if a+ b = 5 ( a and b positive), find the maximum value of a² + b²​

Answer:

Step-by-step explanation:

The graph that represents the function

f(x) = (x + 4)(x + 1)(x - 3)

crosses the x-axis three times: at x = -4, x = -1, and x = 3

because we apply the zero product rule and found the roots -4, -1, and 3

x+ 4= 0 → x = -4

x+1 = 0 → x = -1

x-3 = 0 → x = 3

Triangle ABC is an equilateral triangle. it is equiangular. Therefore, the value of x is 60 degrees.

An equilateral triangle is a triangle that has all it sides and angles equal to each other.

An equilateral triangle is equiangular.

Therefore, the angles of an equilateral triangles are equal to 60 degree each.

Recall the sum of an angle of a triangle is 180 degrees.

Therefore, the value of angle x is 60 degrees.

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Answer:

[tex]\sf \boxed{\bold{x=1}}[/tex]

Explanation:

[tex]\rightarrow \sf 7 log_9 (x + 8) = 7[/tex]

divide both sides by 7

[tex]\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}[/tex]

simplify the following

[tex]\sf \rightarrow \log _9\left(x+8\right)=1[/tex]

apply log rules                   [tex]\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c[/tex]

[tex]\sf \rightarrow x+8 = 9^1[/tex]

simplify

[tex]\sf \rightarrow x+8=9[/tex]

subtract both sides by 8

[tex]\sf \rightarrow x=1[/tex]

[tex]\\ \rm\Rrightarrow 7log_9(x+8)=7[/tex]

[tex]\\ \rm\Rrightarrow log_9(x+8)=1[/tex]

[tex]\\ \rm\Rrightarrow x+8=9^1[/tex]

[tex]\\ \rm\Rrightarrow x+8=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-8[/tex]

[tex]\\ \rm\Rrightarrow x=1[/tex]

Answer:

y= 1/5 x -1

Step-by-step explanation:

Find two points ( any two of the three given)

find the slope between   5,0   and   10, 1

    ( 1-0)/(10-5)   = m = slope   = 1/5

so the line is of the form   y = mx + b :

                                            y = 1/5 x + b     sub in any point to calculate 'b'

                                             1 = 1/5 (10) + b

                                                    b = -1

y = 1/5 x -1   is your answer

Answer:

I believe rectangle.

Step-by-step explanation:

=4(xy−4)

3xy−x

=x(3y−1)

2x²−18x+12

=2(x²−9x+6)

5xy+20x−9y−36

=(y+4)(5x−9)

Answer:

the first option, LON and NOP

Step-by-step explanation:

adjacent angles are side by side and cannot overlap

Answer:

1) angle LOM and angle MON

2) A. angle LON and angle NOP

Answer:

  a)  1.6×10⁻⁶

  b)  2×10⁷

Step-by-step explanation:

You want the product or quotient in standard form of ...

The rules of exponents apply:

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

A number is said to be in scientific notation if there is one digit to the left of the decimal point, and the multiplier is expressed to an appropriate power of 10. The power of 10 may need to be adjusted so the decimal point is in the correct place. In general, the power of 10 represents the place value of that most-significant digit.

In the US, a number is written in standard form as a sequence of digits with an optional decimal point. Integers are written so the least-significant digit has a place-value of 1.

Elsewhere, a number is written in standard form when it is written in scientific notation.

We have given both forms a number here, so you will need to choose the one that is standard form where you are.

The product is (8×2)×10^(-3-4) = 16×10^-7 = 1.6×10^-6

= 0.0000016

The quotient is (6/3)×10^(2-(-5)) = 2×10^7

= 20,000,000

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Answer:

7.5

Step-by-step explanation:

The median is the middle of a set of numbers. In this case, the median is 7.5.

Answer:

Jeremy is 12 years old

Step-by-step explanation:

Jeremy age=X

Sister age=Y

1. X+Y=29 (sum of their ages)

2. X=Y-5 (he is 5 years younger than his sister)

*Substitute eq 2 into eq 1

Y-5+Y=29

2Y=29+5

2Y=36 (divide both sides by 2)

Y =17

Substitute value of Y into eq 1 to find X

X+17=29

X=29-17

X= 12

Checking answer:

12+17=29

17-5=12

Hence why Jeremy is 12

The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees is 0.18.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

In a large company, 45% of the employees wear khaki pants on a daily basis.

40% of employees wearing khaki pants in a random sample of 50 employees

So, 40% of 45% x 50

= [tex]0.40 \times 0.45 \times 50 \\ \\9[/tex]

The probability of getting less than 40% of employees wearing khaki pants in a random sample of 50 employees.

= 9 /50

= 0.18

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Answer:

The answer is given in the picture

Step-by-step explanation:

LET ME KNOW IF YOU NEED EXPLANATION

Step-by-step explanation:

((8x⁶)²)⅙ = (64x¹²)⅙

= (2⁶x¹²)⅙

= 2x²

(625x⁸)¼ = (5⁴x⁸)¼

= 5x²

2x²/5x² = 2/5

Answer:

Surface Area = 96

Step-by-step explanation:

Area of Triangle: Area = 1/2 * Base * Height

Area = 1/2 * 6 * 2 = 6

Area = 6

Area of Rectange: Area = Length * Height

Area = 7 * 3 = 21

Area = 7 * 6 = 42

Area = 21

Surface Area = TopTri + BotTri + LeftRect + MidRect + RightRect

Surface Area = 6 + 6 + 21 + 42 + 21 = 96

Answer:

The answer is True.

Step-by-step explanation:

Step-by-step explanation:

Im maybe wrong but it might be that morgan earns morgans hourly rate on friday is 12$

Answer: The answer to this is 3000,

Step-by-step explanation:  

I think this is the answer because when you find out what 20% of 75000 is, (which is 15000) you can divide 20% by 5 and there is your answer, i hope this helps

Answer:

the answer is B, the graph of g(x) is the graph of f(x) shifted to the right 6 units. hope this helps!

Answer:

C. The graph of g(x) is the graph of f(x) shifted to the left 6 units.

Hope this helps and good luck!

Answer:

31.4 inches

Step-by-step explanation:

36+144 = 180

sqrt(180) = 13.41

6 + 12 + 13.4

The equation n = 30/t is an illustration of an inverse variation

The points on the graph are: (1,30), (2,15), (3,10) and (4,7.5)

The equation is given as:

n = 30/t

When t = 1, we have:

n = 30/1

n = 30

When t = 2, we have:

n = 30/2

n = 15

When t = 3, we have:

n = 30/3

n = 10

When t = 4, we have:

n = 30/4

n = 7.5

So the points on the graph are:

(1,30), (2,15), (3,10) and (4,7.5)

See attachment for the graph of the equation n = 30/t

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the answer is a x equal to or greater than

Answer:

13 dollars would be the answer you're welcome lol

Answer:

C

Step-by-step explanation:

Answer:

$14.55

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

-45 minus 35 is -80 so that's  80 units. and including zero it's 81 units

Answer:

y-intercept= (0,7) and rate of change=

Step-by-step explanation:

The y-intercept of a graph is the point on the graph where it intersects the y-axis or where x=0. In this case it is (0,7) so that is the y-intercept. The rate of change is equal to y2-y1 divided by x2-x1. Basically, just pick 2 random points on the line and subtract their y coordinates, then subtract their x-coordinates and divide the answers with each other. So, one point is (0,7) and another point is (2,4). Therefore, rate of change is 7-4 divided by 0-2. This gives us a rate of change of -3/2

The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent

The angle BAE is a vertex angle, and it is calculated using:

BAE = 180 * (n - 2)/n

Where n= 5; i.e. the number of sides.

This gives:

BAE = 180 * (5 - 2)/5

Evaluate

BAE = 108°

Hence, the measure of angle BAE is 108°

When the vertices A and B are joined together, the shape becomes a trapezoid.

Hence, the name of the quadrilateral ABCD is a trapezoid.

See attachment for the new figure.

From the attached figure, we have:

∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line

Where:

∠EDC = ∠BAE = 108°

So, we have:

∠EDX + 108° = 180°

Subtract 108° from both sides

∠EDX = 72°

Hence, the measure of angle EDX is 72 degrees

The quadrilateral BDXE is a parallelogram.

This is so because the opposite sides of BDXE are parallel, but not congruent

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Answer:

DE=18

Step-by-step explanation:

The reason is because that parallelogram ABCD has most of the sides equal to each other.

The length of DB = 36 and half of 36/2 gets us DE.

DE=36/2=18

DE=18 also equals to BE=18

Diagonals of a parallelogram bisect each other

So

Putting DE=BE

Answer:

The value of a side = 5

Step-by-step explanation:

By using PGT theoram

H² = P² + B²

=> 13² = a² + 12²

=> 13² - 12² = a²

=> 169 -144 = a²

=> 25 = a²

=> √25 = a

=> 5 = a

Answer:

a = 5

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

a² + 12² = 13²

a² + 144 = 169 ( subtract 144 from both sides )

a² = 25 ( take square root of both sides )

a = [tex]\sqrt{25}[/tex] = 5

Answer:

96

Step-by-step explanation:

2 x 8 =16

8 x 7 = 56

3 x 8 = 24

24 + 56 = 80

80 + 16 = 96

Hi!

The area of the entire figure is 76 units squared.

NOTE: This question has two different shapes: a rectangle, and a triangle.

Rectangle Formula:

Length * Width = Area

[tex]LW=A[/tex]

Triangle Formula

(Base * Height) / 2 = Area

[tex]\cfrac{bh}{2}=A[/tex]

Let's first get the rectangle's area:

[tex]LW=A[/tex]

[tex]8*7=A[/tex]

[tex]56=A[/tex]

The area of the rectangle is 56.

Now, for the top triangle:

[tex]\cfrac{bh}{2} =A[/tex]

[tex]\cfrac{8*2}{2} =A[/tex]

[tex]8=A[/tex]

The area of the top triangle is 8.

Now, for the bottom triangle.

[tex]\cfrac{bh}{2} =A[/tex]

[tex]\cfrac{8*3}{2} =A[/tex]

[tex]12=A[/tex]

The area of the bottom triangle is 12.

Now, add them all together:

[tex]56+8+12=76[/tex]