MATHEMATICS HIGH SCHOOL

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

Answers

Answer 1

Answer:

Let

x------> the length of the rectangle

y------> the width of the rectangle

A-----> area of the rectangle

we know that

The area of rectangle is equal to

$A=x*y\nA=40\ units^(2)$

$40=x*y$ --------> equation $1$

$x=6+y$ --------> equation $2$

Substitute equation $2$ in equation $1$

$40=[6+y]*y\n 40=6y+y^(2) \ny^(2) +6y-40=0$

using a graph tool-----> to resolve the second order equation

see the attached figure

the solution is

$y=4$

Find the value of x

$x=6+y\n \n x=6+4=10\ units$

therefore

the answer is

The length of the rectangle is equal to $10\ units$

The width of the rectangle is equal to $4 \ units$

Answer 2

Answer: possible dimensions:
40 x 1
20 x 2
4 x 10
5 x 8

since 10 is 6 more than 4, the length is 10 and the width is 4

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What is the standard form of the parabola whose vertex form is Y=-(X-3)^2+11

Answers

$y=-(x-3)^2+11\ny=-(x^2-6x+9)+11\ny=-x^2+6x-9+11\ny=-x^2+6x+2$

Can someone please help me, this is my last question I have been stuck on it for 30 minThe work of a student to solve a set of equations is shown:

Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z

Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3

In which step did the student first make an error?
Step1
Step 2
Step 3
Step 4

Answers

step 2
he didn't distribute
what he did:
-2(15-2z)=15-2z
that is obviously false

what should have happened is
-2(15-2z)=-30+4z
then add

-2y=-30+4z
2y=4-4z
0=-26
false
no solution
inconsitient, these lines ar paralell

anyway, step 2 is error

The mistake was made in step 2. In simplifying the equation, he has to distribute the -2 through the parentheses. Step 2 simplification should be

-2y = -30 + 4z

When the 2 equations are added, the resultant equation is 0 = -27 therefore it has no solution.

The formula for the area of a square is s2, where s is the side length of the square. What is therea of a square with a side length of 6 centimeters? Do not include units in your answer

Answers

Answer:

Step-by-step explanation:

Area of a square is s² , where 's' is the side length.

For a square of side length = 6 cm ,

The area = (6 cm)² = 36 cm²

* Why did your teacher say that you should not include units in your answer?

Anyway, the area without units is 36 .

Tyrese bought 35 tickets to use at the carnival. He used some of the tickets to ride the bumper cars and play some games. now he has 28 tickets left what is the percent of decrease in the number of ticket that he has?

Answers

Answer:

20%?

Step-by-step explanation:

Final answer:

Tyrese has used 7 out of his 35 initial tickets. This translates to a 20% decrease in the number of tickets he has.

Explanation:

Tyrese started with 35 tickets and now has 28 tickets. To find the percent of decrease in the number of tickets, first, we need to find how many tickets he has used. He has used 35 - 28 = 7 tickets.

Next, we find the percentage decrease using the formula:
Percent Decrease = (Decrease/Original amount) x 100%
So in this case, the decrease is 7 tickets, and the original amount is 35 tickets.
Percent Decrease = (7/35) x 100% = 20%.

Therefore, the percent of decrease in the number of tickets that Tyrese has is 20%.

Learn more about Percent Decrease here:

brainly.com/question/8549621

#SPJ3

Solve the equation. 6 = 2(x + 8)- 5x
a. 2/3
b. 3 1/3
c. - 2/3
d. -3 1/3

Answers

6 =2(x+8)-5x
6 =2x+16-5x
6-16=2x-5x
-10=-3x
10=3x
x=10/3
hence proved

Find a value for k such that the following trinomial can be factored x^2-8x+k

Answers

Answer:

Step-by-step explanation:

x^2-8x+k is a quadratic expression of the form ax^2 + bx + c. Here a = 1, b = -8 and c = k. Focus on x^2-8x and complete the square as follows: Take half of the coefficient of x (that is, take half of -8) and square the result:

(-4)^2 = 16; if we now write x^2-8x+ 16, we'll have the square of (x - 4): (x -4)^2.

Thus, k = 16 turns x^2-8x+k into a perfect square.

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