Work out the area of triangle ABC.

Work Out The Area Of Triangle ABC.

Answers

Answer 1

Answer:

A = 4 cm²

Step-by-step explanation:

The area of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

b = AC = 3[tex]\sqrt{2}[/tex] + [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex]

h = BD

Calculate BD using Pythagoras' identity in Δ ABD

BD² = AB² - AD²

      = (2[tex]\sqrt{5}[/tex] )² - (3[tex]\sqrt{2}[/tex] )²

     = 20 - 18 = 2 ( take square root of both sides )

BD = [tex]\sqrt{2}[/tex]

Then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 4 cm²


Related Questions

is h(x) = 6 a linear function and why

Answers

Answer:

yes, absolutely. specifically it's a horizontal line at 6.

A driver travels for 2 hours at 90 miles per hour, during which her car gets 30 miles per galoon of gasoline. She is paid $0.70 per mile, and her only expense is gasoline at $4 per gallon. What is her net rate of pay, in dollars per hour, after this expense?

Answers

Answer:

Her net rate of pay in dollars per hour after the expense = $26

Step-by-step explanation:

Given:

Driver travels for 2 hours.

Speed = 60 miles per hour

Her car runs at the rate of 30 miles per gallon of gasoline.

She is paid $0.50 per mile.

Expenses is price of gasoline at the rate of $2.00 per gallon.

To find her net rate of pay in dollars per hour.

Solution:

In one hour the driver travels = 60 miles

For each mile she is paid = $0.50

So, for 60 miles she will be paid =

In a gallon of gasoline the car travels = 30 miles

So, to travel 60 miles, the car would require = gallons of gasoline

1 gallon of gasoline cost = $2.00

Expenses for 2 gallons of gasoline =

So, in one hour she gets paid =$30 and her expenses for an hour drive = $4.

Thus, her net rate of pay in dollars per hour after the expense =

Brainlist please

The net rate of pay is $122 for the two hours journey.

The driver travels for 2 hours at 90 miles per hour.

Total distance travelled = 2 hours * 90 miles per hour = 180 miles

Money paid to driver = $0.70 per mile * 180 miles = $126

Fuel consumption = 30 miles per gallon, hence:

Total fuel consumption = 180 miles / (30 miles per gallon) = 6 gallon

Total expense = $4 per gallon * 6 gallon = $24

Net rate of pay = $126 - $24 = $122

The net rate of pay is $122 for the two hours journey.

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5) - 2y = -2x

slope intercept form please someone help i don’t have much time

Answers

[tex]\text{Given that,}\\\\-2y = -2x\\\\\implies y = x\\\\\implies y = x+0\\\\\\\text{This is the slope- intercept form(y=mx+b) of the given equation,}\\ \text{where the slope is 1 and y - intercept is 0.}[/tex]

Which of the following shapes is convex?
М.
OA)
OB)
W
OC)
OD

Answers

Answer:

I think the correct answer is c hope this helps

Graph: y = 3 * x + 5 ​

Answers

Answer:

2

Step-by-step explanation:

take the 3 put on the side

find the interval in which the function is negative.

f(x) = x^2 - 3x - 4

I. (- infinite, -1)

II. (-1, 4)

III. (4, infinite)

A. III only

B. II only

C. I, II

D. I, III​

Answers

Answer:

  B. II only . . . (-1, 4)

Step-by-step explanation:

The function factors as ...

  f(x) = (x +1)(x -4)

The factors are zero when x=-1 and x=4. The value of the function will be negative when one of these factors is negative, between x=-1 and x=4. In interval notation, that interval is ...

  (-1, 4) . . . interval for f(x) < 0 . . . . . . interval description II (only)

Mr.Wedmore works at a car dealership and earns a monthly salary of $2,000. He also earns 25% commission on the gross profit of the car sales. If Mr.Wedmore brought in $10,000 worth of profit, for the dealership, how much would he earn this month

Answers

Answer:

25% of 2000= 500

25% of 10000= 2500

Step-by-step explanation:

3. Solve for side length BD
A
31
D
13 cm
I
47
C
B

Answers

Answer:

A

Step-by-step explanation:

this is beacuse of the ? mark!

Glad this will help

Two fractions in the middle of 1/4 and 3/4

Answers

2/4 and 2.5/4 this is my answer
The right answer is 2/4 and 3/5
2/4 = 0.5 and 3/5 = 0.6 and both these numbers are in between 1/4 = 0.25 and 3/4 = 0.75

The length of a rectangle is 6 inches more than 4 times its width. A similar
rectangle has a length of 18 inches and a width of 4 inches. What is the area of the
first rectangle??

Answers

Answer:

18 × 4 is 72...

so.. the area of rectangle is 72inches²

Step-by-step explanation:

to find the area of rectangle is Lenght multiple with its Width

The quadratic function g(x)=ax^2+bx+c has the complex roots (10+i) and (10-i). You may assume that a=1.
What is the value of b?
What is the value of c?

Answers

The values are [tex]b=-20\text{ and }c=101[/tex]

The quadratic function, expressed in factored form is

[tex](x-(10+i))(x-(10-i))=g(x)[/tex]

Expanding and simplifying

[tex]g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101[/tex]

since

[tex]g(x)=ax^2+bx+c=x^2-20x+101[/tex]

we can equate coefficients of like-terms and conclude that

[tex]a=1,b=-20,c=101[/tex]

Learn more about quadratic equations here: https://brainly.com/question/12995618

how to solve for x (proportions)

Answers

Answer:

16/3 or 5 1/3

Step-by-step explanation:

Cross Multiply

4×4

3×x

16=3x

Divide 3 from 16

x=16/3 or 5 1/3

Please answer this question step by step!

No links please.

Whoever gives correct answer will get a thank you aswell.

Answers

Answer:

[tex]x = \frac{3}{2} [/tex]

Step-by-step explanation:

first distribute

[tex] \frac{36x - 9}{2x} = 15[/tex]

next multiply both sides by 2x

[tex]36x - 9 = 15(2x) \\ 36x - 9 = 30x[/tex]

simplify

[tex] - 9 = - 6x[/tex]

divide both sides by -6

[tex] \frac{ - 9}{ - 6} = x \\ \frac{3}{2} = x[/tex]


[tex] \sf2 + 63 - 36 - 2[/tex]


Here's some points ~ ​

Answers

2+63-2=32

Bye hope this help!

To find the surface area, Brad splits the figure into two pieces, the rectangular prism and
the triangular prism.
He finds the total surface area of the rectangular prism by finding the area of each face
to get 1,104 cm
He then finds the total surface area of the triangular prism by finding the area of each
face to get 1,008 cm
Finally, he adds the surface areas together to get 2,112 cm.
Is Brad's solution correct? Why or why not?
Select the option that correctly answers both questions.
No, he did not find the correct total surface area for the triangular prism.
O No, he did not find the correct total surface area for the rectangular prism.
No, he needs to subtract the areas of the faces where the two prisms are
attached
Yes, he correctly found the sum of the surface areas for each prism.

Answers

The surface area of the figure is the amount of area covered by the figure.

The figure is not given, so I will give a general solution.

The method followed by Brad to calculate the surface area of the prism is correct.

However, whether Brad correctly calculates the areas of the rectangular prism and the triangular prism cannot be determined.

So, the conclusion is that:

If Brad's calculation of the surface areas of the prisms is correct, then the surface area of the figure is correct because 1104 + 1008 = 2112.If otherwise, then the solution is incorrect

Read more about surface areas at:

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help pls i don't know how to do it

Answers

Answer:

y=5x-8

Step-by-step explanation:

Slope=m=(7-3)/(3-2)

y=5x+b=>2=5*2+c=>c=-8

So y=5x-8

[tex]\text{Given that,}\\\\(x_1,y_1) = (2,2), ~ \text{and}~ (x_2,y_2) = (3,7)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{7-2}{3-2} = \dfrac 51 = 5\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y-2= 5(x-2)\\\\\implies y -2 = 5x-10\\\\\implies y = 5x -10 +2\\\\\implies y = 5x -8\\\\\\\text{It is now in a form of y = mx +c}[/tex]

2. Name 3 points that are collinear*
2
s
S
R
O points T, Q, and R
O points T, Q, and S
O points S, Q, and R

Answers

Answer:

T, Q, and R

Step-by-step explanation:

These points are all on the same line, making them collinear.

I hope this helps!!

100 points


Suppose a recipe calls for 2 1/2 cups of liquid made of milk and water. If 1 2/3 cups of milk are used, how much water is needed?

Answers

Answer:

1/3 * 3 = 1 cup of milk

1/2 * 3 = the amount of water needed per cup of milk

1/2 * 3 = 3/2 or 1.5

The recipe calls for 1.5 cups of water per cup of milk.

Hope this helps!

The quantity of water in the liquid is 5/6 cups

How to subtract fractionTotal cups of liquid (milk and water) = 2 1/2 cups

If cups of milk = 1 2/3 cups

Water = Total cups of liquid - cups of milk

= 2 1/2 - 1 2/3

= 5/2 - 5/3

The least common denominator is 3× 2 = 6

= (15-10) / 6

= 5/6 cups

Learn more about fraction:

https://brainly.com/question/11562149

simplify 3^2 x 3^4 x 3^6 A3^10 B3^12 C3^48 D3^0​

Answers

Answer:

[tex]\boxed{\sf\: B)\:3^{12}}[/tex]

Step-by-step explanation:

[tex]\sf 3^2\times \:3^4\times \:3^6[/tex]

Apply exponent rule:

[tex]\hookrightarrow \boxed{\sf a^b\times \:a^c=a^{b+c}}[/tex]

[tex]\sf 3^2\times \:3^4\times \:3^6[/tex][tex]\sf 3^{2+4+6}[/tex]

Add the numbers:

[tex]\sf 2+4+6=12[/tex][tex]\sf \:3^{12}[/tex]

________________________________


Will mark brainliest

Answers

Answer:

Quadrant 3     or aka     Quadrant III

Step-by-step explanation:

The top right quadrant is the first quadrant. Aka Quardant 1

The top left quadrant is the second qudrant. Aka Quadrant 2

The bottom left quadrant is the third quadrant. Aka Quadrant 3

The bottom left quadrant is the fourth quadrtant. Aka Quadrant 4

The heart is located in the bottom left quadrant. Meaning, it is the third quadrant. Aka Quadrant 3

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The average 8- to 18-year-old spends____ per day on average in front of a screen doing very little to
no physical activity.
A. O hours
B 30 minutes
0. 1 hour
D 3 hours or more
Please select the best answer from the choices provided.

Answers

Answer:

3 hours or more

Step-by-step explanation:

why because of the games and entertainment

A coffee pot holds 6 quarts of coffee. How much is this in cups?

Answers

Answer:

24 cups

Step-by-step explanation:

1 quart = 4 cups

6x4= 24 cups

Answer:

24 cups.

Step-by-step explanation:

Each quart is equal to 4 cups. This means you have to do 6x4 to find the answer.

please help me asap, i suck at math tbh :)

ty!

Answers

x intercepts: (9,0)
y intercepts: (0,-6)

Answer:

Y intercept = (0,-6)

X intercept = (9,0)

Step-by-step explanation:

To find the y-intercept of an equation, let x = 0 and then solve for y

6(0) - 9y = 54 (6 times 0 gives us 0)

0 - 9y = 54 (subtract 9y from 0 gives you -9)

-9y = 54 (divide both sides by -9, the left side cancels out and the right side gives you -6)

y = -6 and x = 0

To find the x-intercept of the equation just let y = 0 and then solve for x

6x - 9(0) = 54 (9 times 0 gives us 0)

6x - 0 = 54 (subtract 0 from 6x gives us 6x)

6x = 54 (divide both sides by 6, left side cancels, right side gives 9)

x = 9 and y = 0

Solve for the x

[tex]\frac{36}{x}[/tex] = -9

Answers

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

[tex]:\implies\sf{ \frac{36}{x} = - 9} \\ \\ :\implies\sf{ \frac{36}{ 9} = -x} \\ \\ :\implies\sf{4 = -x} \\ \\ :\implies\sf{x = -4}[/tex]

-324 because 36/-324 is -9. Make sure to add the negative

Find the midpoint of PQ¯¯¯¯¯¯¯¯ with endpoints P(0, 2) and Q(6,−2). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ¯¯¯¯¯¯¯¯ . This line is called the perpendicular bisector.

Answers

Answer:

The midpoint of PQ is (3,0) and the equation if the line perpendicular to PQ is y=3/2(x-3).

Step-by-step explanation:

To find the midpoint, find the average of the x and y values. (0+6)/2=3 and (-2+2)/2=0

In order to make a perpendicular line, we must find the slope first of the original line.

(y2-y1)/(x2-x1) is the formula for slope

(-2-2)/(6-0)= -4/6=-2/3

Now we know the slope which is all we need to start making the equation using the point slope form which is y-y1=m(x-x1) (let m be slope) and we use the midpoint (3,0) as our point. since it is perpendicular, we will take the slope and flip it as well as change the sign

y-0=3/2(x-3) or y=3/2(x-3)

if you'd like, you can distribute and put it in slope intercept form

y=3/2x+9/2

FURNITURE A modern table is constructed with four legs made
of concrete cubes with cube-shaped notches.
a. Define one or more variables and write an expression that
represents the volume of one table leg.

b. Marisol determined that she will use 12,636 cubic inches of
concrete to construct the four table legs. If the sides of the
notches are 40% of the sides of the legs, how long are the sides of the legs?

Answers

The volume of a shape is the amount of space in it.

The expression that represents the volume of one table leg is: [tex]V = l^3 + n^3[/tex]The sides of the legs is 14.37 inches long

(a) The volume of one table leg

Represent the side length of the leg with l, and the side length of the notch with n.

So, the expression that represents the volume of one table leg is:

[tex]V = l^3 + n^3[/tex]

(b) The length of the sides

From the question, we have:

[tex]n = 40\% \times l[/tex]

Express 40% as decimal

[tex]n = 0.40 \times l[/tex]

[tex]n = 0.4l[/tex]

Substitute 0.4l for n in [tex]V = l^3 + n^3[/tex]

[tex]V =l^3 + (0.4l)^3[/tex]

[tex]V =l^3 + 0.064l^3[/tex]

[tex]V =1.064l^3[/tex]

The volume of the 4 legs is given as: 12636

So, the volume of one leg would be 12636/4

So, we have:

[tex]1.064l^3 = \frac{12636}{4}[/tex]

[tex]1.064l^3 = 3159[/tex]

Divide both sides by 1.064

[tex]l^3 = 2968.985[/tex]

Take cube roots of both sides

[tex]l = 14.37[/tex]

Hence, the sides of the legs is 14.37 inches long

Read more about volumes at:

https://brainly.com/question/1972490

whats the rate of change

Answers

The line needs to start at the 0 it can’t be off the 0

Q.

[tex] \frac{9}{6} + \frac{6}{9} = [/tex]

#use method
#good luck​

Answers

Answer:

The answer is 13/6

Step-by-step explanation:

9/6 + 6/9

9/6 = 3/2

6/9 = 2/3

Now,

3/2 + 2/3

Cross Multiply

3 × 3 + 2 × 2/2 × 3

9 + 4/6 = 13/6

Thus, The answer is 13/6

-TheUnknownScientist 72

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

[tex] = \frac{9}{6} + \frac{6}{9} \\ = \frac{27 + 12}{18} \\ = \frac{39}{18} \\ = \frac{13}{6} [/tex]

Hassan surveyed 120 of the students in his school about their favorite color. 114 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?

Answers

Answer:

95%

i think it should be that

5% because you take the 6 that was the difference and then you divide it by the whole and then you multiply the decimal by 100 to get 5%

PLEASE HELP I"LL GIVE BRAINLEST

Carl solves 12 multiplication problems for every 4 addition problems. If he solves 23 addition problems, how many multiplication problems does he solve?

46 multiplication problems

92 multiplication problems

69 multiplication problems

54 multiplication problems

Answers

Answer:

92         4× 23

Step-by-step explanation:

sorry if im incorrect

Answer:

Carl solves 69 multuplication problems

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