I Jared bas as many books as Yamil. If they have 63 books altogether, how many books does each boy have?

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

b

Step-by-step explanation:

the answer is b because both were clear liquids and now they turned yellow change in color is part of chemical reactions so b is correct

Answer:

Step-by-step explanation:

y = kx

If y = 25x , then k = 25

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

Answer:

8th term is 3980.

Step-by-step explanation:

0 12 72 240 598 1250 2322

Differences in successive terms

are:

12   60   168   358   652   1072

   48   108    190   294   420

       60     82     104    126

            22      22      22  

So calculating the 8th term , working from the last line to the first:

126 + 22 = 148

148 + 420 = 568

1072 + 568 = 1658

Finally the 8th number = 2322 + 1658 = 3980

Answer:

5(3x + 2)

Step-by-step explanation:

15x + 10

1. 5(3x + 2)

BC is tangent to circle A, and the value of r is 10.

Given,

BC=24

CD=16

AD=AB=r

To find the value of r, we can use the fact that a tangent line to a circle is perpendicular to the radius at the point of tangency. So we know that angle ABD is a right angle, and we can use the Pythagorean theorem

The Pythagorean theorem can be used to calculate the value of r:

\(AB^2+BC^2=AC^2\)

\(r^2+24^2=(r+16)^2\)

\(r^2= (r+16)^2-24^2\)

\(r^2\)= \(r^2\)+256+32r-576

\(r^2\)=\(r^2\)+32r-320

\(r^2-r^2\)-32r=-320

-32r=-320

r=320/32

r=10

Therefore the correct answer is r=10.

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There is approximately a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 3 odd numbers among the possible outcomes of each die (1, 3, 5), so there are 3 x 3 = 9 ways to obtain an odd sum:

(1,2), (1,4), (1,6), .... (6,1), (6,3), (6,5)

There are 6 possible outcomes for rolling the same number on both dice, so there are 6 ways to obtain doubles:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

We counted (1,1), (3,3), and (5,5) twice in the above two categories, so we need to subtract 2 from the total count.

Therefore, there are 9 + 6 - 2 = 13 ways to obtain an odd sum or doubles.

Therefore, the probability of rolling an odd sum or doubles is:

P(odd sum or doubles) = 13/36

Thus, there is about a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

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Answer:

i have no idea good luck i will try to get the answer for ya though

Step-by-step explanation:

.

A total of 192 students voted altogether.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

Given:

The number of students who voted for Morgan = 64.

Let the number of students who voted for Whitney = n.

According to the question,

n = 2 times the number of students who voted for Morgan

n = 2 x 64

n = 128.

The total number of students who voted = 64 + 128

The total number of students who voted = 192.

Therefore, the required number of votes is 128.

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Answer:

butterflies (b)=50

butterflies in 6 months =20/100×50=10+b =60

butterflies in 12 months =2(6months)

butterflies in 12 months= 120

The population of butterflies after 1 year is 72 butterflies

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the present population of butterflies be A = 50 butterflies

The percentage increase after 6 months = 20 %

The population of butterflies after 6 months = present population of butterflies + percentage increase after 6 months

The population of butterflies after 6 months = 50 + ( 20/100 ) x 50

                                                                         = 50 + ( 0.2 x 50 )

                                                                         = 50 + 10

                                                                         = 60 butterflies

The population after 6 more months =  population of butterflies after 6 months + percentage increase after 6 months

The population after 6 more months =  60 + ( 20/100 ) x 60

                                                              = 60 + 0.2 x 60

                                                              = 60 + 12

                                                              = 72 butterflies

Hence , The population of butterflies after 1 year is 72 butterflies

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To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer:

2,197 is D

Explanation:

4/3 * 3.14 * 13^3 =

2,197

The measure in radians for the central angle is approximately 0.7 radians.

To find the measure in radians for the central angle of a circle, we can use the formula:

θ = s / r

where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.

In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.

Plugging these values into the formula, we have:

θ = 5.6 cm / 8 cm

Simplifying the expression:

θ = 0.7

We may use the following formula to get the centre angle of a circle's measurement in radians:

= s / r

s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.

The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.

When these values are plugged into the formula, we get:

θ = 5.6 cm / 8 cm

Condensing the phrase:

θ = 0.7

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The figure with 2 lines and 2 rays is drawn and labeled and can be seen in the attached picture.

In the question, we are asked to draw and label a figure that has at least 2 lines and 2 rays.

First, we need to note three things:

Now, we are asked to make a figure with 2 lines (that is, two endless collections of points) and 2 rays (that is, a part of the line with a fixed start point, but no end point).

This can be shown in the attached figure.

In the figure, AB and CD are the two lines, and PQ and XY are the two rays.

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Answer:

1.19175359

Step-by-step explanation:

Use ma1hway

Step-by-step explanation:

(3h - 5)(5h + 4) =   3h * 5h    +   3h * 4     - 5*5h    - 5 *4

                              =    15h^2        - 13h    -20

\((3h-5)(5h+4)\)

\(=(3h+-5)(5h+4)\)

\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)

\(=15h^2+12h-25h-20\)

Answer:

Answer:

-6.7x + 3.3y

Step-by-step explanation:

Step 1: Write out expression

3.5x + y - 10.2x + 2.3y

Step 2: Combine like terms (x)

-6.7x + y + 2.3y

Step 3: Combine like terms(y)

-6.7x + 3.3y

Answer:

3.3 y - 6.7 x

Step-by-step explanation:

Rewriting for clarity.

(2.3y + y) + (3.5x - 10.2x)

(3.3y) + (-6.7x)

3.3y - 6.7x

Answer:

8/3 or 2 2/3

Step-by-step explanation:

\(f(x) = -5 * 2\) is one conceivable exponential function (-x). The coordinates of this function are (0, -5) and (-2, -20).

Because the exponent's base falls between 0 and 1, this function depicts exponential decay. The output of the function decreases at an increasing rate as x rises because the value of 2(-x) shrinks. The function starts at a number larger than zero and lowers with time, as shown by the negative sign. The initial value of -5 denotes the function's beginning point. As a result, when x rises, the function's output gets closer to zero but never quite hits it.

Because to the diminishing nature of the exponent's base, the function \(f(x) = -5 * 2(-x)\)  generally indicates exponential decay.

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Question:

Solution:

Notice that the function f(x) = 2-2x is a linear function with slope -2 and y-intercept 2. Then its graph on the given domain is:

Now, the range of the function is found by evaluating the function at the extreme points of the domain. That is:

and

Thus, the range of this function (not taking into account all the real numbers, but with the notation of the exercise) is:

\(\large\texttt{Answer\::}\)

pls refer to the explanation !

\(\large\texttt{Calculations\::}\)

\(\textsf{Area of a circle : $A=\pi r^2$}\)

We're asked to use 3.14 for pi , so we'll do just that .

We have the diameter , so we divide it by 2 to find the radius (remember , the radius is 1/2 of the diameter).

Plug in :

A=3.14*(7)²

A=3.14*49

Multiply :

A=153.86 inches²

\(\footnotesize\texttt{hope\:helpful~}\)

Answer:

Step-by-step explanation:

Given:

Use the area of the circle formula.

AREA OF THE CIRCLE FORMULA:

\(\Longrightarrow: \sf{A=\pi r^2}\)

\(\Longrightarrow: \sf{\pi =3.14}\)

\(\Longrightarrow: \sf{r=\dfrac{14}{2}=7}\)

\(\Longrightarrow: \sf{3.14*7^2}\)

Use the order of operations.

PEMDAS stands for:

BODMAS stands for:

\(\sf{3.14*7^2}\)

First, solve exponents.

\(\Longrightarrow: \sf{7^2=7*7=49}\)

\(\Longrightarrow: \sf{3.14*49}\)

Then, multiply.

\(\sf{3.14*49=\boxed{\sf{153.86}}\)

Solutions:

\(\Longrightarrow: \boxed{\sf{153.86\ in^2}}\)

I hope this helps, let me know if you have any questions.

Answer:

meter equals 1.312 steps because 1 times 1.312 (the conversion factor) = 1.312

The equation of the linear function in slope intercept form is f(x) = -2x + 1

The table can be used to write linear equation in slope intercept form.

Therefore, the equation of the linear function in slope intercept form is as follows:

y = mx + b

where

Therefore,

m = 3 - 5 / -1 + 2

m = - 2 / 1

m = -2

Therefore, the y-intercept can be solved as follows;

using (0, 1)

y = -2x + b

1 = -2x + b

1 = -2(0) + b

b = 1

Hence, the the equation of the linear function in slope intercept form is f(x) = -2x + 1

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Answer:

A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.

Step-by-step explanation:

Answer:

(-2,1)

Step-by-step explanation:

up and right is adding to the current point so (-7+5,4)

down and left is subtracting to the current point so (-2,4-3)

If you combine them, you get: (-7+5,4-3)-which is (-2,1)

Answer:

1000 meters below sea level

Step-by-step explanation:

Since the submarine dives at a depth of 4 times 200 meters, then it dives 800 meters.

Sso the submarine now is at 200 meters + 800 meters =1000 meters below sea level.

The graph of y=-3x-1 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation is  y=-3x-1

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

In the given equation slope is -3.

Let us find few values of x and y.

x    0    1    2     3    4

y    -1   -4   -7    -10  -13

Hence, the graph of y=-3x-1 is given in the attachment.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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