Find the coordinates of the orthocenter of the triangle whose vertices are A(3, 1), B(0, 4) and C(-3, 1).​

The present age of Paul is 52 years and the present age of Matt is 10 years.

We are given that two years ago, Paul =  7 times as Matt

Let the current age of Matt be x and of Paul be y

2 years ago, we will have that:

Age of Matt = x - 2

So, we get the equation as:

Age of Paul = 7 ( x - 2) = 7 x - 14

y - 2 = 7 x - 14

y = 7 x - 14 + 2

y = 7 x - 12

Also, we are given that to year from now, Paul = five times Matt

We get that:

y + 2 = 5 ( x + 2)

y + 2 = 5 x + 10

y = 5 x + 10 - 2

y = 5 x + 8

So, we get:

7 x - 12 = 5 x + 8

7 x - 5 x = 8 + 12

2 x = 20

x = 20 / 2

x = 10

y = 5 (10) + 2

y = 50 + 2

y = 52

Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.

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If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.

Salary of Sam = $25000

Raise in Sam's Salary = $2000

New Total Salary = $25000 + $2000 = $27000

Salary of Charlie = $30000

Raise in Charlie's Salary = $2000

New Total Salary = $30000 + $2000 = $32000

Hence the absolute value of their salaries are same but Charlie will get more in relative terms.

Hence, option d is correct.

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Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved

According to the question we have been given that

[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex]  = [tex]sec(\frac{\pi }{6-x} )[/tex]

And we need to prove that left hand side is equal to the right hand side.

To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :

R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]

          = [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]

[As secƟ = 1/cosƟ)

           = [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]

[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]

                   [tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]          

    R.H.S = L.H.S

or L.H.S = R.H.S

Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved

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The quotient of the given division operation is -343. and The correct option is the first option -343.

According to the statement

We have to find that the value of the quotient.

So, For this purpose, we know that the

Quotient can be defined as the result of the division of a number by any divisor.

In other words, The result of the division is the quotient.

From the given information:

we are to determine the quotient of the given division operation

And

The statement become is:

[tex]\frac{-7^{2} }{-7^{-1} }[/tex]

Then we have to solve this

Then

[tex]\frac{49}{-7^{-1} }[/tex]

Then

49*-7

-343.

the quotient of the given division operation is -343.

So, The quotient of the given division operation is -343. and The correct option is the first option -343.

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Answer:

-343

Step-by-step explanation:

Edge

In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.

Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.

In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.

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The reasoning which shows the given statement correctly is [tex]4^{\frac{3}{2}}[/tex].

Given the statement is "4 to the power of 3 over 2 end exponent".

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

In the given statement 3 over 2 means, 3 is divisible by 2 and it can be written as 3/2.

And it is also given that 4 to the power of 3 over 2 that means we have to write 3/2 in the power of 4 and it can be written as

[tex]4^{\frac{3}{2}}[/tex]

Hence, the reasoning which shows the given statement "4 to the power of 3 over 2" correctly is [tex]4^{\frac{3}{2}}[/tex].

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The term or expression 12b represents the number of raffle tickets sold by the members of the band.

Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

There are b number of members in a jazz band. The jazz band wants to take a tour.

Each of the members sold 12 raffle tickets to raise money for the tour.

Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.

So, the expression for the number of raffle tickets sold by the members of the jazz band will be:

= 12 × b

= 12b

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Answer:

(a) $126

(b) .453333%

Step-by-step explanation:

(a) 476 - 350 = $126

(b)

[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]

Answer: 8.4261

Step-by-step explanation:

Answer:

169 squared I think,hope this helps

Based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

The side-angle-side congruence theorem (SAS) means that two triangles have two pairs of sides that are congruent to each other with a pair of included congruent angles in between the two pairs of congruent sides of both triangles, and thus, both triangles must be congruent to one another.

The diagram shows two triangles that share a common side which is a pair of congruent sides. It also shows a pair of another congruent sides that is marked congruent.

Also, we have a pair of included congruent angles that both triangles have.

Therefore, based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.

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The standard form the linear function is f(x)= -3x-3.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+3. Where:

m= the slope. It can be calculated for Δy/Δx .

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

For the given example: m=5 and b=3.

You should replace in the minimum two given values for x and y in the standard form for a linear equation mx+b . Thus, you will write a system linear where from it, you can find the coefficients m and b. See below.

       y=mx+b

      -3=0*m+b

      -3=b

       y=mx+b

      3= -2*m+b

Now, you find b=-3, then

      3= -2*m-3

      3+3= -2m

       6=-2m

       m= -3

Thus, you can write f(x)= -3x-3.

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There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:

Slope

m = [6.9 - (- 8.5)] / (13.8 - 5)

m = 7 / 4

Intercept

b = - 8.5 - (7 / 4) · 5

b = - 69 / 4

The equation of the line is y = (7 / 4) · x - 69 / 4.

Second, evaluate the equation of the line at different integers:

x= 6

y = (7 / 4) · 6 - 69 / 4

y = - 27 / 4

x = 7

y = (7 / 4) · 7 - 69 / 4

y = - 5

x = 8

y = (7 / 4) · 8 - 69 / 4

y = - 13 / 4

x = 9

y = (7 / 4) · 9 - 69 / 4

y = - 3 / 2

x = 10

y = (7 / 4) · 10 - 69 / 4

y = 1 / 4

x = 11

y = (7 / 4) · 11 - 69 / 4

y = 2

x = 12

y = (7 / 4) · 12 - 69 / 4

y = 15 / 4

x = 13

y = (7 / 4) · 13 - 69 / 4

y = 11 / 2

There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

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Answer:

Q is the point (3, 4).

Step-by-step explanation:

The formulae for the coordinates of a point (h, k) which divides a line  joining the points (x1, y1) and (x2, y2) in the ratio m : n is:

h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)

Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and

m = 5 and n = 2.

So here, for point Q:

h = (5*5) + 2*-2)/(2+5)

    = 21/7

     = 3.

k = (5*8 + (-6*2) / 7

   = 28/7

    = 4.

The addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power". option C

(1.38×10⁴) + (8×10³)

= (1.38 + 8) × 10^(4 + 3)

= 9.38 × 10^7

Options:

9.38×10⁴

2.18×10⁴

9.38×10^7

Therefore, the addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power".

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The correct options for the linear combinations of the vectors are given by:

A, B, C, D, E and F.

The span between two vectors is the set that contains all linear combinations between these two vectors.

Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:

k1u1 + k2u2

In which k1 and k2 are real numbers.

With k1 = 4 and k2 = -7, we get that option A is correct.

For option B, we have to see if it is possible to solve the following system.

The solution is k1 = k2 = 0, which are real numbers, hence option B is correct.

Both vectors u1 and u2 are part of the span, hence options D and F are correct. The size of the span is of infinity, hence option E is correct while option G is not.

The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.

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Answer:

(-1, -4)

Step-by-step explanation:

To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.

4-5 is -1

2-6 is -4

Put them together and we get (-1, -4) as our endpoint B.

Answer:

Step-by-step explanation:

(5+x)/2=2, (6+y)/2=1

for the x value

5+x=4

x=-1

then for the y value

6+y=2

y=-4

then your answer would be (-1,-4)

Answer:

3/8

change to an improper fraction

1 1/8=9/8

3/4 times 2 equals

6/8

9/8-6/8

3/8

Answer: I think the answer is 3/8 or it can be 5/8.

explanation: I hope this helps.

The solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

To find the solution to the inequality given, follow the steps explained below:

-5/2(3x - 2) < 6 - 2x [given]

-5/2(3x) -5/2(-2) < 6 - 2x [distribution property]

-15x/2 + 5 < 6 - 2x [simplify]

-15x/2 + 5 - 5 < 6 - 2x - 5 [subtraction property]

-15x/2 < 1 - 2x

-15x/2 + 2x < 1 - 2x + 2x [addition property]

-11x/2 < 1 [simplify]

-11x/2 × 2 < 1 × 2 [multiplication property]

-11x < 2

-11x/-11 > -2/11 [division property]

x > -2/11

Note: the inequality sign would change if we are dividing both sides by a negative number.

Therefore, the solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.

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Answer:

Less; $25.90 less than at the beginning of the week

Step-by-step explanation:

162-(63.50+23.25+26.45)=162-113.20=48.80

48.80+87.30=136.10; 162>136.10

162-136.10=Δ$25.90

$25.90 less

Answer:

345 pounds

Step-by-step explanation:

Each bucket dumps out 8 ounces of sand

8 ounces = 1/2 pound

So total sand dumped 10 times  = 1/2 x 10 = 5 pounds

Originally sandbox had 7 x 50 = 350 pounds of sand

Sand left in box = 350 - 5 = 345 pounds

Answer:

The answer to the question is 35 degrees

The HHT is more likely to appear first with a probability of 2/3.

The probability is an estimation of the likelihood that an event will occur. It assesses the event's certainty.

The formula for probability is given as;

P(E) = Number of Favourable Outcomes/Number of total outcomes.

Now according to the given question;

Only the second and third flips in the sequence matter. We understand the first flip is an H, and we're not interested in sequences that begin with T.

Lets start with the given format;

H _ _

If we get an HH_, the game is over and HHT will surely win (regardless of the number of heads we get, the next T is an automatic win). If we get an HTT, the game is over.

If we get an HTH, the game is a tie, and we must restart it.

Thus,

P(HHT) = 1/2

P(HTT) = 1/4

P(Draw) = 1/4

P(HHT wins) = P(HHT) / [1-P(Draw)]

                     = (1/2) / (1-1/4)

P(HHT wins) = 2/3

Thus, the probability of occurrence of HHT has more chances with 2/3.

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Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105

First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:

Area of rectangle = Length x Width

Solving gives:
= 17 x 13

= 221 square foot

The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot

= 221 x 5

= $1,105

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Yes parallel line exist in spherical geometry. The radius or diameter and the tangent can be a pair of parallel line in spherical geometry

The tangent of the sphere refers to a line that make contact with only a point in the sphere. The tangent is perpendicular to the center and the radius can be drawn to be parallel to the tangent.

The radius refers to a line running from the center to an end of the circle. Two radius can be drawn say radius A and radius B. Radius A will be drawn perpendicular to the tangent and radius B drawn perpendicular to radius A.

The pair of lines tangent and radius B will be parallel to each other.

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Answer:

(a) 332

Step-by-step explanation:

Find 40% of 237

94.8, Round to 95

237 + 95 = 332

The value of (f.g) (x) is 2. Option B

A function can be defined as an expression or rule that explains the relationship between an independent and dependent variable.

Given the functions;

To determine (f.g) (x), we need to know that it is a composite function

We substitute the value of g(x)  = 2 as x in f(x)

But we have f(x) = x

Then,

(f.g) (x) = 2

Thus, the value of (f.g) (x) is 2. Option B

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Answer:

54

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then

[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]

= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]

= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3

= 6 × 9

= 54

[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \times {3}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \times 9[/tex]

[tex]\qquad \sf  \dashrightarrow \:18[/tex]

The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;

a. The outer perimeter equation is presented as follows;

18•x + 8 = 53 inches

b. The scale factor required for the enlargement of the picture is 2.5

The dimensions of the photo = 4 × 5 inch

Width of the frame = 1 inch

Outer perimeter of the frame = 53 inches

The width of the inside of the picture frame = 4•x

The height of the inside of the picture frame = 5•x

a. The equation for the outer perimeter of the picture frame is therefore;

2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53

Which gives;

2 × (4•x + 2) + 2 × (5•x + 2) = 53

8•x + 4 + 10•x + 4 = 53

A simplified equation for the outer perimeter of the picture frame is therefore;

b. Solving the above equation, we have;

18•x + 8 = 53

18•x = 53 - 8 = 45

18•x = 45

Therefore;

x = 45 ÷ 18 = 2.5

x = 2.5

The width and height of the picture frame are therefore;

Width = 4•x = 4 × 2.5 = 10

Height = 5•x = 5 × 2.5 = 12.5

Which gives;

Width = 10 inches

Height = 12.5 inches

The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;

sf = 12.5/5 = 2.5

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