Help me with this one

Help Me With This One

Answers

Answer 1

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  [tex]x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}[/tex]

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).


Related Questions

Sophie went to the lake with her family. First, they spent 1 1/4
hours fishing. Then, they spent twice as much time swimming. How much time did they spend fishing and swimming in all?

Answers

Answer:

they spend the time for swimming is 11/4 ✖ 2 =22/4

that's means in hours =5 hours 30 minutes

Anyone know the answers to 26 and 28?Please help me I’m sleep deprived

Answers

Answer:

26. 30 ≥ 7.5a + 4.5s         28. $22.50

Step-by-step explanation:

26. The family doesn't want to spend over 30 dollars, so when writing the inequality the amount they spend needs to be less than or equal to 30, hence the greater than/equal to sign. When writing the expression a - amount of adults & s - amount of students.

*remember in the question it states middle and high schoolers both count as students

The 7.5 is cost for adults and the 4.5 is cost for students.

28. You can use the expression created in 26

7.5a + 4.5s

Then substitute in the amount of people into their respective categories.

7.5(2) + 4.5(3) = 22.50

b-8y when b=-6 and y=4

Answers

Answer:

-38

Step-by-step explanation:

b-8y

(-6)-8(4)

-6-32

-38

hope it helps youplease follow me

Lamar is solving the equation x^2 - 12x = -6 by completing the square. Which
shows Lamar's next step and the solution to the equation?

Answers

Answer:

Lamar's next step is x^2 — 12x + 6 = 0

The solution to the equation is x = ± 6√30

Step-by-step explanation:

Can somebody please help me?

Answers

Answer:

The answer is A I am pretty sure. Please tell me if I got it wrong.

Step-by-step explanation:

-X -y -32 = -9
Z= -3x - 1
z = 5y -Z + 23

Answers

Answer:

[tex]x = - \frac{85}{46} [/tex]

[tex]y = - \frac{64}{23} [/tex]

[tex]z = \frac{209}{46} [/tex]

Josh received his allowance on Tuesday. He spends 3/8 of his allowance on Tuesday night and 2/3 of the remainder on Wednesday morning. What part of his allowance is left for the rest of the week?

Answers

Josh starts with 8/8 (or any other fraction that equals 1) of his allowance. He then spends 3/8 of it.

8/8 x 3/8 = 3/8

8/8 - 3/8 = 5/8

He spend 3/8 of his allowance, leaving him with 5/8 left. Then Josh spent 2/3 of that remaining amount.

5/8 x 2/3 = 10/24 = 5/12

Josh has 5/12 of his allowance left for the rest of the week.

Hope this helps!

Charlie borrowed $500 from his aunt. He has already paid back $75. His aunt doesn't charge
any interest and he is planning on making $15 payments each friday

Answers

Answer:

555

Step-by-step explanation:

because it is tyeesgghhhhfdfhf

What is the smallest angle of rotational symmetry for a square?
45°
90°
180°
360°

Answers

Answer:

90 degrees

Step-by-step explanation:

When we want to find the rotational symmetry of a shape, we will take the total angle measure of most shapes (360 degrees) and divide it by the number of angles that shape has. Since a square has 4 angles, thats what we will divide by and the answer we get will be the smallest angle of rotation.

360 / 4 = 90

Best of Luck!

The smallest angle of rotational symmetry for a square is 90°. A square has four sides of equal length and four angles of 90° each, which means that rotating it by any multiple of 90° will result in the same image. Thus, the smallest angle of rotational symmetry is 90°.

What is a polygon?

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

The smallest angle of rotational symmetry for a square is 90°.

This means that the square can be rotated by 90° and still look the same.

It can also be rotated by 180° and 270° to look the same,

but the smallest angle is 90°.

Read more on regular polygon here:

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3. Solve the inverse variation problem. y varies inversely with x. If y=7 when t= -4, find y when = 2.

y= -10

y=0

y=-14

Y = 10​

Answers

y=h/t
h=t*y
h=-4*7= -28
y= -28/2
y= -14

if the value of x=4, y=3 and z= -2 find the value of 2x+3z​

Answers

Answer:

2

Step-by-step explanation:

To find value:

2x + 3z

Given values:

x = 4, y = 3 and z = -2

Solution:

2x + 3z

(Putting the values of x = 4 and z = -2)

= 2(4) + 3(-2)

= 8 - 6

= 2 (Ans)

Answer:

2

Step-by-step explanation:

2×4+3×−2

=8+3×−2

=8+−6

=2

The formula used to convert degrees Celsius to degrees Fahrenheit is
F=?C +32
Convert 68°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?

Answers

Answer:

9

Step-by-step explanation:

The correct conversion is 68°F = 20°C.

What is unit conversion?

Conversion is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are given that;

To convert 68°F

Now,

To solve the formula for C, we need to isolate C on one side of the equation. We can do this by subtracting 32 from both sides and then dividing by 1.8. The steps are:

F = 1.8C + 32

F - 32 = 1.8C

(F - 32) / 1.8 = C

Therefore, the correct formula for C is:

C = (F - 32) / 1.8

To convert 68°F to degrees Celsius, we can plug in F = 68 into the formula and simplify. The steps are:

C = (68 - 32) / 1.8

C = 36 / 1.8

C = 20

Therefore, after conversion the answer will be 68°F = 20°C.

Learn more about the unit conversion here:

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THE PRESENT AGE OF A FATHER IS THREE TIMES THAN THAT OF HIS SON. FIVE YEARS AGO HE WAS FIVE TIMES AS OLD AS HIS SON. FIND THEIR PRESENT AGES.

(STEP BY STEP PLZ) (HOPE U ENJOY IT)​​

Answers

Answer:

fathers age 50 son age 20

PLS HELP WILL MAKE FIRST RIGHT ANSWER GETS BRAINLIEST ​

Answers

Answer:

Subtract four to get the next term.

Step-by-step explanation:

66 - 4 = 62

62 - 4 = 58

58 - 4 = 54

54 - 4 = 50

50 - 4 = 46

46 - 4 = 42

42 - 4 = 38

Answer:

B

Step-by-step explanation:

Subtract 4

Explain the algebraic error in the student’s work. Then, state how the equation r = StartFraction (uppercase A minus uppercase P) Over t EndFraction can be modified to produce the correct result.

Answers

Answer:

The student did not distribute properly to get A= P+Prt. The equation can be fixed by putting a factor of P in the denominator: r=(A-P)/Pt

Step-by-step explanation:

just did it

There is an error in step 2 where distributive property was not followed.

What is Simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Steps taken by the student to solve the formula of the simple interest for the values of '',

Step 1 : A = P( 1 +rt)

Step 2 : A = P + rt

Step 3 : A - p = rt

Step 4 : r = (A - P)/ t

There is an error in step 2 where distributive property was not followed.

Correct steps should be,

Step 1 : A = P( 1 +rt)

Step 2 : A = P + Prt [By distributive property]

Step 3 : A - P = Prt

Step 4 : r = (A-P)/Pt

Therefore, error was made in step 2.

Learn more about simple interest here:

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Write 0.2 as a fraction in simplest form.

Answers

Hi ;-)

[tex]0,2=\dfrac{2}{10}=\dfrac{2:2}{10:2}=\boxed{\frac{1}{5}}[/tex]

Answer:

1/5

Step-by-step explanation:

Answer: 0.2 when converted into a fraction is 1/5.

Hope it helps:)

The running trail in the local park is 2.826 miles long. If the park board were planning to extend the trail by 1.46 miles, what would the new length of the running trail be?
A.
4.093
B.
4.286
C.
4.682
D.
5.216
E.
5.443

Answers

Answer:

The answer is B. 4.286

Step-by-step explanation:

2.826+1.46= 4.286

what are the steps in order needed to solve
x/2-5=20

Answers

x/2-5=20

(x-5*2)/2=20

(x-10)/2=20

x-10=20*2

x-10=40

x=40-10

x=30

Answer:

x/2-5=20

x=20(2-5)

x=40-100

x= -60

r-6

--------- = - 3

- 3

Answers

Answer:

r=0

Step-by-step explanation:

The Coal Utility Company is burning coal to produce electricity. The following cost function illustrates the cost in dollars (C) of removing t% of the hazardous toxins generated from burning coal. What happens to the cost as t approaches 100?
C= 55,000t/100-t for 0 ≤ t < 100

A The cost continues to increase.
B The cost continues to decrease.
C The cost approaches $0.
D The cost approaches $55,000.

Answers

Answer:

the cost continues to increase

Step-by-step explanation:

the cost (C) approaches infinity (or becomes very large) as t approaches 100%. Thus, the correct answer is: A. The cost continues to increase.

To determine what happens to the cost (C) as t approaches 100%, we can take the limit of the cost function as t approaches 100.

The cost function is given as: [tex]\[ C = \frac{55,000t}{100 - t} \][/tex]

Now, let's find the limit of C as t approaches 100:[tex]\[ \lim_{{t \to 100}} C = \lim_{{t \to 100}} \frac{55,000t}{100 - t} \][/tex]

To find this limit, we can use direct substitution:[tex]\[ \lim_{{t \to 100}} \frac{55,000 \times 100}{100 - 100} = \lim_{{t \to 100}} \frac{5,500,000}{0} \][/tex]

Since the denominator approaches 0 as t approaches 100, the limit is undefined (infinite).

Therefore, the cost (C) approaches infinity (or becomes very large) as t approaches 100%. Thus, the correct answer is: A. The cost continues to increase.

To know more about infinity:

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find the exact value without a calculator cos π\8= cos π/4/2

Answers

Answer:

Step-by-step explanation:

1+cos 2a=2cos^2a

cos a=√[(1+cos 2a)/2]

[tex]put~a=\frac{\pi }{8} \\2a=\frac{\pi }{4} \\\\cos\frac{\pi }{8} =\sqrt{\frac{1+cos \frac{\pi }{4} }{2} } \\=\sqrt{\frac{1+\frac{\sqrt{2}}{2} }{2} }\\=\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 80% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?​

Answers

Step-by-step explanation:

the first brand = (65-55)/(80-55) x 180

= 10/25 × 180

= 72 gallons

the second brand = (80-65)/(80-55)×180

= 15/25 × 180

= 108 gallons

1.Give another name for line s
2. Name then intersection of lines r and s
3.Name three non- collinear points
4. Give another name for plane n

Answers

Step-by-step explanation:

1 ) Another name for lines can be x y z etc ...

2 ) line r and s intersect at point B

3 ) point A B D

point D B C

4 ) Another name for plane N can be P Q T etc...

MARK AS BRAINLIST IF IT IS USEFUL

answer if you can please

Answers

Answer:

[tex] - \frac{9}{10} - ( - \frac{3}{10} ) \\ \\ = - \frac{9}{10} + \frac{3}{10} \\ \\ = \: - \frac{ 6}{10} [/tex]

I hope I helped you^_^

Answer:

-3/5

Step-by-step explanation:

1.) -9/10 - (-3/10)

2.) This___(-9)+3___ (DO NOT SIMPLIFY) over 10 or

(-9)+3 / 10

3.) -3/5

solve the following compound inequality. graph the solution. -4 < 3x + 2 <= 2​

Answers

Answer:

-2 < x <= 0

Step-by-step explanation:

Isolate the variable.

-4 < 3x + 2 <= 2

Subtract 2 from each side.

-6 < 3x <= 0

Divide both sides by 3

-2 < x <= 0

28 + 2h = 2h + 6. What does “h” equal?

Answers

I believe the answer is 28=6, but I could be wrong tho.

2h – 2h = 28-6 —> 0 = 22

It cannot be solved because 2h -2h equals zero, so there is no h .

I need help with maths lol

Answers

Answer:

Step-by-step explanation:

To get equivalent expressions, if you are adding or subtracting, the number and letter you get on the left must be the same as the one on the right.

In B. The answer is incorrect because 4t is minus on the left. The letters are different, so 4t must remain minus. Not B

In C the numbers will combine when you add. If they are the same,, they remain the same. They do not become powers the answer for C is 10s. So C is not correct.

In D you are indicating that 6 is multiplied by 4s.  You can only multiply 6 and 4. They don't add. Not D

A is correct.

The LCM of two numbers is 352
The HCF of the numbers is 4.
One of the numbers is 44.
Find the other number.

Answers

Answer:

Let the other number be

x

Given:LCM+HCF=600

⇒14HCF+HCF=600

⇒15HCF=600

⇒HCF=40

⇒LCM=14×40=560

Since HCFxLCM=Product of 2 numbers

=>40×560 = 280×x

⇒x=

280

40×560

⇒x=40×2

⇒x=80

hence the other number is 80.

Solve the equation below.

1.2m+0.65=5

Answers

Answer:

m = 3.625

Step-by-step explanation:

1.2m + 0.65 = 5

~Subtract 0.65 to both sides

1.2m = 4.35

~Divide 1.2 to both sides

m = 3.625

Best of Luck!

The length of a rectangle is 24" and its width is 7". How long is a diagonal?
(A) 22"
(B) 25"
(C) 28"
(D) 31"
(E) 34"

Answers

22”. Hope that helps
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