Which equation is true when x = 3?



A. 8x = 28

B. 28 + x = 25

C. x/3 = 1

D. x - 19 = 16

The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².

Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.

Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:

A = median length × height

Given the following:

Area of trapezium = 25 × 8 = 200 cm².

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Answer:

y = 1/2x - 1

Step-by-step explanation:

The x value is divided by 2 and then has 1 subtracted from it.

also for future posts, put the question in the title that way people know what you need and can click if they know the answer.

Answer:

B. 16x^2 - 9

Step-by-step explanation:

(4x-3) x (4x+3) = 4x(4x) + 3(4x) - 3(4x) - 9 = 16x^2 - 9

Answer:

the answer is B

Step-by-step explanation:

good luck on your assignment

Answer:

(-1,-5)

Step-by-step explanation:

Graph both lines and find the intersection.

The structure of 12-crown-4 is shown below.

12-Crown-4, also known as lithium ionophore V and 1,4,7,10-tetraoxacyclododecane, is a crown ether with the chemical formula C8H16O4. It is a lithium cation-specific cyclic tetramer of the chemical compound ethylene oxide.

12-crown-4 combines with alkali metal cations, similar to other crown ethers. It has a strong selectivity for the lithium cation due to the cavity diameter of 1.2–1.5.

LiClO4 can be used as a template cation in a modified Williamson ether synthesis to create 12-Crown-4:

(CH2CH2O)4 + 2 NaCl + 2 H2O = (CH2OCH2CH2Cl)2 + (CH2OH)2 + 2 NaOH

In the presence of gaseous boron trifluoride, it can also result from the cyclic oligomerization of ethylene oxide.

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Answer:

The height of the ball is the same after 1.5 seconds and 3.5 seconds. ⇒ (A)

Step-by-step explanation:

The quadratic function is represented by a parabola

∵ The quadratic function modeling the height of a ball over time

∴ f(t) = at² + bt + c

→ t is the time in second, f(t) is the height of the ball after t seconds

∵ It is symmetric about the line t = 2.5

∴ The x-coordinate of its vertex is 2.5

→ That means the average of the x-coordinates of any two

   opposite points belong to f(t) is 2.5

∵ The average of 1.5 and 3.5 = \(\frac{1.5+3.5}{2}=\frac{5}{2}=2.5\)

∴ 1.5 and 3.5 have the same value of f(t)

∴ 1.5 and 3.5 have the same height

The height of the ball is the same after 1.5 seconds and 3.5 seconds.

Answer:

y=4x+3 y=mx+b form

Step-by-step explanation:

Answer:

Range is C : {1000,1100,1200,1300,1400,1500,1600}

Answer:

$15973.4

Step-by-step explanation:

The formula for depreciation is:

a(1 - r)^t

a = Initial value =$36,000

r = depreciation rate = 15% = 0.15

t = time in years = 5 years

The depreciation value = $36000 × (1 - 0.15)⁵

= 36000(0.85)⁵

= $15973.39125

Approximately = $15973.4

The value of the boat is $15,973 after 5 years.

Given that,

According to the scenario, computation of the given data are as follows,

Value of boat = \(A (1 - r )^{t}\)

By putting the value, we get

Value = \(36,000(1 - 0.15)^{5}\)

= \(36,000(0.85)^{5}\)

= 36,000 \(\times\) 0.4437053125

= $15,973.4  or $15,973

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Given:-

To find the volume of the cone.

From the given image it is clear,

So now we substitute the known values. so we get,

So the required volume is 125ft^3.

Answer:

that's hard

Step-by-step explanation:

Answer:

The probability of turning over E would be 1/5

Step-by-step explanation:

since there are 5 cards and there is an equal chance you could get any one of them, the probability is one (the amount of cards drawn) over five (the amount of cards total.)

Hope this helps :)

Answer:

638 rupees

Step-by-step explanation:

The radio cost him x.

He sold it at a 10% profit for for x + 10% of x which is the same as 1.1x

1.1x = 605

x = 605/1.1 = 550 rupees

It cost him 550 rupees.

To gain a 16% profit, he must sell it for 550 rupees + 16% of 550 rupees

That is the same as 116% of 550 rupees or 1.16 * 550 rupees

1.16 * 550 rupees = 638 rupees

Answer: 638 rupees

The line plot is attached based on the information given.

A line plot is a graph that shows data as dots or checkmarks above a number line to indicate how frequently each value occurs. Only numerical, discrete data, not continuous data, is shown using line graphs. Line plots categorize the data by showing how often each value appears on a number line. Small data sets make these graphs easy to make, and the revealed frequency patterns allow for interpretation.

Each mark on the line plot represents one of the distances Tomas rode. The number on the horizontal axis represents the day of the week and the vertical axis represents the distance in miles. The line plot shows that on most days, Tomas rode between 3 and 5 1/2 miles.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

The matrix A is [-2 -3 1 3]. This matrix satisfies the given equation A * [1 0 -1 3] = [-2 -3 1 9], and it can be represented as the matrix A = [-2 -3 1 3].

To find the matrix A such that A * [1 0 -1 3] = [-2 -3 1 9], we can express A as a 2x2 matrix with elements a, b, c, and d. By equating the corresponding entries on both sides of the equation, we can solve for the values of a, b, c, and d. The resulting matrix A is [-2 -3 1 3]. Let A = [a b c d] be the 2x2 matrix we are looking for. We want to find the values of a, b, c, and d such that A * [1 0 -1 3] = [-2 -3 1 9]. Multiplying the matrices, we get:

a * 1 + b * (-1) = -2     (Equation 1)

a * 0 + b * 3 = -3        (Equation 2)

c * 1 + d * (-1) = 1      (Equation 3)

c * 0 + d * 3 = 9         (Equation 4)

From Equation 1, we have a - b = -2.

From Equation 2, we have 3b = -3, which implies b = -1.

From Equation 3, we have c - d = 1.

From Equation 4, we have 3d = 9, which implies d = 3.

Substituting the values of b and d back into Equations 1 and 3, we find a = -1 and c = 4. Thus, the matrix A is [-2 -3 1 3]. This matrix satisfies the given equation A * [1 0 -1 3] = [-2 -3 1 9], and it can be represented as the matrix A = [-2 -3 1 3].

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Answer:  c

Step-by-step explanation: matches the graph

The radius of convergence R is infinite.

The coefficients of the power series, we can use the formula for the geometric series:

\((1+z)^{-1} = \sum_{n=0}^\infty (-1)^n z^n\)

where z is a variable that we can replace with \(x/(12+x)\), to get

\(\frac{8}{12+x} = 8\cdot\frac{1}{12}\cdot\frac{1}{1+x/12}\)

= \(\frac{2}{3}\cdot\frac{1}{1-(-x/12)} = \frac{2}{3}\sum_{n=0}^\infty (-x/12)^n\)

We can compare this with the given series to find the coefficients c_n:

\(c_0 = 2/3\)

\(c_1 = -2/3 * (1/12) = -1/18\)

\(c_2 = 2/3 * (1/12)^2 = 1/648\)

\(c_3 = -2/3 * (1/12)^3 = -1/46656\)

\(c_4 = 2/3 * (1/12)^4 = 1/1679616\)

To find the radius of convergence R of the power series, we can use the ratio test:

\(\lim_{n\rightarrow\infty} |\frac{c_{n+1}}{c_n}| = \lim_{n\rightarrow\infty} |\frac{2}{3}\cdot\frac{(-x/12)^{n+1}}{(-x/12)^n}| = |x/12|\)

This limit exists for all x, so the series converges for all x.

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The correct option from the given options is (a) a lower bound on how many donuts he can eat in one sitting.

A lower bound is a value which is equal to or greater than the minimum value of a set. In this given scenario, eight donuts are a lower bound on how many donuts a teenager can eat in one sitting. He might be able to eat more than eight donuts in one sitting but he cannot eat less than eight donuts in one sitting because it's a lower limit.

A lower limit or a lower bound is an absolute minimum. It is the minimum number of donuts that the teenager can consume in one sitting. In this scenario, there is a possibility that the teenager might eat more than eight donuts, but the lower limit is eight.

Therefore, the correct option is (a) a lower bound on how many donuts he can eat in one sitting.

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x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

\(y=b_1x+b_0\)

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line \(y=b_1x+b_0\) that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

\(b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)\)

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

\(y=b_1x+b_0\)

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

\(S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125\)

The regression line is y=0.34375x-0.125

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Answer:

In a plus sign

Step-by-step explanation:

Step-by-step explanation:

the line should be thought the (=) sign (≠)- like this

that means that it does not equal each other because I mean if you solve it, it made it    20=555 and 20 does not equal 555

The number of games Wayne can play is 4.

A linear equation is an equation that when graphed is a straight line. A linear equation has a single variable that is raised to the power of one.

The total cost of the game is a function of the cost per game, number of games he can play and the cost of renting shoes

Total cost = cost to rent shoes + (cost per game x number of games)

$20 = $1.90 + ($4.25 x g)

$20 = $1.90 + $4.25g

In order to determine the value of g, take the following steps:

Combine similar terms: 20 - 1.90 = 4.25g

Add similar terms:  18.10 = 4.25g

Divide both sides by 4.25: 18.10 / 4.25

g = 4.2

g = 4 games

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\(\huge\color{purple}\boxed{\colorbox{black}{Answer ☘}}\)

in ∆ABE

\( \tan(theta) = \frac{p}{b} \\ \tan(60) = \frac{h}{x} \\ \sqrt{3} = \frac{h}{x} \\ h = \sqrt{3}x\)

Now, in ∆CDE

\( \tan(theta) = \frac{p}{b} \\ \tan(30) = \frac{h}{80 - x} \\ \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3}x }{80 - x} (from \: (1)) \\ = > 3x = 80 - x \\ 4x = 80 \\ x = 20\)

distance of pole CD from E = 80 - x = 60m

distance of pole AB from E = x = 20m

\(h = \sqrt{3} x = 20 \sqrt{3}m\)

Step-by-step explanation:

well, we have several right-angled triangles here.

the main one from the point in the street to the 2 tops of the poles.

and the 2 side ones of the poles to the point on the street.

we know the angle above the point in the street is 90 degrees, because the other 2 angles of the main triangle are 30 and 60 degrees. and the sum of all angles in a triangle must always be 180 degrees.

as the angles up are 30 and 60 degrees, so are their mirrored twins at the tops of the poles as part of the main triangle.

the Hypotenuse of the main triangle is the connection between the tops of the poles, and is also 80m long.

so, now that we have established the "picture", we can use the law of sine to get all the other side lengths.

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite of the correlated angles.

so, we know,

80/sin(90) = 80 = a/sin(30) = 2a = b/sin(60)

a = 80/2 = 40m (the connection from the point in the street to the top of the pole under 60°)

b = 80×sin(60) = 69.2820323... m (the connection from the point in the street to the top of the second pole under 30°).

now we use the same principle on the side lengths of the 2 side triangles. their Hypotenuses are the 2 sides we just calculated.

let's start with the one with the round number as Hypotenuse : 40m

40/sin(90) = street distance / sin(30) = 2× street distance

street distance = 40/2 = 20m

that means the street distance of the point in the street to the other pole is 80-20 = 60m

for the pole height(s) we now just use regular Pythagoras

c² = a² + b²

with c being the Hypotenuse.

40² = 20² + pole height²

1600 = 400 + pole height²

1200 = pole height²

pole height = 34.64101615... m

Answer:The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

Answer:

The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

Answer:

the charges from Netflix are less than Plex cause there's a 50 dollar gap for the member ship and for the DVD there's only a 3 dollar gap

Step-by-step explanation:

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

  (b)  21.4

Step-by-step explanation:

There are a couple of interesting relations regarding chords and secants and tangents of a circle. With the right point of view, they can be viewed as variations of the same relation, possibly making them easier to remember.

When chords cross inside a circle (as here), each divides the other into two parts. The product of the lengths of the two parts of one chord is the same as the product of the lengths of the two parts of the other chord.

Here, that means ...

  7x = 10·15

  x = 150/7 = 21 3/7 ≈ 21.4

_____

Additional comment

A secant is a line that intersects a circle in two places. (A tangent is a special case of secant where the two points of intersection are the same point.) When two secants meet outside the circle, there is a special relation between the lengths of the various line segments.

Consider the line segment from the point where the secants meet each other to the far intersection point with the circle. The product of that length and the length to the near intersection point with the circle is the same for both secants.

Here's the viewpoint that merges these two relations:

The product of the lengths from the point of intersection of the lines with each other to the two points of intersection with the circle is the same for each line.

(Note that when the "secant" is a tangent, that product is the square of the distance from the tangent point to the point of intersection with the other line--the distance to the circle multiplied by itself.)

According to the Question,

\( \rm7x = 10 \times 15\)

\( \rm x = \frac{150}{7} \)

\( \bf x = 21.4\)

There are 315 ways of distributing books (four identical math books and five identical history ) to three different students.

Let A, B be any finite sets. The number of ways to choose one element from A and one element from B is N(A)⋅N(B)..

We have, Total number of distinct students = 3

Total number of identical math books = 4

Identical History books = 5

let

Number of distinct ways to distribute identical four math books (n = 4) among three students(k= 3), N(M) = ⁽ⁿ⁺ᵏ⁻¹⁾Cₙ = ⁶C₄ = 6!/4!2! = 15

Number of distinct ways to distribute five history books (n= 5) among three students (k= 3) ,N(H) = ⁽ⁿ⁺ᵏ⁻¹⁾Cₙ = ⁷C₅ = 7!/5! 2! = 7× 3 = 21

Total different (distinguishable) ways can all the books be distributed to the students, N(A) = N(M)⋅N(H) = 15× 21 = 315 ways

Hence , required distribution ways are 315.

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The complete table with the ordered pairs are shown in the diagram attached below.

To complete the table with the ordered pairs, find the equation of the given line.

Slope (m) of the line = rise/run = 2/1

m = 2

The y-intercept (b) = 4 (the line intercept the y-axis at this point).

Substitute m = 2 and b = 4 into y = mx + b:

y = 2x + 4

Use the equation to find the missing ordered pairs of the given table:

When x = -1:

y = 2(-1) + 4

y = 2

When y = 5.5:

5.5 = 2x + 4

5.5 - 4 = 2x

1.5 = 2x

1.5/2 = x

0.75 = x

x = 0.75

When x = 2.6:

y = 2(2.6) + 4

y = 9.2

The image below shows the complete table with the missing ordered pairs.

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Answer:

what do you need?

Step-by-step explanation:

pictures would be nice

Answer:

yea sure whats the problem