Isabel drove 335 miles in 5 hours.
At the same rate, how long would it take her to drive 536 miles?

======================================================

Explanation:

The general quadratic ax^2+bx+c = 0 has these properties

For more information, check out Vieta's formulas.

If we flip the bx term to -bx, thereby getting ax^2-bx+c = 0, then we have these properties

We're told the sum and product of the roots are the same

b/a = c/a

b = c

Example:

The equation x^2-10x+10=0 has the sum of the roots equal to 10, and the product of the roots is also 10. You can use the quadratic formula to confirm this.

Answer:

12

Step-by-step explanation:

good right? if not then your question was wrong

Hey there!

9 - 3x + x - 15

= 9 - 3x + 1x - 15

COMBINE the LIKE TERMS

= (9 - 15) + (-3x + 1x)

= (-3x + 1x) + (9 - 15)

= (-3x + x) + (9 - 15)

= -3x - x + 9 - 15

= -2x - 6

Therefore, your answer should be:

-2x - 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

An asymptote of the tangent occurs at θ=π/2 , and repeats every π units.

Asymptote of the tangent

Due to the fact that tan(x)=sin(x)cos(x), the tangent function is undefined for cos(x)=0. In light of this, whenever cos(x)=0 the tangent function exhibits a vertical asymptote. Similar to the sine function, the tangent function has zeros for integer multiples of because tan(x)=0 when sin(x)=0.

Typically, dashed lines are used to separate asymptotes from the function itself. The vertical lines that frequently appear on the tangent function's graph are spaced 180 degrees apart from one another.

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The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression y = 2x⁺⁴

Applying log on both sides, we get,

log y = log (2x⁺⁴)

log y = log 2 + log x⁺⁴

log y = log 2 + 4 log x

To Check Results,

Taking exponential,

y = e^[log 2 + 4 log x]

y = e^(log 2) × e^[4 log (x)]

y = 2 × e^(log x⁴)

y = 2x⁴

Thus, the answer is verified.

Take expression y - 4x⁻¹ = 0

Applying log on both sides, we get,

log y = log (4x⁻¹)

log y = log 4 + log x⁻¹

log y = 2 log 2 - log x

To Check Results,

Taking exponential,

y = e^[2 log 2 - log x]

y = e^(2 log 2) × e^[-log (x)]

y = e^(log 4) × e^(log x⁻¹)

y = 4x⁻¹

y - 4 x⁻¹ = 0

Thus, the answer is verified.

Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

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Step-by-step explanation:

Answer:

(3x + 2y) (2x - 3y)

Step-by-step explanation:

Check it using the FOIL method - first times first, outer times outer, inner times inner, last times last

The simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .

The given expression is,

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶                                          equation 1

Name the given expression as equation 1.

To simplify the given expression first we need to solve step wise,

[tex]\sqrt[3]{125}[/tex] = [tex]\sqrt[3]{25.25.25}[/tex] = 5

[tex]\sqrt[3]{27}[/tex] = [tex]\sqrt[3]{3.3.3}[/tex] = 3

Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶  = 5[tex]x^{6}[/tex] - 3[tex]x^{6}[/tex]

On further simplifying, we will get

[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 2[tex]x^{6}[/tex]

Thus we can write that the simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .

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The estimate of the quotient 1624 divided by 23 using compatible numbers is 81

The quotient of numbers is the result of dividing the numbers

The statement is given as

1624 divided by 23 using compatible numbers

The expression can be represented as:

1624 ÷ 23

Using compatible numbers, 1624 can be estimated as 1620, while 23 can be estimated as 200:

So, the expression becomes

1624 ÷ 23 = 1620 ÷ 20

Next, we divide the estimated numbers

So, we have

1624 ÷ 23 = 81

Hence, the estimate of the quotient 1624 divided by 23 using compatible numbers is 81

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Answer:  55 degrees

Step-by-step explanation: If the Whole is 180 and you subtract 125 degrees you are left with 55.

The graph given below y = -x + 2 have a negative slope and a positive y intercept. The point (2, 1) lies on the line 3y = 2x - 1

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The graph given below have a negative slope and a positive y intercept. The graph is given by y = -x + 2

Given the equation

3y = 2x - 1

When x = 2:

3y = 2(2) - 1

y = 1

Therefore, The point (2, 1) lies on the given line 3y = 2x - 1

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For the given points, As the distance of AB and CD is same, So AB and CD are congruent.

If and only if their lengths are identical, any two line segments are congruent. The length of the line segment AB is identical to the length of the line segment CD in the aforementioned representations. Consequently, the two line segments AB and CD are similar.

length of AB = √(2+2)² + (1-1)²  =  2

length of CD = √(3-3)² + (2+2)² = 2

As the value of AB = CD So, we can say that AB and CD are congruent.

Graph is attached at the end.

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[tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.

Given: [tex]5^{2x}[/tex] = 56

Taking logarithm on both sides:

=>log([tex]5^{2x}[/tex])  = log (56)

As [tex]log_b(a)^m = m (log_b(a))[/tex],

=> 2x ( log 5) = log (56)

=> 2x = [tex]\frac{log56}{log5}[/tex]

=> 2x = [tex]\frac{1.748}{0.698}[/tex]

=> 2x = 2.504

=> x= 1.252

Hence, [tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.

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It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected

Let the number of fish collected in sample be represented as N.

Let the number of fish affected in it be represented by X.

Therefore, the proportion will be;

= X/N

Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.

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Answer: I can't see the answer choices but 98,673 divided by 222 is 444.5

hope this helps :)

Answer:

29

Step-by-step explanation:

to get from -16 to -7 you have to add 9

to get from -7 to 2 you have to add 9

to get from 2 to 11 you have to add 9

and the same thing for 11 to 20

Answer: The answer

is  29 because the pattern of the number is 999999

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.

Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)

The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.

It should be noted that converting 11/20 to a decimal through division will gives 0.55.

This can be illustrated as follows. It should be noted that the quotient is the value obtained by dividing one value by another. The quotient is 11.

The divisor is the value that divides. It should be noted that in this case, this is illustrated as 20.

It should be noted that 11 is the numerator and 20 is the denominator.

Therefore, it should be noted that converting 11/20 to a decimal through division will gives 0.55.

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after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.

We are given a point:

( 9 , 9 )

We have the scale factor as:

1 / 3

We need to dilate the point using the scale factor.

So, we get that:

( 9 × 1 / 3 , 9 × 1 / 3 )

= ( 3 , 3 )

Therefore, after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.

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Answer:

39.13%

Step-by-step explanation:

14/23=60.87%

Since the question asks how much has miss Taylor cohort fallen by we do this:

100%-60.87%=39.13%

Answer = 39.13%

Hope this helps :)

The domain and range will be a set of all real numbers for all the odd positive integers.

We can write given equation as y² =n²x

if we Put even value of n then we get function similar to y²=x which does not match with the given question

If we put the odd value of n then we get function similar to y³ = x which match with the given question.

Hence the domain and range will be a set of all real numbers for all the odd positive integers.

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Answer:

B. f - g = 17

Answer:

You can use the definition of perfect square trinomials to find which of the given trinomials are perfect squares.

The trinomials which are perfect squares are:

Option B:

Option D:

What are perfect squares trinomials?

They are those expressions which are found by squaring binomial expressions.

How to find which of the given trinomials are perfect square trinomials?

Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.

Let the binomial term was am + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:

Checking all options:

Option A:

Comparing it with the standard form we obtained, we have:

Option B:

Comparing it with the standard form we obtained, we have:

Thus, this trinomial is perfect squares trinomial.

Option C:

Comparing it with the standard form we obtained, we have:

Option D:

Comparing it with the standard form we obtained, we have:

Thus,   this trinomial is perfect squares trinomial.

Thus,

The trinomials which are perfect squares are:

Option B:

Option D:

Step-by-step explanation:

If x=4, then substitute x for 4, multiply by 3 since 3 was being multiplied by x, then subtract 2, which gets you 10

Answer:

neither ordered pair is a solution

Step-by-step explanation:

to determine if the pairs are a solution, substitute the x- coordinate into the left side of the equation and if equal to the right side then they are a solution.

(- 9, 3 ) with x = - 9

6(- 9) = - 54 ≠ 14 ← not a solution

(2, - 4 ) with x = 2

6(2) = 12 ≠ 14 ← not a solution

The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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Answer:

Step-by-step explanation:

33

The difference in price between the two brands when buying 800 g of hot chocolate is 0.

What is arithmetic operation?

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

For brand A

For 160g of hot chocolate is $2.85

For 1g of hot chocolate is 2.85/160

For 800g of hot chocolate is [tex]\frac{2.85}{160} \times 800[/tex]

                                             = 2.85 [tex]\times[/tex] 5

                                             = $14

For brand B

For 200g of hot chocolate is $3.40

For 1g of hot chocolate is 3.40/200

For 800g of hot chocolate is [tex]\frac{3.40}{200} \times 800[/tex]

                                             = 3.40 [tex]\times[/tex] 4

                                             = $14

Difference of brand A and brand B of hot chocolate of 800g is $14 - $14 = 0.

Therefore, the difference in price between the two brands when buying 800 g of hot chocolate is 0.

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The measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

What is an angle bisector ?

The angle bisector is the line or line segment that divides the angle into two identical portions.

Given that line, QS is bisecting the angle PQR into two angles RQS and PQS.

We know that the angle bisector bisects the two angles into two equal halves , i.e.,

∠ PQS = ∠ RQS

So ; the measure of ∠ PQS will be :

∠ PQS = 71°

So , if we want to calculate the measure of ∠PQR then it can be represented as the sum of two angles.

∠ PQR = ∠PQS + ∠RQS

or

∠PQR = 71° + 71°

or

PQR = 142°

Therefore, the measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

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The 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.

We are given that:

Area of a square garden = 75 feet²

Let the side of the square garden be x

x² = 75

x = √ 75

x = 5 √3 feet

Perimeter of the square garden = 4 × x feet

Perimeter = 4 × 5 √ 3 feet

Perimeter = 20 √ 3 feet

P = 34.64 feet.

Now, Tristan only has 32 feet of material.

So, the material is not enough.

Therefore, we get that, the 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.

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Answer:

3+(4x)

Step-by-step explanation:

The algebraic expression will be written as:

x=jelly tots

The number of chocolates=3+(4×x)

=3+(4x)

The algebraic expression for the number of chocolates is 4n + 3 where n is number of packets of Jelly Tots.

Let's use variables to represent the number of Jelly Tots and chocolates:

Let "n" be the number of packets of Jelly Tots.

Now, the number of chocolates is three more than 4 times the number of Jelly Tots.

So, represent the number of chocolates as:

Number of chocolates = 4 * n + 3

4 * n represents 4 times the number of Jelly Tots.

Multiplying the number of Jelly Tots by 4 gives us the chocolates without the additional 3.

- +3 represents the additional chocolates.

Thus, the algebraic expression is 4n + 3.

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