Solve by completing the square

Solve By Completing The Square

Answers

Answer 1

[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]


Related Questions

Determine whether AB¯¯¯¯¯¯¯¯
A
B
¯
is a diameter of the circle. Explain your reasoning.

Answers

Answer: D

Step-by-step explanation:

The shared side and sides AC and AD are congruent, as well as the included angles, so the triangles are congruent. This means that by CPCTC, segments BC and BD are congruent, and thus AB bisects CD. Therefore, AB is a diameter.

Write these numbers in order of size. Start with the smallest number. 3007 4435 399 4011 3333​

Answers

Hey there!

Let's write all these numbers in order.

First, all numbers here are 4-digit numbers, except 1 (it's a 3-digit number)

So the smallest number is the 3-digit number.

399

Now, what's next?

let's check the thousands place (the first digit in the 4-digit numbers)

We see 3, 3, 4 and 4.

3 is smaller than 4.

Now we have 2 numbers: 3007 and 3333.

Well, which one's smaller? that's right, 3007.

So we have

399, 3007.

The third number is 3333 (the thousands place is 3)

so we have

399, 3007, 3333

Now, we have 2 numbers left, and they have a 4 in their thousands place.

The numbers are: 4011 and 4435.

Well, which one's smaller? that's right, 4011, and the greatest number is 4435.

Hence, we have

[tex]\boxed{\boxed{\bold{399,~3007,~3333,~4011,~4435}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

design an instructional activity that could help learner's recognise the decimal fractions can be applied across environmental situation relating to activities in real-life

Answers

An instructional activity that could help learners recognize fractions includes an analog clock, fraction strips, and pattern block.

What is an instructional activity?

Instructional activities are routine segments of instruction that show how the teacher and students will participate and interact with materials and content.

An instructional activity that could help learners recognize fractions includes an analog clock, fraction strips, and pattern block. For example, if one wants to teach students about fractional parts that are divided equally into twelfths, the analog clock can be ideal.

Learn more about fractions on;

https://brainly.com/question/78672

Look at the image below. What is the area of the triangle? units​

Answers

Answer:

7 Units^2

Step-by-step explanation:

If we add an exact copy of the triangle, we can make a parallelogram.

Then we can use the parallelogram's area to figure out the triangle's area.

Hint #22 / 4

The original triangle has \dfrac{1}{2}

2

1

start fraction, 1, divided by, 2, end fraction the area of the parallelogram we just made.

Hint #33 / 4

\begin{aligned} \text{Area of parallelogram} &= \text{base} \times \text{height}\\\\ \text{Area of triangle} &= \dfrac{1}{2} \times \text{base} \times \text{height}\\\\ &= \dfrac{1}{2} \times 7 \times 2\\\\ &= \dfrac{1}{2} \times 2 \times 7\\\\ &= 1 \times 7\\\\ &= 7 \end{aligned}

Area of parallelogram

Area of triangle

 

=base×height

=

2

1

×base×height

=

2

1

×7×2

=

2

1

×2×7

=1×7

=7

Hint #44 / 4

The triangle has an area of 777 units^2

2 squared.

The area of the triangle is 7 square units if the height of the triangle is 2 units, and base length is 7 units.

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle shown in the figure:

The base length = 7 units

The height of the triangle = 2 units

Area of the triangle = (7x2)/2

= 7 square units

Thus, the area of the triangle is 7 square units if the height of the triangle is 2 units, and base length is 7 units.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

Find the greatest common factor (GCF) of 12x and 18x3.

Answers

Answer:

the answer to that question is 6x squared.

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

12x and 18x3

first, simplify 18x3

12x and 54x

Now, cancel the x, we'll add it on in the end

12 and 54

Factor it!

(2 * 3 * 2) and (2 * 3  * 3 * 3)

2 and 3 remain common, so multiply = 6

Add on x from before.

6x is the answer.

How many solutions does this system have?
y=-3x
-9x-4y = 21
one
two
an infinite number
no solution

Answers

This system have one solution.

Find the value of x. Enter only the number.

Answers

Answer: 5

Step-by-step explanation: These two triangles are similar triangles. Since they are similar, they must be scaled equivalently. The scale factor is 5. To know this, 3 times 5 is 15, and being equivalent, we can figure 5 times 5 is 25. Therefore x is 5. That also means that the scale factor of the smallest triangle to the biggest triangle is 5. Thus, x is 5.

Probability and statistics

Answers

Probability and statistics are two branches of mathematics that are used to calculate the possibility of occurrence of an event or trend of data.

What is probability?

Probability is a term to refer to the science that studies the measurement of the certainty of occurrence of an event. Generally, the probability of occurrence is associated with a value between 0 and 1, where an impossible event corresponds to zero and a certain event corresponds to one.

What is statistics?

Statistics is a term to refer to a branch of mathematics that studies different phenomena related to data such as:

VariabilityCollectionOrganizationAnalysisInterpretationPresentation

Another outstanding aspect of statistics is that it is a formal deductive science framed in the formal scientific method.

Learn more about statistics in: https://brainly.com/question/8058700

please help please help please

Answers

light and heat

Step-by-step explanation:

all stars in general produce light and heat

percent of students with brown eys

Answers

Answer:

between 55 to 79 percent

Ted needs 2500 metres of lighting cable for a job. What is this length in kilometres?

Answers

Answer:

2.5km

Step-by-step explanation:

1000m=1km

We have 2500m

2500m=2.5km

2500 m because 1000 metre=1km.

A cat weighs​8 1/4​pounds.

How many ounces does the cat weigh?

Answers

The answer is C 132oz

Answer:

132 ounces

Step-by-step explanation:

1 pound = 16 ounces

8 1/4 x 16 = 132

Graph the following function:
f(x) = x2 + 5x – 6

Answers

Answer:

The graph is in the image below

Step-by-step explanation:

you can use an online graphing calculator like Desmos to graph questions like this

I'm not sure if the x2 is x^2 but I will assume

a rectangular garden is 1.25 meters wide and 3.4 meters long. what is the area of the garden?

Answers

Area = length x width

Area = 1.25 x 3.4 = 4.25 square meters

Write an algebraic expression for the following: 17 more than a number.

Answers

[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]

Let the number be x

Then,the algebraic expression formed is

[tex] \large \purple{ \boxed { \rm{x + 17}}}[/tex]

It states that you need to write it as 17 more than x This means 17 added on to x .

[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}[/tex]

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

Answer:

x+17

Explanation:

Adding more characters. 'A number is x variable, add 17.. x+17

The number 9 is a common factor of _________.
A) 6 and 9
B) 9 and 36
C) 16 and 27

Answers

Answer:

Step-by-step explanation:

B) 9 and 36

hello!

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

9 is a common factor of

9 and 36.

Here's why:

6 is not evenly divisible by 9

16 is not divisible evenly by 9 (it is divisible by 8)

All the other numbers are divisible by 9.

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

note:-

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)

If $2,000 is invested at 4% annual interest compounded quarterly, how long would it take for the account balance to reach $10,000? Round your answer to the nearest tenth.

Answers

Answer:

40.2 years

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which n represents the number of compounding periods per year.  In this case n = 4.  Solve the following equation for t (years):

$10,000 = $2,000(1 + 0.04/4)^(4t):

This is equivalent to

          5   =  1.01^(4t).  Taking the natural logarithm of both sides, we get:

ln 5 = 4t·㏑ 1.01, or

    ln 5                 1.609

-------------- = t = -------------- = 40.2 years

4·ln 1.01             4(0.010)

An object is thrown upward from the top of 96​-foot building with an initial velocity of 80 feet per second. The height h of the object after t seconds is given by the quadratic equation h=16t^2+80t+96. When will the object hit the​ ground?

Answers

The function of the object height is an illustration of a projectile motion

The object will never hit the ground

How to determine when the object hits the ground?

The function is given as:

h=16t^2+80t+96.

When the object hits the ground, h = 0

So, we have:

16t^2+80t+96 = 0

Divide through by 16

t^2+5t+6 = 0

Expand

t^2 + 3t + 2t + 6 = 0

Factorize

t(t + 3) + 2(t + 3) = 0

Factor out t + 3

(t + 2)(t + 3) = 0

Solve for t

t = -2 or t = -3

The time (t) cannot be negative.

Hence, the object will never hit the ground

Read more about projectile motion at:

https://brainly.com/question/1130127

Answer:

6

Step-by-step explanation:

did this question in savvas

Evaluate the function when x= -3, 0, and 1.
f(x) = 5 + 5x - 7

Answers

Answer:

f(-3) = -17

f(0) = -2

f(1) = 3

Step-by-step explanation:

f(-3) = 5 + 5(-3) - 7

5 -15 - 7

-10 - 7

=-17

f(0) = 5 + 5(0) -7

5 + 0 - 7

5 - 7

=-2

f(1) = 5 + 5(1) - 7

5 + 5 - 7

10 - 7

=3

please answer my question I will mark BRAINLIEST
With explanation please of all

Answers

Answer:

See below ↓

Step-by-step explanation:

11)

AB = AC [as angles opposing them are equal]AB = 4 cmB is the answer

12)

x/2 = 9/3 [they are in proportion across the transversal]x = 2 x 3x = 6C is the answer

13)

Let the missing side lengths (which are equal) be xx² + x² = (2√2)²2x² = 8x² = 4x = 2 [length is always positive]A is the answer

There is a rule on Brainly which states you can only answer 3 questions maximum per post.

So I can only help with you this much.

Hope this helped~

Answer:

Its me Viktor Kozhanov may I  have brainliest please

I also answered all you questions so give brainliest to those

as well

Step-by-step explanation:

find product of 9000and800​

Answers

Answer:

7200000

Step-by-step explanation:

What is the surface area?
15
yd
15
yd
15
yd

Answers

Answer:

Step-by-step explanation:

(15x15)x6

225x6

1350

Need help picture below

Answers

Qps is the answer as the arc has full rotated and touched from q p and s

Help help help help ASAP apa

Answers

Answer:

A=49.12

Step-by-step explanation:

The area of the figure=

Area of the triangle + area of the semicircle.

Area of the triangle=

½×the base × the height=

½×6×8=

24ft.

Area of the semicircle=

½πr²=

½×3.14×4²=

25.12ft.

Area of the figure=

24+25.12=

49.12ft

HELP PLEASE ITS DUE TODAY

Answers

3rd option.

The Sun appears so large compared to the other stars because it is so much closer to us than any other star. The Sun is just an average sized star.

how many boxes of enelopes can you buy with $12 if one box cost $3?

Answers

Answer:

Total cost = $12 (Cost of the box) x (Number of boxes) = (Total Cost) ($3)x(n) = ($12) 3n = 12 3n 3 = 12 3 to isolate the n divide by 3 on both sides n = 4 You can buy 4 boxes with $12 if the boxes cost $3 each.

Step-by-step explanation:

Answer:

you can buy 4 boxes hope it helps

Step-by-step explanation:

The side of a goal in soccer is the shape of a right trapezoid. The dimensions are shown below. What is the area of the net needed for both sides of the goal? Чft 8 ft 10 ft​

Answers

Answer:

[tex]61^{2}[/tex]

Step-by-step explanation:

So area equals {(B+b) x h} / 2 the two bases are 4 and 10 which is 14 the height is 8 so 14 times 8 is 112. 112 divided by 2 is 61.  I hope this helps.

In a basketball game, Shawna made 8 baskets, each worth 3 points.
Daryl made the same number of points in the game but made only baskets worth 2 points.
How many baskets did Daryl make?

A.
6 baskets

B.
9 baskets

C.
12 baskets

D.
24 baskets

Answers

Answer: Shawna made 8 baskets worth 3 which mean it's 24. if Daryl made the same shots but worth 2 it would equal 16 . 8 x 2=16

Step-by-step explanation: I can see that 16 is not an answer choice so but if they mean that 2 was taken off of 8 then 6x2=12 so 12 would be your answer. hope this helped :)

what is the sum? complete the equation 3 1/7 + (-5 4/7)

Answers

Answer:

The answer is

[tex] - 2 \frac{3}{7} [/tex]

Brian buys a lawn ornament priced at $78. Shipping and handing are an additional 5% of the price. How much shipping and handing will Brain pay?

Answers

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]

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