Which mathematical statement is missing?

YZ/BC=6/3
∠B≅∠Y
BC/YZ=6/3
∠B≅∠Z

a. The initial height of the ball at time = 0 is 2.0 meters.

b. The ball is at the maximum height at 2.05 seconds.

c. The maximum height of the ball is 23.01 meters.

d. It took the ball 4.20 seconds to hit the ground.

Based on the information provided, we can logically deduce that the height (h) in meters, of this ball above the​ ground is related to time (t) by the following quadratic function:

h(t) = -5t² + 20.5t  + 2

Part a.

In order to determine the initial height of the ball, we would substitute t = 0 as follows;

h(t) = -5t² + 20.5t  + 2

h(0) = -5(0)² + 20.5(0)  + 2

h(0) = 2 meters.

Part b.

In order to determine the time when the ball is at the maximum height, we would differentiate the height function above as follows;

h(t) = -5t² + 20.5t  + 2

h'(t) = -10t + 20.5

10t = 20.5

t = 20.5/10

Time, t = 2.05 seconds.

Part c.

For the maximum height of the ball, we have:

h(t) = -5t² + 20.5t  + 2

h(2.05) = -5(2.05)² + 20.5(2.05)  + 2

h(2.05) = 23.01 meters.

Part d.

Next, we would determine the time when the ball would land by setting the height function to zero (0) as follows;

h(t) = -5t² + 20.5t  + 2

0 = -5t² + 20.5t  + 2

\(t = \frac{-(20.5)\; \pm \;\sqrt{20.5^2 - 4(5)(-2)}}{2(5)}\)

Time, t = 4.20 seconds.

Note: The graph above isn't a correct representation of the height function h(t) = -5t² + 20.5t  + 2.

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Applying the Trapezoid Midsegment Theorem, a. GK = 16 b. x = 10

a. HJ = 40

PQ = 28

PQ = 1/2(HJ + GK)

28 = 1/2(40 + GK)

56 = 40 + GK

GK = 56 - 40

GK = 16

b. HJ = 5x

PQ = 5x - 9

GK = 3x + 2

PQ = 1/2(HJ + GK)

5x - 9 = 1/2(5x + 3x + 2)

2(5x - 9) = 8x + 2

10x - 18 = 8x + 2

10x - 8x = 18 + 2

2x = 20

x = 10

In summary, applying the Trapezoid Midsegment Theorem, a. GK = 16 b. x = 10

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By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

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Answer:

i think 66.5 miles per hour

Step-by-step explanation:

Answer:

205.295 miles divided by 3.12 hours = 65.8 miles per hour

Step-by-step explanation:

We have the next functions

Function notation

Describe the transformation in words

we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit

1) We can determine by the table of values whether a function is a quadratic one by considering this example:

x | y 1st difference 2nd difference

0 0 3 -0 = 3 7-3 = 4

1 3 10 -3 = 7 11 -7 = 4

2 10 21 -10 =11 15 -11 = 4

3 21 36-21 = 15 19-5 = 4

4 36 55-36= 19

5 55

2) Let's subtract the values of y this way:

3 -0 = 3

10 -3 = 7

21 -10 = 11

36 -21 = 15

55 -36 = 19

Now let's subtract the differences we've just found:

7 -3 = 4

11-7 = 4

15-11 = 4

19-15 = 4

So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.

3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2

Answer:

1. 90

2. -12 +5

3. 83

Step-by-step explanation:

90 -12 + 5 = 83

Answer: -5 1/4

Step-by-step explanation:

After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.

Answer: b

Step-by-step explanation:

Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5

Step-by-step explanation:

i don't know the answer because l didn't do history not anything related to it

Answer:

42,996

Step-by-step explanation:

3*16+4*25+2*33=48+100+66=214

Answer:

Step-by-step explanation:

A is correct.  csc x = 1/ sin x

B is correct. y = sin x is a continuous funtion, for all real numbers, x

C is correct. The function y = sin x is a periodic function, and the cycle repeats every 2 radians (or 360°).

D is incorrect. It doesn't actually say anything false, but it does not accurately describe the behavior of the sine function. Look at the graphic I have attached. If you start at the origin, you see y = 0, then increases to 1 when x = π/2, then decreases back to zero when x = π, then decreases even more to -1 when x = 3π/2, then increases back up to zero when x = 2π.

Answer D leaves out the underlined part.

Hope this helps.

The incorrect statement is D because the location is not given.

It is a function that repeats itself in a particular time interval.

The sine function is the reciprocal function is cosecant.

The domain of the sine function is a real number.

The sine function cycle repeats every n radians.

Then the incorrect statement is D because the location is not given.

The graph is given below.

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The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

The function is given as:

y = 2∕3 cos(4∕7x) + 2.

The above function is a cosine function

A cosine function is represented as:

y = A cos(B(x + C)) + D

Where the period is

Period = 2π/B

By comparing the equations, we have

B = 4/7

Substitute B = 4/7 in Period = 2π/B

Period = 2π/(4/7)

Express as product

Period = 2π * 7/4

Divide 4 by 2

Period = π * 7/2

Evaluate the product

Period = 7/2π

Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

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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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Answer:   \(\frac{3}{4}\)c

Step-by-step explanation:

       If one pound of chicken costs c dollars, and we are writing an expression for 3/4 a pound of chicken, our expression will be the price (c) multiplied by how much chicken there is (3/4):

               3/4c

- In mathematics, an expression is a combination of numbers, variables (represented by letters), symbols, and operators, arranged in a way that represents some meaningful mathematical relationship or calculation.

- Expressions can be simple, like 3x or 4 + 5, or complex, like (3x + 4y) / (2x - 5y). Expressions are not equations or inequalities, as they do not contain an equal sign, but they can be used to build equations or inequalities.

The price of 1 pound of chicken is c dollars. To find the price of 3/4 pound of chicken, we can multiply the price of 1 pound by 3/4:

\(\begin{aligned}\sf Price\: of\: \dfrac{3}{4}\: pound\: of\: chicken& =\sf \dfrac{3}{4} \times c \\&=\boxed{\bold{\:\dfrac{3}{4}c\:}}\end{aligned}\)

Therefore, the expression for the price of 3/4 pound of chicken is 3/4c.

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Answer:

30 quarts= 0.8057 bushels

rounded to the nearest hundredths = 0.81

Answer:

5/8 is about 1/2. 2/6 is about 0.

Step-by-step explanation:  2/6 is about 0 because 2 is close to 0. If the numerator is  close to 0 and the denominator is not close to 0 then the benchmark is going to be 0. If the numerator is about half of the denominator then the benchmark is going to be 1/2. If the numerator and denominator is close to each other than the benchmark is going to be 1.

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

An equation is an expression that shows the relationship between two or more numbers and variables.

A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains

Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains

Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

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The probability that Natalie got at least two correct on the last three

true-or-false questions is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The sample space is 2. The question is either correct or wrong.  

The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4

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Answer:

\( - 6x = 3 {x}^{2} + 9 \\ 3 {x}^{2} + 6x + 9 = 0 \\ {x}^{2} + 2x + 3 = 0 \\ so \\ ether \: x = - 2 \\ or \: x = 1 \)

Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

Step-by-step explanation:

(a) Let's start with the first pool. It has 3650 liters of water. For every minute, 27 liters are being drained. Thus, we can write its equation as 3650 liters - 27 liters per minute = end amount of liters. If we write minutes as m, we can say 3650-27m is our expression. Similarly, for the second one, we have 4166-39m as our answer

(b) For this, we just have to make the two expressions equal, so

4166-39m = 3650-27m

The solution is:

(a)

Amount of water in the first pool (in liters) = 3650 liters - 27 liters per minute * x minutes

Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes

(b)

3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here, we have,

(a) With x being the minutes after which you want to calculate the amount of water in the pool, to calculate this amount of water you must subtract the water drained from the initial amount of water that the pool contains.

Knowing that, for example, the water from the first pool drains at a rate of 27 liters per minute, then after x minutes, the total water drained will be 27 liters per minute * x minutes. Then:

Amount of water in the first pool (in liters) =  3650 liters - 27 liters per minute * x minutes

Reasoning in the same way:

Amount of water in the second pool (in liters) = 4166 liters - 39 liters per minute * x minutes

(b)  Now want to know when the two pools would have the same amount of water.  If they have the same amount of water then you can express:

Amount of water in the first pool = Amount of water in the second pool

Replacing the expressions found in (a):

3650 liters - 27 liters per minute * x minutes= 4166 liters - 39 liters per minute * x minutes

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Answer:

360 degrees

Step-by-step explanation:

Remember that triangles have a sum of 180 degrees, and that quadrilaterals have 360 degrees.

You can either use that part, or actually solve for it.

The equation for the sum of the interior angles is:

\(sum=180(n-2)\)       [which "n" is the number of sides]

So, if we add in the number of sides to the equation, it changes to:

\(180(4-2)=180(2)\), which equals to 360 degrees.

The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

Answer:

-1

Step-by-step explanation:

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

4 - 2 + 3 - 6

2 + 3 - 6

5 - 6

-1

9514 1404 393

Answer:

  (x, y) = (4, 4)

Step-by-step explanation:

If you attempt to solve this by clearing fractions, you end up with an extraneous solution. Here, we'll solve the linear equations ...

  7a +4b = 5/4

  8b -14a = 3/2

where a = 1/(4x+3y) and b = 1/(4x-3y)

Dividing the second equation by 2 and adding the first, we have ...

  (7a +4b) +1/2(8b -14a) = (5/4) +1/2(3/2)

  8b = 8/4

  b = 1/4

Substituting into the first equation gives ...

  7a +4/4 = 5/4

  a = 1/28

__

Now, we can get back to solving for x and y.

  4x +3y = 1/a = 28

  4x -3y = 1/b = 4

  8x = 32 . . . . . . . . . add the two equations

  x = 4

  3y = 28 -4x = 28 -4(4) = 12 . . . . . use x in the equation for 'a'; rearrange

  y = 4 . . . . divide by 3

The solution to the system of equations is (x, y) = (4, 4).

_____

Additional comment

If you graph these equations, you find they describe hyperbolas that intersect at (0, 0) and (4, 4). The "solution" (0, 0) is extraneous, as both equations are undefined there.