Evaluate the function below at x=5. Then, enter your solution. f(x)=3(2)^x

Answer:

1) f(x) = 4·x² - 3·x + 6

2) f(x) = -2·x² + 5·x - 1

3) y = 2·(x - 3)² + 5

Step-by-step explanation:

1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows

The general form of a quadratic function is f(x) = a·x² + b·x + c

Where, in (x, y), f(x) = y, and x = x

Therefore for the point (0, 6), we have;

6 = 0·x² + 0·x + c

c = 6

We have c = 6

For the point (2, 16), we have;

16 = a·2² + b·2 + 6

10 = 4·a + 2·b.............................(1)

For the point (3, 33), we have;

33 = a·3² + b·3 + 6

27 = 9·a + 3·b............................(2)

Multiply equation (1) by 1.5 and subtract it from equation (2), we have;

1.5 × (10 = 4·a + 2·b)

15 = 6·a + 3·b

27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;

27 - 15 = 9·a - 6·a+ 3·b - 3·b

12 = 3·a

a = 12/3 = 4

a = 4

From equation (1), we have;

10 = 4·a + 2·b = 4×4 + 2·b

10 - 4×4 = 2·b

10 - 16 = 2·b

-6 = 2·b

b = -3

The function, f(x) = 4·x² - 3·x + 6

2) Where the points are (-1, -8), (0, -1), (1, 2), we have;

For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)

For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)

For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)

Adding equation (1) to equation (3) gives

-8 + 2 = a - b + c +  a + b + c = 2·a + 2·c  where, c = -1, we have

-8 + 2 = -6 = 2·a + 2

2·a = -6 + 2 = - 4

a = -8/2 = -2

From equation (3), we have;

2 = a + b + c

b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5

f(x) = -2·x² + 5·x - 1

3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola

The vertex equation of a parabola is y = a(x - h)² + k

Where;

(h, k) = Vertex (3, 5)

(x, y) = (1, 13)

We have

13 = a·(1 - 3)² + 5

13 = a·(-2)² + 5

13 - 5 = a·(-2)² = 4·a

4·a = 8

a = 8/4 = 2

The equation is y = 2·(x - 3)² + 5.

Answer:30

Step-by-step explanation:

Answer:

x = 84

Step-by-step explanation:

∠ UWV is an angle in a semicircle and is right = 90°

VW = UW  thus Δ UVW is right isosceles, thus

∠ UVW = ∠ WUV = 45° ( sum of angles in triangle ) , thus

x - 39 = 45 ( add 39 to both sides )

x = 84

Answer:

70 degrees

Step-by-step explanation:

Measure of arc ABC is 128 degrees, so measure of arc BC is 128-90 = 38 degrees.

Meausure of arc BCD is 102 + 38 = 140 degrees, so measure of angle A is 140/2 = 70 degrees

Answer:

70°

Step-by-step explanation:

64 * 2 = 128

Inscribed angle is half the arc, so arc BC is 128-90 = 38

A is half of arc BCD, which is 102 + 38 = 140

so m<A = 70°

Answer:

[tex]\huge \boxed{k<1}[/tex]

Step-by-step explanation:

[tex]7k+1<8[/tex]

Subtract 1 from both sides.

[tex]7k+1-1<8-1[/tex]

[tex]7k<7[/tex]

Divide both sides by 7.

[tex]\displaystyle \frac{7k}{7} <\frac{7}{7}[/tex]

[tex]k<1[/tex]

Answer:

400(π+2) feet square

Step-by-step explanation:

let x be the diagonal of the cage=40√2 at the same time it is the radius of the circle ( the tiger can go in circle)

but since the cage is part of the circle and not full turn πr²/8

area of the circleπr²+ half area square

(π(40√2)²)/8 +40²/2

3200π/8+1600/2

400π+800

400(π+2) feet square

Answer:

Slope = -1

Step-by-step explanation:

To find the slope of the line between two points, we simply need to take the difference of the y-coordinates over the difference of the x-coordinates.

(-2, 1) and (3, -4)

Slope = (-4 - 1) / (3 - (-2) )

Slope = -5 / ( 5 )

Slope = - 1

Cheers.

Answer:

See below.

Step-by-step explanation:

This is how you prove it.

<B and <F are given as congruent.

This is 1 pair of congruent angles for triangles ABC and GFE.

<DEC and <DCE are given as congruent.

Using vertical angles and substitution of transitivity of congruence of angles, show that angles ACB and GEF are congruent.

This is 1 pair of congruent angles for triangles ABC and GFE.

Now you need another side to do either AAS or ASA.

Look at triangle DCE. Using the fact that angles DEC and DCE are congruent, opposite sides are congruent, so segments DC and DE are congruent. You are told segments DF and BD are congruent. Using segment addition postulate and substitution, show that segments CB and EF are congruent.

Now you have 1 pair of included sides congruent ABC and GFE.

Now using ASA, you prove triangles ABC and GFE congruent.

Answer: Choice D)  1 - sec^2(a) = tan^2(a) is not an identity.

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

Explanation:

a) is the pythagorean trig identity assuming you meant to write sin^2(a)+cos^2(a) = 1

b) is a rewritten version of tan = sin/cos. You multiply both sides by cos(a).

c) is an identity that you can find through dividing everything in equation (a) by sin^2. I'm assuming you meant to put exponent symbols before each "2".

d) is not an identity. I recommend looking at a table or graph that compares the two sides as separate functions. You should see they are not the same. The actual identity should be sec^2(a) - 1 = tan^2(a). You divide both sides of equation (a) by cos^2 and do a bit of algebra to get it into this form.

Answer:

r= -1/5

Step-by-step explanation:

Step 1: Remove the parentheses (5r-10= -51)

Step 2: Move the constant to the right-hand side and change the sign (5r= -51 + 50)

Step 3: Calculate the sum of -51 +50 (5r = -1)

Last Step: Divide both sides by the equation by 5 (r = -1/5)

The solution for r in the equation is -1/5

The equation given is 5(r-10)= -51

To solve this question, use the distributive property. The distribute property entails expanding the terms in the bracket. This means multiply the terms in the bracket by 5

5(r - 10)

= 5 x (r - 10)

= 5r - 50

The equation then becomes : 5r - 50 = -51

The second step is to combine similar terms. This would be done by making use of the additive property of equalities: 50 would be added to both sides of the equation

5r = -51 + 50

5r = -1

The third step is to divide both sides of the equation by 5

(5r / 5) = (-1 /5)

r = -1/5

A similar question was solved here : https://brainly.com/question/17224218

Answer:

56

Step-by-step explanation:

you have to find the LCM of 7 AND 8.

which is 56

Answer:

The answer is 56

Step-by-step explanation:

Answer:

The number of measles vaccines that Dr. Potter give than polio vaccines is 30

Step-by-step explanation:

The parameters given are;

The number of doses given in a polio vaccine = 6 doses

The number of doses given in a measles vaccine = 3 doses

The number of vaccinations given by Dr. Potter last year = 60 vaccinations

The number of doses given in the 60 vaccinations = 225 doses

Let the number of polio vaccine given last year by Dr. Potter = x

Let the number of measles vaccine given last year by Dr. Potter = y

Therefore, we have;

6 × x + 3 × y = 225.......................(1)

x + y = 60.......................................(2)

From equation (2), we have;

x = 60 - y

Substituting the derived value for x in equation (1), we get;

6 × x + 3 × y = 225

6 × (60 - y) + 3 × y = 225

360 - 6·y + 3·y = 225

360 - 225 = 6·y - 3·y

135 = 3·y

y = 45

x = 60 - y = 60 - 45 = 15

Therefore;

The number of polio vaccine given last year by Dr. Potter = 15

The number of measles vaccine given last year by Dr. Potter = 45

The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.

The number of measles vaccines that Dr. Potter give than polio vaccines =  30 vaccines.

Answer:

they are -7 points away. it would be a negative if you're going down and positive if going up that's how I was explained :D

Step-by-step explanation:

Answer:

5x=2x+2

3x=2

X=2/3

Hope this helps ФωФ

Answer:

1) La opción correcta es;

c) 0

2) La opción correcta es;

c) x = 2

Step-by-step explanation:

1) La forma general de una ecuación cuadrática se puede escribir en la forma;

a · x² + b · x + c = 0

Dónde;

a, y b son los coeficientes de x², x y c es el término constante

Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0

De lo que tenemos;

(0) × x² + b · x + c = 0, lo que da;

(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado

Por tanto, la opción correcta es c) 0

2)

La ecuación dada se presenta como sigue;

f (x) = x² - 5 · x + 6 = 0

Usando el método de prueba y error, tenemos;

Cuando x = 0

f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución

Cuando x = 1

f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución

Cuando x = 2

f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución

Cuando x = -2

f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución

Por tanto, la opción correcta es c) x = 2

Answer:

0.24315

Step-by-step explanation:

Using the z score formula to solve this question

z = (x - μ) / σ,

Such that:

x = raw score

μ = population mean

σ = population standard deviation.

From the question:

x = 3000

μ = 3550

σ = 870

z = (3000 - 3550) / 870

z = -550/870

z = -0.6962

Using the z score table as well as probability calculator(as requested in the question to find the z score)

The probability of having less than 3000 is obtained as:

P(x<3000) = 0.24315

Answer:

2/3

Step-by-step explanation:

Its simple. Ona calculator, if you type in these fractions, you can compare then decimal form values and see which is the biggest:

4/7 = .5714

2/5  = .04

.5/7.0714

2/3 = .66667

Since .6667 is greater than .5714, 2/3 is greater than 4/7

Answer:

B: .57

C: 2/3

Step-by-step explanation:

Divide 4/7 = .57

A: divide 2/5 = 0.4, which is less than 4/7 so we won't include this number as one of the answers

B: .57, which is equal to 4/7

C: divide 2/3 = 0.67, which is greater than 4/7

This question has two answers (B and C), because it is asking which numbers are greater than or equal to.

Answer:

Vertex = (7,5)

Length of latus rectum = 2 units

Step-by-step explanation:

The vertex form of a parabola is

[tex]x=a(y-k)^2+h[/tex]    ...(1)

where, (h,k) is vertex and length of latus rectum is [tex]\left|\dfrac{1}{a}\right|[/tex].

The given equation is  

[tex]x=\dfrac{1}{2}(y-5)^2+7[/tex]    ...(2)

On comparing (1) and (2), we get

[tex]h=7,k=5,a=\dfrac{1}{2}[/tex]

So, vertex of parabola is (7,5).

Length of latus rectum is

[tex]L.R.=\left|\dfrac{1}{a}\right|=\left|\dfrac{1}{\frac{1}{2}}\right|=2[/tex]

Therefore, the length of the latus rectum is 2 units.

Answer:

I) no charge

ii) it will be positively charged

iiI) it will be negatively charged

Step-by-step explanation:

An atom is composed of electrons, neutrons and protons. Electrons are negatively charged while protons are positively charged. The number of electrons and protons in a neutral atom are exactly the same. This ensures the electrical neutrality of the atom.

However, if an atom looses an electron, there are now more protons than electrons present in the atom hence the atom is positively charged.

Similarly, if an atom gains an electron, it now contains more electrons than protons, hence it is negatively charged.

Answer:

$16

Step-by-step explanation:

$24 - $8 = $16

Answer:

$ 16

Step-by-step explanation:

$ 24 - $ 8 = $ 16

Answer:

Step-by-step explanation:

B

Answer:

The answer would be 30% (although I don't see that as an answer).

Step-by-step explanation:

This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.

15/50 = (15*2)/(50*2) = 30/100 = 30%

Answer:

X = 1

Step-by-step explanation:

To solve the system of equation by susbtitution:

3x + y = 9

y = –4x + 10

We can follow the steps thus:

Substitute the value of y in the first equation:

As in the second equation y = -4x + 10 we can substitute in the first equation as follows:

3x + y = 9

3x + -4x + 10 = 9

Combine like terms:

3x + -4x + 10 = 9

Like therms are the therms with X (3x - 4x = -1x):

-1x + 10 = 9

Apply the subtraction property of equality:

-1x + 10 = 9

As 10 is suming, it passes to subtracting the 9:

-1x  = 9 - 10

-1x = -1

Apply the division property of equality:

-1x = -1

Dividing in -1:

x = -1 / -1

Answer:

b

Step-by-step explanation:

The value of x in this system of equations is 1.

3x + y = 9

y = –4x + 10

Substitute the value of y in the first equation:

Combine like terms:

Apply the subtraction property of equality:

Apply the division property of equality:

3x + (–4x + 10) = 9

–x + 10 = 9

–x = –1

x = 1

What is the value of y?

y =  

Answer:

h = 108.8 m

Step-by-step explanation:

x = tanФ h

x = 68m

Ф = 32°

h = unknown

68 = tan(32°) * h

h = 68 / tan(32°)

h = 108.8 m

Answer:

             c(x) = –8x² + 3x – 5

Step-by-step explanation:

Function is quadratic if there is x² and no higher exponent with any x

Answer:

C

Step-by-step explanation:

for edge

Answer:

Step-by-step explanation:

[tex]G = \sqrt{ \frac{m - 5}{2} }[/tex]

To make m the subject square both sides of the equation

That's

[tex] \frac{m - 5}{2} = {G}^{2} [/tex]

Cross multiply

m - 5 = 2G²

Move 5 to the right side of the equation to make m stand alone

We have the final answer as

Hope this helps you

Answer:

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for .

The rectangle is 4 inches long and 3 inches wide. The semi-circle sits on top of the rectangle on a side that is 4 inches long.

Step-by-step explanation:

Answer:

Step-by-step explanation:

From ohms law the expression for voltage is given as

[tex]V= IR[/tex]

Now given that

Voltage, V= [tex]2.4*10^3[/tex] volts

Resistance R= [tex]2*10^6[/tex] ohms

Applying ohms law the current can be calculated by making I the subject of formula

that is I= V/R

[tex]I= \frac{2.4*10^3}{2*10^6} \\\\I= \frac{2.4}{2} *10^(^3^-^6^)\\\\I=1.2*10^-^3[/tex]

The current in amps is 1.2 milli amps

Answer:

Step-by-step explanation:

E is 5 more than d

f is 7 less than d

a) e = d + 5

b) f = d - 7

c) plug the values of e and f

[tex] = d + 5 - (d - 7)[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] = d + 5 - d + 7[/tex]

Since, two opposites add up to zero , remove them from the expression

[tex] = 5 + 7[/tex]

Add the numbers

[tex] = 12[/tex]

Hope I helped!

Best regards!

Answer:

The number is n-0.75

Step-by-step explanation:

Here in this question, we are interested in giving a number which is 75% of 1 less than a number n.

The first thing we do here is to calculate the value of 75% of 1.

That would be;

75/100 * 1 = 0.75

So this value less than n will be;

n- 0.75