Which is the best definition of substitution?
The process of combining the coefficients of terms that have the same variable.
The process of simplifying an expression using the order of operations.
The process of replacing variables with numeric values.
The process of multiplying a base by itself three times.

The third angle of 16 degrees and 102 degrees is 62 degrees.

The third angle of 119 degrees and 23 degrees is 38 degrees.

The third angle of 28 degrees and 87 degrees is 65 degrees.

The third angle of 96 degrees and 51 degrees is 33 degrees.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

In order to determine the missing angle, subtract the sum of the two given angles from 180.

180 - (16 + 102) = 62

180 - (119 + 23) = 38

180 - (28 + 87) = 65

180 - (96 + 51) = 33

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I think using properties can help you mentally find answers to problems because if you know what property you are going to use, then you can know what you are doing, thus it's helping you mentally find answers.

Answer:

Yes, 144>140

Step-by-step explanation:

Since Sinita has 3 boxes of 48 nails, Sinita has a total of 144 nails. (48x3=144)

Sinita needs enough for 35 frames, and each frame uses 4 nails, so she will need a total of 140 nails. (35x4=140)

what Sinita has: 144

what Sinita needs: 140

Sinita has more than what she needs, so yes Sinita has enough nails. (144>140)

Thus, 36° is the smaller angle and 144° is the greater angle.

For instance, the complement angle of 130° and the angle of 50° is 180°. Complementary angles add up to 90 degrees. When the two extra angles are combined, they create a straight line and an angle. The two angles that complement one another do not necessarily need to be close to one another, it should be emphasised. As a result, two angles may be supplementary if their sum is 180 degrees. The study of various shapes is one of the main areas of mathematics.

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The quotient of 7/8 divided by 2/5 will be C. 35/16.

The quotient simply means that we have to divide.

Therefore, the quotient of 7/8 divided by 2/5 will be:

= 7/8 ÷ 2/5

= 7/8 × 5/2

= 35/16

In conclusion, the correct option is C

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The degree of the polynomial formed is 6.

The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.

For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

Now the given functions are:

[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x

Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).

(g°h)(x) is equal to g[h(x)]

=g[2x+5]

=3(2x+5)²-1

=3(4x²+20x+25)-1

=12x²+60x+74

Now we find (f ° g° h)(x)

(f ° g° h)(x)=f[g(2x+5)]

f[g(2x+5)]=f(12x²+60x+74)

f(12x²+60x+74)=(12x²+60x+74)³

Now we have to simplify the expression:

(12x²+60x+74)³

=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]

The largest degree of the variable x in the polynomial is 6.

hence the degree of [f o go h](x) is 6.

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The area of a persian rug in a metre square is given by 10.03 m2. It is calculated by using the concept of area and conversion of units of a quantity.

What is the conversion of units?

Conversion of units is the transformation between various units of measurement for the same quantity, simply the conversion of units deals with converting a quantity into different units without changing its magnitude.

Calculation of the area of the persian rug with given width and length

Given:

Length = 12 feet

Width = 9 feet

The basic step involved in solving this problem is to convert the length and width given in feet into metre

We know that 1 feet = 0.3048 m

Length = 12 × 0.3048

           = 3.657 m

Width = 9 × 0.3048

         = 2.743 m

Area of rug = length × width

=  3.657 × 2.743

= 10.03 m2

Hence, the required area of the persian rug is 10.03 m2.

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Answer:

$45

Step-by-step explanation:

100% = $75

100% - 40% = 60% (discounted price)

60% = 0.6

0.6 x 75 = 45

60% = $45 (discounted price)

Answer:

you have it right.

Domain is 3[tex]\leq[/tex]x[tex]\leq[/tex]positive infinity

Range is 5[tex]\leq[/tex]y[tex]\leq[/tex]positive infinity

Step-by-step explanation:

Answer:

k = -4

Step-by-step explanation:

8 = 2k - 8 - 6k

Collect like terms

8 = -4k - 8

Add 4k to both sides (nice to have variable on left, constants on right)

8 + 4k = -8

Subtract 8 from both sides

4k = -16

Divide both sides by 4

k = -4

Answer:

The first one

Step-by-step explanation:

Because the max is 6, the left ones are only right. Also a point is must be negative so it is the top left one.

Nate's total sales is  83,666.67.

The first step is to determine the commission on sales of $75,000

Commission : 0.025 x $75,000 = $1,875

The second step is to determine the amount of commissions earned on sales above $75,000: $2135 - $1,875 = $260

The next step is to determine the amount earned above $75,000

Amount of sales above $75,000 : $260 / 0.03 = $8,666.67

Total sales for the week :  $8,666.67 + $75,000 = 83,666.67

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Answer:

Step-by-step explanation:

{(0, 2), (1, –1), (2, 3), (3, –2)}

Answer:basically, x never reats with a different y

(x,y)

A is a fn of x since x never repeats

B is a fn of x since x never repeats

C is a fn of x since x never repeats

D is not since we have (1,2) and (1,-2) so this is the answer

Step-by-step explanation:

Answer:

0.03 is the correct answer

Step-by-step explanation:

0.02866009 = 0.03

The frequency tells us how many times the integer appears in the set of numbers.

The integer tells us the numbers that appear in the set of numbers.

To find the mean, we add up all the numbers in the set and divide the sum by the number of integers.

Let's write the information on the graph as a list of numbers:

0, 1, 2, 3, 3, 3, 4, 4, 6, 7, 8, 10

Find the sum:

51

Divide the sum by the number of integers (which is 12):

51/12

= 4.25

The mean is 4.25.

If slopes of the given lines are solved and observed, we get the slope of line E is [tex]m_{E}[/tex] = [tex]\frac{-5}{6}[/tex]

As per question statement, the equation for line A is [tex]y = \frac{6x}{5} - 10[/tex] Line A is parallel to line B, which is perpendicular to line C. The line D is perpendicular to line C and perpendicular to line E.

Before solving this question, we need to know about some basic formulas and concepts of equation for a line.

If Lines are parallel, their slopes are equal and if lines are perpendicular, the product of their slopes is -1.

i.e., if [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are slopes of two lines then if,

[tex]m_{1} = m_{2}[/tex] then lines are parallel

Now slope of line A can be found out by formula [tex]y=mx+c[/tex] hence slope of line A   [tex]m_{A}[/tex]= [tex]\frac{6}{5}[/tex]

Line B is parallel to A so, [tex]m_{B}[/tex] = [tex]\frac{6}{5}[/tex]

Line C is perpendicular to B so [tex]m_{C} * m_{B} = -1\\m_{C} = \frac{-5}{6}[/tex]

Line D is perpendicular to C so [tex]m_{D} *m_{C} = -1\\m_{D} = \frac{6}{5}[/tex]

Line E is perpendicular to D hence [tex]m_{E} * m_{D} = -1\\m_{E} = \frac{-5}{6}[/tex]

Therefore the slope of line E is [tex]\frac{-5}{6}[/tex]

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The equation which is equivalent to the given expression 18 − 15 = − 2x/5 + 7x/15 is (-3 = 5x/5).

The basic equation used to demonstrate and overcome for an unknown quantity is a linear equation for one variable.

The given equation is;

18 − 15 = − 2x/5 + 7x/15

Simplifying the constant and variable part.

- 3 = 5x/5

Multiplying both side by 5;

- 15 = x

or, x = -15.

Thus, the required equivalent equation is - 3 = 5x/5 and the value of variable x is -15.

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Answer:

g(-6) = -6

g(0) = 5

g(7) = 8

h(-6) = 10

h(0) = -1

h(7) = -4

Step-by-step explanation:

g(x) = (1/3) f(x)

g(-6) = (1/3)(-18) = -6

g(0) = (1/3)(15) = 5

g(7) = (1/3) (24) = 8

h(x) = -g (x) + 4

h(-6) = -(-6) + 4 = 10

h(0) = -(5) + 4 = -1

h(7) = -(8) + 4 = -4

I hope this helps!

According to the given statement,

366 liters of natural oil is needed to make 671 L synthetic oil.

Essential oils, which are more natural, are slightly different from synthetic oils. An intentionally created chemical component is present in synthetic oils, which are used as lubricants.

Full synthetics and semi-synthetic oils are the two primary types of synthetic oils. Full synthetics originate from crude oil or byproducts in this situation. Conventional oils are produced using chemical procedures rather than distillation. The resulting synthetic oil has a higher molecular make-up and frequently exhibits more consistent characteristics. Synthetic oils are used in many cosmetic and medicinal goods, just like their more natural equivalents.

According to the given values;

The ratio of natural to synthetic oil

= 6:5

If 671 liters have to be made then,

Add 6+5=11

So, 6/11 of 671liters will be = 366 liters of natural oil

and, 5/11 of 671 liters will be = 305 liters of synthetic oil

Hence, 366 liters of natural oil is needed.

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The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Triangle law of vectors states that for a ΔABC

The sum of vectors of two sides is equal to the third side vector.

Two vectors are said to be Parallel if one vector is scalar multiple of other.

In the given figure

In ΔABC , D is mid point of AB and E is the mid point of AC .

By using triangle law of vectors for ΔADE

AE+AD=ED......(1)

Now using triangle law of vectors addition for ΔABC

CA+AB=CB    ....(2)

(as given that E is the mid point of CA , we can write [tex]AE=\frac{1}{2} CA[/tex]

CA=2AE.....(3)

and D is mid point of AB , we can write [tex]AD=\frac{1}{2} AB[/tex]

AB=2AD......(4)

Substituting (3) & (4) in (2) we get

2AE+2AD=CB

2(AE+AD)=CB

SUBSTIUTTING VALUES OF (AE+AD) from (1) we get

2ED=CB

[tex]ED=\frac{1}{2} CB[/tex]

Hence , the line joining the midpoints of two sides of a triangle is  half of third side.

Since ED is (1/2) of CB i.e. ED is scalar multiple of CB.

Hence they are parallel.

Therefore , The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

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It is not possible that the intersection case is P(A B)=0.5 .

The set of all objects that are members of both sets A and B is represented by the intersection of the two sets A and B, abbreviated as A∩B.

If there is any element x that is an element of both A and B, then we can also say that A intersects (meets) B at x. If A∩B is an inhabited set, which means that there must be some x such that x∈A∩B exists, then A intersects B equivalently.

If A does not intersect B, then A and B are said to be disjoint. They share no elements, to put it simply. If the intersection of A and B contains nothing—A∩B=Ф—then A and B are disjoint.

Explanation:

The likelihood of occurring of an event is called probability.

Consider two events A and B are occurred with probabilities P(A) and P(B)  respectively.

The probability that both the events occurs is,

P(A and B)=P(A∩B)

When both the events are independent,

P(A and B)=P(AB) = P(A)x P(B)

The probability that either A or B occurs is,

P(A or B)= P(AUB) = P(A)+P(B)-P(A∩B)

When both the events are mutually exclusive the probability that either A or B occurs is,

P(A or B)=P(AUB) = P(A)+P(B)

The compliment of the probability is,

P(A)=1-P(A)

The conditional probability of occurring of an event A when it is given that B had already occurred is,

P(A|B)=P(A∩B)/P(B)

Let A represent the situation where the chosen person has a Visa credit card and B represent the situation where they have a Master card. The probability of occurring event A is 0.6 and the probability of occurring event B is 0.4 that is, P(A)=0.6, P(B)=0.4 .

It is known that P(A B)∠P(A) and P(A B)∠P(B) . So, it is not possible that the intersection case, P(A B)=0.5 .

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Answer:

C. 73.5lbs

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

0.153 or 15.3%

Step-by-step explanation:

Subtract save percentage last season from save percentage this season:

0.738 - 0.585 = 0.153

Convert the decimal answer to a percent

0.153 x 100% = 15.3%

The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied.  New total be 11x/10.

Let the original purchase price without discount be 'x';

Tip to installation specialist = 10% of original purchase price

 = (10/100) × x

= x/10;

Her new total is x + x/10 = 11x/10;

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the phrase used to describe a refund or an offer made to clients on the listed price of goods.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. Discounts are sometimes referred to as "off" or "reductions." It should be noted that the discount is always determined using the item's marked price (list price).

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Answer : $611.29

Step-by-step explanation:

.10 x 719.99 =71.99

539.30 (from previous answer) +71.99 =611.29

Answer:

y = (-1/6)x - 4

Step-by-step explanation:

Line equations are usually expressed in the following format:

y = mx + c

Where m is the gradient (slope), and c is the y-intercept.

We can fill in the value of m right away as we are given it in the question:

y = (-1/6)x + c

And we are given the point (-6,-3), so we can fill in the values for x and y, in order to find the value of c:

-3 = (-1/6)(-6) + c

Rearrange and simplify this:

-3 = 1 + c

c = -4

Finally, substitute the value of c back into the original equation to get the final equation of the line:

y = (-1/6)x - 4

The statement that a function is decreasing on an interval if the output values decrease as the input values decrease is FALSE.

A decreasing function refers to a function where the value of the output moves in a different direction from the value of the input.

For instance, in a decreasing function, the value of the output would decrease when the value of the input increases.

In conclusion, it is false that a function is decreasing if the output and the input are both decreasing.

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Answer:

Step-by-step explanation:

(x+4) = -6

x + 4 + 6 = -6 + 6

x = 10

Answer:

5

Step-by-step explanation: