Graph the solution set for the system of inequalities and shade the solutions to the system
y≥x²
y≤x + 2

Answer:

The expression (6 × 10^7) × 0.007 simplified is 4.2 x 10^5.

Step-by-step explanation:

Part A. An explicit expression for the function A(n), the final amount (future value) after n years is 1,500 x 1.0235^n.

Part B. The function for determining the future value of the CD at 2.35% annual compounded interest rate is derived by comparing the present value and the future value and using the difference to calculate the compound interest rate.

The future value is the present value compounded at an interest rate.

The future value formula or function is as follows:

FV = PV(1+r)^{n}

FV = future value

PV = present value

r = annual interest rate

{n} = number of periods interest held

Initial deposit in a ten-year certificate of deposit (CD) = $1,500

Deposit period = 10 years

Amount after 1 year = $1,535.25

Compound interest rate = 2.35% annually ($1,535.25 - $1,500)/$1,500 x 100)

Function for A(n) = 1,500 x 1.0235^n

Thus, from the future value after 1 year, we can derive the compound interest rate.

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Answer:

15.25 - 5.75 h

this my be it but i'm not shore

Answer:

vjjvwplast

Step-by-step explanation:

past I 1 days its just is right

Answer:

x = 27

Step-by-step explanation:

[tex]\displaystyle 4x^{\frac{2}{3}}-5=31\\4x^\frac{2}{3}=36\\x^{\frac{2}{3}}=9\\x=9^\frac{3}{2}\\x=27[/tex]

The factored form of the trinomial x² - 2x - 35 is ( x - 7 )( x + 5 ).

Given the trinomial in the question;

x² - 2x - 35

To simplified in a factored form,

Consider the trinomial in its standard form; ax² + bx + c.

Now, find a pair of integers whose product is c and whose sum is b.

In this case, we use -7 and 5

The product of -7 and 5 = -35

The sum of -7 and 5 = -2

Next, we write the factored form using the integers -7 and 5

( x - 7 )( x + 5 )

Therefore, the factored form is ( x - 7 )( x + 5 ).

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The domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function f(-6) - f(9) as follows:

f(-6) = 2(-6) + 15 {put -6 for x }

f(-6) = -12 + 15

f(-6) = 3

f(9) = 2(9) + 15 {put 9 for x }

f(9) = 18 + 15

f(9) = 33

f(-6) - f(9) = 3 - 33

f(-6) - f(9) = -30

Therefore, the domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.

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Possible question:

Given the function f(x) = 2x + 15. What is f(-6) - f(9)?

3.1 ft more fabric should be produced to make pillows versus a rug.

A fraction is a number expressed in the form of {x/y}, where y ≠ 0.

Given is that 1[tex]\frac{6}{11}[/tex] ft of fabric is needed to make a rug while 4[tex]\frac{1}{2}[/tex] ft of fabric is required to make pillows. Producing a rug is 2[tex]\frac{2}{7}[/tex] times faster than pillows.

We can write -

1[tex]\frac{6}{11}[/tex] x 4[tex]\frac{1}{2}[/tex] = 2[tex]\frac{2}{7}[/tex] x {y}

{17/11 x 9/2} = {16/7 y}

{y} = {6.96 x 7}/16

{y} = 3.1

Therefore, 3.1 ft more fabric should be produced to make pillows versus a rug.

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An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Convert the ratio to a fraction, multiply it by a common factor, and divide it again to obtain the corresponding ratio of 6:4. Therefore, 12/8 is the same as 6:4.

Any two quantities can be compared using the ratio formula a: b a/b. The ratio, on the other hand, proportion formula is expressed as a:b::c:d⟶ab=cd a : b :: c : d ⟶ a b = c d

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The equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16

The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Given that, a line is passing through point (-8, 7) and parallel to a line -9x+8y = -24,

We need to find the equation of the line,

Converting the parallel line equation into slope-intercept form,

-9x + 8y = -24

8y = 9x - 24

y = 9x/8 - 3

Here, slope = 9/8

We know that, two lines which are parallel have equal slopes,

Therefore, the slope for the asked line is 9/8

Now, the equation of line is =

y = 9x/8 + c

To find c, put x = -8 and y = 7 in the equation,

7 = -9 + c

c = 16

Therefore, the equation =

y = 9x/8 + 16

Hence, the equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16

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The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

To find an Equation that is parallel to 2x - y = 7 and passes through the point (10, 0)

Since, Both equations are parallel thus, the slope of the given equation will be the Same.

equation of the first line in slope intercept form: y = 2x - 7

Thus, Slope = 2

From the general formula of the linear equation in slope-intercept form:

y=mx+b,

where m is the slope

b is the y-intercept

in our case,

Slope = 2

So Line,

y = 2x + b

Since line passes through (10, 0)

b= -20

Thus,

Equation of line  y = 2x - 20

Therefore, The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

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The slope-intercept equation of the line that includes the points (0, 12) and (4, 36) is y = 6x + 12.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

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

Where:

Next, we would determine the linear equation representing the line which passes through the points (0, 12) and (4, 36) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 12 = (36 - 12)/(4 - 0)(x - 0)

y - 12 = 6(x - 0)

y = 6x + 12

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If 24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09: 51,960 is invested at 15%, and 22,823 is invested at 9%.

Let's x represent the amount invested at 15%

Let the  amount invested at 9% = 24,783 - x.

Interest earned at 15% is 0.15 * x

Interest earned at 9% is 0.09 * (24,783 - x)

We can set up the equation: 0.15x = 0.09 * 24,783 - 0.09x + 894.09

Solving for x:

0.06x = 24,783 * 0.09 + 894.09

0.06x = 2223.47 + 894.09

0.06x = 3117.56

x = 51,960

So,

(24,783 - x)

24,783 - 51,960

= 22,823

Therefore 51,960 is invested at 15%, and 22,823 is invested at 9%.

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Answer:

f(x) = {

C(x) = 6, 0 < x ≤ 50

C(x) = 8, 50 < x ≤ 100

C(x) = 10, 100 < x ≤ 200

}

Step-by-step explanation:

The relationship is proportional, when, there is no added constant, which shows a proportional relationship represented by the equation y = 1/2x.

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".

here, we have,

y = 1/2x

If the relationship is proportional, there is no added constant. The relation that is proportional is ...

y = 1/2x

Hence, The relationship is proportional, when, there is no added constant.

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Answer: pls see the analysis.

Step-by-step explanation:

For given triangles, The correct proportion will be 16/12=18/x.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

For given triangles ABC and DEF

as ABC ≅DEF

Then AB=DE, BC=EF AND AC=DF

given BC=16, EF=12 and DE=18 then AB=?

Let AB=x then

16/12=18/x as ABC ≅DEF

Hence,

          The correct proportion will be 16/12=18/x.

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The constant of proportionality is the ratio between two quantities that are in proportion. If two quantities are proportional, their ratio is always the same, and this constant ratio is called the constant of proportionality.

Given the two quantities 1.5 and 3.9, the constant of proportionality can be found by dividing one by the other:

k = 3.9 / 1.5

k = 2.6

So the constant of proportionality between 1.5 and 3.9 is 2.6.

Answer:

[tex]\dfrac{9\pm \sqrt{33}}{4} \longrightarrow \boxed {2x^2\:-\:9x+6=0}}[/tex]

[tex]\dfrac{4\pm \sqrt{6}}{2} \longrightarrow \boxed{2x^2 - 8x +5=0}[/tex]

[tex]\dfrac{9\pm\sqrt{89}}{4} \longrightarrow \boxed{2x^2\:-\:9x-1=0 }[/tex]

[tex]\dfrac{4\pm \sqrt{22}}{2} \longrightarrow \boxed{2x^2\:-\:8x-\:3=0}[/tex]

Step-by-step explanation:

Use a quadratic equation solver calculator

Here are the roots for each equation

Equation                          Roots

[tex]2x^2 - 8x +5=0\quad\quad\quad \quad \dfrac{4\pm \sqrt{6}}{2}[/tex]

[tex]2x^2\:-\:10x-\:3=0\quad\quad\quad \dfrac{5\pm \sqrt{31}}{2}[/tex]    

[tex]2x^2\:-\:8x-\:3=0\quad\quad\quad \dfrac{4\pm \sqrt{22}}{2}[/tex]

[tex]2x^2\:-\:9x-1=0 \quad\quad\quad \dfrac{9\pm\sqrt{89}}{4}[/tex]

[tex]2x^2\:-\:9x+6=0\quad\quad\quad \dfrac{9\pm \sqrt{33}}{4}[/tex]

The quadratic equations are solved and the tiles are matched with the following equations

a) 2x²- 8x + 5 = 0 → x = ( 4 ± √6 ) / 2

b) 2x² - 8x - 3 = 0 → x = ( 4 ± √22 ) / 2

c) 2x² - 9x - 1 = 0 → x = ( 9 ± √89 ) / 4

d) 2x² - 9x + 6 = 0 → x = ( 9 ± √33 ) / 4

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a)

2x²- 8x + 5 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 4 ± √6 ) / 2

b)

2x² - 8x - 3 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 4 ± √22 ) / 2

c)

2x² - 9x - 1 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 9 ± √89 ) / 4

d)

2x² - 9x + 6 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 9 ± √33 ) / 4

Hence , the quadratic equations are solved

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Answer: 882

Hope this helps :)

Step-by-step explanation:

Since there is only one other term in the parenthesis, there will only be one step.

Distribute the 9 to 98.

9 * 98 = 882

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9(98)}\\\mathsf{= 98(9)}\\\mathsf{= 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98}\\\mathsf{= 196 + 196 + 196 + 196 + 98}\\\mathsf{= 392 + 392 + 98}\\\mathsf{= 784 + 98}\\\mathsf{= 882}\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathsf{882}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The standard form of the given quadratic equation is;

x² - x - 6

The standard form of a quadratic equation can be written in the form;

ax² + bx + c =0 (In terms of variable x), where a ≠ 0.

The equation is expressed in the question as;

(x + 2)(x - 3)

To convert to standard form, we will just multiply out the bracket to get;

x² + 2x - 3x - 6

= x² - x - 6

Thus,  that final expression is the standard form of the given quadratic expression

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Answer: x = -4

Step-by-step explanation: Multiply both sides of the top equation by 2 so you can cancel the y's.

4x + 3x = -28.

7x = -28

x = -4

Answer: if u don't know that this language is than ill tell u.

its just random words that someone typed in. I'm being honest this is not a language this is some random typed words. trust me pls I'm being honest fr.

Step-by-step explanation: what I did was going a a type of book that has all the language on it so u get to know the language.

Answer: [tex]6 \text{ m}^2[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2}bh=\frac{1}{2}(7.5)(1.6)=6 \text{ m}^2[/tex]

The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as interval notation as

{y∣-11≤y<∞} or [-11,∞). This set represents the function's range.

Endpoints that are part of an interval are indicated by square brackets. Endpoints that are not part of an interval are indicated by parentheses. When using or, parentheses are always used.

As a result, the set of shaded numerals displayed on the interval notation can be used to express the y-axis as {y∣-11≤y<∞} or [-11,∞)

This set displays the functional domain.

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The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Yolanda is building a fence around her garden.

For every 2 feet of fencing, the cost is 12.

The unit rate = 12/ 2 = $6 per feet

The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

Therefore, the complete table is given above.

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Kareem has $22, Raina has $28, Eric has $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raina, Kareem, and Eric have a total of $138 in their wallets.

let Kareem has x dollar.

Then Raina has (x+6) dollar

and, Eric has 4x dollar

So, x+ 4x + x + 6 = 138

6x + 6 = 138

6x = 132

x= 22

Thus, Kareem has $22.

Raina has = 22 +6 = $28

and, Eric has =4x = $88

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Answer: it's 39.

Step-by-step explanation: for this figure, you want to divide it into two parts:    The triangle and the rectangle.

The triangle has a base of 6, and a height of 3.

The formula for area of a triangle is 1/2 bh.

So the area of the triangle is 9!! 6 x 3 is 18.. divided by two is 9.

Then the rectangle, a= b(h)

the height is 6 while the base is 5.

When you multiply thsoe two you get 30.

The value of p and q are set to be equal ( option B)

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angles In a triangle is 180.

Therefore to find p

p+80+20 = 180

p = 180-(100)

p = 80

To find angle q

q+45+55 = 180

q = 180-(45+55)

q = 180-100

q = 80

q = 80= p

therefore the values of p and q are equal

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