Solve 2x2 – 6x + 10 = 0 by completing the square.

A)

x = 3∕2 + i , x = 3∕2 – i

B)

x = 3 + i, x = 3 – i

C)

x = 3∕2 + 1∕2 i, x = 3∕2 – 1∕2i

D)

x = 3 + i, x = 3 – i

[tex]\huge\underline\mathtt\colorbox{cyan}{3/8}[/tex]

[tex]\huge\mathsf\colorbox{white}{}[/tex]

Total shared part:

1/4 + 1/8

Taking LCM and adding:

2/8+1/8

Adding gives:

3/8

Answer:

8x + 13

Step-by-step explanation:

"Like terms" means the same kind of algebraic expression...the 6x and the 2x are "like terms" because they both have an x in them. The 9 and the 4 are both constants, which means they are plain numbers. So 6x and 2x is 8x .

9+4 is 13 just like elementary school.

So all together,

6x + 9 + 2x + 4

6x + 2x + 9 + 4

8x + 13

We can rearrange the terms because the problem has all addition in between the terms.

Answer:

4.25 as decimal and 4 1/4 as a fraction

Step-by-step explanation:

Recall the binomial theorem:

[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Take a = x/3, b = -3, and n = 7. Then we get the x⁵ and x⁴ terms when 7 - k = 5 and 7 - k = 4, respectively; or when k = 2 and k = 3.

[tex]k=2 \implies \dbinom 72 \left(\dfrac x3\right)^{7-2} (-3)^2 = 21 \cdot \dfrac{x^5}{243} \cdot 9 = \dfrac79 x^5[/tex]

[tex]k=3 \implies \dbinom 73 \left(\dfrac x3\right)^{7-3} (-3)^3 = 35 \cdot \dfrac{x^4}{81} \cdot (-27) = -\dfrac{35}3 x^4[/tex]

Then when multiplying this expansion by x - 6, we get an x⁵ terms from the products

[tex]\dfrac79 x^5 \cdot (-6)[/tex]

and

[tex]-\dfrac{35}3 x^4 \cdot x[/tex]

so that the x⁵ term in the overall expansion of (x/3 - 3)⁷ (x -  6) has a coefficient of

[tex]\dfrac79\cdot(-6) + \left(-\dfrac{35}3\right) \cdot 1 = \boxed{-\dfrac{49}3}[/tex]

a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.

• If x = -2, then

f(-2) = 2 (-2) + 3 = -4 + 3 = -1

• If x = -1, then

f(-1) = 2 (-1) + 3 = -2 + 3 = 1

• If x = 0, then

f(0) = 2 (0) + 3 = 0 + 3 = 3

and so on.

b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!

But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).

Answer:

£55

Step-by-step explanation:

50% is just another way to say 1/2. This means that 1/2 of £110 is £55.

Answer

First one is A

Second one is B

Third one is D

Problem 1

Answer: Choice A

(30, 225); Rocket reaches max height of 225 ft after 30 seconds.

-------------------

Explanation:

Distribute the 0.25 through to get

y = 0.25(60x-x^2)

y = 15x - 0.25x^2

y = -0.25x^2 + 15x

This is in standard form y = ax^2+bx+c with a = -0.25, b = 15 and c = 0.

The first two values mentioned lead to this x coordinate of the vertex.

h = -b/(2a)

h = -15/(2*(-0.25))

h = -15/(-0.5)

h = 30

This tells us the answer is between A and C.

If you were to plug x = 30 into the original equation, you'll get y = 225. It means that after x = 30 seconds, the rocket has reached its max height of 225 feet. Therefore, the answer must be choice A.

===========================================================

Problem 2

Answer:  Choice B

(x-3)^2 = -8(y-6)

-------------------

Explanation:

vertex = base of the bulb = (3,6)

focus = top of the bulb = (3,4)

This flashlight is pointed downward, which forms a downward opening parabola.

The distance from the vertex to the focus is p = 2 units. This is known as the focal distance.

We'll plug that in along with the vertex (h,k) = (3,6) in the formula below

4p(y-k) = (x-h)^2

4*2(y-6) = (x-3)^2

8(y-6) = (x-3)^2

Unfortunately that equation above produces a parabola that opens upward. To fix things, we stick a negative out front on either side, which will reflect the parabola over the x axis to make the parabola open downward. That leads us to choice B.

===========================================================

Problem 3

Answer:  D) square

-------------------

Explanation:

We can form a point by intersecting the plane through the point where the two cones meet. The plane needs to be parallel to the base of each cone.

We can also form a line. To do so, we intersect the plane at exactly  along the edge of the cone. Make the plane tangent to the cone.

Lastly, we can form a circle by intersecting any plane parallel to the cone's base. This plane cannot pass through the meeting point of the two cones. Rather, the plane passes through one of the cones.

Those three previous paragraphs mean that we can rule out choices A,B,C. The only thing we can't form is a square. We can form straight lines, but we cannot form perpendicular lines needed to get a square. Nice work on selecting the correct answer.

The sequence gives the order in which the the different types of foods are

given to the giant panda.

The possible first five terms of the sequences are;

[tex]\begin{tabular}{l|c|c|c|c|c|}Sequence Term& 1&2&3&4&5\\First Sequence&Biscuits&Bamboo&Biscuits&Bamboo&Biscuits\\Second Sequence&Biscuits /Bamboo&Bamboo&Bamboo/Biscuit&Bicuits &B/Bamboo\end{array}\right][/tex]

Reasons:

Inductive reasoning is the reasoning based on the given observation

What the giant panda bear at the zoo eats on the first two days of the week are;

First day; 34 pounds of highly nutritious biscuits

Second day; 37 pounds of bamboo

Given that the number of terms in the sequence = 5

By inductive reasoning, we have;

[tex]\begin{tabular}{l|c|c|c|c|c|}Sequence Term& 1&2&3&4&5\\First Sequence&Biscuits&Bamboo&Biscuits&Bamboo&Biscuits\\Second Sequence&Biscuits /Bamboo&Bamboo&Bamboo/Biscuit&Bicuits &B/Bamboo\end{array}\right][/tex]

The pattern used to write the First Sequence is as follows;

The pattern used to create the Second Sequence is as follow;

The sequence that is more likely is the First Sequence

Learn more about inductive reasoning here:

https://brainly.com/question/2192957

https://brainly.com/question/12522297

Answer:

D is a function.

Step-by-step explanation:

cause the line is related to both x and y

The relation that represents a function is the relation (d)

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4) represent the given parameter

Next, we test the options

Relation (1)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (2)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (3)

This relation is not a function

This is because it fails the vertical line test i.e. some output values all point to the same input value,

Relation (4)

This relation is a function

This is because the inputs all point to different output values

Hence, the relation that is a function is graph (d)

Read more about functions at

brainly.com/question/22340031

#SPJ6

Answer:

c. m < 13

Step-by-step explanation:

13 - 7 is equal to 6 so m must be less than 13 to be less than 6.

Answer:

[tex]q\le \:12[/tex]

Step-by-step explanation:

Solving

[tex]\mathrm{Switch\:sides}[/tex]  (Not a required step)

[tex]q+3\le \:15[/tex]

[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]

[tex]q+3-3\le \:15-3\\=q\le \:12[/tex]

[tex]\bold{q\le \:12}[/tex]

Graphing

Answer: x= 1.9

Step-by-step explanation:

Answer:

it will be an 91 or 88

Step-by-step explanation:

Answer:

[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]

The answer would be C and F

Answer: 1 & -5

Step-by-step explanation

Answer:

Last month (2,014) = (2,014) Month before last month

Your answer would be 2,014 = 2,014

The digits are all the same. Therefore, I concluded that the numbers were the same. This means that a equal sign should be used.

Hope this helps. Pls mark brainliest. :S

Answer:

86 m, 59 cm

Step-by-step explanation:

a. perimeter is 2L + 2W

320 = 2L + 2(74)

320 = 2L + 148

172 = 2L

86 m is length

b. area = L x w

5723 = 97 x w

5723/97 = 2

59 cm is width

[tex]x+x(2x)=x+2x^2\\\\\text{when x =2}\\\\2+ 2(2)^2 = 2+ 2(4) = 2+ 8 = 10[/tex]

[tex]\text{So, the answer is (a).}[/tex]

Answer:

-8

Step-by-step explanation:

Pluck in the values:

P = 3 + (-11)

P = 3 - 11 = -8

Answer:

113 each day

Step-by-step explanation: i cant draw it out but just put it into a bubble or something sorry

Answer:

1. 59  2.90  4.31   3. Sorry I dunno

Step-by-step explanation:

1. the 59 degrees is the same.

2. It's a perfect angle

3. Sorry

4.180-90-59=31

Answer:

the answer is  2,500

Step-by-step explanation:

any number higher than 5 you round up but any number lower than 5 you round down.

4 is lower than 5 so you round it down and the 5 stays the same, and replace it with 0's.

Answer:

Option D:  [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]

Step-by-step explanation:

GIven the following inequality statement:

[tex]\displaystyle\mathsf{7x\:+\:6\:\geq \:\frac{-x}{2}}[/tex]

Start by eliminating the fraction on the right-hand side.

Multiply both sides of the inequality statement by 2:

[tex]\displaystyle\mathsf{2(7x\:+\:6)\:\geq \:\bigg[\frac{-x}{2}\bigg](2)}[/tex]

2(7x + 6) ≥ -x

Next, distribute 2 into the terms inside the parenthesis:

14x + 12 ≥ -x

Subtract 12 from both sides:

14x + 12 - 12 ≥ -x - 12

14x  ≥ -x - 12

Add x to both sides:

14x + x  ≥ -x + x - 12

15x ≥ - 12

Divide both sides by 15 to isolate x:

[tex]\displaystyle\mathsf{\frac{15x}{15}\:=\:\frac{-12}{15}}[/tex]

[tex]\displaystyle\mathsf{x\geq -\frac{4}{5}}[/tex] or  [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]

Therefore, the correct answer is Option D:  [tex]\displaystyle\mathsf{-\frac{4}{5}\:\leq\:x}[/tex]

Answer:

A

Step-by-step explanation:

An exponential function has the form

y = a[tex](b)^{x}[/tex]

Use the given solutions to find a and b

Using (0, 3 ) , then

3 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , so

a = 3

y = 3[tex](b)^{x}[/tex]

Using (1, 12 ) , then

12 = 3[tex]b^{1}[/tex] = 3b ( divide both sides by 3 )

4 = b , then

h(x) = 3[tex](4)^{x}[/tex] → A