MATHEMATICS HIGH SCHOOL

3. At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 items that each cost the same amount, but each was $1.50 less than the items that Spongebob bought. Both Spongebob and Patrick paid the same amount of money. What was the individual cost of each person's items?

Answers

Answer 1
Answer:

Answer: Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

Step-by-step explanation:

Let x be the cost of each item bought by Spongebob.

Then, cost of each item bought by Patrick = x- 1.50

Then, cost of 3 items bought by Spongebob =  3x

Cost of 5 items bought by  Patrick = 5(x-1.50)

If both Spongebob and Patrick paid the same amount of money then

3x= 5(x-1.5)\n\n\Rightarrow\ 3x=5x-1.5*5\n\n\Rightarrow\ 3x=5x-7.5\n\n\Rightarrow\ 5x-2x=7.5\n\n\Rightarrow\ 3x=7.5\n\n\Rightarrow\ x=(7.5)/(3)\n\n\Rightarrow\ x=2.5

Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $2.5-$1.5=$1

Hence, Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1
Answer 2
Answer:

Answer: Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

Step-by-step explanation:

Let x be the cost of each item bought by Spongebob.

Then, cost of each item bought by Patrick = x- 1.50

Then, cost of 3 items bought by Spongebob =  3x

Cost of 5 items bought by  Patrick = 5(x-1.50)

If both Spongebob and Patrick paid the same amount of money then

Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $2.5-$1.5=$1

Hence, Cost of each item bought by Spongebob = $2.5

Cost of each item bought by Patrick = $1

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Is the quotient 2.7 divided by 3 greater than 1?

Answers

no, the quotient of 2.7 divided by 3 is not greater than 1

2.7 ÷ 3 = 0.9

Which of the following would be an acceptable first step in simplifying the expression (sinx)/(1 + sinx) ?A. 1/(cscx + sinx)
B. sinx + 1
C. (sinx(1 - sinx))/((1 + sinx)(1 - sinx))

Answers

C. (sinx(1 - sinx))/((1 + sinx)(1 - sinx))

Answer:

multiply the denominator by its conjugate (1-sinx)/(1-sinx)

Step-by-step explanation:

[sinx (1-sinx)] / [(1+sinx)(1-sinx)]

!50 POINTS! (1 SIMPLE GEOMETRY QUESTION)

QUESTION BELOW
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Answers

Answer:

x= 40.33

Step-by-step explanation:

In geometry, alternate exterior angles are a pair of angles that are on the outer side of two parallel lines but on opposite sides of the transversal. In other words, they are the angles that are not on the same line as the parallel lines.

The alternate exterior angles are always equal in measure. This is because when a transversal intersects two parallel lines, it creates two pairs of alternate exterior angles, and each pair of angles is supplementary to each other (meaning that their measures add up to 180 degrees).

In this case:

a° = b°

Since,, the alternate exterior angles are always equal in measure.

3x+17 = 138

subtracting 17 on both sides

3x + 17-17 = 138-17

3x = 121

dividing both sides by 3.

(3x)/(3) = (121)/(3)

\sf x \approx 40.33

The value of x is 40.33 which  proves that r is parallel to s.

Answer:

c)  40.3

\hrulefill

Step-by-step explanation:

According to the Alternate Exterior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the alternate sides of the transversal are congruent.

Therefore, if lines r and s are parallel, then a° = b°.

To find the value of x that proves line r is parallel to line s, solve a° = b° for x.

\begin{aligned}a^(\circ)&=b^(\circ)\n\n3x+17&=138\n\n3x+17-17&=138-17\n\n3x&=121\n\n(3x)/(3)&=(121)/(3)\n\nx&=40.33333....\n\nx&=40.3\; \sf (nearest\;tenth)\end{aligned}

Therefore, the value x that proves line r is parallel to line s is:

\Large\boxed{x=40.3}

Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.. .

Answers

f ( x ) = - 2 x² + 12 x + 5 = - 2 ( x² - 6 x ) + 5 = - 2 ( x² - 6 x + 9 - 9 ) + 5 =
- 2 ( x² - 6 x + 9 ) + 18 + 5 = - 2 ( x - 3 )² + 23 
f ( x ) = a ( x - k )² + h ( the vertex form ), k = 3, h = 23. 
a = - 2 < 0, that means the vertex coordinates ( 3, 23 ) represents a maximum.

Answer:

3,23 maximum

Step-by-step explanation:

Urgent mathematics help needed!! URGENT Please use the graph and instructions on the picture to answer the following questions!!! Will mark brainliest!!!

1. Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable. (Hint: USE DESMOS) 2pts


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Answers

Hello,

Please, see the attached files.

Thanks.

Solve for m f=gmn/d^2

Answers

f = gmn/d²

gmn = fd²

m = fd²/gn
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