MATHEMATICS HIGH SCHOOL

Solve the system of equations. 2x − 5y = 3
x − 3y = 1
(4, 1)
(5, 2)
(7, 2)
(9, 3)

Answers

Answer 1

Answer:

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

$2x-5y = 3\n\n x -3y = 1$

Now, we will use "Substitution Method" to find the values of x and y:

$x=1+3y\ -(3)$

Put the value of x in first equation i.e.

$2x-5y = 3$

$2(1+3y)-5y=3\n\n2+6y-5y=3\n\n2+y=3\n\ny=3-2\n\ny=1$

Now, we use the value of y in equation (3),

$x=1+3y\n\nx=1+3*1\n\nx=1+3\n\nx=4$

Hence, values of (x,y) is (4,1).

Therefore, First Option is correct.

Answer 2

Answer: 2x - 5y = 3
x - 3y = 1...multiply by -2
---------------
2x - 5y = 3
-2x + 6y = -2 (result of multiplying by -2)
--------------add
y = 1

x - 3y = 1
x - 3(1) = 1
x - 3 = 1
x = 1 + 3
x = 4

solution is (4,1)

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Find the product.
(n + 8)(n - 2)

Answers

(n)(n)=n^2
8n-2n=6n
(8)(-2)=-16
Solution:
n^2+6n-16

n^2-n*2+8n-16

n^2-2n+8n-16

=n^2+6n-16

What is the vertex of the quadratic function f(x)=(x-6)(x+2)

Answers

For this case we have the following function:

We rewrite the function making distributive property.

We have then:

To find the vertex of the function, we derive:

We equal zero and clear the value of x:

We evaluate the function for the value of x obtained:

Then, the vertice of the parabola is:

Answer:

the vertex of the quadratic function f(x)=(x-6)(x+2) is:

$(x, y) = (2, -16)$

(2,-16) should be the correct answer..

What does it mean to cube something, thank you

Answers

To multiply it by itself three time eg 2x2x2

Answer:

In math, a cube is a number multiplied by itself three times. The cube of 2 is 8 (2 x 2 x 2). ... As a verb, cube means to cut into cube shapes.

Step-by-step explanation:

6. The lengths of two sides of a triangle are 5 cm and 8 cm. Between what two measuresshould the length of the third side fall

Answers

Answer:

triangle inequality: the sum of the length of two sides of a triangle must always be greater than the length of the third side.

we know 2 sides whose sum = 5+8 = 13cm

the 3rd side must be <13 included

the length of the third side must be less than 13 cm, i.e. between 1 and 13 (it cannot be equal to 0 because in this case it does not exist)

When Mac was asked to duplicate Angle TAR, he used his protractor to measure angle TAR and then to make Angle MAC. Is his construction correct? Explain.

Answers

There is no image! Next time, use an image attached to your question. You can take a screenshot, or a picture of your screen with another device.

Final answer:

Mac was somewhat correct in utilizing a protractor to duplicate angle TAR. However, in geometric construction, angles are usually duplicated using a compass and straight edge.

Explanation:

In terms of duplicating angle TAR to create angle MAC, Mac was somewhat correct in his use of a protractor to measure and recreate the angle. However, the exact correctness of his construction could be contingent upon additional elements. In simple terms, yes, you can duplicate an angle by using a protractor. You would simply need to measure the degree of the original angle and then replicate this on a separate point using the same degree measurement. Nonetheless, in proper geometric construction, an angle is duplicated using a compass and a straight edge rather than a protractor.

For instance, if Angle TAR measures 30 degrees, Mac will set his protractor at an intersect point M to measure and create angle MAC, that also measures 30 degrees. It's essential to note that while the measure of the angles are identical, the lengths of the sides of the angles will not necessarily be identical unless defined to be so.

Yet, using a protractor is not necessarily the exact method of angle duplication as described in classic geometric construction. There, one uses a compass and straightedge to duplicate an angle. This process generally involves drawing an initial line, creating an arc crossing the angle's sides with a compass, and then duplicating this arc on the other line to assure both angles are comparable.