solve for x on the diagram below

Answer:

2 : 3

Step-by-step explanation:

We'll begin by calculating the area of the entire garden. This can be obtained as follow:

Length of garden (L) = 12 m

Width of garden (W) = 5 m

Area of entire garden (A) =?

A = L × W

A = 12 × 5

Area of entire garden is 60 m²

Next, we shall determine the area of the garden reserved for flower. This can be obtained as follow:

Length of flower garden (L₁) = 12 – 4

= 8 m

Width of flower garden (W₁) = 3 m

Area of flower garden (A₁) =?

A₁ = L₁ × W₁

A₁ = 8 × 3

A₁ = 24 m²

Next, we shall determine the area of the garden reserved for grass. This can be obtained as follow:

Area of entire garden (A) = 60 m²

Area of flower garden (A₁) = 24 m²

Area of grass garden (A₂) =?

A = A₁ + A₂

60 = 24 + A₂

Collect like terms

A₂ = 60 – 24

A₂ = 36 m²

Finally, we shall determine the ratio of the area of the garden reserved for flowers to the area reserved for grass. This can be obtained as follow:

Area of flower garden (A₁) = 24 m²

Area of grass garden (A₂) = 36 m²

Ratio of flower garden to grass garden = A₁ : A₂

= 24 : 36

= 24 / 36

= 2 : 3

Therefore, the ratio of the area of the garden reserved for flowers to the area reserved for grass is 2 : 3

Answer:

Amira is currently 24 years old and Pam is currently 12 years old

Step-by-step explanation:

Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].

We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].

Therefore, we have a system of equations:

[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]

Substitute the first equation into the second one:

[tex]2p-9+p-9=18[/tex]

Combine like terms:

[tex]3p-18=18[/tex]

Add 18 to both sides:

[tex]3p=36[/tex]

Divide both sides by 3:

[tex]p=\frac{36}{3}=\boxed{12}[/tex]

Now substitute this into any of the equations (I'll choose the first):

[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]

Therefore, Amira is currently 24 years old and Pam is currently 12 years old.

Answer:

I dont know. sorry sorry

Answer:

D

Step-by-step explanation:

(the line is a / shape, so the slope is positive)

(the line crosses the y axis at (0,-2))

(using the above information, we can conclude that the equation is y=2x-2)

or

slope = m = rise/run = 2/1 = 2

y=mx+b

y=2x+b

Choose any point on the line) (1,0)

0=2(1)+b

b=-2

y=2x-2

Answer:

Last option. She didn't use the reciprocal.

Answer:

The second, third, and fourth

Step-by-step explanation:

When you multiply two fractions, you multiply the numerator and denominator, not add them. Also, when you divide by a fraction and want to turn it into multiplication, you multiply by the reciprocal, which she didn't do. Hope this helps!

Answer:

Step-by-step explanation:

Because it is a 45-45-90 triangle

b=5

a= 5[tex]\sqrt{2}[/tex]

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required number line is not included in the question.

A general explanation is as follows:

An open circle means > or <

A closed circle means >= or <=

Take, for instance, the attached number line:

The open dot on -3 means >-3 or <-3

The arrow points to the right direction, means >-3 i.e. greater than -3

Hence, the inequality is:

[tex]x > -3[/tex]

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

260/4=520/8

Method 1: Cross Multiply

Method 2: Find GCF

Answer:

Step-by-step explanation:

The greatest common factor of 5 and -20 is 5

x: the greatest common factor is x

y: the greatest common factor is y^3

Answer: 5xy^3(y - 4x)

Answer: A. 20 is the answer.

Step-by-step explanation:

x+40 = 3x

or, 40 = 3x-x

or, 2x = 40

or, x = 40/2

so, x = 20

Answer:

A is the answer...........

Explanation

8x+3=3x+8

8x-3x=8-3

5x=5

x=5/5

x=1

Answer:

70 [milliliters]

Step-by-step explanation:

Since the solution consists of 90% alcohol, the 63 milliliters of alcohol must represent 90% of the entire solution. Let the solution have [tex]x[/tex] milliliters in total. We have the following equation:

[tex]0.9x=63[/tex]

Divide both sides by 0.9:

[tex]x=\frac{63}{0.9}=\boxed{70}[/tex]

Therefore, there are 70 milliliters in the solution.

Answer:

[tex]thank \: you[/tex]

Answer:

First, find the function of the line:

Therefore, the function is [tex]y=\frac{3}{4} x[/tex].

Since it's the area under the graph that's shaded(not ≥ or >) and the graphed line is dotted(not ≤ or ≥), then the inequality would be [tex]y<\frac{3}{4} x[/tex].

Step-by-step explanation:

here's the answer to your question

Answer:

[tex]Pr = 0.4286[/tex]

Step-by-step explanation:

Given

Let

[tex]U \to\\[/tex] Undergraduates

[tex]G \to[/tex] Graduates

So, we have:

[tex]U = 3; G =5[/tex] -- Total students

[tex]r = 4[/tex] --- students to select

Required

[tex]P(U =2)[/tex]

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

So, we have:

[tex]Total = ^{U + G}C_r[/tex]

[tex]Total = ^{3 + 5}C_4[/tex]

[tex]Total = ^8C_4[/tex]

[tex]Total = \frac{8!}{(8-4)!4!}[/tex]

[tex]Total = \frac{8!}{4!4!}[/tex]

Using a calculator, we have:

[tex]Total = 70[/tex]

The number of ways of selecting 2 from 3 undergraduates is:

[tex]U = ^3C_2[/tex]

[tex]U = \frac{3!}{(3-2)!2!}[/tex]

[tex]U = \frac{3!}{1!2!}[/tex]

[tex]U = 3[/tex]

The number of ways of selecting 2 from 5 graduates is:

[tex]G = ^5C_2[/tex]

[tex]G = \frac{5!}{(5-2)!2!}[/tex]

[tex]G = \frac{5!}{3!2!}[/tex]

[tex]G =10[/tex]

So, the probability is:

[tex]Pr = \frac{G * U}{Total}[/tex]

[tex]Pr = \frac{10*3}{70}[/tex]

[tex]Pr = \frac{30}{70}[/tex]

[tex]Pr = 0.4286[/tex]

1.) 10+2√21

2.) 8-2√15

3.) 38+2√10

solution to all the answers:

NUMBER 1:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (√3 +√7)^2, then it should look like this: 3 + 2√21 + 7.

=> add the numbers: 10 + 2√21.

NUMBER 2:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (√5 -√3)^2, then it should look like this: 5 - 2√15 + 3.

=> add the numbers: 8 - 2√15.

NUMBER 3:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (2√5 + 3√2)^2, then it should look like this: 20 + 12√10 + 18.

=> add the numbers: 38 + 12√10.

I HOPE THIS HELPED!!

Answer:

Step-by-step explanation:

7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis

7x -14 -3x -9 = 5x -15 +x , isolate like terms

7x -3x -5x -x = 14 +9 -15, combine like terms

-2x = 8, divide both sides by -2

x= -4

msin²x+cos²x=m-1

since the interval are 0 and π/4

Therefore

msin²(0)+cos²(0)=m-1

m(0)+1=m-1

1=m-1

m=2

use π/4 now

msin²(π/4)+cos²(π/4)=m-1

m(1/2)+(1/2)=m-1

m+1=2(m-1)

m+1=2m-2

-m=-3

m=3

Therefore

m=2 or 3

Answer:

in 3.04 years the will give required intrest

Answer:

To find the leading coefficient, first expand the function:

[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]

The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².

To find the vertex: see image below

Vertex = (-3, -5)

Answer:

c. 20/21

Step-by-step explanation:

You just multiply straight

3×7 = 21

4×5 =20

21/20 <---- and it can't be reduced farther than this.

Answer:

C. ²¹⁄₂₀

Step-by-step explanation:

OKOKOK DON'T WORRY I'M HERE :)))

--

When multiplying fractions, you multiply the numerators together and then multiply the denominators together.

The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).

The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).

Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.

Hope this helped!!

Answer: the answer to this is 3x-2

Step-by-step explanation:

Answer:

The fourth option.

x + b/2a = +- sqrt((b^2 - 4ac)/(4a^2))

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

a1 = 4

an=an-1 *3

a2 = a1 *3 = 4*3 = 12

a3 = a2*3 = 12*3 = 36

Answer:

12 starfish

Step-by-step explanation:

Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:

x + y = 19

5x + 8y = 116

Solve by elimination by multiplying the top equation by -8:

-8x - 8y = -152

5x + 8y = 116

Add these together and solve for x:

-3x = -36

x = 12

So, he has 12 starfish.

The total number of starfish is 12 starfishes

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of starfish be = x

Let the number of spiders be = y

The number of legs for spiders = 8

The number of legs for starfish = 5

So , the equation will be

The total number of legs for x starfish = 5x

The total number of legs for y spiders = 8y

The total number of creatures = 19

So , x + y = 19   be equation (1)

And ,

The total number of legs = 116

So , 5x + 8y = 116   be equation (2)

Now , from equation (1) , x = 19 - y

Substituting the value of equation (1) in equation (2) , we get

5x + 8y = 116

5 ( 19 - y ) + 8y = 116

95 - 5y + 8y = 116

95 + 3y = 116

Subtracting 95 on both sides , we get

3y = 21

Divide by 3 on both sides , we get

y = 7

So , the number of spiders is 7 spiders

Substituting the value of y in equation (1) , we get

x + y = 19

x + 7 = 19

Subtract 7 on both sides , we get

x = 12

Therefore , the value of x is 12

Hence , The total number of starfish is 12 starfishes

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

Answer:

$310

Step-by-step explanation:

The first step is to add the costs of the textbook together :

$68.41 + $105.35 + $72.49 + $59.91 = $306.16

In order to round off to the nearest ten dollars, look at the units figure, if the number is greater or equal to 5, add 1 to the ten figure. If this is not the case, add zero. Replace the unit digit with zero

The unit digit is greater than 6, so 1 is added to the tens digit. The amount becomes $310

Answer:

arithmetic

Step-by-step explanation:

because it bounced double

Answer:

82,83,84,80,84,86,91,96,95,99,97,92

Answer:

The answer is 1

Step-by-step explanation: