Find all values of x that satisfy the equation below. (x + 1)² - 25/9
= 0​

Answer:

C

Step-by-step explanation:

C

The output of  [tex]R(x) = x^{2} - 3x- 1[/tex] when x = -2 is 9.

PEMDAS exists as an acronym for the terms parenthesis, exponents, multiplication, division, addition, and subtraction.

To estimate the value of R(-2)

Substitute the value of x = -2, then

[tex]R(-2) = (-2)^{2} - 3(-2) - 1[/tex]

By using the PEMDAS order of operations

Calculate exponents, [tex](-2)^2 = 4[/tex]

= 4 - 3(-2) - 1

Multiply and divide (left to right), 3(-2) = -6

= 4 - (-6) - 1

Add and subtract (left to right),

4 - (-6) - 1 = 9

Therefore, the value of R(-2) = 9.

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Answer:

∠ C = ∠BCD = 30°

Step-by-step explanation:

∠ EDF = ∠GFC  = 110°                [ corresponding angles ]

Now consider triangle BCF

∠FBC  + ∠ABC = 180°                [ straight line angle ]

∠FBC  + 100° = 180°

∠FBC  = 180 - 100 = 80°

∠BFC + ∠GFC = 180°                  [ straight line angle ]

∠BFC + 110° = 180°

∠BFC = 180 - 110 = 70°

Sum of angles of triangle is 180°

Therefore , in triangle BCF

That is ,

       ∠F + ∠B + ∠ C  = 180°

          70° + 80° + ∠C = 180°

           ∠C = 180 - 150 = 30°            

Answer:

93

Step-by-step explanation:

So, you basically basic math it, or calculator.

Step-by-step explanation:

this is solved like this

[tex] log_{3}(6) \: - log_{3}(4) \\ = log_{3}( \frac{6}{4} ) \\ = log_{3}( \frac{3}{2} ) \\ = log_{3}(1.5) \\ [/tex]

Answer:

(0,8)

Step-by-step explanation:

Let X be 0 and solve for Y to get the intercept

y= - 4([tex]10^{x}[/tex]) + 12

y= - 4 * [tex]10x^{0}[/tex] + 12

y= - 4 * 1 + 12

y= - 4 + 12

y=8

when x=0, y=8

(0,8) is y intercept

The y-intercept of the given function is (0,8).

We have given that,

The graph of the function f(x) = 10^x

The y-intercept of function gif g(x)=4f(x) + 12

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Let X be 0 and solve for Y to get the intercept

[tex]y= - 4(10^x) + 12[/tex]

[tex]y= - 4 (10^0) + 12[/tex]

[tex]y= - 4 * 1 + 12[/tex]

[tex]y= - 4 + 12[/tex]

[tex]y=8[/tex]

when x=0, y=8

The y-intercept of the given function is (0,8).

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Answer:

3rd quadrant.

Step-by-step explanation:

We know that

4x + 7 < -3

5 - 3*y ≥ 11

We should isolate both of the variables in these inequalities:

for the first one we get:

4x + 7 < - 3

4x < -3 - 7

4x < -10

x < -10/4

So x is smaller than a negative number, then we know that x is negative, from this we already know that the point will be on quadrants 2 or 3.

For the other inequality we get:

5 - 3*y ≥ 11

5 - 11 ≥ 3y

-6 ≥ 3y

-6/3 ≥ y

-2 ≥  y

So we can see that y is equal to or smaller than a negative number, then y is a negative number.

So both values, x and y, are negatives.

This means that the point P(x, y) is in the 3rd quadrant.

Answer:

The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

Step-by-step explanation:

Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.

Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').

he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')

The total time is thus t + t' = 36/(v + v') + 32/(v - v')

Since the whole trip takes 6,5 hours,

36/(v + v') + 32/(v - v') = 6.5  (1)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v')  (1)

(v - v')36 + (v + v')32 = 6.5(v + v')(v - v')  (1)

36v - 36v' + 32v + 32v' = 6.5(v² + v'²)

68v - 4v' = 6.5(v² + v'²)        (2)

Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').

he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')

The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')

Since the whole trip takes 180 minutes = 3 hours,

4/(v + v') + 40/(v - v') = 3  (3)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v')  (1)

(v - v')4 + (v + v')40 = 3(v + v')(v - v')  (1)

4v - 4v' + 40v + 40v' = 3(v² + v'²)

44v - 36v' = 3(v² + v'²)      (4)

Dividing (2) by (4), we have

(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)      

(68v - 4v')/(44v - 36v') = 6.5/3

3(68v - 4v') = 6.5(44v - 36v')

204v - 12v' = 286v - 234v'

204v - 286v = 12v' - 234v'

-82v = -222v'

v = -222v'/82

v = 111v'/41

Substituting v into (2), we have

68v - 4v' = 6.5(v² + v'²)      

68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]        

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²    

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²

[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²

[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²

[7384/41]v' = 6.5[14002/1681]v'²

[7384/41]v' = [91013/1681]v'²

[91013/1681]v'² - [7384/41]v' = 0

([91013/1681]v' - [7384/41])v' = 0

⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or v' =  7384/41 × 16841/91013

⇒ v' = 0 or v' =  180.097 × 0.185

⇒ v' = 0 or v' =  33.33 km/h

Since v' ≠ 0, v' = 33.33 km/h

Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h

So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

Answer:

b. 113.04 ft³

Step-by-step explanation:

To find the volume of this composite figure, we must find the volumes of the shapes it is composed of. After finding the volumes, add the volumes.

This figure is composed of a circular cone and a cylinder.

To find the volume of a cylinder, multiply the radius by itself twice, then multiply the product pi, lastly multiply the product by its height.

[tex]v=\pi *r^2*h[/tex]

To find the volume of a circular cone, multiply the radius by itself twice, then multiply the product by the height, then multiply the product by pi, lastly multiply the product by 1/3.

[tex]v=1/3*h*\pi* r^2[/tex]

Now that we know the formulas, we can find the volume of this figure.

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

The height of the cylinder is 3 feet. The radius is 3 feet as well.

Remember: 3.14 will be used for pi (π).

[tex]v=\pi *3^2*3=84.78[/tex]

The volume of the cylinder is 84.78 feet.

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

Further more, we find the volume of the circular cone.

The height of the cone is 3 feet. The radius is 3 feet as well.

[tex]v=1/3*3*\pi *3^2=28.26[/tex]

Lastly, we add the volumes of both shapes.

[tex](84.78+28.26)[/tex]

[tex]=113.04.[/tex]

113.04 does not need to be rounded to the nearest hundredth.

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

Therefore, the volume of this composite figure is 113.04 ft.

Answer:

12

Step-by-step explanation:

using pythagoras theorem

here 15 is hypotenuse since it is opposite 0f 90 degree

9 and x are the other smaller sides of a triangle

according to pythagoras thorem the sum of square of two smaller sides of a triangle is equal to the square of hypotenuse. So,

9^2 + x^2 = 15^2

81 + x^2 = 225

x^2 = 225 - 81

x^2 = 144

x = [tex]\sqrt{144[/tex]

x = 12

Answer:

6+2x=16-x.

Step-by-step explanation:

X will represent the missing number. Sum means 6, twice that number means multiply it by two, equal represents =, minus represents this, therefor the equation 6+2x=16-x represents the correct answer.

Answer:

64, 125, 216

Step-by-step explanation:

1, 8, and 27 are perfect cubes, i.e., each is the cube of an integer, and they're perfect cubes of consecutive positive integers:

1 = 1³ = 1×1×1

8 = 2³  

27 = 3³

Therefore, the next three-term numbers of the given sequence are:

64 =  4³

125 = 5³ and

216 = 6³

Therefore, the final sequence will look like this:

1, 8, 27, 64, 125, 216

Answer:

10%

Step-by-step explanation:

if the total hours of sports being played is 50 hours, and the time playing soccer is 5 hours, you just divide 5 by 50 (technically will be .1, but to make it a percent you multiply by 100)

[tex]\longrightarrow{\green{ (a + b)(a - b) }}[/tex] 

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex] ={a}^{2} - {b}^{2} [/tex]

[tex] = (a + b)(a - b)[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

1190 m^3

Step-by-step explanation:

l = 1700 cm = 17 m

b = 14 m

h = 1000 cm = 10 m

Total volume = l × b × h

= 17 × 14× 10

= 2380 m^3

since it is half filled ,

Volume is half , so,

volume of water in pond = 2380 ÷ 2

= 1190 m^3

Answer:

100

Step-by-step explanation:

Based on the histogram given :

The vertical axis gives the number of student in the school :

For the range :

0 - 5 = 40

5 - 10 = 30

10 - 15 = 20

15 - 20 = 5

20 - 25 = 3

25 - 30 = 2

Taking the sum :

(40 + 30 + 20 + 5 + 3 + 2) = 100

Answer:

The numbers are 21 and 63

Step-by-step explanation:

let one number be x

let the other number be 3 times the other = 3x

3x + x = 84

4x = 84

x = 21

3x = 3×21 = 63

Answer:

The probability is 1/12.

Step-by-step explanation:

Number of elements in sample space is 6 . Even numbers are 2, 4 and 6 so the there are 3 three even numbers.

So, the probability of getting 3 on the first chance and then an even number in the second chance is

[tex]P = \frac{1}{6}\times \frac{3}{6}\\\\P = \frac{1}{12}[/tex]

Answer:

65 degree, 15 degree

Step-by-step explanation:

In triangle GEF,

∠E = ∠G (Given)

Let's say,

∠E = ∠G = x

∠E + ∠G + ∠F = 180 (Angle sum property of Triangle)

=>x + x + ∠F = 180

=>2x + ∠F = 180

=>2x + 50 = 180

=>2x = 180-50

=> 2x =130

=> x = 130/2

=> x = 65

=>∠E = ∠G = 65

=>∠GEF = ∠EGF = 65 Degree

∠EGF + ∠CGF = 180

=>65 + ∠CGF =180

=>∠CGF = 180 - 65

=> ∠CGF = 15

Answer:

Kevin's weekly sales will have to be worth more than $4000 in order for Dollar Deal to pay more.

Step-by-step explanation:

Dollar Deal offers $8/h plus 10% commission.

If he spends x hours, then offer after x hours and s amount from sales is;

8x + 10%s

This can be rewritten as; 8x + 0.1s

Now, Great Discounts offers $18/h with no commission.

Thus after 8 hours for 5 days, total number of hours = 40 hours.

Thus, great discounts offer = 18 × 40 = $720

Now, dollar deal will offer; 8(40) + 0.1s = 320 + 0.1s

Thus, for dollar deal to pay more weekly, then;

320 + 0.1s > 720

0.1s > 720 - 320

0.1s > 400

s > 400/0.1

s > 4000

Answer: 10:9

Step-by-step explanation:

brother 1-   1m 60cm

brother 2-  1m 44cm

_________________________________________________________

the ratio would be brother 1 : brother 2 => 1m 60cm : 1m 44cm

_________________________________________________________

convert both the values to cm

1m = 100cm

brother 1 would be 100cm + 60cm or 160cm

brother 2 would be 100cm + 44cm or 144cm

_________________________________________________________

[tex]\frac{160}{144} = \frac{10}{9}[/tex] when simplified

the ratio of brother 1 to brother 2 would be 10:9

Answer:

Your just now have finals ?

Step-by-step explanation:

Ay, good luck tho homie !

Answer:

ok so if the scale is 2:49 that can be simplified as 1:98

so that means the real one is 98 times bigger then 24

98*24= 2352 cm or 196 feet

Answer:

Step-by-step explanation:

It's not the correct choice. If a root is given, that is the same thing as the solution. We go backwards from a solution to a factor, which is what you need to do here.

If x = 2i is the solution, then the factor is

(x - 2i). Likewise, with the other one.

If x = 3i is the solution, then the factor is

(x - 3i). The leading coefficient of 1 just sits outside the first set of parenthesis, and because multiplication is commutative, it doesn't matter which set you put first. Thus, the one you want looks like this:

f(x) = (x - 2i)(x - 3i) or

f(x) = (x - 3i)(x - 2i).

length=8 units

Step-by-step explanation:

Answer:

El saldo de la cuenta de  Ana María es de -$16.500 , es decir, Ana María debe al banco $16.500.

Step-by-step explanation:

Ana María tiene $ 30.000 en su cuenta vista y retira $ 18.000 para un pago. Para saber la cantidad de dinero que posee en su cuenta luego de retirar el dinero debes realizar la diferencia (resta) entre lo que tiene inicialmente y la cantidad que retira:

$30.000 - $18.000= $12.000

Ahora el Banco paga un cheque de $ 26.000 con cargo a la cuenta de Ana María, por lo que debe restarse la mencionada cantidad a la suma de dinero que Ana María posee luego del retiro de dinero [un cheque con cargo a la cuenta de una persona indica que para el titular de la misma significa una salida de fondos, y por tanto, una disminución de su saldo]:

$12.000 - $26.000= - $14.000

Finalmente le descuentan una comisión por mantenimiento de la cuenta equivalente a $ 2.500, por lo que se debe realizar la diferencia entre la cantidad calculada previamente y $2.500:

- $14.000 - $2.500= -$16.500

El saldo de la cuenta de  Ana María es de -$16.500 , es decir, Ana María debe al banco $16.500.

Answer:

y = square root x2 - 5

Step-by-step explanation:

y=[tex]\sqrt{x} -5[/tex]

(the top option)

Answer:

=0=−6

Step-by-step explanation: