Penny is selling candles for $3 each at a fundraiser.
If she starts selling with $4 to help her make change, how many candles, x, will she
have to sell to end up with $19?

Answer:

  A)  ASA

Step-by-step explanation:

You want to know the relevant congruence postulate given the markings of angles and sides shown in the diagram.

The arc and hash marks show on the angles mean the angles with matching markings are congruent. Two angles are shown as congruent to their corresponding angles in the other triangle.

The hash mark on the sides mean the sides with matching markings are congruent. One side between the marked angles is shown as congruent to the corresponding side in the other triangle.

The letters A and S in the congruence postulate designations refer to corresponding Angles and Sides, respectively. So, two angles with a side between them would be identified as ASA.

The ASA congruence postulate applies.

Option A) ASA is the correct answer for the given triangle in the question. ASA is the congruence correspondence.

What is congruence correspondence?

Each triangle's vertices must match one another exactly. This expression signifies that each triangle's side and angle measurements match up with a side or angle of the other triangle. To have a one-to-one correspondence, triangles don't necessarily have to be congruent, but when they are, knowing the correspondence of the triangles is important to determine precisely which sides and which angles are congruent.

According to congruence postulate,

Angles with matching markings are congruent if an arc or hash mark appears on them. The relationship between two angles and the corresponding angles in the other triangle is demonstrated.

The hash marks on the sides indicate that the markings on the sides that match are consistent. The opposite triangle's equivalent side is shown to be congruent to the side between the highlighted angles.

The congruence postulate designations begin with the letters A and S, which stand for matching Angles and Sides, respectively. Therefore, ASA would be used to describe two angles with a side in between them.

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The value of the composition (g . h)(0) is 0

A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.

These variables are;

The functions are;

The composite function is gotten by substituting the value of x of the independent variable in the function.

The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;

(g . h) = 5√x

Now, substitute the value of x as 0, we have;

(g . h)(0) = 5√0

Find the square root

(g . h)(0) = 5(0)

Find the product

(g . h)(0) = 0

Hence, the value is 0

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We have two parralel lines with angles 32x + 4 and 34x - 2

From the figure, the angles are corresponding angles

Corresponding angles are equal

That is,

34x - 2 = 32x + 4

Collect the like terms

34x - 32x = 4 + 2

2x = 6

Divide both sides by 2

2x / 2 = 6 / 2

x = 3

The answer is 3

Given:

4 5 6 7

Given that you picked a card at random, without replacement, you then pick a second card at random.

Let's find the probability of picking an even number and then picking an even number.

Number of possible events = 4

Number of even numbers = 4, 6, ==> 2 even numbers.

Hence, to find the probability, we have:

Therefore, the probability of picking an even number and then picking an even number is 1/6.

ANSWER:

Using a linear function, it is found that:

a) Sales are increasing at a constant rate of 30 purchases/month.

b) The linear function is: p = S(t) = 30t + 3990.

c) The total purchases will be of 5130 in June 2010.

d) The sales will be of 5400 in March of 2011.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, we have that:

The slope of 30 is the constant rate of purchases per month, and the linear function is given by:

p = S(t) = 30t + 3990.

June 2010 is 3 x 12 + 2 = 38 months after April 2007, hence the purchases will be of:

S(38) = 30 x 38 + 3990 = 5130.

The sales will be of 5400 in t months after April 2007, for which:

S(t) = 5400

Hence:

30t + 3990 = 5400

t = (5400 - 3990)/30

t = 47 months.

One month shy of four year, hence in March of 2011.

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The most appropriate choice for linear equation will be given by-

Liam have 43 chairs

What is linear equation?

At first, we need to know the meaning of algebraic expressions.

Algebraic expressions consists of numbers and variables connected with addition,subtraction, multiplication and division sign.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions with an equal to sign

A one degree equation is known as linear equation.

Let the number of chairs in one row be x

Number of chairs in 8 rows = 8x

3 chairs are left

Total number of chairs = 8x + 3

Number of chairs in 6 rows = 6x

13 chairs are left

Total number of chairs = 6x + 13

By the problem,

[tex]8x+3=6x+13\\8x-6x=13=3\\2x=10\\x=\frac{10}{2}\\x=5[/tex]

Number of chairs Liam has =

                                                  [tex]6\times 5 + 13\\30+13\\43[/tex]

Liam has 43 chairs

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Find the area of each room and then add the three areas.

The total square footage to be covered is 459.

Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:

Then, the area is equal to 51 square yards.

The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:

The total cost for the carpeting is $1303.56.

Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.

The cost for 2 rolls would be 2*$99 = $198.

Add the cost of the two rolls of padding and the carpeting job to find the total cost:

Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.

Therefore, the answers are:

Part 1) 459 square feet.

Part 2) 51 square yards.

Part 3) $1303.56

Part 4) 2 rolls for $198

Part 5) $1501.56

First find the length of the segment KL

Apply the formula for distance between two points as;

d = √{y2-y1}^2 + {x2-x1}^2 where

y1= -3 , y2 = 3 , x1 = -2 and x2 = 4

d= √ {3--3}^2 + { 4--2}^2

d= √ 9^2 + 6^2

d= √ 81 + 12

d= √93 = 9.6

So the length of the segment is 9.6

From point K {-2, -3} , find 1/3 of the length to locate point L

This will be : 1/3 * 9.6 =3.2

This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}

d = √{y2-y1}^2 + {x2-x1}^2

3.2 = √{y--3}^2 + {x--2}^2

3.2 =√ {y+3}^2 +{x+2}^2

3.2^2 = {y+3}^2 + {x+2}^2

10.3 = y^2 + 6y + 9 + x^2 +4x +4

10.3 = y^2 + 6y +x^2 +4x +9+4

10.3 = y^2 + 6y +x^2 +4x +13

0=y^2 +6y +x^2 +4x +13-10.3

0= y^2 +6y +x^2 +4x +2.7

y^2 + 6y +x^2 +4x +2.7 = 0

{-0.9,-0.5)

Answer:

Triangle ABC is congruent to DCE by SAS Theorem.

Step-by-step explanation:

Since AB is parallel to DC, we can say that BC is congruent to CE and AC is congruent to DE, then:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangle is congruent.

Triangle ABC is congruent to DCE by SAS Theorem.

Solution:

Given the figure below:

The area of the shaded region is expressed as

step 1: Evaluate the area of the semicircle.

The area of the semicircle is expressed as

Thus, we have

step 2: Evaluate the area of the triangle.

The area of the triangle is expressed as

step 3: Evaluate the area of the shaded region.

Recall that

Thus, we have

Hence, the area of the shaded region is

The coordinates of the fourth side are (6, -8)

Let the coordinate of the fourth side be (x, y)

The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)

Solving these equations:

x - 3 = 3

x = 3 + 3 = 6

and

y - 2 = -10

y = -10 + 2 = -8

The coordinates are (6, -8)

Given:

13th term = -60

33rd term = -160

Find:

14th, 15th, 16th, and 17th term

Solution:

For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:

Let's plug in the values of a₃₃ and a₁₃ in the formula above.

Then, solve.

Hence, the common difference between the terms is -5.

So, the next 4 terms after a₁₃ are shown below:

The sets of the real numbers are

Whole numbers

Integers

Rational numbers

Irrational numbers

The whole numbers mean positive integers with zero

The integers mean positive , negative whole numbers, and zero

Rational numbers mean

EXPLANATION

Since the degree is 6, the polynomial has 6 zeros:

Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:

In conclusion, the remaining zeros are: 5 - i, 7 + i

we have

0.4275

if we round to the nearest thousand, we look at the third digit of our number

0.4275

do you know the answer now?

0.42 is not correct

and only 2 decimals will be rounded to the nearest hundreth

becuase we have a 5 after 7, the number will be rounded up

0.428

this is the answer

if we would have for example

0.3521

the rounded to the nearest thousand would be 0.352

The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given function,

x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6

The graph of this function has been plotted below,

The vertex is the point where the function is changing its sign of slope or turning point.

It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.

The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so  [0,6] will be the range of the function.

Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".

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We want to find the solutions for the following system

We already know the value for the y variable, if we substitute this value on the second equation it is possible to find the x value.

And those are the results for our system

Answer

Given expression

By factorization, we have

Now to check, using FOIL method, we have

F = First, i.e 3x(3x) = 9x²

O = Outer = 3x(+10) = +30x

I = Inner = +10(3x) = +30x

L = Last = +10(+10) = +100

The general form of a linear equation is given by:

y = kx

where k is a constant.

From the given options you can notice that the only equation similar to the previous one is:

y = 1/6 x

Then, the previous equation is the linear equation.

The required slope m is 3 and the y-intercept is - 5.

On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.

Given : The line y = 3x - 5

This is of the form y = mx + c which is the equation of the line.

On comparing these two equations

Thus the slope is 3 .

And y intercept is :

y = 3x - 5 and when x = 0

y =- 5.

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A graph which represents the solution to this inequality is shown in the image attached below.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

Next, we would evaluate and simplify the given inequality in order to determine the graph which represent its solution as follows:

1/5y - 1/2x > 2

Subtracting 2 both sides, we have:

1/5y - 1/2x - 2 > 2 - 2

1/5y - 1/2x - 2 > 0

(2y - 5x - 20)/10 > 0

2y - 5x - 20 > 0

2y > 5x + 20

Dividing both sides by 2, we have:

y > 5x/2 + 10

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The perimeter of pentagon is 150 so option D is correct.

Given:

Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.

3(3x-10) = 5(x+10)

9x - 30 = 5x + 50

9x - 5x = 30 + 50

4x = 80

divide by 4 on both sides

4x/4 = 80/4

x = 80/4

x = 20.

perimeter of pentagon = 5(x+10)

= 5(20+10)

= 5*30

= 150.

Therefore the perimeter of pentagon is 150 so option D is correct.

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Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.

Solution;

The events are independent

k(x)=3h(x)+4x^4/g(x). given the following table of values,  k'(-1) will be 3.

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative. the procedure for determining a function's derivative, or rate of change, in mathematics. Differentiation is the method used to calculate a function's derivative. The derivative is the rate at which two variables, x and y, change relative to one another.

Given Data

k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]

k(x) = -3h'(x) + 4[tex]\frac{4x^{3} g(x)- x^{4}g'(x) }{gx^{2} }[/tex]

k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g(-1)}{g(-1)^{2} }[/tex]

k'(-1) = -3(-1) + 4(0)

k(-1) = 3 + 0

k'(-1) = 3

k(x)=3h(x)+4x^4/g(x). given the following table of values,  k'(-1) will be 3.

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Area A = ?

Bag area covers = 54 ft2

Square Area S = 18ft X 18 ft

. = 324 ft2

Then now divide S/B

S/B = 324/54

. = 36/6

. = 6

Then answer is

Brett will need 6 bags of fertilizer

Answer:

add the number of sides then divide the number by the number of sides

The number of caffeinated teas that the tea shop serve is 5.

Number of teas served = 25 teas.

Percentage that was caffeinated.= 20%

Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:

= 20% × 25

= 0.2 × 25

= 5

Therefore, 5 are caffeinated

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Answer: the complex solutions are:

Step-by-step explanation: x = 5i , -5i , 3/5 ,-2