y= -3x^2-24x-46 write in vertex form

Answer:

C. 14 inches

Step-by-step explanation:

The area of a square is given by

A = s^2

We know the area is 196 in ^2

196 in^2 = s^2

Take the square root of each side

sqrt(196) = sqt (s^2)

14 =s

Each side is 14 inc

Answer:

C.14

Step-by-step explanation:

a=length time width so 14*14=196  

Answer:

[tex]\boxed{1) V = 40 000(0.89)^{n}, \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_{n} = -2^{n}}[/tex]

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is  

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is [tex]\boxed{ V= 40 000(0.89)^{n} }[/tex]

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth [tex]\boxed{ \text{\$15 476}}.[/tex]

2) Profit function

Income from 1 lawn = $15

  Income from x lawns =  15x

Less gas and supplies =         -50        

                 Net income = 15x – 50

The function is [tex]\boxed{f(x) = 15x - 50}[/tex].

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8)  = 2

a₃/a₂ =   -8/(-4)  = 2

a₂/a₁ =   -4/(-2)  = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is [tex]\boxed{a_{n} = -2^{n}}[/tex].

Answer:

C

Step-by-step explanation:

The excluded values are the values of x that make the denominator of the rational function equal to zero as this would make the function undefined.

Equate the denominator to zero and solve for x to obtain the values that x cannot be.

x² - 2x - 35 = 0

(x - 7)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 5 = 0 ⇒ x = - 5

Excluded values of x are x = - 5, x = 7 → C

Answer:

x = - 6

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] x² = 24 ( multiply both sides by 3 )

2x² = 72 ( divide both sides by 2 )

x² = 36 ( take the square root of both sides )

x = ± [tex]\sqrt{36}[/tex] ← note plus or minus

x = ± 6

solutions are x = - 6, x = + 6

The smallest solution is x = - 6

Answer:

A and E

Step-by-step explanation:

Answer:

101

Step-by-step explanation:

360 - (78+91+90)

360- 259 = 101

HOPE THIS HELPS!!

Place a point on your paper and then use a compass to construct a circle.

Answer with explanation:

To construct an inscribed polygon with a compass and straightedge:

The first step is:

   1.⇒Draw the polygon either it is Regular or Irregular

→A polygon is said to be regular, if it's all sides and all Interior Angles are equal.

→Draw the perpendicular bisector of all the sides of Polygon.

→The point where these two perpendicular bisector meet is center of the circle.

→Draw the circle which will pass through all the vertices of the Polygon you have drawn.

Answer:

18/19 = About 95%

Step-by-step:

If only six are noble gases, 108 are not noble gases.

114-6= 108

So, the probability of not picking a noble gas is 108 out of 114. This simplifies to 18/19 which is about 95%.

Answer:

0.63

Step-by-step explanation:

M: The selected dog is a male. P(M) = 24/40 = 0.6

B: The selected dog is a boxer. P(B) = 22/40 = 0.55

M and B: 14/40 = 0.35

P(M/B) = 0.35 / 0.55 = 0.63

Answer:

A

Step-by-step explanation:

if you need one comment below

Answer: A. (12x3) x 60= 2160 pages per 60 minutes or 1 hour.

(12x3) solve first = 36 pages printed per minute by 3 printers.

36 pages per minute x times 60 minutes =

= 2160 pages, is how many pages 3 printer printing 12 pages a minute can print in 60 minutes or 1 hour.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-3y=x-5&\text{subtract x from both sides}\\x+5y=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-3y=-5\\x+5y=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad2y=2\qquad\text{divide both sides by 2}\\.\qquad\qquad y=1\\\\\text{Put the value of y to the second equation:}\\x+5(1)=7\\x+5=7\qquad\text{subtract 5 from both sides}\\x=2[/tex]

The solution of the system of equations is (2, 1).

The elimination method is a process that uses elimination to reduce the simultaneous equations into one equation with a single variable.

The given system of equations  are;

[tex]\rm -3y=x-5\\\\x+5y=7[/tex]

From equation 1

[tex]\rm -3y=x-5\\\\x = -3y+5[/tex]

Substitute the value of x in the equation 2

[tex]\rm x+5y=7\\\\-3y+5+5y=7\\\\2y =7-5\\\\2y=2\\\\y=\dfrac{2}{2}\\\\y=1[/tex]

Substitute the value of y in the equation 1

[tex]\rm -3y=x-5\\\\-3(1)=x-5\\\\-3=x-5\\\\x=5-3\\\\x=2[/tex]

Hence, the solution of the system of equations is (2, 1).

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Answer:

D :If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5. Then the correct option is D.

If the statement is: p ⇒ q

Then the Contrapositive statement will be: ~q ⇒ ~p

p: 3x + 7 = –5 q: 4x + 12 = –4

The value of x in both cases is the same. Then the p and q are converses with each other.

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

Then the correct option is D.

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Answer:

151

Step-by-step explanation:

23+26=$49

49+25=74

74+24=98

98+6=104

104+24=128

128+23=151

Alan earned a total of $198 from gardening by adding all individual earnings together.

The student is asking about the total amount earned by Alan from gardening. To find the total, we simply add all the amounts mentioned: 23 + 26 + 25 + 24 + 23 + 24 + 6 + 24 + 23. Adding these up, Alan earned a total of $198 from gardening.

So if you distribute 4 in the first parentheses, you get 12x+20y+8z.

Then you distribute 3 in the second parentheses. You'll get 3x-3z. That all equals 12x+20y+8z+3x-3z.

Now you have to start combining numbers with the same variable. Start with x. 12x+3x is 15x.

y has no other common variable, it's left alone.

8z-3z is 5z

All together now with the numbers in simpler form, the equation is 15x+20y+5z

Jenna's would be the right answer because when you distribute 5 in her answer you get 15x+20y+5z

Answer:is jennas right i think i got it ty

Answer:

The area of the shaded region is [tex]44.24\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

step 1

Find the area of circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=4\ cm[/tex]

substitute

[tex]A=\pi (4)^{2}[/tex]

[tex]A=16\pi\ cm^{2}[/tex]

step 2

Find the area of rectangle

The area of rectangle is equal to

[tex]A=(3)(2)=6\ cm^{2}[/tex]

step 3

Find the difference

[tex]16\pi\ cm^{2}-6\ cm^{2}[/tex]

assume

[tex]\pi=3.14[/tex]

[tex]16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}[/tex]

ANSWER

3 must be factored from 3x² +9x

EXPLANATION

The given function is

[tex]y = 3 {x}^{2} + 9x - 18[/tex]

To write the given function in vertex form, we need to complete the square.

But before we come complete the square, we must ensure that the coefficient of the quadratic term is unity.

Hence we factor 3 from 3x² +9x to obtain:

[tex]y = 3( {x}^{2} + 3x) - 18[/tex]

The first choice is correct.

The first step to rewrite the equation y=3x^2 + 9x - 18 in the form y=a(x-h)^2 + k is to complete the square.

The first step to rewrite the equation y=3x^2 + 9x - 18 in the form y=a(x-h)^2 + k is to complete the square. To do this, we need to factor out a from the quadratic term:

y=3(x^2 + 3x) - 18

Next, we take half of the coefficient of x (which is 3) and square it to find h:

h = (3/2)^2 = 9/4

Now, we add this value inside the parentheses and subtract it outside:

y=3(x^2 + 3x + 9/4) - 18 - 9/4

Simplifying further, we get:

y=3(x + 3/2)^2 - 81/4

So, the equation y=3x^2 + 9x - 18 can be rewritten in the form y=a(x-h)^2 + k as y=3(x + 3/2)^2 - 81/4.

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Answer:

answer is b

Step-by-step explanation:

The Scale factor is 2.

A dilation in mathematics is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilatation is a resemblance to the space in Euclidean space.

Given

in pre -- image sides are 4, 5, 3

in the image, the sides are 4(2), 5(2), 3(2)

The scale factor is 2.

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[tex]\bf (x^9y^6z^{15})^{\frac{1}{3}}\implies \stackrel{\textit{distributing the exponent}}{\left(x^{9\cdot \frac{1}{3}}y^{6\cdot \frac{1}{3}} z^{15\cdot \frac{1}{3}} \right)}\implies x^3y^2z^5[/tex]

Answer:

187.5

Step-by-step explanation:

50 × 3 =150

50 ÷ 4 = 12.5

12.5 ×3= 37.5

150 + 37.5 =187.5

Answer:

187.5

Step-by-step explanation

50 × 3 =150

50 ÷ 4 = 12.5

12.5 ×3= 37.5

150 + 37.5 =187.5

Great Question!

The last year part is extra information. 1200÷12 (months in a year)= 100

He will have to wash 100 cars each month.

The correct probabilities are that not choosing a black pen is about 0.83, choosing a black pen is about 0.17, choosing a red or blue pen is about 0.33, choosing an orange pen is about 0.17, not choosing a purple or blue pen is about 0.67, and finally, choosing a green or red pen is about 0.33.

In this mathematics problem, we discuss the probabilities related to Ms. Simon and her colored pens, specifically black and red.

A. The probability of randomly not choosing a black pen is 5/6 or about 0.83 (there are five other colors).

B. The probability of randomly choosing a black pen is 1/6 or about 0.17 (only one black pen out of six).

C. The probability of randomly choosing a red or blue pen is 2/6 or about 0.33 (two desired colors out of six).

D. This is correct because The probability of randomly choosing an orange pen is 1/6, which rounds to about 0.17.

E. The probability of randomly not choosing a purple or blue pen is 4/6 or about 0.67 (four other colors), so this is correct.

F. The probability of randomly choosing a green or red pen is 2/6 or about 0.33 (not 0.5 as stated).

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Answer:

1)[tex]cos(x)sin^{2}x[/tex]

2)0

Step-by-step explanation:

for part 1:

Given cos(x) - cos^3(x)

= cos(x) (1- cos^2(x))

Using the identity [tex]cos^{2}x +sin^{2}x=1\\ sin^{2}x=1-cos^{2}x[/tex]

= cos(x)sin^2(x)

for part 2:

given

=[tex]cos\frac{5\pi }{8}cos\frac{\pi }{8}  + sin\frac{5\pi }{8}sin\frac{\pi }{8}[/tex]

Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)

=[tex]cos(\frac{5\pi }{8} -\frac{\pi }{8})[/tex]

=[tex]cos\frac{4\pi }{8}[/tex]

=[tex]cos\frac{\pi }{2}[/tex]

=0!

Answer:

A. (3 × 4) + (3 × 7)

3(4 + 7)

B. (5 × 9) - (5 × 6)

5(9 - 6)

C. 32 +16 = 48

8 (4 + 2)

D. 4(100 - 3)

97 × 4

E. 7(60 + 6)

66 × 7

Step-by-step explanation:

Answer:

y= -4x-1/3

Step-by-step explanation:

i think. but dont quote me on that. and Stan BTS!!!!!!

Answer:

19 units

Step-by-step explanation:

There are two sides that are equal; they are 4 units long.

The unequal sides are 7 and 4 in length.

Add up these four sides to obtain the perimeter:

P = 4 + 4 + 4 + 7 = 19 units

The perimeter of a figure is the distance around the figure.

To find the perimeter of the trapezoid shown, we can simply add the sides. Each square represents 1 unit.

Once we count each square that has a line through it, we will get

7 + 4 + 4 + 4 = 19

Therefore, the perimeter of the trapezoid is 19 units.

Answer: It is 15/17

Step-by-step explanation:

Tan is adjacent over hypotenuse

Hope you can understand

Answer:

D: 56 and 77

Step-by-step explanation:

Answer:

  F.  4h ≥ 18

Step-by-step explanation:

Liang wants ...

   distance ≥ goal

We know that ...

   distance = speed · time . . . . . . where speed = 4 mph, and time = h hours

Then the appropriate inequality for Liang's goal of 18 miles or more is ...

  4h ≥ 18