Find the missing side of triangle

Answer:

[tex]f(x)=\begin{cases}x^2 + 3; & \text{ } x<1 \\ -2\cdot x+5; & \text{ } x\geq 1 \end{cases}[/tex]

Step-by-step explanation:

The y-intercept (when x = 0) on the quadratic graph is 3, the upper quadratic graph does not intersect the x-axis, and the endpoint of the function has an open circle that stops at x = 1. The starting point extends to the boundaries of the graph

Therefore, the piecewise function shown in the quadratic graph is given as follows;

f(x) = x² + 3; x < 1

The straight line graph has a negative slope and starts at x = 1, with a closed circle, extending to higher values of x to the boundaries of the graph

Two points on the straight line graph are (1, 3) and (5, -5), therefore, the slope is (-5 - 3)/(5 - 1) = -2

The equation of the function is y - 3 = -2·(x - 1)

∴ y = f(x)  -2·x + 2 + 3 = -2·x + 5

f(x) = -2·x + 5; x ≥ 1

Answer:

1. 90-68= 22

2. 90-80= 10

3. 90-3= 87

Step-by-step explanation:

A complement angle is found by their sum being 90 degrees. So, you are looking for the angle that would add to the given angle to = 90.

For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°

Step-by-step explanation:

hope this helps you thank you

[tex]\boxed{ \sf{Answer}} [/tex]

[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]

Use the algebraic identities ⟶

Squaring on both the sides

[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]

[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]

[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

2nd option x=-12.........

Answer:

-8

Step-by-step explanation:

you know, all you have to do in such a case is simply taking the given -2 and put it, where there is "x" in the function expression and then calculate this. if necessary with a calculator.

2×2×x with x=-2 is

2×2×-2 = -8

Answer:

- 8

Step-by-step explanation:

f ( x ) = 2 . 2 x

f ( - 2 )

= 2 . 2 ( - 2 )

= 2 x 2 x ( - 2 )

= - 8

Answer:

y = 0.8x – 2

Step-by-step explanation:

Slope (m) =  

ΔY/ ΔX =  4 /5 = 0.8

y=.8x+b

plug in point

b=-2

Answer:

1/81

Step-by-step explanation:

9^2 = 81

We know that a^ -b = 1/a^b

9^-2

1/9^2

1/81

Answer:

1/81

Step-by-step explanation:

Edge

Answer:

If x is the required number, equation will be 9+4x=8

Answer:

f(x) = -3(x+3)(x-1)

Step-by-step explanation:

x = -3 & 1; f(x) = 9

f(x) = a(x-r1)(x-r2)

f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)

9 = a(3)(-1); 9 = a(-3)

a = -3

f(x) = -3(x+3)(x-1)

Answer:

f(x) = -3x^2 - 6x + 9.

Step-by-step explanation:

As the x intercepts are - 3 and 1 we can write it as:

f(x) = a(x - 1)(x + 3)    where a is a constant to be found.

As the - intercept is at (0, 9),  x =0 when f(x) = 9 so we can also write:

a( 0 - 1)(0 + 3) = 9

(-1)(3)a = 9

a = 9 / -3

= -3.

So the equation is f(x) = -3(x - 1)(x + 3)

In expanded form it is

-3(x^2 + 2x - 3)

= -3x^2 - 6x + 9.

Answer:

First part: 0.35 miles per minute

Second part: 3.5 miles in 10 minutes

Step-by-step explanation:

Think about this as a fraction. Fractions can't be added nor subtracted unless they share the same denominator. So for this case, we have to turn hours into minutes. So 21 mph becomes 21 miles per 60 minutes. Then, we divide 60 from each side to find the speed per minute. 21/60 = 0.35, so the answer to the first part is 0.35 miles per minute.

Using what we got, we can answer the second part of the distance covered in 10 minutes. So, we just multiply 0.35 by 10 which is 3.5 miles covered in 10 minutes.

980 miles

Step-by-step explanation:

5 hours =490miles

1 hour =490/5=98miles

10hours = 98×10=980miles

9514 1404 393

Answer:

  a) 30.7 million

  b) 1.5% per year

  c) 42.0 million

  d) 2017

Step-by-step explanation:

a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.

__

b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.

The population is growing by 1.5% per year.

__

c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.

  P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0

The population in Canada in 2021 is predicted to be 42.0 million.

__

d) For this we need to solve for t when P(t) = 40.

  40 = 30.7·1.015^t

  40/30.7 = 1.015^t

Taking logarithms gives ...

  log(40/30.7) = t·log(1.015)

  t = log(40/30.7)/log(1.015) ≈ 17.773

In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.

_____

Additional comment

The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.

Answer:

c part ....

please mark brainlest

Answer:

Step-by-step explanation:

4x-8<5x+4

4x<5x+12

-x<12

flip sign

x > -12

Answer:

-12 < x

Step-by-step explanation:

4x-8<5x+4​

Subtract 4x from each side

4x-4x-8<5x-4x+4​

-8 < x+4

Subtract 4 from each side

-8-4 < x+4-4

-12 < x

Answer:

150

Step-by-step explanation:

-5pqr

Let p = 3, q= -5, and r = 2

-5(3)(-5)(2)

-15(-5)(2)

75(2)

150

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{pink}{☆Answer}}}}}}:)}[/tex]

See this attachment

Answer:

7/6

Step-by-step explanation:

(7x/12)/(x/2)

=7/6

Answer:

14

Step-by-step explanation:

10000 = 5000[tex](1.05)^{t}[/tex]

2 =  [tex](1.05)^{t}[/tex]

ln(2) = t ln(1.05)

t = ln(2)/ln(1.05)

[tex]\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots[/tex]

For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.

If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,

then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

For $5000 invested at 5% p.a. compound interest with yearly

rests to double in value, we need to find the time.

So,

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

[tex]10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21[/tex]

Hence, The time will be 14 years. So, option D is correct.

Learn more about compound interest here:

https://brainly.com/question/1329401

#SPJ2

Answer:

-$0.26

Step-by-step explanation:

Calculation to determine the expected value of playing the game once

Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]

Expected value= ($18/38 x $5) - (20/38 x $5)

Expected value= ($2.37-$2.63)

Expected value= -$0.26

Therefore the expected value of playing the game once is -$0.26

502.5 = -502.5

Now

x = -502.5

= -5025/10

= -1005/2 feet

Answered by Gauthmath must click thanks and mark brainliest

Answer:

[tex]\angle 72=BC-86/2[/tex]

[tex]144+86=BC[/tex]

[tex]BC=230[/tex]

[tex]BC=230/2[/tex]

[tex]\angle BAC= 115[/tex]°

~OAmalOHopeO

Answer:

4

Step-by-step explanation:

Hi there!

Range = largest number from data given - smallest number from data given

From the given data, 58, 59, 57, 59, 55,

59 is the largest number and 55 is the smallest number

So the range = 59 - 55 = 4

Answer:

Option (3)

Step-by-step explanation:

Given functions are,

f(x) = [tex]\frac{1}{4^x}[/tex]

g(x) = log(2x)

By using a graphing utility we can draw the graphs of the given system of equations.

Common points of the graph will be the solutions of the equations,

From the graph attached,

Solution of the functions is → (0.937, 0.273)

                                             → (0.9, 0.3)

Option (3) will be the answer.

Answer:

A.

[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]

Answer:

Step-by-step explanation:

Multiplication is Commutative. the term can be multiplied in either order. the product will be the same as the previous product.

OAmalOHopeO

# Sin θ = 9/15.

# Cos θ = 12/15.

# Cosec θ = 15/9.

# Sec θ = 5/4

Step-by-step explanation:

[tex]by \: using \: pythagorian \: triplets[/tex]

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {9}^{2} + {12}^{2} = {c}^{2} [/tex]

[tex]81 + 144 = {c}^{2} [/tex]

[tex]225 = {c}^{2} [/tex]

[tex]c = 15.[/tex]

[tex] \sin θ = \frac{9}{15} [/tex]

[tex] \cos θ = \frac{12}{15} = \frac{4}{5} [/tex]

[tex] \csc θ = \frac{15}{9} [/tex]

[tex] \secθ = \frac{5}{4} [/tex]

Answer:

$ 645.85

Step-by-step explanation:

First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.

A = 6500 (1 + 0.025)^5 = 7354.15

That is the amount that would be in the account at the end of the 5 years.

Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).

8000 - 7354.15 = 645.85

Your final answer would be rounded to the nearest cent, or the hundredths place.

Answer:

[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]

Hence b^3=-1