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Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer:

9cm

Step-by-step explanation:

The CIRCUMFERENCE OF A CIRCLE is the distance round the circle.

It has the formular 2πr.

were r = radius

C = 2πr

72 = 2 × 3.142 × r

72 = 6.284r

dividing bothsides by 6.284

r = 72/ 6.284

r = 11.457

AB is an arc.

Lenght of an arc

[tex] \frac{ \alpha }{360} \times 2\pi \: r \\ \\ \frac{45}{360} \times 2 \times 3.142 \times 11.457 \\ \\ \frac{45}{360} \times 71.995 \\ \\ = 8.999 \\ \\ = 9cm[/tex]

Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]

So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]

Answer:

60

Step-by-step explanation:

Let's call the number A.

We are told that:

(2/3)A - 8 = 32

Multiply both sides by 3 and rearrange:

3*[(2/3)A - 8 = 32]

2A - 24 = 96

2A = 120

A = 60

CHECK:

Does (2/3) of 60 minus 8 equal 32?

(2/3)*(60) = 40

40 - 8 = 32

YES

The number is 60

The expression that is equivalent to -9/6 is = 9/-6. That is option A.

Fraction is represented by a numerator and a denominator which can be either positive or negative.

From the fraction given, -9/6. The numerator is 9 while the denominator is 6.

The expression that is equivalent to -9/6 is = 9/-6 and not -9/-6 because the negatives are cancelled out.

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Answer:

[tex]\boxed{Circuit_{\Delta ABC} = 15~cm }[/tex]

Step-by-step explanation:

The ABC triangle is an equilateral triangle.

[tex]\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

The drawing in the attachment.

I am entering meaningfully:

a - side length of an equilateral triangle

[tex]a=\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

[tex]P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}[/tex]  -   equilateral triangle area formula

[tex]P_{\Delta} =\dfrac{25 \sqrt{3} }{4}~~\land~~P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}~~\Rightarrow~~\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}\\\\\\\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}~~\mid~~\div ~~\dfrac{\sqrt{3} }{4} \\\\\\\dfrac{a^{2} \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } =\dfrac{25 \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } \\\\a^{2} =25~~\\\\a^{2} =5^{2} ~~\land~~a > 0~~\Rightarrow~~\boxed{a=5~cm}\\\\\\[/tex]

[tex]Circuit_{\Delta ABC} =a+a+a\\\\Circuit_{\Delta ABC} =3a~~\land~~a=5~cm\\\\\boxed{Circuit_{\Delta ABC} =3\cdot 5 = 15~cm }[/tex]

Answer:

answer is D. 35/60

Step-by-step explanation:

35 divided by 60 is = 0.583333

which is a repeating decimal

Among the options, only a rational number (35/60) is equivalent to a repeating decimal. The correct answer is option (d).

To identify which of the given rational numbers is equivalent to a repeating decimal, we need to check their decimal representations.

a. 24/60 = 2/5 = 0.4 (terminating decimal, not repeating)

b. 30/64 = 15/32 = 0.46875 (terminating decimal, not repeating)

c. 29/50 = 0.58 (terminating decimal, not repeating)

d. 35/60 = 7/12 = 0.583333... (repeating decimal, as 3 repeats infinitely)

Among the options, only option d (35/60) is equivalent to a repeating decimal.

The repeating decimal representation is 0.583333... where the digit 3 repeats indefinitely.

This can be represented as 0.58(3).

The correct answer is option (d).

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Answer:

[tex]a_n = 5 + (n-1)(-4)[/tex]

Step-by-step explanation:

So the explicit formula is generally defined as [tex]a_n = a_1 + d(n-1)[/tex]. where d is essentially the "slope", basically how much it's changing from term to term. anyways if you look at the recursive formula you'll notice it's taking the previous term and subtracting 4. This is what d is going to be, -4 and since a_1 is given you plug that in as well. This gives you the equation

[tex]a_n = 5 -4(n-1)[/tex] which can also be written as [tex]a_n = 5 + (n-1)(-4)[/tex]

The information about the triangle shows that

TRS ≅ △SUT because of SAS, CPCTC.

It should be noted that from the information given, W is the intersection point of line segments TS and RU.

Also, RWS and UWT are equal because they're vertical angles.

Therefore, by AAS, TUW and SRW are equal. Also, TRS ≅ △SUT because of SAS, CPCTC.

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Answer: SAS and CPCTC

Step-by-step explanation:

Because of SAS, △TRS ≅ △SUT, and because of CPCTC, ∠RST ≅ ∠UTS.

Trust me!

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

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Answer:

b) The two triangles are similar by SAS

Step-by-step explanation:

From the diagram below, we can tell that

SAS similarity (Side-Angle-Side similarity) is a criterion used to determine whether two triangles are similar.

It states that if two sides of one triangle are proportional to two sides of another triangle, and the included angles between these sides are congruent, then the two triangles are similar.

In other words, if in two triangles, the ratio of the lengths of corresponding sides is equal, and the included angles between these sides are congruent, then the two triangles are considered similar.

The corresponding angles are congruent and the sides are in proportion

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The multiplicative rate of change of the exponential function is 0.5.

In this problem we have three that are part of a exponential function, whose form is shown below:

[tex]y = a\cdot r^{x}[/tex]     (1)

Where:

We notice that for Δx = 1, the value of y is halved. Hence, the multiplicative rate of change of the exponential function is 0.5.

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Answer:

55

Step-by-step explanation:

[tex] \frac{n(n + 1)}{2} \\ n = 10 \\ substitutig \\ \frac{10(10 + 1)}{2} \\ \\ \frac{10(11)}{2} \\ \\ \frac{110}{2} = 55 [/tex]

Answer:

A. The function is always decreasing

Step-by-step explanation:

we read a graph from left to right, so we can always compare the increase/decrease of a function by seeing how an x value compares with an x value to the left

(I am aware that this paragraph is really confusing)

we can see that as x increases, from -∞ to 0,

y decreases in correspondence

and that as x increases, from 0 to ∞,

y decreases in correspondence also

So, even though the graph doesn't quite look like it, when x < 0; the function decreases, when x > 0; function decreases--so the function is always decreasing

hope this helps!! have a lovely day :)

The correct expression for the inverse proportion is k/6 = 3/1

Given the inequality xy = k

If y is inversely proportional to x, then;

y = k/x

Given that y = 6, and  x = 3, then;

6 = k/3

Swap

k/3 = 6

k/6 = 3/1

Hence the correct expression for the inverse proportion is k/6 = 3/1

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The graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

The inequalities given in the task content can be solved as follows;

For –2x + 4 ≤ 8

-2x ≤ 8 -4

x >= -2

For –2x + 4 > –6

–2x > –6 -4

x < 5

Hence, the graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

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Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:

[tex]\mu = 15 \times \frac{45}{120} = 5.625[/tex]

The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004[/tex]

[tex]P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02[/tex]

[tex]P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057[/tex]

[tex]P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107[/tex]

[tex]P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150[/tex]

[tex]P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169[/tex]

Then:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507[/tex]

0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

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Step-by-step explanation:

[tex]f(x) = {x}^{4} + 4 {x}^{3} - 2 {x}^{2} + 11x - 6[/tex]

[tex]f(3) = {3}^{4} + 4. {3}^{3} - 2. {3}^{2} + 11.3 - 6[/tex]

[tex]f(3) = 81 + 4.27 - 2.9 + 33 - 6[/tex]

[tex]f(3) = 81 + 108 - 18 + 33 - 6[/tex]

[tex]f(3) = 198[/tex]

Answer:

Step-by-step explanation:

x4 + 4x3 - 2x2 + 11x - 6 for x = 3

3^4 + 4 * 3^3 - 2 * 3^2 + 11 * 3 - 6 =

81 + 4 * 27 - 2 * 9 + 11 * 3 - 6 =

81 + 108 - 18 + 33 - 6 =

198

Answer:

3 < QS < 13.

I just did it on edge

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

Here, we have,

As per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.

x + 8 > 5

x > -3

x + 5 > 8

x > 3

8 + 5 > x

13 > x

Hence, In triangle QRS the length of QS can lie between 3 < QS < 13.

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Answer:

a

Step-by-step explanation:

(3/4) to the power of 2 means to multiply it by itself and so, 3/4 times itself is 9/16

Answer:

Step-by-step explanation:

Hello

[tex]\large\displaystyle\text{$\begin{gathered} \sf Apply \ the \ third \ exponent \ rule-: \bigg(\dfrac{x}{y}\bigg)^m=\dfrac{x^m}{y^m} \end{gathered}$}}[/tex]

Solve-:

[tex]\large\displaystyle\text{$\begin{gathered} \sf \bigg(\dfrac{x}{y}\bigg)^2= \dfrac{3^2} {4^2} =\boxed{\sf{\frac{9}{16}}} \end{gathered}$ }}[/tex]

[tex]\pmb{\tt{done \ !!}}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

The number of possible passwords is 26^4 * 10^4.

We will make 4 picks from each category (letters and numbers).

We can duplicate them (i.e., pick each character more than once.)

so, for your 4 picks from the letters, you'll have

26 * 26 * 26 * 26 = 26^4 possible selections.

For each of these, you'll have 4 picks from the digits. Similar reasoning, this works out to

10^4 combinations of digits.

This means you'll have 26^4 * 10^4

Possible combinations of 4 letters and 4 digits, and, for each of these, you now need to work out how many unique ways to arrange them.

We will have 8 possible choices for the 1st character, 7 for the second, 6 for the third, etc. This works out to 8!

different orderings for each of your

26^4 * 10^4

The number of possible passwords is 26^4 * 10^4.

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Answer:

0.3 gallon

Step-by-step explanation:

To do this problem, we must divide the amount of cement by the number of feet to see how much cement he used for each foot.

15/50 = 0.3 gallon

Answer:

0.3 gallons per foot

Step-by-step explanation:

We know that he used 15 gallons of cement for 50 feet.

We want to find the amount per foot or the amount per each 1 foot.

So we have to divide the 15 gallons by the 50 feet.

15 / 50 = 0.3 gallons per foot.

Answer:

there is no ans that is the ans

Answer:

x³ + y³ + z³ = [ (x +y +z)(x² + y² + z² -xy - yz - xz) ] + 3xyz

Step-by-step explanation:

x³ + y³ + z³ = [ (x +y +z)(x² + y² + z² -xy - yz - xz) ] + 3xyz

Answer:

the widths of the wire :)

Step-by-step explanation:

Answer:Empirical probabilities.
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Answer:

80

Step-by-step explanation:

mean = 140+20=160

160/2

= 80

Answer: 160

Step-by-step explanation:

Just took it

Answer:

the second one I think, as it is clearer and makes more sense

The jump will be from 0 to 0.8, and the other jump from 0.8 to 1.1 in the right direction. Then the correct option is B.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The expression is given below.

⇒ 0.8 + 0.3

The sign of both terms are similar that is positive.

If the sign of the number is positive, then we move rightward. Similarly, if the sign of the number is negative, then we move leftward.

First, the jump will be from 0 to 0.8, and the other jump from 0.8 to 1.1 in the right direction. Then the correct option is B.

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The reflection of segment AB over the line x = 1, will be the line segment EF. Then the correct option is B.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The line segment AB is given.

Then the reflection of segment AB over the line x = 1, will be the line segment EF.

Then the correct option is B.

The missing diagram is given below.

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Answer:

Step-by-step explanation:

Reflecting a Line Segment Across the X-axis or Y-axis

Step 1: Identify the endpoints of the line segment.

Step 2: Reflect the endpoints of the line segment.

Step 3: Connect the reflected endpoints in a straight line to form the reflected line segment.

A reflection across line moves each point to such that line is the perpendicular bisector of the segment connecting

Answer:

24p^2q^2 - 42pq + 15

Step-by-step explanation:

Answer:

Hence the expression [tex]$$(6pq-3)(4pq-5)=24p^2q^2-42pq+15$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 6pq & - & 3 \\ \times & {} & {} & {} & 4pq & - & 5 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 30pq & + & 15 \\ {} & {} & 24{{p}^2}{{q}^2} & - & 12pq & {} & {} \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & 24{{p}^2}{{q}^2} & - & 42pq & + & 15 \\ \end{matrix}$$[/tex]

Answer:

x = -5

Step-by-step explanation:

We can use the below formula to find the line of symmetry.

( x - a )² + b

Here,

line of symmetry = +a

Vertex = +b

And now let us take a look at the given equation.

y = x² + 10x + 22

To find the line of symmetry from the given equation we have to make the given equation as the given formula.

Let us use the completing square method for that.

y = x² + 10x + 22

Put zero instead of y.

x² + 10x + 22 = 0

x² + 10x = -22

x² + 10x + 25 = -22 + 25

( x + 5 )² = 3

( x + 5 )² -3 = 0

Therefore,

line of symmetry of the line is = -5

∴ x = -5

The longest possible altitude of the third altitude (if it is a positive integer) is 83.

According to statement

Let h is the length of third altitude

Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.

From Area of triangle

A = 1/2*B*H

Substitute the values in it

A = 1/2*a*12

a = 2A / 12 -(1)

Then

A = 1/2*b*14

b = 2A / 14 -(2)

Then

A = 1/2*c*h

c = 2A / h -(3)

Now, we will use the triangle inequalities:

2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

2A/h < 2A/12 + 2A/14

Solve it and get

h > 6.46

From all the three inequalities we get:

6.46<h<84

So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.

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The gradient of the given graph is 1.5

From the question, we are to determine the gradient of the graph

Gradient is given by the formula

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Where m is the gradient

Picking the points (-2, -2) and (2, 4) on the line

Then,

x₁ = -2

y₁ = -2

x₂ = 2

y₂ = 4

Putting the parameters into the equation, we get

[tex]m = \frac{4--2}{2--2}[/tex]

[tex]m = \frac{4+2}{2+2}[/tex]

[tex]m = \frac{6}{4}[/tex]

m = 1.5

Hence, the gradient of the given graph is 1.5

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