Help with QUESTION 9 AND 11:

The value of x at the point of intersection is given as follows:

x = -1.

We must test for both definitions of the second function, and find which solution is in the correct range.

For the first definition, the solution is given as follows:

2x + 1 = x

2x - x = -1

x = -1.

-1 is less than 1, hence x = -1 is one solution to the system of equations.

For the second definition, the solution is given as follows:

2x + 1 = -x + 2

3x = 1.

x = 1/3.

Which is less than one, while the function is defined for values greater than 1, hence it is an extraneous solution.

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Troy has an album that holds 400 compact discs, and each page holds 4 compact discs. If 66% of the album is empty, that means that 34% of the album is filled with compact discs. Since each page holds 4 compact discs, that means that 34% of 400 compact discs is 136 compact discs. Since each page holds 4 compact discs, that means that 136 compact discs is 34 pages. Therefore, 34 pages are filled with compact discs.

Answer:

34 pages are full

Step-by-step explanation:

The measure of angle TSK is given as follows:

m < TSK = 35º.

On a triangle, the sum of the measures of the internal angles is of 180º.

For triangle TSK, the internal angle measures are given as follows:

Then the measure of angle TSK is obtained as follows:

m < TSK + 22 + 123 = 180

m < TSK = 180 - 145

m < TSK = 35º.

Meaning that the last option is correct.

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Answer:

6.28375

Step-by-step explanation:

times the radius will fit = x

8 * x = 50.27

x= 50.27÷8

x=6.28375

Answer: Around 9,284 books.

Step-by-step explanation:

   First, we will find how large this sample is by using addition.

753 + 74 + 30 = 857

   Next, since we are looking for the expected minor or major damage, we will find the number of books from this sample that meet the requirements.

74 + 30 = 104

   Now, we will find the percentage of this sample that meets the criteria.

(104 / 857) * 100 ≈ 12.13536%

   Lastly, we will use this value to determine how many books in the collection are likely to have minor or major damage.

76,500 * 12.13536% = 9,283.55 ≈ 9,284 books

Answer:

Mrs. Parker should expect around 9284 books in the library's collection to have minor damage or major damage.

Step-by-step explanation:

To calculate the expected number of books with minor or major damage in the entire collection, we can scale up the sample proportion to the size of the full collection.

First, let's find the proportion of books with minor or major damage in the sample:

Proportion = (74 + 30) / (753 + 74 + 30) = 104 / 857 = 0.1214

Next, we'll scale up this proportion to the size of the full collection:

expected number of books with minor or major damage = proportion * 76,500 = 0.1214 * 76,500 = 9283.5472578763

Finally, we round the result to the nearest whole number:

expected number of books with minor or major damage = round(9283.5472578763 ) = 9284

So, Mrs. Parker should expect around 9284 books in the library's collection to have minor damage or major damage.

The coordinates of the image of triangle ABC are A''(x, y) = (- 4, 2), B''(x, y) = (0, 0) and C''(x, y) = (2, 4).

Triangles are generated by the location of three distinct points on Cartesian plane. In this problem we find the representation of a triangle, whose vertices are listed below:

A(x, y) = (1, 0), B(x, y) = (3, - 1), C(x, y) = (4, 1)

We need to apply the following rigid transformations:

Translation

(x, y) → (x - 3, y + 1)

Dilation centered at the origin with scale factor 2

(x, y) → (2 · x, 2 · y)

Now we proceed to determine the coordinates of the image:

Translation

A'(x, y) = (- 2, 1), B'(x, y) = (0, 0), C'(x, y) = (1, 2)

Dilation

A''(x, y) = (- 4, 2), B''(x, y) = (0, 0), C''(x, y) = (2, 4)

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In a cas e whereby a fruit cocktail, for every 20 ml of orange juice you need 45 ml of apple juice and 100 ml of coconut milk the ratio of apple juice to coconut milk to orange juice expressed in its simplest form is 9: 20 : 4

The concept that will be used here is ratio.

The amount of orange juice can be expressed as  20mL

The amount of apple juice can be expressed as  45mL

The amount of coconut milk can be expressed as  100 mL

Then the ratio of the three can be expressed as :

(apple: coconut: orange)

= 45: 100 : 20

We can divide through by 5, then we have

9: 20 : 4

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Answer:

Step-by-step explanation: it it D

(y2-y1)/(x2-x1)

ex:-1-(-3)/-1-(-2)=2

The average rate of change of the function between x = a and x = a + h is -6

The slope is -6

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

g(x) = -6x + 1

The interval is given as

x = a and x = a + h

So, we have

g(a) = -6a + 1

g(a + h) = -6(a + h) + 1

This gives

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

Subtract the functions

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

g(a) - g(a + h) = -6h

The average rate is then calcualated as

Average = [g(a) - g(a + h)]/(a - a - h)

This gives

Average = (-6h)/-h

Evaluate

Average = -6

This also represents the slope

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The value of x is 11.78.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

In a figure, the four angles sum must equal 360.

Now,

The four angles are:

6x + 7, 5x + 13, 12x + 9, and 73

Solve for x.

6x + 7 + 5x + 13 + 12x + 9 + 73 = 360

23x + 89 = 360

23x = 360 - 89

23x = 271

x = 11.78

Thus,

x is 11.78.

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Complete question:

In the figure measurement angle 1 is 6x + 7°, measurement angle 2 equals 5x + 13°, and measurement angle 3 equals 12x + 9° and measurement angle 4 equals 73°.

What is the value of x?

The value of 4(3/2) times 1 is 6.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

Given:

4(3/2) times 1

Simplifying 4 (3/2) we get

= 4(3/2)

= 12/2

= 6

Now, we have to find 6 times of 1.

= 6 x 1

= 6

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Answer:

Step-by-step explanation:

[tex]\mathrm{3x+5=5(x+3)}[/tex]

Expand:-

[tex]\mathrm{3x+5=5x+15}[/tex]

Subtract 5x from both sides:-

[tex]\mathrm{-2x+5=15}[/tex]

Subtract 5 from both sides:-

[tex]\mathrm{-2x=15-5}[/tex]

[tex]\mathrm{-2x=10}[/tex]

Divide both sides by -2:-

[tex]\mathrm{\cfrac{-2x}{-2}=\cfrac{10}{-2}}[/tex]

[tex]\mathrm{x=-5}[/tex]

___________________

Hope this helps!

The compound interest is $348,966.97 and the future value is $464,966.97.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest to calculate the future value of the investment:

[tex]FV=P(a1+r/n)^{nt}[/tex]

where:

P = the principal amount (the initial investment)$116,000

r = the annual interest rate (as a decimal)=0.0429

n = the number of times the interest is compounded per year=52

t = the number of years=34

Plugging in these values, we get:

FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸

FV = $464,966.97

So the future value of the investment after 34 years is $464,966.97.

Compound interest = $464,966.97 - $116,000 = $348,966.97

Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.

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Answer:

77.4 (nearest tenth)

Step-by-step explanation:

76 is 100% of the original number.

To increase a number by 1.8% it will be 100% + 1.8% = 101.8% of the original number.

[tex]\begin{aligned}\implies \sf 101.8\%\; of\; 76&=\sf \dfrac{101.8}{100} \times 76\\\\&=\sf \dfrac{101.8 \times 76}{100}\\\\&=\sf \dfrac{7736.8}{100}\\\\&=\sf 77.368\\\\&=\sf 77.4\; (nearest\;tenth)\end{aligned}[/tex]

Therefore, the result when the number 76 is increased by 1.8% is 77.4 to the nearest tenth.

The minimum cost after assigning the jobs to different machines is 48. The solution has been obtained by using the cost function.

What is a cost function?

For some fixed factor prices, the cost function calculates the lowest cost of generating a specified level of output. The economic potential of a corporation is described by the cost function.

According to the cost function, the optimal assignment in order to minimise the total cost is by assigning:

Job J1 to machine M2 having a cost of 11

Job J2 to machine M3 having a cost of 12

Job J3 to machine M1 having a cost of 14

Job J4 to machine M4 having a cost of 11

From this, we get the total minimum cost as:

11 + 12 + 14 + 11 = 48

Hence, the minimum cost after assigning the jobs to different machines is 48.

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Answer:

0.4850 knots.

Step-by-step explanation:

To convert the speed of the California Current from centimeters per second to knots, we can use the conversion factor of 1 knot = 0.514444444 cm/s.

So, 0.25 cm/s * 1 knot / 0.514444444 cm/s = 0.4850 knots.

Therefore, the California Current moves at a speed of approximately 0.4850 knots.

The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

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The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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Answer:

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

Step-by-step explanation:

Given,

The equation is  

5x-2w+t

and also given the

x=3

w=1/2

and t=8

Now ,

if we substitute the value of x,w and t,

We get,

5 × 3 - 2 × (1/2) + 8

= 15 - 1 + 8

= 22

So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.

Answer:

$416.67

Step-by-step explanation:

8% = 0.08

adding 8% to something means you add 0.08 of it

original = 100% = 1

original + 8% increase = 1 + 0.08 = 1.08

1.08 of original price = new price = 450

1.08 * original price = 450

450/1.08 = original price = $416.67

Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

x = 415.

Check attached image 1.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

We know that the sum of angles DBE and CBE equal 90°. Hence:

[tex]DBE+CBE=90[/tex]

In terms of variable "x", this is:

[tex](0.1x-22)+(0.3x-54)=90[/tex]

[tex]0.1x-22+0.3x-54=90[/tex]

[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]

[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]

[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]

x = 415.

Answer:

$ 546.00

Step-by-step explanation:

Simple Interest = P x r x  t

where t = number of years

r = interest rate per year as a decimal

P = amount invested(deposit)

We are given that r = 7.8% per year = 7,8/100 = 0.078

However, since this is the yearly interest, the monthly interest = 0.078/12

The time period is 42 months

Initial deposit = $2,000

Therefore interest
I = 2000x (0.078/12) x 42 =  $ 546.00

In a linear equation. , $12,215 did he save in tax by using Schedule A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given,

      Taxable income with out deductions = $63,110

                     total deductions = $10,312

       the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is

                          tax = $12,215

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The inequality that determines the maximum number of people that can go to the park is given as follows:

5.75 + 29.75x ≤ 210.

The costs associated with going to the park are given as follows:

Hence the total cost for x people going to the park is given by the following equation:

C(x) = 5.75 + 29.75x.

They can spend at most $210, hence the inequality that determines the maximum number of people that can go to the park is given as follows:

C(x) ≤ 210

5.75 + 29.75x ≤ 210.

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The composite function is given below with examples.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Consider two functions f(x) and g(x).

Now,

f o g = f(g(x)) is called a composite function.

f(x) = 2x + 1

g(x) = x + 2

So,

(f o g)(x)

= f(g(x))

= f(x + 1)

= 2 (x + 1) + 1

= 2x + 2 + 1

= 2x + 3

Thus,

The composite function is given above with examples.

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The functions are matched as follows -

y = √x ⇒  d. Square root

y = |x| ⇒  g. Absolute value

y = x² ⇒  h. Quadratic

y = 1/x² ⇒  f. Reciprocal Squared

y = 1/x ⇒  b. Reciprocal

y = x³ ⇒  a. Cubic

y = ∛x ⇒  e. Cube root

y = x ⇒  c. Linear

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The first function is given as -

y = √x

Since, this function contains a square root symbol, so it is a square root function.

The second function is given as -

y = |x|

Since, this function contains absolute value symbol, so it is a absolute value function.

The third function is given as -

y = x²

Since, this function contains power of 2 and x is squared, so it is a quadratic function.

The fourth function is given as -

y = 1/x²

Since, this function contains power of 2, x is squared and the value is reciprocal of x², so it is a reciprocal squared function.

The fifth function is given as -

y = 1/x

Since, this function contains reciprocal value of x, so it is a reciprocal function.

The sixth function is given as -

y = x³

Since, this function contains power of 3 and x is cubed, so it is a cubic function.

The seventh function is given as -

y = ∛x

Since, this function contains a cube root symbol, so it is a cube root function.

The second function is given as -

y = x

Since, this function contains y equal to x, so it is a linear function.

Therefore, all the different functions are identified.

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Answer:

15.40 ounces to 16.90 ounces.

Step-by-step explanation: