The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?



Choose the correct answer.
6.2 + b = 14.5
9.3 + b = 14.5
12.4 + b = 14.5
18.6 + b = 14.5

Answer:

D) f(x) 3 cos 4x-4 (I just took it)

Answer:

Option C is correct .i.e., ∠3 and ∠7

Step-by-step explanation:

Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.

From Given Figure,

Following are pairs of corresponding angles,

∠1 and ∠5

∠2 and ∠6

∠4 and ∠8

∠3 and ∠7

Therefore, Option C is correct .i.e., ∠3 and ∠7

Answer:

f(-7)=0 that is option 4th is correct.

Step-by-step explanation:

If we have given any polynomial  then its factor means that value is giving zero of that polynomial

And opposite sign of factor is the zero of the polynomial

For example:

x+a is factor of any polynomial f(x) then f(-a)=0

Similarly, If x+7 is a factor of any polynomial then f(-7)=0

Hence, option 4th is correct.

Final answer:

The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.

Explanation:

The area of a rectangle can be found by multiplying its length and width.

In this case, the length is 15 feet and the width is 9 feet.

To find the area, multiply 15 feet by 9 feet:

Area = 15 feet x 9 feet = 135 square feet

Therefore, the area of the rectangle is 135 square feet.

car 1 = x

 car 2 = y

x+y =40 gallons

x=40-y

15x +20y = 675

15(40-y) +20y = 675

600-15y +20y =675

600+5y = 675

5y=75

y=75/5 = 15 gallons

x=40-15 =25 gallons

 Car 1 used 25 gallons

 Car 2 used 15 gallons

the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].

To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]

The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:

- [tex]\( a \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the number of terms.

In our series:

- [tex]\( a = 3 \)[/tex] (the first term),

- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:

 - [tex]\( \frac{-6}{3} = -2 \)[/tex]

 - [tex]\( \frac{12}{-6} = -2 \)[/tex]

 - [tex]\( \frac{-24}{12} = -2 \)[/tex]

So, [tex]\( r = -2 \)[/tex].

Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:

[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]

Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:

[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]

[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]

[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]

[tex]\[ S_8 = -255 \][/tex]

So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].

5 + 2*SQRT(x) = 15

 subtract 5 from each side

2*SQRT(x) = 10

(2*SQRT(x))^2 =10^2

2^2 *x = 100

4x=100

x=400/4

x = 25

558.16 x 12 = 6697.92 every year

6697.92 x 30 = 200937.60 total

200937.60-150000 = $50,937.60 total interest paid

Answer:

[tex]n=\frac{3}{2},\,\,n=2[/tex].

Step-by-step explanation:

The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is  to factorize the polynomial  on the left hand side. To factorize you can do the following:

(1) [tex]2n^2-7n+6[/tex]. The given polinomial

(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex].  Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]

(3)  [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.

(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]

(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]

Then the given equation can be written as:

[tex]{(2n-3)(n-2)=0[/tex]

The product of two expression equals zero if and only if one of the expression is zero. From here we have that

[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]

From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].

Final answer:

The magnitude of 6 + 2i is 2√10.

Explanation:

To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:

|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10

Therefore, the magnitude of 6 + 2i is 2√10.

Assuming a regularly shaped rectangle, the formula for the area is given as:

A = L * W

where L and W are the length and width respectively

A = 3.6 x 10^2 miles * 2.8 x 10^2 miles

A = 100,800 square miles

or

A = 10.08 x 10^2 miles

Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Step-by-step explanation:

The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]

and height , [tex]H=2.8\times 10^{2}\, miles[/tex]

Area of rectangle , [tex]A=L\times W[/tex]

=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]

=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]

Hello!

The number of pairs of shoes each man can repair is its speed times the time.

Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.

Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.

Thus, we can equate:

[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]

That is the speed of the assistant. Then, the speed of the repairman is:

[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]

That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)

To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.

To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.

Let's denote the time it takes the repairman to repair one pair of shoes by x hours.

Since the assistant takes twice as long, their time would be 2x hours for one pair.

Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.

Now, we express their combined work rate as the sum of their individual work rates.

The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.

Together, this should equal their combined rate of 2 pairs per hour:

1/x + 1/(2x) = 2

Solving this equation for x, we first find a common denominator and get:

2/2x + 1/2x = 2

3/2x = 2

3 = 4x

x = 3/4

Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.

Answer:

Option C. is the correct option.

Step-by-step explanation:

Equation of line is represented as y = mx + c

where m = slope of the line

c = y - intercept

Since line is passing through origin (0, 0) and a point (6, 2)

Therefore y intercept of the line will be 0.

c = 0

Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]

[tex]m=\frac{2-0}{6-0}[/tex]

[tex]m=\frac{2}{3}[/tex]

So the equation will be

[tex]y=\frac{1}{3}x[/tex]

Therefore, option C. is the answer.

It is given in the question that

You will be charged 12.5% interest on a loan of $678.

So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125

So we have to find the value of 0.125 of 678.

[tex]0.125*678 = 84.75[/tex]

Therefore the interest that you will have to pay on loan is $84.75 .

We can solve this problem by using the formula:

s = σ / sqrt(n)

where,

s = standard deviation of the sample

σ = standard deviation of the population = 3 years

n = number of samples = 100

Substituting:

s = 3 years / sqrt (100)

s = 0.3 years                       (ANSWER)

Answer:

  B.  The amount spent on grapes compared with the weight of the purchase.

Step-by-step explanation:

Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.

___

In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.