Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane.

What is the solution to the equation f(x)=g(x) ?

Answer:

Step-by-step explanation:

The first part tells us that y is, or is anywhere below ½x-3

The second part tells us that above 6-2x

Since we don't know what x is, we cannot actually find y.

The best answer to this question is:

6-2x < y < ½x-3

Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.

Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.

Answer:

64 times

Step-by-step explanation:

16 hours to minutes: 16*60 = 960 minutes

vaping every 15 minutes: 960/15 = 64

The instantaneous rate of change of the function is 5/π

The function is given as

[tex]f(x) =\cos(x - \pi) + 4[/tex]

Where

[tex]x = \pi[/tex]

Calculate f(π) as follows

[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]

This gives

[tex]f(\pi) =\cos(0) + 4[/tex]

Evaluate the expression

[tex]f(\pi) =5[/tex]

The instantaneous rate of change is then calculated as;

[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]

This gives

[tex]f'(x) = \frac{5}{\pi}[/tex]

Hence, the instantaneous rate of change of the function is 5/π

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Mean = 3.5

Median = 3

Distribution is negatively skewed.

What is skew in the distribution?

The distribution has no skewness if the mean and median are equal.

The median exceeds the mean in a favorably skewed distribution.

The distribution is also negatively skewed if the median is lower than the mean.

Given,

Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8

Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]

Mean = [tex]\frac{56}{16}[/tex]

Mean = [tex]3.5[/tex]

Median = mid value of the data set when the values are arranged in   ascending order

Here,

the two mid values = [tex]3, 3[/tex]

Median = [tex]\frac{3+3}{2}[/tex]

Median = [tex]\frac{6}{2}[/tex]

Median = [tex]3[/tex]

Now, as the mean is larger than the median therefore the distribution will be skewed negatively.

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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.

ヾ(•ω•`)o

The graph that represents Lola's Purchase is as shown in the attached file.

Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

Representing expense in the equation form gives us;

Expense on pencils + expense on erasers < 3

Thus;

0.25X + 0.50Y < 3

Dividing through by 0.25, we have;

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)

The correct graph is attached below.

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Answer:

Quadrant II

Step-by-step explanation:

This is because the top right is I, the top left

is II, the bottom left is III, and the bottom right is IV.

Answer:

A) y = 16/(x^2), B) 4/5

Step-by-step explanation:

For A, we can plug in some of the table values to check it. I will try 2 and 3

2. 4 = 16 / (2^2)

    16/4 = 4

3. 16/9 = 16 / (3^2)

   16/9 = 16/9

B) We can just input y into the formula 25 = 16 / (x^2)

This leaves us with +-4/5

Answer:

see explanation

Step-by-step explanation:

(a)

given y varies inversely as x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k substitute any ordered pair from the table into the equation

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , then

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is x = [tex]\frac{4}{5}[/tex]

Answer:

10

Step-by-step explanation:

A scale factor of 2/3 means multiplying all side lengths by 2/3

15*2/3=10

2 items should be placed on the ballot to maximize the total number of votes cast on all items.

According to the statement

items on which people vote = 30

people who will vote = 240

batch containing items = 3

number of batches formed = 10

now we find the number of items placed on ballot to maximize the number of votes.

we find the average number by each items got the vote.

Average = items in batch / total votes

Average = 3/240

but if we add 2 items in the ballot then average become half.

So, 2 items should be placed on the ballot to maximize the total number of votes cast on all items.

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Answer:

B.) as x --> -∞, f(x) --> ∞ and x --> ∞, f(x) --> ∞

Step-by-step explanation:

F(x) is another way of representing "y". That being said, the question is asking you the behavior of the graph in terms of the y-axis. On both sides of the function, there is an arrow pointing upwards, towards infinite, positive y-values. Therefore, as "x" approaches -∞ and ∞, f(x) is approaching ∞ (positive infinity).

65 sequences.

Lets solve the problem,

The last term is 0.

To form the first 18 terms, we must combine the following two sequences:

0-1 and 0-1-1

Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent

So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:

2x + 3y = 18

Case 1: x=9 and y=0

Number of ways to arrange 9 identical 2-term sequences = 1

Case 2: x=6 and y=2

Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28

Case 3: x=3 and y=4

Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35

Case 4: x=0 and y=6

Number of ways to arrange 6 identical 3-term sequences = 1

Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65

Hence the number of sequences are 65.

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Formula: U*V=R*T

3*1=4*x

3=4x

x=3/4

Hope it helps!

Answer:

[tex]\sf PR =\dfrac{3}{4}[/tex]

Step-by-step explanation:

It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.

 TP * PR = UP * PV

    4 * PR = 3 * 1

          [tex]\sf PR = \dfrac{3}{4}[/tex]

Answer:

(or 5/2 or 2 1/2)

Step-by-step explanation:

Remember PEMDAS

10 * (1^2 * 2^-2)

10 * (1 * 0.25)

10 * 0.25 =

2.5

The Area of given figure is 341.6 square.

According to the statement

we have to find the total area of given figure.

Here a= 10 and h= 11

So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))

where the a represent the base of given solid or sides of the equilateral triangle

And h represent the slant height of the solid.

So, Substitute the values in above formula then

A = 10(10 + √((10)^2 + 4(11)^2))

A = 10(10 + √((100 + 4(121))

A = 10(10 + √(100 + 484)

A = 10(10 + √(584)

A = 10(10 + 24.16)

A = 10(34.16)

A= 341.6

So, The Area of given figure is 341.6 square.

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Answer:

option 3

Step-by-step explanation:

6x + 3x² - 4x ← collect like terms

= 6x - 4x + 3x²

= x(6 - 4) + 3x²

= x(2) + 3x²

= 2x + 3x²

Answer:

Option 3: [tex]2x+3x^{2}[/tex]

Step-by-step explanation:

Combine like terms: [tex]6x-4x=2x[/tex]

Put the equation together: [tex]2x+3x^{2}[/tex]

The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].

168 is  the largest number of stamps that Jenna could be putting on each page

What is the Greatest Common Factor?

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

So the largest number of stamps that Jenna could be putting on each page

would be gcd of 1008 and 840.

840 = 2 x 2 x 2 x 3 x 5 x 7

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.

∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.

Hence 168 is  the largest number of stamps that Jenna could be putting on each page

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The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.

The values of x given according to the task content are; x = –2 and x = 2.

By considering equation; x²-4 =0

x² = 4

x = ±2

Also, by considering 4x²= 16;

x² = 16/4 = 4

x = ±4.

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Answer:

The circumference

Step-by-step explanation:

[tex]circumference \: = 2\pi \times radius \\ c = 2\pi(4.4) \\ c = 8.8\pi = 27.65[/tex]

Answer:

Step-by-step explanation:

circumference is 2πr

r=d/2

r=4.46m

C=2π(4.46)=28.02

The quadrilateral is a parallelogram because both pairs of opposite sides are parallel and since the product of the slopes of both pairs of adjacent segments is -1, the quadrilateral is a rectangle

Answer:

The guy above is somewhat right.

Hope this helps!

Step-by-step explanation:

The quadrilateral is a rectangle.

Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;

Variation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.

The required answers to the given questions are:

1. y [tex]\alpha[/tex] x

 ⇒ y = kx

where k is the constant of proportionality.

Given that, y = 5 and x =3, then;

5 = 3x

x = [tex]\frac{5}{3}[/tex]

Thus,

y = [tex]\frac{5}{3}[/tex] x

2. v [tex]\alpha[/tex] w

  v = kw

Given: v = 21, w = 8

Then,

21 = 8k

k = [tex]\frac{21}{8}[/tex]

Thus,

v = [tex]\frac{21}{8}[/tex]w

3.  q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]

  y = [tex]\frac{k}{q}[/tex]

Given: q = 5, q = 6

Then,

5 = [tex]\frac{k}{6}[/tex]

k = 5 x 6

k = 30

Thus,

p = [tex]\frac{30}{q}[/tex]

4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]

  y = [tex]\frac{k}{x}[/tex]

Given: y = 11, x = 3

Then,

11 = [tex]\frac{k}{3}[/tex]

k = 11 x 3

k = 33

Thus,

y = [tex]\frac{33}{x}[/tex]

5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]

F = [tex]\frac{k}{l}[/tex]

Given; F = 20 pounds, l = 1.5 ft

20 = [tex]\frac{k}{1.5}[/tex]

k = 20 x 1.5

k = 30

F = [tex]\frac{30}{l}[/tex]

When l = 6 ft, then;

F = [tex]\frac{30}{6}[/tex]

F  = 5 pounds

The amount of force required is 5 pounds.

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Answer:

y=x^2-10

Step-by-step explanation:

Check the picture below.

The requried measure of the angle m∠C in the given circle is 15°.

In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.

Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82

Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.

∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°

Thus, the requried measure of the angle m∠C in the given circle is 15°.

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The function f(x) is vertically compressed to form g(x)

The functions are given as

f(x) =x^2

g(x) =3x^2

Substitute f(x) =x^2 in g(x) =3x^2

g(x) =3f(x)

This means that the function f(x) is vertically compressed to form g(x)

See attachment for the function g(x)

Also, both functions have the same domain and range

The complete table is:

x      -2    -1    0   1    2

g(x)  12    3    0    3   12

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The odds in simplest form against getting two numbers greater than 4 is 1 : 4.

Probability determines the odds that a random event would happen. The odds  the event occurs is 1 and the probability that the event does not occur is 0.

The odds of getting two numbers greater than 4 = 2 x (numbers greater than 3 in a cube / total number of sides in a cube)

2(3/6)

2 x 1/2 = 1 : 4

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The two points are B'=(-6,-8).

To plot the points:

Plot a new point that is 8 units down and also has the same x coordinate.

Given - Point B = ( -6, 0 )

Represent the new point with B':

In Point B = ( -6, 0 )  

[tex]x=-6,y=0[/tex]

This means that B' has an x coordinate of -6.

Next, is to determine the y coordinate:

If a point (x,y) is translated b units down, the new point is (x, y, -b)

In this case:

The y coordinate of B is 0 and b = 8.

So, the new y coordinate is 0 - 8 = -8

So, we have B'=(-6,-8).

Therefore, the two points are B'=(-6,-8).

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The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding

Given that one number is 4 more than another,

⇒x = y + 4              (equation (1))

Their sum is 60,

⇒x + y = 60

y + 4 + y = 60      (From (1))

2y + 4 = 60

2y = 56 ⇒ y = 28

x = y + 4 = 28 + 4 = 32

Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.

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The experimental probability of landing on red is 7/20 or 0.35 or 35%

The complete question is added as an attachment

From the question, we have the following outcomes:

Red = 7

Green = 5

Blue = 5

Yellow = 3

The total number of spins is

Total = Red + Green + Blue + Yellow

This gives

Total = 7 + 5 + 5 + 3

Evaluate the sum

Total = 20

The experimental probability of landing on red is the calculated as:

P(Red) = Red/Total

Substitute the known values in the above equation

P(Red) = 7/20

Evaluate

P(Red) = 0.35

Express as percentage

P(Red) = 35%

Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%

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The slope in question seven is 1. Below are the solutions to the remaining questions

Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.

Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.

1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise

2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.

3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2

4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.

5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0

6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.

7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be  

Slope = Δy ÷ Δx

Slope = (5 - 4) ÷ (-10 + 11)

Slope = 1 ÷ 1

Slope = 1

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