1. It is h before closing time at the grocery store. It takes about h for Jane to find 1 item on her shopping list. How many items can she find before the store closes? (a) Create a model or write an equation for the situation. (b) Find the solution. Explain what you did. (c) State the solution as a full sentence.

Given

Procedure

The answer would be (x+4)^2 = 25

Answer:

Explanation:

We're asked to create a polynomial of degree 6 that has no real roots.

Let's consider the below polynomial;

To determine its roots, we'll follow the below steps;

Step 1: Subtract 1 from both sides of the equation;

Let's begin by listing out the information given to us:

Line m is perpendicular to line P

Line P: (x, y) = (-4, -1), (1, 1)

We will proceed to calculate for the slope of the line P (as shown below):

Slope (m) = Δy/Δx

Slope (m) = (1 - - 1)/(1 - - 4) = 2/5

Slope (m) = 2/5

The slope of a parallel line is the negative reciprocal of the slope of the line.

Line m: slope (m) = -1/(2/5) = -5/2

Line m: slope (m) = -5/2

We calculate for the equation of the line using the point-slope equation. We have

y - y1 = m(x - x1) ⇒

(x1, y1) = (1, 1)

y - 1 = 2/5 (x - 1) ⇒ y - 1 = 2/5x - 2/5

y = 2/5x - 2/5 + 1

y = 2/5x + 3/5

We will proceed to put the value of the new slope into the equation. We have:

y = -5/2x + b ; (x, y) = (1, 1) ⇒ 1 = -5/2(1) + b

⇒ b = 5/2

Substitute the value of b into the point-slope equation, and we obtain the equation of line m. We have:

y = -5/2x + 5/2

Parallelogram. Option A is correct

In order to determine the best name for a quadrilateral with the given vertices, we will find the measure of the distance AB, BC, CD, and AD using the distance formula as shown;

For the measure of AB with coordinates A(5,-2), B(2,2);

For the measure of BC with coordinates B(2,2) and C(1, -5)

For the measure of CD with coordinates C(1,-5), and D(-2,-1);

For the measure of AD with coordinates A(5, -2), and D(-2,-1);

For the slopes;

Check if the length AB is perpendicular to AD

For the slope of AD

Since AB is not perpendicular to AD, hence the quadrilateral is not a rectangle and also not a square or rhombus since all the sides are not equal.

From the given distances, you can see that opposite sides are equal (AB = CD and BC = AD ), hence the best name for a quadrilateral is a parallelogram.

We have that the area is 6205 cm^2 and the widht is 73 cm.

since it is a rectangle, we must use

Now, we only replace values and find the value of the length

The length of the window is 85 cm.

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.

Here we have an arithmetic sequence with a common difference of 6, so the recursive formula is:

Tₙ = Tₙ₋₁ + 6

Where T₁ = 4.

Here we have the following sequence:

4, 10, 16, 22, ...

This seems to be an arithmetic sequence, to check this, we need to take the difference between consecutive terms and see if this is constant.

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

So yes, this is an arithmetic sequence and the common difference is 6, this means that each term is 6 more than the previous one, so the recursive formula is:

Tₙ = Tₙ₋₁ + 6

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We are given the radius of the circle =5

then the circumference is given by

then the cicumference of the semicircle is

Now let's find X

given the radius=5

the diameter = 2r = 5*2 = 10 in

then X is given by

now the lateral side of the rectangle is given by

12-5= 7 in

then

the composite perimeter is

then the composite perimeter is 56.7 in

Let x be the all sale for individual.

Determine the expression for total income of individual.

The total income was at least 70000. So last year income is 70000 or more than 70000.

Setermine the inequality for the sales.

The first step number that is not justified and the reason it is not justified:

From the attached image

Step 1: is said to be correct cause all the range are equivalent and parallel

Step 2: is said to be correct AECF is a parrelologram because it is a quadilateral with two opposite equal sides

Step 3: is correct

Step 4: is correct

Step 6 : is not correct , because corresponding parts of the congruent triangle are not congruent.

Step 7: is correct , because its a rhombus.

Let P(x) be the polynomial such that the given set is its solution set.

Now notice that:

Therefore (x-4) and (3x+1) divide to P(x), then:

Simplifying the above result we get:

Setting k=1 we get that:

Answer: Second option.

We can determine the strength of a correlation by A. The more closely two variables follow the general trend, the stronger the correlation (which may be positive or negative).

Correlation is a statistical term that reflects how closely two or more variables are related to one another. Correlation is measured on a scale of -1 to +1, with 0 indicating a negative correlation and > 0 indicating a positive correlation. A value of 0 implies that there is no association.

A positive correlation is a two-variable association in which both variables move in lockstep. A positive correlation exists when one variable declines while the other increases, or when one variable increases while the other falls. The number one represents a perfect positive association.

If there is an increase or decrease in one variable results in increase or decrease in the other then there is correlation. If the value of correlation is close to either extremities (+1 or +1) then there is strong correlation.

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The Equation is 10 + x= 30 and 20 actors are from third grade.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

There are 30 actors in a school play.

There are 10 actors from second grade.

The rest are from third grade.

let the actors in third grade is x.

Equation is:

Actors from second grade + Actors from third grade = Total actors

10 + x= 30

Now, solving

Subtract 10 from both side

10 +x - 10 = 30 - 10

x = 20

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we are told that VIP is located at (-2,7) and then she drops her pass. Then she moves on a slope of -9. To determine where you can catch up, we simply analyze what would be the next position by incrementing x by 1.

In this case, we are told that the slope is -9.

Recall that given points (a,b) and (c,d) the slope of the line that joins this points is given by

Lets call the next point (-1,y) . So using this, we have

So, by adding 7 on both sides, we get

So, the next position, following a slope of -9 and starting at (-2,7) is (-1,-2)

The simplified form of the expression (2 1/6 ) × (1 1/3) is 26/9.

Given the expression in the question;

(2 1/6 ) × (1 1/3)

To simplify, first convert from mixed to improper fraction.

(2 1/6 ) × (1 1/3)

( (2×6 + 1)/6 ) × (1 1/3)

( (12 + 1)/6 ) × (1 1/3)

( 13/6 ) × (1 1/3)

( 13/6 ) × (1×3 + 1/3)

( 13/6 ) × (3 + 1/3)

( 13/6 ) × (4/3)

Now, cancel the common factor 2.

13/6 × 4/3

13/3 × 2/3

( 13 × 2 ) / ( 3 × 3 )

( 26 ) / ( 9 )

26/9

Therefore, the simplified form is 26/9.

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The function is

1) x-intercept(s)

The x-intercepts refer to the points on which the function intercepts with the x-axis, in other words, when y=h(x)=0

So, given that condition, we get

Therefore, there are two x-intercepts, and those are the points

2) y-intercepts

The y-intercepts happen when x=0. So,

So, there is only one y-intercept and it's on the point (0,-8)

3) Vertex

The general equation of a parabola is

There is another way to express the same function, which is called the 'vertex form':

What is particularly useful of this vertex form is that the vertex is the point (h,k)

So, transforming h(x) into vertex form:

Therefore, the vertex is the point (h,k)=(1,-9)

4) Axis of symmetry

In general, the equation of the axis of symmetry is given by

Therefore, in our particular problem,

Thus, the equation of the line that is the axis of symmetry is

Then, the axis of symmetry is the line x=1.

Summing up the information in the four previous steps, we get

Side-Angle-Side Theorem states that triangles are congruent if any pair of corresponding sides and their included angle are congruent.

How do we know that their sides are congruent, by similarity ratios, means a ratio of the lengths of the sides to see if they have the same ratio or scale factor:

Then, since their sides are congruent and they have the same angle, they are congruent by SAS.

Answer

x = 35°

y = 145°

z = 25°

Explanation

We are told to solve for x, y and z.

Considering the first triangle with angles 55°, x° and the right angle (90°).

The sum of angles in a triangle is 180°.

So,

x° + 55° + 90° = 180° (Sum of angles in a triangle is 180°)

x° + 145° = 180°

x = 180° - 145° = 35°

Then, we can solve for y. Angles x and y are on the same straight line, and the sum of angles on a straight line is 180°

x° + y° = 180°

35° + y° = 180°

y° = 180° - 35°

y° = 145°

We can then solve for z°. The big triangle has angles (55° + 10°), z° and the right angle (90°).

The sum of angles in a triangle is 180°.

So,

55° + 10° + z° + 90° = 180°

z° + 155° = 180°

z = 180° - 155°

z° = 25°

Hope this Helps!!!

SOLUTION:

Step 1:

In this question, we are meant to:

Translate the following word phrases to an algebraic expression and simplify:



“8 times the difference of 6 times a number and 3”

Step 2:

Assuming the unknown number be y, we have that:

CONCLUSION:

The final answer is:

To determine how much of the wall is blue we first need to find its area. The wall is a rectangle, then its area is the product of its height and length:

Hence, the area of the wall is 140 square ft. To determine how much of the wall is already painted we multiply this by 1/2, then:

Therefore, 70 square ft are blue.

The value of the composite function g(f(x)) is 1 / 3 (81x² - 216x + 144) + 4

A composite function is a function that depends on another function. In a composite function, the output of one function becomes the input.

Therefore, let's solve the function as follows;

f(x) = 1 / 3 x² + 4

g(x) = 9x - 12

The value of g(f(x)) can be found as follows:

To find g(f(x)) we have to substitute the f(x) in g(x).

Therefore,

g(f(x)) = 1 / 3 (9x - 12)² + 4

(9x - 12)(9x - 12) = 81x² - 108x - 108x + 144

(9x - 12)(9x - 12) = 81x² - 216x + 144

Therefore,

g(f(x)) = 1 / 3 (81x² - 216x + 144) + 4

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Solution:

Since the slope of the given function represents the rate at which the temperature changes, the answer is the slope of the equation, that is, the correct solution would be:

ANSWER

$3100

EXPLANATION

Sally deposits $2500 at 8% interest for 3 years.

We want to find the amount she can withdraw at the end of the period.

To know this, we have to first find the interest.

Simple Interest is given as:

Therefore:

Therefore, after 3 years the interest will be $600.

The amount she can withdraw after this period is therefore the sum of the principal and the interest:

$2500 + $600 = $3100

She can withdraw $3100 at the end of the period.

Given the inequality below:

Solving algebraically as shown below:

Solving graphically as shown below the plotting of x < 12.2

The number line graph is the number line showing x < 61/5, as shown below:

The interval notation of the solution is (- ∞, 61/5) or (- ∞, 12.2)

Given:

The given mathematical expression is,

Required:

To solve the given expression.

Explanation:

Let us solve the given mathematical expression by using BODMAS rule.

Therefore, first, we calculate within brackets and then will perform subtraction.Thus, we get,

Final Answer:

The solution of the given mathematical expression is, 5.

Percentage of the bill = 0.185*100=18.5%

The average rate of change of a function f(x) from x1 to x2 is given by:

In this case we need the first three seconds so x1=0 and x2=3.

Calculate the values of the function at x=0 and x=3 to get:

f(0)=150 and f(3)=0.

Substitute these values into the formula for average rate of change:

Hence the avearage rate of change of the function for the first three seconds is -50.

Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).

Given the matrix

its determinant is computed as follows:

ad - cb

In this case, the matrix is

and its determinant is

2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6

In any pair of similar triangles, (side side side )

Each correspondent side has the same ratio so let's examine

ΔCDE and ΔFGH

To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.

Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.