cos^4a=1/8(3+4cos2a+cos4a)​

Answer:

The maximum value of (2·x - 10) is 20

Step-by-step explanation:

Given that the maximum value of f(x) = 20

f(x) = -4·x² + bx + c

We are required to find the maximum value of (2·x - 10)

f'(x) = -8·x + b = 0

x = b/8

f''(x) = -8, therefore, f'(x) is the maximum point

20 = -4·x² +8·x²  + c

20 = -4·(b/8)² + b×(b/8) + c

20 = -b²/16 + b²/8 + c

20 = b²/16 + c

f(2·x - 10) = -4·(2·x - 10)² + b·(2·x - 10) + c

f(2·x - 10) = b·(2·x - 10) + c - (16·x²-160·x +400

Differentiating to find the maximum gives;

f'(2·x - 10) = d(b·(2·x - 10) + c - (16·x²-160·x +400)/dx = 2·b -32·x +160 = 0

x = (2·b +160)/32 = 0.0625·b +5

At the maximum point, therefore, we have;

b·(2·(0.0625·b +5) - 10) + c - (16·(0.0625·b +5)²-160·(0.0625·b +5) +400

At the max value of f(2·x - 10) = b²/16 + c

Since b²/16 + c = 20, we have the maximum value of (2·x - 10) = 20.

Answer:

nw to s so it makes it 2.1

Step-by-step explanation:

the answer 5.6

Answer:

Option (2)

Step-by-step explanation:

Let the equation of the line is,

y - y' = m(x - x')

where (x', y') is a point lying on the given line.

And m = slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Line given in the graph passes through two points (-5, -1) and (-2, -3).

Slope of the line 'm' = [tex]\frac{-3+1}{-2+5}[/tex]

                                 = [tex]-\frac{2}{3}[/tex]

Therefore, equation of the line passing through(-5, -1) and slope of the line = [tex]-\frac{2}{3}[/tex] will be,

y - (-1) = [tex]-\frac{2}{3}[x-(-5)][/tex]

[tex]y+1=-\frac{2}{3}(x+5)[/tex]

[tex]y=-\frac{2}{3}x-\frac{10}{3}-1[/tex]

[tex]y=-\frac{2}{3}x-\frac{13}{3}[/tex]

Option (2) will be the answer.

Answer:

if x>0 and y=0 the point is located on the x-axis

Answer:

x-axis on the right side

Step-by-step explanation:

the point (x,y) located on the x-axis

example x=1, y=0

Answer:

The question is incomplete. You can’t reduce 84 unless yo7 want it as a power of numbers. Most likely the question is a fraction or eqaaution

Step-by-step explanation:

Statement 1. [tex]\angle BCA\cong\angle DAC.[/tex]

Reason 1. Alternate interior angles formed when two parallel lines are cut by a transversal are congruent.

Statement 2. [tex]\overline{AC}\cong\overline{AC}.[/tex]

Reason 2. Reflexive congruence of segments (a segment is congruent to itself).

Statement 3. [tex]\triangle ACD \cong\triangle CAB.[/tex]

Reason 3. SAS congruence (using our two congruences above and the given congruence).

Statement 4. [tex]\angle ACD=\angle CAB.[/tex]

Reason 4. Corresponding parts of congruent triangles are congruent.

Statement 5. [tex]\overline{AB}\parallel\overline{CD}.[/tex]

Reason 5. If the alternate interior angles formed when two lines are cut by a transversal are congruent, then the lines are parallel.

Statement 6. [tex]ABCD[/tex] is a parallelogram.

Reason 6. The quadrilateral satisfies the definition of a parallelogram: a quadrilateral where both pairs of opposite sides are parallel.

Answer:

D. 10 feet

Step-by-step explanation:

40/8 = x/2 --> cross multiply

8x = 80

x = 10

Option D is correct, the person who casts a 2 feet shadow is 10 foot tall.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that At a certain time of day, a 40-foot building casts a 8 foot shadow.

We need to find how tall is a person who casts a 2 foot shadow.

Let x be the height of the person.

Let us form a proportional equation

40/8=x/2

Apply cross multiplication

80=8x

Divide both sides by 8

x=10

Hence, the person who casts a 2 foot shadow is 10 foot tall.

To learn more on Ratios click:

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Answer:

Option (D)

Step-by-step explanation:

Function in red is,

f(x) = x²

When a function f(x) is translated h units to the left, rule to be followed,

f(x) → f(x + h)

If the function is translated 2 units left,

Translated function (in blue) will be,

g(x) = (x + 2)²

Option (D) will be the answer.

Answer:

4

Step-by-step explanation:

We see that a point is (1, 4) so the answer is 4/1 = 4.

Hey there! :)

Answer:

Second choice: 4.

Step-by-step explanation:

The constant of proportionality is also the slope, or rate of change. The slope formula can be used to solve this problem:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in points from the graph into the equation.

[tex]m = \frac{4 - 0}{1 - 0}[/tex]

m = 4.

Therefore, the constant of proportionality is 4.

Answer:

f(3) = 8

Step-by-step explanation:

f(x) = 5x - 7

Put x as 3 and evaluate.

f(3) = 5(3) - 7

f(3) = 15 - 7

f(3) = 8

Answer: 8

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

[tex]\text{2, 1, 3, 1, 1}[/tex]

Step-by-step explanation:

[tex]\text{There are a total of 8 computers and 16 school-aged children,} \\\text{therefore there must be 2 children per computer.}\\\frac{16}{8}=2 \text{ (As shown)}\\\text{The families each with 4, 2, 6, 2, 2 children should get;}\\\text{2, 1, 3, 1, 1 computers respectively.}[/tex]

Answer: 9953/10000

Step-by-step explanation:

There is no simplifying this and this is the fraction it is at its least form!, Hope this helped!

<!> Brainliest is appreciated! <!>

Answer:

9953/10000

Step-by-step explanation:

0.9953 as a fraction is written as 9953/10000(nine-thousand fifty-three over ten-thousand)

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

y=9x

Step-by-step explanation:

(0,0),(1,9)

when x=0, y=0, means b=0

m is the slope =9

y=9x

Answer:

yes the answer is 9 on any question

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The area of the square can be calculated using S^2 = x^2

The area of the circle is pi * r^2

= 22/7 * (x-1)^2

= 22(x-1)^2/7

So we need the value of x, that will make;

x^2 = 22(x-1)^2/7

In this kind of scenario, since we have options, it is best to test values instead of going through long calculations

Let’s try 2.29

So;

2.29^2 = 22/7(2.29-1)^2

5.2441 = 5.23

So close , but let’s see if any other value will

give us a closer value

Let’s work with 1.66

1.66^2 = 22/7(1.66-1)^2

2.7556 = 1.369

This is far from what we need

Let’s try 0.5

0.5^2 = 22/7(0.5-1)^2

Thus gives a negative answer on the right hand side, so no need trying

And lastly 1.25

1.25^2 = 22/7(1.25-1)^2

1.5625 = 0.1946

So the first test still gives the most probable answer to a decimal place accuracy

Answer:

b. 2.29

Step-by-step explanation:

the answer above is correct please give them the brainiest  

Answer:

3x² + 1

Step-by-step explanation:

The perimeter is the sum of the exterior lengths of a polygon.

Here, the perimeter will be the sum of the lengths of the triangle. Two of them are given: 5x² + x - 4 and 3x + 2. Let's say the third side is A. Then, we know that:

P = 8x² + 4x - 1 = (5x² + x - 4) + (3x + 2) + A

On the right side, we have:

(5x² + x - 4) + (3x + 2) + A

5x² + 4x - 2 + A

This is equal to 8x² + 4x - 1:

5x² + 4x - 2 + A = 8x² + 4x - 1

Solve for A by isolating it:

A = (8x² + 4x - 1) - (5x² + 4x - 2) = 8x² + 4x - 1 - 5x² - 4x + 2 = 3x² + 1

The third side is thus 3x² - 1.

Answer:

(5+a)/ ( a-1)

Step-by-step explanation:

f(x) = ( 3+x) / (x-3)

Replace x with a+2

f(a+2) = ( 3+a+2) / (a+2-3)

Combine like terms

         = (5+a)/ ( a-1)

Answer:

C. (5+a)/(a-1)

Step-by-step explanation:

f(a+2)=(3+a+2)/(a+2-3)=(5+a)/(a-1)

I hope this helps you

Answer:

26 boys.

Step-by-step explanation:

You know that there are 36 students on the soccer team, and 19 are girls. 36 - 19 = 17. There are 17 boys on the track team.

There are 18 boys on the basketball team.

To find out how many boys are on the track team, all you need to do is...

61 - (17 + 18) = 61 - 35 = 26.

There are 26 boys on the track team.

Hope this helps!

Answer: 8435

Step-by-step explanation:

No. of girls = 4562 - 689 = 3873

Total strength = 4562 + 3873

= 8435

Answer:

8435

Step-by-step explanation:

Boys= 4562

Girls= 4562-689= 3873

Total= 4562+3873= 8435

Answer:

y=2(x+2)(x+3)

Step-by-step explanation:

First, we need to factor the right side:

y=2(x^2+5x+6)

Now, we can have an incomplete equation like this:

y=2(x+_)(x+_)

In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!

So, our factored form is

y=2(x+2)(x+3)

============================================================

The list of triangles are:

The diagram below is probably a better way to see all the triangles.

Step-by-step explanation:

Can you please attach the picture of the prism.

Answer:

360.124 in expanded and exponential form :

300+60+1/10+2/100+4/1000

Answer:

The x-intercept is the location on the graph when the output is 0.

f(x) > 0 is intervals of the domain where the graph is above the x-axis.

y-intercept is the location on the graph when the input is 0.

f(x) < 0 is intervals of the domain where the graph is below the x-axis.

The fourth:

The second equation in system 2 is the difference of the equations in system 1. The first equation in system 2 is the first equation in system 1.

Ax + By - (Lx + My) = Ax + By - Lx - My = (A - L)x + (B - M)y

Answer:

The answer is __

because of __

Step-by-step explanation:

Answer: b, c, and e

Step-by-step explanation:

I hope I helped

The standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have a table as given in the image attached at the end of answer.

The slope of the line will be -

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 2)/(- 4 + 10)

m = - 1/6

The standard form of the equation of straight line is given by -

y - y₂ = m(x - x₂)

y - 1 = -1/6(x + 4)

Therefore, the standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

To solve more questions on straight lines, visit the link below-

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[Refer to the image attached for complete question]

Answer:

Cheapest price is £25.38

Step-by-step explanation:

To determine the cheapest price that Sue can get the 10 rolls of wallpaper, calculate the cost of getting 10 rolls at each given price offer

=>Cost of getting 10 rolls at £9.21 per roll:

10 × £9.21 = £92.1

=>Cost of getting 10 rolls at £25.38 per pack of 3 rolls

£25.38 = 3 rolls

x = 10 rolls

x = (25.38*10)/3 = 253.8/3

10 rolls would cost x = £84.6

=>Cost of getting 10 rolls at £42.85 per pack of 5 rolls:

£42.85 = 5 rolls

x = 10 rolls

x = (10*42.85)/5 = 428.5/5

x = £85.7

From our calculation, getting 10 rolls at the price offer of £25.38 per pack of 3 rolls is the cheapest.

Therefore, the cheapest price is £25.38

Answer:

Not a function

Step-by-step explanation:

For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.

Answer:not a function

Step-by-step explanation:

because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers

Answer:

so the value of x is 8.3333≈8.3

Step-by-step explanation:

3x:10=5:2

[tex]\frac{3x}{10}=\frac{5}{2}[/tex]

by cross-multiplication

3x×2=5×10

6x=50

6x/6=50/6

x=8.33

i hope this will help you :)