In the rectangle ABCD shown below, AB=4 and BC=2. Let E be the midpoint of the side BC, and let AE cut BD at F. Prove that ∠BCF=45°.

Answer:

\(\frac{5}{2}\) or 2.5cm

Step-by-step explanation:

Hello! Let's help you with your question here!

Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.

To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:

\(A=\pi r^2\)

Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!

\(A=\frac{1}{4} \pi r^2\)

The reason why we put a \(\frac{1}{4}\) at the front of \(\pi r^{2}\) is because we're only solving for a quarter of a circle instead of the entire circle.

Now that we have our formula! We can calculate the area of the quarter circle as follows:

\(A=\frac{1}{4}\pi 15^2\)

\(A=\frac{\pi 15^2}{4}\)   -We combine the fraction \(\frac{1}{4}\) into the rest of the equation.

\(A=\frac{225\pi }{4}\)   - Evaluating \(15^2\)

Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:

\(A=9\pi r^2\)   -We're using the area of circle A to find the radius of B.

\(\frac{225\pi }{4} =9\pi r^2\)   - Plugging in the area of the quarter circle.

\(\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }\)   - We divide \(9\pi\) to get rid of it on the right side.

\(\frac{25}{4} =r^2\) - When dividing by \(\pi\), the numerator \(\pi\) gets cancelled out.

\(\sqrt{\frac{25}{4} }=r\)   -We square root to get rid of the squared.

\(\frac{5}{2}=r\)    - Square rooted both numerator and denominator.

And there we have it! We finally get a radius of \(\frac{5}{2}\) or 2.5cm.

Answer:

no sure about the answer

Answer:

x= -4,y=2............

2.05

750 + 6% = 7.95

10.00 - 7.95 = 2.05 :)

Answer:

coaches students to improve their communication skills

Step-by-step explanation:

Answer:

helps students with speech disabilities

Step-by-step explanation:

Got it right

\(\cos \theta = \dfrac 12\\\\\implies \theta = 2n\pi \pm \dfrac{\pi}3\\\\\text{For n =0 ~ \text{and}~ n=1}\\\\\\\theta = \dfrac{\pi}3 , \dfrac{5\pi}{3}\\\\\text{In degrees,}\\\\\theta = 60^{\circ} , ~ 300^{\circ}\)

Answer:

135 degrees

Step-by-step explanation:

135 degrees form the interior angle of a regular octagon

Answer:

135°

I hope this helps you

:)

Answer:

(a) 0.0000245

(b) 0.000025

Step-by-step explanation:

The complete question is:

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is  50 /10,000  = 0.005.  Compute the probability that two randomly selected chips are defective under the assumption of independent events.

Solution:

(a)

In this case we need to compute the conditional probability of selecting two defective chips, i.e. the selection of the second defective chip is dependent on the first defective chip.

The probability of selecting the first defective chip is:

\(P(1D)=\frac{50}{10000}=0.005\)

Now there are 9999 chips left and 49 defective chips among them.

The probability of selecting the second defective chip is:

\(P(2D)=\frac{49}{9999}=0.0049\)

Compute the probability that two randomly selected chips are defective using conditional probability as follows:

P (Two defective chips) \(=P(1D)\times P(2D)=0.005\times 0.0049=0.0000245\)

Thus, the answer is 0.0000245.

(b)

Compute the probability that two randomly selected chips are defective under the assumption of independent events as follows:

The above statement implies that the selection was done with replacement.

The probability is:

P (Two defective chips) \(=P(1D)\times P(2D)\)

                                      \(=\frac{50}{10000}\times \frac{50}{10000}\\\\=0.005\times 0.005\\\\=0.000025\)

Thus, the probability that two randomly selected chips are defective under the assumption of independent events is 0.000025.

Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

Answer:

x=18

Step-by-step explanation:

since x+24 is in parenthesis, we need to distribute 1/2 to all the parts inside the parenthesis.

1/2 * x = 1/2x

1/2 * 24= 12

1/2x+12=21

subtract 12 from both sides

1/2x= 9

divide 1/2 from both sides

x=18

so your answer would be x=18

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(\frac{1}{2}(x+24)=21 \rightarrow \frac{1}{2}x + 12 = 21\\\\x = 18\)

»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\frac{1}{2}(x+24) = 21\\\rule{150}{0.5}\\\\\rightarrow \frac{1}{2}*x = \frac{1}{2} \\\\\rightarrow \frac{1}{2} * 24 = 12\\\\\rightarrow \frac{1}{2}x + 12 = 21\\\\\rightarrow \frac{1}{2}x + 12 - 12 = 21 - 12\\\\\rightarrow \frac{1}{2}x = 9\\\\\rightarrow (\frac{1}{2}x)2 = 9 * 2\\\\\rightarrow\boxed{x = 18}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Jane has 6 - 14 - 12 = -20 boxes of beads left.

Jane initially had 6 boxes of beads.

She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.

To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.

First, let's calculate the total number of boxes used and given away:

Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister

Total boxes used and given away = 14 + 12

Total boxes used and given away = 26

Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:

Boxes left = Initial number of boxes - Total boxes used and given away

Boxes left = 6 - 26

Boxes left = -20

The result is -20, which implies that Jane has a deficit of 20 boxes of beads.

This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.

It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.

If the result were positive, it would represent the number of boxes remaining.

However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.

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Answer:

7

Step-by-step explanation:

If you take 8 and subtract it by 15, you will get the remaining answer.

8-15= 7

7+8=15

Understand now?

You could probably use this for the rest of that page

I would love to have brainliest for this question also

Answer:

x=2

y=2

x=1.3 or 4/3

y=-4

Step-by-step explanation:

In the given system of linear equation, the value of y is 1/2 and the value of x is 3/2.

Given is a system of linear equations, we need to find its solution,

y = -x + 2

y = 3x - 4

To find the values of x and y that satisfy both equations simultaneously, we can solve the system of equations by setting the two expressions for y equal to each other:

-x + 2 = 3x - 4

Now, let's solve for x:

Adding x to both sides:

2 = 4x - 4

Adding 4 to both sides:

6 = 4x

Dividing by 4:

x = 6/4

x = 3/2

Now, substitute the value of x back into either of the original equations to find the value of y.

Let's use the first equation:

y = -x + 2

y = -(3/2) + 2

y = -3/2 + 4/2

y = 1/2

Therefore, the solution to the system of equations is x = 3/2 and y = 1/2.

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The store that has a better deal on DVDs is Store A.

The amount more that Sheila will save from buying from the store with the better deal is $ 1.00.

The store with the better deal is the store that has a lower price per unit of DVDs.

Price per unit of DVD in store A:

= Cost of DVD / Number of DVDs

= 9.45 / 3

= $3.15

Price per unit of DVD in Store B :
= 12.80 / 4

= $ 3.20

Store A therefore has the better deal and the amount that Sheila will save from 20 DVDs is :

= ( 3.20 x 20 ) - ( 3.15 x 20)

= $ 1.00

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A graph of quadrilateral DEFG with points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9) is shown on the coordinate plane in the image below.

In Mathematics and Geometry, a quadrilateral can be defined as a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.

In this scenario, we would use an online graphing tool to plot quadrilateral DEFG based on the given coordinates or its points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9).

Based on the graph of quadrilateral DEFG with points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9), this quadrilateral is composed of two pairs of opposite sides that are parallel and as such, we can logically deduce that it most likely represents a square.

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Check the picture below.

Answer:

Marisol made $138.75 on the sale of the jacket

Step-by-step explanation:

First we are told that Fernando bought a jacket for $185, and sold it for 1 1/12 what he paid.

Therefore, 1 1/2 of 185;

= 1.5 × 185 = $277.5

Therefore, Fernando sold the Jacket for $277.5

Next, we are told that:

Marisol spent 1/5 as much as Fernando on the same jacket

This means that Marisol spent 1/5 of $185 on the jacket

= 1/5 × 185 = 0.2 × 185 = $37

Therefore, Marisol spent $37 to buy the same jacket

Next, Marisol sold the jacket for 1/2 as much as Fernando. Since Fernando sold the Jacket for $277.5, Marisol sold the jacket for 1/2 of 277.5, and this is calculated as:

1/2 of 277.5 = 0.5 × 277.5 = 138.75

Therefore, Marisol made $138.75 on the sale of the jacket.

The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it which is true.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Similar polygons are those whose perimeter ratios are identical to their respective scale factors. The common fraction of the sizes of two matching sides of two identical polygons is known as a scale factor.

The given statement is true.

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Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

The two polynomials whose difference is 2x^2 + x + 4 are

6x² + 3x + 5 and 4x² + 2x + 1.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The difference between the two polynomials is 2x² + x + 4.

The two polynomials are:

6x² + 3x + 5 _____(1)

4x² + 2x + 1 ______(2)

The difference between (1) and (2)

6x² + 3x + 5 - 4x² - 2x - 1

2x² + x + 4

Thus,

The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.

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Answer: It is 144 but add pi symbol

Step-by-step explanation:

In conclusion the exact volume of the cone is 144π cubic inches.

How to solve and what does volume mean?

The radius of the circular base is half the diameter, which is 12/2 = 6 inches.

The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²2)(12)

V = (1/3)π(36)(12)

V = (1/3)(432π)

V = 144π

Therefore, the exact volume of the cone is 144π cubic inches.

Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.

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The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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The correct answer is C.

The red graph is the exact same as the black graph, just translated up one unit.

y - 1 = f(x) can be written into y = f(x) + 1, which represents the black function but translated up one.

Answer:

area of ABC=1/2 b×h=1/2×20×6=30m²

Answer:

60 m^2

Step-by-step explanation:

( Base * Hight / 2 = Area)

20 * 6 = 120

120 / 2 = 60

The perimeter of an equilateral triangle is just 3s as all the sides are, well, equal so

P=3s and we are told that P=24.6 so

3s=24.6

s=8.2 cm

Answer:

Step-by-step explanation:

Note

I think the question means "What do you multiply -26 by to get - 468

call the number that you need x

x * -26 = - 468                        Divide both sides by - 26

-26x/-26 = - 468/ - 26           There are 2 minus signs on the right. They cancel.

x = 18

Conclusion

When you multiply 18 * -26 the answer is --468

Answer: 18

Answer:

9

5

Step-by-step explanation:

Wyatt's class:

Each group of 3 students eats 1 1/2 pizzas.

There are 18 students.

18/3 = 6

There are 6 groups of 3 students.

Since each group of 3 students eats 1 1/2 pizzas, 6 groups eat

6 * 1 1/2 = 6 * 3/2 = 18/2 = 9

Answer: 9 pizzas

Jennifer's class:

There are 15 students. Each student eats 1/3 of a pizza.

15 * 1/3 = 15/3 = 5

Answer: 5 pizzas

Answer:

9

5

Answer:

D im pretty sure. "Uses a convex eyepiece lens”

Step-by-step explanation:

I am taking quiz rn

The correct label that could be written in the area marked X is "Uses a convex eyepiece lens".

The Venn diagram is a mathematical representation of the system of scenarios.

Here,
The overlapping area between the two circles represents the features that both types of telescopes share. Reflecting telescopes use concave eyepiece lenses the primary optical element while refracting telescopes use a convex eyepiece lens. So the X in the overlapping area represents the fact that there are some telescopes that “Use a convex eyepiece lens".

A concave mirror is used in reflecting telescopes to collect and focus light, while a convex eyepiece lens is used to magnify the image. The other two options ("Uses a convex mirror" and "Uses a concave mirror") are not accurate for both types of telescopes.

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The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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ok

Probability of bankrupt = 1/24

Probability of lose a turn = 1/24

Probability of Bankrupt and lose your turn = 1/24*1/24 = 1/576

Result = P = 1/576