y=x^2+6x+8 solve by completing the square.

Answer:   [tex]\log_2(20)[/tex]

Work Shown:

[tex]\log_2(4) + \log_2(5)\\\\\log_2(4*5)\\\\\log_2(20)\\\\[/tex]

The rule used is [tex]\log_{b}(\text{x}) + \log_{b}(\text{y}) = \log_{b}(\text{xy})[/tex]

[tex]\large{\textbf{Heya !}}[/tex]

✏[tex]\large\sf{\bigstar Given:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar To\quad Find:-}[/tex] ✏

✏[tex]\large{\sf{\bigstar Solution\quad steps:-}[/tex]

`To find what we want we need to apply ㏒ rules

[tex]\large{\sf{\longmapsto{log_ba+log_bc=log_b(ac)}[/tex]

using formula,

[tex]\large{\sf{\longmapsto{log_24+log_25=log_2(4\cdot5)}[/tex]

simplifying,

[tex]\large{\sf{\longmapsto{log_220}[/tex]

`hope it was helpful ! ~

The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.

Lateral surface area of cone = πrl

Lateral surface area of cylinder = 2πrh

Lateral surface area of cone A = πrl = πrh

Lateral surface area of cylinder B = 2πrh

This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.

The answer is: A. True.

Learn more about the lateral surface area of a cone and cylinder on:

https://brainly.com/question/28071721

#SPJ1

The figure description helps; Choice A; by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.

The triangle inequalities theorem postulates that the sum of lengths of two sides of a triangle must be greater than the length of the third side.

On this note, it follows that the since the sum of sides given in the description 7 and 4 is less than 15, the segments cannot be used to form a triangle.

Read more on triangle inequalities;

https://brainly.com/question/22559323

#SPJ1

The matched answers are:

1. semicircle

2. central angle

3. Radius

4. Secant

5. center

6. tangent

7. diameter

8. minor arc

9. chord

10. major arc

A circle is the locus of points equidistant from a given point called the center of the circle.

A circle can be described if its radius and the center of the circle is known.

Analysis:

1. RCH  is called a semicircle when a diameter divides a circle into two equal parts, a part is called the semicircle.

2. ∠RAH is the central angle, because it is the angle subtended at the Center of the circle.

3. CA is the radius of the circle, a line drawn from the center to any point on the circumference of the circle.

4. MR is a secant, a line that cuts the circle into two parts.

5. A is the center of the circle.

6. MT is the tangent, because line MT touches the circle at a point T.

7. CH is the diameter of the circle, a line that divides the circle into two semi circles.

8. CT is the minor arc, the curved line that is found in the smaller part of the divided circle.

9. HT is chord, it is a line that divides the circle into two unequal parts.

10. CRH is  major arc, the curved line of the bigger portion of the divided circle.

Learn more about properties of circle: brainly.com/question/4244936

#SPJ1

In quadrant II, [tex]\cos(A)[/tex] will be negative. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = -\sqrt{1 - \sin^2(A)} = -\dfrac{\sqrt{15}}4 \approx \boxed{-0.9682}[/tex]

The requried, rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.

To find cos(A) in quadrant II, we can use the given information and the trigonometric identity  [tex]sin^2(A) + cos^2(A) = 1[/tex].

Given [tex]sin(A) = 1/4[/tex], we can find  [tex]cos(A)[/tex]  as follows:

[tex]sin^2(A) + cos^2(A) = 1[/tex]

[tex](1/4)^2 + cos^2(A) = 1[/tex]

[tex]1/16 + cos^2(A) = 1[/tex]

Now, let's solve for [tex]cos^2(A)[/tex]:

[tex]cos^2(A) = 1 - 1/16[/tex]

[tex]cos^2(A) = 16/16 - 1/16[/tex]

[tex]cos^2(A) = 15/16[/tex]

Next, find the value of [tex]cos(A)[/tex] by taking the square root:

[tex]cos(A) = \pm \sqrt{(15/16)[/tex]

Since we are in quadrant II, where cosine is negative, we take the negative value:

[tex]cos(A) \approx -\sqrt{(15/16)[/tex]

Now, calculate the approximate value of cos(A):

[tex]cos(A) \approx -0.9682[/tex]

Rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.

Learn more about trigonometric identity here:

https://brainly.com/question/28927169

#SPJ4

I didn't quite get what u meant by exponential form of the function but here

Answer:

8 books have not been read.

Step-by-step explanation:

Let X be the number of books Tara owns.

We learn that she has read 95%, which would mean (0.95)*(X) have already been read.

5% have not been read.  5% 0f 160 books equals (0.05)*(160) = 8 books have not been read.  Impressive.

Answer:

18a-8b

Step-by-step explanation:

i think this right but i think u messed up putting an equal sign instead of a subtraction.

Answer:

A. (-1, 3) (3, 2) (-2, 1)

B. [tex]\sqrt{17}[/tex]   [tex]\sqrt{5}[/tex]  [tex]\sqrt{26}[/tex]  

Step-by-step explanation:

The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].

MIDPOINTS

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)

[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)

Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].

DISTANCE

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]  

a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.

(4-6)/2=-1  (4+2)/2=3

Repeat for other sides.

(2-6)/2=-2 (2+0)/2=1

(2+4)/2=3  (4+0)/2=2

Coordinates of midpoints are (-1,3), (-2,1), (3,2)

b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.

sqrt((-1+2)^2 + (3-1)^2)

Sqrt(5)

Repeat.

Sqrt(17)

Sqrt(26)

The lengths of the inner triangle are as follows:

(-1,3), (-2,1) = Sqrt(5)

(-1,3), (3,2) = Sqrt(17)

(-2,1), (3,2) = Sqrt(26)

The seventh term of the sequence is 364.5

From the question, we are to determine the seventh term of the sequence

Using the formula,

[tex]a_{n} = ar^{n-1}[/tex]

Where [tex]a_{n}[/tex] is the nth term

a is the first term

and r is the common ratio

From the given information,

a = 1/2

r = 3

Thus,

[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]

[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]

[tex]a_{7} = \frac{1}{2} \times 729[/tex]

[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]

Hence, the seventh term of the sequence is 364.5

Learn more on Geometric progression here: https://brainly.com/question/24643676

#SPJ1

There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)

There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by

The number of ways =  [tex]_{n+r-1}C_r[/tex]

Where the combination [tex]_{n}C_r[/tex] is calculated as

[tex]_{n}C_r=\frac{n!}{r!(n-r)!}[/tex]

It is given that there are 4 varieties of donuts in a shop. I.e., n = 4

Number of donuts to be selected r = 12 (one dozen)

And also given that at least one donut of every variety has to be selected.

Since there are 4 varieties, at least one from each of these means the count is 4.

So, the remaining number of donuts to be selected is 12 - 4 = 8.

So, r becomes 8 i.e., r = 8

On substituting,

the number of ways of selecting the remaining 8 donuts = [tex]_{4+8-1}C_4[/tex]

⇒ [tex]_{11}C_4[/tex]

⇒ [tex]\frac{11!}{4!(11-4)!}[/tex]

⇒ [tex]\frac{11!}{(4!)(7!)}[/tex]

⇒ 330

Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.

Learn more about combinations here:

https://brainly.com/question/11732255

#SPJ4

These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

According to the statement

A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.

And we have to find the probability of tossing a head and drawing a red marble. and probability of drawing two blue marbles if the first marble is not replaced.

here we solve this problem by Probability

So, Probability of drawing red marble = Number of red marble / total number of marbles.

Probability = 2/6

Probability = 1/3.

Then

Probability of drawing blue marbles = number of blue marbles /total marbles

Probability = 3/6

Probability = 1/2.

1st blue marble Probability =1/2

2nd blue marble Probability = 1-(1/2) = 1/2.

These are non dependent events because they do no affect the probability of each others.

So, These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

Learn more about PROBABILITY here https://brainly.com/question/251701

#SPJ1

Answer:

Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Step-by-step explanation:

Another example of  multiplying a Pythagorean triple is

Take the known Pythagorean triple 5, 12 and 13:

5 12 13   * 2  = 10 24 26

and 26^2 = 10^2 + 24^2

     676 = 100 + 576 = 676

The solution to the system of equations is (-1, 3) and (3, -1)

The system of equation is given as:

y = -x^2 + x + 5

y = -x + 2

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-1, 3) and (3, -1)

Hence, the solution to the system of equations is (-1, 3) and (3, -1)

Read more about system of equations at:

https://brainly.com/question/12895249

#SPJ1

Answer:

graph 1,

3,-1 and -1,3

Step-by-step explanation:

See screenshot

Answer:

  (c)  0.18

Step-by-step explanation:

If the x-values are exhaustive, then the p(X=x) values must total 1.00.

  0.11 +? +0.62 +0.09 = 1.00

  0.82 +? = 1.00 . . . . . . . simplify

  ? = 0.18 . . . . . . . . . subtract 0.82

P(X=3) = 0.18

For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

To know more about brain tumour, here

https://brainly.com/question/13606763

#SPJ4

The answers are:

Given that:

The perimeter of vegetable plot:

= 4m + 3.5m + 4m + 2m + (3.5 + 2m)

= 19m

Area of vegetable plot:

(1.3 x 5.5) + ( (4 - 1.3) x 3.5)

rounding up to one decimal place = 67.6m²

To know the numbers of meter fence that one can buy, the equation will be:

(perimeter of vegetable plot + the left plot)  - gates.

(19m + (6.5 + 4 + (6.5 - 2) ) )m  - (2.5ft x 2)

= 19m + 15m - 1.5424m

=32.476

=32.5m

Therefore, the answers are:

Learn more about perimeter from

https://brainly.com/question/19819849

#SPJ1

Answer:

The more on these factors forecasters must rely, the more innovative a new product or service design is: Subjective Estimates.

Option (e) is correct.

A subjective estimate is a specific type of estimate that is founded on a person's subjective evaluation or in-depth comprehension of the possibility of a specific outcome.

A subjective estimate only takes into account the subject's ideas and prior experiences rather than employing data or exact calculations.

Individual subjective evaluations are highly biased and differ from person to person.

Contrarily, a subjective estimate is incredibly prone to revision, even when only one person's viewpoint is taken into account.

Learn more about subjective estimates here:

https://brainly.com/question/17111746

#SPJ1

The sequence of the ball is   3, 1, 1/3, 1/9,...

The ball starts bouncing with a height of 3 feet.

Each bounce reaches a third of the height of the previous bounce.

Therefore,

a = first term = 3

r = common ratio = 1 / 3

Therefore,

nth term = arⁿ⁻¹

where

First term = 3

2nd term = 3 × (1 / 3) = 1

Third term = 3 × (1 / 3)² = 1 / 3

Fourth term = 3 × (1 / 3)³ = 1 / 9

Therefore, the sequence of the ball is   3, 1, 1/3, 1/9,...

learn more on sequence here: https://brainly.com/question/13042200

#SPJ1

The radius of this circle is (B) 4.9 cm.

To solve this problem, we need to, first of all, convert the angle from radians to degrees.

data;

[tex]\frac{7\pi }{6rads} =210^{0}[/tex]

Length of an Arc:

The formula for the length of an arc is given:

[tex]l_{arc} =[/tex] θ/360 × [tex]2\pi r[/tex]

Let's substitute the values and solve:

[tex]18=\frac{210}{360} *2\pi r\\18=3.663r\\r=\frac{18}{3.663} \\r=4.9cm[/tex]

From the calculations above, the radius of this circle is 4.9cm.

Therefore, the radius of this circle is (B) 4.9 cm.

Know more about radius here:

https://brainly.com/question/24375372

#SPJ4

Complete question

A circle has a central angle measuring 7pi/6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi.

(A) 3.7 cm

(B) 4.9 cm

(C) 14.3 cm

(D) 15.4 cm

Answer:

-9/2

In alternate forms -4•5,-4 1/2

Answer:

B. (3x - 9) (x + 3i)

Step-by-step explanation:

[tex]\bf 3 {x}^{2} = + 27[/tex]

Therefore, B is your answer!!!!

Answer:

[tex]254 \frac{12}{17}[/tex] or approximately 254.71

Step-by-step explanation:

First, you need to find out how many gallons it will take to travel 866 miles. Because the car's avg miles/gallon is 13.6, you divide 866 by 13.6. However, this gets you an irrational number. To avoid this, make 13.6 into a fraction. Now divide 866 by [tex]13 \frac{3}{5}[/tex]. This becomes 866 ÷ [tex]\frac{68}{5}[/tex]. Convert this into a multiplication problem by converting [tex]\frac{68}{5}[/tex] into its reciprocal. This gets you 866 × [tex]\frac{5}{68}[/tex]. This gets you [tex]\frac{2165}{34}[/tex]. Now that you have the amount of gallons it will take to get to your destination, multiply it by 4. [tex]\frac{2165}{34}[/tex] × [tex]4[/tex][tex]= \frac{4330}{17}[/tex]. This becomes [tex]254 \frac{12}{17}[/tex] or approximately 254.71.

The fill up are:

5. ∠B ≅ ∠B

6. AA Similarity Postulate          

7.   a/c = c/a

8. a² = cx

9. ∠CDA ≅ ∠BCA

10. ∠A ≅ ∠A

11. ΔCBA ~ ΔDBA  

The above answers shows that:

5. Reflexive Property

6. AA Similarity Postulate

7. Polygon Similarity Postulate

8. Cross Multiply and Simplify

9. All right angles are Congruent

10. Reflexive Property

11. AA similarity Postulate

To prove the above:

Note that the full proof of the Pythagorean theorem is that:

We are given: Δ ABC as a right triangle, with a right angle at ∠C.

Then the  Prove: A²+B² =C²

Therefore, If you follow the theories above, you will see that the answers given are correct.

Learn more about triangle from

https://brainly.com/question/14686407

#SPJ1

Answer:

2.8kg

Step-by-step explanation:

There are 7 parts of meat for every 3 parts so there are 7+3=10 parts in total.

4/10=1 "part"

there are 7 parts of meat so (4/10)*7=28/10=2.8kg of meat.

Answer:

Step-by-step explanation:

The key word "product" tells us to multiply.

And, you probably know, but "integer" just means "number".

The question is, essentially:
A × B = 162 where A is half of B.

As someone who was never gifted in math, my best suggestion for something like this is to grab a calculator and start dividing 162 by all the numbers below 10. You will know you've got your answer when the calculator gives you a number that is twice the number you divided by.

In this case, I divided 162 by 9 and got 18. Since 9 is half of 18, and multiplied they make 162, we know this is the correct answer.

Hope this helps

The price of shirt is $12 and the price of tie is $2.5.

According to the statement

We have given that:

Let money spent on shirt = X and money spent on tie is Y.

So, 6X + 3Y = $79.5 and 3X + 2Y = $41 then

We have to find the the cost of each shirts.

Here we use the Elimination method.

Now,

6X + 3Y = $79.5  -(1)

3X + 2Y = $41  -(2)

By elimination method

Multiply (1) by 3 and (2) by 6 then

18X + 9Y = $238.5

18X + 12Y = $246

Then solve it and equation become

-3Y = -$7.5

Y = 2.5

It means the cost of tie is $2.5 and now the cost of shirt is

6X + 3Y = $79.5  

6X + 3(2.5) = $79.5  

6X + 7.5 = $79.5  

6X = $72

X = $12.

So, The price of shirt is $12 and the price of tie is $2.5.

Learn more about Elimination method here https://brainly.com/question/12691830

#SPJ1

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

The probability that at least 9 customers ordered an item from the value menu is 0.927​.

In an experiment with two possible outcomes, the likelihood of precisely x successes on n repeated trials is known as the binomial probability (generally refereed as binomial experiment).

As per the given problem-

This likelihood is a binomial one, so take note. In this instance, a success is defined as a consumer placing an order from the value menu, hence we are looking for such probability between 9 to 14 success, inclusive.

The probability is indeed the complements of the likelihood of any success, ranging from 0 to 8. The procedures below can be used to figure out the probability from such a binomial distribution utilizing Excel.-

Subtract the preceding probability from 1 to get the likelihood of 9 to 14 people ordering out from value menu.

The likelihood is 1 x 0.073 = 0.927.

Therefore, the probability that at least 9 customers ordered an item from the value menu is 0.927.

To know more about binomial probability experiment, here

https://brainly.com/question/9325204

#SPJ4