Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?

Answer:

Formulas

[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\textsf{Area of a semicircle}=\dfrac{1}{2}\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Radius of a circle}=\sf \dfrac{1}{2}d\quad\textsf{(where d is the diameter)}[/tex]

[tex]\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}[/tex]

Use the above formulas to calculate the various measurements, remembering to calculate the radius first when given the diameter.

a) Radius = 2.7 cm

[tex]\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)[/tex]

[tex]\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)[/tex]

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b)  Diameter = 45 mm

[tex]\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm[/tex]

[tex]\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)[/tex]

[tex]\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)[/tex]

a)  Radius = 8.5 cm

[tex]\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)[/tex]

[tex]\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)[/tex]

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b)  Radius = 24 mm

[tex]\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)[/tex]

[tex]\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)[/tex]

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c)  Diameter = 32 cm

[tex]\sf \implies Radius =\dfrac{32}{2}=16\:\:cm[/tex]

[tex]\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)[/tex]

[tex]\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)[/tex]

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d)  Diameter = 15 m

[tex]\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m[/tex]

[tex]\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)[/tex]

[tex]\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)[/tex]

The absolute function will be f(x) = | x - 5 | - 4.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x - h | + k

Where h,k is the vertex of the absolute function.

f(x) = | x - 5 | - 4

Therefore the absolute function will be f(x) = | x - 5 | - 4.

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The statement correctly describes the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.

The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right

if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.

Given graph : y = ln(x), has a vertical and horizontal translation.

As we know, y = ln(x - h) + k | where h is the vertical shift, and k is the horizontal shift.

Therefore, comparing y = ln(x - 7) + 3 it with different function we can write the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.

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Answer:

the first choice is not a polynomial because you can't divide by a variable.

Answer:

NM= JL + LM + JK

NM= 32 + 20 + 60

NM= [112]

NM= 10,58

Step-by-step explanation:

Hope it helps!!

The plot of the graph  y = –1.5(4)^x is shown below of which its domain and range exist on all real values

The standard exponential function is expressed as y = ab^x

where

The exponential function shows an increase along the y-axis and towards the x-axis

According to the equation, we are to plot the graph  y = –1.5(4)^x of which its domain and range exist on all real values

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Answer:

42 cm

Step-by-step explanation:

The first rectangle has a length of 4 and a Width of 7. the second rectangle has a length of 2 and a width of 7.

The formula for area of a rectangle is A=l*w

SO,

Rectangle 1: A= L*W

A=4*7

A=28

Rectangle 2:

A=L*W

A=2*7

A=14

Now, add both areas since they are both part of one whole recatngle.

28+14

= 42

Answer:

The answer is zero there is no solving.

Step-by-step explanation:

cause you do

60/n=20/7, and then you move all the terms to the left

now it is: 60/2-(20/7)=0

the domain to this is n=0

add the numbers and variables together and get

60/n-(+20/7)=0 now get rid of the parentheses and now you got

60/n-20/7=0

and all that is 0

kinda hope this help lol

Answer:

  612.5 cm²

Step-by-step explanation:

The ratio of areas of similar figures is the square of the scale factor. The scale factor is the ratio of corresponding side lengths. Here, we must find the scale factor.

__

The only given side of trapezium B corresponds to an unknown side of trapezium A. We can find the length of that unknown side using the area formula.

  A = 1/2(b1 +b2)h . . . . . parallel sides b1, b2; height h

  98 cm² = 1/2(16 cm +b2)(7 cm) . . . . use known values

  28 cm = 16 cm +b2 . . . . . . . . . . divide by 3.5 cm

  b2 = 12 cm . . . . . . . . . . . . . . subtract 16 cm

The top side of trapezium A is 12 cm long.

Now we have the lengths of corresponding (top) sides, so we can find the scale factor. It is their ratio. We choose to express it as (size of B)/(size of A).,

  k = (30 cm)/(12 cm) = 2.5

The area of trapezium B will be that of trapezium A multiplied by the square of the scale factor:

  area B = (k²)(area A) = (2.5²)(area A)

  area B = 6.25×98 cm² = 612.5 cm²

The area of trapezium B is 612.5 cm².

Question 2.1.1

Reason:

Use the distance formula to find the distance from the origin (0,0) to the terminal point (-3, 4)

[tex](x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-(-3))^2 + (0-4)^2}\\\\d = \sqrt{(0+3)^2 + (0-4)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The pythagorean theorem is a similarly related alternative path you can take.

This triangle is a 3-4-5 right triangle.

====================================================

Question 2.1.2

Reason:

r = distance from origin to terminal point

r = 5, calculated back in the previous problem above.

sin(alpha) = y/r = 4/5

cos(alpha) = x/r = -3/5

sin(alpha)+cos(alpha) = (4/5)+(-3/5) = 1/5

====================================================

Question 2.1.3

Reason:

Recall that tangent is the ratio of sine over cosine

tan = sin/cos

Therefore,

[tex]\tan(\alpha) *\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)*\cos(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\1[/tex]

This assumes that neither sin(alpha) nor cos(alpha) are zero. Otherwise, we have a division by zero error.

Taking into account the definition of ratio and proportion, the airline should sell 440 tickets.

The ratio is the comparison of two quantities and is measured from the division of two values.

The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if [tex]\frac{a}{b}[/tex] corresponds to the ratio, then [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] equals a proportion.

An airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. The airline wants to fill all the seats (100%) on the flight.

This can be represented by the proportion:

[tex]\frac{374}{85}[/tex] = [tex]\frac{amount of tickets}{100}[/tex]

Solving:

amount of tickets= 100×[tex]\frac{374}{85}[/tex]

amount of tickets= 440

Finally, the airline should sell 440 tickets.

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im not in collage but I'll try ok so its most likely

Factor then solve to find the complex solutions.

x=2πn, for any integer n

if i was right could i get brainly?

By identifying the maximums, we see that in each blank we need to write:

1) 2

2) 2

3) greater.

First, we need to find the maximum of the function g(x).

You can see that for x = 2 we have the maximum of the parabola, which gives y = 9.

Then the maximum profit is got when 2 employees earn overtime.

We also need to find the maximum for the table. Notice that the maximum value of the table also happens for x = 2, and this time the maximum is y = 16.

So we can see that the maximum of Cathy's cupcakes is larger than the maximum of Jimmy's.

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The missing number given the mean of the data set is 16.

Mean is the average of a data set. It is determined by adding all the numbers in the data set and dividing the sum by the numbers in the data set.

Missing number = (mean x total number in the data set) - sum of numbers in the data set

(18 x 7) - ( 21 + 11 + 27 + 22 + 13 + 16)

126 - 110

= 16

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Answer:

The answer is below :

Answer:

what does this mean. oh wAit iM dematerializinG mvxhkgd

hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd

The calculation of the interest based on the price given shows that vehicle B has a lower interest.

From the information given, vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months. The interest will be:

= (25000 × 5 × 5)/100

= $6250

Vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 months. The interest will be:

= (29000 × 4 × 5)/100

= $5800

Therefore, the calculation of the interest based on the price given shows that vehicle B has a lower interest.

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Answer:

2,550 dollars hope u get a good grade

Step-by-step explanation:

the andswer is 220.32

Step-by-step explanation:

when you take 204 times the 8percent interest

204 x .08

you get 16.32

now add 16.32 and 204 and thats what you owe for your loan

Answer:

10 %

Step-by-step explanation:

15 mn = 1/4 h

We have :

[tex]\frac{\frac{1}{4} }{\frac{5}{2} } =\frac{1}{4} \times \frac{2}{5} =\frac{2}{20} =\frac{1}{10}=0.1[/tex]

Then the percentage that 15 mn represents of 5/2 h is :

0.1 × 100 = 10 %

Answer:

58 degrees

Step-by-step explanation:

XYZ is 90 degrees. XYO is 32 degrees. Angle x takes up the space leftover in the right angle, so simply subtract 32 from 90.

90-32= 58

Hope this help! (if it does pls consider giving me brainliest)

Answer:

Option C

Step-by-step explanation:

A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.

Answer:

Step-by-step explanation:

-3x - 2y + 2(-2) = 19

-3x -2y - 4 = 19

-3x - 2y = 23

2x + y - 6 = -20

2x + y = -14

-3x -2y = 23

2x + y = -14

-3x - 2y = 23

4x + 2y = -28

x = -5

-10 + y = -14

y = -4

x= -5, y = -4, z= -2

The height of a woman whose femur (f) measures 49 centimeters is equal to 173.15‬ centimeters.

A function can be defined as a mathematical expression that defines and represents the relationship that exists between two or more variable of a data set.

In order to determine the height of a woman whose femur (f) measures 49 centimeters, we would substitute this numerical value into the first function as follows:

G(f) = 2.57f + 47.22

G(49) = 2.57(49) + 47.22

G(49) = 125.93 + 47.22

G(49) = 173.15‬ centimeters.

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Answer:

the answer is B

Step-by-step explanation:

the answer is B if it correct  can i have brainalliest

Answer:

1. 3608

2.3956

3. 714

Step-by-step explanation:

jap darab ke apa ni

Answer:

sorry i can't see it properly I am very sorry

Answer:

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y).

Step-by-step explanation:

The rotation of angle 180 degree about origin is described below.

Rotation 180° about the origin is a geometric transformation that involves rotating a figure or shape around the point (0,0),

Also known as the origin, by an angle of 180 degrees.

This means that every point on the shape is moved to an equal distance away from the origin but on the opposite side of the origin.

This transformation is a reflection where the shape is flipped along,

the x-axis or y-axis or both, depending on the shape's orientation.

The rotation 180° about the origin is a common transformation in various geometrical applications, such as computer graphics, engineering, and physics.

It is a simple transformation that can be easily represented and performed using matrices or complex numbers.

Therefore,

rotation 180° about the origin is a geometric transformation that is important in various applications and involves rotating a shape around the origin by an angle of 180 degrees, resulting in a reflection of the shape across the x or y-axis.

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Answer: Heyaa! ~

Your Answer is 3069

Step-by-step explanation:

(-4589)+(+7658)= 3069

Hopefully this helps you! ~

let's say the segment is A(-3,8) and B(6,-4) and point C splits it on a 1:5 ratio from A to B, let's check for C coordinates.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-3,8)\qquad B(6,-4)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{5}\implies \cfrac{A}{B} = \cfrac{1}{5}\implies 5A=1B\implies 5(-3,8)=1(6,-4)[/tex]

[tex](\stackrel{x}{-15}~~,~~ \stackrel{y}{40})=(\stackrel{x}{6}~~,~~ \stackrel{y}{-4})\implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-15 +6}}{1+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{40 -4}}{1+5} \right)} \\\\\\ C=\left(\cfrac{-9}{6}~~,~~ \cfrac{36}{6} \right)\implies C=\left( -\cfrac{3}{2}~~,~~6 \right)[/tex]

Answer:

Factory A = 1200

Factory B= 1350

Factory C= 1050

Factory D = 1100

Step-by-step explanation:

Factory B as the fastest rate of production