Dan earns £8.80 per hour. How much will he earn for 6 hours work?

In general, linear equations have one solution. However, they can have infinitely many solutions in some cases.

A linear equation in mathematics is an equation that can be written in the form

ax + b = 0

The values of x that make this equation true are the solutions to the equation. Generally speaking, linear equations have one solution, which means that there is only one value of x that will make the equation true. However, in some cases, linear equations can have infinitely many solutions. For example, if a = 0 and b = 0, then any value of x will make the equation true.

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The required equation of the line in the slope-intercept form is given as x = -3.

Given that,
to determine the equation of the line passing through (-3,2 and perpendicular to the line y = -4,

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the given line y = -4 is,
m = 0
Slope of the required line = -1/ 0
Now,
Slope intercept form of the equation,
y - y₁ = m (x - x₁)
y - 2 = -1/0{x + 3}
x = -3

Thus, the required equation of the line in the slope-intercept form is given as x = -3.

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Answer:

w=10/9

Step-by-step explanation:

Answer:

A linear function can be represented by a graph that is a straight line. The equation for a linear function is of the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The slope of the line tells us how steep the line is, and whether it has a positive or negative slope. A positive slope means that the line is sloping upwards from left to right, while a negative slope means that the line is sloping downwards from left to right.

Answer:

18b-45

Step-by-step explanation:

9(2b-5)

9*2b-9*5

18b-9*5

18b-45

Answer:

9(2b - 5)

Distribute

9(2b - 5)

18b - 45

Solution

18b - 45

When we dilate the area , it is multiplied by the square of dilation factor .

In the question ,

it is given that ,

the area of the figure ,

we have to explain what will happen to the area when we dilate the figure .

let the figure be a square ;

let the unit square's length be x ,

and let the dilation factor be "k" ;and

So ,the comparison square's length be kx .

the area of the original square is = x² and

the area of the new square is = (kx)²

So , the ratio of the areas will be = (kx)²/x²

simplifying further ,

we get ,

= k² .

Therefore , the area gets multiplied by k² .

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Answer: no

Step-by-step explanation: the slope stays the same because the image and pre- image are parallel which means their slope is equal

The quotient of given polynomials division is x+2. So, the correct answer is option A.

A quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Given that, (x²+3x+2)÷(x+ 1)

x²+3x+2 can be written as

x²+1x+2x+2 (Splitting of middle term)

= x(x+1)+2(x+1)

= (x+1)(x+2)

Now, (x+1)(x+2)÷(x+1)

= [(x+1)(x+2)]/(x+1)

= (x+2)

Therefore, option A is the correct answer.

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What is the quotient of the following division problem (x²+3x+2)÷(x+ 1).

a. x+ 2

b. x +1

c. x²+3x +2

d. 0

The balance of Marissa’s retirement account after 15 years if She makes an initial deposit of $1,000. Her contributions are $500 a month for the next 15 years is $8500.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given data:

Initial deposit = $1000

Her contributions are $500 a month for the next 15 years

Amount after 15 years = Initial deposit  + 15 × 500

Amount after 15 years = $1000 + 7500

Amount after 15 years = $8500

Therefore, the balance of Marissa’s retirement account after 15 years if She makes an initial deposit of $1,000. Her contributions are $500 a month for the next 15 years is $8500.

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The polynomial function is P(x) = x⁴ - 14x³ + 59x² - 50x - 74

A polynomial is a function in which the least power of the unknown is 2.

The root of a polynomial is the value of the unknown which makes the polynomial equal zero.

Since we have that the given polynomial has roots 1 - √3 and 6 - i.

We also know that their conjugates 1 + √3 and 6 + i are also roots of the polynomial.

So, the factors of the polynomial are

So, the required polynomial is P(x) = [(x - 1) + √3][(x - 1) - √3][(x - 6) + i][(x - 6) - i]

= [(x - 1)² - (√3)²][(x - 6)² - i²]    (Since a² - b² = (a - b)(a + b))

= [(x - 1)² - 3][(x - 6)² - (- 1)]

= [(x - 1)² - 3][(x - 6)² + 1]

Expanding the brackets, we have

= [x² - 2x + 1 - 3][(x² - 12x + 36 + 1]

= [x² - 2x - 2][(x² - 12x + 37]

= x⁴ - 12x³ + 37x² - 2x³ + 24x² - 74x - 2x² + 24x - 74

Collecting like terms, we have

= x⁴ - 14x³ + 59x² - 50x - 74

So, the polynomial is P(x) = x⁴ - 14x³ + 59x² - 50x - 74

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Answer:

A and B

Step-by-step explanation:

The triangle is labeled that all three sides are equal and all three angles are equal; thus, it is an equilateral triangle and “B” is correct.

Acute triangles have all acute angles. Understanding that the triangle is equilateral, equilateral triangles have all equal angles, and the total of all three angles in a triangle is 180, we can determine that all three angles are acute and the triangle is acute, so “A” is right. (one angle = x; three angles are equal and add up to 180 —> 3x = 180; x = 60; all angles are acute).

The cost of each apple is equal to $0.23.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=8x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=8 and b=3.

The question gives:

You should convert the data into an equation:

15A+2.75=6.20

15A=6.20-2.75

15A=3.45

A=3.45/15

A=0.23

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Multiplying 3/8 by the whole part and the fractional part is 21/32.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the whole and fractional part can be 1 3/4.

Therefore, the multiplication by 3/8 will be:

= 3/8 × 1 3/4.

= 3/8 × 7/4

= 21 / 32.

The fraction is 21/32.

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Complete question

Multiply 3/8 by 1 3/4 which depicts the whole part and the fractional part.

The area of the triangle will increase at a rate of 3.81 m² per second

Given,

The length of the sides of the triangle are base, 12 m and hypotenuse 15 m

Area of the triangle = 1/2 bh

We have to find h;

That is,

Sin ∅ = opposite side /hypotenuse = h/15

h = 15Sin ∅

d∅/dt = 0.06rad/s

Now,

A = bh/2 = 12 × 15sin∅/2

A = 90sin∅,

By differentiating this equation with respect to A, we have

d(A)/dt = 90cos∅d∅/dt

d(A)/dt = 90cos∅(0.06)

∅ = π/4, cosπ/4 = 0.7071

90×0.7071×0.06

= 3.81m²/s

That is,

The area of the triangle will increase at a rate of 3.81 m² per second

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By using the concept of depreciation, it can be concluded that-

The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.

What is growth?

Growth is the exponential increase in the value of an asset or article or population at a certain rate over a certain period of time

EPA calculated that the air pollution should decrease by approximately 8% each year

The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.

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Complete Question

One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8% each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?

The coordinates of the point dividing the join of given points will be equal to (1, 3).

If we need to find the coordinates of a point P(x, y) dividing the join of points (x₁, y₁) and (x₂, y₂) in the ratio m:n then the formula is expressed as

P(x, y) = [(mx₂ + nx₁/m + n), (my₂ + ny₁/m + n)]

We have the values as m:n = 2:3 and

(x₁, y₁) = (-1, 7) and (x₂, y₂) = (4, -3)

On using the above formula we get

P(x, y) = [2(4) + 3(-1)/2 + 3, 2(-3) + 3(7)/2 + 3]

P(x, y) = [(8 - 3)/5, (-6 + 21)/5]

P(x, y) = (1, 3) which is the required coordinate.

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Complete Question:

Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3.

The marked price is $1518 and the rate of the discount is 8.9%.

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price. Typically, MP is used to indicate it.

This was the initial selling price, but $194 was deducted, making the final price $1394.

Use the following formula to determine percent markdown:

(Markdown amount/Selling price)×100 is the percent markdown.

To locate Markdown

Original Selling Price – Markdown Price

Connect what you have now.

Markdown=$1518-$1394

M=124

The Markdown, as we already know, is 124.

At this point, Percent Markdown equals (124/1394)×100 PM=0.088952654×100

PM=8.9 (rounded)

As a result, the growth rate is 8.9%.

And $1394+$124=$1518.

Hence, The marked price is $1518 and the rate of the discount is 8.9%.

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1. The fraction of full-time employees who work in the bank is 16/31.

2. The fraction of pieces that David need to fix to complete the puzzle is 9/27

3. The fraction of girls that wore red outfits is 1/2.

4. The fraction of books on the shelf that are in Spanish is 2/7.

1. Alocal community bank has 31 employees on it’s rolls. 15 employees work part-time at the bank. The fraction of full-time employees will be:

= (31 - 15) / 31

= 16/31

2. David was gifted a 28 piece puzzle by his aunt. He has fixed 19 pieces of the puzzle. The fraction of pieces that David need to fix will be:

= (28 - 19)/28

= 9/28

3. 20 girls were dressed in green outfits and 10 girls donned red outfits at a dance recital. The fraction of girls that wore red outfits will be:

= 10/20

= 1/2

4. A section of Tina’s bookshelf has 15 French books and 6 Spanish books. The fraction of books on the shelf that are in Spanish will be:

= Spanish books / Total books

= 6 / (15 + 6)

= 6/21

= 2/7

The above illustrate the fraction.

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Answer:

The answer to the problem is:

(i) The speed of the car at B is -4 ms$^{-1}$.

(ii) The distance AB is 32 meters.

(iii) The time taken for the car to travel from B to C is 10 seconds.

Step-by-step explanation:

To find the speed of the car at B, we can use the formula $v = v_0 + at$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:

$v = 20 + (-6)(4) = 20 - 24 = -4$ ms$^{-1}$

Thus, the speed of the car at B is -4 ms$^{-1}$.

To find the distance AB, we can use the formula $d = v_0t + \frac{1}{2}at^2$, where $d$ is the distance, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:

$d = (20)(4) + \frac{1}{2}(-6)(4^2) = 80 - 48 = 32$ meters

Thus, the distance AB is 32 meters.

To find the time taken for the car to travel from B to C, we can use the formula $v^2 = v_0^2 + 2ad$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $d$ is the distance. In this case, $v_0 = -4$ ms$^{-1}$, $v = 20$ ms$^{-1}$, $a = 2$ ms$^{-2}$, and $d$ is the distance from B to C. We can find this distance by using the formula for distance and setting $t = 0$, since we're looking for the time it takes the car to travel from B to C, not from A to B:

$d = (20)(0) + \frac{1}{2}(-6)(0^2) = 0 - 0 = 0$ meters

Thus, the distance from B to C is 0 meters. Plugging these values into the formula gives us:

$20^2 = (-4)^2 + 2(2)(0) = 16 + 0 = 16$

We can solve this equation for $t$ to find the time it takes the car to travel from B to C:

$t = \sqrt{\frac{v^2 - v_0^2}{2a}} = \sqrt{\frac{20^2 - (-4)^2}{2(2)}} = \sqrt{\frac{400}{4}} = \sqrt{100} = 10$ seconds

Thus, the time taken for the car to travel from B to C is 10 seconds.

The velocity-time graph for the journey from A to C would have a positive slope from A to B, a negative slope from B to C, and a positive slope from C to the end of the journey.

It will take 27 minutes 30 seconds to complete eleven questions.

When two values are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is that the number of questions [y] completed and time [x] it takes to complete them are proportional to each other.

The number of questions [y] completed is proportional to the time [x] it takes to complete them.

That means,

y ∝ x

y = kx, where k is constant.

k = y/x

So, we can write;

y₁/x₁ = y₂/x₂

According to the question:

Let  y₁= 6, x₁= 15, y₂= 11.

Substituting the values,

6/15 = 11/x₂

x₂ = 11 x 15 / 6

x₂ = 11 x 5 / 2

x₂ = 55 /2

x₂ = 27. 5

x₂ = 27 minute and 30 seconds.

Therefore, it will take 27 minutes 30 seconds to complete 11 questions.

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The pole and the birdhouse both stand 18.75 feet tall.

Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?

To answer a word issue with algebra:

Establish a variable.

Utilizing the variable, write an equation.

Make the equation work.

Use the variable to determine the answer if it is not the word problem's solution.

A person standing close by casts a shadow that is five feet long. The individual is 4 feet tall..

Assume that for the birdhouse and the pole are (x) ft tall.

The shadow is now 5 feet long for a person that is 4 feet tall.

Then, for one feet long person, the shadow would be (5/4) feet long.

Then, for 15 feet long -

[tex]\frac{x}{15}[/tex] = [tex]\frac{5}{4}[/tex]

x = (15 x 5)/4

x = 75/4

x = 18.75 feet tall

As a result, both the pole and the birdhouse are 18.75 feet tall.

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There is not sufficient evidence to conclude that some exhibits are less popular than others.

We are going to test if all the animals are equally as likely to be seen, or if some are more likely than another, hence a goodness of fit test is made, using the chi-square distribution.

The test statistic for the chi-square distribution is given as follows:

Chi-squared = sum ((O - E)²/E)

In which:

The total number of measures in this problem is given as follows:

133 + 172 + 163 + 165 + 134 + 155 + 148 = 1070.

There are seven types of animals, hence the expected value is obtained as follows:

E = 1070/7 = 152.86.

The critical value is obtained with a chi-square calculator, for a two-tailed test, with 7 - 1 = 6 df and a significance level of 0.1, hence it is of:

Chi squared = 10.64.

Hence the conclusion will be reached as follows:

The test statistic is calculated as follows:

Chi-squared = 1/152.86 x [(133 - 152.86)² + (172 - 152.86)² + (163 - 152.86)² + (165 - 152.86)² + (134 - 152.86)² + (155 - 152.86)² + (148 - 152.86)²]

Chi-squared = 9.13.

Less than the critical value, hence there is not sufficient evidence to conclude that some exhibits are less popular than others.

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The class mean and standard deviation of the distribution used should be of most concern.

What is mean and standard deviation?

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6 feet is the greatest distance apart by using the greatest common factor that Al can place the fence post.

The greatest common factor (GCF) of a set of numbers is the largest factor that all of the numbers share.

Given:

The length of the garden is 18 feet.

The width of the garden is 30 feet.

We need to find the greatest common factor between 18 and 30. These numbers can be expressed as follows (using multiplication of prime numbers).

18 = 2*3*3

30 = 2*3*5

2*3 = 6 appears in both cases and is the greatest common factor.

Therefore, 6 feet is the greatest distance apart that Al can place the fence post

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The required measurement of each interior angle of the animal pen

An  interior angle is a point inside a shape. The polygons are the shut shape that has sides and vertices. A standard polygon has generally its interior angle equivalent to one another. For instance, a square has generally its  interior angle equivalent to the right point or 90 degrees.

The question expects us to track down the inside point of a customary heptagon.

To do this initially compute the outside angle of that polygon.

The amount of outside angle is 360°. A heptagon has 7 sides.

Along these lines, one exterior angle = 360°/7 = 51.4°

inside angle+exterior angle=180°

Interior angle = 180-51.4 = 128.6°

Thus, required interior angle is 128.6°.

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Answer: 282

Step-by-step explanation:

Answer:

[tex]x^{1}[/tex]=[tex]\frac{-3-\sqrt{7} }{2}[/tex] [tex]x^{2}[/tex]=[tex]\frac{-3+\sqrt{7} }{2}[/tex]

Step-by-step explanation:

1) collect like terms and move everything to the left

2[tex]x^{2}[/tex]2+3x-3+3x+4=0

2[tex]x^{2}[/tex]2 +6x-3+4=0

2) find the coefficients so you can plug them into the quadratic formula

a=2, b=6, c=1

3) plug these into the quadratic formula

4) use a calculator to solve both the positive and negative equations

Answer:

= 5√7 - 3√77: 63 or 5√7 - 3√77/63

The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

Equations:

y + 2x = -1

y = x + 4

y - x = 4

Using elimination method,

y + 2x = -1

y - x = 4

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

x = 3

The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

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