Based on the diagram, which of the following statements must be true?

A. No lines are parallel
B. a || b and l || m
C. l || m
D. a || b

The amount in a continuously compounded account for the given conditions is $2330.64 .

It is given that principal is 2000 , annual interest rate is 5.1 % , time is 3 years

Putting [tex]P=\$2000 , \ r= 5.1\% , \ t=3 \ years[/tex] in equation (1) , we get

  [tex]A=2000\times 2.71^{0.051 \times 3}\\A=200\times 2.71^{0.153}\\ \ A=2000\times1.1653\\A =\$2330.64[/tex]

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The constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

The graph is the given parameter

On the graph, we have the following point

(x, y) = (2, 50)

The constant of proportionality for the relationship plotted, on the graph is represented with k, and the formula is

k = y/x

This gives

k = 50/2

Evaluate

k = 25

Substitute k = 25 in k = y/x

25 = y/x

When x = 10. we have

25 = y/10

This gives

y = 250

Hence, the constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

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The option d ,that is , x= 5y is the equation that represents inverse variation between x and y.

1: A mathematical connection between two variables that can be described by an equation in which the sum of their products equals a fixed value.

2: an expression of inverse variation by an equation or function; contrast with direct variation.

In an inverse variation, the inverse percentage establishes the link between two quantities or variables. The inverse relationship between two quantities, x and y, is provided by:

x ∝ 1/y

or

x = k/y

xy = k

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Answer:

22°, 79° and 79°

Step-by-step explanation:

Let x  be the vertex angle and y each of the congruent angles.

The sum of all angles =180°

So x + y + y = 180

x + 2y = 180 ·········· Equation (1)

Given "The measure of each of the congruent angles of an isosceles triangle is 9 less than 4 times the vertex angle", the equation is

y = 4x - 9

Substitute for y in terms of x in equation 1

⇒ x + 2(4x - 9) = 180

⇒ x + 8x - 18 = 180

⇒ 9x - 18 = 180

⇒ 9x = 180 + 18

⇒ 9x = 198

⇒ x = 198/9 = 22

So vertex angle is 22°

Substituting for x in Equation 1:
22 + 2y = 180
2y = 180 - 22
2y = 158
y = 158/2
y = 79°

So each congruent angle is 79°

The exponential function for the value of car is V = 25,000 × e^( r × T) and the value of the car after 5 years is $ 1109.26.

The original value of a car is $25,000.

The value of the car after one year is $21,250.

Let V be the value of the car after T years.

Let the rate at which the value of the car increase be r.

From, [tex]\[ A = Pe^{r \times T} \][/tex]

Then,

[tex]\[ V = 25,000 \times e^{ r \times T } \][/tex]

The value of the car after one year is $21,250.

[tex]\[ 21,250 = 25000 \times e^{ r \times T } \][/tex]

Divide both sides by 25000

[tex]\frac{21250}{25000} = e^{1 \times r }[/tex]

Now, taking the log of both sides

[tex]\[ \ln (21250/25000) =\ln e^{1 \times r} \][/tex]

By the property of logarithm,

[tex]\ln e^{(1 \times r)} = r[/tex]

Therefore,

㏑(21250/25000) = r

Now, the value of the car after 5 years will be:

[tex]\[ V = 25,000 \times e^{ r \times T} \]\\\\[/tex]

[tex]\[ V = 25000 \times e^{ \ln (\frac{21250}{25000} ) \times 5 } \][/tex]

V = 25000 × 0.4437053125

V = $ 1109.26

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Answer:

a) 6 hours

b) 12 hours

c) 36 hours

Step-by-step explanation:

let hours taken to mow lawns = x

baby sit hours = 2x

walk dogs hours = 3(2x) = 6x

x+2x+6x = 54

thus, x = 6

Answer:

False

True

missing info

missing info

Step-by-step explanation:

2.8mm = 28cm    False since 28 cm = 280 mm

1760 ml < 10 litres     True since 1760 ml = 1.76 l

18g > 0.17    missing units

1.68 = 168cm    missing units

Answer:

= 17

Step-by-step explanation:

If f(x)=3x+2, then replacing x=5 we get f(5)=3x5+2=15+2=17

Answer:

the answer to the equations is 17

Step-by-step explanation:

x=0 is an extraneous solution of the equation and x = 8 is not an extraneous solution of the equation.

√(3x+1) - √(x+1) = 2

√(3x+1) = 2 + √(x+1)

Squaring both the sides of the equation

(√(3x+1))² = (2 + √(x+1))²

3x + 1 = (2)² + (√(x+1))² + 2(2) (√(x+1))

3x + 1 = 4 + x + 1 + 4(√(x+1))

3x + 1 = 5 + x + 4(√(x+1))

2x - 4 = 4(√(x+1))

Squaring again on both the side of the equation, we get

(2x - 4)² = (4(√(x+1))²

4x² + 16 - 16x = 16x + 16

4x² - 32x = 0

4x(x - 8) = 0

4x = 0 and x - 8 = 0

x = 0 and 8

Check for Extraneous Solution by keeping value of x in the original equation √(3x+1) - √(x+1) = 2

Let x=0

√(3(0)+1) - √(0+1) = 2

0 ≠ 2

LHS ≠ RHS

x = 0 is an extraneous solution of the equation

Let x=8

√(3(8)+1) - √(8+1) = 2

✓25 - ✓9 = 2

5 - 3 = 2

2 = 2

LHS = RHS

∴ x=8 is not an extraneous solution of the equation.

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The exponent property which must be applied first to simplify the expression as given in the task content is; The power of a power property.

It follows from the task content that the exponent property which must be applied first in a bid to simplify the expression be determined.

Since the expression given is;

(4y)³ • (2g)² • y • g

Consequently, to solve the parentheses, the power of a power property must be used first so that we have;

4³•y³ • 2²•g² • y • g

The expression can then be further simplified by using the the product of a power property on like terms so that the simplified form is therefore;

256g³y⁴.

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The translations for each sentence are listed below:

Herein we find nine sentences that must be translated in terms of algebraic expressions, that is, combinations of constants, variables and operators. Now we proceed to present the result of each case:

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According to the distributive property:

[tex] \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma [/tex]

So, applying this to our equation:

[tex]7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y[/tex]

The required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

GIven that,
For the given Venn diagram which expression represents the shaded area

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The total area of A and B
= AUB
Area of unshaded area,
= (A'∩B) ∪ (A ∩ B')

Thus, the required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

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the slope is 3 for the equation

Answer:

the slope is 3 for the equation

Step-by-step explanation:

The number of pizza left is 1/12

Nicole and Daniel are splitting a pizza

Nicole gets 1/4 of the pizza

Daniel gets 2/3 of the pizza

let 1 represent the total amount of pizza

1- (1/4 + 2/3)

1- 11/12

= 1/12

Hence 1/12 of the pizza is left from the total amount of pizza

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If the length of the rectangle given is larger than the width of the rectangle then the inequality which represents given situation is 13x-9 > 4.5x+8

What is an inequality?

Inequality is a kind of equation which compares two mathematical expressions instead of equating them using relations like less than, greater than, less than or equal to, greater than or equal to.

Given that Victoria drew a diagram of her laptop which is in the shape of the rectangle. The dimension are Length 13x-9 and width 4.5x+8

If the length is given greater than width, then this can be represented by  inequality: length > width

i.e. 13x-9 > 4.5x+8

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The complete question is mentioned below :

Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:

Length: 13x - 9 units

Width: 4.5x + 8 units

If the length is greater than the width, which inequality represents this situation?

The required value of z using given conditions and functions is 7.92.

What is a function?

A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.

Calculation for the value of z

Given value of z = 1.5, x = 9, y = 4

Consider z as a function varying directly with x and inversely with y i.e.

z = kx / y        —-- 1

Putting the values of x, y, z, we get,

1.5 = k × 9 / 4

6 = 9 × k

k  = 6 / 9

k = 2 / 3 = 0.66

Now, calculating z for x = 6, k = 0.66 and y = 0.5, using function,

z = (0.66 × 6) / 0.5

= 3.96 / 0.5

= 7.92

Hence, the required value of z = 7.92.

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Answer:

B. x = (4/3)

Step-by-step explanation:

-x + (3/7) = 2x - (25/7)

(-x + (3/7) = 2x - (25/7)) × 7

-7x + 3 = 14x - 25

-14x        -14x

-21x + 3 = -25

         -3     -3

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

-21x = -28

÷-21    ÷-21

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

x = (4/3)

I hope this helps!

Answer:

x=-5nakalimutan ......................

......

Answer:

Triangular inequality:  Length of third side must be less than the sum of the lengths of the other 2 sides.

x < 18 + 29

x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x

x > 11    so minimum length = 12

Difference  = 46-11 = 35

Answer:

arccos(439/1976)

Step-by-step explanation:

The largest angle is opposite the longest side. So, by the Law of Cosines, if we let this angle be x,

[tex]x=\arccos \left(\frac{7.6^2 + 5.2^2 - 8.2^2}{2(7.6)(5.2)} \right) \\ \\ =\arccos(439/1976)[/tex]

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

The fact that logs represent exponents gives rise to four fundamental properties. The first three are easy to remember: A product's log equals the total of its elements' logs. The log of a quotient is proportional to the distinction between the numerator as well as denominator logs. Power multiplied by that of the logarithmic of the base equals the log of power.

log₃2/x

Applying the property of log  (log a/b = log a +log b)

log₃2/x

log₃2 + log x

Applying the property (logₐᵇ = a log b)

log₃2

2log3

we get substituting the.(log₃2 + log x)

2log3 + log x

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

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The Nethanel's monthly Social Security benefit is :$ 705.88

What makes the household monthly income of $1,800?

The household monthly income of $1,800 comprises the monthly income and social security of Nethanel Stuck and his wife monthly income from social security which is 70% of Nethanel's

total income=$600+x+(70%*x)

total income=$1,800

Nethanel social security=x

wife's monthly income=70%*x=0.70x

1800=600+x+0.70x

1800-600=1.70x

1200=1.70x

x=1200/1.70

x=Nethanel's monthly Social Security benefit=$ 705.88

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[tex]100^{\frac{-3}{ 2} }[/tex] can be simplified into 0.001.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 100 = 5 x 5 x 2 x 2 = [tex]10^{2}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e.,[tex](x^{m} )^{n} = x^{mn}[/tex]

According to the given condition,

∴ [tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2})^{\frac{-3}{2} }[/tex]

Applying the law of indices mentioned above,

[tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2 X}^{\frac{-3}{2} })[/tex]

= [tex]10^{-3}[/tex] = 0.001.

Thus,  [tex]100^{\frac{-3}{2} }[/tex] can be simplified into 0.001.

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After solving the equation the value of x in (4x - 1) = 36 is  37/4

We have been asked to find x in (4x - 1) = 36

⇒ (4x - 1) = 36

⇒ 4x = 36 + 1

⇒ 4x = 37

⇒ x = 37/4

So, x is equal to 37/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The inequalities and their graphs are;

1)  -x - 5 ≤ -2 is represented by the third graph

2) 6 + x ≤ 3 is represented by the fourth graph

3) x - 4 < -7 is represented by the second graph

4) 2x > -6 is represented by the first graph

1) We are given the inequality;

-x - 5 ≤ -2

Rearranging gives us;

-x ≤ -2 + 5

- x ≤ 3

Divide both sides by -1 to get;

x ≥ -3

The graph must be a closed circle starting at -3 and pointing to the right.

It is the third graph in the link at the end of this answers.

2) We are given the inequality; 6 + x ≤ 3

Rearranging gives;

x ≤ -6 + 3

x ≤ -3

The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.

3) We are given the inequality; x - 4 < -7

Rearranging gives us;

x < -7 + 4

x < -3

The graph must be an open circle starting at -3 and pointing to the left.

Thus, it is the second graph.

4) We are given the Inequality; 2x > -6

Divide both sides by 2 to get;

x > -6/2

x > -3

It must be a graph with an open circle starting at -3 and then to the right.

Thus, it is the first graph as seen in the attached link

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

[tex]\large\text{If we were to find the difference between the two years you have}\\\large\text{provided you would have to go back (almost like you're going}\\\large\text{back in time). You're going to take the highest year (238 B.C.)}\\\large\text{from the lowest year (15 B.C.) and you should have your equation}\\\large\text{and answer if you did what you were told.}[/tex]

[tex]\large\text{Equation: }\rm{238\ B.C. - 15\ B.C.}[/tex]

[tex]\large\text{Get your number line ready because this will make the equation easier to}\\\large\text{solve.}[/tex]

[tex]\large\text{Start at 238 and go back 15 spaces to your 15 to your left.}[/tex]

[tex]\large\text{If you did the right calculation you should be at: 223}[/tex]

[tex]\huge\text{Thus, your answer can be: \boxed{\mathsf{238\ B.C. - 15\ B.C. }}}\huge\checkmark[/tex]

[tex]\large\text{Remember: \textsf{difference} means subtraction/subtract}[/tex]

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

Answer:

Alternate Exterior Angles

Answer:

alternate interior angles