A total of 376 tickets were sold for the school play. They were either adult tickets or student tickets. There were fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answer:

This is a ssa situation, no triangle is possible.

Step-by-step explanation:

"SSA" means "Side, Side, Angle".

In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.

In triangle ABC:

Given:

The angle that is between the sides a and b is angle C.

Therefore, as angle A is not the angle between the given sides, ΔABC is an SSA triangle.

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 44^{\circ}}{12.6}=\dfrac{\sin B}{19}\)

\(\implies \sf \sin B=\dfrac{19\sin 44^{\circ}}{12.6}\)

\(\implies \sf \sin B=1.0475007...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, although this is an SSA situation, no triangle is possible.

Answer:

Yes

Step-by-step explanation:

Congruent means equivalent so if <6 is = to <3 then due to <3 being = to <1 <6 also has to be = to <1.

The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is  y = -7/5(x) -53/5

Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)

The slope-intercept form of a straight line is:

y = mx + c

where m is the slope and c is the y-intercept

For perpendicular case:

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₁ x m₂ = -1

-7/5 x m₂ = -1

m₂= 5/7

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = 5/7 (-4) + c

-5 = -20/7 + c

c = -15/7

Thus, the equation of the line is y = 5/7(x) -15/7

For parallel case:

When the two lines are parallel, they have equal slope i.e. m₁ = m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₂= -7/5

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = -7/5(-4) + c

-5 = 28/5 + c

c = -53/5

Thus, equation of the line is y = -7/5(x) -53/5

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a) The point (1, 15) is at 3 / 4 of the way from points R to S.

b) The point (- 3, 7) is at 1 / 4 of the way from points R to S.

In this problem we must determine the line segment ratio associated to a given point within a line segment, this can be found by using the line segment formula:

Q(x, y) = R(x, y) + k · [S(x, y) - R(x, y)]

Q(x, y) = (- 5, 3) + k · [(3, 19) - (- 5, 3)]

Q(x, y) = (- 5, 3) + k · (8, 16)

Q(x, y) = (- 5 + 8 · k, 3 + 16 · k)

Now we proceed to find each ratio:

Q(x, y) = (1, 15)

(1, 15) = (- 5 + 8 · k, 3 + 16 · k)

k = 3 / 4

The point (1, 15) is at 3 / 4 of the way from points R to S.

Q(x, y) = (- 3, 7)

(- 3, 7) = (- 5 + 8 · k, 3 + 16 · k)

k = 1 / 4

The point (- 3, 7) is at 1 / 4 of the way from points R to S.

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Answer:

y=2x+6

Step-by-step explanation:

Answer:

∠b=82°

Step-by-step explanation:

143°=∠c+∠b (exterior angle property)

143°=61°+∠b

∠b=143-61

∠b=82°

Answer:

g = -0.5

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

Answer:

g = -0.5 or -1/2

Step-by-step explanation:

-10(g – 6) = 65 : apply distributive property

(-10 • g) + (-10 • -6) = 65 : multiply

-10g + 60 = 65 : apply property of equal subtraction

-10g + 60 – 60 = 65 – 60 : subtract

-10g = 5 : apply property of equal division

-10g ÷ -10 = 5 ÷ -10 : divide

g = -0.5

In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

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After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer: It’s B.

Step-by-step explanation: Got it on edge

Answer:

Answer: It’s B.

Got it on edge

Step-by-step explanation:

Got it right on edge

Answer:

option c : k = 8

Step-by-step explanation:

Given ( x+ 2 ) is a factor of f(x) , that is f( -2 ) = 0

\(f(x) = x^3 -9x^2 + kx + 6 0\\\\f(-2) =0\\\\(-2)^3 - 9(-2^2) + k (-2) + 60 = 0\\\\-8 - 36 -2k + 60 = 0\\\\-2k + 16 = 0\\\\-2k = -16\\\\k = \frac{-16}{-2} = 8\)

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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Answer:

Sorry, I don't exactly know what you mean by a b c d, however the graph of y=|x|-5 should be two rays with slopes of 1 and -1, meeting at the point (0,-5)

The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

can't understand the language

Answer:

I this 500$

Step-by-step explanation:

Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

Answer:

3  3/11

Step-by-step explanation:

The best way to divide fractions is to not divide them at all.

Convert both mixed numbers into improper fractions.

4 times 2 is 8

8 + 1 is 9

I have 9/2 halves. Don't forget to put the negative back in.

1 times 8 is 8

8 + 3 is 11

I have 11/8 eighths. Dont forget to put the negative back in.

You will end up with

-9/2 ÷ -11/8

Flip the second fraction and change the division sign to a multiply sign

-9/2 × 8/-11

Multiply the numerators together and the denominators together

-9 x 8 and 2 x -11

-72 / -22

Dividing a negative by a negative will give us a positive

72 / 22

Simplify by dividing the top and bottom by 2

36/11

We cannot simplify further. You can answer like this or convert back into a mixed number.

There are 3 sets of 11 in 36, with 3 left over

3  3/11

Answer:

\( = - (5 \frac{3}{5} )\)

Step-by-step explanation:

\( - 4 \frac{1}{2} \div ( -1 \frac{3}{8} )\)

\( = - 4 \frac{1}{2} \div -1 \frac{3}{8} \)

\( = \frac{(2 \times ( - 4) + 1)}{2} \div \frac{(8 \times ( - 1) + 3}{8} \)

\( = \frac{ - 7}{2} \div \frac{ - 5}{8} \)

\(= \frac{ - 7}{2} \times \frac{8}{ - 5} \)

\( = \frac{ (- 7 )\times 8}{2 \times ( - 5)} \)

\( = \frac{ - 56}{( - 10)} \)

\( = - (5 \frac{6}{10} )\)

\( = - (5 \frac{3}{5} )\)

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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The cost of packaging the box of chocolates per weight unit is;  ¹/₄x²/(x + 2)

We are given the cost of packing the box as;

C(x) = ¹/₄x²

where;

x is the number of chocolates

We are told that a box can never have fewer than 3 chocolates.

Now, the weight of a box of chocolates is given by; W(x) = x + 2

Thus, cost per unit weight is;

C(x)/W(x) = ¹/₄x²/(x + 2)

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Answer:

A =625 ft^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

100 =4s

Divide each side by 4

100/4 = 4s/4

25 = s

A = s^2 for a square

A = 25^2

A =625

The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵

Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y

Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²

Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³

Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴

Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)

Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

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Answer:

\(A)58\)

Step-by-step explanation:

\([Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\\)

\(Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58\)

\(Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58\)

Answer:

1 cause its going to be one sometimes

Answer:

x = 9

Step-by-step explanation:

1+1 = x - 7

2 = x - 7

Add 7 to both sides to isolate the x:

2 + 7 = x - 7 + 7

9 = x

Hope this helps!

The z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

The mean of the set of data is equal to the sum of all the quantities in the data, and divide by the no of quantities.

Given:

The standard deviation, d = 182.56,

The mean, m = 265.95,

The observation value, X = 235.90

Calculate the z score by the following formula given below,

Z = (X - m) / d,

Here, Z is the Z score,

Z = 235.90 -  265.95 / 182.56

Z =  -0.165

Therefore, the z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

C

Step-by-step explanation:

I took the test and got it right

Answer:

C: 75 degrees

Step-by-step explanation:

180-155=25 which makes the angle to the other side of angle x

80+25=105

180(full angle measurement of triangle)-105=75

Btw I also had this on my quiz and got it right

Answer:

d = 24

Step-by-step explanation:

1.25 = 3d/96 + 2d/96

1.25 = 3d + 2d / 96

1.25 = 5d/96

96 • 1.25 = 96 • 5d/96

96 • 1.25 = 5d

120 = 5d

120/5 = 5d/5

d = 24