If the hypotenuse of a 30-60-90 triangle is 20, what is the length of the longer leg? Giveanswer in exact form - NO decimal answers.

The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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Ten to fifty is the range of the scores. The most frequent result is a 10 with a right-skewing bias.

Probability histogram

The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.

The distribution is skewed to the right because the highest bar in the histogram is to the left and there is a tail of lower bars to its right.

The most frequent score is 10 due to the fact that the top bar in the histogram is centered at 10.

The result is:

Ten to fifty is the range of the scores.

The most frequent result is a 10 with a right-skewing bias.

Ten to fifty is the range of the scores.

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Answer:

\(x^2 - 6x + 10\) or in general: \(a(x^2 - 6x + 10)\) where "a" is any constant real number except zero.  

Step-by-step explanation:

If we're given a complex root of a polynomial to be: \((a+bi)\text{ or }(a-bi)\), then we know that its conjugate is also a root of the polynomial: \((a-bi)\text{ or }(a+bi)\).

So since we're given the root: \((3+i)\), then we know that its conjugate: \((3-i)\) is also a root. Thus we have two roots so far.

The Fundamental Theorem of Algebra simply states that any polynomial, with degree "n", will have "n" roots, which can consist of both real and imaginary solutions.

So let's say I have a polynomial: \(x^6+3x+2=0\), this has 6 roots, according to the Fundamental Theorem of Algebra, since the degree of the polynomial is 6 (remember the degree is simply the variable with the highest degree)

Since we already have two roots, and a quadratic function has a degree of two, we know that these are all the roots the quadratic has, since the Fundamental Theorem of Algebra states that a quadratic will only have 2 roots.

We can generally express any polynomial in factored form, that is: \(a(x-b)(x-c)(x-d)...=y\)

where "b", "c", and "d", and so on... are zeros of the function. This aligns with the behavior of zeros, since if we plug any of them into the function, then one of the factors will become zero, and since zero times anything is zero, well the entire thing is zero.

For example if I plug in "b", which is zero we get: \(a(b-b)(b-c)(b-d)...=y\implies a(0)(b-c)(b-d)=y\implies 0=y\)

this is since plugging in zero, makes the factor: \(x-b\) equal to zero, making the entire thing zero.

One last thing to mention is the "a" value in front which just generally determines the stretch/compression of the polynomial.

So with this information, we can write a polynomial:

\(a(x-(3+i))(x-(3-i))\)

From here let's distribute the negative sign:

\(a(x-3-i)(x-3+i)\)

Now this may look a bit tough to distribute, but you may notice a pattern here, we have a difference of squares. It may not be obvious, but if we make one substitution, let's say: \(u=x-3\), then we get the equation

\(a(u-i)(u+i)\)

The difference of squares is expressed as: \(a^2 - b^2 = (a-b)(a+b)\), so our expression will expand out into:

\(a(u^2 - i^2)\)

The substitution was just to make things a bit more clear, but let's just substitute x-3 back into the equation.

\(a((x-3)^2 - i^2)\)

From here, we know that i^2 is simply -1, since: \(\sqrt{-1} = i, \text{ so }i^2 = -1\)

We can also easily expand out the polynomial using FOIL

\(a((x^2 - 6x + 9) -(-1))\\a(x^2 - 6x + 9 + 1)\\a(x^2 - 6x + 10)\)

You may notice the "a value, and that's just a constant, which determines the stretch/compression of the polynomial, and can be any real number, except for zero since that will make the entire thing zero regardless of what x is. For the sake of simplicity, let's just write this to be 1.

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;

A. 5.00x - 2.25x = 5000

We are told the materials costs $2.25 per purse.

She sells the materials for $5 each.

If the number of materials she purchased was x, it means that;

Selling price - Cost price = 5.00x - 2.25x

Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.

Since the formula for profit is;

Profit = Selling Price - Cost Price

Then, we will have;

5.00x - 2.25x = 5000

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Answer:  5.00x - 2.25x = 5000

Step-by-step explanation:

Answer:

50h(5h - 2)

Step-by-step explanation:

Open up all the parenthesis on each answer

only the first one is correct

Answer:

50h(5h-2)

Step-by-step explanation:

Solution given

250h² - 100h

50*5*h*h-50*2*h

taking common

50*h(5*h-2)

50h(5h-2)

here taking common and keeping remaining on bracket

50h(5h-2)

Answer:

111

Step-by-step explanation:

we can get by finding the difference of 180 degree minus 69 degree

x+69 degree = 180 degree

x= 180 degree-69 degree

x=111 degree

According to the circle graph, the percentage of the Simpsons’ annual expenses that is Federal taxes is 34%

A circle graph also known as pie chart has a shape of a circle and each section are represented in percentages or degrees

From the question, we have:

Federal taxes = 24%

State/local taxes = 10%

Housing and household = 23%;

Food = 6%

Medical care = 8%

Transportation = 11%

Recreation = 3%

Clothing = 5%

Other = 10%

The above means that the percentage of the Simpsons’ annual expenses that is Federal taxes will be:

= 24% + 10%

= 34%

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Answer:

\(\frac{5\sqrt{5} }{3}\)

Answer:

\(\frac{5\sqrt{5}}{3}\)

Step-by-step explanation:

Extend DC to F. Triangle FAE and DBE are similar with ratio 5:4. Thus, AE=(5AB)/9, AB=\(\sqrt{3^2+6^2} =\sqrt{45} =3\sqrt{5}\) and \(AE=\frac{5(3\sqrt{5})}{9}\) which can be simplified to \(\frac{5\sqrt{5}}{3}\).

Hope this helped! :)

The value of angle RPQ in the circle is 115 degrees.

The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.

If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The angle is 115°.

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The item most likely to weigh 2 kilograms is a roast chicken.

The size, breed, and any other ingredients or stuffing used can all affect the weight of a roast chicken. Weights of roast chickens can range from petite ones weighing less than 1 kilogram to larger ones weighing more than 2 kilograms.

The other things that we have there would either weigh less than 2 Kg such as a tea bag or much more than 2 Kg such as a horse. The egg and the tea a very light and would be less than 2 Kg in weight while the bag and the horse would be above 2 Kg in weight.

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Therefore, the equivalent expression with a denominator of (x-6) is: (-8 / (x-6)).

An expression is a mathematical phrase that can contain numbers, variables, and operators. It can represent a value or a calculation, but it does not have an equal sign. Expressions can be simple or complex and can involve arithmetic operations, such as addition, subtraction, multiplication, division, and exponentiation, as well as functions, logarithms, trigonometric functions, and more.

Here,

To write the rational expression (8/6-x) as an equivalent expression with a denominator of (x-6), we need to multiply both the numerator and denominator by a suitable expression that will result in the denominator of (x-6).

To do this, we can use the difference of squares identity:

a ²- b² = (a + b)(a - b)

In this case, we can rewrite the denominator of (6-x) as (-(x-6)), which is in the form of the difference of squares with a = 6 and b = x. So we can rewrite the expression as:

8 / (6 - x) = -8 / (x - 6)

Now the denominator is in the form of (x-6).

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Answer:

30 and 60 degrees

Step-by-step explanation:

30 and 60 are complementary angles. 60 is two times the measure of its complementary angle, or 30. 60+30=90.

Complementary angles are angles that add up to 90 degrees.

Angle one = x

Angle two = 2x

2x + x = 90 degrees

Combine like terms.

3x = 90 degrees.

Divide both sides by 3

x = 30

Angle one = x = 30 degrees

Angle two = 2x = 2(30) = 60 degrees.

Answer:

\(y-8=-\frac{1}{2}(x-(-6))\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we need to find -1/2.

Using point-slope form, the equation is \(y-8=-\frac{1}{2}(x-(-6))\).

Answer: The inequality is: n ≥ 36/37

Step-by-step explanation:

Let's solve your inequality step-by-step.

n − 5n + 6 ≥ −7(5n−6)−6

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

Step 1: Simplify both sides of the inequality.

−4n + 6 ≥ −41n + 42

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

Step 2: Add 41n to both sides.

−4n + 6 + 41n ≥ − 41n+ 42 + 41n

37n + 6 ≥ 42

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

Step 3: Subtract 6 from both sides.

37n + 6 − 6 ≥ 42 − 6

37n ≥ 36

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

Step 4: Divide both sides by 37.

37n/37 ≥ 36/37

n ≥ 36/37

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

Answer:

n ≥ 36/37

Source: https://www.mathpapa.com/calc.html?q=x+y%3D7%2C%20x+2y%3D11

,  Hope this helps :)

Have a great day!!

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

The domain of exponential functions is all real numbers. The range is all real numbers greater than zero. The line y = 0 is a horizontal asymptote for all exponential functions. When a > 1: as x increases, the exponential function increases, and as x decreases, the function decreases.

the probability is 7/15

Step-by-step explanation:

because there are 7 girls and 8 boys

Answer:

Up to eight times

Step-by-step explanation:

\((30 - 13) \div 2 \\ 17 \div 2 = 8.5\)

Answer:

ZDM is not a name for the angle, 6 square units is the area, A the cylindar, 26 degrees

Step-by-step explanation:

Area of triangle is 1/2 base x height

116-90 = 26 degrees to angle ABC

The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m

is (3.84/8)

A function is defined as a relation between a set of inputs having one output each.

Given that, A marine biologist is studying the growth of a particular species of fish when the marine biologist concluded her study, the length of the fish was approximately 9.19 cm

A) For m = 0

f(0) = 5(1.07)⁰ = 5 cm

The length of the fish was approximately 9.19 cm.

m = 9

Domain = [0, 9]

Reasonable domain to plot the growth function = [0, 9]

B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm

C) average rate of change of the function f(m) from m = 1 to m = 9

For m = 1

f(1) = 5(1.07) = 5.35 cm

For m = 9

f(9) = 5(1.07)⁹ = 9.19 cm

Change in 9 - 1 = 8 months = 9.19 - 5.35 = 3.84 cm

average rate of change of the function f(m) from m = 1 to m = 9,

= (3.84/8)

= 0.48 cm per month

Hence, The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m is (3.84/8)

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Answer:

x=5.09 seconds (times at max)

Step-by-step explanation:

Answer: Option 3

Step-by-step explanation:

The graph is an arrow pointing left with an open circle at x=-12.

The solution to the inequality x < -12 is (-∞, -12) or {x | x < -12}.

Option C is the correct answer.

We have,

The solution to the inequality x < -12 represents all the values of x that are less than -12.

In other words, it is the set of real numbers that are to the left of -12 on the number line.

To represent this solution set, you can use interval notation or set notation.

In interval notation, the solution would be written as (-∞, -12), where the parentheses indicate that -12 is not included in the solution set, and the symbol "∞" represents negative infinity, indicating that the values extend indefinitely to the left.

In set notation, the solution set can be expressed as {x | x < -12}, where the vertical bar "|" means "such that" and the inequality condition x < -12 specifies the values of x that satisfy the inequality.

Therefore,

The solution to the inequality x < -12 is (-∞, -12) or {x | x < -12}.

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Answer:

B.

Step-by-step explanation:

If he makes 70% then 70% as a decimal would be 0.700 which is B

Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability that he makes at least two of the free throws is 0.0700.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head when a coin is tossed is 1/2

We have,

Each free throw is independent of the other.

Percentage of making free throws = 70%

The probability that he makes at least two of the free throws.

= 70%

= 70/100

= 0.07

This can be written as 0.0700.

Thus,

The probability that he makes at least two of the free throws is 0.0700.

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Answer:

- 2 - 3 is the same thing as -2 + -3. This is because taking away 3 is the same thing as adding - 3. -2 -3 is just a more simplified version of -2 + -3.

Hope this helps!

Answer:

Step-by-step explanation:

Using the formula for calculating the energy used up during the process;

Energy used up = Amount of CO₂ created.

Energy used up in the process = Power * Time.

Given Parameters:

Power = 3,030Watts

Converting to Kilowatts, power = 3030/1000 kW

Power (in kW) = 3.03kW

Time taken = 34 minutes

Converting to hour;

Since 60 minutes = 1hr

34minutes = (34/60)hr

34minutes = (17/30)hr

Required:

Energy used up = 3.03 * 17/30

Energy used up = 51.51/30

Energy used up = 1.717 kW/hr

Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.

Answer:

NO. It sounds terrifying, and nearly deadly with the lack of oxygen..all the pollution from things like cars and factories, the littering, the deforestation, the animals that are either endangered or extinct.

Step-by-step explanation:

Answer:

x = 100

Step-by-step explanation:

All you need is contained in the sheet attached

Answer:

x = 100

Step-by-step explanation:

3 log2(x) - 2 log2(5x) = 2

We know that a log(c) = log c^a

log2(x)^3 - log2(5x)^2 = 2

log2(x^3) - log2(25x^2) = 2

We know that log a - log b = log a/b

log2(x^3 /25x^2) = 2

Simplify

log2(x /25) = 2

Raise each side to  base 2

2^log2(x /25) = 2^2

x/25 = 4

Multiply each side by 25

x = 4*25

x = 100

The distance it will take to drive from Toronto to buffalo (distance between Toronto and buffalo is 154km) is 1.75 hours.

We are given that;

distance = 154 km speed = 88 km/hr

Now,

we need to use the formula:

time = distance / speed

where time is in hours, distance is in kilometers, and speed is in kilometers per hour.

Plugging these values into the formula, we get:

time = 154 / 88 time ≈ 1.75

Therefore, by speed the answer will be 1.75 hours.

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