ASAP please help me!!

x - the first number,

y - the second number

We have:

[tex]\begin{cases}y=5x\\y+21=2(x+21)\end{cases}\\\\\\\begin{cases}y=5x\\y+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\5x+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\3x=21\quad|:3\end{cases}\\\\\\\begin{cases}y=5x\\\boxed{x=7}\end{cases}\\\\y=5x\\\\y=5\cdot7\\\\\boxed{y=35}[/tex]

So answer is 7 and 35.

Answer:

[tex]\bold{x = 34^\circ}[/tex]

Step-by-step explanation:

Given:

[tex]cos x = sin (x + 22^\circ)[/tex]

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

[tex]sin(90^\circ-\theta )=cos\theta[/tex]

OR

[tex]cos(90^\circ-\theta )=sin\theta[/tex]

We can apply above property to solve for [tex]x[/tex] as per given equation.

[tex]cos x = sin (x + 22^\circ)[/tex]

Changing [tex]cosx[/tex] to sine form:

[tex]cosx=sin(90^\circ-x)[/tex]

[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]

[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]

So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:

[tex]\bold{x = 34^\circ}[/tex]

Answer:

22 hours

Step-by-step explanation:

For one month, Audrey has to pay $350 for her payment and $35 for gas, meaning that she will need to pay $385 per month.

$350 + $35 = $385

Audrey makes $17.50 an hour.  Set up an equality to find the amount of hours she must work to pay for her car payment and gas.

17.50x > 385

(17.50x)/17.50 > 385/17.50

x > 22

Audrey must work at least 22 hours to pay for her car payment and gas.

Answer:

see below

Step-by-step explanation:

3)   8

4)  4

5)  14

6)  47

7)  18/5

8)  3/2

9)  255/4

10)  16

11)  21

12)  40

13)  73.5

14)  1

15)  25/2 or 12.5

16)  0

17)  48

18)   862

19)  9765625

20)  343

21)  8.1x10⁻³

22)  10.24

23)  1/156

24)  n⁷

25)  y⁶

26)  t⁴

27)  error is 0.4² should be 0.02²

28)  5⁴ = 5 x 5 x 5 x 5 = 625

29)  9

30)  100

31)  1

32)  1331

33)  125

34)  1024

35)  64

36)  1296

37)  1/16

38)  16/81

39)  27/125

40)  1/216

hope you enjoy the answers.

Answer:

thx

Step-by-step explanation:

The bottom face is a circle of area pi*r^2 = pi*5^2 = 25pi square feet

The lateral surface area is pi*r*L = pi*5*13 = 65pi square feet

Those two areas combine to 25pi+65pi = 90pi square feet

The surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

We have a cone shown in the picture.

The radius of the cone r = 5 ft

The slant height l = 13 ft

As we know, the lateral surface is given by:

S = πrl

Here,

S is the surface area

r is the radius of the cone base

l is the slant height.

S = π(5)(13)

S = 65π square ft

Thus, the surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.

Learn more about the cone here:

brainly.com/question/16394302

#SPJ5

Answer:

Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation

Step-by-step explanation:

Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation Assignment: 06.05 Data Observation hi

Answer:

1.47 is the answer

Answer:

1.4666667 rounded off to 1.47

Step-by-step explanation:

Step-by-step explanation:

Here,

[tex]1. \: (2x + 2) + (3 - 5x)[/tex]

open brackets,

[tex]2x + 2 + 3 - 5x[/tex]

[tex] = - 3x + 5[/tex]

now,

[tex]2. \: (3x - {4x}^{4} ) + (2x + {5x}^{4} [/tex]

open brackets,

[tex] = 3x - {4x}^{4} + 2x + {5x}^{4} [/tex]

simplifying like terms,

[tex] = {x}^{4} + x[/tex]

Hope it helps...

Answer:

[tex]96ft^{2}[/tex]

Step-by-step explanation:

Step 1: Find the area of the base

[tex]\frac{bh}{2} =\frac{(8)(6)}{2}=\frac{48}{2}=24ft^{2}[/tex]

Step 2: Find volume

[tex]=\frac{1}{3}(24)(12) \\=\frac{1}{3}(288)\\=96ft^{3}[/tex]

Answer:

Right angle triangle

Step-by-step explanation:

12m

15m

9m

Assume the Longest side=15m

Using Pythagoras theorem

c^2=a^2 + b^2

Where,

c=hypotenuse

a=adjacent

b=opposite

Let a=9m

b=12m

c^2=a^2 + b^2

=9^2 + 12^2

=81 + 144

c^2=225

c=√225

=15m

Therefore, the triangle XYZ is a right angle triangle

Answer:

30 will be the ans to this question

Step-by-step explanation:

5^2 +5

=25+5

=30

Answer:4th option

Step-by-step explanation:

Answer: D. Set B has a higher mean and a Higher standard deviation than Set A

Step-by-step explanation:

Set A and Set B has the same amount of data and all are identical except the maximum. In this scenario, the larger the numbers, the higher the mean. Since the maximum of Set B is greater that Set A, Set B has a higher, mean.

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

The higher the standard deviation, the larger the gap between data sets. Since Set B has a larger maximum, this means it is further away from other data comparing to Set A, thus, Set B has a higher standard deviation

Answer: They purchased  12 uniforms

Step-by-step explanation:

If the equipment cost $612 in total and the uniforms cost $25 each and they spent a total for $912 then we could represent it by the equation  25x + 612 = 912   where x is the number of uniforms that the school purchase.

25x + 612 = 912   solve for x   by subtracting 612 from both sides

         612     612

25x = 300     divide both sides by 25

x = 12

Answer:

5 + 7

Step-by-step explanation:

3 + 2 = 5, 4 + 3 = 7

Answer:

Simplified expression: 5 + 7

Answer: 12

Step-by-step explanation:

Answer:

T > (L + D)/B...multiply by B

TB > L + D ... subtract L

TB - L > D

can you plz mark me brainiest ;<

tank chu hope this helps TwT

Answer:

18.72 cubic feet

Step-by-step explanation:

Volume of the aquarium = lwh

V = 5.2*1.8*2 = 18.72 cubic feet

Answer:

64,890

Step-by-step explanation:

105×3 =315

103×2= 206

315×206= 64,890

Answer:

6.489× 10⁴

Step-by-step explanation:

(3×105)×(2×103)

315× 206

64,890

6.489×10⁴

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]3x^2+ 7x - 11 =0\\\\\Delta=b^2-4ac=7^2-4*3*(-11)=49+132=181\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-\sqrt{181}}{6}=-3.40894...\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+\sqrt{181}}{6}=1.075604...[/tex]

So, it gives -3.41 and 1.08

Thank you.

Answer:

0.04%

Step-by-step explanation:

If there are 1000 penguins per square miles, the total number of penguins in a  10 square miles will be 1000*10 = 10,000 penguins/10square miles

Since a polar bear has a territory of 10 square miles, and can only eat four penguins within the 10square miles;

Percentage of penguins that the polar bear can eat will be expressed as;

number of penguin eaten per 10square miles/total number of penguin per 10square miles * 100

Percentage of penguins that the polar bear can eat = 4/10,000 * 100%

Percentage of penguins that the polar bear can eat = 4/100%

Hence, the percentage of penguins that the polar bear can eat in the 10 square miles is 0.04%

Answer:

Fencing required = 1586 m

Step-by-step explanation:

The given statements can be thought of a triangle [tex]\triangle ABC[/tex] as shown in the diagram attached.

A be the 1st vertex, B be the 2nd vertex and C be the 3rd vertex.

Distance between 1st and 2nd vertex, AB = 435 m

Distance between 2nd and 3rd vertex, AC = 656 m

[tex]\angle A =49^\circ[/tex]

To find:

Fencing required for the triangular field.

Solution:

Here, we know two sides of a triangle and the angle between them.

To find the fencing or perimeter of the triangle, we need the third side.

Let us use Cosine Rule to find the third side.

Formula for cosine rule:

[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\Rightarrow cos 49^\circ = \dfrac{656^{2}+435^{2}-BC^{2}}{2\times 435\times 656}\\\Rightarrow BC^2 = 430336+189225-2 (435)(656)cos49^\circ\\\Rightarrow BC^2 = 430336+189225-570720\times cos49^\circ\\\Rightarrow BC^2 =619561-570720\times cos49^\circ\\\Rightarrow BC \approx 495\ m[/tex]

Perimeter of the triangle = Sum of three sides = AB + BC + AC

Perimeter of the triangle = 435 + 495 + 656 = 1586 m

Fencing required = 1586 m

Answer:

The translation S(x, y) for the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5)

Step-by-step explanation:

Identity transformation is the transformation that results in the copying of the source data to the destination data without change.

Given that T(x, y) = (x + 2, y + 5)

The identity transformation I = S(T(x, y)) that would allow a data (x, y) to remain the same at the destination after the transformation T(x, y) is given as follows;

Where S(x, y) = ( x - 2, y + 5), we have;

S(T(x, y)) = S(x + 2, y + 5) = (x + 2 - 2, y + 5 - 5) = (x, y)

Therefore the translation S(x, y) that would yield the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5).

Answer:

-1.2 Hope this helps!

Step-by-step explanation:

Answer:

The correct answer is $4.75/month.

Step-by-step explanation:

To find the unit price per month, or the amount that of the subscription that will be paid each month, we must divide the total price ($28.50) by the number of months covered (6 months).  

$28.50/6 = $4.75

Therefore, the unit price per month is $4.75/month.

Hope this helps!

Answer:

[tex](3y+5)(9y^{2} -15y+25)[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]x^2+x-42\\\\\text{The sum of the zeroes is -1=-7+6 and the product is -42=-7*6.}\\\\\text{So, we can factorise.}\\\\x^2+x-42\\\\=x^2+7x-6x-42\\\\=x(x+7)-6(x+7)\\\\=(x+7)(x-6)[/tex]

So, the possible dimensions of the rectangle are (x+7) and (x-6).

Thank you.

Answer:

Step-by-step explanation:

[tex] \sf{ {x}^{2} + x - 42}[/tex]

Here, we have to find two numbers which subtracts to 1 and multiplies to 42

⇒[tex] \sf{ {x}^{2} + (7 - 6)x - 42}[/tex]

⇒[tex] \sf{ {x}^{2} + 7x - 6x - 42}[/tex]

Factor out x from the expression

⇒[tex] \sf{x(x + 7) - 6x - 42}[/tex]

Factor out 6 from the expression

⇒[tex] \sf{x(x + 7) - 6(x + 7)}[/tex]

Factor out x + 7 from the expression

⇒[tex] \sf{(x + 7)(x - 6)}[/tex]

So, the possible dimensions of the rectangle are x + 7 and x - 6 .

Hope I helped!

Best regards!

Step-by-step explanation:

Let the number be x

The number is multiplied by 4

That's

4 × x = 4x

One is added to it

= 4x + 1

The whole result is squared

That's

Hope this helps you

Answer:

[tex]\huge \boxed{(4x+1)^2 }[/tex]

Step-by-step explanation:

[tex]\sf Let \ the \ number \ be \ x.[/tex]

[tex]\sf x \ is \ multiplied \ by \ 4.[/tex]

[tex]x \times 4[/tex]

[tex]\sf 1 \ is \ added.[/tex]

[tex]4x+1[/tex]

[tex]\sf The \ result \ is \ squared.[/tex]

[tex](4x+1)^2[/tex]

Answer:

  35

Step-by-step explanation:

The law of sines tells us ...

  sin(C)/c = sin(A)/a

  a·sin(3A) = c·sin(A)

Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...

  sin(A)(4cos(A)^2 -1) = (c/a)sin(A)

  4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9

  cos(A)^2 = 25/36

  cos(A) = 5/6

__

Now, the angle B will be the difference between 180° and the sum of the other two angles:

  B = 180° -A -3A = 180° -4A

Using appropriate trig identities, we can write ...

  sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)

  = 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)

  = 4sin(A)cos(A)(2cos(A)^2 -1)

Filling in our value for cos(A), this becomes ...

  sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)

__

The law of sines tells us ...

  b/sin(B) = a/sin(A)

  b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35

The length of side b is 35 units.

Simplify

Let's simplify step-by-step.

x(5)−3(x−4)

Distribute:

=x(5)+(−3)(x)+(−3)(−4)

=5x+−3x+12

Combine Like Terms:

=5x+−3x+12

=(5x+−3x)+(12)

=2x+12

Answer:

=2x+12

Answer:

They determine how much to make by how much demand there is for said product from the consumer.

Step-by-step explanation:

Answer:

Infinite Number of Solutions

Step-by-step explanation:

Since 4*x= 4x

and 4*4= 16

its 4x+16

which is 4x+16=4x+16

Since there are the same, and both equal each other, there are an infinite number of solutions.

Answer:

infinite number of solutions

Step-by-step explanation:

4(x + 4) = 4x + 16

Distribute on the left side.

4x + 16 = 4x + 16

Subtract 16 from both sides.

4x = 4x

Divide both sides by 4.

x = x

x = x is a true equation for every value of x.

Answer: infinite number of solutions