Practice
1. Consider the functions k(x)=x-1, m(x) = x + 2, n(x) = x - 3, and f(x) = k(x) m(x) - n(x).
a. Graph k(x), m(x), and n(x).
b. Determine the degree of the function f(x). Explain
your reasoning.
c. Determine the zeros of f(x). Explain your reasoning.
d. Determine the intervals over which the value of f(x) is
positive. Determine the intervals over which the value
of f(x) is negative. Explain your reasoning.
e. Sketch f(x).
AY
X

Answer:n1=-9,n2=10

Step-by-step explanation:

The sequence of transformations is described as follows:

B. Reflection over the y-axis, translation 6 units right and 4 units up, dilation with center (0,0) and scale factor 2.

The two polygons have vertical symmetry, hence the reflection was over the y-axis.

Two equivalent vertices are given as follows:

R(4,-4) and V(2,-4).

After the reflection over the y-axis, the coordinates would be of:

R'(-2,-4).

The polygon increases after the transformation, hence the dilation has a scale factor greater than 1, which is of 2, as VZ = 8, RU = 4.

With a dilation with scale factor of 2, the coordinates of R'' would be given as follows:

R''(-4,-8).

The coordinates of V are:

(2,-4).

Hence the translation is:

Hence option B is correct.

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Answer:

Hotdogs: $12

Buns: $6

Altogether (Hotdogs plus Buns): $18

Step-by-step explanation:

She wants 48 hot dogs, and each package contains 8 hotdogs.

48/8 = 6

She'd have to buy 6 packages

6 packages x $2 each = $12

She'd be spending $12 on the hotdogs

She'd also have to get an equivalent amount of buns

Each bag has 12 buns. She needs 48 buns.

48 buns /12 per bag = 4 bags

She would need to buy 4 bags of buns

$1.50 per bag x 4 bags = $6

She'd be spending $6 on buns

Adding the amount she spends on both the buns and hotdogs, she spends $18

Answer:

3340 miles

Step-by-step explanation:

Multiply 4x835=3340 miles

Answer:

y÷3

Step-by-step explanation:

y/3 is the same as y÷3

The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.

Interior angles are those that lie inside a polygon.

To calculate an interior angle of a hexagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Recall that, the sum of an interior and exterior angle is 180°

Where:

Substitute the value of a into equation 2

Hence, the value of the interior angle is 118°.

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As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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The percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line

The value of the coefficient of determination r2 = 0.9617*0.9617 = 0.9249

percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line is = 92.49%

So, percentage is unexplained = (100 - 92.49)%

= 7.51%

Therefore, the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line is 92.49% . The percentage which is unexplained is 7.51% i.e. (100%−92.49%) .

Hence the variation in X and the least-squares line is 7.51%

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A matrix is a form of writing items in rows and columns.

The matrice B is

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

A matrix is a form of writing items in rows and columns.

[tex]\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex]

We have,

[tex]A=\left[\begin{array}{ccc}3&-2\\4&5\\-1&-6\end{array}\right][/tex]

B = 3A

We will multiply 3 with all the items in matrices A.

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

This is in the form of

[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]

Now,

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

Thus,

The matrice B is

[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]

This is in the form of

[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]

The value of [tex]b_{11}[/tex] = 9

The value of [tex]b_{22}[/tex] = 15

The value of [tex]b_{31}[/tex] = -3

The value of [tex]b_{32}[/tex] = -18

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Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3

We know that if we transform point (x,y) by using dilation with scale factor k then the coordinate of the image will be (kx,ky).

Given: under a dilation, the point (2, 6) is moved to (6, 18)

Here (x,y)=(2,6) and (kx,ky)=(6,18)

x = 2

kx = 6

k = 6/x

k = 6/2

k = 3

Similarly taking y into account

y = 6

ky = 18

k = 18/y

k = 18/6

k = 3

Hence, Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3

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Answer:

Step-by-step explanation:

k=x÷y

Multiply both sides of the equation by y.

ky=x

Swap sides so that all variable terms are on the left-hand side.

x=ky

Triangle xyz was translated up 2 and right 3 units, creating triangle cab.

To find out the relationship between the parts of the two triangles must be true:

YZ ≅ AB

A translation is known as a rigid transformation.  This is because it preserves congruence.  Since CAB is created from XYZ, this tells us that:

X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.

Since the triangles are congruent, the corresponding pieces are congruent as well.

Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.

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For corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock

The consolidated tax return is defined as a single income tax return filed by an affiliated group of corporations that combines their tax liability.

The percentage is the ratio that can be represented as the fraction of hundred.

The voting stock is defined as the shares that give the stockholder, that is the right to vote on the policymaking of the corporation

Here, p must own 80% of s's voting stock

Hence, for corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock

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The quotient of the division is 2x² - x - 11 and 0 is the remainder.

Given,

The expression; 2x³ + x² - 10x -11 ÷ x + 1

We have to find the quotient and remainder

One of the arithmetic operations carried out on two given polynomials is to divide them. In this, the divisor is typically a polynomial of lower degree than the dividend.

Lets solve ;

2x³ + x² - 10x -11 / x + 1   (2x²)

= -x² - 10x - 11 / x + 1   (-x)

= -11x - 11  / x + 1  (-11)

= 0

Here,

The quotient = 2x² - x - 11

Remainder = 0

That is,

The quotient of the division is 2x² - x - 11 and 0 is the remainder.

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The perimeter of the parallelogram ABCD is, 58 units.

What is perimeter?

The length of a shape's boundary taken as a whole is referred to as its perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

Consider the given vertices, A(1, 1), B(17, 1), C(22, 13), D(6, 13).

The perimeter of parallelogram is the sum of all sides of parallelogram.

So, first to find the length of each side of parallelogram, using the distance formula,

[tex]d = \sqrt{(x_2 -x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]AB = \sqrt{(17-1)^2+(1-1)^2}=\sqrt{16^2-0} = 16\\ BC = \sqrt{(22-17)^2+(13-1)^2} = \sqrt{5^2+12^2}= \sqrt{25+144}=13\\ CD = \sqrt{(6-22)^2+(13-13)^2} = \sqrt{16^2+0}=16\\ AD = \sqrt{(6-1)^2+(13-1)^2}=\sqrt{5^2+12^2} =\sqrt{25+144}=13[/tex]

Therefore, the perimeter of the parallelogram ABCD is,

P = AB + BC + CD + AD

P = 16 + 13 + 16 + 13

P = 58

Hence, the perimeter of  the parallelogram ABCD is, 58 units.

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When you cube root a number, the answer is always smaller. This is true.

The cube root, denoted by, is the inverse of the cube of a number. For example, 216, or the cube root of 216, equals 6 because multiplying 6 three times yields 216. In other words, because 6³ = 216.

A number's cube root is a value that, when multiplied by itself three times, yields the original value. For example, the cube root of 27 is 3, denoted as 3³ because multiplying 3 by itself three times yields 3 x 3 x 3 = 27.

In this case, we have showed that the answer will be smaller than the original number.

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The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:

Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).

In conclusion, the coordinates of the image after a dilation are  (36, -28).

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Answer:

GCF = 7

Step-by-step explanation:

The greatest common factor is equal to the product of the prime factors that all of the original numbers have in common.

The greatest common factor of 49, 21 and 49 is 7.

60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

[tex]^{5} P_{3}[/tex]

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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Answer:

Step-by-step explanation:

Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

What do you mean by system of linear equations?

A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.

Let, the cost per pound of peanut be $x and for M&M's be y

so, according to the question, we are getting two linear equations,

$8x + $5y = $55.27..................(i)

$6x + $4y = $42.70....................(ii)

Solving this two systems of linear equations , x=$3.79 and y=$4.99

Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

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The radical expression 2√2 + 3√5 cannot be simplified

From the question, we have the following parameters that can be used in our computation:

2√2 + 3√5

The above expression is a radical expression

The radicals in the expression are √2 and √5

The numbers 2 and 5 do not have common factors

This means that 5 cannot be expressed in terms of 2, and vice versa

So, we cannot simplify the given expression 2√2 + 3√5

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Answer:

Step-by-step explanation:

The proportional relationship is:

Let's find the value of k for each pair and compare:

As we see thee of the pairs have same value of k, 5/3 and one is different 7/4.

The answer is no.

Answer choices given in the comment:

The postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.

First, let us understand the congruency of the triangle:

When two triangles have the same sides and angles, they are congruent. That is, one's three sides are equal to the other's three sides, and one's three angles are equal to the angles of the other.

In triangles ABD and CBD;

Side BD = side BD (common)

∠ABD = ∠CBD (90 degrees)

Side AB = side CB (common)

For this triangle pair, the postulate that fit are:

SAS since the two sides and the included angle are equal in both triangles.

Thus, the postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.

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The statement about the changing features of the family that is not true of todays Commonwealth Caribbean societies is C. parents are becoming more autocratic.

It should be noted that nowadays, men and women choose their own partners, husband and wives usually treat each other as equals and generally, families have fewer children

While role changes are often difficult, many positive things can occur as a result. Families may learn to work better together and support one another. Learning new tasks can help children gain confidence. Families may discover that, despite the changes, life can still be enjoyable.

In conclusion, the correct option is C.

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The measure of  ∠x is 190°

Define Exterior angle

In the given diagram, all angles marked is an exterior angle

And, we know sum of exterior angle is 360°

So, now just equate the given values to 360 degree

x + 60 + 110 = 360

x + 170 = 360

x = 360 - 170

x = 190°

Hence, the measure of ∠x is 190°

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Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.

Step-by-step explanation:

Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.

Answer:

Step-by-step explanation:

put the day and the amount of money you made