A rectangular room is 4 times as long as it is wide, and its perimeter is 50 meters. Find the dimension of the room

Answer:

yes

Step-by-step explanation:

yes

Answer:

[tex]x=22\text{ and } y=123[/tex]

Step-by-step explanation:

By definition, the interior angles of a triangle must sum to 180°. Therefore:

[tex](2x+13)+(57)+(3x)=180[/tex]

Combine like terms:

[tex]5x+70=180[/tex]

Subtract 70 from both sides:

[tex]5x=110[/tex]

And divide both sides by five. Hence:

[tex]x=22[/tex]

Next, notice that y and the 57° angle form a linear pair. By definition, linear pairs equal 180°. Therefore:

[tex]y+57=180[/tex]

So:

[tex]y=123[/tex]

Alternatively, we can use the Exterior Angle Theorem, which states that the exterior angle is equivalent to the sum of the two interior angles opposite to the exterior angle. In other words:

[tex]y=(2x+13)+(3x)[/tex]

Since we've determined that x = 22:

[tex]y=(2(22)+13)+(3(22))=44+13+66= 123[/tex]

We acquire the same answer.

Answer:

$190

Step-by-step explanation:

My knowledge!

Hope it helps!

Answer:

190

Step-by-step explanation:

Step 1 find total amount of money she has saved

To do this simply multiply the amount of money she saves per week ( 4.75 ) by the number of weeks ( 8 )

Hence money she has saved = 8 * 4.75 = 35

Step 2 subtract cost of camera by amount of money she has saved

228 - 38 = 190

So we can conclude that she needs 190 more dollars to purchase the camera.

Answer:

Question 1

probability of a red marble in the first draw = 1/10

probability of a orange marble in the second draw = 4/9

probability of getting red in first and orange in second (without replacement) = 1/10 * 4/9 = 2/45,

Question 2

6 outcomes

1/6

Answer:

y = 2x-5

y=-x+4

Step-by-step explanation:

Just need to solve the:

x+y=4

y-2x=-5

And we have:

x=3

y=1

Then replace x and y into the answer to find the correct one

Step-by-step explanation:

c) since m = undefined => the equation is

x = -2

d) the equation is

y-2= -1/7 (x+7)

=> y = -1/7 x -1+2

<=> y = -1/7 x + 1

Answer:

The answer is 1 * 3.

Step-by-step explanation:

To find the size of the resulting matrix, start by finding the dimensions of both matrices. For the dimensions of a matrix, it goes rows by columns. To find the dimensions of a matrix, count the number of rows, and then count the numbers of columns.

For the first matrix, the dimensions are 1 by 3. For the second matrix, the dimensions are 3 by 3.

An easy way to see if matrices that are being multiplied produce a real answer, find the dimensions of each matrix and see if the two inner numbers match.

For these matrices being multiplied, the dimensions are 1 by 3 and 3 by 3, and the two inner numbers are 3, which means they match.

Then, begin solving for the answer resulting from the matrices being multiplied. Start by multiplying each row in the first matrix by each column in the second matrix. Next, simplify each element of the matrix by multiplying out all the expressions. Finally, the matrix in the most simplified form is [tex]\left[\begin{array}{ccc}11&11&-2\\\end{array}\right][/tex]. Thus, resulting in a 1 * 3 matrix.

Answer:

A.5

Step-by-step explanation:

divide 40 by 7 which is equal to 5

Answer:

No, because 2^3 × 3^2 is equivalent to 72 which is a much smaller number than 6^5 which is equal to 7,776.

Step-by-step explanation:

2^3 × 3^2 = 6^5 ??

Use PEMDAS:

(2 × 2 × 2) × (3 × 3) = 6 × 6 × 6 × 6 × 6

(4 × 2) × 9 = 36 × 6 × 6 × 6

8 × 9 = 216 × 6 × 6

72 = 1,296 × 6

72 = 7,776

Step-by-step explanation:

no because they just added they exponents together. 6^5 is like saying 6 multiplied by itself 5 different times. same with the other numbers. if you switch the exponents around and multiply at different times it's like multiplying different numbers, because 2^3 is multiplying 2 by itself 3 individual times. if you move the exponent to the 6, you are multiplying a completely different number by its own self, so the two different methods cannot be congruent.

(I'm sorry I hope that made sense)

also you can just check with the calculator, this is just an explanation on why it will show up like that on the calculator

9514 1404 393

Answer:

  (-3, -6)

Step-by-step explanation:

The scale factor multiplies each coordinate.

  A' = 3A = 3(-1, -2) = (-3, -6)

The image of A is ...

  A'(-3, -6)

B

The y-values go from at least -6 to at most 9 so B fits that

Answer:

-6 <=y <=9

Step-by-step explanation:

Answer:

1.72 ≤ t ≤ 1.85

Step-by-step explanation:

Given :

Distance = 100 miles ;

Speed = 56 miles per hour, to the nearest 2 miles per hour

Hence, the speed range is :

(56 - 2) mph ; (56 + 2) mph

Range of possible Time taken, t :

Distance / speed ;

100 / 58 ≤ t ≤ 100 / 54

1.72 ≤ t ≤ 1.85

Answer:

[tex]g(x) = |x-4|+6[/tex]

Step-by-step explanation:

shift 4 to the right --> x-4

shift 6 up --> +6

Answer: 6x^2 + 10x -2

Añade todos los lados de la figura y combina los términos iguales por ejemplo todos los que tienen “x” en frente, súmales

Answer:

90

Step-by-step explanation:

Answer:

Step-by-step explanation:

mode means most repeated number . here in this given data 7 is repeated maximum number of times . so mode is 7.

to find median arrange the data from ascending to descending order.

Data = 1,2,3,4,5,7,7,7,8,8

median = N + 1/2    (N means no of data )

=10 + 1/2

=11/2

=5.5

= 5th term + 6th term/2

=5+7/2

=12/2

=6

mean = sum of data / no of data

=3+7+2+4+7+5+7+1+8+8/10

=52/10

=5.2

range = largest value - smallest value

=8 - 1

=7

Answer:

A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z

Answer:

the correct answer is 4,000 grams

Answer:

an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle (since the sign is "left than")

Step-by-step explanation:

Given the inequalities

17+4x < 9

Subtract 17 from both sides

17+4x -19 < 9 - 17

4x < -8

Divide both sides by 4

4x/4 < -8/4

x < -2

To represent the solution on a number line, an open circle will be at -2(since the inequality sign does not include "equal to") and the line is drawn to the left of the circle.

Answer:

8.24243226

Step-by-step explanation:

Same as the previous one I answered.

Tan = Opposite/ Adjacent

Adjacent = Opposite / Tan(20)

Answer:

[tex]A=\frac{513\pi}{8}[/tex]

Step-by-step explanation:

1.Approach

To solve this problem, find the total area of the circle. Then multiply the total area by the fraction of the circle that is shaded.

2.Find the area of the circle

The formula to find the area of a circle is the following,

[tex]A=(\pi)(r^2)[/tex]

Where ([tex]r[/tex]) represents the radius of the circle, that is the distance from the center of the circle to the circumference of the circle (the outer edge). ([tex]\pi[/tex]) represents the numerical value (3.1415..).

Substitute the given values into the formula and solve for the area.

[tex]A=(\pi)(r^2)\\\\A=(\pi)(9^2)\\\\A=(\pi)(81)[/tex]

3.Find the percent of the circle that is shaded

There are a total of (360) degrees in a circle. It is given that (75) degrees are not shaded. To find the fraction of a circle that is shaded, subtract (75) form (360). Then put this value over (360) and simplify.

[tex]360 - 75 = 285[/tex]

Now put this number over (360) to find the fraction of the circle that is shaded.

[tex]\frac{285}{360}[/tex]

[tex]=\frac{19}{24}[/tex]

4.Find the area of the shaded region

Now multiply the total area by the fraction that the shaded region occupies.

[tex](81)(\pi)*(\frac{19}{24})\\\\=\frac{(81)(19)(\pi)}{24}\\\\=\frac{513(\pi)}{8}[/tex]

Answer:

24 servngs

Step-by-step explanation:

3 cups makes 9 servings.

The rate of servings to cups is 9 servings to 3 cups which is a unit rate of 3 servings per cup.

1 quart = 4 cups

2 quarts = 2 * 4 quarts = 8 cups

3 serviongs/cup * 8 cups = 24 servings

Answer: 24 servings

Answer:

+ 5 = length 2x + 2(x + 5) = 38

x = √29

Step-by-step explanation:

By the Pythagorean theorem,

A² + B² = C²

14² + x² = 15²

x² = 15² - 14²

x² = 29

x = √29

Step-by-step explanation:

A^2+B^2=C^2

14^2+x^2=15^2

196 + X^2=225

X^2=225-196

x^2=29

X=√29

Answer:

A) 47.17

B) 10.2 feet

Step-by-step explanation:

dont forget to switch the calculator to degrees when doing this

For A)

arcsin(11/15)=angle of elevation

47.17=angle of elevation

For B)

tan(47.17)=11/x

11/tan(47.17)=x

10.2=x

read comments for other stuff that i forgot to put in here

Angle of elevation is equals to 47.14 degrees and distance from the base of the house is equals to [tex]2\sqrt{26} foot[/tex].

" Angle of elevation is defined as the angle between horizontal plane and the observation line of sight."

Formula used

[tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]

Pythagoras theorem

[tex](Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}[/tex]

According to the question,

Length of the ladder ' hypotenuse'= 15 foot

Height to reach a point ' perpendicular' = 11feet

'[tex]\alpha[/tex]' represents the angle of elevation

[tex]'x'[/tex] represents the base of the house

Substitute the value to get the value of angle of elevation we have,

   [tex]sin\alpha = \frac{11}{15}[/tex]

⇒ [tex]\alpha = sin^{-1} (0.7333)[/tex]

⇒[tex]\alpha = 47.14[/tex] degrees

Substitute the value in the formula to get the value of base we have,

[tex](15)^{2}= (11)^{2} +x^{2}[/tex]

⇒[tex]x^{2} = 225 - 121[/tex]

⇒[tex]x^{2} = 104[/tex]

⇒[tex]x=\sqrt{104}[/tex]

⇒[tex]x= 2\sqrt{26}[/tex] foot

Hence, angle of elevation is equals to 47.14 degrees and distance from the base of the house is equals to [tex]2\sqrt{26} foot[/tex].

Learn more about angle of elevation here

https://brainly.com/question/21137209

#SPJ2

Answer:99904.

Step-by-step explanation:

Find the LCM of

5

10 = 2x5

15 = 3x5

20 = 2x2x5

25 = 5x5

LCM = 2x2x3x5x5 = 300

Take the smallest 5-digit number: 10000 and divide it by 300 to get 33.33. Round it off to 34 and multiply it by 300 to get 10200. Finally add 4 to 10200 to get 10204 which is the smallest final 5-digit number.

Check: 10204/5 = 2040 as quotient and a remainder of 4. Correct.

10204/10 = 1020 as quotient and a remainder of 4. Correct.

10204/15 = 680 as quotient and a remainder of 4. Correct.

10204/20 = 510 as quotient and a remainder of 4. Correct.

10204/25 = 408 as quotient and a remainder of 4. Correct.

Answer: 10204.

To get the greatest 5-digit number take 99999 and divide it by 300 to get 333.33. Round it off to 333 and multiply it by 300 to get 99900. Finally add 4 to 99900 to get 99904 which is the final greatest 5-digit number.

Check: 99904/5 = 19980 as quotient and a remainder of 4. Correct.

99904/10 = 9990 as quotient and a remainder of 4. Correct.

99904/15 = 6660 as quotient and a remainder of 4. Correct.

99904/20 = 4995 as quotient and a remainder of 4. Correct.

99904/25 = 3996 as quotient and a remainder of 4. Correct.

Answer: 99904.

Answer:

There are 21 distinct numbers on the list

Step-by-step explanation:

Square of integers between - 20 and 20

-20² = 400

-19² = 361

-18² = 324

-17² = 289

-16² = 256

-15² = 225

-14² = 196

-13² = 169

-12² = 144

-11² = 121

-10² = 100

-9² = 81

-8² = 64

-7² = 49

-6² = 36

-5² = 25

-4² = 16

-3² = 9

-2² = 4

-1² = 1

0² = 0

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

20² = 400