The line $x = 4$ is an axis of symmetry of the graph of $y = ax^2 + bx + c.$ Find $\frac{b}{a}$.

Answer:  see proof below

Step-by-step explanation:

Use the following Half-Angle Identities:    tan (A/2) = (sinA)/(1 + cosA)

                                                                     cot (A/2) = (sinA)/(1 - cosA)

Use the Pythagorean Identity: cos²A + sin²B = 1

Use Unit Circle to evaluate: cos 45° = sin 45° = [tex]\frac{\sqrt2}{2}[/tex]

Proof LHS → RHS

Given:                       [tex]cot\ (22\frac{1}{2})^o-tan\ (22\frac{1}{2})^o[/tex]

Rewrite Fraction:     [tex]cot\ (\frac{45}{2})^o-tan\ (\frac{45}{2})^o[/tex]

Half-Angle Identity:   [tex]\dfrac{sin(45)^o}{1-cos(45)^o}-\dfrac{sin(45)^o}{1+cos(45)^o}[/tex]

Substitute:                  [tex]\dfrac{\frac{\sqrt2}{2}}{1-\frac{\sqrt2}{2}}-\dfrac{\frac{\sqrt2}{2}}{1+\frac{\sqrt2}{2}}[/tex]

Simplify:                      [tex]\dfrac{\frac{\sqrt2}{2}}{\frac{2-\sqrt2}{2}}-\dfrac{\frac{\sqrt2}{2}}{\frac{2+\sqrt2}{2}}[/tex]

                               [tex]=\dfrac{\sqrt2}{2-\sqrt2}-\dfrac{\sqrt2}{2+\sqrt2}[/tex]

                               [tex]=\dfrac{\sqrt2}{2-\sqrt2}\bigg(\dfrac{2+\sqrt2}{2+\sqrt2}\bigg)-\dfrac{\sqrt2}{2+\sqrt2}\bigg(\dfrac{2-\sqrt2}{2-\sqrt2}\bigg)[/tex]

                               [tex]=\dfrac{2\sqrt2+2}{4-2}-\dfrac{2\sqrt2-2}{4-2}[/tex]

                               [tex]=\dfrac{4}{2}[/tex]

                               = 2

LHS = RHS:  2 = 2  [tex]\checkmark[/tex]

Answer:

answer is 27/7

Step-by-step explanation:

F(19) means u have to put the value of x as 19

so by putting 19 we get

3/19+2 -root (19-3)

so 3/21 - root 16

or 3/21 -4

or 3- 84/21

or 81/21

ans= 3x27/3x7= 27/7

thank u

Answer:

6x+2y just add them lol

Step-by-step explanation:

Answer:

8x + 3y - 2x - y

8x - 2x + 3y -y

6x - 3y

is your answer

brain list plzzz

Answer:

Area = 154 m²

Step-by-step explanation:

i pressume base = 14 m

height = 22 m

Area of a triangle = 1/2 * base * height

Area = 1/2 * 14 * 22

Area = 154 m²

The area of the triangle is given by the equation A = 154 m²

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the area of the triangle be represented as A

Now , the value of A is

Let the height of the triangle be h

The value of h = 22 m

Let the base of the triangle be b

The value of b = 14 m

Now , area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of the triangle A = ( 1/2 ) x 22 x 14

Area of the triangle A = 154 m²

Therefore , the value of A is  154 m²

Hence , the area of the triangle is  154 m²

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Answer:

The answer is

Step-by-step explanation:

(2y⁴)³

Using the rules of indices

That's

So for the above expression we have

Simplify

We have the final answer as

Hope this helps you

Answer:

D, 160

Step-by-step explanation:

Base: from a rectangle 6×8 a square 4×4 is removed.

Base area: 6×8-4×4=48-16=32 square units.

Volume: base are × height=32×5=160cubic units.

Answer: D, 160

Answer:

The correct option is;

A Dilate circle A by a scale factor of 3

Step-by-step explanation:

The given parameters are;

The center of circle A is (4, 6)

The radius of circle A = 5

The center of circle B = (1, 0)

The radius of circle B = 15

Therefore, circle A is similar to circle B and is equivalent to circle B, scaled down by a factor of 3

Radius of circle A = 5,

Radius of circle B = 15 = 3 × 5

Therefore, the scale factor for the dilation (transformation) of circle A to circle B is 3.

For a circle to be similar dilate circle A by a scale factor of 3

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The given parameters are;

Therefore, circle A is similar to circle B and is equivalent to circle B, scaled down by a factor of 3

The radius of circle A = 5,

Radius of circle B = 15 = 3 × 5

Therefore, the scale factor for the dilation (transformation) of circle A to circle B is 3.

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Answer:

Step-by-step explanation:

-2(36) - 18 - 8

-72 - 26

-98 is the solution

Answer:  (-1.5, -0.5)

Step-by-step explanation:

Answer:

The answer is 64.

16-12=4.

4×16×1=64.

Answer:

The answer is 64.

Step-by-step explanation:

16-12=4.

4×16×1=64.

Answer:

Why is looking at cash flow an important step in a good financial plan ? At the most fundamental level, a company's ability to create value for shareholders is determined by its ability to generate positive cash flows, or more specifically, maximize long-term free cash flow

Step-by-step explanation:

Answer:

Well,

Step-by-step explanation:

First, we need it so we don't get in low finical areas and owe the government tons of money. We also need it for our houses and if you start checking your cash flow and you see its low and you want to make it higher than that helps too! But, its very good for your bank account and helps you grow ideas to your financial plan. Hopes this helps!

Answer:

b = sqrt(161)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + b^2 = 15^2

64 + b^2 = 225

Subtract 64 from each side

b^2 = 225-64

b^2 =161

Take the square root of each side

sqrt(b^2) = sqrt(161)

b = sqrt(161)

Answer:

6c^4 - 2c^3 + 4

Step-by-step explanation:

Answer: 6[tex]c^{4}[/tex] - 2[tex]c^{3}[/tex] + 4

Step-by-step explanation:

[tex](4c^{4} +1)- (7c^{3} -3)+(2c^{4} + 5c^{3} )[/tex]

[tex]= 4c^{4} +1-7c^{3} +3+2c^{4} +5c^{3}[/tex]

Combine like terms

[tex]= 6c^{4} -2c^{3} + 4[/tex]

Answer:

They "y" value = (4 * 24) + 4 which equals

100

Step-by-step explanation:

Answer:

The innings pitched last season is 225.

Step-by-step explanation:

Given that,

Earned run average = 2.80

Allowed earned run = 70

The given equation is

[tex]E=\dfrac{9R}{I}[/tex]

We need to calculate the innings pitched last season

Using given equation

[tex]E=\dfrac{9R}{I}[/tex]

[tex]I=\dfrac{9R}{E}[/tex]

Where, E = earned run

R = allowed earned run

I = innings pitch

Put the value into the formula

[tex]I=\dfrac{9\times70}{2.80}[/tex]

[tex]I=225[/tex]

Hence, The innings pitched last season is 225.

Answer:

17⋅24+32-13=427

Step-by-step explanation:

17⋅24=408   408+32=440   440-13=427

Answer:

[tex]\boxed{a \leq 3}[/tex]

Step-by-step explanation:

Hey there!

Well to find "a" we need to single it out.

3a - 4 ≤ 5

+ 4 to both sides

3a ≤ 9

Divide both sides by 3

a ≤ 3

Hope this helps :)

a ≤ 3 is value of a inequality.

What are an example of inequality?

3a - 4 ≤ 5

+ 4 to both sides

3a ≤ 9

Divide both sides by 3

a ≤ 3

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Answer:

about $1.90

Step-by-step explanation:

$320 per week.

There are 168 hours in a week.

$320 divided by 168 hours = about $1.90 an hour

Check: $1.90 x 168= $319.2 (rounded to $320)

Answer:

28

Step-by-step explanation:

After substituting -2 for m and 5 for n, the original expression becomes:

|(-2)^2 - 7| + (5)^2, or

|4 - 7| + 25  or

|-3| + 25 = 28

Answer:

2 cents

Step-by-step explanation:

you would just divide the Flav-O-Squeeze price by 12 since there are 12 pouches and the Turbo Taste price by 20 since there are 20 pouches and then you would get 1 pack of Flav-O-Squeeze is 49 cents and 1 pack of Turbo Taste is 51 cents and if you subtract them Turbo Taste is 2 cents more then Flav-O-Squeeze

The cost of Turbo Taste per pouch is $0.02.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mike is buying a box of juice pouches. Flav-O-Squeeze costs $5.88 for 12 pouches. Turbo Taste costs $10.20 for 20 pouches.

The more cost will be calculated as,

Cost of Turbo Taste = 10.20 / 20 = $0.51

The cost of Flate-O-Squeeze = 5.88 / 12 = $0.49

The more cost of Turbo-Taste = 0.51 - 0.49

The more cost of Turbo-Taste = $0.02

Therefore, the cost of Turbo Taste per pouch is $0.02.

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Answer:

Its a rational number

Step-by-step explanation:

because a rational number has fractions and -22 is a fraction or a decimal

Answer:

8.17.4 miles per 1 gallons 9. 2 miles per second.

Step-by-step explanation:

so you have yo divide 384 divided by 22 then boom.

Once again you have to divide 60 which is 1 hour (60 minutes is an hour) to the 32 miles. :)

Problem 8

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

Explanation:

You divide the number of miles over the number of gallons to get this result

384/22 = 17.45

Another way you could think of it is to say

384 miles = 22 gallons

Then you divide both sides by 22 getting

17.45 miles = 1 gallon

Showing that 1 gallon of gas gets you roughly 17.45 miles

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

Problem 9

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

Explanation:

Check out the attached diagram below. For the first column, I placed "32 miles" over "1 hour" to indicate "32 miles per hour". The second column is from the idea that 1 hour = 60 minutes. This helps us convert from hours to minutes. Note how the "hour" units cancel when we divide.

The third column helps us convert from minutes to seconds. We have the "minutes" units cancel out when they divide. It's important that one "minute" unit is on top, and the other is on the bottom. Finally, the last column helps us convert from miles to feet since 1 mile = 5280 feet.

Once this table formed, you multiply the numbers across the top to get 32*1*1*5280  = 168960

And you multiply everything along the bottom row: 1*60*60*1 = 3600

The last step is to divide the two results (top row over bottom row) getting

168960/3600 = 46.933 approximately

So 32 mph converts to roughly 46.933 ft per second.

Side note: the conversion method I used is called the "railroad method" or "railroad tracks method" as the table lines form what appears to be railroad tracks of sorts.

Answer:

[tex] - 2m - 5m = 9m - 12 \\ ⟶ - 2m - 5m - 9m = - 12 \\ ⟶ - 16m = - 12 \\ ⟶ - m = \frac{ - 12}{16} \\ ⟶ - m = \frac{ - 6}{8} \\ ⟶ m = - ( - \frac{6}{8} ) \\ ⟶m = \frac{6}{8} [/tex]

[tex]m=0.75[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 0.75}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 2m - 5m = 9m - 12}[/tex]

Collect like terms

⇒[tex] \sf{ - 7m = 9m - 12}[/tex]

Move 9m to left hand side and change it's sign

⇒[tex] \sf{ - 7m - 9m = - 12}[/tex]

Collect like terms

⇒[tex] \sf{ - 16m = - 12}[/tex]

Divide both sides of the equation by -16

⇒[tex] \sf{ \frac{ - 16m}{ - 16} = \frac{ - 12}{ - 16} }[/tex]

Calculate

⇒[tex] \sf{ m = 0.75}[/tex]

Hope I helped!

Best regards!!

Answer:

64

Step-by-step explanation:

Hello, we can write this two digit number 'ab', a and b being positive integer between 0 and 9.

For instance , 54, a = 5 and b =4

The number can be written 10*a+b (54=5*10+4, for instance)

The sum of a two digit number is 10.

a + b = 10

The value of the number is 16 times the units digit.

10a + b = 16b <=> 10a = 16b - b = 15b

[tex]<=> a = \dfrac{15}{10}b=\dfrac{3}{2}b=\dfrac{3}{2}(10-a)=15-\dfrac{3}{2}a\\\\<=> \dfrac{2+3}{2}a = 15\\\\<=> 5a=30 <=> a = 6[/tex]

and then, b = 10 - 6 = 4.

So the solution is 64.

Thank you

Answer:

A) 435,050/6,215,000= 0.07= 7%

B) 4,972,000/6,215,000= 0.8= 80%

C) 6,215,000-(4,972,000+435,050)= 807,950

807,950/6,215,000=0.13=13%

Answer: Answer is  in the steps.

Step-by-step explanation:

One situation is this.

Jason borrowed $5 from his best friend during a field trip and agreed to pay him back the next school day.The next day, he came back to school with $10 and used $5 to pay his friend back.Now answer the this question. How much does Jason owe his best friend now?

The answer to the question will be zero because Jason has already paid his friend all the money he borrowed.

Answer:

the corresponding point for the function f(x) − 4 is (0,-9)

Step by Step Explanation --

Given that (0, -5) is on the graph of f(x),

WE need to find the corresponding point for the function f(-4x}

f(x) means the output y

f(x)-4 means subtract 4 from the output y

In the given point  (0, 5) , x is 0  and y is -5

To get the corresponding point we subtact 4 from y

that is [-5]- 4 = -9

the corresponding point for the function f(x) − 4 is (-3,1)

Step-by-step explanation:

Answer:

(0,-5)

Step-by-step explanation:

Answer:

37.68cm (i used 3.14 for pi)

Answer:

Step-by-step explanation:

From Thales' theorem:

                                        [tex]\dfrac y7\ =\ \dfrac45\\\\y=\dfrac45\cdot7\\\\y = \dfrac{28}5\\\\y = 5.6[/tex]

Answer:

401 MILES

Step-by-step explanation:

miles from A to B:

64 * 5.5 = 352 miles

miles from A to C:

352 + 49 = 401 miles