Find the average rate of change of f(x) = -3x² + 1 over each of the following intervals.
(a) From 2 to 4
(b) From -2 to 0
(c) From 2 to 5

Answer:

[tex](0, -\frac{15}{2} )[/tex]

Step-by-step explanation:

When a straight line crosses the y-axis, the point that touches it is called the y-intercept. We can find the y-intercept by plugging in zero as the value for 'x', as any x value on the y-axis is zero. So plugging in x = 0 into the equation '3x - 2y = 15', we get -2y = 15, so y = -15/2. The point would be [tex](0, -\frac{15}{2} )[/tex], as x = 0 when y = -15/2.

To form equations from word problems, we can derive mathematical operations as well as variables from the given information.

In this case, each time Walker reads a certain number of pages, we subtract that from the total number of pages left to know how many pages is left to read.

Let r represent the pages left to read.

792 pages in total

Walker reads 15 pages a day during the week and 25 pages a day during the weekend.

5 weeks have passed

r = 792 - (5×15 + 2×25)×5

The decimal: 0.4545...

Can be written in fraction form as 45/99.

Here we have the number:

N = 0.4545...

Notice that the repeating digits are two, 4 and 5.

Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:

100*0.4545... = 45.4545...

Now if we subtract the original number, we get:

45.4545... - 0.4545... = 45

This means that:

(100 - 1)*0.4545... = 99*0.4545... = 45

Then we can multiply and divide our number by 99, so we get:

[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]

So the fraction is 45/99

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Answer:

4y⁷x²

Step-by-step explanation:

    Prime factorize each expression.

28y⁷x² = 2 * 2 * 7 * y⁷ * x²

8y⁸v⁴x⁶ = 2 * 2 * 2 * y⁸ * v⁴ * x⁶

GCF = 2 * 2 *y⁷*x²

        = 4y⁷x²

Answer:

Jane is 11 1/4 years old.

Step-by-step explanation:

Subtract all of the numbers given.

[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].

To subtract this, we need to find a common denominator.

A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.

The new expression will look like this:

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].

Now we can subtract.

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]

Reduce the answer.

[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]

In decimal form 11.25

Hope this helps!

If not, I am sorry.

The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.

We need to find the volume of the copper wire.

The formula to find the volume of a cylinder is πr²h.

Now, the volume of the copper wire=πr²h=[tex]\frac{22}{7} \times (0.6)^{2} \times 200000=2,26,080[/tex] mm³=226.080 cm³

If the density of copper is 8.9 g/cm³, find the mass of the wire.

We know that [tex]Density=\frac{Mass}{Volume} }[/tex].

⇒8.9 g/cm³=[tex]\frac{Mass}{226.080}[/tex]

⇒Mass=2,012.112 g/cm³

Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

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Answer:

339

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given information:

Therefore:  [tex]y=240b^x[/tex]

To find an expression for the population after 1 hour, substitute x = 1 into the found equation:

[tex]\implies y=240b^1[/tex]

[tex]\implies y=240b[/tex]

We are told that the population after 9 hours is double the population after 1 hour.  Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:

[tex]\implies 2(240b)=240b^9[/tex]

[tex]\implies 480b=240b^9[/tex]

[tex]\implies 480=240b^8[/tex]

[tex]\implies 2=b^8[/tex]

[tex]\implies b=\sqrt[8]{2}[/tex]

[tex]\implies b=2^{\frac{1}{8}}[/tex]

Therefore, the final exponential equation modelling the given scenario is:

[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]

[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]

To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:

[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]

[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]

[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]

Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.

Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

The average speed of the Australian team's laser boat in the San Francisco final was 68.81 km/h.

The laser boat is a type of boat that uses the wind to move on the water. This type of boat is used in the SailGP Championship.

In the phase of San Francisco, the United States the winner was the team of Australia that had an average speed of 68.81 km/h and a maximum of more than 90 km/h.

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Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

It is defined as the difference between the maximum value in the data set to the minimum value in the data set.

We have:

The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets:

Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}

Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}

Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}

Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}

The IQR for Alyssa:

IQR = Q3 - Q1

IQR = 8 - 5 = 3

The IQR for Bryant:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

The IQR for Camila:

IQR = Q3 - Q1

IQR = 10 - 2 = 8

The IQR for Devon:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

Thus, Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

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The equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]

The expression is given as:

[tex](3m^{-4})^3 * (3m^3)[/tex]

Expand the brackets

[tex]27m^{-12} * 27m^3[/tex]

Apply the law of indices

[tex]729m^{-12+3}[/tex]

Evaluate the sum

[tex]729m^{-9}[/tex]

Hence, the equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]

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Answer:

the height: h=2,25

Step-by-step explanation:

volume of rectangular box = wide*long*the height

----> the height = volume of rectangular box / ( wide*long) = 2,25

give me 5 stars and hearts^^

Answer:

x = 20°

Step-by-step explanation:

x° + 2x°+ (x+10)° = 90°

4x° + 10° = 90°

4x° = (90 -10)°

x° = (80/4)°

x = 20°

Hope this helps

Answer:

x = 20

Step-by-step explanation:

Key points:

Diagram notation

In the diagram, there are three angles, each with an expression representing the measure of their angle (in degrees).  Angles are adjacent (next to each other with the same vertex) such that collectively they form one large angle.

The small square in the lower left corner means that the large angle is a right angle.  All right angles are 90°.

Note:  The expressions for each angle all have a degree marking, so each angle is measured in degrees.  The unknown value x, is a number without any units, the expression is simplified, and then the units "degrees" are applied.  So in the end, the answer for "x" will not have units; "x" will just be a number.

Angle Addition Postulate

The Angle Addition Postulate states that the sum of the measures of two adjacent angles is equal to the measure of the large angle formed by those adjacent angles.  

[tex](\text{measure of first angle})+(\text{measure of second angle})=(\text{measure of the combined angle})[/tex]

Solving the given problem

By applying the Angle Addition Postulate a couple times, the sum of the measures of all three angles in the diagram is equal to the measure of the large angle formed by those three angles.

[tex](\text{measure of first angle})+(\text{measure of second angle})+(\text{measure of third angle})=(\text{measure of the large right angle})[/tex]

or

[tex](x)+(2x)+(x+10)=(90)[/tex]

From here, to solve for x, we'll need to combine like terms, isolate x, and simplify.

Start with the Associative Property of Addition to combine like terms:

[tex](x+2x+x)+10=90\\4x+10=90[/tex]

To isolate x, subtract 10 from both sides and simplify...

[tex](4x+10)-10=(90)-10\\4x=80[/tex]

... then divide by 4 on both sides and simplify.

[tex]\dfrac {4x}{4}=\dfrac {80}{4}\\x=20[/tex]

So, x=20

The correct option regarding the inverse function is given by:

B.They are reflections of each other.

The inverse function is the reflection of the original function over the line y = x, that is, they are reflections of each other, hence option B is correct.

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The correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

Here we have two pieces of information

Gas station A:-

3 gallons for $9.15

1 gallons for  $9.15 / 3 = $ 3.05

Gas station B:-

P = 3.08g

It means that station B is selling the gasoline at a higher price.

Therefore the correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

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Answer: The answer is x = +/- [tex]\sqrt{y+1}[/tex].

Step-by-step explanation: You can solve this by simply rearranging the equation to make x by itself.

-[tex]x^{2}[/tex] = -y - 1

Then cancel out the -1 by dividing it through to obtain.

[tex]x^{2} =y+1[/tex]

The final step is to square root both sides to get rid of the exponent.

x = [tex]\sqrt{y+1}[/tex]

This should be the answer since square roots have a +/-.

#A

New side

Area

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

Answer:

A)  (x + 8)² cm² = (x² + 16x + 64)  cm²

B)  (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given side length of square field:

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

⇒ Area of field = (x + 8)² cm²

Expand and simplify:

⇒ Area = (x + 8)²

⇒ Area = (x + 8)(x + 8)

⇒ Area = x(x + 8) + 8(x + 8)

⇒ Area = x² + 8x + 8x + 64

⇒ Area = (x² + 16x + 64)  cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

⇒ Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

⇒ Area = (x² + 19x + 84) cm²

Answer:

18

Step-by-step explanation:

We know that y is 1.5 times x, so when x = 12, y = (1.5)(12)=18

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of x is 8, when the value of y is 12.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Given Variables y and x have a proportional relationship, therefore, we can write,

y ∝ x

y = k × x

21 = k × 14

21/14 = k

k = 1.5

Therefore, the equation for the relationship between x and y can be written as,

y = 1.5x

now, the value of x when the value of y is 12 is,

12 = 1.5 × x

x = 8

Hence, the value of x is 8, when the value of y is 12.

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Answer:

a=75

b=70

c=110

d=105

e=110

f=105

Step-by-step explanation:

Step-by-step explanation:

[-5, 4] because it is an empty circle, meaning less than

The point on the graph f(x) = 3.4ˣ is (0, 1)

None of the given options is correct.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.

Let's try each option:

A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.

B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.

C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.

D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.

Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.

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The value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other known as parallel lines.

We have a perpendicular line shown in the picture.

The measure of the angle (4x - 6) is equal to 90 degree.

4x - 6 = 90

4x = 96

x = 24

Similarly, the measure of the angle (x + 6y) is equal to 90 degree:

x + 6y = 90

Plug x = 24

24 + 6y = 90

y = 11

Thus, the value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.

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0 planes contain points J, K, and N.

Given that, planes X and Y and points J, K, L, M and N.

We need to find exactly how many planes contain points J, K, and N.

From the figure, we can see Point J doesn't belong to the planes X and Y and Point K and N belong to the plane X.

Since, points J, K, and N together do not belongs to any single plane, the planes contain points J, K, and N is 0.

Therefore, 0 planes contain points J, K, and N.

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Answer:

2 planes.

Step-by-step explanation:

The third option is correct.

Answer:

Step-by-step explanation:

[tex]\bf 2(xy-7)[/tex]  [tex]\bf when[/tex]  [tex]\bf x=-1/y=3[/tex]

Substitute with x and y with 3:-

[tex]\bf 2\left(\left(-1\right)(3)-7\right)[/tex]

First, Multiply -1 and 3 = -3

[tex]\bf 2(-3-7)[/tex]

Subtract  7 from -3 = -10

[tex]\bf 2(-10)[/tex]

Multiply 2 and -10 = -20

[tex]\bf -20[/tex]

The y-intercept of the line is (0 -6). The given function has no vertical and horizontal asymptotes

A linear equation is an equation that has a leading degree of 1. Given the equation

g(x) = 4x - 6

The y-intercept occurs at a point where x = 0

g(0) = 4(0) - 6

g(0) = -6

Hence the y-intercept of the line is (0 -6)

The given function has no vertical and horizontal asymptotes

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The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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