Is (1, -1) a solution to this system of equations?
y= –6x + 5
y= x – 2

Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

10² × [tex]10^{5}[/tex] = [tex]10^{(2+5)}[/tex] = [tex]10^{7}[/tex]

Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

[tex]10^{2}*10^{5}=10^{2+5}=10^{7}[/tex]

It took Bailey 45 days to paint the house and Andrew 11.25 days to paint the house.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Andrew can paint the neighbor's house 4 times as fast as Bailey. Andrew and Bailey worked together, it took them 5 days.

Let the time it took Bailey to paint the house be x days, and the time it took Andrew to paint the same house be y. Then,

Establishing the system of equation,

1/x + 1/y = 1/9. . . (1)

x = 4y. . . (2)

Putting (2) into (1) gives,

1/4y + 1/y = 1/9

5/4y = 1/9

4y = 5 x 9 = 45

y = 11.25

x = 4(11.25) = 45

Hence, it took Bailey 45 days to paint the house and Andrew 11.25 days to paint the house.

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Step-by-step explanation:

If you write down the amount of time Bryant spends sleeping every night, you will see a sequence of numbers between 6 and 9 hours inclusive.

Answer:

Option B

Step-by-step explanation:

The equation of the horizontal asymptote of f(x) is given as follows:

x = 5/4.

The rational function f(x) in the context of this problem is defined as follows:

f(x) = (-4x² + 54x - 47)/(4x - 5).

The horizontal asymptote of a function happens at a value of x which is outside the function's domain.

For a rational function, the denominator cannot be zero, hence the value of x that represents the horizontal asymptote of f(x) is obtained as follows:

4x - 5 = 0

4x = 5

x = 5/4.

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The required solution of the given system of equations is x = 5 and y = -1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x+4y=8 - - - - - (1)

x-4y=4 - - - - (2)

Put x from equation 2 to equation 1
12y + 12 + 4y = 8
16y = -4
y = -1/4

Now,
Put y in equation 2
x - 4 {1/4} = 4

x = 5

Thus, the required solution of the given system of equations is x = 5 and y = -1/4.

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the equation of the tangent line to the curve y = 2 sin x at the point (π/6, 1) will be y = √3 x + 0.093.

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.

y = mx + b

1) m = slope of the tangent line = derivative at the point (pi/6, 1)

Function: y = 2sinx

Derivative: y ' = 2cosx

evaluate at x = pi/6=> y ' = 2cos(pi/6) = √3

2) equation using the slope and the point (pi/6, 1)

y - 1 = √3 ( x - pi/6 )

y = √3 x - √3(pi/6) +1 =√3 x + 0.093

y = √3 x + 0.093

m = √3, b = 0.093

Therefore, y = √3 x + 0.093 will be the equation of the tangent line to the curve y = 2sin x at point (π/6, 1).

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If Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. her boat speed in still water is;3 km/h.

Let's x represent the  Jane's boat speed in still water

Upstream, her speed was x - 2 km/h.

Downstream, her speed was x + 2 km/h.

Let's d represent the distance between the start and end point

Let the  time it takes to cover d at a speed of x - 2 km/h=  30 min.

Let the  time it takes to cover d at a speed of x + 2 km/h=  10 min.

So we have:

d / (x - 2) = 30 min and

d / (x + 2) = 10 min.

Multiplying both sides of each equation

d * x - 2d = 30 * (x - 2)

d * x + 2d = 10 * (x + 2).

Adding the two equations and solve for x

2d * x = 40 * x + 20

20 * x = 40 * x + 20

20 * x = 60 * x

x= 3 km/h

Therefore Jane's boat speed in still water is 3 km/h.

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If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

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Answer:

C

Step-by-step explanation:

Converting 40% into a decimal would be .40

Since you want to find 40% of 35, we would multiply

(35)(.40) = 14

Answer: x=3

Step-by-step explanation:

3(x+6)-10=17

3x+18-10=17

3x+8=17

3x=17-8

3x=9

x=3

The body mass index of the patient who weighs 68kg and is 60 inch tall is 29.3 kg/m².

This question is incomplete, the complete question is;

What is the body mass index IBM of a patient who weighs 68kg and is 60 inch tall?

Body mass index IBM is simply a measure of body fat of a person.

Its is calculated using the mass and height of a person.

It can be calculated using the formula;

BMI = Mass (kg) / Height² (m)

Given the data in the question;

Plug the given values into the above formula and simplify.

BMI = Mass (kg) / Height² (m)

BMI = 68kg / ( 1.524m )²

BMI = 68kg / 2.322576 m²

BMI = 29.3 kg/m²

Therefore, the BMI of the patient is 29.3 kg/m².

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According to the information in the table, the correct options are: The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A. (option B).

To identify the correct option that matches the information in the survey table, we must read each of the options and compare it with the information in the table to establish one as true.

Based on the above, we can infer that the correct option is option B because the number of employees who voted for coffee in group B is greater than the number of employees who voted for coffee in group A.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Options:

A. The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.

B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.

C. The estimates for both groups show an equal number of employees would have voted for coffee.

D. The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.

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The rate of increase is 150%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Desk were on sale for $200 the sale is over,

and they have gone back up to the full price of $300.

The rate of increase,

= 300 x 100 / 200

= 150%

Therefore, the rate is 150%.

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Answer:

70 * 12 = 840

1400 + 840 = 2240

$2,240 monthly

Step-by-step explanation:

Hope it helps! =D

Answer:

2170

Step-by-step explanation:

Write out the first 3 terms:

a 1 = 1400 ← rent in 1st year

a 2 = 1470 ← rent in 2nd year

a 3 = 1540 ← rent in 3rd year

Arithmetic Sequence: d=70

Explicit Formula:

an = a 1+(n−1)d

a 12 = 1400+(12−1)(70)

a 12 = 2170

Answer:

12x-5.5 all you have to do is simplify

Answer:Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Step-by-step explanation:

Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Answer:

Median

Step-by-step explanation:

The best measure of center in this case would be the median, as the presence of a few outliers (first-graders who were behind in language acquisition) would greatly affect the mean, while the median would provide a better representation of the typical vocabulary knowledge of first-graders in the group.

Proportionately, if Hayden uses 4 cups of flour and 5 cups of sugar to make cupcakes, he will eat 20 cupcakes.

Proportion refers to the relative size or ratio of one value compared to another quantity.

Proportions are represented as fractional values with decimals, percentages, or fractions.

The quantity of flour for 1 cupcake = 1/5 cups

The quantity of sugar for 1 cupcake = 1/4 cups

The quantity of flour Hayden uses = 4 cups

The number of cupcakes from 4 cups = 20 (4 ÷ 1/5)

The quantity of sugar Hayden uses = 5 cups

The number of cupcakes from 5 cups of sugar = 20 (5 ÷ 1/4)

Thus, according to the proportion of cupcake ingredients to the available quantities of ingredients, Hayden will make and eat 20 cupcakes.

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A cupcake requires 1/5 cup of flour and 1/4 cup of sugar to make.

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

The length of time it will take Rachel to pay off her credit card balance can be calculated by dividing the outstanding balance by the monthly payment amount and then adding the number of months needed to pay off the balance.

Balance = $8,281

Monthly payment = $250

Annual interest rate = 16%

To calculate the length of time it will take to pay off the balance, we would first need to calculate the monthly interest rate, which can be done by dividing the annual interest rate by 12:

Monthly interest rate = 16% / 12 = 1.33%

Next, we can calculate the monthly payment amount, including the interest:

Monthly payment amount = $250 + ($8,281 * 1.33%)

By continually subtracting the monthly payment amount from the balance and adding the monthly interest, we can determine the length of time it will take to pay off the balance.

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

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The event with a sample space of S = {A, B} is (d) choosing a tile from a pair of tiles, one with the letter A and one with the letter B.

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

Sample space of S = {A, B}

In probability, the sample space is the set of all possible outcomes of a random event.

In the case of choosing a tile from a pair of tiles, one with the letter A and one with the letter B, there are only two possible outcomes: A or B.

Therefore, the sample space S is {A, B}.

In contrast, for the other events listed:

In each of these events, there are more than two possible outcomes, so the sample space is a set with more than two elements.

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The equation of the line that runs through the point (0,-1) and (1,2) in slope-intercept form is y = 3x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the diagram, the line runs through the point (0,-1) and (1,2).

First, we determine the slope of the line

Slope m = change in y / change in x

Slope m = (2 - (-1)) / (1 - 0)

Slope m = (2 + 1) / (1 - 0)

Slope m = 3/1

Slope m = 3

Next, plug the slope m = 3 and point (0,-1) into the point slope formula.

y - y₁ = m( x - x₁ )

y - (-1) = 3( x - 0 )

y + 1 = 3x - 0

y + 1 = 3x

Subtract 1 from both sides

y + 1 - 1 = 3x -1

y = 3x - 1

Therefore, the equation of the line is y = 3x - 1.

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Answer: 3 , 4 and 5 are correct options

Step-by-step explanation:

The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

First, we have to determine the two lines.

Line₁.

(0, 2) and (1, - 1).

m = (- 1 - 2)/(1 - 0).

m = - 3.

- 1 = - 3(1) + b.

b = 2.

y = - 3x + 2.

Line₂.

(0, - 2) and (3, 0).

m = (0 + 2)/(3 - 0).

m = 2/3.

0 = (2/3)(3) + b.

b = - 1.

y = (2/3)x - 1.

So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

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Answer:

The annual interest you would earn on each bond depends on the bond's coupon rate, which can be calculated by dividing the bond's current yield (Column 2) by 100. For Bond A and C, the coupon rate would be 7.5%, and for Bond X and Y, it would be 8.4%. The annual interest you would earn on each bond would be the coupon rate multiplied by the bond's face value (Column 1). For Bond A and C, the annual interest would be 7.5% * $15 = $1.125, and for Bond X and Y, it would be 8.4% * $15 = $1.26.

The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the cost of each cappuccino and y represent the cost of each house lattes.

Two cappuccinos and three house lattes was $14.55, hence:

2x + 3y = 14.55   (1)

Also:

One cappuccino and two house lattes was $8.77, hence:

x + 2y = 8.77    (2)

From both equations:

x = 2.79, y = 2.99

The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

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From the properties of similarity, the value of x is 24.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

By comparing corresponding sides of the shapes, we get that

6/9 = 14/21 = 2/3

So that,

16/x =2/3

multiply both sides by 3/2 we get,

(16/x)*(3/2) = 1

multiply both sides by x we get,

16*3/2 = x

⇒ x = 48/2

⇒ x = 24

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The rate of change of the height is approximately -1.67 meters per minute.

The volume of a cone can be written as V = (1/3)πr²h.

Differentiating with respect to time t, we get

dV/dt = (1/3)π (2rh dr/dt + r² dh/dt)

Given that the radius is decreasing at a constant rate of 1 meter per minute and the volume is decreasing at a rate of 61 cubic meters per minute, we can substitute these values into the equation to find dh/dt:

61 = (1/3)π (2rh + r² dh/dt)

dh/dt = (61 - (2rh)) / (r² * (1/3)π)

Substituting in the given values of r = 2 meters and h = 41 cubic meters, we get:

dh/dt = (61 - (2 * 2 * 41)) / (2² * (1/3)π)

dh/dt = (61 - 164) / (4 * (1/3)π)

dh/dt = -103 / (4 * (1/3)π)

Approximating π to 3.14, we get

dh/dt = -103 / (4 * (1/3) * 3.14)

dh/dt ≈ -1.67

So the rate of change of the height is approximately -1.67 meters per minute.

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Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

Answer: 3

Step-by-step explanation:

Answer:

The answer to the expression is -5 + 10 - 8 = -3.

Step-by-step explanation: