what are the zeros of the function f(x)=2x^2 + x - 28

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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-20

Given the function f(x) = 2x^4 + 6x^2 + 4 at x = 1, the slope of the tangent of the function is expressed as:

Substitute the value of x = -1 into the fucntion

Hence the slope of the tangent to the function at x = -1 is -20

Answer:

slope = - 32 , y- intercept = 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 32x + 5 ← is in slope- intercept form

with slope m = - 32 and y- intercept c = 5

\(\frak{Hi!}\)

\(\orange\hspace{300pt}\above2\)

                          We have the equation \(\boldsymbol{\sf y=-32x+5}\).

                          We need to know its slope and y-intercept.

                         If an equation has the y=mx+c form,  the slope is always

                         multiplied by x, the x co-ordinate. Such is the case here,

                          thereupon we note that the slope is \(\boldsymbol{\sf{-32}}\).

                         As for the y-intercept, that's a constant. Do you remember

                         that constants have no variables attached to them?

                         Since the only number that has no variables attached to it is

                         5, we note that this is the desired value, the y-intercept.

done!!

\(\orange\hspace{300pt}\above3\)

                        \(\large\boldsymbol{\sf{calligraphy}}\)

Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

There is no variable so it would just be 42

Step-by-step explanation:

3+4*6

Answer:

so the answer is 42

Step-by-step explanation:

(3+4) = 7 x 6= 42

distributive property is  multiplication over addition

The ratio of the amount that Cheng and Amira paid is 1:2 respectively.

The amount earned by Amira when they sell the apartment is $28,000.

The given parameters:

Let the amount paid by Amira = x

The amount paid by Amira is calculated as follows;

\(x+ y = 36,000\\\\ x + 12,000 = 36,000\\\\ x = 36,000 - 12,000\\\\ x = 24,000\)

The ratio of the amount each paid is calculated as follows;

\(\frac{y}{x} = \frac{12,000}{24,000} = \frac{1}{2} = 1:2\)

The amount earned by Amira when they sell the apartment is calculated as follows;

\(x_2 = \frac{2}{1+ 2} \times \$42,000\\\\ x_2 = \frac{2}{3} \times \$42,000 = \ \$28,000\)

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Answer:

The slope of Zane is 18.50/2 = 9.25

Subtract both slopes to find the true statement.

10.5 - 9.25 = 1.25

The correct statement is:

Abrielle earns $1.25 more than Zane.

Answer:

what the person on the top said. Their right.

Equation:- 2y-x=10

For L to intersects Y axis then X cordinate must be zero

so put value of X as zero (0)

2y=10

So Y cordinate is equal to 5

Cordinate:- (0,5)

Cramer's rule states that the solution to a system of equations can be determined by taking the determinant of the coefficient matrix, which in this case is 4, and then dividing each equation's determinant of the corresponding matrix by the determinant of the coefficient matrix. This allows us to solve for the variable y.

Cramer's Rule is a method used to solve systems of linear equations. It states that the solution to a system of equations can be determined by taking the determinant of the coefficient matrix and then dividing each equation's determinant of the corresponding matrix by the determinant of the coefficient matrix. This gives us the solution for the variable y. To calculate the determinant of the coefficient matrix, we take the product of the diagonal elements and subtract the product of the elements that are not on the diagonal The determinant is calculated by taking the product of a and d, and then subtracting the product of b and c. Once we have the determinant of the coefficient matrix, we can calculate the determinants of each equation's corresponding matrix by replacing the y in the equation with 1 and the other coefficients with the original coefficients of the equation. We then divide each equation's determinant by the determinant of the coefficient matrix to solve for y. This method is useful as it allows us to solve a system of equations with multiple variables in a quick and efficient manner.

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Answer:

b

Step-by-step explanation:

The time needed for the battery to run down one sixth of its capacity of 3 600 milli-Ampere-hours is given as follows:

2.4 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 2, y decays by 500, hence the slope is given as follows:

m = -500/2

m = -250.

One sixth of the battery is given as follows:

1/6 x 3600 = 600.

Hence the time needed is given as follows:

600/250 = 2.4 hours.

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The required piecewise function is

          f(x) = 2x + 7,           if -6 ≤ x ≤ -1

           f(x) = 4 ,                  if -1 < x ≤ 3

           f(x) = -0.5x + 4.5,   if 3 < x ≤ -1

What is Equation of line ?

       (y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

The equation of line passing through (x₁, y₁) and (x₂, y₂) is given by,

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

From the given graph,

we observe the points for 1st line which is -6 ≤ x ≤ -1

(-6, -5) and (-1, 5)

Now, determine the equation of line.

Let, (-6, -5) = (x₁, y₁)

       (-1, 5) = (x₂, y₂)

Now, plug in the values

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

(y - (-5)) / (5 - (-5)) = (x - (-6)) / ((-1) - (-6))

(y + 5) / 10 = (x + 6) / (-1 + 6)

(y + 5) / 10 = (x + 6) / 5

y + 5 = 2(x + 6)

y + 5 = 2x + 12

y = 2x + 7

For 2nd line, which is -1 < x ≤ 3

By observing graph, we can say it is y = 4

For 3rd line, which is 3 < x ≤ -1

From the given graph we observe the points are

(3, 3) and (6, 1.5)

Let, (3, 3) = (x₁, y₁)

      (6, 1.5) = (x₂, y₂)

Now, plug in the values in

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

(y - 3) / (1.5 - 3) = (x - 3) / (6 - 3)

(y - 3) /  (-1.5) = (x - 3) / 3

y - 3 = (-1.5) (x - 3) / 3

y - 3 = -0.5 (x - 3)

y - 3 = -0.5x + 1.5

y = -0.5x + 1.5 + 3

y = -0.5x + 4.5

Hence, the required piecewise function is

           f(x) = 2x + 7,           if -6 ≤ x ≤ -1

           f(x) = 4 ,                  if -1 < x ≤ 3

           f(x) = -0.5x + 4.5,   if 3 < x ≤ -1

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Answer:

\( \sf {a}^{6} \)

Step-by-step explanation:

Given expression

\( \sf \: {a}^{0} \: • \: \: {a}^{6} \)

To find expression solution

\( \sf \: {a}^{m} \: {a}^{n} = {a}^{m + n} \)

\( \sf {a}^{0} + {a}^{6} = {a}^{0 + 6} \)

\( \sf \therefore \: {a}^{6} \)

\( \: \Large \mathbb{SOLUTION:}\)

\( \: \: \rm{ {a}^{0} \times {a}^{6} }\)

\( \: \: \text{Calculate the power }\)

\( \: \: \underline{\underline{\rm{{a}^{6} }}}\)

The number 842 is the number whose digit 4 is ten times larger than in the number 384

To solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.

In the number 384, the digit 4 is in the ones place, which means that its value is 4.

To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.

The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.

Therefore, the correct answer is 842.

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The exact values of the six trigonometric functions for angle θ are:

sinθ = -0.6

cosθ = -0.8

tanθ = 0.75

cscθ = -1.67

secθ = -1.25

cotθ = 1.33

We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the terminal side of angle θ and the x and y axes:

h² = (-12)² + (-9)²

h² = 144 + 81

h² = 225

h = 15

Let us use the definitions of the six trigonometric functions to find their respective values of sine, cosine and tan functions

sinθ = opposite/hypotenuse = (-9)/15 = -0.6

cosθ = adjacent/hypotenuse = (-12)/15 = -0.8

tanθ = opposite/adjacent = (-9)/(-12) = 0.75

cscθ = 1/sinθ = -1.67

secθ = 1/cosθ = -1.25

cotθ = 1/tanθ = 1.33

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The probability that the first ball chosen is black and the second ball chosen is red is 24.24%

First, we shall obtain the total balls present in the box. Details below:

Total ball = 4 + 8

Total ball = 12 balls

Next, we shall obtain the probability of chosen a black ball first. Details below:

P(B) = n(B) / n(T)

P(B) = 8 / 12

Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:

P(R | B)= n(R) / n(T)

P(R | B) = 4 / 11

Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:

P(B ∩ R) = [P(B) × P(R | B)] × 100

P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100

P(B ∩ R) = 0.2424 × 100

P(B ∩ R) = 24.24%

Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%

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This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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9514 1404 393

Answer:

  $189.32

Step-by-step explanation:

Add all of the numbers shown to the beginning balance to find the ending balance.

  $92.19 -39.35 +49.76 +87.35 +9.97 -10.60 = $189.32

Tristan's balance at the end of the month was $189.32.

__

There should be no confusion. Money deposited into the account increases the balance by the amount deposited.

Money spent from the account decreases the balance by the amount spent.

Here, amounts deposited are given a plus sign (+); amounts spent are given a minus sign (-).

__

Additional comment

It can be tedious to enter these numbers correctly into a calculator. Many folks prefer a calculator that provides a "tape", a record of the amounts and operations the calculator uses in the computation. Alternatively, you can put the numbers in a spreadsheet and use the SUM function to do the addition for you. That, too, makes it easy to check that numbers have been entered correctly.

The attachment shows the calculation done in a spreadsheet.

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Compound interest accrued on a principal of $4,000.00 at a rate of 6% per year compounded four times each year during a 20-year period, totaling $13,163.

Over a specific time period, compound interest builds up on both the principal and interest. A principal is also included when accounting for interest that has accrued on it over time. The cumulative principal value is used to calculate interest for the upcoming period as well. The new way of calculating interest now utilised in all financial and commercial transactions around the world is called compound interest. When we look at the compound interest values gathered over various time periods, we can quickly see the power of compounding.

Given

Principal = $4000

Time = 20 years

Rate = 6%

Compound Interest

A = P(1 + r/n)^nt

A = 4000( 1 + 6/4)^(6)(4)

A = 4000( 1 + 0.015)^80

A = 13162.65

A = 13163

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Answer:

\(\boxed {\boxed {\sf 9 \ arrangements }}\)

Step-by-step explanation:

Let's set up a proportion using the following setup:

\(\frac{arrangements}{minutes} =\frac{arrangements}{minutes}\)

We know that the florist can arrange 4 in 92 minutes.

\(\frac{4 \ arrangements}{92 \ minutes} = \frac{arrangements}{minutes}\)

We don't know how many the florist can arrange in 207 minutes, so we say x arrangements can be completed in 207 minutes.

\(\frac{4 \ arrangements}{92 \ minutes} = \frac{ x \ arrangements}{ 207 \ minutes}\)

\(\frac{4}{92} =\frac{x}{207}\)

Solve for x by isolating it on one side of the proportion.

x is being divided by 207. The inverse of division is multiplication. Multiply both sides of the proportion by 207.

\(207*\frac{4}{92}=\frac{x}{207}*207\)

\(207*\frac{4}{92}=x\)

\(207*0.0434782609=x\)

\(9=x\)

The florist can arrange 9 arrangements in 207 minutes.

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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The recursive formula of the linear growth model is Pₙ = Pₙ ₋ ₁ + 5

The explicit formula of the model is P(n) = 7 + 5n

37 cars are sold in the 6th week

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

P₀ = 7

P₁ = 12

So, the common difference is

d = 12 - 7

Evaluate

d = 5

The recursive formula of the linear growth model is

Pₙ = Pₙ ₋ ₁ + d

So, we have

Pₙ = Pₙ ₋ ₁ + 5

Here, we have

P₀ = 7

d = 5

The explicit formula of the linear growth model is

P(n) = P₀ + nd

So, we have

P(n) = 7 + 5n

This means that

n = 6

So, we have

P(6) = 7 + 5 * 6

Evaluate

P(6) = 37

Hence, 37 cars are sold in the 6th week

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The exponential function is in the form

y = a * b^t where a is the initial value and b is the growth( decay) rate

a = 1500

b = 1 - percent decrease in decimal form

b = 1 - .0675

.9325

y = 1500 ( .9325)^t

Answer:

A

Step-by-step explanation:

edge 2021

Answer:

See below.

Step-by-step explanation:

I've never seen one asked quite this way, but I think I have it figured out.

The objective here is to get the right answer for each square. The answer is either the one next to the 'x', which means you put an 'x' in the tic-tac-toe square or the answer is the one next to the 'O', which means you put an 'O' in the tic-tac-toe square.

I will number them boxes 1-3 on the top row, 4-6 for the next, and 7-9 for the bottom row.

Box 1: In a fraction, you subtract the bottom exponent from the top exponent, so the proper exponent is 10 - 2 = 8. That is an O for g^8.

Box 2: A power raised to a power - multiply the exponents. 2*6=12. That is an X for m^12 for box 2.

Box 3: for multiplying the same base, you add the exponents. 4+5=9. That gives us y^9, which is a X for box 3.

Box 4: j is a factor four times, so that is j^4. That puts an O in Box 4.

Box 5: In a fraction, you subtract the bottom exponent from the top exponent, so we get -2 - (-6) = -2 + 6 = 4. The correct expression is h^4, so we have an X for box 5.

Box 6: A power to a power, you multiply the exponents so the first part becomes m^8. Now we have m^8 * m^5. For multiplying the same base, you add the exponents. 8+5=13. That gives us m^13, which puts an O in box 6.

Box 7: The top is a power to a power so we multiply the exponents. 4*5=20. The top is b^20.

On the bottom, for multiplying the same base, you add the exponents. 2+3=5, so the bottom is b^5.

Now we have a fraction, (b^20)/(b^5). In a fraction, you subtract the bottom exponent from the top exponent, so we have 20 - 5 = 15, and thus b^15. That gives us an X for box 7.

Box 8: A fraction IS a division, so we do divisons and fractions the same way. The p^3 on the left is the top (numerator) and the p^2 part is the bottom (denominator). So 3-2=1. But P^1 is just P, so we have an O for box 8.

Box 9: For the numerator, it is a power to a power so we multiply the exponents and get k^12.

For the denominator, we are multiplying the same base, so you add the exponents. 7 + (-5) = 2, and we get k^2 for the denominator

Now we have the fraction of k^12 OVER k^2.  In a fraction, you subtract the bottom exponent from the top exponent. 12-2=10. We get k^10, giving us an X for box 9.

So here is what we get for tic-tac-toe.

0   X   X

O   X   0

X   O   X

We get 3 in a row in boxes 3, 5, and 7. The exponents in those problems are 9, 4, and 15 respectively. The product of thse 3 numbers is 540.

This was a LOT of steps, so I encourage you to check every little multiplication and addition I did.

Hope this helps.