What is the measure of ∠BCD? Enter your answer in the box. ° quadrilateral A B C D with side A B parallel to side D C and side A D paralell to side B C. angle B is 103 degrees.

Answer:

75 ft

Step-by-step explanation:

Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.

For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.

[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]

So putting in the given values to get:

[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]

Therefore, the value of x is the closest to 75 ft.

(1, 1), (4, -25)

You can evaluate the function to see.

f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2

f(1) = -3^(1-1) +2 = -1 +2 = 1

f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0

f(4) = -3^(4 -1) +2 = -27 +2 = -25

_____

Or, you can graph the points and the curve.

Answer:

(1, 1), (4, -25)

Step-by-step explanation:

Each of these sequences goes into the classification box above it.

If the difference of terms is a constant, it is arithmetic.

... (3 -(-1)) = 4 = (7 -3), so the first sequence is arithmetic

If the ratio of terms is a constant, it is geometric.

... 12/36 = 1/3 = 4/12, so the second sequence is geometric

The third sequence has neither constant differences nor constant ratios, so is neither arithmetic nor geometric.

Answer:

as discriminant = 9, it has two real solutions.

Step-by-step explanation:

for eqn ax^2 + bx + c, discriminant = b^2 - 4ac

y = 4x^2 - 5x + 1

discriminant = (-5)^2 - 4(4)(1)

= 25 - 16

= 9

as discriminant > 0, it has two real solutions.

Answer:

Discriminant = 9 and the equation has two real solutions

Step-by-step explanation:

For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.

If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.

In this case, y = 4x^2 - 5x + 1.

So its discriminant = -5^2 - 4*4*1

= 9 so it has two real solutions.

Answer:

d  31 degrees

Step-by-step explanation:

We can use the formula

<C = 1/2 (arc AE - arc BD)

Let substitute in what we know

ARC AE = 120

ARC BD = 58

<C = 1/2 (120 - 58)

<c = 1/2(62)

<c = 31

The mode is the number in the set that appears the most.

In the given data set, the number 45 is listed twice while all the other numbers are only listed once.

The mode is 45.

Answer:

45

Step-by-step explanation:

The value which appears most often or has the highest frequency in a data set is said to be the mode.

Here we are given the following data set:

{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}

For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.

Answer:

3

Step-by-step explanation:

if the length and width is 3, 3 times 3 is 9

Answer:

2<x<∞

Step-by-step explanation:

The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.

The arrow goes to positive infinity. Which gives us our upper or left bound.

Answer:

r>(greater than or equal to)2.5

Step-by-step explanation:

Answer: y=54

Step-by-step explanation: so 24/4 is 6 soooo 9*6=54 ez

Answer:

y =54

Step-by-step explanation:

We can use the equation y =kx

If we know y and x we can solve fork

24 = k*4

24/4 = k

6 =k

y = 6x

Substitute in 9

y =6*9

y =54

Answer:

A is the right one

Step-by-step explanation:

it is right on edge

We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

BCD is a right angle triangle

We have to find the angle B from the triangle

BD is the hypotenuse which is √89

DC is the opposite side of angle B

We can find angle B by using sine function.

Or we can find the length of BC by using pythagorean theorem

then find the tanB function

tanB=8/BC

Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

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Answer:

35 x 10.6, 140 x 2.65 and 371 x 1

Step-by-step explanation:

Answer:

February

Step-by-step explanation:

February is colder by 7°F

-9 - 7 = -16

~

Answer:February

Step-by-step explanation:

If you see the number line below -16 is more far than -9

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

' ' '

-16 -9 0

[tex]\dfrac{13x+10}{2x^2-5x-25}[/tex]

Multiply the first fraction by (x-5)/(x-5) and the second by (2x+5)/(2x+5). Now, you have both fractions with the common denominator (2x+5)(x-5).

[tex]\dfrac{3}{2x+5}+\dfrac{5}{x-5}=\dfrac{3(x-5)}{(2x+5)(x-5)}+\dfrac{5(2x+5)}{(2x+5)(x-5)}\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}=\dfrac{3x-15+10x+25}{2x^2-5x-25}\\\\=\dfrac{13x+10}{2x^2-5x-25}[/tex]

See the attachment

The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.

The function is linear for x ≥ 2, so matches selection C, not A.

Answer:

A=6

B=8

Step-by-step explanation:

The hypotenuse QR is twice the length of BC, so PQ will be twice the length of AB, 2·3 = 6; and PR will be twice the length of AC, 2·4 = 8.

In similar triangles PQR and ABC:

Side PQ (a) is 40/3 units.

Side PR (b) is 50/3 units.

To find the unknown side lengths in similar triangles PQR and ABC, we can use the properties of similar triangles. Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.

In this case, we have triangles PQR and ABC:

PQR:

RQ = 10

QP = a

RP = b

ABC:

AB = 3

AC = 4

BC = 5

Since the triangles PQR and ABC are similar, the ratios of corresponding sides must be equal. Specifically, the ratio of the sides in triangle PQR to the sides in triangle ABC should be the same. We can set up proportions to solve for a and b:

RQ / AB = QP / AC = RP / BC

10 / 3 = a / 4 = b / 5

Now, we can solve for a and b separately.

From the first part of the proportion:

10 / 3 = a / 4

Cross-multiply:

10 * 4 = 3 * a

40 = 3a

Now, divide by 3 to solve for a:

a = 40 / 3

From the second part of the proportion:

10 / 3 = b / 5

Cross-multiply:

10 * 5 = 3 * b

50 = 3b

Now, divide by 3 to solve for b:

b = 50 / 3

So, the unknown side lengths are:

a = 40/3

b = 50/3

Therefore, in similar triangles PQR and ABC:

Side PQ (a) is 40/3 units.

Side PR (b) is 50/3 units.

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Answer:

9

Step-by-step explanation:

Otf the 15 that have a view of the river, 6 have both selections.

The remaining 9 only have a view of the river.

x³y⁴

The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...

Find the highest power of each of the factors, and multiply those together.

The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...

... x³y⁴

_____

Then the two fractions are ...

... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)

Answer:

None, the answer will be the same

Step-by-step explanation:

Answer:

a. Infinitely many solutions

Step-by-step explanation:

The given equations are  2x - y = 3

4x = 6 + 2y

We can use substitution method to solve these system of equations.

2x - y = 3

y = 2x - 3

Now plug in y = 2x - 3 in the second equation, we get

4x = 6 + 2(2x - 3)

4x = 6 + 4x  - 6

4x = 4x

Here we get infinitely many solution.

Both the equations are the same.

Thank you.

Answer:

The side lengths are 4, 5, and 6.

Step-by-step explanation:

Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.

It isn't clear which point is the midpoint of what segment. If it is true that ...

then ...

Answer:

4, 5, 6

Step-by-step explanation:

(x, y) = (6, -6)

Divide the first equation by 2 to get equal and opposite coefficients for x.

... -2x -y = -6

Add this to the second equation to eliminate x.

... (2x +4y) +(-2x -y) = (-12) +(-6)

... 3y = -18 . . . . . . . . simplify

... y = -6 . . . . . . . . . . divide by 3

Substitute this vaue into any of the equations to find x. We choose to use the reduced first equation above.

... -2x -(-6) = -6

... -2x = -12 . . . . subtract 6

... x = 6 . . . . . . . divide by -2

The solution to the system is (x, y) = (6, -6).

We can use a modified form of the Pythagorean Theorem to find the length of  x, also known as side b.

Pythagorean Theorem:

a^2 + b^2 = c^2

We can fill in the values of a^2 and c^2, and then solve for b.

14^2 + b^2 = 25^2

196 + b^2 = 625

Subtract 196 from both sides.

b^2 = 429

√ both sides.

b = 20.7

To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.

To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.

The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.

Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.

The Diameter of Hydrogen Atom in Scientific Notation is :

✿  1.06 × 10⁻¹⁰ Meters

Answer:

Step-by-step explanation: I just solve it.

Answer:

102 ≤ heart rate ≤ 183.6

Step-by-step explanation:

... lower limit ≤ heart rate ≤ upper limit

Put 16 where "a" is and do the arithmetic.

... lower limit = 0.5(220 -16) = 102

... upper limit = 0.9(220 -16) = 183.6

Then the inequality is ...

... 102 ≤ heart rate ≤ 183.6

_____

Comment on the problem

There is nothing to "solve" here. One only needs to evaluate the limits.

In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.

Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.

The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).

For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.

Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.

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1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.

2. To find the inverse of a function, swap x and y, then solve for y.

... x = 3y

... x/3 = y . . . . . matches f(x) = x/3

3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)

4. See 2.

... x = 3(y -2)³

... (x/3) = (y -2)³ . . . . divide by 3

... ∛(x/3) = y -2 . . . . .take the cube root

... 2+∛(x/3) = y . . . . .add 2

... f(x) = 2+∛(x/3) . . . . is the inverse

5. See 2.

... x = 2y -3

... x+3 = 2y . . . . . add 3

... (x+3)/2 = y . . . .divide by 2

... f(x) = (x+3)/2 . . . .  is the inverse

A composite function is the combination of multiple functions.

The correct answers are:

1. Test for inverse function

To test if two functions are inverse of one another, we simply find their composites.

Assume the functions are g(x) and h(x).

We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]

If they are equal, then both functions are inverse functions

2. Inverse of f(x) = 3x

Rewrite as:

[tex]y = 3x[/tex]

Swap y and x

[tex]x = 3y[/tex]

Make y the subject

[tex]y = \frac x3[/tex]

Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]

3. True statements

A function has unique ordered pairs; so, it will pass the vertical line test.

Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.

Hence;

(b) All answers are correct

4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]

Rewrite as:

[tex]y = 3(x - 2)^3[/tex]

Swap x and y

[tex]x = 3(y - 2)^3[/tex]

Solve for y: Divide both sides by 3

[tex](y -2)^3 = \frac x3[/tex]

Take cube roots of both sides

[tex]y -2 = \sqrt[3]{\frac x3}[/tex]

Add 2 to both sides

[tex]y =2 + \sqrt[3]{\frac x3}[/tex]

Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]

5. The inverse of [tex]f(x) =2x - 3[/tex]

Rewrite as:

[tex]y =2x - 3[/tex]

Swap x and y

[tex]x =2y - 3[/tex]

Solve for y: Add 3 to both sides

[tex]2y = x + 3[/tex]

Divide both sides by 2

[tex]y = \frac{x + 3}{2}[/tex]

Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]

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6/100 = 0.06

43/100 = 0.43

3/10 = 0.3

23/1,000 = 0.023

Hope this helps!

Final answer:

To convert fractions to decimals, divide the numerator by the denominator and combine with any whole number for mixed numbers, resulting in 0.06, 0.43, 0.3, and 4.023 respectively for the given fractions.

Explanation:

The question asks to change fractions to decimals. Here are the step-by-step conversions:

a. 6⁄100: This fraction means 6 divided by 100, which is 0.06.

b. 43⁄100: Similarly, 43 divided by 100 is 0.43.

c. 3⁄10: Dividing 3 by 10 gives you 0.3.

d. 4 23⁄1,000: For the mixed number, you have the whole number 4 and the fraction 23⁄1,000. The fraction part is 23 divided by 1,000, which is 0.023. So, you combine the whole number and the decimal to get 4.023

Converting fractions to decimals involves dividing the numerator by the denominator and adding any whole number part if it's a mixed number.

Answer:

About 2614 years.

Step-by-step explanation:

We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:

[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]

and we can solve for t:

[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]

The estimated age of the bird skeleton is 2614 years.

Answer:

Step-by-step explanation:

The distance to the lookout is the sum of distances before and after the rest stop:

... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi

The distance from the lookout is 1/2 mile shorter, so is ...

... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi

Then the total hike is ...

... total distance = "to" distance + "from" distance

... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi

... total distance = 7 mi

The water each hiker will bring is ...

... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal

Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.

First, we need to determine the total distance each hiker will travel:

The return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:

Summing up the distances:

Calculating Total Water Needed:

Each hiker brings 1/4 gallon of water per mile:

Thus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.

To find a1, put 1 in the given equation and evaluate.

... a1 = -3·1 +1

... a1 = -2

Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...

... a[n] = a[n-1] - 3