what is -27/40 as a decimal number. AND NO LINKS pls and thank you :)

Answer:

Part 1)

[tex]\displaystyle \left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)[/tex]

Or simplified:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Part 2)

The value of x for which the given expression will be the lowest is:

[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]

And the magnitude of ∠BAC is 60°.

Step-by-step explanation:

We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.

Please refer to the diagram below.

Part 1)

Since we know that the area of the triangle is one:

[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]

Simplify:

[tex]\displaystyle CD = 1[/tex]

From the Pythagorean Theorem:

[tex]\displaystyle x^2 + CD^2 = b^2[/tex]

Substitute:

[tex]x^2 + 1 = b^2[/tex]

BD will simply be (2 - x). From the Pythagorean Theorem:

[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]

Substitute:  

[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]

We have the expression:

[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]

Substitute:

[tex]\displaystyle = \boxed{\left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)}[/tex]

Part 2)

We can simplify the expression. Expand and distribute:

[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]

Simplify:

[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]

Simplify:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 2√3, b = -4, and c = (4 + 2√3).

Therefore, the x-coordinate of the vertex is:

[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]

Hence, the value of x at which our expression will be the lowest is at √3/3.

To find ∠BAC, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]

Therefore:

[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]

Answer:

A

Step-by-step explanation:

4(1)+4(9x)=4+36x

Answer:

Step-by-step explanation:

We can see that there are roots at (-2,0) and (-1,0)

also, the root at (-2,0) should bounce right off

and the root at (-1,0) should go through

With all that being said it has to be B

you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,

131000/100 = 1310 x 3 = 3930

the commission is $3930.00

hope it helps :)

Answer:

Not similar.

Step-by-step explanation:

The answer is D.

Answer:

There are 3 possible values for a.

Step-by-step explanation:

a/b=2/3

3a=2b

If b>5 and b<13

apply all possible values

b=6 -> 3a=12 ==> a=4 1st possibility

b=7 -> 3a=14 ==> a=4.something Not a possibility

b=8 -> 3a=16 ==> a=5.something Not a possibility

b=9 -> 3a=18 ==> a=6 2nd possibility

b=10 -> 3a=20 ==> a=6.something Not a possibility

b=11 -> 3a=22 ==> a=7.something Not a possibility

b=12 -> 3a=24 ==> a=8  3rd possibility

Answer:

5 trees per day

Step-by-step explanation:

Answer:

5 trees per day

Step-by-step explanation:

(1, 5)

(2,10)

the day increases by 1 and the trees increase by 5

Answer:

It is expected that linearization beyond age 20 will be use a function whose slope is monotonously decreasing.

Step-by-step explanation:

The linearization of the data by first order polynomials may be reasonable for the set of values of age between ages from 5 to 15 years, but it is inadequate beyond, since the fourth point, located at [tex](x,y) = (20, 5.5)[/tex], in growing at a lower slope. It is expected that function will be monotonously decreasing and we need to use models alternative to first order polynomials as either second order polynomic models or exponential models.

Answer:

-6

Step-by-step explanation:

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

=( -1 )(6)

= -6

Answer:

8 munutes

Step-by-step explanation:

let :

x is the final level for both tanks (in ft) and

t is the time (in minutes)

the equation :

x = 6 - 0.5 t (eq.1)

x = 10 - 1t (eq.2)

eq. 1 = eq. 2

=>

6-0.5t = 10-1t

1t - 0.5t = 10-6

0.5t = 4

t = 4/0.5 = 8

t = 8 minutes

Answer:               8 minutes

Step-by-step explanation:

Write an equation for the level of oil in each tank.

Let t = the number of minutes.

Tank A: y = 6 − 0.5t

Tank B: y = 10 − 1t

Solve the system by using a table of values

When t = 8 minutes, the level in both tanks will be at 2 feet.

Answer: Rational

This is because the number is in the form P/Q where P and Q are integers

We have P = -13 and Q = 12.

You can think of "rational" as in "ratio" which is very closely tied to fractions. Any rational number is a fraction of two integers. The denominator can never be zero.

Answer:

Rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Decimal form: − 1.08 3

3 repeats itself, so it's rational.

Answer:

7π + 7π + 196 ( could also be 14π + 196)

Step-by-step explanation:

14 is the length of the square. However it is also the diameter of the circle.

If you do diameter x π you will get the circumfrance. Which in this case is 14π. If your trying to find half of the circumfrance you would do 14π ÷ 2 which is 7π.

After finding 7π for one half a circle you do the same for the other and also get 7π

After finding the 2 half circles find the square which is 14 x 14 = 196

196 + 7π + 7π if you don't want bother pi's there it could also be seen as 196+ 14 π

Step-by-step explanation:

Part A: Linear Equation.

We can find the slope

[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]

So our equation is

[tex]y = - 10x + 15[/tex]

Part B: Exponential Equation

We know that

[tex]15 = a \times b {}^{0} [/tex]

B to the zero power is 1 so

[tex]15 = a[/tex]

This means a =15. Now let find b.

[tex]5 = 15 \times b {}^{1} [/tex]

[tex] \frac{1}{3} = b[/tex]

So the equation is

[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]

Answer:

-3 < x <= 3

Step-by-step explanation:

draw it on a number line to check

Answer:

-3>x[tex]\leq \\[/tex]3

Step-by-step explanation:

> is the greater than

< is the less than

hope this helped have a great day

Answer:

[tex]6(6+4)=5(5+x)[/tex]

[tex]6(10)=5(5+x)[/tex]

[tex]60=5(5+x)[/tex]

[tex]12=5+x[/tex]

[tex]x=7[/tex]

~OAmalOHopeO

Answer: 62

Step-by-step explanation:

[tex]\displaystyle\bf 9x^2-4x-7 =0 \\\\ Synthetic \ \ division\ \ if \ \ x-3 =0 => x=3 \\\\ then \ \ 3| \underline{ \ 9 \ | \ -4 \ | \ -7 \ | } \\\\ . \!\! \qquad\qquad +|3*9| \ \ 23*3 | \\ .\!\!\!\!\!\1 \qquad \qquad \qquad | \ 23 \ | \ \ \ \boxed{62}[/tex]

Answer:

Step-by-step explanation:

This is classic right triangle trig. If you're solving for x, which you are, you have to consider how the given sides relate to that angle. The side with a length of 50 is opposite the angle x, while the side of length 36 is adjacent to angle x. The trig ratio that utilizes the sides opposite and adjacent is tangent; HOWEVER, we are looking for a missing angle. Finding missing angles on your calculator requires the 2nd button. To find the missing angle x, you are looking for the angle that has a tangent ratio of 50 over 36 (opposite over adjacent...Toa in SohCahToa). Hit the 2nd button on your calculator and then the tangent button (in degree mode, not radian mode) and you will see this on your screen:

[tex]tan^{-1}([/tex]

After the parenthesis, enter the fraction and then hit the enter button to get the angle measure in degrees:

[tex]tan^{-1}(\frac{50}{36})=54.2[/tex] degrees.

It's very important that you learn how to use your calculator to find the trig identities that give you the ratio in decimal form and how to find the missing angles. Missing angles always use the 2nd button along with whatever trig identity you are using.

Answer: 16x^2 + 24x + 9

Step-by-step explanation:

Simplified version: (4x+3)^2

Pay per shelf = $3.25

No of shelfs per hour = 5

Total hours per day = 8

Total days to find pay of = 7

= 3.25×5×8×7

= 910

Therefore she is paid $910 after 1 week.

Must click thanks and mark brainliest

Answer: m = 3.89

Step-by-step explanation:

(3m/5)+(m/2) =(4/1)+(2/5)

= (taking LCM) (6m+5m)/10 = (20+1)/5

or, 11m/10 = 21/5

or, 55m = 210

or, m = 210/55

so, m = 3.89

Answer:

B

Step-by-step explanation:

option B is not similar.

the ratio of each side isn't same

Answer:

25

Step-by-step explanation:

Step-by-step explanation:

given that the coordinate is (0,1)(4,3)

x¹=0, y¹=1, x²=4 y²=3

M=> Gradient => (y²-y¹)/(x²-x¹)

M=(3-1)/(4-0) => 1/2

Therefore the slope-intercept equation

M=(y-y¹)/(x-x¹)

1/2 = (y-1)/(x-0)

x=2y-2

2y=-2-x

y=-x/2 - 1

The volume of a cube is Side ^3

Find the cubic root of the volume to find the side length:

Side = cubicroot(216) = 6 feet.

The area of a face of a cube is s^2

Area of a face = 6^2 = 36 square feet.

Area of 2 faces = 36 x 2 = 72 square feet

Answer: 72 square feet

Answer:

72 ft²

Step-by-step explanation:

To find the length of each side we have to cube root the volume

∛216 = 6

We only have to find the areas for two faces (the top and bottom)

6 x 6 = 36 = area for one face

36 x 2 = 72 = area for two faces

Answer:

the answer is (10,35)

Step-by-step explanation:

i took the quiz and im 100% sure

ty have a great day :)

Answer:

y = 4.8(x) + 0

Step-by-step explanation:

In this question, Javier managed to print 240 brochures in 50minutes from 8:00 to 8:50. If we divide these values we see that he printed 4.8 brochures per minute. The same result is given for the 10 minutes from 8:50 to 9:00 where he printed 48 brochures. Therefore, we can get the following linear formula from these values.

y = 4.8(x) + 0

In this case, b would equal 0 because Javier is starting from 0 brochures made when he gets to work at 8:00 a.m

Answer:

Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up