A local real estate company has 5 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions.

Answer:

v > -7.1

Step-by-step explanation:

The given situation can be written in an algebraic way:

Say x the width of the rectangle and y its height.

- The width of a rectangle is 8 inches less than its length:

x = y - 8

- The area of the rectangle is 9 square inches:

xy = 9

In order to find the values of y and x, you first replace the expression

x = y - 8 into the expression xy = 9, just as follow:

you apply distribution property, and order the equation in such a way that you obtain the general form of a quadratic equation:

Next, you use the quadratic formula to solve the previous equation for y:

here you have a = 1, b = -8 and c = 9. By replacing these values you obtain:

Hence, you have two solutions for y:

y1 = 4 + 5 = 9

y2 = 4 - 5 = -1

You select only the positive solution, because negative lengths do not exist in real life. Hence, you have y = 9.

Finally, you replace the value of y into the expression x = y - 8 to obtain x:

Hence, the width and length of the given recgtangle are:

width = 1 in

length = 9 in

The Law of Cosines

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:

Calculating:

Now we can apply the law of the sines:

Combining the first and the last part of the expression above:

Substituting the known values:

The last angle can be ob

Answers:

R = (6, -1)

S = (1, -5)

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Explanation:

R'' is located at (7,3)

Reflect this over the x axis to get R'(7,-3). We flip the sign of the y coordinate while keeping the x coordinate the same. The rule is [tex](x,y) \to (x,-y)[/tex]

Then we apply the inverse of (x+1, y-2) which is (x-1, y+2). Notice the sign flips.

Let's apply this inverse transformation to determine the coordinates of point R.

[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(7,-3)\to(7-1,-3+2)\\\\(7,-3)\to(6,-1)\\\\[/tex]

Therefore, point R is located at (6, -1)

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Point S'' is at (2,7)

It reflects over the x axis to get to (2,-7)

Then we apply that inverse transformation to get

[tex](\text{x},\text{y})\to(\text{x}-1,\text{y}+2)\\\\(2,-7)\to(2-1,-7+2)\\\\(2,-7)\to(1,-5)\\\\[/tex]

Point S would be located at (1, -5)

A property ostates that if two lines that are tangent to the circle intersect in an external point, they are congruent, i.e. they have the same length.

From this expression we can determine the possible values of x. The first step is to equal the expression to zero

The expression obtained is a quadratic equation, using the queadratic formula we can determine the possible values of x:

For our expression

The coefficients are

a=1

b=0

c=-9

Replace them in the formula

Now calculate both possible values:

Positive:

Negative:

The possible values of x are 3 and -3

Answer:

45,000

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).

First Digit:

Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.

Second, Third, Fourth Digit:

Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.

Fifth (Last) Digit:

For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.

Answer Explanation:

Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:

[tex]9*10*10*10*5[/tex]

[tex]=45,000[/tex]

Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.

The graph of f(x) is a parabola with "arms up"

The vertex of the parabola is (0,-3)

Then we can know all the problem ask us:

increasing: (-3, infinity)

decreasing: (minus infinty, -3)

DNE maximum, beacuase it's arbitrarily large.

The minimum is the vertex: minimum of -3 at x = 0

The domain is all real numbers

The range is [-3, infinity)

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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:

We focus on a and b. Always will be a squared x, but a and b vary. a lot

A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.

Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.

Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"

When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.

All the information the problem ask, you can get it by those numbers.

To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100

Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:

For the same value of x, the first function is 100 and the second 2

we are given two recipes for cookies and we are asked which of the two contains more sugar. To do that we need to find the amount of sugar per cookie for each recipe.

For recipe A we have:

This means:

For recipe B we have:

This means:

Since 1/18 is greater than 1/24, this means that there is more sugar per cookie in recipe B than in recipe A.

Answer:

10

Step-by-step explanation:

30 -2

28 -3

25 -4

21 -5

16 -6

= 10

Answer:

  10

Step-by-step explanation:

Given the sequence 30, 28, 25, 21, 16, you want to know the next number.

First differences between successive terms are ...

  28 -30 = -2

  25 -28 = -3

  21 -25 = -4

  16 -21 = -5

These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:

  -3 -(-2) = -1

  -4 -(-3) = -1

  -5 -(-4) = -1

This observation tells us the next second difference is ...

  -5 +(-1) = -6

And the next number in sequence is ...

  16 +(-6) = 10

The next number is 10.

__

Additional comment

When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.

Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...

  a(n) = 31 -(n)(n+1)/2

Divide side R'O' (8) by th scale factor (2/3)

8 : 2/3= 12

Given

PR and SU are parallel lines.

To find the pair of corressponding angles.

Explanation:

From, the figure,

Since PR and SU are parallel and the corressponding angles lie in the same corner.

Then,

Hence, the answer is Option c).

We will determine the solution as follows:

*First: From the text, we have the following expressions:

&

Here x represents apples and y represents bananas.

*Second: From the first expression, we solve for either x or y, that is [I will solve for ]:

*Third: Now, using the value for x, we replace in the second expression and solve for y, that is:

*Fourth: We replace the found value of y on the first expression and solve for x:

So, the number of apples was 5 and the number of bananas was 3.

The distance, x, from one corner to another corner three corners away is 4. 70cm

The distance, y, from one corner to another corner two corners away is 4. 07cm

It is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees

Also note that the have the trigonometric identities;

Using the cosine identity, we have;

sin θ = adjacent/ hypotenuse

substitute the values

cos 60 = 2.35/x

cross multiply

x = 2. 35/cos 60

x = 2. 35/ 0. 5

x = 4. 7 cm

Then, we have,

sin 60 = y/ 4. 7

y = sin 60 × 4.7

y = 0. 8660 × 4. 7

y = 4. 07cm

Hence, the values are 4. 7cm and 4. 07cm

Learn more about trigonometric identities here:

https://brainly.com/question/22591162

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Answer:

Alternative D. At least three stereos were sold on one day of the month.

Explanation:

Now, let's evaluate the options:

A. At least one stereo was sold on each day of the month

It is false.

We can not affirm that. For example, all the stereos can be sold on only one day of the month

B. Exactly two stereos were sold on the same day during the month

It is false.

Same explanation as A.

C. At least one stereo was sold on either Monday, Wednesday, or Friday during the month

It is false.

We can not affirm that too. The explanation is the same as for alternative A.

D. At least three stereos were sold on one day of the month.

It is true.

If two stereos are sold every day, for a month of 30 days, 60 stereos are sold. So, on some days 3 or more stereos are sold.

Also, if all the stereos are sold on the same day, more than 3 stereos were also sold.

So, alternative D is correct.

Given the graph of parallel lines and a transversal

There is an angle = 90

This means the transversal is perpendicular to the parallel lines

So, All the angles are right angles

So, the measure of all angles = 90

So,

As shown : in the figure

The pitch of the roof is the angle between the roof and the horizontal line

As shown we have a right angle triangle

The opposite side to the angle = 4 ft

And the adjacent side to the angle = 12 ft

According to the given sides, we will calculate the angle using tan function

So, let the angle = x

So,

So, the pitch angle of the roof = 18.435

instead of writing the angle , just we will write the slope = rise/run

So, the pitch of the roof = 1/3

ANSWER

9y² + 8xy³

EXPLANATION

To divide this polynomial by the given monomial, we can distribute the denominator into the sum,

Then, each coefficient simplifies with the coefficient of the monomial, since both are multiples of 7. Also, in the first term, x cancels out, and we have to subtract 1 from the exponent of y. In the second term, we subtract 1 from both the exponents of x and y,

Hence, the result is 9y² + 8xy³.

879,087.

EXPLANATION

To find the number of lawnmowers, we need to first find 70% of the number of lawnmowers that was kept in the past. Then add the to the number of lawnmowers kept in the past.

From the given question;

Number of lawnmowers kept in the past = 517, 110.

70% of lawnmowers kept in the past = 70% of 517 110

Number of lawnmowers now kept in store = number of lawnmowers kept in the past + 70% of lawnmowers kept in the past

= 517 110 + 361 977

= 879,087.

When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.

As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.

Hence, the division is equivalent to 0.542.

That's how the division works when you divide by a power of 10.

The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.

The expression for the hight of a equlatral triangle is,

Here, ''

Solution:

Given:

The circumference (C) of a circle is given by;

Hence,

Thus,

Therefore, the circumference of the circle is 100.48m

In order to find the height of the parallelogram, we can use the following formula for its area:

Where A is the area, b is the base and h is the height of the parallelogram.

Using A = 54 and b = 9, we can solve the equation for h:

So the height of the parallelogram is 6 inches.

4) The given triangle is a right angle triangle. Taking 30 degrees as the reference angle,

hypotenuse = 34

adjacent side = x

opposite side = y

We would find x by applying the Cosine trigonometric ratio which is expressed as

Cos# = adjacent side/hypotenuse

Cos 30 = x/34

Recall,

To find y, we would apply the Sine trigonometric ratio. It is expressed as

Sin# = opposite side/hypotenuse

Sin30 y/34

Recall, Sin30 = 0.5. Thus

0.5 = y/34

y = 0.5 * 34

y = 17

SOLUTION

Given the information on the question tab;

Final answer:

Each dark chocolate truffle costs $3.13

Answer: 14

Step-by-step explanation:

1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.

1 pumpkin = 4/4

3.5 pumpkins = 14/4

If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.

The bills are:

125

115

138

Since she wants an estimate that is greater than the actual total, she can round these numbers to the nearest ten.

125 will be rounded to the next tens, which is 130

115 will also be rounded to the next tens, which is 120

138 gets bumped to the next tens, that is 140

The total estimate is the sum of the 3 estimates we just made. That is:

130 + 120 + 140 = $390

A)

If This number 7.787887888... could be written as a ratio

Then it is called rational.

Since it has 7.78788788788... is an infinite number, with a repeating pattern notice it in bold. Then the only possible answer is:

Yes, it as a rational number, with a repeating pattern.

A.

The given figure is;

It is given that :

The measurements of angles 1 and 3 are the same.

The measurement of angle 2 equals 110°.

PART A:

Since, angle 1 , 2 and 3 are lie at the same point on the same line

Thus, from the property of angle on a line

Sum of all angles on a strainght line at a point is equal to 180 degree

thus;

Angle1 + Angle2 + Angle 3 = 180

Angle 1 + Angle 2 + Angle1 = 180 {Angle1 = Angle 3, given}

2(Angle 1) + Angle 2 = 180

2 (angle 1) + 110 = 180 {Angle 2 = 110, given}

2(Angle 1) = 180 -110

2(Angle 1) = 70

Angle 1 = 70/2

Angle 1 = 35

Since, angle 2 = 110

The sum of angle 1 and 2 is 110 + 35

Sum of angle 1 and 2 = 145

PART B:

From the properties of the rectangle;

All the angles of a rectangle are 90°

In the given rectangle;

Thus, in the triangle form by the angle3, 4 and the right angle

Sum of all angles in a triangle is equal to 180

Angle 3 + Angle 4 + 90 = 180

35 + Angle 4 + 90 = 180

Angle 4 + 125 = 180

Angle 4 = 180 - 125

Angle 4 = 55

.....

To describe the transfer we will review what the points of the blue and red triangle are.

Blue triangle

I = (-2, 8)

I' = (4, 4)

First, we will determine the x-axis translation

6 units right

Now let's calculate the y-axis transfer

4 units down

The answer would be 6 units right and 4 units down​