Lydia wants to ride her bicycle 34 miles this week. She has already ridden 7 miles. If she rides for 5 more days, which equation could be used to determine xx, the average number of miles she would have to ride to meet her goal?

Answer:

Statement 2  A supports statement 2 Best

Step-by-step explanation:

statement two is correct a citizen under the age of 18 cannot vote.

An inverse statement means the opposite of the original statement.

So, A would best support the answer.

I apologize if I am wrong in any way please kindly correct me.

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Answer:

A.

Statement 2 is the contrapositive of statement 1.

Step-by-step explanation:

The point (-7, 1) is in fact a solution for the inequality y < 0.5x + 9

A point is a solution of a inequality only if it makes the truth value of the inequality true.

In this case, it would mean that the right side of the inequality is strictly larger than the left side.

So to check that, we just need to replace the values of the point on the inequality.

The values are x = -7 and y  = 1, replacing that in the given inequality we will get:

1 < 0.5*(-7) + 9

1 < -3.5 + 9

1 < 5.5

This is true, 5.5 is larger than 1, then we conclude that the point (-7, 1) is in fact a solution for the inequality y < 0.5x + 9

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According to the question, the function f(x) is bounded with constant number. And the exponential function base e is not bounded. Similarly, logarithmic function base e is also not bounded.

Bounded values can be calculated with the help of asymptotes namely, vertical, horizontal and oblique. The vertical, horizontal and oblique asymptotes are constant values which grows the values of the function f(x) without bound.

A basic logarithmic function is a function with no horizontal shift as well as no vertical shift. All logarithmic function passes through a constant points and touches the horizontal axis which results into asymptotes. It either increases from left to right, or decreases from left to right.

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Answer:

Step-by-step explanation:

For 3 hours it cost him $78.25

25 + 17.75 + 17.75 + 17.75= 78.25

He had left from $102.17 subtract from $78.25 is $23.92

Answer:

23.92

Step-by-step explanation:

17.75x3=53.25

53.25+25=78.25

102.17-78.25=23.92

The problems he got correct on the second test is 12.

Ratio expresses the relationship between two or more numbers. It shows the the number of times that one value is contained within other value(s). Ratio is used to compare two or more numbers. The sign used to represent ratio is :

The first step is to determine the total number of questions on the math test : (sum of ratios x answers gotten incorrect on the first test) / ratio of the answers gotten incorrect

(8 x 10) / 5 = 16

Answers gotten correct on the second test : (ratio of correct answers / sum of ratios) x total number of questions

(6/8) x 16 = 12

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Answer:

Step-by-step explanation:

5 pounds

Answer: 6

Step-by-step explanation:Shannon buys a bag online for $32.00 including tax, and the shipping is $4.00. If she decided to buy more of the same bags and it doesn't change the shipping cost, how many can she buy with $100.00

The Volume of the given Hemisphere is  1071.8 cm³ rounded to 1 decimal place whose radius is 8cm

The Volume of the sphere  is given by the formula 4/3 πr³

The volume of hemisphere is half of sphere

So, The volume of hemisphere is 2/3 πr³

From the given figure it is clear that the radius of the hemisphere is 8cm

Here, we will use the value of π as 3.14 and not 22/7

So, Substituting the values in the formula of Volume of hemisphere

the Volume of hemisphere =2/3 π (8)³

                                      =2/ 3× 3.14 × 512

                                     = 1071.7867 cm³

Hence, the Volume of hemisphere 1071.7867 cm² or 1071.8 cm² rounded to 1 decimal place whose radius is 8cm

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The amount the PTA at Greenville High School raised this year is $30,023.

The percentages are also called the centesimal ratio, and are usually accompanied by the symbol “%”, which reads “percent”.

The fact that the PTA at Greenville High School raises 30% less funds this year compared to last year means that the amount raised this year is 70% of last year's funds, in essence, 70% multiplied by last year's:

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Answer:

m=2

Step-by-step explanation:

An equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

The index form of a number is simply that number written as an exponential expression, or even as a single number that is raised to another number.

Index form is also known as standard form

Given the index form;

⇒ 8.723 x 10-¹⁰

⇒ 8. 723 × 10^ -(10)

This means that there 10 zero digits from the left end of the given decimal, it is expressed as;

0. 0000000008723

Thus, an equivalent form of the index 8.723 x 10-¹⁰ is 0. 0000000008723

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The Magnitude of all the vectors is the same.

As you know, a vector is an object with both Magnitude and direction. To find the size of a vector, we need to calculate the length of the vector. Variables such as velocity, distance, force, and momentum are vector variables. But velocity, mass, distance, volume, temperature, etc., is a scalar quantities. A vector has both Magnitude and direction, while a scalar has only one Magnitude.

The Magnitude of a vector is the length of the vector. The Magnitude value of vector a is represented by ∥a∥.

The formula for its Magnitude is given below for a two-dimensional vector a= (a1, a2).

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A composite function exists as a function that depends on another function. The value for f/g(10) is 1/5

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = x+5 and g(x) = x²-25

A function exists described as a relationship between one variable and another variable.

(f/g)(x) = f(x)/g(x) = (x+5) / (x²-25)

The domain of a function exists the set of all possible inputs for the function.

When the denominator is zero, the function remains undefined.

Hence, x cannot take the values 5 and -5.

The function (f/g)(x) is defined for all values of x except x = 5, -5.

Hence, the domain is all integers except x = 5, -5

⇒ (f/g)(10) = (10 + 5) / (100 - 25)

simplifying the above equation, we get

⇒ (f/g)(10) = (15) / (75)

⇒ (f/g)(10) =  1/5

Therefore, the value of (f/g)(10) is 1/5.

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Answer:

Box of oat:

24*5*25(all in cm)=3000 cm3

cereal:

26*4*2.8=291.2 cm3

oat is grater by 2708.8

Step-by-step explanation:

28mm was changed to 2.8 cm

The total surface area or surface area of the given sphere is 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm

The total surface area or surface area of a sphere is given by the formula 4πr²

From the given figure it is clear that the radius of the sphere is 2.6cm

Here, we will use the value of π as 3.14 and not 22/7

So, Substituting the values in the formula of Total surface area of a sphere.

the total surface area =4 π (2.6)²

                                              4 × 3.14 × 6.76

                                              = 84.9056 cm²

Hence, the total surface area or surface area of the given sphere is 84.9056 cm² or 84.9 cm² rounded to 1 decimal place whose radius is 2.6cm

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The function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.

Consider the compound interest formula:

y = P(1 + r/n)ⁿˣ

y here stands for the car's potential value.

P represents the value of the new car.

r is a measure of how quickly a car's value declines.

The number n indicates how frequently the car's value depreciates each year.

x represents the number of years.

Given P = 25000

r = -15% = -0.15 (Since the value of the car depreciates)

n = 1

x = x

Using the given values, we get the function as,

y = 25000(1 + (-0.15)/1)ˣ

⇒ y = 25000(1 - 0.15)ˣ

⇒ y = 25000(0.85)ˣ

Therefore, the function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.

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The quadratic function of the jump is y = -0.22x^2 +0.89x + 6.11 if the jump changes so that the axis of symmetry becomes X=2 , the height stays the same 7 and also passes through the point (5,5)

Quadratic function involving vertex is given by

y = a(x-h)^2 + k

Where (h,k) is the vertex which is given as (2,7)

y = a(x-2)^2 + 7

y = a(x-2)(x-2)  + 7

y = a(x^2 -4x +4) + 7

Recall that

h = -b/2a

k = -(b^2 -4ac)/4a

2 = -b/2a

-b = 4a

b = -4a

Put b = -4a

k = -(b^2 -4ac)/4a

7= -(b^2 -4ac)/4a

7 = -((-4a)^2 -4ac)/4a

7 = -(16a^2 - 4ac)/4a

7 =  (-16a^2 + 4ac)/4a

7 = -4a + c

c = 7 + 4a

The path of the jump also passes through (5,5)

y = ax^2 + bx + c

5 = a5^2 + b5 + c

5= 25a +5b + c

Put b = -4a in above

5= 25a +5(-4a) + c

5= 25a -20a+ c

5 = 5a + c

Put c = 7 + 4a

5 = 5a + 7 +4a

Collect like terms

5-7 = 5a + 4a

-2 = 9a

a = -2/9

Put a in

y = a(x^2 -4x +4) + 7

y = -2/9(x^2 -4x +4) + 7

y = (-2x^2 +8x -8)/9 +7

Multiple through by 9

9y = -2x^2 +8x -8 + 63

9y = -2x^2 +8x + 55

Dividing through by 9

y = -0.22x^2 +0.89x + 6.11

Therefore the equation of the jump is

y = -0.22x^2 +0.89x + 6.11.

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Answer: B

Step-by-step explanation:

The distance on the map that represents an actual distance of 4 kilometers is 3.2cm.

The actual number of kilometers that is represented by 5 centimeters on the map is 6.25 kilometers.

A scale drawing is a smaller version of a larger image. In this question, the map is a scale drawing of the city. The scale drawing is reduced using constant dimensions using a scale.

A scale gives the ratio of the length of the scale drawing to the actual diagram or object. In this question, every 4cm on the map represents 5km in the city.

The distance on the map = (4 x 4) / 5

16 / 5 = 3 1/5 cm = 3.2 cm

The actual distance = (5 x 5) / 4

= 25 / 4 = 6 1/4 = 6.25 kilometers

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Since lines a and b have the same slope, then: the lines are parallel.

The slope of a line is the rise/run or change in y / change in x. When two lines lie parallel to each other, they will have equal slope value.

On the other hand, when two lines lie perpendicularly to each other, their slopes will be negative reciprocal.

For example, if a line has a slope of 2/3, the slope of the line that is parallel to it will be 2/3 also, while the slope of the line that is perpendicular to it will be -3/2.

Thus:

The slope of line a = 2/3

The slope of line b = 2/3

Therefore, since lines a and b have the same slope, then: the lines are parallel.

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Answer: the lines are parallel.

The value of given expression for x=0 is 1, x=-2 is 0.44 and x=2 is 2.25.

Given the expression is (3/2)ˣ.

Firstly, we will simplify the given expression (3/2)ˣ for x=0.

Substitute the value x=0 in given expression, we get

(3/2)ˣ =(3/2)⁰

As we know that something raise to power zero is 1.

So, we get

(3/2)ˣ =1

Now, we will simplify the given expression (3/2)ˣ for x=-2.

Substitute the value x=2 in given expression, we get

(3/2)ˣ =(3/2)²

Now, we will square the expression to simplify it, we get

(3/2)ˣ =9/4

(3/2)ˣ =2.25

Furthermore, we will simplify the given expression for x=-2.

Substitute the value x=-2 in given expression, we get

(3/2)ˣ =(3/2)⁻²

Now, we will square the given expression, we get

(3/2)ˣ =(9/4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, w eget

(3/2)ˣ =1/(9/4)

(3/2)ˣ =4/9

(3/2)ˣ =0.44

Hence, the value of expression (3/2)ˣ  for x=0, 2 and -2 is 1, 2.25 and 0.44.

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-1 is the extraneous solution

To know the value of x first we need to remove the square root of the equation

[tex]\sqrt \sqrt{x +25}[/tex]  = [tex]\sqrt{x + 5}[/tex]

So to get the value we have to square both sides of the equation

[tex](\sqrt\sqrt{x +25})^{2}[/tex] = [tex](\sqrt{x + 5} )^{2}[/tex]

We get

[tex]\sqrt{x +25}[/tex]= x + 5

Now again we have to square both sides of the equation

x + 25 = [tex](x + 5)^{2}[/tex]

x + 25 =[tex]x^{2}[/tex] + 10x + 25( As we know [tex](a + b)^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] + 2ab )

[tex]x^{2}[/tex] + 9x = 0

x( x + 9) = 0

Therefore x = 0, -9

1 = [tex]\sqrt{-1}[/tex]

9 = [tex]\sqrt{81}[/tex]

The square root of 81 is 9 but the square root of -1 is an imaginary number

so the correct choice is " 9 is the solution of the equation " and -1 is the extraneous solution

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Answer:

6

Step-by-step explanation:

The correct option for showing the interval (-∞, -7) is Option C.

What is Interval?

An interval includes all the numbers that come between two particular numbers.

The given interval is (-∞, -7).

Now, On the number line (-∞, -7) is shown as;

The interval is open interval.

Hence, At point -7 the graph is in open circle.

And, The graph is going left side.

Hence, The correct option for showing the interval (-∞, -7) is Option C.

Which is shown in figure.

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Answer:

4x + 5y - 2

Step-by-step explanation:

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Answer:

Range = 77

Step-by-step explanation:

1. Reorder all the values in your data set from low to high.

13, 45, 46, 56, 66, 67, 89, 90

2. Subtract the lowest number from the highest number.

90 - 13 = 77

The quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

So, find the quotient of (x³+2 x²-x+6) / (x+3) using the Polynomial long division method:

Therefore, the quotient of (x³+2 x²-x+6) / (x+3) is (B) x²-x+2.

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The measure of angle ABD (m ∠ABD) is 44°

The measure of angle CBD (m ∠CBD) is 44°

The measure of angle ABC (m ∠ABC) is 88°

From the question, we are to calculate the measures of the given angles

From the given, information, we have that BD bisects ∠ABC

Thus,

m ∠ABD = m ∠CBD

From the given diagram,

m ∠ABD = (6x + 14)°

and

m ∠CBD = (3x + 29)°

Then,

(6x + 14)° = (3x + 29)°

Solve for x

(6x + 14)° = (3x + 29)°

6x + 14 = 3x + 29

Collect like terms

6x - 3x = 29 - 14

3x = 15

x = 15/3

x = 5

Put the value of x into the equations

m ∠ABD = (6(5) + 14)°

m ∠ABD = (30 + 14)°

m ∠ABD = 44°

Since

m ∠ABD = m ∠CBD

Then,

m ∠CBD = 44°

and

m ∠ABC = m ∠ABD + m ∠CBD

m ∠ABC = 44° + 44°

m ∠ABC = 88°

Hence, the m ∠ABD = 44°, m ∠CBD = 44°, and m ∠ABC = 88°

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