Question 2 of 10
If f(x) x/2-3 and g(x) = 4x^2 + x - 4, find (f + g)(x).
A. 4x+3x-7
B. 4x2+x-1
C. 66²-7
D. 4x + x-

Answer:

[tex]-1\leq x<\infty[/tex]

Step-by-step explanation:

We want to convert the interval [-1, ∞) to inequality notation using x as the variable.

The interval [-1, ∞) reads: "All real numbers between -1 and positive infinity."

In other words, it is all numbers greater than or equal to -1 and less than positive infinity.

Therefore:

[tex]-1\leq x<\infty[/tex]

Note that we do not use "or equal to" for the infinity as we can never really "equal" infinity.

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Explanation:

Let's label the friends as A,B,C,D.

Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.

Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.

Person C's probability is 5/14 and person D has a probability of 4/13

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

So we have these fractions: 7/16, 6/15, 5/14, 4/13

Once again, we have the numerators and denominators counting down by 1 each time.

Multiplying those fractions gets us...

(7/16)*(6/15)*(5/14)*(4/13)

(7*6*5*4)/(16*15*14*13)

840/43680

(1*840)/(52*840)

1/52

So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.

1/52 = 0.0192 = 1.92% approximately

So this happens about 1.92% of the time.

[tex]{ \bf{ \underbrace{Given}}}[/tex]:

Diameter of the circle "[tex]d[/tex]" = [tex]36[/tex]

Value of [tex]π[/tex] = [tex]3[/tex]

[tex]{ \bf{ \underbrace{To\:find}}}[/tex]:

The circumference "[tex]C[/tex]" of the circle.

[tex]{ \bf{ \underbrace{Solution }}}[/tex]:

[tex]\sf\pink{The\:circumference \:"C"\:of\:the\:circle\:is\:108.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = 3 \times 36[/tex]

[tex] = 108[/tex]

Therefore, the circumference of the circle is [tex]108[/tex].

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Answer:

[tex]\Longrightarrow: \boxed{\sf{108}}[/tex]

Step-by-step explanation:

Apply the formula for the circle's circumference.

[tex]\text{Circumference circle formula:}[/tex]

[tex]\Longrightarrow: \sf{C=\pi d}[/tex]

[tex]\Longrightarrow:\sf{C=?}\\\\\Longrightarrow:\sf{\pi =3}\\\\\Longrightarrow:\sf{d=36}[/tex]

Multiply.

[tex]\sf{3*36=\boxed{\sf{108}}[/tex]

I hope this helps! Let me know if you have any questions.

Answer:

Step-by-step explanation:

[tex](5^3)^5=5^{15}[/tex] which is absolutely huge. In scientific notation it is

3.051757813 × 10¹⁰

Answer:

(5×5×5)=125

125^5=30,517,578,125

final answer=30,517,578,125

Answer:

x = 27

Step-by-step explanation:

I'm going to use letters to label the parts of the triangle while explaining how to solve for x:

Angle A = x (bottom left angle of the triangle)

Angle B = 4x (top angle of the triangle)

Angle C = empty angle (bottom right angle of the triangle)

Angle D = 3x + 54 (angle outside of the triangle)

A line has a angle measurement of 180 degrees.

Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.

To find Angle C, we would subtract Angle D's equation from 180 like this:

180 - (3x + 54)

Now Angle C equals 180 - (3x + 54)

Now we have all the angles inside the triangle. To find x, we are going to sum up  Angle A, B, & C and set it equal to 180.

We set the equation to 180 because a the sum of the interior angles for a triangle is 180.

The equation looks like this:

(180 - (3x + 54)) + 4x + x = 180

Now we use basic algebra to solve it:

(180 - (3x + 54)) + 4x + x = 180

(distribute the - to (3x + 54))

180 - 3x - 54 + 4x + x = 180

(add like terms on the left side of the equation)

126 + 2x = 180

(subtract 126 from both sides)

2x = 54

(divide both sides by 2)

x = 27

To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.

Hope it helps (●'◡'●)

Answer:

-1.540

Step-by-step explanation:

H0 : μ = 18

H0 : μ ≠ 18

The sample size, n = 48

Sample mean, xbar = 17

Sample standard deviation, s = 4.5

α = 0.05

The test statistic :

(xbar - μ) ÷ (s/√(n))

(17 - 18) ÷ (4.5 / √48))

-1 ÷ 0.6495190

= -1.5396

= -1.540 (3 decimal places ).

Answer:

El área es 2 veces el cuadrado del ancho del rectángulo.

Step-by-step explanation:

El área de un rectángulo viene dado por:

[tex] A = a*l [/tex]

En donde:

a: es el ancho

l: es el largo

Si el largo es el doble del ancho:

[tex] l = 2a [/tex]

Entonces el área es:

[tex] A = a*l = a*(2a) = 2a^{2} [/tex]

Por lo tanto, el área es 2 veces el cuadrado del ancho del rectángulo.

Espero que te sea de utilidad!  

Answer:

c

Step-by-step explanation:

Hi!

These two angles are alternate interior angles, so they are congruent. Thus:

∠A = ∠B

6x + 5 = 4x + 45

Solve for x:

2x + 5 = 45

2x = 40

x = 20

Solve for ∠A by substituting in this value:

∠A = 6(20) + 5 = 125°

Answer:

[tex]\frac{15}{ \sqrt{31} - 4}} = \sqrt{31} + 4[/tex]

Step-by-step explanation:

[tex]\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4[/tex]

Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

Answer:

Step-by-step explanation:

1) Least common denominator of 4 and 2 is 4

To eliminate the fraction, each term should be multiplied by 4

ANS:option c

2) Mercury level of water 'y' years = Initial measure +rate of increase 'y' years

0.05 +0.1y = 0.12+0.06y

Ans : Option c

3) 4b +6 = 2 - b + 4

Add 'b' to both sides

4b + b + 6 = 2 + 4

5b + 6 = 6

Subtract 6 from both sides

5b = 6 - 6

5b = 0

 b = 0

Ans : Option b

4) Maximum decimal places in this equation is 2. So, to eliminate decimal places, The equation should be multiplied by 100

Ans: option d

5) y +6 = -3y + 26

Add 3y to both the sides

y + 6 + 3y =  26

y + 3y + 6 = 26

4y + 6 = 26

Subtract 6 from both sides

4y = 26-6

4y = 20

Divide bothe sides by 4

y = 20/4

y = 5

Ans: option c

6) '2x' is  subtracted from both side of the equation.

Ans: option a - subtraction property of equality

Answer:

The answer:

The choose (C) –3

Answer:

27 cm²

Step-by-step explanation:

The surface area is the area of the square plus the area of the 4 congruent triangles.

area of square = 3² = 9 cm²

area of 1 triangle = [tex]\frac{1}{2}[/tex] × 3 × 3 = 4.5 cm²

area of 4 triangles = 4 × 4.5 = 18 cm²

Total surface area = 9 + 18 = 27 cm²

Step-by-step explanation:

SA of a pyramid

=L(2h+L)

=3(2(3)+3)

=3(9)

=27cm^2

Answer:

5/4

Step-by-step explanation:

slope = rise/run

slope=y2-y1/x2-x1

slope=9-(-1)/15-7=10/8=5/4

So the answer is 5/4.

Answer:

5/ 4

Step-by-step explanation:

slope of a line is the rate of change of y co-ordinates with respect to the change in x co-ordinates.

therefore,

[tex]slope = \frac{9 - (-1}{15-7) } \\ = \frac{10}{8} \\ = \frac{5}{4} [/tex]

as we were given 2 points the rate of change of x and y co-ordinates will be equal to the difference between the values of each for the two points.

Answer:

pls i don't know

Answer:

a

Step-by-step explanation:

ok

Answer:

D. 8/9

Step-by-step explanation:

Answer:

I guess that we want to find the equation for each case.

First, let's define the translations:

Horizontal translation.

For a function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, the translation is to the left

if N < 0, the translation is to the right.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

if N > 0, the translation is upwards

if N < 0, the translation is downwards.

Now that we know these, we can find the equations for each case:

1. the graph of y = x² is moved five units upward

the graph is given by a vertical translation of 5 units upward.

y = x^2 + 5

2 the graph of y = 5x² is moved six units to the left

this is:

y = 5*(x + 6)^2

3: the graph of y = -2x² is moved seven units downward

this is:

y = -2x^2 - 7

4: the graph of y = -x² is moved two units to the left and four units downward

now we have two translations, first 4 units to the left and then 4 units downwards, this gives:

y = -(x + 4)^2 - 4

5: the graph of y = -3x² is moved two units to the right

Remember that to move the graph to the right, we need to have N negative, then:

y = -3(x - 2)^2

Answer:

(x + 6)² + (y - 4)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 6, 4 ) and r = 3 , then

(x - (- 6) )² + (y - 4)² = 3² , that is

(x + 6)² + (y - 4)² = 9

Answer:

The cost of an adult ticket is $12.50

Step-by-step explanation:

The given information are;

The cost of two adult tickets and three children tickets = $43.00

The cost of one adult ticket and one child ticket = $18.50

Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;

2·x + 3·y = 43.00...(1)

x + y = 18.5...(2)

(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;

2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6

2·x - 2·x + 3·y - 2·y = 0 + y = 6

∴ y = 6

The cost of each the children ticket = $6.00

From equation (2), where y = 6, we get;

x + y = 18.5

∴ x + 6 = 18.5

x = 18.5 - 6 = 12.5

The cost of an adult ticket, x = $12.50.

Answer:

[tex]y=|x-(-2)|+2[/tex]

Step-by-step explanation:

Hope this is helpful.

The required absolute function is given as y = |x - 2| + 2.

Given that,
From the graph, y = |x - h| + k, values of h and k is to be determined,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph and function, h represents the shift on the x-axis, which 2 units left so the value of h is 2, while k is given the shift of the function over the y-axis which 2 units up means that k = 2

Thus, The required absolute function is given as y = |x - 2| + 2.

learn more about function here:

brainly.com/question/21145944

#SPJ2

Answer:

95%-70%=15%

$876.08×15% =$131.412

Answer:

512.51

Step-by-step explanation:

Hope this helps! :)

Answer:

one solution

Step-by-step explanation:

Answer:

She has 23 nickels and 5 dimes.

Step-by-step explanation:

Let n = the number of nickles and d = the number of dimes.

The number of each = 28. Set up the equation:

n + d = 28

Solve for n:

n = 28 - d

The total amount is $1.65 or 165 cents:

5n + 10d = 165

Substitute:

5(28 - d) + 10d = 165

140 - 5d + 10d = 165

140 + 5d = 165

5d = 165 - 140

5d = 25

d = 5, the number of dimes.

Solve for n:

n = 28 - d

n = 28 - 5 = 23, the number of nickles.

Proof:

5n + 10d = 165

5(23) + 10(5) = 165

115 + 50 = 165

165 = 165

Hope this Helps! Have an Awesome Day!!! <3

Step-by-step explanation:

Answer:

Sofia has 23 nickles & 5 dimes

Step-by-step explanation:

The number of each is 28

Form an equation:

[tex]n+d=28[/tex]

Solve for n:

[tex]n=28-d[/tex]

The total amount is $1.65 for 165 cents:

[tex]5n+10d=165[/tex]

Substitute:

[tex]5(28-d)+10d=165[/tex]

[tex]140-5d+10d=165[/tex]

[tex]140+5d=165[/tex]

[tex]5d=165-140[/tex]

[tex]5d=25[/tex]

[tex]d=25/5[/tex]

[tex]d=5[/tex]

Solve for n:

[tex]n=28-d[/tex]

[tex]n=28-5=23[/tex] ⇒ the number of nickles

CHECK:

[tex]5n+10d=165[/tex]

[tex]5(23)+10(5)=165[/tex]

[tex]115+50=165[/tex]

[tex]165=165[/tex]

hope this helps....

Answer:

1042-96i

Step-by-step explanation:

(3 + 16i)(6 - 64i)

6(3 + 16i)(3 - 32i)

(6) 9 - 96i + 48i +1024