Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.

EFGH is a square as all its sides are equal and all its angles are right angles.

Let's start by considering the sides. We know that AE = BF = CG = DH, and we also know that the opposite sides of a square are parallel and equal in length. Therefore, we can say that:

AE = DH (opposite sides of square ABCD)

BF = AE (opposite sides of square ABFE)

CG = BF (opposite sides of square BCGF)

DH = CG (opposite sides of square CDHG)

Thus, we have shown that all four sides of EFGH are equal in length, and so EFGH may be a square.

Now, let's consider the angles. Since AE and BF are opposite sides of a square, we know that angle AEB = angle BFA = 90 degrees. Similarly, we can show that angle BFC = angle CGD = angle DHE = 90 degrees.

Next, we observe that E, F, G, and H are midpoints of the sides of square ABCD. Therefore, we can say that:

EF || AB, and EF = 1/2 * AB

FG || BC, and FG = 1/2 * BC

GH || CD, and GH = 1/2 * CD

HE || DA, and HE = 1/2 * DA

Since opposite sides of a square are parallel, we can also say that:

EF || GH, and EF = GH

FG || HE, and FG = HE

Now, we have two pairs of parallel sides with equal lengths, which means that opposite angles are equal. Therefore, we can say that:

angle FEG = angle GHE (corresponding angles)

angle EFG = angle HEF (corresponding angles)

Combining these with the right angles we established earlier, we have shown that all four angles of EFGH are right angles, and so EFGH is a square.

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A triangle has three sides, three angles, and three vertices (also known as corners).

A triangle is a geometric shape that consists of three line segments that connect three non-collinear points.

Each of these line segments is called a side of the triangle. The three points where these sides meet are called the vertices (singular: vertex) of the triangle.

The triangle also has three interior angles formed by its sides. These angles are located inside the triangle, and their sum is always equal to 180 degrees.

In summary, a triangle is defined by its three sides, three angles, and three vertices.

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The vertical asymptotes of y = 6tan(0.2x) is [tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

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

y = 6tan(0.2x)

The equation is a trigonometry function

The best way to determine the vertical asymptotes is with the use of a graphing tool

Using the above as a guide, we have the following:

From the graphing tool, we have

[tex]\:x=\frac{5\pi }{2}+\frac{\pi }{0.2}n[/tex]

This gives

[tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

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Ans:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

z = -37/50

Step-by-step explanation:

Now we have to,

→ Find the required value of z.

The equation is,

→ 51z - 21 = z - 58

Then the value of z will be,

→ 51z - 21 = z - 58

→ 51z = z - 58 + 21

→ 51z = z - 37

→ 51z - z = -37

→ 50z = -37

→ [ z = -37/50 ]

Hence, value of z is -37/50.

The amount of money Abdoulaye would have saved in w weeks is given by the equation A = 10w + 70 and in 9 weeks Abdoulaye saved $ 160

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial amount of money Abdoulaye saved be = $ 70

The amount of money Abdoulaye saves each week = $ 10

Let the number of weeks be w

So , the amount of money Abdoulaye saved w weeks is = ( amount of money Abdoulaye saves each week x w ) + initial amount of money Abdoulaye saved

Substituting the values in the equation , we get

The amount of money Abdoulaye saved w weeks is A = 10w + 70

Now , when w = 9 weeks

Substitute the value of w = 9 , we get

A = 10w + 70

A = 10 ( 9 ) + 70

A = 90 + 70

A = $ 160

Hence , the equation is A = 10w + 70

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The required cost of the dinner not including sales tax was $34.28.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

To find out how much the dinner cost before sales tax, we need to subtract the sales tax amount from the total cost.

We know that the sales tax rate is 8%. To find the sales tax amount, we can multiply the total cost by 8% (or 0.08):

Sales tax = 0.08 * $37.26 = $2.98

To find the cost of the dinner before sales tax, we can subtract the sales tax amount from the total cost:

Cost before sales tax = $37.26 - $2.98 = $34.28

Therefore, the cost of the dinner not including sales tax was $34.28.

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Answer:

the perimeter of the polygon is 36 feet.

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all its sides. In this case, you have three sides with lengths of 14 ft, 15 ft, and 7 ft. To find the perimeter, simply add these lengths together:

Perimeter = 14 ft + 15 ft + 7 ft

Perimeter = 36 ft

So the perimeter of the polygon is 36 feet.

The length of

KL = 7.8units

LM = 7.1 units

MN = 8.5 units

NK = 7.8units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

KL = √1-(-4)²+3-(-3))²

KL = √5²+6²

KL = √ 25+36

KL = √ 61 = 7.8 units

To find the length KN

KN = √ 1-7)²+ 3(-2)²

KN = √ 6²+5²

KN = √ 36+ 25

KN = √ 61 = 7.8 units

to find LM

LM = √-4-1)²+-3(-8)²

LM = √25+25

LM = √50

LM = 7.1 units

to find MN

√ 7-1)²+ -2-(-8)²

MN= √ 6²+6²

MN = √ 36+36

MN=√ 72

MN = 8.5 units

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The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

where:

μ1 = mean bumper repair cost for small pickups ($1090)

μ2 = mean bumper repair cost for small utility vehicles ($485)

s1 = standard deviation of bumper repair cost for small pickups ($403)

s2 = standard deviation of bumper repair cost for small utility vehicles ($382)

n1 = sample size for small pickups (5)

n2 = sample size for small utility vehicles (8)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator. Since the degrees of freedom (df) for a Welch's t-test are unequal, the critical value can be approximated using the degrees of freedom formula:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / (((s1^2 / n1)^2) / (n1 - 1) + ((s2^2 / n2)^2) / (n2 - 1))

Plugging in the values, we get:

df = ((403^2 / 5) + (382^2 / 8))^2 / (((403^2 / 5)^2) / (5 - 1) + ((382^2 / 8)^2) / (8 - 1)) = 9.57

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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The value of X in the right angle triangle that is given above would be = 28.89

The given figure shows a right triangle with a hypotenuse with a length of 48. An indicated angle has a measure of

53∘.

To calculate the missing side the formula;

cos 0 = adj/hyp

where, adj = X

hyp = 48

0 = 53°

cos 53° = X/ 48

Make X the subject of formula;

X = 48 × cos 53°

X = 48 × 0.601815023

X = 28.887121104

X = 28.89 ( to two decimal places)

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The value of the length of  hypotenuse when base length is  11cm and angle is 24°:  12.04 cm

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

The length of hypotenuse = x

The length of base =  11 cm

The angle = 24°

It is known that,

cosФ = base/hypotenuse

         = 11/x

cos24° = 11/x

x = 11/cos24°

  = 12.4

Therefore, the length of the hypotenuse is approximately 12.04cm.

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The equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Hence, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = (y2 - y1) / (x2 - x1)

The coordinates of the points are:

(-8, 3) and (-6, 0)

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates we have:

m = (0 - 3)/ (-6 + 8)

m = -3/2

Using the point slope form:

y - y1 = m (x - x1)

Substituting the values of slope and coordinates we have:

y - 3 = -3/2(x + 8)

2(y - 3) = -3(x + 8)

2y - 6 = -3x -24

2y = -3x -18

Hence, the equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

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Answer:

Planes

Step-by-step explanation:

You can think of a plane as a sheet of paper that goes on in all directions.

Answer:

B. planes

Step-by-step explanation:

The grammer makes sense

The x-coordinate of P is given as follows:

x = 4.

The x-coordinate of P is obtained applying the proportions in the context of this problem.

The partition ratio is 2:4, hence the equation to obtain the coordinates is given as follows:

P - A = 2/6(B - A)

P - A = 1/3(B - A).

Then the x-coordinate of P is obtained as follows:

x - 10 = 1/3(-8 - 10)

x - 10 = -6

x = 4.

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Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).

A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.

In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.

Step-by-step explanation:

Answer: The composite function (g f)(x) is found by first applying the function f to x and then applying the function g to the result. In other words, (g f)(x) = g(f(x)).

So, for the given functions g(x) = x - 5 and f(x) = -x - 1, the composite function is:

(g f)(x) = g(-x - 1) = (-x - 1) - 5 = -x - 6

Evaluating the composite function at x = 7, we get:

(g f)(7) = -7 - 6 = -13

Step-by-step explanation:

The error in the expression 4 + 2x - 1/2(10 - 4x) is the missing parentheses.

Parentheses are a sort of punctuation mark that is used to separate or distinguish content inside a phrase. They frequently assist to clarify the meaning of a statement by adding information. Parentheses can also be used to denote a break or to divide items in a list.

Error in the given question: Missing parentheses

Corrected expression: 4 + 2x - 1/2(10 - 4x)

The problem may be fixed by ensuring that the proper syntax is used when declaring variables. If the variable is a string, for example, it should be stated as "var myVariable ='string value';". If it is an integer, define it like "var myVariable = 42;".

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The requried graph with the x-axis labeled a number of side dishes and the y-axis labeled cost in dollars and a line going from point [0,5.25] through point [3, 9.75]. Option C is correct.

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

Here,
Calculate the slope of the given relation in the table, using any two of the ordered pair,
m = 11.25 - 8.25 / 4 - 2
m = 3/2
m = 1.5

Now calculate the slope in each option, the slope of any option matches with m = 1.5 then that will be the required graph, so the slope of the graph mentioned in option C matches with m = 1.5.

Thus, Option C is the required answer.

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Answer:

200 lb

Step-by-step explanation:

Let her original weight be [tex]x[/tex].

[tex]0.12x=24 \implies x=200[/tex]

The meaning of 5 = f(I) is that the 5% have an income of $6000

The average rate is that %0.054 per thousand of dollars

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

The graph

The equation is given as

5 = f(I)

This means that:

We find x when f(I) = 5

Using the graph, we have

x = 6

This means that the income is $6000

This is calculated as

Rate = (f(x2) - f(x1))/(x2 - x1)

Substitute the known values in the above equation, so, we have the following representation

Rate = (1.8 - 4.5)/(10 - 60)

Evaluate

Rate = 0.054

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The measure of sinx from the trigonometry is 7/25

Given the following trigonometry

tan x = 7/24

Since tan theta = opposite/adjacent

Determine the hypotenuse

h^2 = 7^2 + 24^2

h^2 = 49 + 576
h^2 = 625

h = 25

The value of sin x will be given as:

sinx = opposite/hypotenuse

sinx = 7/25

Hence the exact value of sinx where sinx>0 is 7/25

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The volume of the pyramid is 400 cubic cm and the surface area is

340 sq cm.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

The volume of a pyramid is = (1/3)×l×w×h and the surface area of a pyramid is (1/2)×PL + B, where P = perimeter of the base, L = height, and

B = area of the base.

Therefore, The volume is =  (1/3)×10×10×12 cubic cm.

= 1200/3 cubic cm.

= 400 cubic cm

And, The total surface area is,

= (1/2)[2(10 + 10)×12 + (10×10) sq cm.

= 240 + 100 sq cm.

= 340 sq cm.

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The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P

Now , the equation will be

The fraction of doctors who are general practitioners be n ( A ) = 7/17

The fraction of doctors who are under the age of 45 n ( B ) = 4/17

And ,

The fraction of doctors who are both n ( A ∩ B ) = 2/17

Now , from the set theory formula ,

n(A∪B) = n(A) + n(B) - n(A⋂B)

And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )

Substituting the values in the equation , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )

On simplifying the equations , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17

Hence , the probability is 9/17

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Answer:

-2x^4+4x^3+8x

Step-by-step explanation:

please check the answer given

The value of x in the proportion 1650 = x(156.25) is 10.56

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Given the proportion:

1650 = x(156.25)

We are required to solve for x. To find x, divide both sides of the equation by 156.25:

1650 / 156.25 = x(156.25) / 156.25

x =  1650 / 156.25

x = 10.56

The value of x is 10.56

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Answer:

  5/4

Step-by-step explanation:

You want the product abc when 5x^-2y^(3/2)/√(25xy^4) is written as ax^by^c.

The applicable rules of exponents are ...

  [tex]a^ba^c=a^{b+c}\\\\\dfrac{1}{\sqrt{a}}=a^{-\frac{1}{2}}\\\\(a^b)^c=a^{bc}[/tex]

Using these rules, the expression can be simplified to ...

  [tex]\dfrac{5x^{-2}y^{\frac{3}{2}}}{\sqrt{25xy^4}}=(5x^{-2}y^{\frac{3}{2}})(5^2xy^4)^{-\frac{1}{2}}=(5x^{-2}y^{\frac{3}{2}})(5^{2(-\frac{1}{2})}x^{-\frac{1}{2}}y^{4(-\frac{1}{2})})\\\\=5^{1-1}x^{-2-\frac{1}{2}}y^{\frac{3}{2}-2}\\\\=1\cdot x^{-\frac{5}{2}}y^{-\frac{1}{2}}[/tex]

From this last expression, we determine ...

The product of the values of interest is ...

  abc = (1)(-5/2)(-1/2)

  abc = 5/4

Answer:

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

Let the number of pizzas be x.

The average cost per pizza is:

If we need the average cost be at most $3.50, we need an inequality:

This is translated as:

The blanks are:

18 points in 15 hour is greater than 45 points in 36 hours.

The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.

45 points in 36 hours and 18 points in 15 hours.

Points per hour

45 points in 36 hours is given by,

[tex]\frac{45}{60} =1.25[/tex] points.

18 points in 15 hours is given by,

[tex]\frac{18}{15}[/tex] = 1.2 points.

On comparing these points 1.2 > 1.25.

Hence, 18 points in 15 hour is greater than 45 points in 36 hours.

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The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

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The distance of the point P to the plane is 42/√629 units. The solution has been obtained by using vectors.

What are vectors?

An item with both magnitude and direction is said to contain a vector. An object's motion from one point to another is described by a vector.

We are given three points Q, R and S. So, we will find equation of the plane defined by the three points.

Vector RQ = < 5, 1, -4 >  and RS = < 7, 6, -7>  and their cross product

RQ x RS = < 5, 1, -4 > x < 7, 6, -7> = < 17 , 7, 23>  = n  

This is a vector normal to the plane.

So, the equation of the plane is 17x + 4y + 18z = 139

The distance is calculated using

⇒d = (|A·Mx + B·My + C·Mz + D| )/(√A² + B² + C²)

⇒d = (|-17·3 + (-4)·1 + (-18)·7 + 139|)/((-17)² + (-4)² + (-18)²)

⇒d = 42/√629

Hence, the distance is 42/√629 units.

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