What is the perimeter P of △DEF to the nearest whole number?

A triangle DEF. The length of DF is 10. The base angle E is 49 degrees and F is 42 degrees.

Answers

Answer 1

Answer:

perimeter of ΔDEF  ≈ 32

Step-by-step explanation:

To find the perimeter of the triangle, we will follow the steps below:

First, we will find the length of the side of the triangle DE and FF

To find the length DE, we will use the sine rule

[tex]\frac{sin E}{e} = \frac{sin F}{f}[/tex]

angle E  = 49 degrees

e= DF = 10

angle F = 42 degrees

f= DE =?

we can now insert the values into the formula

[tex]\frac{sin 49}{10}[/tex] = [tex]\frac{sin 42}{f}[/tex]

cross-multiply

f sin 49° = 10 sin 42°

Divide both-side by sin 49°

f = 10 sin 42° / sin 49°

f≈8.866

which implies DE ≈8.866

We will now proceed to find side EF

To do that we need to find angle D

angle D + angle E + angle F = 180°  (sum of interior angle)

angle D + 49° + 42° = 180°

angle D + 91° = 180°

angle D= 180° - 91°

angle D = 89°

Using the sine rule to find the side EF

[tex]\frac{sin E}{e} = \frac{sin D}{d}[/tex]

angle E = 49 degrees

e= DF = 10

ange D = 89 degrees

d= EF = ?

we can now proceed to insert the values into the formula

[tex]\frac{sin 49}{10}[/tex] = [tex]\frac{sin 89}{d}[/tex]

cross-multiply

d sin 49° = 10 sin 89°

divide both-side of the equation by sin 49°

d= 10 sin 89°/sin 49°

d≈13.248

This implies that length EF = 13.248

perimeter of ΔDEF = length DE + length EF + length DF

                                   =13.248   +  8.866  + 10

                                    =32.144

                                     ≈ 32 to the nearest whole number

perimeter of ΔDEF  ≈ 32


Related Questions

please help me on this!

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Answer:

The rocket reached its maximum height at 1.25 seconds.

Step-by-step explanation:

PLZ ANSWER THIS ASAP

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Answer:

C. Hollow cone frustum

Step-by-step explanation:

Revolved it in my head, because the line isn't touching the triangle it will be hollow, because the triangle has a slope the shape will taper.

help pls tysm
What are two examples of financial institutions?

Answers

Answer:

The major categories of financial institutions include central banks, retail and commercial banks, internet banks, credit unions, savings, and loans associations, investment banks, investment companies, brokerage firms, insurance companies, and mortgage companies

Step-by-step explanation:

sorry i did not put 2 examples, i put too many examples lollll

Answer:

There are two primary types of financial institutions non-depository and depository.

Step-by-step explanation:

an insurance company would fall under the non-depository group, and a credit union would be defined as a depository institution.

Please help me (this is one questionn)

Answers

Answer:

Below.

Step-by-step explanation:

Reading off the graph:

y-intercept  = (0, 2.5)

x-intercept = (3.5, 0)

if(x+3) and 133 digree is a pair of vertically opposite angles then the measure of x is

Answers

Answer:

x=130

Step-by-step explanation:

as vertically opposite angles are equal therefore,

133=X+3

x=133-3= 130

I hope it helps

A box contains 56 balls. The probability of selecting a red ball at random is 5/7. How many balls in the box are not red?

Answers

Answer:

Brain to me plz

Step-by-step explanation:

2/7 is the balls are not red, so 2/7 multiplyed by 56

which is 16

Answer:

16 balls

Step-by-step explanation:

If 5/7 of the balls are red then the fraction of balls that are not red is;

[tex]\frac{7}{7} - \frac{5}{7} = \frac{2}{7}[/tex]

Which means 2/7 of the balls are not red. So to get the number;

[tex]= \frac{2}{7} * 56 \\= 2 * 8\\[/tex]

= 16

∴16 balls are not red

explain why 3 into 5 into 7 + 7 into 11 is a composite number​

Answers

Answer:

As per BODMAS rule: 3 x 5 x 7 + 7 = 105 + 7 = 112. 112 is an even number and is therefore a composite number

Step-by-step explanation:

you need to do BODMAS so

3 x 5 x 7 = 105

then add 7 so there for 112

112 is an even number and therefore a composite number

Boa tarde gentiii Abaixo aparecem quatro sequências. Defina cada uma delas como RECURSIVA ou NÃO RECURSIVA. a) (5, 7, 9, 11, 13, 15, 17, 19, ...) b) (1, 4, 9, 16, 25, 36, 49, 64, ...) c) (1, 8, 27, 64, ...) d) (2, 5, 8, 11, 14, 17, ...)

Answers

Answer:

a) (5, 7, 9, 11, 13, 15, 17, 19, ...) Recursivo

b) (1, 4, 9, 16, 25, 36, 49, 64, ...) Recursivo

c) (1, 8, 27, 64, ...) Recursivo

d) (2, 5, 8, 11, 14, 17, ...) Recursivo

Step-by-step explanation:

Uma função recursiva é aquela em que os termos subsequentes da função são calculados com base nos termos anteriores

O comportamento recursivo é exibido pelos objetos quando consiste em seguir as partes;

1) Uma base que é predefinida

2) Um processo ou etapa recursiva que produz termos subsequentes pela aplicação de certos processos

Para a série;

a) (5, 7, 9, 11, 13, 15, 17, 19, ...)

Aqui 5 é a base e os termos subsequentes são encontrados adicionando 2 ao termo anterior, portanto, é uma função recursiva

aₙ = aₙ₋₁ + 2

b) (1, 4, 9, 16, 25, 36, 49, 64, ...)

Aqui 1 é a base e os termos subsequentes são encontrados ao quadrado da soma da raiz do termo anterior e 1, portanto, é uma função recursiva

aₙ = (√ (aₙ₋₁) + 1) ²

c) (1, 8, 27, 64, ...)

Aqui 1 é a base e os termos subsequentes são encontrados elevando à potência de três a soma da raiz cúbica do termo anterior e 1, portanto, é uma função recursiva

aₙ = (∛ (aₙ₋₁) + 1) ³

d) (2, 5, 8, 11, 14, 17, ...)

Aqui 2 é a base e os termos subsequentes são encontrados adicionando 3 ao termo anterior, portanto, é uma função recursiva.

Two bags contain coloured cubes.
Bag 1 has 3 red cubes and 1 blue cube.
Bag 2 has 3 green cubes, 1 yellow cube, and 1 red cube.
Is the probability that you will get a red cube from Bag 1 and the yellow cube from Bag 2 more or less than the probability of getting the blue cube from Bag 1 and a green cube from Bag 2? Explain.

Answers

Answer:

equal

Step-by-step explanation:

Bag 1 has 3 red cubes and 1 blue cube.  = 4 cubes

Bag 2 has 3 green cubes, 1 yellow cube, and 1 red cube.= 5 cubes

P ( red bag 1) = red /total = 3/4

P (yellow  bag 2) = yellow /total = 1/5

P(red bag1 , yellow bag2) = 3/4* 1/5 = 3/20

P ( blue bag 1) =blue /total =1/4

P (green  bag 2) = green /total = 3/5

P(blue bag1 , green bag2) = 1/4* 3/5 = 3/20

The probabilities are equal

Find the slope of the line that passes through (3, 2) and (10, 3).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

m=1/7x

Step-by-step explanation:

Answer:

[tex] slope= \frac{1}{7} [/tex]

Step-by-step explanation:

[tex](3 \: \: \: \: \: \: \: 2) = > (x1 \: \: \: \: \: \: \: x2)\\ (10 \: \: \: \: 3) = > (y1 \: \: \: \: \: \: \: y2)[/tex]

[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{2 - 3}{3 - 10} \\ = \frac{ - 1}{ - 7} \\ = \frac{1}{7} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

LAST QUESTION!!WILL GIVE BRAINLIEST!!! AT LEAST LOOK!!! SHARE YO SMARTNESS!!! EASY BUT IM DUMB!!!!!!


Which is not a pair of congruent angles in the diagram below?

A) EAB=CDB
B) ABE=DBC
C) AEB=DCB
D) AEB=CDB

Answers

It’s the letter B because angle

Answer:

The Correct answer is D

Step-by-step explanation:

I got it right on my test :)

Simplify the expression:
6b – 2b+ 5b – 8

Answers

Answer:

9b-8

Step-by-step explanation:

6b+5b-2b-8

11b-2b-8

9b-8

A focus group is made up 12 males and 4 females. Half of the males have college degrees. A member is selected at random from the geoup. What is the probability that the member is a male with a college degree?

Answers

Answer:

3/8

Step-by-step explanation:

We first have to find the probability that the person selected is a male and then multiply that by the probability that the male has a college degree.

There are 12 males and 4 females. There are 16 people in total. The probability of selecting a male is:

12/16 = 3/4

Half of the males have a college degree. Therefore, 6 males have a college degree. The probability that a selected male has a college degree is:

6/12 = 1/2

Therefore, the probability that a male is selected and that the male has a college degree is:

3/4 * 1/2 = 3/8

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Answers

Answer:

Yes,she had enough

½pound=8ounces

she needs a total of 24ounces

Step-by-step explanation:

She had enough because ½pound is 8ounces thus 16ounces+8ounces add up to 24ounces.

Answer:

Yes,she had enough

½pound=8ounces    she needs a total of 24ounces

Step-by-step explanation:

If v varies directly as w, and v=24 when w=8, find the equation that relates v and w.

Answers

Answer:

v = 3w

Step-by-step explanation:

Given that

v ∝ w

The, v = k w ---------------(1)

Where k is the constant of proportionality

Now, v = 24, w = 8

Putting in (1)

24 = k(8)

Dividing both sides by 8, we get

k = 3

Putting k =3 in (1)

v = 3w

This is the required equation connecting both

ANSWER:
It is given that v varies directly as w.
V=24 and W=8
So,simpler way is 24/8=3
As ratio is written in the form of p/q.
So,we can say that v=3w.
HOPE IT HELPS!!!!
PLEASE MARK BRAINLIEST!!!!

what would be the answer???

Answers

Answer:

120

Step-by-step explanation:

The sum of the angles in a quadrilateral is 360 degrees

2t+t+2t+t = 360

6t = 360

Divide by 6

6t/6 = 360/6

t = 60

Angle Z = 2t

Angle Z = 2*60 = 120

Answer:

[tex]120 \: \: degrees[/tex]

Second answer is correct.

Step-by-step explanation:

The sum of the angles in a qudrilateral = 360°

[tex]t + 2t + t + 2t = 360 \\ 6t = 360 \\ \frac{6t}{6} = \frac{360}{6} \\ t = 60[/tex]

angle z

[tex]2t = 60 \times 2 \\ \: \: \: \: \: \: \: = 120[/tex]

Help please.... question number 1

Answers

Answer:

20

Step-by-step explanation:

The height of the platform is when t=0

h(0) = -4(0)^2 + 75(0) +20

        =20

The height of the platform is 20

does y = 2x + 3 and y = 2x – 11. intercept

Answers

Answer:

yesssssssssssssssssssssssssssssss

BRAINLIEST WILL BE MARKED(THAT MEANS- 3 EXTRA POINTS) HERE! GRAPHING HELP 101

The graph of f(x)=x2 is shown.

Use the parabola tool to graph the function g(x)=(1/5x)2.m
The 1/5 is a fraction.
The graph with the blue highlight is my answer. LET ME KNOW IF MY ANSWER IS RIGHT OR WRONG! ASAP PLEASE AND THANK YOU WILL MARK BRAINLIEST!

Answers

Answer:

I think its wrong. For g(5)=(5/5)^2=1 and in your graph is something close to 3. The correct graph for [tex]g(x)=(\frac{1}{5}x)^2[/tex] is

Answer:

False

Step-by-step explanation:

Took the test and this is what I got

Select the correct answer from each drop-down menu.

Let e(x) be the elevation, in meters, of a cable car from the ground, x minutes after it begins descending from the top

e(t) = 840 – 52.51

meters from the ground

minutes after it

Since e(14) = , the elevation of the cable car will be

from the top of the hill,

Answers

Corrected Question

e(x)=840-52.5x

Let e(x) be the elevation, in meters, of a cable car from the ground, x minutes after it begins descending from the top of a hill. Since e(14) = ?, the elevation of the cable car will be meters from the ground minutes after it begins descending from the top of the hill.

Answer:

e(14) =105 meters

Elevation of the cable car 14 minutes after it begins descending from the top of the hill= 105 meters from the ground

Step-by-step explanation:

Given the elevation, e(x) in meters, of a cable car from the ground , x minutes after it begins descending from the top of a hill.

e(x)=840-52.5x

e(14)=840-52.5(14)

e(14)=840-735

e(14)=105 meters

Since e(14) =105 meters, the elevation of the cable car will be 105 meters from the ground 14 minutes after it begins descending from the top of the hill.

A line passes through (-1,7) and (2,10) which answer is the equation of the line

Answers

Answer: -x + y = 8

Step-by-step explanation:

So first you are going to want to find the slope of the equation. The equation for that it (y2 - y1)/(x2 - x1) = (10 - 7)/(2 - -1) and that equals 1. So your slope will be 1.

Now you have half of your equation complete, currently it looks like, y = x + b. So we have to find the y intercept. You can do that by plugging in a pair of coordinates into the current equation and solve for b.

Lets plug in (2,10)

10 = 2 + b

10 - 2 = b

b = 8

So now you have your equation in slope intercept form, y = x + 8. Just move the x over to the left side and there is your answer.

-x + y = 8

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long. If the hook is 5 meters from the flagpole, how tall is the flagpole?

Answers

Answer:

12 meters

Step-by-step explanation:

Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.

From Pythagoras theorem;

c^2 = a^2 + b^2

a^2= c^2 - b^2

a= √c^2-b^2

From the question

c= 13 metres

b= 5 metres

a= the unknown

a= √c^2-b^2

a= √(13)^2 - (5)^2

a= √169 - 25

a= √144

a= 12 meters

Answer:

The flagpole  12 meters tall

Step-by-step explanation:

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long

∵ The hook is 5 meters from the flag pole

∵ The flagpole and the ground ⊥ to each other

By using Pythagoras theorem:

hypothenus side is 13m

base is 5m

how tall is the flagpole is x

[tex]13^2=x^2+5^2\\\\169=x^2+25\\\\x^2=169-25\\\\x^2=144\\\\x=12m[/tex]

The flagpole  12 meters tall

Prove that 6+7 root 2 is irrational

Answers

Answer:

Step-by-step explanation:

49 is a perfect square, since it equals 7*7; 56 is not. If you have 35.2 and 37T, 36 is the perfect square between the two integers. Take the square root of the perfect square. If you have your square roots for memory, you know that the square root of 36 is equal to 6.

Given r,s,t are midpoints of AC,AB, and CB use the figure below to complete the following problem

Answers

Answer:

The first option, RT.

Step-by-step explanation:

RESUELVE EL SIGUINTE PORBLEMA En la escuela "Soy Feliz porque soy diverso", hay 230 estudiantes en total. De estos, 35 son mujeres. a) ¿Cuántos son hombres? b) ¿Qué parte del total de los estudiantes son hombres? 2. María se ha gastado 13 del dinero que le dieron de paga sus abuelitos en comprar un libro de aventuras. También se ha gastado 29 de la paga en comprar una cartuchera. ¿Qué fracción de su paga se ha gastado María? Datos: Libro de aventuras = 13 Cartuchera = 29 Solución: 13+ 29=3+29= 59

Answers

Answer:

1) a. 195 are males

b. Males are the 85 %

2) 1/2

Step-by-step explanation:

Number of all the students: 230

35 are females

x are males

Then 35 + x = 230

x = 230 - 35 → 195

To determine the amount of males, from the total we apply the percent.

Percent = (Amount of males / Total of students) . 100

% = (195 / 230) . 100 = 85 %

2. In first place, Maria spent 13 for the book.

In second place, Maria spent 29 for the pencil box.

In total, she has spent 13+29 = 42

But, how many dolars have the grandpa gave to her?.

We can also apply percent and fractions, where:

(Book / Total) + (Pencil box/Total) + (What she did not spend/Total) = 1

13 + 29 + x = T

13/T + 29/T + x/T = 1, in conclussion x = 42

Total of money given = 84

Then, Maria has not spent the half of money→ 1/2

what is the slope-intercept equation of the line below?​

Answers

Answer:

4

Step-by-step example

Slop is the

What is 46% of 22? Use a fraction and express your answer in simplest form.

Answers

Answer:

10 3/25

Step-by-step explanation:

46/100x22 =46x22 divide by 100

1012/100

10 12/100 both twelve and hundred can be divided by 4 thus final answer is ten whole(10) and three over twenty five(3/25)

I have been asking for assistance for an hour and a half now, I will greaty appreciate anyone that can help with this..Find the Slopes,and for the third one find Mid-point

Answers

Answer:

1st graph: m = -1/2. (m is the slope)

2nd graph: m = 3/2.

3rd graph: Midpoint = (1/2, 1/2)

Step-by-step explanation:

1st graph:

Find the slope by looking for two points on the line. Use the formula [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

We can derive the points (-3, 0) and (1, -2). Plug these into the equation above.

[tex]m= \frac{-2-0}{1-(-3)}[/tex]

Simplify this, giving you: m = -1/2.

2nd graph:

Use the same formula as stated above. From this graph, you can plug in the points (-1, 1) and (1, 4)

[tex]m = \frac{4-1}{1-(-1)}[/tex]

Simplifying gets you: m = 3/2.

3rd graph:

To find the midpoint, use the formula: [tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]

Plug in the end-points of the graph, or (-3, 2) and (4, -1).

You get:

[tex](\frac{-3+4}{2}, \frac{2-1}{2})[/tex]

Simplify:

Midpoint = (1/2, 1/2)

Now look at this information
[tex]2y + 3 \leqslant 11[/tex]

What is the largest value that y could be?​

Answers

Answer:

4

Step-by-step explanation:

Given

2y + 3 ≤ 11 ( subtract 3 from both sides )

2y ≤ 8 ( divide both sides by 2 )

y ≤ 4

Since y has to be less than or equal to 4

Then the largest value y could be is 4

Point A lies on the circle and has an x-coordinate of 1.


Which is the correct calculation of the y-coordinate of point A?




Answers

Answer:

y=0

correct way to solve it is y= xtan(theta)

Step-by-step explanation:

You did not mention if it is trigonometry but we assume that it is.

In trigonometry, a point with x-coordinate = 1 at a circle is horizontal line. the angle at this point is 0.

The correct way to solve it is to say tan = opposite/adjacent

since the angle is zero, and adjacent side x=0, tan 0=opposite/1

opposite (y) = 1 tan 0

y = 1*0 =0

Answer:

d

Step-by-step explanation:

u do the thing and u do it right and somehow it equals 2 (edge 2022)

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