Solve for x and find the measure of angle AED and angle AEC

(not drawn to scale)

Answer:

√7

Step-by-step explanation:

Let :

AC = x

BD = y ; AD = 3 - y

Since, AD = BC

Then BC = 3 - y

Taking △BDC a d applying Pythagoras

Hypotenus² = opposite² + adjacent²

BC² = CD² + BD²

(3 - y)² = (√3)² + y²

9 - 6y + y² = 3 + y²

-6y + y² - y² = 3 - 9

-6y = - 6

y = 1

AD = 3 - y ; AD = 3 - 1 = 2

Taking △ADC

AC² = CD² + AD²

AC² = (√3)² + 2²

AC² = 3 + 4

AC² = 7

AC = √7

Answer:

x=4

Step-by-step explanation:

3/4x +4 = 7

3/4x +4-4 = 7-4

3/4x = 3

Multiply each side by 4/3

4/3 * 3/4x = 3 *4/3

x = 4

Answer:

x = 4

Step-by-step explanation:

3/4x + 4 = 7

3/4x = 3

To remove the denominator, we multiply by 4 on both sides

3x = 12

x = 4

9514 1404 393

Answer:

Step-by-step explanation:

1. There will be no solution if the equation is a contradiction. Usually, it is something that can be reduced to 0 = 1.

If we choose to make our equation ...

  x = x +1

Subtracting x from both sides of the equation gives ...

  0 = 1

There is no value of the variable that will make this be true.

__

2. Something that reduces to x = c will have one solution. One such equation is ...

  0 = x+1

  x = -1 . . . . subtract 1 from both sides

__

3. Something that reduces to x = x will have an infinite number of solutions.

One such equation is ...

  x+1 = x+1

Subtracting 1 from both sides gives ...

  x = x . . . . true for all values of x

An amount of $ 5272 he will have in the account at the beginning of year 9. Option D is corect.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

The expression is;

[tex]\rm A(n) = 4500(1+0.02)^{n-1}[/tex]

At the beginning of 9-year value of n is 9,substitute the value to get he amount;

[tex]\rm A(n) = 4500(1+0.02)^{n-1} \\\\ \rm A(n) = 4500(1+0.02)^{9-1} \\\\ A(n) = \$ 5272[/tex]

Hence, option D is corect.

To learn more, about equations, refer;

https://brainly.com/question/10413253

#SPJ1

Answer:

c) ( x-15)/-8

Step-by-step explanation:

c) (x-15) / -8

Answer:

Solution given:

y = -8x + 15

interchanging role of x and y

we get

x=-8y+15

solve for y

x-15=-8y

divide both side by-8

we get

-8y/-8=(x-15)/-8

y=(x-15)/-8

:.

C. y = (x - 15)/-8 is a required inverse.

Answer:

14.4

Step-by-step explanation:

since the longest side is 24,find the shortest side

√20^2-12^2

√400-144

√256

=16

which means the other shortest side is 24-16

which is 8

then you have to use the 12 and 8 to find the unknown side

√12^2+8^2

144+64

√208

14.4

I hope this helps

Answer:

B or (-2/3)

Step-by-step explanation:

Perpendicuar lines have negative inverse slopes SO

3/2 ---> -2/3

Answer: [tex]\dfrac{8}{3}\ m[/tex]

Step-by-step explanation:

Given

Length of the plank is [tex]6\ m[/tex]

Foot of the flank is [tex]4\ m[/tex] away from the wall

Lizard climbs 2 m up the wall

from the figure, the two triangles are similar

[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]

So, the distance from the wall is

[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]

Answer:

C.

[tex]{ \tt{f(x) = \frac{12}{x} - 18}} \: and \: { \tt{g(x) = \frac{12}{x + 18} }}[/tex]

Step-by-step explanation:

[tex]{ \tt{f(x) = \frac{12}{x} - 18}}[/tex]

Let inverse be m:

[tex]{ \tt{m = \frac{12}{x} - 18 }} \\ { \tt{x(m + 18) = 12}} \\ { \tt{x = \frac{12}{m + 18} }} \\ \\ { \boxed{ \sf{f {}^{ - 1} (x) = g(x) = \frac{12}{x + 18} }}}[/tex]

Answer:

Answer is D

Step-by-step explanation:

cuh s

7^4/7^0

= 7^4/1 (n^0 = 1)

= 7^4

Must click thanks and mark brainliest

Answer:

x=45°

Does the answer help you?

Answer:

2)

3)

4)

5)

6)

Step-by-step explanation:

Answer:

1.08915145

Step-by-step explanation:

First of all do 39 x 52, which equals 2028. Then to do the second part of the equation we move the two bottom numbers place value up by one giving us 38 x 49 which is 1862. And then we put 2028 divided by 1862 into our calculators and get the answer as 1.08915145.

Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.

✧ Let us assume :

Seena's age be x

Her mother's age be 4x

✧ After 5 years :

Seena's age = x + 5

Her mother's age = 4x + 5

✧ Ratio of age after 5 years :

Seena's mother = 3

Seena's ratio = 1

Hence, the equation is :

[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]

By cross multiplying we get

[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]

[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]

[tex] \looparrowright \frak{x = 10}[/tex]

Hence, the ages are

Seena's age = x = 10 yrs

Her mother's age = 4x = 4 × 10 = 40 years

∴ Seena's age is 10 and her mother's is 40 respectively

Answer:

Step-by-step explanation:

find the value of a and b if 5+√3/7+2√3=a-b√3

Answer:

x = 19

Step-by-step explanation:

The two angles with measures are supplementary.

6x + 9 + 4x - 19 = 180

10x - 10 = 180

10x = 190

x = 19

Answer:

10x -10

Step-by-step explanation:

this answer is really sure

Answer:

x=61.71428 or 61 5/7

Step-by-step explanation:

We can use a ratio to solve

7 pieces              12 pieces

-----------------   = ---------------

36 seconds          x seconds

Using cross products

7x = 36*12

7x = 432

Divide by 7

7x/7 = 432/7

61 5/7

x=61.71428

Answer:

66

Step-by-step explanation:

Answer:

given values are:

1200 = 20×30 + 1/2 × 30²a

1200= 600 + 1/2 × 900a

600 = 450a

a = 600 / 450

a = 1.33 m/s²

v² = 20² +2 × 1.33 × 1200

v²= 400 + 3192

v = √3592

v = 59.9 ≈ 60 m/s

Answer:

240

Step-by-step explanation:

We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:

Hypotenuse/leg = leg/part

Where,

Hypo = 400

Leg = x

Part = 144

Substitute

400/x = x/144

Cross multiply

400*144 = x*x

57,600 = x²

√57,600 = x

240 = x

x = 240

Answer:

the original population of the city is 7,505,833

Step-by-step explanation:

Given;

new of the population of the city, Y = 9,007,000

the percentage increase of the city, = 20% = 0.2

Let the original population of the city = X

New population, Y = X  + 0.2X

                           Y = X(1 + 0.2)

                           Y = X(1.2)

                           Y = 1.2X

                           X = Y/1.2

                           X = (9,007,000) / 1.2

                           X = 7,505,833

Therefore the original population of the city is 7,505,833

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

Step-by-step explanation:

Let the numbers be x and y.

We have:

Substitute y and solve for x:

Then y is:

The numbers are:

Answer:

23•1

Step-by-step explanation:

83°/360°×100km=23•1

Answer:

x = 4, -4, 7i, -7i

Step-by-step explanation:

(x^2 – 16)(x^2 + 49) = 0

x^2 – 16 = 0 or x^2 + 49 = 0

x^2 = 16 or x^2 = -49  

x = ± 4 or x^2 = ±7√-1  =±7i

Answer:

36

Step-by-step explanation:

(-6)² = (-6) × (-6)

= +36

The required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

The formula for calculating the volume of the conical lid's is expressed as

[tex]V = \frac{1}{3} \pi r^2h[/tex] where:

r is the radius

h is the height

v is the volume

Given the following

r = x

If the conical lid’s height is 2 centimeters less than the radius, x, then;

h = x - 2

V = 25π cm³

Substitute the given values into the formula as shown:

[tex]25 \pi = \frac{1}{3} \pi x^2 (x-2)\\3(25) = x^2(x-2)\\Expand\\75=x^3-2x^2\\Swap\\x^3-2x^2 = 75\\Equate \ to \ zero\\x^3-2x^2 - 75 = 0[/tex]

Hence the required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

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Answer:

Plant B

Step-by-step explanation:

When you compare the number of tomatoes she picks from plant B with plant A, you will notice that plant B has not produced less tomatoes than plant A in any day but it has either produced the same or more number of tomatoes.