You want to put a 4 inch thick layer of topsoil for a new 23 ft by 31 ft garden. The dirt store sells by the cubicyards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.

We are given that

Note: Given the cosine function

then

Comparing the question with what is written in the note

We have

We want to find

(a). Amplitude

From the given question, the amplitude (a) is

(b).Period

From the given question, the period is

(c). Phase Shift

From the given question, the phase shift is

We have a big integer and want to write in scientific notation.

To do this we need to count how many places we need to move the decimal point.

In this case we need to move the decimal point to left so the exponent of 10 will be positive.

So,

We move the decimal point 29 places to left so the exponent of 10 is 29.

Given:

Jim baked 48 cookies with 4 scoops of flour.

So, the unit rate will be = 48/4 = 12 cookies/scoop of flour

So, for 96 cookies, the number of scoops of flour will be =

96/12 = 8

So, the answer will be 8 scoops of flour

Answer:

[tex]f^{-1}[/tex](x) = x/2 - 3/2

Step-by-step explanation:

Swap x and y and solve for y.

Original equation:

y = 2x + 3

Swapped equation:

x = 2y + 3

Now, solve for y:

x -3 = 2y

y = (x-3)/2

If it's wrong, it might just be the way you format your answer, since Pearson (what I assume you're using) is specific about that.

Maybe, [tex]f^{-1}[/tex](x) = x/2 - 3/2 or [tex]f^{-1}[/tex](x) = (x-3)/2

The value of the expression after simplification is found as -3.

For the given expression;

5x + 8 = 2x - 1

Subtract 8 from  both side.

5x + 8 - 8 = 2x - 1 - 8

Simplify

5x = 2x - 9

Subtract both side by 2x.

5x - 2x = 2x - 9 - 2x

3x = -9

Divide both side by 3.

3x/3 = -9/3

x = -3

Thus, the value of the expression is found as -3.

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Solution

Step 1

Two distinct lines intersecting each other at 90° or at right angles are perpendicular to each other.

Hence apply this to question 8 the type of lines shown in the figure is perpendicular lines. Option C

Step 2

To explain this as stated above line A and line B intersect each other at a right angle hence line A and B are perpendicular lines. The line segments are seen below.

A dilation means an elongation of the sides of a figure

So in a dilation the sides are bigger than at the original figure

A key formula for found dilation is Pithagoras theorem

For calculate T'R'

T'R' is the exact diagonal of OT' and OR', that means

OT' + OR' = T'R' in vectorial sum

OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum

So then T'R'^2 = 5^2 + 5^2 = 50.

and T'R'= √50

Now find TR to find the factor of dilation that is

T'R'/TR

The first face is a triangle with height 5in and base 12in

Traingular face area = 1/2 x bh

=1/2 x 12 x 5

= 30 in^2

The area of the other triangular base = 30 in^2

Area of left side face = Length x breadth

= 5 x 4 = 20in^2

Area of the slant face = Length x breadth

= 13 x 4 = 52in^2

Area of the bottom face = Length x breadth

= 12 x 4 = 48in^2

Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2

=180in^2

The numbers under consideration are:

Converting all the numbers to decimal:

Therefore, the numbers can be written as:

48.4, 48.5, 48.09, and 48.6

Out of these numbers, only 48.6 is closest to 49

Answer:

x=-1

Explanation:

Given the equation:

First, expand the brackets:

Next, collect like terms and simplify:

The solution to the equation is -1.

The definition of geometry net is the 2-dimensional shape that if folded, it will produce or yield to the 3-dimensional image

Since the triangular pyramid, has 4 sides (4 triangular faces), when we unfold it on the edges from one tip/corner, it will produce a 2-dimensional image of 3 triangles attached to the sides of one triangle

Answer: -$0.26, -$0.7, $0.65, and -$1.6

The number of days = 5

Average price = Total change in price / the number of days

For Stock A

Total change in price = -$1.30

Average price = - 1.30 / 5

Average price = -$0.26

STOCK B

Average change in price = -$0.14

From, Average price = Total price / number of days

Total price = Average price x number of days

Total price = -0.14 x 5

Total price = - $0.7

For stock C

Average price = 3.25 / 5

Average price = $0.65

Stock D

Average price = Total price / number of days

Total price = Average price x number of days

Total price = -0.32 x 5

Total price = - $1.6

The answer are -$0.26, -$0.7, $0.65, and -$1.6

to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions

to do that we can multiply 4 and 1 by 100, like this:

now we can add the fractions

So the answer is: 419/100

Answer

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Explanation

The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.

u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)

v = <4, -3> = 4i - 3j

Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5

u = (4i - 3j)/5 = (4i/5) - (3j/5)

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Hope this Helps!!!

Answer

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Explanation

The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.

u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)

v = <4, -3> = 4i - 3j

Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5

u = (4i - 3j)/5 = (4i/5) - (3j/5)

u = <(4/5), (-3/5)>

Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1

Hope this Helps!!!

Explanation:

x ^-3y^ -3

We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.

In the given question,

We have to prove the formula sin 3A+sin A = 4sinAcos^2A

The given expression is sin 3A+sin A = 4sinAcos^2A

To prove the formula we take the left side terms to the right side terms

The left side is sin 3A+sin A.

As we know that sin 3A = 3sinA − 4sin^3A

To solve the left side we put the value of sin 3A in sin 3A+sin A.

=sin 3A+sin A

=3sinA − 4sin^3A+sin A

Simplifying

= (3sinA+sin A) − 4sin^3A

= 4sinA − 4sin^3A

Taking 4sinA common from both terms

= 4sinA(1 − sin^2A)

As we know that cos^2A=1 − sin^2A. So

= 4sinAcos^2A

We proved the right hand side.

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The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

It is known that East and West are the opposite of each other.

So, 15 2/3 towards the east let's take it positively.

And 21 3/4 towards left let's consider it negative.

So, the distance from the home

⇒ | ( 15 + 2/3) - (21 +3/4) |

⇒ | 15 -21 + 2/3 - 3/4 |

⇒ | -6 + (8 - 9)/12 |

⇒ | -6 - 1/12 |

⇒ | -(6 +1/12) |

⇒ 6 1/12

Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".

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Answer:

4x+32

Step-by-step explanation:

mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32

We are given two triangles that are congruent and we are asked to mark the parts that are congruent by CPCTC, this stands for Corresponding Parts of Congruent Triangles are Congruent. This means that when two triangles are congruent then their corresponding sides and angles are also congruent.

We notice that the following segments are corresponding segments and therefore congruent:

And also the following angles are corresponding angles and therefore congruent:

Therefore, from CPCTC we know that the corresponding parts are:

Answer:

Height = 13.5cm

Explanation:

The area of a parallelogram is obtained using the formula below:

Substituting the given values:

In order to know the length of the shadow, we will use a trigonometric function in this case for the data given and the distance we want to find we will use the sine

we isolate S

the length of the shadow is 144.89ft

Option D has an incorrect inequality.

Since option D Says:

"All real numbers that are greater than or equal to - 7 1/2 or less than or equal to zero"

Greater than or equal is represented with the symbol ≤ or ≥.

So the correct inequality is for this statement is:

x ≤0 or x>-7 1/2

Not

x < 0 or x>-7 1/2

Note that the x and 0 part doesn't have an equal sign.

according to the equation and information given we can see that the equation is in the form

in which k is the constant of proportionality

use one of the points to find the constant

replace withone of the points to see if its true in all the points

according to this the equation for the table will be

Answer:

The number of shirts sewn at most, when there is just 1 spool of thread left is;

Explanation:

Given a graph that relates the number of spools of thread left to the number of shirts sewn.

We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.

To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.

Tracing the line down we can observe that it is at shirt sewn equals 5.

So, the number of shirts sewn at most, when there is just 1 spool of thread left is;

Answer:

The expected total cost of a service call for 6 hours of labor at company B is $239.5

Step-by-step explanation:

To solve this, we'll find the expression that models the cost at company B.

First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:

This way,

Therefore, we'll have that the hourly rate for company B is $35.

Now, we know that the charge for service is $3 less than at company A. This way,

We can conclude that the charge for service at company B is $29.5

Using this data, we'll have that the expression that models the cost for company B is:

Using x = 6 (six hours of labor),

Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5

Step-by-step explanation:

There is no table attached, please recheck and resend.

Juan's bananas cost half ( 1/2) as much as apples.

x= the cost of an apple in dollars

y= the cost of a banana in dollars

Multiply the cost of an apple by 1/2 (half). that expression must be equal to the cost of a banana.

y = 1/2 x (option b)

Step 1

Plot the triangles

let

A)

we can see that angle in B is 90 ° and length AB is different to BC, When one of the three angles measure 90 degrees and the angles or lengths of other two sides are not congruent, then the scalene triangle is called right scalene triangle

right scalene

Step 2

triangle 2

in this case, we have that length AC equlas AB,also we can see that angle A is smaller than 90 ° ,an acute angle measure less than 90 degrees,so

so

a triangle in which two sides have the same length is called acute isosceles

Step 3

A(3,5),B(5,6),C(3,0)

an obtuse scalene triangle can be defined as a triangle whose one of the angles measures greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. All three sides and angles are different in measurement.so this is an

obtuse scalene

Step 4

finally, A(2,4),B(3,5), C(2,6)

An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.

we can see that

therefore, this is an

rigth isosceles

I hope this helps you

Answer:(3,5) (4,5) (3,6)

acute isosceles

Step-by-step explanation:

The months in which the income was greater than the expenses are:

June, July and August

Solution

For this case we have the following polynomial:

For this case the higher degree is 2 then the answer is:

Degree= 2

Leading Coefficient of the polynomial: 8