How do I put this into standard form??
.215(x+1.862)(x-2.862)

[tex]\\ \rm\rightarrowtail \dfrac{sin(180+A)+2cos(180+A).cos(A-180)}{2cos^2(360+A)-cos(-A)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2(cos^2A-sin^2A)}{2cos^2A-cosA}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2cos^2A-2sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2-2sin^2A-2sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA-4sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA(4sinA-1)}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail -tanA\left(\dfrac{4sinA-1}{2cosA-1}\right)[/tex]

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, We have

The given function represents the total distance in miles covered by the traveller.

For initial interval that is x = 1 , Distance covered by the traveller

[tex]\sf{ f(x) = -45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(1) + 270 }[/tex]

[tex]\sf{ f(1) = - 45 + 270 }[/tex]

[tex]\sf{ f(1) = 225 }[/tex]

For final interval that is x = 3, Distance covered by the traveller

[tex]\sf{ f(x) = - 45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(3) + 270 }[/tex]

[tex]\sf{ f(1) = - 135 + 270 }[/tex]

We have to find the average rate of change over the given time interval

Average rate of change in the given time interval

[tex]\sf{ = }{\sf{\dfrac{ f(1) + f(3) }{3 - 1}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 + ( -135) }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 - 135 }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 90 }{ 2}}}[/tex]

[tex]\sf{ = 45 }[/tex]

Hence, The average rate of change over the given interval is 45 miles per hour.

Answer:

40%

Step-by-step explanation:

6.75 + 1.25 = 8 (Total she just spent)

8 (Total she just spent) + 12 (Total she had left) = 20 (Total she started with)

8/20 = 0.4 = 40%

(Total spent / total she started with = 40%)

Answer:

(0.5, -3)

Step-by-step explanation:

(-3, -1) (4, -5)

midpoint formula

(x1 + x2) /2, (y1 + y2) /2

-3 + 4 = 1 / 2 = 0.5

-1 + -5 = -6 / 2 = -3

We're given:

To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:

[tex]4.5(8x + 4)-4(5.5x + 1.5)[/tex]

Open up the parentheses:

[tex]= 36x +18 -22x - 6[/tex]

Combine like terms:

[tex]= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12[/tex]

The area of the walkway around the garden is 14x + 12.

Answer:

B.

Step-by-step explanation:

-5x + 10 > -15

-5x + 10 - 10 > -15 - 10

-5x > -25

-5x / -5 > -25/(-5)

x < 5

Step-by-step explanation:

[tex]m + 148 = 3m + 10[/tex]

[tex]148 - 10 = 3m - m[/tex]

therefore

3m = 138

m = 138/3

m = 46°

pls give brainliest

So

The range is

So

Option D is correct

Answer:

.25

Step-by-step explanation:

.25 or 1/4 is one-fourth of 1

You can divide 1 by 4 to get .25

Answer:

all you have to do is round to the nearest.

Step-by-step explanation:

just do it .

Step-by-step explanation:

11.

x is sin(60) in a circle with radius of 8.

x = sin(60)×8 = 6.92820323... ≈ 6.9

12.

x is sin(30) in a circle with radius "diagonal length".

6 is cos(30) in the same circle.

6 = cos(30)×r

r = 6/cos(30) = 6.92820323...

x = sin(30)×r = 3.464101615... ≈ 3.5

13.

similar to 12.

but we refer to the angle at the bottom right vertex.

remember, the sum of all angles in a triangle is always 180°.

so, the angle over there at the right is

180 - 90 - 68 = 22°

x = sin(22)×r

25 = cos(22)×r

r = 25/cos(22) = 26.96336857...

x = sin(22)×r = 10.10065565... ≈ 10.1

14.

9 is the sine of the complementary angle of 49 in a circle with radius x.

the complementary angle is the angle that adds up with the original angle to 90° and is therefore

90 - 49 = 41°

9 = sin(41)×x

x = 9/sin(41) = 13.71827778... ≈ 13.7

18.

we use the extended Pythagoras :

c² = a² + b² - 2ab×cos(C)

with c being the side opposite of the angle C.

so we have

LK² = 16² + 24² - 2×16×24×cos(29) =

= 256 + 576 - 768×cos(29) =

= 832 - 671.7079351... = 160.2920649...

LK = 12.66065026... ≈ 12.7

19.

law of sine

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being always opposite to the corresponding angles.

to find the angle at H we need to find the angle at G first, because we don't know GF yet.

so,

28/sin(76) = 18/sin(G)

sin(G) = 18×sin(76)/28 = 0.623761538...

G = 38.59134528...°

remember the 180° rule in triangles.

H = 180 - 76 - G = 65.40865472...° ≈ 65.4°

20.

GF is now calculated using the law of sine again.

28/sin(76) = GF/sin(H)

GF = 28×sin(H)/sin(76) = 26.23980579... ≈ 26.2

Answer:

A

Step-by-step explanation:

It could just be it was dilated (I think thats the word) by 3. 6×3=18, 8×3=24

The value of z is equal to 50.28.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

These numbers are represented by a ratio between two integers numbers ([tex]\frac{a}{b}[/tex]), where b[tex]\neq[/tex]0.  Besides, this ratio can be simplified in decimal form.

For solving this equation, firstly, rewrite the information given:

                                          [tex]y=512x \;(1)\\ \\ z=50.25+x \;(2)\\ \\ y=15.5 \;(3)[/tex]

As the question gives the values for y, you can find x.

                                        [tex]y=512x\\ \\ 15.5=512x\\ \\ x=\frac{15.5}{512} =0.03[/tex]

Applying x=0.03 in the equation (3), you can find z.

                              [tex]z=50.25+x \\ \\ z=50.25+0.03\\ \\ z=50.28[/tex]

Learn more about the system of equations here:

https://brainly.com/question/384631

A beam of length 10m can support a weight of 62kg.

It is given that

Weight W ∝ 1/ Length L

W ∝ 1/L

W = k/L...........eq1

where k is constant of proportionality

The constant of proportionality is the ratio that relates two given values.

It is given that when L= 2m, W = 310kg

310 = k/2

k = 620

So put the k value in eq1,

eq1 becomes,

W = 620/L

when L = 10

W = 620/10

W =62kg

Therefore, a beam of length 10m can support a weight of 62kg.

To get more about the constant of proportionality visit:

https://brainly.com/question/26171814

Answer:

break it down to prime factorization

so the ans will be 2^3 * 3^2 *11

Answer:

10 cm

Step-by-step explanation:

Out of that [tex]160 cm^2[/tex], part of it is given by the surface of the top and bottom faces, which have area [tex]2\times 5 cm^2 = 10 cm^2[/tex] each, for a total of [tex]20 cm^2[/tex] . We are then left with [tex]140 cm^2[/tex] of surface from the side area. That area you can imagine as a rectangle of height h (which we need to know) and base [tex]5+2+5+2 cm = 14 cm[/tex] (imagine it as a box opened on a flat surface)

At this point we have [tex]140cm^2 = 14 cm \times h \rightarrow h= 10 cm[/tex]

Answer:

Step-by-step explanation:

Minimum Amount = circumference of the pond.

Formulas

C = pi * d

Givens

pi = 3.14

d = 30 feet

Solution

C = pi*d             Substitute for the givens.

C = 3.14 * 30      Multiply

C =  94.2

Answer:

(x - 3) is not a factor

Step-by-step explanation:

If (x - h) is a factor of f(x) then f(h) = 0

here

f(x) = x³ - 5x² - 4x + 6 , then

f(3) = 3³ - 5(3)² - 4(3) + 6 = 27 - 5(9) - 12 + 6 = 27 - 45 - 6 = - 24

since f(x) ≠ 0 then (x - 3) is not a factor of f(x)

Answer: C - 4 = 14

Step-by-step explanation: In the expression, "c" is colin's age so, if you subtract 4 years for his age, you get Katie's age, which is 14.

Answer: 16

Step-by-step explanation:

Answer: 43

Step-by-step explanation:

so the investigator found the skid marks were 75 feet long hmmm what speed will that be?

[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}[/tex]

nope, the analysis shows that Charlie was going faster than 35 m/h.

now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been

[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d[/tex]

Answer:

5145cm²

125/343=1875/x

x=1875×343÷125=5145

Answer:

70 meters

Step-by-step explanation:

Based on the given conditions, formulate:: 45x5/3

Cross out the common factor: 14x5

Calculate the product or quotient: 70

The width of the parking lot in the drawing is, 70 milliliters.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

She used the scale 5 millimeters: 3 meters.

And, The actual width of the parking lot is 42 meters.

Hence, We can formulate;

The width of the parking lot in the drawing = 42 × 5 / 3

                                                                  = 70 milliliters

Learn more about the multiplication visit:

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Answer:

35

Step-by-step explanation:

There are 3 angles in a triangle

∠1 , ∠2 , ∠3

Of which

∠1 = ∠2

∠3 = 110

By angle sum property

∠1 + ∠2 + ∠3 = 180

∠1 + ∠2 = 180-110

∠1 + ∠2 = 70

∠1 = 70 ÷ 2

=35

∠1 = ∠2 = 35

Hence , 35+35+110 = 180

Answer:

35°, 35°, 110°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the equal angles be x , then

x + x + 110 = 180 , that is

2x + 110 = 180 ( subtract 110 from both sides )

2x = 70 ( divide both sides by 2 )

x = 35

the measure of each angle is 35° , 35° , 110°

Answer:

A= Origen C= q1 B=Q2

Step-by-step explanation

your left-hand side is quadrant TWO Your top right-hand corner is Quadrant ONE and your second to the last one is left-hand side down Is Quadrant THREE last but not least is Quadrant FOUR. And the zero in the middle means ORIGEN.