Translate the following into an algebraic expression: The number that is 40% more than five more than a number a.

[tex] \huge{ \bold{ \bigstar \: pythagoras \bigstar}}[/tex]

Pythagoras :

[tex] {10}^{2} = {x}^{2} + {x}^{2} [/tex]

[tex]100 = 2{x}^{2}[/tex]

[tex]100 \div 2 = {x}^{2} [/tex]

[tex]50 = {x}^{2} [/tex]

[tex]x = \sqrt{50} [/tex]

[tex]x = \sqrt{25 \times 2} [/tex]

[tex] \red{x = 5 \sqrt{2} }[/tex]

Answer:

Step-by-step explanation:

Compare this to a similar figure with hypotenuse √2 and leg lengths all 1.

Write and solve an equation of ratios, as follows:

  x        10

------ = ------

  1        √2

              10√2

'then x = --------  =  5√2

                  2

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

                              ↓                 ↓                  ↓                 ↓

                                factor last              factor 2nd    factor 1st

Proof LHS → RHS:

Given:        2 cos16A + 1

                  let α = 8A, then 2·cos2α + 1

Identity:     2(2cos²α - 1) + 1

Distribute:  4cos²α - 2 + 1

Simplify:    4cos²α - 1

Factor:     (2cosα - 1)(2cosα + 1)

Substitute: (2cos8A - 1)(2cos8A + 1)

                                       let β = 4A, then 2·cos2β + 1

Identity:                           2(2cos²β - 1) + 1

Distribute:                      4cos²β - 2 + 1

Simplify:                         4cos²β - 1

Factor:                           (2cosβ - 1)(2cosβ + 1)

Substitute:                     (2cos4A - 1)(2cos4A + 1)

                                                           let Ф = 4A, then 2·cos2Ф + 1  

Identity:                                               2(2cos²Ф - 1) + 1

Distribute:                                          4cos²Ф - 2 + 1

Simplify:                                             4cos²Ф - 1

Factor:                                               (2cosФ - 1)(2cosФ + 1)

Substitute:                                        (2cos2A - 1)(2cos2A + 1)      

(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)   [tex]\checkmark[/tex]

Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

Step-by-step explanation:

Answer:

[tex]f(x)=5x+12\\\\ f^{-1}(x):\\ y=5x+12\ \ \ |Subtract\ 12\\ y-12=5x\ \ \ |Divide\ by\ 5\\ \frac{y-12}{5}=x\\\\ f{-1}(x)=\frac{x-12}{5}[/tex]

Step-by-step explanation:

Answer:

f^-1(x) = x/5 - 12/5

Step-by-step explanation:

f(x) = 5x + 12

y = 5x + 12

x = 5y + 12

5y = x - 12

y = x/5 - 12/5

f^-1(x) = x/5 - 12/5

Area of a quarter of circle

A = 1/4 * π * R²

A = 1/4 * π * 12²

A = 36 * π cm²

Perimeter of a quarter of circle

P = 1/4 * 2 * π * R²

P = 1/4 * 2 * π * 12²

P = 72 * π cm

Area of a right triangle

A = b * h / 2

A = 12 * 12 / 2

A = 72 cm²

Length of hypotenuse

L = 12√2 cm

Area of blue

A = 36 * π - 72

Perimeter of blue

Hope it helps

xxx

Step-by-step explanation:

-16t2 + 47t + 3 = 0

-16t2 + 48t - t + 3 = 0

-16t( t - 3) - 1 ( t - 3) = 0

-16t - 1 = 0. t - 3 = 0

-16t = 1 t = 3

t = 1/ - 16.

Answer:

Only A is divisible by 24.

Step-by-step explanation:

A number is divisible by 24 if it's divisible by both 3 and 8.

Numbers are divisible by 3 if all their digits add to a multiple of 3, and numbers are divisible by 8 if the last 3 digits are divisible by 8.

Let's look at A, 13944. The numbers add up to [tex]1+3+9+4+4=21[/tex], which is divisible by 3.

944 is divisible by 8, and it makes 118.

So A works.

B is 15746.

[tex]1+5+7+4+6=23[/tex], so this won't work as 23 isn't divisible by 3.

C is 15966.

[tex]1+5+9+6+6=27\div3=9[/tex], so this works for 3 but let's check 8.

[tex]966\div8=120.75[/tex] so it's not divisible by 8, therefore not divisible by 24.

D is 16012.

[tex]1+6+0+1+2=10[/tex] and 10 isn't divisible by 3, so it doesn't work.

Hope this helped!

Answer:

Third grade secondary = 87 students

Step-by-step explanation:

First grade = 30/100 x 250 = 75 students

Second grade = 35/100 x 250 = 87.5 rounded off to 88 students. Because students can't be half thus can't be in decimal. So round off to the nearest whole number.

Third grade = 250 - 88 - 75 = 87 students

Answer:

third grade secondary = 87 students

Step-by-step explanation:

:T

Answer:

f = 10/3

Step-by-step explanation:

-15 + 6f = 5

-15 + 15 + 6f = 5 + 15

6f = 20

6f/6 = 20/6

f = 20/6 = 10/3 = 3.333...

Answer:

10/3

Step-by-step explanation:

-15+6f=5

6f=5-(-15)

6f=5+15

6f=20

f=20/6

simplify

f=10/3

Answer:

I think DFG= 82 (BEING ALTERNATIVE ANGLE)

Answer:

1) 0.00001

2) 0.00012

3)0.0000851

Step-by-step explanation:

Move the decimal place the amount of times being the same as the amount of zeros. Move it to make the number smaller because you are dividing.

1) move the decimal point to the right 3 times (because there are 3 zeros in 1000)

Hope that helped!!! k

Woah woah, no need to panic! I’ve got this taken care of for you!

1. 0.01 divided by 1,000= 100,000.000

Change the divisor 0.01 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.

We then have the equations:

100000 ÷ 1 = 100,000.000

and therefore:

1,000 ÷ 0.01 = 100,000.000

Both calculated to 3 decimal places.

2. 0.012 divided by 100= 8,333.333

Change the divisor 0.012 to a whole number by moving the decimal point 3 places to the right. Then move the decimal point in the dividend the same, 3 places to the right.

We then have the equations:

100000 ÷ 12 = 8,333.333

and therefore:

100 ÷ 0.012 = 8,333.333

Both calculated to 3 decimal places.

3. 0.000851 divided by 10= 11,750.881

Change the divisor 0.000851 to a whole number by moving the decimal point 6 places to the right. Then move the decimal point in the dividend the same, 6 places to the right.

We then have the equations:

10000000 ÷ 851 = 11,750.881

and therefore:

10 ÷ 0.000851 = 11,750.881

Both calculated to 3 decimal places.

I hope this helped! <3

- ʕ•ᴥ•ʔ

Answer:

The correct answer is;

ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Step-by-step explanation:

The given information are;

The point of intersection of GA ∩ TN = I

Segment TI is congruent to segment NI (Given)

Segment GI is congruent to segment IA (Given)

Angle ∠GIT is congruent to angle ∠AIN (Vertically opposite angles)

Therefore, we have;

Triangle, ΔGIT is congruent to triangle ΔNIA (Side Angle Side (SAS) rule of congruency)

Two triangles are said to be congruent by the Side Angle Side (SAS) rule of congruency,  when two of the sides and the included angle (the angle in between the two sides) of one of the triangle are equal to two sides and the included angle of the other triangle.

Therefore, the correct answer is ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Answer:

△GIT≅△AIN

By Rule: SAS

Answer:

24

Step-by-step explanation:

(9 + x)/(20 + x) = 0.75

Solve that for x, the number of additional free throws taken.

9 + x = 15 + 0.75 x

0.25 x = 6

x=24

The required number of additional shots that were shot is 24.

Given that,
He had made only 9 of 20 shots. By the end of the season, he had made all the additional shots he had taken, thereby ending with a season record of 3:4.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Let the extra shots be x,
Now, according to the question,
Number of shots will be 9 + x and 20 + x,
And their ratio is 3:4
9 + x / 20 + x = 3 / 4
[9 + x] × 4 = 3 [20 + x]
36 + 4x = 60 + 3x
x = 60 - 36
x = 24

Thus, the required number of additional shots that were shot is 24.

Learn more about Ratio here:

brainly.com/question/13419413

#SPJ2

Answer:

False

Step-by-step explanation:

So, in Mathematics we use more precise language: When the order doesn't matter, it is a Combination. When the order does matter it is a Permutation.

Answer:

c25

Step-by-step explanation:

Answer:

Rons costs less by 4 dollars

Step-by-step explanation:

Sams

y = 15x+25

x=3

y = 15*3+25

  = 45+25

  =70

Rons

Using averaging

for 3 hours  Add 2 and 4 hours and divide by 2

(49+ 83) / 2 = 132/2= 66

Rons costs less by

70-66 =4

Answer:

The last answer or Distance a number is from zero

Step-by-step explanation:

It's this answer because absolute value is just how far a number is from zero for example | -1 | is equal to 1 because -1 is 1 away from zero. Hope this helps :)

Answer:

The last answer or Distance a number is from zero i think i dont know

Step-by-step explanation:

15.

[tex]FH=2\cdot UH\\\\5x-7=2\cdot19\\\\5x=38+7\\\\5x=45\quad|:5\\\\\boxed{x=9}[/tex]

16.

[tex]KU=UM\\\\3x+3=4x-4\\\\4x-3x=3+4\\\\\boxed{x=7}[/tex]

Answer:

15) x=9 16) x=7

Step-by-step explanation:

19(2)=5x-7

38=5x-7

5x=38+7

5x=45

x=45/5

x=9

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

3x+3=4x-4

3=4x-3x-4

3=x-4

x=3+4

x=7

Answer:

Step-by-step explanation:

Circumference of the circle = 2 x pi x r

= 2 x 3.14 x 26.85

= 168.618 Inches

after rounding to nearest tenth, 168.6 inches

Answer:

168.6 inches

Step-by-step explanation:

The formula for finding the circumference of a circle is:

[tex]\pi r2[/tex] (Basically multiplying [tex]\pi[/tex] by the diameter since the radius is half the diameter)

Let's substitute and solve!

3.14(26.85 × 2) =

3.14 × 53.7 =

168.61800............but if we round to the nearest tenth, it will be 168.6 inches!

Hope that helps and maybe earns a brainliest!

Have a great day!    >   <

                                   U

Answer:

C

Step-by-step explanation:

It is c because you are adding. the 6 and o.

Answer:

Would be C.

Step-by-step explanation:

Just adding the 6 and the 0 basically.

Answer:

0.25 or 1/4

Step-by-step explanation:

1/3 * 75/100 = 75/300 = 1/4 = 0.25

[tex]75\%\cdot\dfrac{1}{3}=\dfrac{3}{4}\cdot\dfrac{1}{3}=\dfrac{1}{4}[/tex]

Answer:

g(-12) is 10

Step-by-step explanation:

[tex]g(x) = 1 - \frac{3}{4} x [/tex]

when x is -12:

[tex]g( - 12) = 1 - \frac{3}{4} ( - 12) \\ g( - 12) = 10[/tex]

[tex] \sf \: g(x) = 1 - \frac{3}{4} x \\ \sf \:g(-12) = \: ? \\ \\ \sf \: Substitute\: the \: value \: of \: x \: as \: -12 \\ \\ \sf \:1 - \frac{3}{4} (-12) \\ \sf \: = 1 - \frac{3}{4} \times -12 \\ \sf \: = 1 + 9 \\ \sf \: = \underline{\bf \: 10}[/tex]

Hope it helps.

RainbowSalt2222

Answer:

20 and 1/4.

Step-by-step explanation:

9x^2 * y^(-2), for x = -3 and y = 2.

9(-3)^2 * 2^(-2)

= 9 * 9 * (1/4)

= 81 * 1/4

= 81 / 4

= 20.25

= 20 and 1/4.

Hope this helps!

Answer:

Step-by-step explanation:

Let's fill the values in.

9(-3)*2(2)*-2

Using PEMDAS, we would first multiply the two numbers where x and y used to be.

-27 * 4 * -2

Now we would finish multiplying this.

216.

Hope this helps!! <3

Answer:

x + y ≥ 45

Step-by-step explanation:

This is because the total amount of minutes could be equal to 45, meaning your inequality sign has to have a line underneath it.

Additionally, x + y is greater than or equal to because the amount could be more than 45... therefore, 45 is not greater than x + y

Hi there! Hopefully this helps!

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

If the total time he spent on both is 45 minutes or more, the answer is:

x + y ≥ 45.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hints for next time

(≥ Means greater than or equal to.)

(≤ Means less than or equal to)

(> Greater than)

(< Less than)

Answer:

a) ◇G = ◇H - T◇S wiĺl be negative.

b) It will be a spontaneous reaction.  

Explanation:

As ◇H is less than 0 and T◇S is greater than 0 so if we put it in the equation we would get the negative maximum result. And when the energies are with negative sign they are said to be spontaneous.

Answer:

-2 < x - 1 < 0

Step-by-step explanation:

2. -2 < x - 1 < 0

Answer:

The first one

Step-by-step explanation:

This line is the best fit for the scatter plot because it touches a lot more points than the second

Answer:

The first line

Step-by-step explanation:

Hey there!

Well the first lie is a positive slope just like the dots whereas,

the second line is a negative slope.

Therefore, the first line is the line of best fit.

Hope this helps :)