Solve for x.



A.
x = 4
B.
x = 3
C.
x = 12
D.
x = 1v

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:

Step-by-step explanation:

The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]

Substitute:

[tex]x^2+20.2^2=(14.7+x)^2[/tex]           use (a + b)² = a² + 2ab + b²

[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex]          subtract x² from both sides

[tex]408.04=216.09+29.4x[/tex]        subtract 216.09 from both sides

[tex]191.95=29.4x[/tex]         divide both sides by 29.4

[tex]x\approx6.5\ cm[/tex]

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:

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

Answer:

25%

Step-by-step explanation:

% increase = (3.50 - 2.80)/(2.80) x 100

= 25% increase

The required percent increase of the price of a bag of bagels from $2.80 to $3.50 is 25%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To find the percent increase of the price of a bag of bagels, we can use the formula,

percent increase = [(new value - old value) / old value] x 100%

In this case, the old value is $2.80 and the new value is $3.50. Substituting these values into the formula, we get:

percent increase = [(3.50 - 2.80) / 2.80] x 100%

percent increase = (0.70 / 2.80) x 100%

percent increase = 0.25 x 100%

percent increase = 25%

Therefore, the percent increase in the price of a bag of bagels from $2.80 to $3.50 is 25%.

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The house is 10 units far from the base of the ladder?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that

length of ladder = 26 feet

And height of house = 24 feet

According to given scenario it will form a right angled triangle.

In which the length of ladder is hypotenuse

Height of house be perpendicular

And base we have to calculate.

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

Now plug the values

(26)²= (24)² + (Base)²

(26)²= (24)² + (Base)²

676  =  576 + (Base)²

(Base)² = 100

  Base = 10 units

Thus, the base is of 10 units.

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Answer:

B

Step-by-step explanation:

This is the Georiga Mile STONE?????????????

Answer:

His money earned $36 after 3 months

Step-by-step explanation:

* Lets revise the rules of simple interest

- Simple Interest Equation (Principal + Interest)

 A = P(1 + rt)

- Where:

• A = Total amount (principal + interest)  future amount

• P = Principal Amount

• I = Interest Amount

• r = Rate of Interest per year in decimal; r = R/100

• t = Time Period involved  

* To calculate the interest I use the formula

  I = P × r × t

* Lets solve the problem

- The rate is annual

- The interest calculated after 3 months

∴ I = P × R/100 × t/12

∵ P = $3600.00

∵ R = 4%

∵ t = 3 month

∴ I = 3600.00 × 4/100 × 3/12 = $36

* His money earned $36 after 3 months

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:

The quadratic function x^2 -3x + 40 has roots x=8 and x= -5.

Step-by-step explanation:

If a polynomial has roots x=8 and x=-5, then we know that the factorized form is:

(x-8)(x+5)

So, to find the polynomial we need to expand the polynomials:

(x-8)(x+5) = (x^2 +5x - 8x + 40) = x^2 -3x + 40

Answer:

x² - 3x - 40 = 0

Step-by-step explanation:

The roots are x=8 and x= -5

The quadratic equation will be;

(x-8)(x+5) = 0

Therefore;

x² - 8x + 5x -40 = 0

x² - 3x - 40 = 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:

7/12

Step-by-step explanation:

1 1/3 - 3/4

= 4/3 - 3/4

= 16/12 - 9/12

= 7/12

Answer:

[tex]1\frac{1}{3}-\frac{3}{4}=\frac{7}{12}[/tex]

change [tex]1\frac{1}{3}[/tex] into [tex]\frac{4}{3}[/tex]

[tex]=\frac{4}{3}-\frac{3}{4}[/tex]

get like denominators:

12

[tex]\frac{16}{12}-\frac{9}{12}[/tex]

16 - 9 = 7

Hope this helps and have a great day!!!

Answer: It is 15/17

Step-by-step explanation:

Tan is adjacent over hypotenuse

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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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:

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!

just open the bracket and do algebra. the answer should be C

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%.

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:

I believe the answer would be C.

Step-by-step explanation:

First, simply look at the roots of each answer choice. A rational number is any number that can be written as a fraction.

In the first option choice [A.], the square root of 8 is 2.8284.... a long decimal that continues for a whi;e. So, it can't be written as a fraction.

In the second option choice [B.], the square root of 24 is 4.8989.... another long decimal that continues for a while. So, it can't be written as a fraction.

In the third option choice [C.], the square root of 81 is 9. 9 can be written as a fraction [for example 27/3] So it's the correct answer.

In the last option choice [D.], the square root of 2 is 1.4142.... another long decimal that continues for a while. So, it can't be written as a fraction.

This is why C. is the right answer! I hope this helps!!!

Answer:

6/8

Step-by-step explanation:

Formula

Tan(A) = side opposite / side adjacent

Givens

side opposite = 6

side adjacent = 8

Tan(A) = 6/8

Answer:

6/8

Step-by-step explanation:

tan A = opp / adj = 6 / 8 = 3/4.  This corresponds to the last answer choice.

The area of a right triangle with legs of 10in and 24in is 120 square inches, calculated using the formula Area = 0.5 * base * height.

The area of a right triangle can be calculated using the formula:

Area = 0.5 * base * height

In this case, the base and height can be taken as the two legs of the right triangle. Given the lengths of the legs as 10in and 24in, the area can be calculated as:

Area = 0.5 * 10in * 24in = 120 square inches

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.

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:

y= -4x-1/3

Step-by-step explanation:

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

Answer:

101

Step-by-step explanation:

360 - (78+91+90)

360- 259 = 101

HOPE THIS HELPS!!

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]

[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:

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: