Clayton is buying school supplies for the start of grade 10. He notices that 12 pens as Staples costs
$6.25. Calculate the unit price of 1 pen.

Answer:

x = -1

Step-by-step explanation:

x² + 6x = -5

x² + 6x -( -5) = 0

x = (-x + 4)/2

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = (-6 + 4)/2

x = (-6 - 4)/2

x = -1

To empty the tank in the shape of prism completely, Colin has to wait 150 minutes for the water of the pond to at zero level.

What is the prism volume formula?

Given :

A pond in the shape of a prism.

Colin uses a pump to empty the pond. The level goes down by 20 cm in the first 30 minutes.

Solution :

We know that the volume of the prism is given by,

Volume = ( Base area ) × height

Base area = 1/2 ( 1.4 + 0.6 ) × 2    ⇒2 m²

Volume  = 2 × 1 = 2m³

Given that the level of pond goes down by 20 cm in the first 30 minutes. Therefore, the volume becomes,

Volume = 2 × 0.8 = 1.6m³

Now, the rate of emptying the tank is,

[tex]= \frac{2 - 16}{30} = \frac{1}{75}[/tex]  m³/min

time = volume / rate

        = [tex]\frac{2}{\frac{1}{75} }[/tex]  = 150

Therefore, Colin has to wait 150 minutes for the pond to completely empty

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Answer:17.67

Step-by-step explanation:

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Answer:  [tex]\textsf{28 1/3}[/tex]

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Given: [tex]\textsf{We are given 9 numbers}[/tex]

Find: [tex]\textsf{Determine the mean of the numbers}[/tex]

Solution:  In order to determine the mean of the numbers the first step that we need to do is to add up all of the numbers.  After adding up all of the numbers we divide it by the amount of numbers that were provided to us.

Add up the numbers

Divide it by the amount of numbers provided

Therefore, the mean of the numbers provided is [tex]\textsf{28 1/3}[/tex]

If M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

As given in the question,

M is the midpoint of AB

Let coordinates of A(x₁ ,y₁) , B(x₂ ,y₂) and M(x ,y)

So,

x = (x₁ + x₂)/2

⇒-2 = (x₁ + (-7))/2

⇒ x₁ = 7-4

⇒x₁ =3

y = (y₁+ y₂)/2

⇒8 = (y₁ +16)/2

⇒ y₁ = 16-16

⇒ y₁ =0

Therefore, if M is the midpoint of AB , B(-7,16) and M(-2,8)  then coordinates of the missing endpoint A are (3,0).

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The simplification of the given algebraic expression is;

yz = (z + 1)/z(z - 1)

We are given y left parenthesis z right parenthesis which is expressed as; yz

Now, we are given the algebraic expression that yz equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction

z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction is expressed as; (z² - 1)/z(z - 1)²

Thus, our main expression is;

yz = (z² - 1)/z(z - 1)²

Factorizing the numerator and denominator gives;

yz = (z + 1)(z - 1)/z(z - 1)(z - 1)

(z - 1) is common to both numerator and denominator and as such, we now have;

yz = (z + 1)/z(z - 1)

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Answer:

5 feet

Step-by-step explanation:

We are told that the height of the dome can be modelled by the equation:

[tex]\boxed{h = -2d^2 + 100}[/tex]

The question is essentially asking us: for what value of d will the value of h be 50 feet?

To solve this, we have to substitute h in the equation with 50 and then solve for d.

∴ [tex]50 = -2d^2 + 100[/tex]

⇒ [tex]50 + 2d^2 + 100[/tex]

⇒ [tex]2d^2 = 100 - 50[/tex]

⇒ [tex]d^2 = \frac{100 - 50}{2}[/tex]

⇒ [tex]d^2 = 25[/tex]

⇒ [tex]d = \sqrt{25}[/tex]

⇒ [tex]d = \bf 5[/tex]

This means that 5 feet from the center of the dome, the height of the dome is 50 feet.

The temperature required on Thursday at 5:00 a.m. was observed as -7°F

given,

The temperature on Wednesday at 5:00 p.m. = 15°F

the temperature dropped 22°F in the following 12hours

The temperature on Thursday at 5:00 p.m. was 27°F.

the temperature on Thursday at 5:00 a.m. is calculated with a vertical number line.

number line - A number line is defined as the number marked on the line calibrated into an equal number of units.

For example -1, 0, 1, and so on.

Thus, the temperature on Thursday at 5:00 a.m. is

=15° - 22°

= -7°

The temperature required on Thursday at 5:00 a.m. was observed as -7°F

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From Vieta's formulas, we have

[tex]3x^2 - 4x + 1 = 3 (x - \alpha) (x - \beta) \\\\ ~~~~~~~~~~~~~~~~~ = 3x^2 - 3 (\alpha + \beta) + 3\alpha\beta \\\\ \implies \begin{cases} \boxed{\alpha + \beta = \frac43} \\\\ \boxed{\alpha\beta = \frac13} \end{cases}[/tex]

a) Note that

[tex](\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2 \\\\ \implies \alpha^2 - \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta - 2\beta^2[/tex]

We have exact values for [tex]\alpha+\beta[/tex] and [tex]2\alpha\beta[/tex], but sadly not for [tex]-2\beta^2[/tex]. This means we'll need to solve for [tex]\beta[/tex] explicitly.

By factorizing, we have

[tex]3x^2 - 4x + 1 = (3x - 1) (x - 1) = 0 \\\\ \implies x = \dfrac13 \text{ or } x = 1[/tex]

Then the value of [tex]\alpha^2-\beta^2[/tex] depends on which is chosen to be the larger root, and

[tex]\alpha^2 - \beta^2 = \dfrac1{3^2} - 1^2 = \boxed{-\dfrac89} \text{ or } \alpha^2 - \beta^2 = 1^2 - \dfrac1{3^2} = \boxed{\dfrac89}[/tex]

While we're at it, we can also immediately find

[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \left(\dfrac43\right)^2 - 2\cdot\dfrac13 = \dfrac{10}9[/tex]

b) Combine fractions to get

[tex]\dfrac2{\alpha^2} + \dfrac2{\beta^2} = \dfrac{2\beta^2 + 2\alpha^2}{\alpha^2\beta^2} \\\\ ~~~~~~~~~~~~~ = 2 \cdot \dfrac{\alpha^2 + \beta^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = 2\cdot \dfrac{\frac{10}9}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{20}[/tex]

c) Combine fractions again.

[tex]\dfrac2{\alpha^2} - \dfrac2{\beta^2} = 2 \cdot \dfrac{\beta^2 - \alpha^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = -2\cdot \dfrac{\pm\frac89}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{\pm16}[/tex]

Answer: Even functions

Symmetric about the yy-axis

When you plug -x−x into the function, it will simplify to be the same as the original function. This means that it doesn’t matter whether you plug in xx or -x−x, your output will be the same. So

f(-x)=f(x)f(−x)=f(x)

Below are graphs that are even and symmetric about the yy-axis.

even functions are symmetric about the y-axis

Odd functions

Symmetric about the origin

When you plug -x−x into the function, it will simplify to be negative of the original function, or the original function multiplied by -1−1. This means that when you plug -x−x into the function, you’ll get the same output as you do when you plug in xx, except it will be negative (or have the opposite sign as the original output). So

f(-x)=-f(x)f(−x)=−f(x)

Below are graphs that are odd and symmetric about the origin. Be sure to visually compare quadrants that are diagonal from each other (quadrants 1 and 3, and quadrants 2 and 4).

odd functions are symmetric about the origin

Neither even nor odd

Not symmetric about the yy-axis, and not symmetric about the origin

The function has no symmetry. It’s possible that a graph could be symmetric to the xx-axis, but then it wouldn’t pass the Vertical Line Test and therefore wouldn’t be a function.

functions that are neither even nor odd

hope this helps!!

The equation shows that the slope of the line is -2 and the y-intercept is 4 that is the line will pass through the point (0, 5)

The standard linear equation is expressed as y = mx + b where;

Given the linear equation  y=-2x+5

The equation shows that the slope of the line is -2 and the y-intercept is 5 that is the line will pass through the point (0, 5)

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Answer:

Your answer is C.125,000

Step-by-step explanation:

Answer:

Make y the subject of the formula which will give the answer below

y=1/3x-3

select C

The ratio of cell A's length to cell B's length is  [tex]2\times10^{15} :1[/tex]

It is given that length of cell A is [tex]2\times10^7m[/tex] which is in scientific notation and length of cell B is 0.00000001 m which is in standard form.

On converting length of B in scientific notation , we get

[tex]0.00000001 =1.0\times10^{-8}m[/tex]

The ratio of length A to length B is given by

[tex]\frac{2\times10^7}{1.0\times10^{-8}} =\frac{2\times10^{15}}{1}[/tex]

which can be written as [tex]2\times10^{15} :1[/tex]

Yes, finding ratios is easier when numbers are represented in scientific notation. This is because scientific notation is a mathematical methodology used to describe very large or very small numbers in a compact and simple form, raised to powers of ten.

Hence , it is easier to calculate or solve mathematical operations using numbers in scientific notation.

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A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:

y = -0.4908x² + 5.8845x + 1.3572

For the number of students that are absent 10 days after the outbreak, we have:

y = -0.4908(10)² + 5.8845(10) + 1.3572

y = -0.4908(100) + 58.845 + 1.3572

y = -49.08 + 58.845 + 1.3572

Number of students, y = 11.12 ≈ 11 students.

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Answer:

see explanation

Step-by-step explanation:

the shaded area is calculated as

outer circle area - inner circle area

since CAB is a tangent to the inner circle at A then OAB = 90° and

Δ OAB is right

using Pythagoras' identity in the right triangle to express R in terms of r and d , then

R² = d² + r²

------------------------------------------

A( outer Δ ) = πR² = π(d² + r² ) = πd² + πr²

A ( inner Δ ) = πr²

Then

shaded area = πd² + πr² - πr² = πd²

The method used to collect data for the given scenario is: observational study.

Now,

Hence, the method used to collect data is observation, i.e., observational study is being made here.

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(COMPLETE QUESTION:

Use the drop-down menus to identify the method used to collect data for each scenario.

While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.)

Answer:

See explanation

Step-by-step explanation:

d=degree change

d=-4-27

d=-31 degrees

Answer:

Correct answer is D.

Step-by-step explanation:

A. 6 = 3-3 ×

B. 1 = -4-3 ×

C. 2 = 1-3 ×

D. 0 = 3-3 ✓

The error in the closure is equal to the difference in the actual value of evaluation and the measured value of evaluation of the same point which is equal to 0.02 units.

There is a discrepancy between the existing coordinates and the computed coordinates. The amount by which a quantity obtained by a series of related measurements differs from the true or fixed value of the same quantity sometimes known as a closure mistake. The difference between the real value of a series of angles and its exact value in theory. likewise known as an angular mistake of closure. The degree to which two azimuth readings for a line that were obtained through distinct surveys or along different routes do not perfectly match one another. is also known as an azimuth closure error.

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Answer:

x - 5 = 65

Step-by-step explanation:

Hey there!

4a + 1 + a + 3

= 4a + 1 + 1a + 3

COMBINE the LIKE TERMS:

= (4a + 1a) + (1 + 3)

= (4a + a) + (1 + 3)

= 4a + a + 1 + 3

= 5a + 4

Therefore, your answer should be:

5a + 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.

If the purchase is made for $ 1000 and above. the discount = 20 %

Now the cost of Shredmaster 5000 = $ 1199

Now, the price after the discount will be

Price = 1199 - 20 % of 1199

Price = 1199 - 20 / 100 × 1199

Price = 1199 - 0.20 × 1199
Price = 1199 - 239.8

Price = $ 959.2

The function will be:

g (x) = x - 0.2 x

g (x) = 0.8 x for x > 1000.

Therefore, the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.

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Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Given,

The interest rate i= 8.145%

Number of weeks in an year n= 52

We know,

Effective interest rate =[tex](1+\frac{i}{n})^{n}-1[/tex]

Substitute the values

[tex]R_{1}=(1+\frac{0.08145}{52})^{52}-1\\ R_{1}= 0.084789[/tex]

Case 2

Compounded semiannually

[tex]R_{2}=(1+\frac{0.08145}{2})^{2}-1\\ R_{2}=0.083108[/tex]

The difference is

[tex]R_{1}-R_{2}= 0.084789-0.083185[/tex]

=0.001604

=0.1604%

Hence, the Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually

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Answer:

Your answer will be 11.04

Step-by-step explanation:

1.38 × 8= 11.04

12 lies between 9 and 16 so √12 lies between 3 and 4.

Perfect square-: Those whole numbers in which we can pair the factors are known as perfect square.

We can write the number 40 as 2 × 2 × 2 × 5. This is not a perfect square because we cannot pair the factors.

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.

We write 40−−√ to be the square root of 40, and can investigate between which two whole numbers it lies.

Consider the table of perfect squares below:

Whole number 1 2 3 4 5 6 7 8 9 10 11 12

Whole number squared 1 4 9 16 25 36 49 64 81 100 121 144

The number 40 lies between 36 and 49 hence 40−−√ lies between 6 and 7.

Similarly, 12 lies between 9 and 16 so √12 lies between 3 and 4.

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The rate of decrease in the revenue reduces each year, resulting in an

approximate quadratic equation model that is concave upwards.

The variables are;

x = Number of years since 2,000

y = Revenue for  physically recorded music in millions of dollars

Find out -

To model the decline using a quadratic equation.

The general form of the quadratic equation is; y = a·x² + b·x + c

When y = 5547, x = 8

We get;

5547 = a·8² + b·8 + c = 64·a + 8·b + c

5547 = 64·a + 8·b + c...(1)

When y = 3113, x = 11

We get;

3113 = a·11² + b·11 + c = 121·a + 11·b + c

3113 = 121·a + 11·b + c...(2)

When y = 2056, x = 14

We get;

2056 = a·14² + b·14 + c = 196·a + 14·b + c

2056 = 196·a + 14·b + c...(3)

Subtracting equation (2) from equation (1) gives;

5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b

2434 =  -57·a - 3·b...(4)

Subtracting equation (3) from equation (2) gives;

3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b

1057 = -75·a - 3·b...(5)

Subtracting equation (5) from equation (4) gives;

2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a

1377 = 18·a

a = 76.5

From, equation (4), 2434 =  -57·a - 3·b, we have;

2434 =  -57 × 76.5  - 3·b

Therefore;

b = -2264.8

From equation (1), we get;

5547 = 64 × 76.5 + 8×(-2264.8) + c

Therefore;

c = 5547 - (64 × 76.5 + 8×(-2264.8)) = 18769.

c = 18769.

Therefore, the quadratic model is;

Verifying, we have in year 2012, x = 12

y = 76.5×12² - 2264.8×12 + 18769. = 2607.74

Thus ,the completed table and comparison of the predicted physical revenue and actual values is presented in the attachment;

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Answer:

infinite solution

Step-by-step explanation:

because thats the right answers

Answer:

  10√2

Step-by-step explanation:

You want the simplified form of the radical expression 2√200 -10√2.

Radicals are simplified by removing perfect squares from under the radical. Radicals with the same radicand are "like terms" and can be combined.

  [tex]2\sqrt{200}-10\sqrt{2}=2\sqrt{10^2\cdot2}-10\sqrt{2}\\\\=2\cdot10\sqrt{2}-10\sqrt{2}=(20-10)\sqrt{2}=\boxed{10\sqrt{2}}[/tex]

Answer:

[tex]10 \sqrt{2} [/tex]

Step-by-step explanation:

Simplify.

[tex]2 \sqrt{200} \\ = 2 \sqrt{100 \times 2 } \: \: \: \: \\ = 2 \sqrt{100} \times \sqrt{2} \\ = 2 \times 10 \times \sqrt{2} \\ = 20 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Now let us solve the given expression.

[tex]2 \sqrt{200} - 10 \sqrt{2} \\ 20 \sqrt{2} - 10 \sqrt{2} \\ 10 \sqrt{2} [/tex]