Six times a number increased by five is fifty-three. What is the number?

To begin with, we can simplify y using the Pythagorean identity:

y = 2 cos²(x) + 3 sin²(x) + 5

y = 2 (cos²(x) + sin²(x)) + sin²(x) + 5

y = 2 + sin²(x) + 5

y = sin²(x) + 7

Next, we can further rewrite this using the half angle identity for sine:

y = (1 - cos(2x))/2 + 7

y = 15/2 - 1/2 cos(2x)

Now, since cos(x) is bounded between -1 and 1, we have

max(y) = 15/2 - 1/2×(-1) = 15/2 + 1/2 = 8

and

min(y) = 15/2 - 1/2×1 = 15/2 - 1/2 = 7

Then the sum of the maximum and minimum is 8 + 7 = 15.

Answer: 186 students

Step-by-step explanation:

7x23+25= 186

Answer:

∠ABC measures 85° and ∠DEF measures 95°.

Step-by-step explanation:

We are given that ∠ABC and ∠DEF are supplementary. Then by definition:

[tex]\displaystyle m\angle ABC + m\angle DE F = 180^\circ[/tex]

Substitute:

[tex]\displaystyle \left(9x+4\right) + \left(13x-22\right) = 180[/tex]

Solve for x. Combine like terms:

[tex]22x -18 = 180[/tex]

Add:

[tex]\displaystyle 22x = 198[/tex]

And divide. Hence:

[tex]\displaystyle x = 9[/tex]

To find the measure of ∠ABC, substitute and evaluate:

[tex]\displaystyle \begin{aligned}m\angle ABC &= 9x + 4 \\ &= 9(9) + 4 \\ &= 81 + 4 \\ &= 85^\circ \end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned}m\ngle DE F &= 13x - 22 \\ &= 13(9) - 22 \\ &= 117-22 \\&= 95^\circ \end{aligned}[/tex]

In conclusion, ∠ABC measures 85° and ∠DEF measures 95°.

Answer:

Step-by-step explanation:

Answer:

14...

plz mark me brailiest

Answer:

(13, 5 )

Step-by-step explanation:

The translation

(x, y ) → (x + 3, y - 4)

Means add 3 to the x- coordinate and subtract 4 from the y- coordinate, so

(10, 9 ) → (10 + 3, 9 - 4 ) → (13, 5 )

Density is mass per unit volume,

ρ = m/v

Solving for mass gives

m = ρv

so that a gas with density 0.824 g/L that occupies 3.00 L has a mass of

m = (0.824 g/L) (3.00 L) = 2.47 g

Step-by-step explanation:

1. -2m-5m-9m=-12

2. -16m= -12

3. m= -12/ -16

4. m=3/4

i have written / sign as a sign of division .

Answer:

3/10

Step-by-step explanation:

Difference = Red - blue

red = 9/10

blue = 3/5 = 6/10       multiply top and bottom by 2

Difference = 9/10 - 6/10 = 3/10

Answer:

9000

Step-by-step explanation:

(x/2)-(x/3) = 1500

(x/6)=1500

x= 9000

Answer:

You didn't put the question well but if I am right, the question is asking of g(x) if f(x) is 2x.

then g(x)=2x+2

Answer:

[tex]{ \underline{ \sf{it \: is \: {10}^{9} }}}[/tex]

Step-by-step explanation:

[tex](10 {}^{4} ). \frac{ {10}^{12} }{ {10}^{7} } = ( {10}^{4} ). {10}^{(12 - 7)} \\ \\ = ( {10}^{4} ). {10}^{5} \\ = {10}^{(4 + 5)} \\ = {10}^{9} [/tex]

Answer:

[tex]10^{9}[/tex]

Step-by-step explanation:

I. [tex]10^{4} * 10^{12-7}[/tex]

= [tex]10^{4} * 10^{5}[/tex]

= [tex]10^{4 + 5}[/tex]

= [tex]10^{9}[/tex]

Answer:

The number is 0 or 100

Step-by-step explanation:

Let the number be x.

ATQ, x^3=100x^2, x^2(x-100)=0, x=0, 100

Answer:5435

Step-by-step explanation:

Answer:

10⁸

Step-by-step explanation:

[tex]( \frac{10 ^{5} }{ {10}^{3} } ) ^{4} \\ (10 ^{5 - 3} ) ^{4} \\ (10 ^{2} )^{4} \\ (10 ^{2 \times 4} ) \\ (10^{8} )[/tex]

I hope it helped U

stay safe stay happy

because the expression is raised to a power, you're going to multiply the power inside the expression with the power outside the expression. Thus:

[tex] \frac{10 ^{20} }{10^{12} } [/tex]

Since the powers are being divided, you can just subtract 20 by 12. Then you would get:

[tex]10^{8} [/tex]

Answer:

5x-1

Step-by-step explanation:

solution

5x-3+2

or, 5x-1

Answer:

h = 4

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = M (h, 3 ) and (x₂, y₂ ) =  N (- 2, - 9 )

m = [tex]\frac{-9-3}{-2-h}[/tex] = [tex]\frac{-12}{-2-h}[/tex] , then

[tex]\frac{-12}{-2-h}[/tex] = 2 ( multiply both sides by - 2 - h )

2(- 2 - h) = - 12 ( divide both sides by 2 )

- 2 - h = - 6 ( add 2 to both sides )

- h = - 4 ( multiply both sides by - 1 )

h = 4

Answer:

a) 25%

10%+15% = 25%

b) doesn't have any idea

Answer:

2

Step-by-step explanation:

Answer:

x = - 1, x = 2

Step-by-step explanation:

Given

x + (x + 1) + (x + 2) = (x + 1)² ← expand using FOIL , then

x + x + 1 + x + 2 = x² + 2x + 1 , that is

3x + 3 = x² + 2x + 1 ( subtract 3x + 3 from both sides )

0 = x² - x - 2 ← in standard form

0 = (x - 2)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 2 = 0 ⇒ x = 2

[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]

[tex] \sf3(p - 6) + 15 = 0 \\\sf 3p - 18 + 15 = 0 \\\sf 3p - 3 = 0 \\ \sf3p = 3 \\ \sf \: p = \frac{3}{3} \\ \boxed{\bf p = 1}[/tex]

The value of p is 1.

_______

Hope it helps.

RainbowSalt2222

[tex]\\ \rm\longmapsto 3(p-6)+15=0[/tex]

[tex]\\ \rm\longmapsto 3p-18+15=0[/tex]

[tex]\\ \rm\longmapsto 3p-3=0[/tex]

[tex]\\ \rm\longmapsto 3p=3[/tex]

[tex]\\ \rm\longmapsto p=\dfrac{3}{3}[/tex]

[tex]\\ \rm\longmapsto p=1[/tex]

Answer:16x-6

Step-by-step explanation:4(4x-1) distributed is 16x-6

Answer:

Two numbers that have a mean of 10 and a range of 4 are the numbers 12 and 8.

Hope this helps!

Answer:

12 and 8 it is easy and i rlly hope it helps

Answer:

26

Step-by-step explanation:

p²+m

=> 5²+1

=> 25 + 1

=> 26

Answer:

26

Step-by-step explanation:

Substitute the given values into the expression

p² + m

= 5² + 1

= 25 + 1

= 26

Answer:

Step-by-step explanation:

6x + ( 14x - 5 ) + ( 17 - 3x )

= 17x + 12

- ( 2 - x ) -3 ( 6 + 8x ) -12,

= -23x - 32

( 4x - 9 ) + 8 ( 2x + 3 ) -7x

= 13x +15

The round trip distance between the national park and city Y is 593 miles.

Given:

To find :

The round trip distance between the national park and city Y

Solution:

According to the question, the round trip distance between City X and City Y is 647 miles.

Let the distance from City X to City Y = d

Let the distance from City Y to City X = d

[tex]d+d=647 miles\\2d=647 miles\\d=\frac{647miles}{2}=323.5 miles[/tex]

Distance from City X to City Y = 323.5 miles

Distance of City X from national park = 27 miles

From the figure, the distance of the national park from the City Y = d -27 miles:

[tex]= 323.5 miles - 27 miles = 296.5 miles[/tex]

The distance from national park to City Y = 296.5 miles

When we will be going on the round trip between the national park and city Y we will be first traveling 296.5 miles from the national park to the City Y and then 296.5 miles from City Y to the national park.

So, the round trip distance between the national park and city Y:

[tex]296.5 miles + 296.5 miles = 593 miles[/tex]

So the round trip distance between the national park and city Y is 593 miles.

Learn more about- Round trip Distance

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Answer:

(-4,5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2

(-10 +2)/2 = -8/2 = -4

To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2

(8 +2)/2 = 10/2 = 5

(-4,5)

Answer:

(-4 , 5)

Step-by-step explanation:

(x₁ , y₁) = (-10 , 8)        & (x₂ , y₂) = (2 , 2)

[tex]Midpoint = (\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2})\\\\[/tex]

               [tex]=(\dfrac{-10+2}{2},\dfrac{8+2}{2})\\\\=(\dfrac{-8}{2},\dfrac{10}{2})\\\\=(-4 , 5)[/tex]