Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x.The missing length, x, is ____centimeters.

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:

1.16 m (approximately)

Step-by-step explanation:

Let x be the width of the path.

Total area  = (5+2x)(3+2x) = 39

Expand and simplify

4x²+ 16x+15-39 = 0

4x² + 16x - 24 = 0

Simplify

x² + 4x -6 = 0

Rational factoring does not work, so use quadratic formula

x = +/- sqrt(10) -2

= 1.16 or -5.16 (reject)

= 1.16 m (approximately)

Answer:

12.3455882353

Step-by-step explanation:

(103/8) = 12.875

(9/14) = 0.64285714285

0.64285714285 x 14 = 9

(9/17) = 0.5294117647

12.875 - 0.5294117647 = 12.3455882353

a) The area of Australian desert is 3,830,040km²

b)The approximate number of dingos will be  517,055

a) Given the following parameters;

Area of Sahara desert = 9,000,000km²

If the Australian desert is 42.556% of the size of the Sahara desert in Africa, then the area of the Australian desert is expressed as:

Area of Australian desert = 0.42556 * 9,000,000

Area of Australian desert = 3,830,040km²

b) If dingo density is approximately 0.135 animals km² during the dry season, the approximate number of dingos in the Australian desert during this season. will be:

number of dingos =  0.135 * 3,830,040km²

number of dingos = 517,055.4

Hence the approximate number of dingos will be  517,055

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Answer:

keeping in mind that the vertex is half-way between the focus point and the directrix, and since the focus point is above the directrix, meaning the parabola is a vertical parabola opening upwards, the parabola will more or less look like the one in the picture below, with a distance from the vertex of "p" being positive since it's opening upwards.

\(\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\begin{cases} h=0\\ k=0\\ p=\frac{1}{2} \end{cases}\implies 4(\frac{1}{2})(y-0)~~ = ~~(x-0)^2\implies 2y=x^2\implies y=\cfrac{1}{2}x^2\)

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

I hope this helps!

Step-by-step explanation:

Please mark brainiest

Answer:

35%

Step-by-step explanation:

Assuming that there are no other animals in the vet other than dogs and cats, that means the total amount of animals is 21 + 39, which is 60 animals. To find the percent of cats, simply place the number of cats based on the ratio (21) over the total number of animals (60) and multiply by a 100:

21/60 = 0.35

0.35 x 100 = 35%

Hope this helps!!

Answer:

35%.

Step-by-step explanation:

Fraction that  are cats =  21 / (21+39)

= 21/60

= 100 * 21/60

= 35%.

Answer:

D. There are four terms

A. The entire expression is a difference

Answer: I'm not Einstein sorry

Step-by-step explanation:

Have to be smart as Einstein.................Which I'm not

Answer:

Step-by-step explanation:

The correct answer is a. A larger sample size was used.As per the Law of Large Numbers, the more times an experiment is repeated, the closer the actual results will be to the expected probability. In this case, rolling the cube 100 times provides a larger sample size than rolling it only 20 times. The more rolls that are made, the greater the likelihood that the actual results will converge towards the expected probability of 1/2 for rolling an even number.Option b, The 100 tosses were controlled better, is not relevant to this scenario since the fairness of the cube is assumed.Option c, The expected probability changed when the cube was rolled 100 times, is not true. The expected probability of rolling an even number on a fair six-sided die is always 1/2, regardless of the number of times it is rolled.Option d, The thrower considered only the even rolls, and disregarded the odd rolls, is not a valid assumption. The question states that the number of even rolls was recorded, but it does not imply that odd rolls were disregarded.

The values of function f(x) positive, and negatives are (-infinity, infinity )

A function is a procedure or link that connects every element of one non-empty set A to at least one element of another non-empty set B. The phrases "domain" and "co-domain" are used in mathematics to define a function f between two sets, A and B. The constraint F = (a,b)| is satisfied by all values of a and b.

In the case of the question,

f (x) = x²

f (x) will be positive for all x values. As a result of the function:

x² = x × x

That is, when any number or integer is multiplied by itself, the result is positive. (For example, - - = + and + + = +)

As a result, f (x) = x2 will be positive for (,).

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Answer:

x= 1 y= -1

Step-by-step explanation:

Pick an equation to isloate x or y

5x+2y=3 becomes x=-2y+3/5

Subsitute that into second equation : 2(-2y+3y/5) + 3y=-1

Example and simplify.  

Do the same to find x variable

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

8%

Step-by-step explanation:

Answer: Nicholas spent $7 per candy bar

Step-by-step explanation:

32 - 4 = 28

28 divided by 4 = 7

The correct answer is d. 2x³+5x.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots.

The correct answer is d. 2x³+5x.

To multiply 2x by (x²+5), we use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this property, we get:

2x * (x² + 5) = 2x * x² + 2x * 5

= 2x³ + 10x

So, the correct expression is 2x³+5x, option d. 2x³+5x. The other options provided are not correct. Option a. 2x³+10x² has an extra term of 10x² which is not present in the original expression. Option b. 2x³+10x has an extra term of 10x which is not present in the original expression. Option c. 2x²+10x has an extra term of 2x² which is not present in the original expression. So, the correct answer is d. 2x³+5x.

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Answer:

x = 1

r+7 = ..

5g = 9

8r = 12

A, C, D and F

Answer:

The volume of a sports ball with a diameter of 19 centimeters is approximately 3,591.364 cubic centimeters.

(Hope this helps! Btw, I am the first to answer. If this answer is wrong, I apologize..)

Answer: 3591.36 cm cubed

Step-by-step explanation:

volume formula for a sphere

(4πr^3)/3

diameter = 19

radius  = 9.5

4π(9.5^3)/3

4π(857.375)/3

10774.092/3

3591.364

rounded

3591.36 cm cubed

Answer:

F(10) = P(x = 10) = 0.3

F(5) = P(x = 5) = 0.4

F(1) = P(x = 1) = 0.3

Step-by-step explanation:

Given the following :

Probability estimates given:

Very successful = 0.3

Moderately successful = 0.4

Unsuccessful = 0.3

Yearly revenue (X) :

Very successful = $10 million

Moderately successful = $5 million

Unsuccessful = $1 million

The probability mass function of X:

f(x) = probability of each valie of x

When x = 10:

F(10) = P(x = 10) = 0.3

When x = 5:

F(5) = P(x = 5) = 0.4

When x = 1:

F(1) = P(x = 1) = 0.3

Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.

Answer:

A

Step-by-step explanation:

Answer:

See below ↓↓

Step-by-step explanation:

Important facts given [needed to solve]

Solving :

Interest paid

The balance based on the.data given in the table is shown below.

Balance from day 1 to 10 = 11000

Balance from day 11 to 21= 8000

Balance from day 21 to 30- 5500

Balance on day 31 7500

Balance from day 1 to 10= 11000

Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500

Balance on day 31- 7500

The average daily balance of the credit card for the month of december is:

Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.

Total balance from each day in cycle=

(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000

Average daily balance=104000 / 31

= 8145

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Answer:

B

Step-by-step explanation:

4^5 means that we are multiplying 4 to itself 5 times.

4 * 4 * 4 * 4 * 4

Best of Luck!

Answer:

B.

Step-by-step explanation:

4^5 means 4 x 4 x 4 x 4 x 4

Answer:

A. The zeroes are -3 and -2/3 because y= (x + 3) (3x + 2)

Step-by-step explanation: