If DF =61 and EF = 18 find DE

We want to factor the expression x - a, in such a way that we have one factor written as:

(√x - √a)

We will find that the factorized expression is:

(√x - √a)*(√x + √a)

Here we need to remember two things:

First, (√x)^2 = √(x^2) = x

also:

(x^2 - y^2) = (x + y)*(x - y)

Now, using the first property, we can rewrite our original expression as:

(x - a) = ( (√x)^2 - (√a)^2)

Now, using the second property, we can rewrite it as:

( (√x)^2 - (√a)^2) = (√x - √a)*(√x + √a)

Then we have:

(x - a) = (√x - √a)*(√x + √a)

Thus, we have factorized (x - a) in such a way that one of the factors is  equal to (√x - √a)

If you want to learn more, you can read:

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9514 1404 393

Answer:

  (a)

Step-by-step explanation:

Add A to both sides of the equation:

  X -A +A = B +A

  X = B + A

The sum of the two matrices is the matrix that is the sum of corresponding terms.

  x11 = B11 +A11 = -9+2 = 7

  x12= B12 +A12 = 5-7 = -2

These calculations are sufficient to match the answer with choice (a).

Answer:

79/120

Step-by-step explanation:

5/24+9/20

to add the fractions the denominator (bottom part) has to be the same. ex you can add one third and one third to make two thirds. but you wont know what 1/2 + 1/3 is.

convert to same denominator. to do this, the fractions themselves need to stay the same value but the bottom number needs to change. ex 1/2=2/4 and 1/3= 2/6. when you multiply and divide the top and bottom part of the fraction by the same number, the value of the fraction stays the same. ex 3/6 divide both parts by 3 you get 1/3. so 3/6=1/3

to get the common denominator we have to find the least common multiple, or LCM (since 5 and 9 dont share any common factors.)

24 and 20 LCM

=120

convert both 5/24+9/20 to x/120 and y/120

5/24 multiply by 5 on top and bottom

=25/120

9/20 multiply by 6 on top and bottom

=54/120

25/120+54/120

=(25+54)/120

=79/120

let length be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]

[tex]\\ \sf\longmapsto x=4(28)[/tex]

[tex]\\ \sf\longmapsto x=112[/tex]

Step-by-step explanation:

there is something wrong with your problem description.

the offered answer options do not fit to the solution as it is described.

2/8th of a rope is 28 meters long. how long is the whole rope ?

as the other answer said : 2/8 = 1/4

and 1/4th of the rope x = 28 m

1/4 × x = 28

x (the length of the whole rope) = 4×28 = 112 meters

but - maybe the original problem said that 7/8th (and not 2/8th) of a rope is 28 m.

7/8 × x = 28

1/8 × x = 4

x = 32 m

then A (32) would be the right answer !

Answer:

12.6 ft

Step-by-step explanation:

please mark this answer as brainlist

Answer:

No, the sale price wasn't consistent with the ad

Step-by-step explanation:

The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.

Answer:

-2, - 1, - 2 and - 3

Step-by-step explanation:

As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)

Answer:

1 ft

Step-by-step explanation:

1, 480/30=16

2, 16/16=1

3, 1 ft

Answer:

27

Step-by-step explanation:

f is a function defined by

{(-3, 1), (-2, 2), (-1, -3), (0, -1), (1, 3), (2, -2), (3, 0)}

so f (1) = 3. Then

h (g (i (j (f (1))))) = h (g (i (j (3))))

j is defined by

{(-3, 0), (-2, 1), (-1, 2), (0, -1), (1, -2), (2, 3), (3, -3)}

so j (3) = -3, and

h (g (i (j (f (1))))) = h (g (i (-3)))

And so on. Next you have i (-3) = 2, then g (2) = 0, and finally, h (0) = 0, so your answer is correct.

Answer:

A) [tex]430-45m = 310-25m[/tex]

B) 6 months

Step-by-step explanation:

A) for Jonah, the equation would be [tex]430-45m[/tex]

Because the money is being spent on the subs, you subtract that from his original savings.

The same thing is said for Rodrick, but his equation would be [tex]310-25m[/tex]

to find out the number of months it will take for both gamers to have the

same amount of money left, you set their equations equal to each other:

[tex]430-45m = 310-25m[/tex]

B) you solve for m.

[tex]430-45m = 310-25m[/tex]

first by subtracting 310 on both sides to get:

[tex]430-310-45m=-25m[/tex]

[tex]120-45m=-25m[/tex]

then add 45m on both sides because we cant have negative months

[tex]120=-25m+45m[/tex]

[tex]120=20m[/tex]

divide by 20 on both sides to get the number of months

[tex]\frac{120}{20} =\frac{20m}{20}[/tex]

[tex]m=6[/tex]

Answer:

Estimated expenses for next 2 years:

Rent = 1100 * 12 * 2 = 26,400

Gym membership = 450 * 2 = 900

Gym monthly fee = 40 * 12 * 2 = 960

Renter's insurance = 60 * (12 * 2 / 6) = 240

Groceries = 300 * 12 * 2 = 7200

Eating out & entertainment = 175 * 52 * 2 = 18,200

Total estimated living expenses = $53,900

Step-by-step explanation:

Step-by-step explanation:

Z will stay the same since the 2 will divide into 1

Answer:

26

Step-by-step explanation:

Answer: 3.14 · 4²

Step-by-step explanation:

A = π · r²

A = 3.14 · 4²

Hope this helps!

Answer: the radians should be 125

Step-by-step explanation:

Answer:

1/2x + 3/2(x+1) - 1/4 = 5

1/2x + 3/2(x) + 3/2 - 1/4 = 5

1/2x + 3/2(x) + 6/4 - 1/4 = 5

4/2(x) + 5/4 = 5

2x + 5/4 = 5

2x = 15/4

x = 15/8

Let me know if this helps!

Answer:

x = 15/8

Step-by-step explanation:

1/2x + 3/2(x+1) - 1/4=5 ​

1/2x + 3/2x + 3/2 - 1/4 = 5

2x + 5/4 = 5

2x = 15/4

x = 15/8

Answer: D

Step-by-step explanation:

[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]

Answer:

D

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Anything other than making x - 3 = 0 will make x - 3 have a value. No matter what happens  (x - 3)^2 is positive. There is a minus sign outside the brackets which makes (x - 3)^2 negative.

That means that something is always taken away from 5 unless x = 3. Try and find any value that will make a number bigger than or equal to five that isn't x = 3.

By the way, I'm assuming the question is y = 5 - (x - 3)^2

Answer:

x= i√30

Step-by-step explanation:

I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.

Okay, so first you want to subtract 30 from both sides

x^2=-30

Then you take the square root of each side.

√(x^2)=√-30

x=√-30

Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=√-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.

Final answer: x = i√30

Answer:

4

Step-by-step explanation:

(y+2)²=[(-4)+2]²

=(-4+2)²

=-2²

=4

Step-by-step explanation:

you gave me only one system of 2 equations. not 2 systems or more.

maybe you missed something.

I can solve this one system in two ways, though.

substitution :

x - 3y = 16

3x - 2y = 13

the first equation gives us

x = 3y + 16

that we can use now in the second equation

3×(3y+16) - 2y = 13

9y + 48 - 2y = 13

7y + 48 = 13

7y = -35

y = -5

x = 3y + 16 = 3×-5 + 16 = -15 + 16 = 1

that's it. that is all the secret of substitution. you use one equation to express one variable by the other. and then you use that in the second equation to have suddenly only one equation with one variable that you can solve. and then from that result you calculate back the other "substituted" variable.

elimination :

x - 3y = 16

3x - 2y = 13

we multiply one equation completely by a factor and then add both equations. of course we should pick a factor that will eliminate one variable, when we add the equations.

e.g.

multiply the first equation by -3

-3x + 9y = -48

3x - 2y = 13

--------------------

0 7y = -35

y = -5

now we pick any one of the equations to use that result and calculate the other variable

e.g. the second equation

3x - 2×-5 = 13

3x + 10 = 13

3x = 3

x = 1

done.

as you can see : of course, both results are identical.

use the described principles to solve any other systems of equations you might have missed here.

[tex]The \: text \: tells \: us \: that \: we \: can \\ predict \: her \: height \: by \: taking \\ her \: age \: in \: months, \: adding \: 75, \\ and \: multiplying \: by  \: \frac{1}{3} . \: So \: our \\ equation \: is [/tex]

[tex]h = (m + 75). \frac{1}{3} [/tex]

(or)

[tex]h = \frac{1}{3} (m + 75)[/tex]

b) Determine her predicted height on her second birthday

To predict Asia’s height on her second birthday, we substitute m=24

into our equation (because 2 years is 24 months) and solve for h.

[tex]h = \frac{1}{3} (24 + 75)[/tex]

[tex]h = \frac{1}{3} (99)[/tex]

[tex]h = 33[/tex]

Asia’s height on her second birthday was predicted to be 33 inches.

Q(x)=x^2+3x+2

[tex]\\ \sf\longmapsto Q(-4)[/tex]

[tex]\\ \sf\longmapsto (-4)^2+3(-4)+2[/tex]

[tex]\\ \sf\longmapsto 16+(-12)+2[/tex]

[tex]\\ \sf\longmapsto 16-12+2[/tex]

[tex]\\ \sf\longmapsto 4+2[/tex]

[tex]\\ \sf\longmapsto 6[/tex]

The value of the function at x = - 4 will be 6. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The function is given below.

Q(x) = x² + 3x + 2

The value of the function at x = - 4, then we have

Q(-4) = (-4)² + 3(-4) + 2

Simplify the equation, then we have

Q(-4) = (-4)² + 3(-4) + 2

Q(-4) = 16 - 12 + 2

Q(-4) = 18 - 12

Q(-4) = 6

The value of the function at x = - 4 will be 6. Then the correct option is D.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Answer:

12* 12 = 144

thus 4*12 = 48 feet of fence

Step-by-step explanation:

It sounds like R is the region (in polar coordinates)

R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}

Then the integral is

[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]

Answer:

16cm

Step-by-step explanation:

Area is A = bh

to find a base, b = A/h

A=80

h=5

so then we have b = 80/5 = 16

Answer:

Step-by-step explanation: