MATHEMATICS HIGH SCHOOL

Use the intercepts to graph the equation. -x+2y=4

Answers

Answer 1
Answer:

Answer:

X-intercept: To find the x-intercept, set y to 0 and solve for x.

-x + 2(0) = 4

-x = 4

x = -4

So, the x-intercept is (-4, 0).

Y-intercept: To find the y-intercept, set x to 0 and solve for y.

-0 + 2y = 4

2y = 4

y = 4/2

y = 2

So, the y-intercept is (0, 2).

Step-by-step explanation:

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Mona is planning a 1,163 mile driving trip. His car gets an average of 19 mpg, and the cost of gas is about $3.96/gallon. What is the approximate driving cost of the trip? Round answer to the nearest whole number.I need help asappp

Answers

Answer:

$242

Step-by-step explanation:

1,163 divided by 19 is 61.2105263158 which means 61.2105263158 gallons will be used. 61.2105263158 times 3.96 is 242.393684211. 242.393684211 rounded to the nearest whole number is 242.

hope this helps

Seperate the number 53 into 3 parts so that the second number is 3 less than the first number and the third number is twice the first number. Give the value of the second number.

Answers

Hello,

Let a the first, b the second and c the third.
a+b+c=53
b=a/3
c=2a
==>a+a/3+2a=53
==>10a/3=53
==>a=15.9
c=2*a=2*15.9=31.8
b=a/3=15.9/3=5.3

Proof: a+b+c=15.9+5.3+31.8=53

The second number is 5.3

Consider the following system of equations: y = −x + 2
y = 3x + 1

Which description best describes the solution to the system of equations?

Line y = −x + 2 intersects line y = 3x + 1.
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
Line y = −x + 2 intersects the origin.

Answers

Answer:    

The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.

Step-by-step explanation:

The first equation is given to be :

y = -x + 2

x       0         2

y       2         0

The second equation is :

y = 3x + 1

x       0        -1/3

y       1         0

Now, The graphs of both the equation are attached below :

So, By seeing the graph, We can observe :

  • Line y = −x + 2 intersects line y = 3x + 1.
  • Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
  • Lines y = −x + 2 and y = 3x + 1 intersect the y-axis

But the description that best describes the solution to the system of equations is : Line y = −x + 2 intersects line y = 3x + 1.

Hence, The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.

y = -x + 2
y = 3x + 1

  -x + 2 = 3x + 1
+ x         + x
          2 = 4x + 1
        - 1         - 1
          1 = 4x
          4     4
         ¹/₄ = x

y = 3x + 1
y = 3(¹/₄) + 1
y = ³/₄ + 1
y = 1³/₄
(x, y) = (¹/₄, 1³/₄)

The answer is A.

Find the sum of place value of 5 in the no 505

Answers

Place values are determined by the position of a digit in the number multiplied by 10 for each digit it has to its right.

Since there are two "5" digits in the number, let us break them down to their respective place values.

1.) 5: one's place: 5
2.) 5: hundred's place: 5 x 10 x 10 = 500

Adding the place values:
500 + 5 = 505

Therefore the sum is 505.

Don completes the square for the equation x^2 + 6x + 3 = 0. Which of the following equations reveals the vertex of the parabola?

Answers

x² + 6x + 3 = 0

y = x² + 6x + 3
y - 3 = x² + 6x 

6x ⇒ 6x / 2x = 3 ⇒ 3² = 9

y - 3 + 9 = x² + 6x + 9
y + 6 = (x+3)² 
y = (x+3)² - 6

vertex of the parabola is (x+3)²

y = (x+3)(x+3)  - 6
y = x(x+3)+3(x+3) - 6
y = x² + 3x + 3x + 9 - 6
y = x² + 6x + 3

What is the reflection of the point (-5,2) in the line y=2?

Answers

Answer:

-2/5

Step-by-step explanation:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).
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