7
1
-5
35
-4 24
-3 15
-2 8
-1 3
0 0
1 -1
Match the average rates of change of f(x) to the corresponding intervals.
-7
-4
300
[-5, -1]
(-4,-1]
[-3, 1]
-2,1]

Answer:

(x+6)+x=20 Andy

Step-by-step explanation:

X represents Andy

X+6 represents juana who did 6 more problems

(X+6)+x=20

2x+6=20

2x=14

X=7

The area of the rectangle is 104 inches²

Define Area of Rectangle

The area of a rectangle is the space occupied by the rectangle inside its perimeter.

Given that, the perimeter is 42 inches

we know, the formula of perimeter of rectangle = 2(L + W)

so, the first equation will be

2(L + W) = 42

or, 2L + 2W = 42       ----------eq(i)

Next, the length of a rectangle is 5 inches longer than its width, so

L = W + 5

or, L - 5 = W              --------------eq(ii)

Now, the eq(i) is

2L + 2W = 42

Put W value from eq(ii),

2L + 2(L- 5) = 42

=> 2L + 2L - 10 = 42

=> 4L - 10 = 42

=> 4L = 52

=> L = 13

We got, L = 13 put this value in any of the equation

I'm putting the value in eq(ii) as it easy for to solve

=> 13 - 5 = W

=> W = 8

If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that

2(13) + 2(8) = 42  (correct)

13 - 5 = 8 (correct)

Now, we got length and width so now just put the values of L and W in area of rectangle formula,

Area of rectangle = Length * width

                            = 13 * 8

Area of rectangle = 104 inches²

Hence, The area of the rectangle is 104 inches²

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Distance between two coordinates:

Given point: b) (10, -5) and ( -6, 7)

Substitute the value in the expression of distance formula

The distance between coordinates (10,-5) & (-6,7) is 20 unit

Answer:

with?

Step-by-step explanation:

Answer: You have to use a calculator

Step-by-step explanation:

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Answer:

[tex] 7^2[/tex]

Step-by-step explanation:

Answer:

7²

Step-by-step explanation:

the product of a number and its multiplicative inverse is equal to 1 , that is

a ×[tex]\frac{1}{a}[/tex] = 1

given

[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and

[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1

Part A: The multiplication expression is  L×w

Part B: The expression is written as N= r+ g + w + b

The final product = 200 boxes

It is crucial to note that the formula for determining the area of a rectangle is expressed as;

Area = lw

Given that;

The area can be calculated by multiplying the length and the width and also by then adding the number of boxes.

We have the expression as;

10( 4 + 5 + 4 + 7)

Also,

L × w =  r + g + w + b

Hence,  we have that L×w is a multiplication expression.

Total number of boxes for the length = 20

Total number of boxes for the width = 10

Total area = L×w = 20×10=200

We have;

N= r+ g + w + b

but r = g = b

Also,

L×B =  3r + w

Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.

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We want to find the places where the line

2x - 3y = 12

intercepts y-axis and x- axis

When the line intercepts y axis, we know that x=0, we replace it in the equation so we can find y value:

2x - 3y = 12

↓

2 · 0 - 3y = 12

↓

0 - 3y = 12

-3y = 12

y = 12 / -3

y = -4

In the same way, we find the interception with x- axis when y = 0. We find the value of x replacing y by 0 in the equation:

2x - 3y = 12

↓

2x - 3 · 0 = 12

↓

2x - 0 = 12

2x=12

x = 12 / 2

x = 6

We locate both points: y = -4 and x = 6:

Finally, we join the points with a straight line

The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.

If  [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]

Here,

For first option

[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]

For second option

[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]

For the third option,

[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]

For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]

[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]

Fourth option does not have an expression greater than 1

Fourth option is correct.

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For a 44° elevation angle, the grade will be 96%.

Given that,

if the angle of elevation of the road is 44 degrees,

The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)

A tangent ?

One of the six basic trigonometric functions is tangent, denoted as tan().

The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.

[tex]tan \alpha = sin\alpha /cos \alpha[/tex]

The tangent of the angle is the ratio of rise to run.

tan(angle) = grade

tan(44°) ≈ 0.96 = 96%

Therefore, The grade will be 96% for an angle of elevation of 44°.

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The given expression is

It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.

In other words, the answers can't be more precise than the least precise number in the sum.

The measure of ∠C is 121 degrees.

Given that:-

There is a triangle ABC.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

We have to find the measure of ∠C.

We know that,

The sum of all the angles of a triangle is 180 degrees.

Hence, we can write,

m∠A + m∠B + m∠C = 180 degrees

(x + 6)° + (3x - 15)° +  (5x + 36)° = 180 degrees

(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees

9x + 27 = 180 degrees

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

x = 17 degrees

Hence,

The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.

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A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

Also, the correct greatest common factor of 66 and 36 is given by:

Greatest common factor (GCF) = 6

By applying the distributive property of multiplication, we have:

66 + 36 = 6(11 + 6)

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Answer:

3=6 5=10 7=14

Step-by-step explanation:

here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .

Investor purchased 50 shares of stock in a company for $40.

So, the total initial amount he invested is

Then the rate of return is:

So, the requied rate of return is 10.0%.

a) (2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form

The number in standard form is 345

explanation:

The given two multiplication of the numbers is :

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])

First we multiply the non exponential terms as shown below

2.3 × 1.5 = 3.45

Now we multiply the exponential terms as shown below

[tex]$10^4[/tex] × [tex]$10^{-2}[/tex] = 100

Now multiplying the exponential and non exponential term we get the number in standard form as shown below

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])  in standard form 345

(3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form 0.0000002

(8 ×  10^-3) ×  (2 ×  [tex]10^-4[/tex] in standard form  1.6 × [tex]10^-6[/tex]

(6 × 10²)/(3 × 10-5) in standard form 20,00,0000

5.1 × [tex]$10^-1[/tex] in ordinary number is 0.51

(1.7 × [tex]10^4[/tex]) × (8.5x ×[tex]0^-2[/tex]) in standard form  1.445 × 10³.

3.45 x  100 = 345

Therefore, the number in the standard form is 345

b) (3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form

The number in standard form is 0.0000002

explanation:

By dividing 3.6 by 1.8 we get “2”, hence the above equation becomes,

(2 × [tex]10^-5[/tex]) /[tex]10^2[/tex]

We know that

[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]

Therefore the above equation becomes,

2 × [tex]10^-7[/tex]

since the exponent of 10 is negative , therefore 7 zeros are written on the left hand side of the number = 0.0000002

Therefore, the number in the standard form is 0.0000002

c) (8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex]) in standard form

The number in standard form is 1.6 × [tex]10^-6[/tex]

explanation:

Given the product of scientific notations:

(8 ×  [tex]10^-3[/tex]) ×  (2 ×  [tex]10^-4[/tex])

This can be expressed as:

(8 × 2) ×  ([tex]10^-3[/tex] × [tex]10^-4[/tex])

= 16 ×  [tex]10^-3[/tex]-4

= 16 × [tex]10^-7[/tex]

= 1.6 × [tex]10^1[/tex] × [tex]10^-7[/tex]

= 1.6 × [tex]10^-6[/tex]

Therefore, the number in the standard form is 1.6 × [tex]10^-6[/tex]

d) (6 × 10²)/(3 × 10-5) in standard form

The number in standard form is 20,00,0000

e)  5.1 × 10^-1 as an ordinary number

The ordinary number is 0.51

usual form of 5.1 × [tex]10^1[/tex] is

5.1 ×  1/ [tex]10^1[/tex]

= 5.1/10

= 0.51

Therefore , ordinary number is 0.51

f) (1.7 × [tex]10^4[/tex]) × (8.5 × [tex]10^-2[/tex])  in standard form.

The number in standard form is 1.445 × 10³.

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The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the height of the third tree be x.

By the given condition, this will be:

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

The first relation will give x ≥ 32 - 24 = x ≥ 8

The second relation will give:

8 + 16 + x ≤  42

24 + x ≤  42

x ≤  42 - 24

x ≤  18

The inequality is 8 ≤ x ≤ 18.

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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let height of the third tree be x.

By the given condition

The sum of three palm tree heights range from 32 to 42 feet

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

Solve these inequalities

8 + 16 + x ≥ 32

24+x ≥ 32

x≥ 32-24

x≥ 8

and 8 + 16 + x ≤  42

24+ x ≤  42

x≤  42-24

x ≤ 18

Hence the inequality is 8 ≤ x ≤ 18.

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Answers:

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

Explanation:

Question 1

27x^6 = (3x^2)^3 which is one cube and y^3 is another cube

Therefore 27x^6+y^3 is a sum of two cubes.

It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.

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

Question 2

81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.

We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.

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

Question 3

64x^3 = (4x)^3 is a perfect cube

but 9z^9 is not a perfect cube

We can see this if we computed 9^(1/3) and the result is a non-whole number.

The answer here is the same as the previous question.

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

Question 4

36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension  36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.

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

Question 5

1 is a perfect cube since 1 = 1^3

d^12 is a perfect cube because d^12 = (d^4)^3

Therefore, we have a difference of two cubes.

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

Question 6

729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.

However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.

The overall expression is "neither".

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

Question 7

343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube

y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.

We have a difference of cubes.

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

Question 8

4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.

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

Question 9

144^(1/3) isn't a whole number, so we get a similar result to problem 8.

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

Question 10

64j^6 = (4j^3)^3 is one cube

k^9 = (k^3)^3 is another cube

We have a difference of cubes

Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of  negative 2 and 19 over 48

information gotten from the question include

Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.

Division is a basic mathematical operator that performs the function of sharing

division of fraction is done as follows

7 and 2 over 3

= 7 2/3

= 23/3

negative 3 and 1 over 5.

= -3 1/5

= -16/5

= 23/3 ÷ -16/5

= 23/3 * -5/16

= -115/48

= -2 19/48

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Answer:

y = [tex]\frac{28+3x}{4}[/tex]

Step-by-step explanation:

- 3x + 4y = 28 ( add 3x to both sides )

4y = 28 + 3x ( isolate y by dividing both sides by 4 )

y = [tex]\frac{28+3x}{4}[/tex]

The value of x in the vertical angles is 12.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Vertically opposite angles are congruent.

Therefore, the vertical angles measures 84 degrees and 8x - 12.

Let's find the value of x using the principle of vertically opposite angles.

Therefore,

84 = 8x - 12

add 12 to both sides of the equation

84 + 12 = 8x - 12 + 12

96 = 8x

divide both sides by 8

x = 96 / 8

x = 12

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We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.

Given

V(5, -2)

T(10, -3)

Procedure

For V:

The equation of the horizontal straight line corresponds to y = -2.

The equation of the vertical straight line corresponds to x = 5

For T:

The equation of the horizontal straight line corresponds to y = -3.

The equation of the vertical straight line corresponds to x = 10

The domain of the function will be; [0 ∞) and the domain is continuous.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The number c of calories consumed is a function of the number b bars

eaten is represented by the linear function b = 130c

The domain of the linear function would be [0 ∞).

A whole number or a decimal number may be c.

Any data which can be expressed as a decimal is continuous data.

Therefore, the domain of the function will be; [0 ∞) and the domain is continuous.

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Answer:

See below.  I added words tro the first question "Is a" so that I could answer it.

Step-by-step explanation:

f(x) = -3x³ + 9x² - 5x + 15

f(x) = -(x-3)(3x² + 5)

x((9-3x)x-5)+15

-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16

=======

a) Is a [ghost happy]?

O Yes  Yes, as long as it can haunt.

O No

b) Is x + 1 a factor of f(x)?

O Yes  Yes

No

1 a factor of f(x)?  

Always

c) Is a 3 a factor of f(x)?

O Yes

O No    No, as far as I can see.

Answer:

12 ft

Step-by-step explanation:

To find the base (b), you would first need to sketch a right triangle using the following:

a = 9

c = 15

Using the Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex], you would change it to [tex]c^{2} -a^{2} =b^{2}[/tex]  to fit the question. Next, you would plug in the numbers to the corresponding letter.

[tex]15^{2} -9^{2} =b^{2}[/tex]

[tex]225-81=144^{2}[/tex]

[tex]\sqrt{144} =b[/tex]

[tex]12=b[/tex]

The horizontal distance from the tent pole to the rope along the ground will be equal to 12 feet.

According to the Pythagoras theorem, if a triangle has a straight angle (90 degrees), the hypotenuse's square is equal to the total of its other two sides' squares.

As per the given in the question,

Height of tent pole, p = 9 feet

Height of rope, h = 15 feet

Let the horizontal distance from pole to rope is b.

Use Pythagoras' theorem,

h² = p² + b²

15² = 9² + b²

b² = 225- 81

b = √144

b = 12 feet.

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Answer

The height of the child in a year time = 124.8 cm

Explanation

The child is currently 120 cm tall.

The child grows 4% bigger in 1 year.

We now need to calculate how tall the child is in that 1 year.

New height for the child = (Current height) + (Increase in height)

Current height = 120 cm

Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm

New height for the child = (Current height) + (Increase in height)

= 120 + 4.8

= 124.8 cm

Hope this Helps!!!

P = 2L + 2W

P = 72

L = 12W (that's an odd way to put it -- 6x 2x)

P = 2(12W) + 2W

P = 24W + 2W

72 = 26W

W = 2.769

Answer:

see explanation

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2

Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )

P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )

R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )

S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )