The area of a rectangle is 252 cm², and the length is 3 less than 2 times the width. Find the dimensions of the rectangle.

Answer:

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

to

r > s

The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.

Both matrices are 1 x 4 matrices. This notation says there is 1 row and 4 columns. The number of rows must match up, as well as the number of columns, in order for matrix addition to be possible. This is so the corresponding elements pair up and add together. For instance, the 5 and -2 pair up and add together for matrices A and C.

Answer: 33

Step-by-step explanation:

there ages m and b.

m = b + 12

m - 17 = 4(b - 17) m = 4b - 51

3b = 63

b = 21

m = 21 + 12 = 33

Hope this helps :)

Answer: Michael is 33 years old.

Step-by-step explantation: Okay, think of it like this, Michael's age for right now is x since we still do not know Michael's age. Pay close attention to the first sentence. What does it say?  m = b + 2. Now pay attention to the second sentence. What does it say? m - 17 = 4 ⋅ (b = 17). Now, let's move on to the system of equations. As you can see here, the system of equations is

{m = b + 12

{m - 17  = 4 ⋅ (b - 17}.

Now for more equations.

m - 17 = 4b - 68

m = 4b - 68 + 17

m = 4b - 51

m - 4b = -51

-

b + 12 - 4b = -51, through the substitution from the first equation we saw

-3b = -51 - 12

3b = 51 + 12

b = 51/3 + 12/3

b = 17 + 4

b = 21

-

m = 33.

Answer:

67

Step-by-step explanation:

Answer:

y= -x/2+8

Step-by-step explanation:

Cause I know UwU

Answer:

distance island dock to Dock A = 4.99 km

distance island dock to Dock K = 6.35 km

Step-by-step explanation:

Always make a scetch to visualize the situation.

You need to construct two triangle both with a streight angle, so you can use Pythagoras to calculate the unknown distances between the island dock L, and each of the other two docks A an K.

I chose to introduce an extra letter, the letter C. In total you have the letters A K L and the letter C.

The letter C has a streight angle of 90° between ACL and it has the same streight angle of 90° with KCL. It is crucial that you see that the distance of LC is exactly the same in triangle LAC and that LC has exactly the same distance in the other triangleLKC.

The distance between AK = 2.3 km.

I define the distance between K and point C as 2.3 + x, because the distance x is unknown.

KC = 2.3 + x

Further more, when you make a picture, you can see that the distance between A and point C = x.

From such a picture, it would show clearly, that K is further away in respect to L then point A. From the picture it would be clear that the angle of LKC is smaller then the angle of LAC, so LKC = 45° and LAC = 64°.

Because angle LKC = 45° and we choose C to have an angle of 90°, the TRIANGLE LKC must be a special triangle... In any triangle, the sum of the three angles together, must add up to 180° .

If that is true, then we have 45 + 90 + 45 (because that adds up to 180). Now that means triangle LKC must have two equal sides (because of the same angels of 45° ).

So we know the distance KC = LC and we already defined KC = 2.3 + x.

Now we know enough to solve the problem.

AK = 2.3 km

angle of LKC = 45°

angle of LAC = 64°

AC = x

KC = 2.3 + x

LC = KC

LC = 2.3 + x

Try to calculate the distance x by using tan. After that you can use Pythagoras to find the other distances.

tan(LKC) = ( LC ) / ( KC )

tan(LKC) = ( x+2.3 ) / ( x+2.3 )

That is not helpful. Let's try the other triangle...

tan(LAC) = LC / AC

tan(LAC) = ( x+2.3 ) / x

tan(64) = ( x+2.3 ) / x

Solve the equation which means you try to find the value for x.

x * tan(64) = ( x+2.3 )

tan(64) * x -x = 2.3

tan(64) * x - 1* x = 2.3

Try to get x outside of the braquets...

x* ( tan(64) - 1 ) = 2.3

x* (2.0503038415793 - 1 ) = 2.3

1.0503038415793 * x = 2.3

x = 2.3 / 1.0503038415793

x = 2.19

Now use Pythagoras a² + b² = c² in triangle LAC to find distance LA.

LA² = AC² + LC²

AC = x = 2.19

LC = 2.3 + x = 4.39

LA² = 2.19² + 4.39²

LA = SQRT( 4.79 + 20.16 )

LA = SQRT( 24.95 )

LA = 4.99 km

Now use Pythagoras a² + b² = c² in triangle LKC to find distance LK.

LK² = KC² + LC²

KC = 2.3 + x = 4.39

LC = 2.3 + x = 4.39

LK² = 4.39² + 4.39²

LK = SQRT( 20.16 + 20.16 )

LK = SQRT( 40.32 )

LK = 6.35 km

Answer: 100

Step-by-step explanation:

Answer:

The square root of 10000 is 100

Step-by-step explanation:

Answer:

c d

Step-by-step explanation:

no explanation

take out a minus from first two fractions

*diagram of the dot plot is attached below

Answer:

$2.15

Step-by-step Explanation:

Mean daily pocket money or average daily pocket if the group if students shown in the for plot that is attached below = the sum of the pocket money received by the students ÷ the total number of students.

From the diagram of the dot box attached below, the total number if students = 13 (each dot represents a student)

Sum of the pocket money received by the students = 4(1) + 5(2) + 3(2) + 4(2)

= 4 + 10 + 6 + 8

Sum = 28

Therefore, mean daily pocket money = 28 ÷ 13 = $2.15

Answer:

Composite Numbers.

Answer:

(5x²+2y² + 2xy)(5x²+2y² - 2xy)

Step-by-step explanation:

It must be: 25x⁴+4x²y²+4y⁴

Then solution is:

Answer: 50, 75, 40, 125

Step-by-step explanation:

a) x = 5*20/2 = 50

b) x = 5*30/2 = 75

c) x = 2*100/5 = 40

d) x = 5*50/2 = 125

Answer:

[tex] \boxed{n = 6} [/tex]

Step-by-step explanation:

[tex] = > 2 = \frac{n}{3} \\ \\ = > \frac{n}{3} = 2 \\ \\ = > n = 2 \times 3 \\ \\ = > n = 6[/tex]

Answer:

Step-by-step explanation:

If the parent function is f(x) = x² and the transformed function is g(x) = a(x)²

For a > 1, then the transformed function g(x) will be vertically stretched by a factor of 'a'

For 0 < a < 1, then the transformed function will be vertically compressed or shrink by a factor of 'a'

For a function f(x) = x² when transformed to f(5x) = (5x)²

g(x) = 25x²

Therefore, graph of the parent function f(x) will be vertically stretched by 25 units.

Answer:

D. (2, 1)

Step-by-step explanation:

slope = 1/2

y-intercept = 0

Equation: y = 1/2 x

Choice A:

x = 0

y = (1/2)(0) = 0

Choice A does not work.

Choice B:

x = 1/2

y = (1/2)(1/2) = 1/4

Choice B does not work.

Choice C:

x = 1

y = (1/2)(1) = 1/2

Choice C does not work.

Choice D:

x = 2

y = (1/2)(1) = 1

Choice D works.

Answer: D. (2, 1)

Answer:

x=5

Step-by-step explanation:

2x+10=20

   -10   -10

2x=10

then divide both sides by 2

x=5

Answer:

x = 5

Step-by-step explanation:

Given

2x + 10 = 20

Subtract 10 to both sides

(2x + 10) -10 = 20 - 10

2x = 10

Divide both sides by 2

[tex]\frac{2x}{2} =\frac{10}{2}[/tex]

x=5

Check your work. Substituted 5 for x

2x + 10 = 20

2(5) + 10 =20

10 + 10 = 20

20 = 20

Answer:

The answer is 415 because it is already in standard notation.

Answer:

the median time for the 50 yard dash is 8 seconds

Step-by-step explanation:

hope this helps :)

Answer:

c. 81

Step-by-step explanation:

(x^3)^1/6= √81

x^(3*1/6)= √81

x^(1/2)= √81

√x=√81

x=81

Answer: A

Step-by-step explanation:

Answer:

the correct answer i believe is A. :)

If x = 0, then the value of the function f(0) will be negative 15. And if the value of the function f(x) is 27. Then the value of x will be 3.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The table is given below.

If x = 0, then the value of the function f(0) will be

f(0) = -15

And if the value of the function f(x) is 27. Then the value of x will be

x = 3

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Answer:

if x = 0, then f(0) = -15 and if f(x) = 27, then x = 3

Step-by-step explanation:

i look at the table for 0 and 27 and then look at the numbers next to it

Answer:

The first part is [tex]4+12x=28[/tex]

The second part is multiply both sides by 4

The third part is (not sure cause i got subtract 16 from both sides) but i think it is subtract 3 to both sides

The fourth part is [tex]x=8[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}\left(16+12x\right)=28\\\mathrm{Multiply\:both\:sides\:by\:}4\\4\cdot \frac{1}{4}\left(16+12x\right)=28\cdot \:44\cdot \frac{1}{4}\left(16+12x\right)=28\cdot \:4\\Simplify\\16+12x=112\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\16+12x-16=112-16\\\mathrm{Simplify}\\12x=96\\\mathrm{Divide\:both\:sides\:by\:}12\\\frac{12x}{12}=\frac{96}{12}\\Simplify\\x=8[/tex]

Answer:

4) BC=30.14

11)XZY≈47.5°

Step-by-step explanation:

4) we use cosine law because we have two length known and one angle known

BC²=AB²+AC²-2ABcos55°

BC²=23²+20²-2*23*20cos55°=908.6

BC=√908.6= 30.14 cm

11) we use cosinee law because three length known

cosXZY=(22²+20²-17²)/(2×22×20)

cosXZY=0.676

XZY^= cos^-1 0.676

XZY^=47.5°

Answer:

13

Step-by-step explanation:

We only need to pay attention to the x. We multiply 3 and 4 to get 12. Then we add 1 to get 13.

Answer:

13

Step-by-step explanation:

3x + 1

Let x = 4

3*4 +1

Multiply

12+1

13

Answer: i think its b.

Step-by-step explanation:

Answer:$43

Step-by-step explanation:

65 -22 =43