In the triangle DEF, the length DX = 3cm, XE = 7cm, and EF = 8cm.
a. Using a pair of compasses only and a ruler, construct the triangle DEF. Leave in your
construction arcs. Be sure to include these for the perpendicular line at X.
b. Measure the length of the side DF.

c. Measure the height of the triangle, XF.

d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.


e. Use compasses to bisect the angle D. You must leave your construction arcs in.

Answer: A = 30

Step-by-step explanation:

Hello, to find the area of a triangle, you first have to follow,

Step 1. The area of a triangle is A = 1/2 * b * h, so plug in the other numbers

Step 2. A = 1/2 * 6 * 10

Step 3. Get rid of the fraction by doing 10 * 1/2. A = 6 (10 * 1/2)

Step 4. A = 6 * 5

Step 5. A = 30

The area of the rose garden =129 square feet.

Consider the following diagram.

From the figure we can observe that the dimensions of the rectangular garden are: length = 15 ft and width = 9 ft

Let us assume that A₁ be the area of the rectangular garden.

Using the formula for the area of rectangle,

The area of the rectanguler garden would be,

A₁ = 15 × 9

A₁ = 135 ft²

Also, the dimensions of the rectangular patch of grass is 2 feet × 3 feet.

Let us assume that A₂ represents the area of the rectangular patch of grass.

Using the formula for area of rectangle, the area of rectangular patch of grass is:

A₂ = 2 × 3

A₂ = 6 ft²

Let a be the area of the rose garden.

So, the required area would be,

A = A₁ - A₂

A = 135 - 6

A = 129 ft²

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Find the complete question below.

The product of (x+y+z)(x^2+y^2+z^2-xy-yz-zx) is x³ + y³ + z³ -2x²y - 2xyz- xy²  - y²z - xz²

It is important to note that algebraic expressions are expressions that are composed of terms, coefficients, variables, factors and constants.

These expressions are also made up of arithmetic or mathematical operations. These operations are;

From the information given, we have that;

(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

expand the bracket by multiplying the variables

x³ + xy² + xz² - x²y - xyz - x²z -xy²+ y³ + yz² - x²y - y²z - x² + x²z +y²z + z³ - xyz -yz² - xz²

collect like terms

x³ + y³ + z³ -2x²y - 2xyz- xy²  - y²z - xz²

Hence, the expression is x³ + y³ + z³ -2x²y - 2xyz- xy²  - y²z - xz²

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Answer:

the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).

Step-by-step explanation:

To factorise the quadratic expression 14x^2 - x - 3, we can use the following steps:

So, the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).

Answer:

Step-by-step explanation:

14×14-×-3

196-×-3=196-3

=193

Answer:

Step-by-step explanation:

The dot product of two vectors u and v is given by the formula:

u · v = u[0] * v[0] + u[1] * v[1] + u[2] * v[2]

where u[0], u[1], and u[2] are the components of vector u and v[0], v[1], and v[2] are the components of vector v.

Plugging in the values from the vectors u = [2, 3, 4] and v = [5, 6, 7], we get:

u · v = 2 * 5 + 3 * 6 + 4 * 7 = 10 + 18 + 28 = 56

Therefore, the dot product of the vectors u and v is 56.

The variable expression for x = 5 given 6×(x - 9) - 5 is evaluated to give a result of -24 using PEDMAS.

P – Parentheses First: B – Brackets First

E – Exponents

D – Division

M – Multiplication

A – Addition

S – Subtraction

We shall evaluate the value of the expression 6×(x - 9) - 5 for x = 5 as follows:

we deal with bracket first;

6×(x - 9) - 5 = 6 × (5 - 9) - 5

we multiply next;

6×(x - 9) - 5 = 6 × -4 - 5

6×(x - 9) - 5 = -24 - 5

lastly we subtract

6×(x - 9) - 5 = -29.

Therefore, the variable expression for x = 5 given 6×(x - 9) - 5 is evaluated to give a result of -24 using PEDMAS.

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Answer: x = 46°

Step-by-step explanation:

Answer: 37.5

Step-by-step explanation:

62.5 * (3/5) = 37.5

There are several ways to find the zeros of the function x^4–18x^2+12x+80. You can graph the equation and see where it crosses the x axis.The graph crosses at x=-4,-2. This means that -4, and -2 are roots, and (x+4) and (x+2) are factors. I like synthetic division the best when it comes to factoring. I teach synthetic division when we get to problems like this, so I will assume that you are familiar with it.First take the coefficients of the equation x^4–18x^2+12x+80 I have to usex^4 +0 x^3 –18x^2+12x+80 : 1 0 -18 12 80. I will use -4 first.If you are not supposed to graph it, then you can use synthetic division. It can take longer because you have to “guess “ at the factors using an educated guess from the factors of =/- p/q . Where p is the last coefficient and q is the first coefficient.In this case we need to find the factors of 80/1 . These are 1,2,4,5,8,10,16,20,40,80. So possible roots are +/- (1,2,4,5,8,10,16,20,40,80). Students usually start with the smaller numbers and work up, So I would try 1 first then 2 etc.Now another way to find the factors is to use 10 as x and to see what the answer is, then try to factor the results. f(x)=x^4–18x^2+12x+80 f(10)=10,000–1800+120+80=8400I can factor 8400 into 100 *6 *14, or (10+0) *(10+0)*(10–4)*(10+4). 0 is not a factor from above, but +/- 4 is. So I could try those two numbers. Looking at the possible roots using 10 as my x, I would need to look at 9,11, 8,12, 0,20 -4,26, etc

Answer:

La respuesta de su problemamatemático es X= 6.63

Answer: 21

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

9 + 10 = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19

Answer:

B

Step-by-step explanation:

Use the distance formula.

Answer: e = 1/18

Step-by-step explanation:

e = 18/320

e = 1/18

Answer: 0.05625

Step-by-step explanation: So, you divide 18 by 320, and that gives you 0.05625, and you can double check by multiplying 0.05625 by 320, which gives you 18.

Answer:

x = 13

Step-by-step explanation:

I put it into my calculator, let me know if that helped :)

The skid marks be to the nearest foot is 913 ft.

The length of the skid marks can be calculated using the formula d = μV2/2gdf, where μ is the coefficient of static friction, V is the velocity, g is the acceleration due to gravity, and df is the drag factor. In this case, the coefficient of static friction can be assumed to be 0.9, the velocity is 35 mi/h, the acceleration due to gravity is 32.2 ft/s2, and the drag factor is 0.97. Plugging these values into the formula, we get [tex]d = 0.9(35 mi/h x 5280 ft/mi/h)2/2(32.2 ft/s2)(0.97) = 912.5 ft[/tex]. To the nearest foot, this is 913 ft.

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Answer:

$121.95

Step-by-step explanation:

The cost of the same journey before midnight is,

⇒ $58

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

After midnight, the cost of any taxi journey increases by 45%.

And, One journey costs $84.10 after midnight.

Now, Let the cost of the same journey before midnight is x

Hence, WE can formulae;

x + 45% of x = 84.10

x + 0.45x = 84.10

1.45x = 84.10

x = $58

Thus, The cost of the same journey before midnight is,

⇒ $58

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a) The estimate for the total number of deer in the park is given as follows: 630 deers.

b) The assumption that he made was that the proportion was followed.

The total number of deer in the park is estimated applying the proportions in the context of this problem.

The next week, the gamekeeper caught 70 deer. 10 of the deer had a tag around one of their hooves, hence the fraction of marked deers is given as follows:

10/70 = 1/7.

He had marked 90 deers, hence the estimate for the total number of deers, considering a constant proportion, is given as follows:

1/7 x n = 90

n = 90 x 7

n = 630 deers.

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Answer: -1/12

Step-by-step explanation:

Answer:

-1/12

Step-by-step explanation:

9/4 - 7/3

To start, we need to make the denominators the same number.  In order to do that, we need to identify the factor they have in common.

4, 8, 12

3, 6, 9, 12

Twelve is the common factor, so we will use this.  Remember, whatever you do to the bottom, you must do to the top, and vice versa.

4 * 3 = 12

/12

3 * 9 (numerator) = 27

27/12

     Now, we must figure out 7/3.

3 * 4 = 12

4 * -7 = -28

-28/12

Now, take the new fractions and subtract them.

27/12 - 28/12

-1/12

[tex]y=2\frac{2}{3}+16[/tex] is the answer as it passes perpendicular and through point A

The length of BC is 6 inches.

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

Given;

Part a;

The length of the secant CD, times its external segment, FC, equals the square of the tangent segment CB;

Mathematically, it can be written as;

RT*ST=TU^2

Part b;

RT*ST=TU^2

TU^2=9*4

TU=6

Therefore, the distance of TU in circle will be 6 inches.

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The values of the terms, a₁, a₂, and a₁₀ of the sequence are;

(a) a₁ = 1, a₂ = 1/2, a₁₀ = 1/10

(b)  [tex]\lim\limits_{n\to {\infty}}[/tex] aₙ = 0

A sequence is an ordered collection of objects such as numbers in which repetition of the object is possible, and the objects (or numbers) are referred to as the terms of the sequence.  

The sequence, [tex]\{a_n\}^\infty_{n = 1}[/tex] with values, aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n + 1}} }[/tex]

(a) a₁ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{1 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^2} } = -[\frac{1}{x} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{1} ) = 0 + 1 = 1[/tex]

Therefore; a₁ = 1

a₂ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{2 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^3} } = -[\frac{1}{2\cdot x^2} ]^{\infty}_1[/tex]

[tex]-[\frac{1}{2\cdot x} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{2 \times 1} ) = 0 + \frac{1}{2} = \frac{1}{2}[/tex]

Therefore; a₂ = 1/2

a₁₀ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{10 + 1}} } = \int\limits^{\infty}_1 {\frac{dx}{x^{11}} } = [-\frac{1}{10\cdot x^{10}} ]^{\infty}_1[/tex]

[tex][-\frac{1}{10\cdot x^{10}} ]^{\infty}_1 = -\frac{1}{\infty} - (-\frac{1}{10\times 1} ) = 0 + \frac{1}{10} = \frac{1}{10}[/tex]

Therefore; a₁₀ = 1/10

b) The limit, [tex]\lim \limits_{n\to \infty} a_n[/tex] can be evaluated as follows;

aₙ = [tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx[/tex]

[tex]\int\limits^{\infty}_1 {\frac{dx}{x^{n+1} } } \, dx = [-\frac{1}{n\cdot x^n} ]^{\infty}_1 = -\frac{1}{n\times \infty } - (-\frac{1}{n\times 1^n} )= \frac{1}{n}[/tex]

aₙ = 1/n

Therefore;

[tex]\lim \limits_{n\to \infty} a_n = \frac{1}{\infty}[/tex] = 0

[tex]\lim\limits_{n\to {\infty}} a_n[/tex] = 0

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Answer:

Step-by-step explanation:

If there is a hole in the graph at x = -6, that means that there was initially an expression in both the numerator and the denominator that was the same, which is the hole very loosely defined. If the hole is at x = -6, then the factor for that solution is (x + 6). One of those has to be in both the numerator and denominator in order for them to cancel out. This is called a removeable discontinuity. Because the x-intercept is at x = 3, the factor for that zero is (x -3). That has to go in the numerator also. Our equation then for the rational function graphed is

[tex]y=\frac{(x+6)(x-3)}{(x+6)}[/tex] which FOILs to

[tex]y=\frac{x^2+3x-18}{x+6}[/tex]

The predicted cost of postage for 2013 is 45 cents.

We need to use the exponential regression model to predict the cost of postage for the year 2013, given that it was 63 years since 1950.

Let's assume that the cost of postage can be modeled using the exponential function:

C(t) = a * e^(kt)

where:

We can use the two data points we have to solve for a and k:

Using the above data points, we can solve for k as follows:

0.03 = a * e^(0 * k)

0.46 = a * e^(63k)

Dividing the second equation by the first equation, we get:

15.333 = e^(63k)

Taking the natural logarithm of both sides, we get:

k = ln(15.333)/63

Evaluate

k = 0.043

Now that we have k, we can use it to predict the cost of postage in 2013:

C(63) = a * e^(63k)

C(63) = 0.03 * e^(63 * 0.043)

C(63) = 0.45

Hence, according to the exponential regression model, the cost is 45 cents.

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Complete question

The cost of first-class postage in 2013 was raised to 46 cents.

According to the exponential regression model, what was the predicted cost for 2013 if the cost of postage was 3 cents in 1950

Start by noting that 2013 is 63 years since 1950.

Answer:

4.81 meters

Step-by-step explanation:

1 m = 100 cm

where m = meters

         cm = centimeters

481 centimeters need to be converted:

= 481 cm × [tex](\frac{1 m}{100 cm})[/tex]

The cm in the numerator and denominator will completely cancel each other out:

= [tex]\frac{481}{100}[/tex] m

= 4.81 meters

Answer:

0.072337963 or 125/1728

Step-by-step explanation:

simply put it into a calculator

Answer:

Step-by-step explanation:

In "The Jungle" by Upton Sinclair, Jurgis is a character who starts out with a positive and optimistic outlook on life. He is full of hope and ambition when he arrives in America with his family, eager to make a better life for himself. However, after he is injured on the job and becomes unable to work, his attitude changes dramatically. He becomes disillusioned and bitter, losing his hope and faith in the American Dream.

In my opinion, Jurgis's response to his injury reflects the harsh realities of life for immigrants and the working class in America during that time. The injury not only physically incapacitates him, but it also robs him of his ability to provide for his family and live out his dreams. The experience shows the extent to which the system is stacked against those in Jurgis's position and serves as a powerful commentary on the injustices and inequalities of the time.

Answer: To find the volume of the combined shape, we need to find the volume of the cone and the volume of the hemisphere and add them together.

For the cone:

Volume = 1/3 * pi * r^2 * h

Where r is the radius and h is the height. In this case, r = 8 cm and h = 12 cm. So,

Volume = 1/3 * pi * 8^2 * 12 = (1/3) * pi * 64 * 12 = 256 * pi cm^3

For the hemisphere:

Volume = (2/3) * pi * r^3

Where r is the radius. In this case, r = 8 cm. So,

Volume = (2/3) * pi * 8^3 = (2/3) * pi * 512 cm^3

Adding the volumes of the cone and the hemisphere, we have:

Volume = 256 * pi + (2/3) * pi * 512 cm^3 = 256 * pi + 341.3333 * pi cm^3

To the nearest integer, the volume of the combined shape is:

Volume = round(256 * pi + 341.3333 * pi) = round(597.3333 * pi) = 1876 cm^3

Step-by-step explanation:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points on the function are given as follows:

(10, 110) and (20, 220).

The slope is given by the change in the output divided by the change in the input, hence:

m = (220 - 110)/10

m = 11.

Hence:

y = 11x + b.

When x = 10, y = 110, hence the intercept b is given as follows:

110 = 11(10) + b

b = 0.

Hence the function giving the cost for x people is of;

y = 11x.

The cost for 60 people would be of:

y = 11(60)

y = $660.

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Supplementary angles are angles that have a sum of 180 degrees.

Let the angle be x.

We're given:

Solve for x:

[tex]x=67.4+(180-x)\\x=67.4+180-x\\2x=247.4\\x=123.7[/tex]

Solve the the supplementary angle:

[tex]180-x\\= 180-123.7\\= 56.3[/tex]

The angle measures 123.7 degrees and its supplementary angle measures 56.3 degrees.

The value of A + B + C is 1.21 for the distribution function.

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

From the given data the values of A, B, and C are 1 / 8, 3 / 8, and 23 / 32.

The value of the sum of A, B, and C is calculated as:-

E = A + B + C

E = 1 / 8 + 3 / 8 + 23 / 32

E = ( 4 + 12+ 32 ) / 32

E = 39 / 32

E = 1.21

Therefore, the solution for the distribution function is E = 1.21.

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