The prime factor trees for 14 and 15 are
shown.
a) Write down the lowest common
multiple (LCM) of 14 and 15 as the
product of its prime factors.
b) Hence, work out the lowest common
multiple (LCM) of 14 and 15.
2
14
7
3
15
5

The population of the city till next year will be 101,808.

Given, a population of a city increases by 0.8% per year.

Presently the population of the city is = 101,000

Next year's population will be = ?

population increases by 0.8% per year = 1+0.8%

Hence the expression can be written as:

present population of city × population increases by 0.8% per year

= 101,000 × (1+0.8%)

= 101,000 × (1+0.008)

= 101,000 × (1.008)

multiply the terms.

=101808

Hence when the population of the city increases by 0.8% per year, then next year's population will be 101,808.

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Answer:

Since Lines t and l are straight lines and are intersecting, Angle 1 and 4 are vertically opposite angles.

Angle 1 = Angle 4 (vertically opposite angles)

Angle 1 = 62 degrees

Therefore Angle 4 = 62 degrees

Step-by-step explanation:

The points (2, - 5) and (- 1, 1) lie on the equation of the line - 2 · x - y = 1.

According to Euclidean geometry, a line can be constructed from two distinct points on a plane. Then, we can find the equation of the line based on the coordinates of two points set on Cartesian plane, whose standard form is shown below:

a · x + b · y = 1

In this question we have the coordinates of two points: (2, -5), (- 1, 1). If we substitute in the equation of the line, then we find the following system of linear equations:

2 · a - 5 · b = 1

- a + b = 1

Then, we find the solution to the system by using numerical methods:

(a, b) = (- 2, - 1)

The equation of the line - 2 · x - y = 1 contains the points (2, - 5) and (- 1, 1).

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Answer:

If a b and c d lie in plane, z, so my screen is a plane, so let's just think of that here's a b! Now I didn't say they were parallel. It just said a b and c d, so they lie in a plane.

Step-by-step explanation:

I just did this on edge

Answer:

x=6

Step-by-step explanation:

1. Combine like terms

2. Add 9 to both sides

3. Divide by 4 on both sides

4. Arrive at solution

5. Plug solution in to equation.

Answer:

-3

Step-by-step explanation:

first you start with by adding 9 to both sides to balance

-2x+6x-9=15

          +9 +9

Giving you -2x+6x=24 now you start by dividing

I started by dividing -2

-2x+6x=24

÷(-2)      ÷(-2)

Giving you x+6x=(-12) again divide

x+6x=(-12)

 ÷6   ÷6

Giving you x+x=(-6) we know that x+x is = to 2x next we divide agian

2x=(-6)

÷2  ÷2

Giving you the answr x=(-3)

The value of f(2k+4) for k=1 and f(x)= 4-x is -2

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value.

We are given a function f(x)= 4-x

We have to find f(2k+4).

[tex]f(2k+4)=4-2k-4[/tex]

Now substitute k=1

We get,

[tex]f(2+4)=4-2-4\\f(6)=-2[/tex]

Hence, The value of function f(2k+4) at k=1 for the function f(x)=4-x is -2

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Step-by-step explanation:

the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.

the standard form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

so, we see for f(x) the vertex is (-4, 1).

the axis of symmetry uses the x coordinate of the vertex and is

x = -4

for h(x) we see in the graphic that the vertex is (1, -3).

so, the axis of symmetry is

x = 1

FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be

h(x) = 2(x - 1)² - 3

Using the conversion factor, we know that 30 miles are approximately 48 km.

So, 30 miles is how many kilometers:

Then, 5 miles:

Similarly 30 miles:

Rounding off: 48 km approximately

Therefore, using the conversion factor, we know that 30 miles are approximately 48 km.

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The statements that are true concerning two similar figures include:

The ratio of the corresponding angles equals 1.

The ratio of corresponding side lengths are equal. That is option A and C.

Ratio is defined as the number of time a proportion is doing in another proportion.

The similarity that exists between figures or shapes such as a triangle is being proven using Congruence & Similarity. That is,

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The frequency of the heights are:

a = 15

b = 20

c = 40

d = 15

Histogram :

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Now Calculating the frequency by studying the given histogram.

By studying the given histogram, 1 division of the x-axis = 0.5

For height, [tex]0\leq h\leq 50[/tex], the histogram reaches up to 30 divisions which indicates that the frequency is 15.

For height,[tex]50\leq h\leq 75[/tex], the histogram reaches up to 40 divisions which indicate that the frequency is 20.

For height, [tex]75\leq h\leq 100[/tex], the histogram reaches up to 80 divisions which means the frequency is 40.

For height,[tex]100\leq h\leq 150[/tex], the histogram reaches up to 30 divisions which indicate that the frequency is 15

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

Explanation:

The coefficients of each term are 3 and 5. They are the first things mentioned in each parenthesis grouping. The coefficients multiply to 3*5 = 15. This is the coefficient of the final answer.

The 'a' terms are a^2 and a^3. They multiply to a^2*a^3 = a^(2+3) = a^5. Add the exponents because we're using the rule a^b*a^c = a^(b+c). The base must be the same for this rule to apply.

The b terms are b^7 and b^8. They multiply to b^7*b^8 = b^(7+8) = b^15

--------

To summarize

This is how we end up with 15a^5b^15 as the final answer

A field of mathematics called linear equations is essential to computer graphics. It investigates matrices, linear transformations, and vectors. These subjects were covered in Subsection 2.3. 8 in a two-dimensional setting.

A continuous response variable is described by a linear model as a function of one or more predictor variables. They can assist you in analyzing experimental, monetary, and biological data or in understanding and predicting the behavior of complex systems. A statistical technique used to build a linear model is called linear regression.

Depending on the context, the phrase "linear model" is used differently in statistics. The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though.

By using a linear combination of predictor variables, linear models can be used to describe a response variable. A continuous variable with a response that is at the very least roughly regularly distributed is required.

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Answer:

2.99  is the fixed monthly membership fee

Step-by-step explanation:

The inequality of the equation x(2x+3) > 20 is x<-4 or x>5/2.

Given, the expression is x(2x+3) > 20

open the brackets.

⇒ 2x²+3x>20

⇒ 2x²+3x-20>0

Factorize the equation.

⇒ 2x²+8x-5x-20>0

⇒ 2x(x+4)-5(x+4)>0

⇒ (x+4)(2x-5)>0

hence, (x+4)>0 or (2x-5)>0

(x+4)>0

⇒ x<-4

(2x-5)>0

⇒ 2x > 5

⇒ x >5/2

Hence we get the required inequality for the given equation.

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The inequality (302+5)-1+4 (202)- 3) ≤ 125 is false for the given question.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on either side are not equal.

It indicates that the expressions on the left and right should be greater or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is defined by the inequality symbols '≠'.

We have given the inequality  

(302+5)-1+4 (202)- 3) ≤ 125

Lets simplify

(302+5)-1+4 (202)- 3) ≤ 125

1111 ≤ 125

Thus, The inequality is false.

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The total amount of Zach's paycheck was $174.

The fraction of the paycheck spent by Zach on the new video game is 2/6. The cost of the video game is $58. We need to find the total amount that Zach had in the paycheck.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

Let the total amount of the paycheck be "x". Using the information above, we can form an equation as given below :

(2/6)*x = 58

x = (6/2)*58

x = 174

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The equation for a rectangle's perimeter is P = length + breadth + length + breadth. Alternatively, P=2(length + breadth). The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter.  

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The unit price of the pair of gloves is $5.19.

Here, a package of 5 pairs of insulated gloves costs $25.95.

We have to find the unit price of the pairs of gloves.

5 pairs of insulted gloves = $25.95

So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.

Unitary method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.

So by using the unitary method we have:

1 pair of insulated gloves = 25.95/ 5

                                          = 5.19

Therefore the unit price of the pair of gloves = is $5.19.

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The slope of the line containing the pair of points (5,-10) and (-3,-10) = m = 0.

Slope of a line

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Given that the line containing the pair of points (5,-10) and (-3,-10).

Slope of a line = (y2 - y1)/ (x2 - x1)

Here

y1 = -10

x1 = 5

y2 = -10

x2 = -3

Therefore slope of a line = m = [-10 - (-10)]/ (-3 - 5)

                                                = 0/ (-8)

                                                = 0

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The number of miles that the truck drove is 550 miles.

From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:

20x + 2.25y = 1457.50 ....... i

x = number of hours

y = number of miles driven

The driver drove an average of 50 miles per hour. This will be illustrated as:

y/x = 50

y = 50x

Substitute into equation i

20x + 2.25y = 1457.50

20x + 2.25(50x) = 1457.50

20x + 112.50x = 1457.50

Collect like terms

132.50x = 1457.50

Divide

x = 1457.50 / 132.50

x = 11

y = 50x = 50 × 11 = 550 miles

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Answer: 40 seconds

Step-by-step explanation:

This is basically a very simple algebra problem.

Let x be the number of seconds it takes for the statement to be true

120 + x/4 = 150 - x/2

Add x/2 to both sides:

120 + 3x/4 = 150

Subtract 120 from both sides:

3x/4 = 30

Therefore x = 40.

Solve similar problems with an equation, where the variable is the thing you need to find.

Since 1 dozen = 12, 12 cupcakes = 1 1/4 cups of flour

36/12 = 3

36 = 1 1/4(3)
36 cupcakes = 3 3/4 cups of flour

Answer:

8 1/4 cups

Step-by-step explanation:

You multiple 11/4 by 3 and change the answer to a mixed fraction

As per direct variation,

Part A) Decorators fee is $198.132

Part B) Tax for the purchase is $71.10

Part C) The total amount spend by the family is $1849.232.

Direct variation:

Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:

y=kx

for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

Given,

A family used a professional decorator to furnish their new home.

The decorator selected $1,580 worth of furnishings for their home.

The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.

The decorator’s fee was 12% of the furnishings , excluding the tax.

Here we need to find the following:

Part A) Decorator's fee

Part B) Tax amount

Part C) Total cost.

We know that, the decorator’s fee was 12% of the purchases.

So, the equation is then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee for the purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

Therefore, the decorators fee is $198.132

Decorator selected furnishings cost = $1,580.

Tax = 4.5%

Decorator’s fee = 12% of the purchases.

So, it can be calculated as,

Tax = 4.5% × 1580

Tax = 0.045 × 1580

Therefore, the tax for the purchase is $71.10

Amount paid = 1580 + 71.10 = 1651.10

Now, the total amount paid by the family is,

=> purchase amount + decorator fee

=> 1651.10 + 198.132

=> 1849.232

Therefore, the total amount spend by the family is $1849.232.

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Answer:

First number = 4

Second number = 9

Step-by-step explanation:

If the first number = x, the second number = x + 5.

The calculation can be expressed as follows:

x + 2(x + 5) = 22

First, expand the bracket 2(x + 5):

x + 2x + 10 = 22

Combine like terms:

3x + 10 = 22

Subtract 10 from both sides:

3x = 12

Divide both sides by 3:

x = 4

First number = 4

Second number = 4 + 5 = 9

The coordinate of B is option  C (0,-2). A spherical or elliptical coordinate system known as the geographic coordinate system is used to measure and transmit positions on Earth as latitude and longitude. Of the several spatial reference systems in use, it is the most basic, traditional, and often utilized. It also serves as the foundation for the majority of others.

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space. Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.

A coordinate system in geometry is a method for determining the location of points or other geometric objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

the coordinates of B(-5,0)

the translation rule

(x,y)---------(x+5,y-2)

so

B(-5,0)-----B(-5+5,0-2)

(-5,0)--------(-5+5,0-2)----------(0,-2)

Hence, the correct answer is (0,-2)

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The compound interest formula is given by the formula

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

For the second year

P=26500+25000=51500

For the third year

P=54590 + 25000=79590

For the fourth year

P=84365.4 + 25000=109365.4

For the fifth year

P= 115927.324 + 25000 =140927.324

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Because of the fact, the angle is ∠BCA = 10x - 10 and ∠ABC = 30 lies on a straight line and ∠BCA is obtuse while ∠ABC is acute, we can just set them equal to 180 to find the value of x.

So we will set up the equation:
   10x - 10 + 30 = 180

1. Combine Like Terms (eg. -10 and 30)
[tex]10x - 10 + 30 = 180[/tex]
= [tex]10 x + 20 = 180[/tex]

2. Subtract 20 on both sides
[tex]10x + 20 = 180[/tex]
       [tex]-20 -20[/tex]

= [tex]10x = 160[/tex]
3. Divide 10 into both sides
[tex]\frac{10x}{10} = \frac{160}{10}[/tex]

And we will get:
[tex]x = 16[/tex]

Check Your Work!
Now if we replace x in the equation for 16 like below we do in fact get 180:
[tex]10(16) - 10 + 30 = 180[/tex]
[tex]160 - 10 + 30 = 180[/tex]

[tex]150 + 30 = 180[/tex]