Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
4
≤
x
≤
7
4≤x≤7.

Answer:

-3,6

Step-by-step explanation:

Answer:

By the Pythagorean theorem, it follows that the hypotenuse of this triangle has length c = √a2 + b2, the same as the hypotenuse of the first triangle. Since both triangles' sides are the same lengths a, b and c, the triangles are congruent and must have the same angles. ... If a2 + b2 = c2, then the triangle is right.

Step-by-step explanation:

Answer:

x  =  500 yd

y  =  250 yd

A(max) = 125000 yd²

Step-by-step explanation:

Let´s call x the side parallel to the stream ( only one side to be fenced )

y the other side of the rectangular area

Then the perimeter of the  rectangle  is  p  =  2*x  + 2* y  ( but only 1 x will be fenced)

p  =  x  +  2*y

1000  =  x   +  2 * y         ⇒    y  =  (1000 - x )/ 2

And   A(r)  =  x * y

Are as fuction of x

A(x)  =  x  *  (  1000  -  x ) / 2

A(x)  =   1000*x / 2 -  x² / 2

A´(x)  =  500  -  2*x/2

A´(x)  =  0              500   -  x   =  0

x  =  500 yd

To find out if this value will bring function A to a maximum value we get the second derivative

C´´(x)  =  -1         C´´(x) < 0  then efectevly we got a maximum at  x  = 500

The side  y  = ( 1000  -  x ) / 2

y  =  500/ 2

y  =  250 yd

A(max)  =  250 * 500

A(max) = 125000 yd²

Answer:

The cofunction of [tex]\tan \frac{2\pi}{11}[/tex] is [tex]\cot \frac{7\pi}{22}[/tex].

Step-by-step explanation:

In trigonometry, a function is a cofunction of another if and only if [tex]f(A) = g(B)[/tex], where A and B are complementary angles. In this case, the complementary function of a tangent function must be a cotangent function, this is:

[tex]\tan \frac{2\pi}{11} = \cot \left(\frac{\pi}{2} - \frac{2\pi}{11} \right)[/tex]

[tex]\tan \frac{2\pi}{11} = \cot \frac{7\pi}{22}[/tex]

[tex]\tan \frac{2\pi}{11} = \frac{1}{\tan \frac{7\pi}{22} }[/tex]

[tex]0.642 = \frac{1}{1.556}[/tex]

[tex]0.642 = 0.642[/tex]

Answer:

Correct

Step-by-step explanation:

4 + 3 = 7

1 + 6 = 7

Therefore the statement is true :)

Answer:

4+3=1+6 is correct

Step-by-step explanation:

4+3=7

1+6=7

Very complicated math lol

Answer:

-3

Step-by-step explanation:

The number 4 is the plotted point on the y-axis, meaning the next point would be located down 3 and right 1 (-3 over 1) and so on. The rise over run is the m in y=mx+b.

Answer:

[tex](a)\ h = d * \tan(\theta)[/tex]

[tex](b)\ h = 30.57m[/tex]

Step-by-step explanation:

Given

[tex]\theta = 17^o[/tex]

[tex]d =100m[/tex]

[tex]h = ??[/tex]

See attachment for illustration

Solving (a): Trigonometry ratio to calculate h.

From the attachment, we have:

[tex]\tan(\theta) = \frac{h}{d}[/tex]

Multiply both sides by d

[tex]d * \tan(\theta) = \frac{h}{d} * d[/tex]

[tex]d * \tan(\theta) = h[/tex]

Rewrite as:

[tex]h = d * \tan(\theta)[/tex]

Solving (b): The value of h

We have:

[tex]\theta = 17^o[/tex]

[tex]d =100m[/tex]

So:

[tex]h = 100m * \tan(17^o)[/tex]

[tex]h = 100m * 0.3057[/tex]

[tex]h = 30.57m[/tex]

Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}(4)(6)[/tex]

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

Answer:

Each friend pays $14 on lunch

Step-by-step explanation:

Answer: 3.9047 rounded to the nearest thousandth is 3.9050, or 3.905.

Step-by-step explanation:

You round 47 up to 50, which gets you to 3.9050, which you can then reduce it to 3.905.

Answer: $240

Step-by-step explanation:

Given

Ahmad earns 6 days daily from 9 am to 5 Pm at a rate of $30 per hour

The total no of hours he worked on a single day is 8 hours

So, the amount he earns on daily basis is

[tex]\Rightarrow 8\times 30\\\Rightarrow \$240[/tex]

Answer:

10.7

Step-by-step explanation:

use

a^2+b^2=c^2

...........

Answer:

x ≈ 10.72

Step-by-step explanation:

Use the Pythagorean Theorem, or

a² + b² = c²

to find x.

a² + b² = c²

9² + x² = 14²

81 + x² = 196

Subtract 81 from both sides.

x² = 115

Take the square root.

x = √115

When rounded to the nearest hundredth as a decimal, the answer is

x = 10.72.

Answer:

21.42 cloves of garlic

Step-by-step explanation:

50 ÷ 7 = 7.14

7.14 x 3 = 21.42

Answer:

They are similar because if you do the expression shown for the first expression it will equal the same thing since 6 x 4d = 24d and 6 x p = 6p

24d + 6p which is equivalent to 24d + 6p

You use the distributive property.

You have 6(4d + p) and 24d + 6p

the 6 is being multiplied into each number in the (), so it is basically

6 x 4d + 6 x p

that gives you 24d + 6p, which is why they are equal

Answer:

t  =  2.25 h

Step-by-step explanation:

In the case, I cover distance d in 3 hours

d =  3 * v₁      (1)

In the second case my speed increase by 1/3 then my speed is  

v₁ + (1/3) v₁   =  (3/3  + 1/3  ) *v₁

my new speed is   (4/3) * v₁  and

d  =  (4/3)*v₁ * t    (2)

Dividing (2) by  (1)  we get

1   = (4/3) *v₁*t/ 3*v₁

1  =  (4/9)*t

t = 9/4  h

t  =  2.25 h

look it up hare

sorry if it's not what your looking for

Answer:

2.44%

Step-by-step explanation:

[tex]\frac{22}{900} *100%[/tex]= 2.44%

Answer:

x=-15.2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

=2.5(6*4)/6

=2.5*4(6 and 6 gets cancel)

=10

Answer:

-15+3x=-7+5x

-15+7=5x-3x

-8=2x

-8/2=x

-4=x

6x=6*-4

=-24

Step-by-step explanation:

Answer:

[tex] - 15 + 3x = - 7 + 5x \\ 3x - 5x = - 7 + 15 \\ - 2x = + 8 \\ - x = 4 \\ x = - 4 \\ therefore = \\ 6x = 6 \times ( - 4) \\ 6x = - 24 \\ i \: hope \: this \: was \: helpful[/tex]

Answer:

-5 ; 1/2

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENERAL CONCEPTS TO BE USED IN THIS QUESTION :-

Lets say there's a quadratic polynomial f(x) = ax² + bx + c , whose factors are (x - α) & (x - β). To find the values of x for which f(x) will be zero , equate the factors of f(x) with 0.

⇒ (x - α) = 0 & (x - β) = 0

⇒ x = α & x = β

Hence, it can be concluded that if (x - α) & (x - β) are factors of f(x) , then α & β are the roots of f(x).

SOLUTION :-

Factorise f(x) = 2x² + 9x - 5.

[tex]=> 2x^2 + 10x - x - 5[/tex]

[tex]=> 2x(x + 5) - 1(x + 5)[/tex]

[tex]=> (x + 5)(2x - 1)[/tex]

So , the factors of f(x) are (x + 5) & (2x - 1). Now equate the factors with zero.

⇒ (x + 5) = 0 & (2x - 1) = 0

⇒ x = -5 & x = 1/2

∴ The zeroes of f(x) = 2x² + 9x - 5 are (-5) & (1/2)

VERIFICATION :-

1) Put x = -5 in f(x) = 2x² + 9x - 5

⇒ f(-5) = 2(-5)² + 9×(-5) - 5

           = 50 - 45 - 5

           = 50 - 50  

           = 0

2) Put x = 1/2 in f(x) = 2x² + 9x - 5

[tex]f(\frac{1}{2} ) = 2 \times (\frac{1}{2} )^2 + 9 \times \frac{1}{2} - 5[/tex]

       [tex]= 2 \times \frac{1}{4} + \frac{9}{2} - 5[/tex]

       [tex]= \frac{1}{2} + \frac{9}{2} - 5[/tex]

       [tex]= \frac{ 1 + 9 - 10}{2}[/tex]

       [tex]= \frac{0}{2}[/tex]

       [tex]= 0[/tex]

Answer:

Step-by-step explanation:

angle 1=130 degree(being alternate angles)

angle 2=50 degree

angle 2 +130=180 degree(being co interior angle)

angle 2=180-130

angle 2=50 degree

Answer:

m<1 = 50

m<2 = 130

Step-by-step explanation:

From the picture, you can inference that m<1 looks like 130 degrees, and m<2 does not. You can tell because m<1 looks like a wide-angle, while m<2 looks like a closed-angle. So, m<1 is 130 degrees.

To find m<2 subtract 180 by 130 because 180 is the measure of a straight angle.

180 - 130 = 50

So m<1 = 50

Answer:

C when multiplying negative numbers if you multiply a negative by a negative you get a positive.

Answer and Step-by-step explanation:

THE QUESTION IS NOT FROM A QUIZ, IT IS FROM A HOMEWORK ASSIGNMENT.

The unit rate is D. $4.00 per pound.

This is because we see on the graph that at 1 pound of fudge, the cost is 4 dollars.

When looking at the unit rate, you want to look at y value for when x is 1.

#teamtrees #PAW (Plant And Water)

Answer:

6 (24÷3) -2

6 (8) -2

48-2

=46

Brackets of division multiplication add and subtract

Answer:

Step-by-step explanation:

y=7(3)^-4

y=7*1/3^4

y=7/81