2)h}²h,

or, V = (3πh³)/4.

Differentiating this with respect to time, we get:

dV/dt = (3π/4)(3h²)dh/dt.

Now, we need to calculate the rate of change of height, when the height is  2 feet, thus we take h = 2

Using dV/dt = 16 from (i), we can write:

16 = (3π/4)(3(2)²)dh/dt.,

or, 16 = 9π(dh/dt),

or, dh/dt = 16/9π = 0.5659 ft./min.

Thus, the rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min.

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The next term in the sequence is -1.

Given a sequence is defined recursively by the formula f(n+1)=f(n)+3.

An ordered list of integers that frequently follows a pattern or function is known as a sequence. Sequences can have a finite or indefinite length. Terms refer to the distinct components of a sequence. The individual numbers or parts that make up a sequence are known as its terms.

The first term of the sequence is -4.

That means f(1)=-4            .......(1)

When compare f(1) with f(n+1), we get

n=0

So, when n=0 then it is the first term of the sequence.

When n=1 then substituting this in the given formula, we get

f(1+1)=f(1)+3

f(2)=f(1)+3

Now, Substitute the value of f(1) from equation (1), we get

f(2)=-4+3

f(2)=-1

Hence, the next term in the sequence when the sequence is defined recursively by the formula f(n+1) = f(n)+3 and the first term of the sequence is –4 is -1.

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Answer:

8

Step-by-step explanation:

because there is 8 in the question

The 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.

Given that the perimeter of the triangle is 44 cm.

Let us consider a side 's' which is 4 cm shorter than the second side.

That means the second side is 4 cm longer than s, hence the second side is s+4 cm in length.

We also have that the side of length s is of length twice as long as the third side.

Hence, the length of the third side is half that of s so, it is of length s/2.

Hence, at the end 44=s+(s+4)+(s/2)=s(2+1/2)+4

⇒ s(5/2)=40

⇒ s=8*2=16

So, the 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.

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Answer:

Step-by-step explanation:

A triangle with side lengths of 5 meters, 7 meters and 9 meters is

an obtuse triangle

Answer:

x^2=9

so we find the sqare root of both sides

x=square root of 9

x=-3 or 3

Hope This Helps!!!

Answer:

ok sure will do the answer is

Step-by-step explanation:

Answer:

He will need to pay 5.4 Ghana cedis into his educational fund.

Step-by-step explanation:

We need to multiply 4 1/2 by 120 since it is a percentage. We convert 4 1/2 into a decimal which is 4.5. Now, we just need to multiply 120 by 4 1/2 to get an answer of 5.4.

On the base of visual inspection , it can be said that the Group A has an average lower than the Group B

It is the simple form of data visualization , in which the frequency of a data is marked as dots on x and y axis.

The dot plot is given for two groups of 30 people , who go to painting class.

It has been asked that which group most likely has a lower mean age of painting students .

On the base of visual inspection , it can be said that the Group A has an average lower than the Group B

It can be said so as the dots are highest at the age of 19 in Group A , and the whole distribution lies between 9 to 19 age of people ,

while in Group B the age of the people is wide distributed and therefore the average age will be more ,

By calculation it is proved that the average age of Group A is 15.967

and the average age of Group B is 19.7.

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The probability they choose a black and a brown puppy is 0.2857 (option B)

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability they choose a black and a brown puppy = (number of black puppies / total number of puppies) x ( (number of brown puppies / total number of puppies - 1)

3/7 x 4/6 = 0.2857

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First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.

Given  four definitions of equation, expression, algorithm but mixed.

We have to match the definitions with appropriate term.

We know that expression is a combination of numbers, symbols, fraction, coefficients, indeterminants mostly not found in equal to form. It exhibits a behaviour only.

Algorithm is a computer programming to do a specific task in a predetermined way.

Equation is a relationship between two variables expressed in equal to form. In this we have to put the value of variables and the equation gives us a value.

Hence  First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.

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Answer:

First Question x = [tex]17\sqrt{2}[/tex] Second Question x = 36

Step-by-step explanation:

First Question:

Since The triangle is isosceles, [tex]17^2 +17^2=x^2[/tex] (Pythagoras)

[tex]x=17\sqrt{2}[/tex]

Second Question

This is half an equilateral triangle, so [tex](\frac{1}{2}x)^2+(18\sqrt{3})^2=x^2[/tex]

[tex]\frac{3}{4}x^2=972[/tex]

[tex]x^2=1296[/tex]

[tex]x=36[/tex] (cannot be negative)

Answer:

5x+8

Step-by-step explanation:

The from is the key word

That means the second term is first

6x^2 -2x +6 - (6x^2 -7x -2)

Distribute the minus sign

6x^2 -2x +6 - 6x^2 +7x +2

Combine like terms

5x+8

No, it isn't true that blending problems arise when one must decide which of two or more ingredients is to be chosen to provide a product.

Given sentence "Blending problems ...............................supply a product."

We have to answer whether the given sentence is true or false.

We can say that the given sentence is fake. the sole objective functions allowed for applied math problems maximizing profits and minimizing costs.

Blinding problems are a typical application of mixed integer applied mathematics. They involve blending several resources or materials to make one or more products similar to a requirement. Mixed integer linear programs are linear problems during which some variables are required to require integer values.

Hence the given statement is fake regarding arise of blending problems.

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Question is incomplete because it should includes:

State whether the statement is true or false.

Answer:

3(n-5)=2n+16

Step-by-step explanation:

3 lots of 'n' and 5 means 3 times both values so these values are put into a bracket with a common multiplier (ie. the 3)

3(5 - n)

16 more than 2 lots of 'n' means that n has to be doubled. n + n = 2n. add 16 to this and we have

2n + 16

if these values are both equal (hence why they are in an equation) then all that is needed is for them to be set equal alongside each other.

3(n-5) = 2n+16

:)

The length of one leg of the right triangle is 5√10

The leg of a right triangle can be found as follows;

Therefore, using trigonometric ratios,

sin 45 = opposite / hypotenuse

sin 45 = x / 10√5

1 / √2 = x / 10√5

cross multiply

10√5 = x√2

divide both sides by √2

x = 10√5 / √2

x = 10√5 / √2 × √2 / √2

x = 10√10 / 2 = 5√10

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Answer:

10.63 inches

(b)2+(h)2=(H)2

(8)2+(7)2=(H)2

64+49=(H)2

113=(H)2

H=10.63

The diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

The diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

In the question, we are asked to determine the diagonal length of the photo frame bought by Mike, having measurements of 8 inches in length and 7 inches in width.

We know the photo frame is in the shape of a rectangle, as it has a length and a width.

We also know that the diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

So, by substituting l = 8 and w = 7, in the above relation, we can calculate the diagonal of the photo frame as:

d = √(8² + 7²),

or, d = √(64 + 49),

or, d = √113,

or, d = 10.63.

Therefore, the diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

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1) [tex]\overline{AC} \cong \overline{BD}[/tex] and [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)

2) [tex]ABCD[/tex] is a parallelogram (a quadrilateral with diagonals that bisect each other is a parallelogram)

3) [tex]ABCD[/tex] is a rhombus (a parallelgoram with congruent diagonals is a rhombus)

4) [tex]\overline{BE} \cong \overline{EC}[/tex] (halves of congruent segments are congruent)

Answer:

B The vertex is at (2,2)

Or could possibly be

C the axis of symmetry is x=2

Answer:

z=15

Step-by-step explanation:

z-7+7=8+7 ( add 7 on btoh sides to cancel out)

z=15 ( left with 7)

Answer:

a) 50 meters

b) 2354 meters

c) 12 seconds

d) 24.13 seconds

Step-by-step explanation:

Hello!

We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.

Equation: [tex]h = -16t^2 + 384t + 50[/tex]

Plug in 0 for t:

The height at which Lincoln shot the bullet is 50 meters.

We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.

Standard form of a Parabola: [tex]y = ax^2 + bx + c[/tex]

The y-intercept is the "c" value.

Given our equation: [tex]h = -16t^2 + 384t + 50[/tex]

The c-value is 50. This proves that the y-intercept is 50.

We want to find the highest point of the graph. To do that, we can find the vertex.

We can utilize the Axis of Symmetry (AOS) to find the Vertex.

First, find the AOS using the formula: [tex]AOS = -\frac{b}{2a}[/tex]

Plug it into the formula:

Plug in 12 for t in the equation:

Therefore, the highest point of the bullet is 2354 meters.

We answered this in the last question. The t-value when h is at its highest is 12.

We have to solve for the values of t when h is 0 (when it touches the ground).

Set the equation to 0, and solve using the quadratic formula.

Quadratic formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.

It takes approximately 24.13 seconds for the bullet to hit the ground.

Answer:

-5 and 6

Step-by-step explanation:

-5 * 6 = -30

-5 + 6 = 1

The area of the sector rounded to 4 decimal place is 78.6396 cm²

area of sector = ∅/ 360 × πr²

Therefore,

Hence,

area of a sector = 46 / 360 × 3.14 × 14²

area of a sector = 46 / 360 × 3.14 × 196

area of a sector =   46 / 360 × 615.44

area of a sector =   28310.24 / 360

area of a sector = 78.6395555556

Hence,

area of a sector = 78.6396 cm²

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A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The length of Jk can be either 10 or 26.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Since in a rectangle the opposite sides are equal, therefore, the sides NM and JK will be equal.

JK = MN

8x - 14 = x² + 1

0 = x² - 8x + 15

x = 5, 3

Hence, the length of Jk can be either 10 or 26.

The complete questions are:

Quadrilateral JKMN is a rectangle, if NM= 8x - 14 and JK= x squared + 1, find JK.

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Step-by-step explanation: