As seen in the diagram below, Shandra is building a walkway with a width of xx feet to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the pool and the walkway will be 168 square feet, how wide should the walkway be?

3 hearts

4 triangle

H:T

3:4

So, ratio of hearts to triangles in simplest form is 3:4

(we can't simplify any further - HCF of 3 & 4 is 1)

Hope this helps!

Answer:

[tex]x=\boxed{6.6}[/tex]

[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]

Step-by-step explanation:

Geometric Mean Theorem - Altitude Rule

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments.  The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:

[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]

From inspection of the given diagram:

[tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]

Substitute the found value of x into the expression for DE:

[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]

Solution:

[tex] - 18 \sqrt{10} [/tex]

[tex] = - 6 \sqrt{2} \: \: • \: \: 3 \sqrt{5} [/tex]

2. Apply radical rule : [tex] \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex] , [tex]a \geqslant 0[/tex], [tex]b[/tex]

[tex] = 6 \sqrt{2 \: • \: 5} \: • \: 3[/tex]

=[tex]6 \sqrt{10} •3[/tex]

[tex] = - 18 \sqrt{10} [/tex]

Answer: C

Step-by-step explanation:

We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,

[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]

Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]

Answer:

1/3

Step-by-step explanation:

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2812\\ P=\textit{original amount deposited}\dotfill & \$1900\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2812=1900[1+(0.08)(t)]\implies \cfrac{2812}{1900}=1+0.08t\implies \cfrac{37}{25}=1+0.08t \\\\\\ \cfrac{37}{25}-1=0.08t\implies \cfrac{12}{25}=0.08t\implies \cfrac{ ~~ \frac{12}{25} ~~ }{0.08}=t\implies 6=t[/tex]

Answer:

not equivalent

Step-by-step explanation:

solve for x

4-5x=24

-5x=20

x = - 4

5x=20

x = 4

no they are not equivalent

There are 4.15E12 ways to select the members of the committee to have the same number of Reds as Blues

The given parameters are:

Reds = 44

Blues = 56

Committee member = 10

To have the same number of Reds as Blues, the committee must have 5 reds and 5 blues.

So, the number of ways is;

Ways = 44C5 * 56C5

Evaluate the combination expressions:

Ways =  1.086008 E+6 *  3.819816 E+6

Evaluate the product

Ways =  4.15E12

Hence, there are 4.15E12 ways to select the members of the committee

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Answer:

x = -8

y = 0

Step-by-step explanation:

The two shown equations can be added together:

   x + 4y = -8

+ ( x - 4y = -8 )

The two x's would combine to make two x, the 4y and -4y cancel out to zero, and -8 added to -8 is -16:

2x = -16

Therefore, x = -8. We can plug this into the first equation to get:

-8 + 4y = -8

Subtracting 8 on both sides yields:

4y = 0

Now divide by 4 on both sides to get

y = 0

We can check these values by plugging them into the second equation:

(-8) - 4(0) = -8

-8 - 0 = -8

-8 = -8

Since -8 always equals -8, the answer is correct.

A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.

B. Each employee will get 7 hours of training, assuming your organization has 10 employees.

The training cost of employees varies from one organization to another.

The training cost also depends on the training provider and the number of hours of training being offered.

Training budget = $3,000

One-time fee = $200

Remainder after the one-time fee = $2,800 ($3,000 - $200)

Training costs per employer per hour = $40

Hours of training to purchase = 70 ($2,800/$40)

Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.

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Answer:

  12

Step-by-step explanation:

The problem statement tells us the definition of 3f(x). In order to find the value of 3f(2), we substitute 2 for x and do the arithmetic.

__

  3f(x) = 3x² . . . . given

  3f(2) = 3·2² = 3·4 = 12 . . . . . substitute 2 for x

The value of 3f(2) is 12.

Answer:

  E.  18.6

Step-by-step explanation:

The diagonals of a rhombus bisect each other at right angles. The means all of the triangles shown are right triangles, and the two marked angles are complementary.

__

Complementary angles total 90°.

  (x°) +(4x -3)° = 90° . . . . . the marked angles are complementary

  5x = 93 . . . . . . . . . . . .  divide by °, add 3

  x = 93/5 = 18.6 . . . . . divide by the coefficient of x

The value of x is 18.6.

Answer:

266[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

if a 45 minute workout is 1000 calories, at the same rate, a 12 minute workout would be 266 calories and 2 thirds. [tex]\frac{12}{45}[/tex] x 1000 = 266[tex]\frac{2}{3}[/tex]

Answer:

-3ab

Step-by-step explanation:

-27/9= 3

(a^2)/a=a

(b^2)/b=b

u₁₂ represents the amount of loan remaining after 12 years

The function is given as:

u₀ = 8000

[tex]u_n = u_{n-1}(1 + 0.054) - 500[/tex]

Given that the subscript n in [tex]u_n[/tex] represents number of years and [tex]u_n[/tex] represents the amount left to be paid after n years.

We can conclude that:

u₁₂ represents the amount of loan remaining after 12 years

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Answer:

(18,27) , because the rate of change of the function is 4/3

Step-by-step explanation:

Answer:

-34+x/4

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

Since you did not specify, we will assume that your equation is equal to 0.
1. (-34+2x)/(-8) = 0     (multiply both sides by -8)
2. (-34+2x) = 0  (add 34 to both sides)
3. 2x = 34 (divide both sides by 2)
4. x = 17

Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.

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Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degrees. It is a type of quadrilateral.

The question is incomplete.

The complete question is:

Rhiannna has a rectangular bedspread that measures 234 in. By 245 in. She wants to sew a fringe around the edge of the bedspread. What length of fringe does Rhiannna need to purchase. Rhiannna gets a new bedspread that is 33 in length. What length of the fringe does Rhiannna need for the longer bedspread?

We know perimeter of the rectangle = 2(length + width)

= 2(234 + 245 )

= 958 inches

Rihannon gets a new bedspread that is 33 in length:

New perimeter = 2(33) + 958 = 1024 inches

Thus,  Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.

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Answer:

[tex]15[/tex]

Step-by-step explanation:

if [tex]f(x) = x^2 -2x[/tex], then that means that [tex]f(5) = (5)^2 - 2(5)[/tex] which equals [tex]15[/tex].

Step-by-step explanation:

A function f is defined by f (x) = 2x - 5. Write down the values of In mathematics, a function means a correspondence from one value x of the first set to another value y of the second set. NCERT Solutions Class 11 Math's Chapter 2 Exercise 2.3 Question 3 A function f is defined by f (x) = 2x - 5.

Answer:

is that the ixl

website ????????????????????????????????

Answer:

$60

Step-by-step explanation:

cost = $50 + $0.25x

Since x = 40

$(50 + 10) = $60

Answer:

$60/month

Step-by-step explanation:

So the equation would be 50 + (0.25 * 40), solve parenthesis 50 + 10, so answer would be $60.

Answer: x=12

Step-by-step explanation:

Answer:

  x=1

Step-by-step explanation:

The equation can be simplified and solved using the rules of exponents and the usual inverse operations.

__

Interpreted according to the Order of Operations, your equation is ...

  ((2^2)x)^3 = 64

  (4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)

  x^3 = 1 . . . . . . . . . . . . . . divide by 64

  x = ∛1 = 1

__

Perhaps you want x in the exponent:

  (2^(2x))^3 = 64

  2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)

  6x = 6 . . . . . . . . match exponents

  x = 1 . . . . . . divide by 6

_____

Additional comment

Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.

Answer:

l

Step-by-step explanation:

The options that are true as a result of doubling the rectangle dimensions are;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

We are told that;

Doubling the dimensions of a rectangle increases the area by a factor of 4.

Now, p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.

Thus, using conditional statements notation, we can say that;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

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