Based on triangle inequality theorem, what are the restrictions on the values of y

A t-shirt and a pair of shorts cost $29.75 together. jason paid $228.55 for 12 t-shirts and 5 shorts. Then ted pay for 2 t-shirts and 4 pairs of shorts is $59.4

A t-shirt and a pair of shorts cost $29.75 together.

jason paid $228.55 for 12 t-shirts and 5 shorts.

how much will ted pay for 2 t-shirts and 4 pairs of shorts

let T denote for t shirt and S denote for shorts

then T+ 2S=29.75

       12T+ 5S=228.55

solving these equation

multiply by 12 in 1 , we get

12T+ 24S= 357

12T+ 5S=228.55

substract these two equation we have

19S=128.45

S= 6.76

we can substitute in 1 we get

T + 13.52 =29.75

T=16.23

Hence , 2T + 4S = 32.46+27.04=59.4

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The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

If g(x) is the inverse of f(x), 2 is the value of f(g(2)).

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

Given

[tex]&x \rightarrow f(x) \\[/tex]

[tex]&-6 \rightarrow 1 \\[/tex]

[tex]&-3 \rightarrow 2[/tex]

[tex]$$g(x)=f^{-1}(x)[/tex] inverse

To find the value of f(g(2)).

For two functions f(x) and g(x) where f(x) and g(x) are inverse; f(g(x))=x

So, by comparison: f(g(2)) = 2.

Therefore, the inverse of the function f(g(2)) = 2.

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A) The end behavior of the polynomial graph is that;

as x → -∞, y → -∞, and as x → ∞, y → ∞

B) The given graph polynomial represents an even degree polynomial.

The end behavior of the graph of a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.

Now, we see from the graph that as x approaches a larger value, y values are getting increasingly negative. This means that as x approaches negative infinity, the values of y approach negative infinity.

In a similar approach, we can see that as the values of x approach positive infinity, the values of y also approach positive infinity.

Thus, we can say that option  D is correct.

B) Odd-degree polynomial functions, are those that have graphs that extend diagonally across the quadrants while even-degree polynomial functions are those that have graphs that open upwards or downwards.

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The ending balance for a amount of Rs. 341,000 with a interest rate of 4% for the time period of 3 years is Rs. 381920.  

What is interest?

In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).

Information given in the question,

Principle amount = 341,000

Time period = 3 years

Interest rate is 4 % which can be written as 0.04 in decimals.

We can calculate the ending balance using this formula formula for simple interest:

[tex]S.I. = Principle \times Interest \times time[/tex]

Putting the values given in the question

S.I. = (341000)(0.04)(3)

S.I. = 40,920

Interest is 40,920.

The ending balance is the sum of Principle amount and Interest. So,

ending balance = 341000+40920

ending balance = 381920  

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The range of the exponential function f(x) is 1 / 32 ≤ f(x) ≤ 16.

Exponential functions are monotonous functions, that is, functions that are increasing or increasing but never both. Functions are defined by the following three features:

In this problem we find a function with an input variable (x) and an output variable (f(x)). Since exponential functions are monotonous functions we can determine the bounds of the range by the function evaluated at x = - 5 and x = 4. Thus:

f(- 5) = 2⁻⁵

f(- 5) = 1 / 2⁵

f(- 5) = 1 / 32

f(4) = 2⁴

f(4) = 16

The range of the function f(x) = 2ˣ for - 5 ≤ x ≤ 4 is 1 / 32 ≤ f(x) ≤ 16.

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Given:

Find-:

Match the item

Explanation-:

(1)

The commutative property of addition is:

So the commutative property of addition is:

(2)

The multiplicative inverse is:

So value is:

(3)

Associative property of addition

So the value is:

(4)

Additive identity.

The property of additive identity is:

So the value is:

(5)

The distribution property is:

Answer:

w = 135

Step-by-step explanation:

-27 = -w/5

multiply both sides by 5:

5(-27) = 5(-w/5)

-w = 135

divide both sides by -1:

-w/-1 = 135/-1

w = 135

The value of w is 135 in the equation -27 = -w/5 .

We are provided with the equation mentioned below:

-27 = -w/5

As per the question we have to simplify and solve this above mentioned equation. To simplify this provided equation we will follow the steps mentioned below:

-27 = -w/5                                                      equation 1

On multiplying both the sides of equation 1 with 5, we will get

(-27) × 5 = (-w/5) × 5

- 135 = -w                                                       equation 2

On multiplying both the sides of equation 2 with -ve sign, we will get

w = 135

Thus, we can write that the value of w is 135.

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Answer:

because the six is a negative number (-6)

[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 8 - 5}{ - 8 - ( - 2)} \\ m = \frac{ - 13}{ - 8 + 2} \\ m \frac{ - 13}{ - 6} \\ m = \frac{13}{6} [/tex]

ATTACHED IS THE SOLUTION.

I also provided you with the formula to calculate the slope between the points.

formula to calculate the slope between the points.GOODLUCK

5.25 pounds of mashed potatoes is required to fill the container.

In the question, we were told the container was 4/6 filled and the chef used  3 2/4 pounds which is equal to 14/4 pounds of mashed potatoes.

In doing this, we are calculating the volume of the container.

Let's equate this and find how many pounds will fill the container.

[tex]\frac{4}{6}fill = \frac{14}{4} pounds\\ 1 fill = x pounds[/tex]

Let's cross multiply both sides and solve for x.

[tex]\frac{4}{6}fill = \frac{14}{4} pounds\\1 = x pounds\\x = \frac{1 * \frac{14}{4} }{\frac{4}{6} }\\x = \frac{21}{4} = 5.25 pounds[/tex]

To fill the container, we need 5.25 pounds of mashed potatoes.

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The values of the inequality -d ≥ 7 are  -12, -8 and -7.1

The inequality is

-d ≥ 7

The inequality is the equation that shows the relationship between the numbers or algebraic expression. The relationship maybe greater than, greater than or equal, less than, less than or equal. In inequality there is no equal relationship.

The given inequality is

-d ≥ 7

Divide both sides of the given inequality  by -1

-d/-1 ≥ 7/-1

d ≤ -7

Therefore the value of d is less than -7

So the values are -12, -8 and -7.1

Hence, the values of the inequality -d ≥ 7 are  -12, -8 and -7.1

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If we solve for the value of x using the graph we get the coordinates of X as X( [tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

What is the linear equation with two variables ?

A linear equation with two variables is any equation that can be expressed in form ax + by + c = 0, where a, b, and c are all real values.

The given equation is a form of linear equation with two variables.

The equation is 16x + 28y = 112.

From graph it is clear that coordinates of Y are Y(1 , -1).

So , let's check for the value of x by putting the values of y in given expression.

i.e.,

The resulted equations will be :

16 x + 28 (1) = 112

or

16x + 28(-1) = 112

So ,

16 x + 28 = 112    --- -- -- ----- ----- ---- ---- ---- ---- ---- ---- ---- Equation 1

16x - 28 = 112     --- -- -- ----- ----- ---- ---- ---- ---- ---- ---- ---- Equation 2

The values of x will be :

x = 84 / 16 = 21 / 4

or

x = 140 / 16 = 35 / 4

The coordinates of X will be X([tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

Therefore , solving for the value of x using the graph we get the coordinates of X as X( [tex]\frac{21}{4}[/tex] , [tex]\frac{35}{4}[/tex] ).

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Answer:

B

Step-by-step explanation:

12 multiplied by 5 is 60 and 10 multiplied by 6 is 60. which is the lowest that they both will meet

Answer:

Step-by-step explanation:

-11+?=15

?=15+11

15+11= 26

So, -11+26=15.

?-(-3)= 5

?+3=5

?=5-3

?=2

So, 2-(-3)=5.

?+(-4)=7

?-4=7

?=7+4

?=11

So, 11+(-4)=7.

?+-8=3

?=3+8

?=11

So, 11+-8=3.

-2+?=1

?=1+2

?=3

So, -2+3=1.

?-12=-4

?=-4+12

?=8

So, 8-12=-4.

36 cm tall will their stacks be when they are the same height for the first time.

Given,

Two students in Mrs. Johnson's preschool class are stacking blocks:

The height of Reece's block = 4 cm

The height of Maddy's block = 9 cm

We have to find the height of the stacks when they are same height for the first time.

Here,

We have to find the least common multiple.

Least Common Multiple (LCM):

The smallest number that is a multiple of both of two numbers is called the least common multiple.

So here,

We have to find the least common multiple of 4 and 9.

Here, the least common multiple of 4 and 9 = 36

Then,

36 cm tall will their stacks be when they are the same height for the first time.

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A complex number z = a + bi has the trigonometric form z = r(cosθ + I sinθ ), where r = |a + bi| is z's modulus and tanθ = b.

the angle generated by the complex number on a polar graph having one real axis and one imaginary axis. This may be calculated using the right angle trigonometry for the trigonometric functions. Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

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His lifetime earnings when he retires at the age of 68 is $2,817,385.1728.

The total number of years Demarcus will work is 68 - 24 = 44 years.

Now, there are about 52.1429 weeks per year; therefore, the number of weeks in 44 years will be:

44 years × 52.1429 weeks/year = 2294.2876 weeks

We are also told that Demarcus gets paid once every two weeks; this means the number of payments made in 44 years will be:

2294.2876 / 2 = 1147.1438 payments

Since each payment is worth $2,456.00, the total amount earned from 1147.146 payments will be:

1147.146 payments × 2456 per payment = $2,817,385.1728

Hence, Demarcus' lifetime earnings if he retires at the age of 68 will be $2,817,385.1728.

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Answer:

0 miles driven:$45, 1 miles driven:$47.5, 2 miles driven:$50, 3 miles driven:$52.5

Step-by-step explanation:

Answer:

i think y=1/2x+1 or y+3=1/2 times (x+8)

Step-by-step explanation:

The working equation when dealing with problems regarding compounded interest is

where A is the future value, P is the principal value, r is the annual rate, and n is the number of compounding periods.

The problem compounds quarterly, hence, we have n = 4.

We derive the working equation to solve for t, as follows:

Substitute the values of A, P, n, and r on the derived equation above and solve for t, we get

Therefore, the $4000 investment grows to $5780 in 9.25 years.

Answer: Equation is x+45 = 90

It solves to x = 45

Explanation:

The two angles are complementary, which by definition means they join together to form a right angle. The two pieces x and 45 add to 90 degrees.

To solve the equation x+45 = 90, we subtract 45 from both sides to get x = 45.

As a check x+45 = 45+45 = 90.

Answer: 0.195

Step-by-step explanation:

The base length of triangle for the store is b ≤ 5in.

Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object.

A polygon also includes a triangle.

Triangle's characteristics:

Given:

height of triangle(h)=4in

Area of triangle(A)≤ 10in²

let base length of triangle be b

Area of triangle is given by:

Area = (1/2) × base × height

(1/2) × b × 4 ≤ 10

2b ≤ 10

b ≤ 5 in

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Answer:

Step-by-step explanation:

32=2⁵

therefore=2⁵×⅕

=2

Answer: The answer is y

Step-by-step explanation:

The recursive formula for the sequence 13, 3, -7, -17 is 3 + 10n.

It should be noted that the nth term for an arithmetic sequence is illustrated by the formula:

= a + (n - 1)d.

where a = first term = 13

d = common difference = 3 - 13 = 10

n = number of terms

Therefore, the recursive formula will be:

a + (n - 1)d.

= 13 + (n - 1)10

= 13 + 10n - 10

= 3 + 10n

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In the given figure,

(7x + 73) + (10x + 22) = 180 ........(Because they are linear pair)

⇒ 7x + 73 + 10x +22 = 180

⇒ 17x + 95 = 180

⇒ 17x = 180-95

⇒ 17x = 85

⇒ x = 85/17

⇒ x = 5

Now, 7x +73 = z ....................(Because they are vertically opposite angles)

⇒ 7 x 5 + 73 = z

⇒ z = 35 + 73

⇒ z = 108°

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Answer: ...

Step-by-step explanation: Find the hypotenuse x. Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x. angle A + angle B + angle C = 180 degrees. Solve for x in fractions, we simply do the cross multiplication and simplify the equation to find x.