math 3- Piecewise defined function

Step-by-step explanation:

[tex]y = 2x - 4[/tex]

[tex]3x + y = 1[/tex]

[tex]y = 1 - 3x[/tex]

Equating,

[tex]2x - 4 = 1 - 3x[/tex]

[tex]2x + 3x = 1 + 4[/tex]

[tex]5x = 5[/tex]

[tex]x = 1[/tex]

Placing it,

[tex]y = 1 - 3( 1)[/tex]

[tex]y = 1 - 3[/tex]

[tex]y = - 2[/tex]

Answer: The answer is A

Answer:

its A!!!! i just did it!

Step-by-step explanation:

Answer:

The two parallel sides a and b are 17 cm and 23 cm respectively

Step-by-step explanation:

Area of a trapezium = {(a+b)/2} h

Where

h = height = 18 cm

a = parallel side 1 = x

b = parallel side 2 = x + 6

Area of a trapezium = {(a+b)/2} h

360 = {(x + x + 6) / 2} 18

360 = { (2x + 6) / 2} 18

360 = (2x + 6) 9

360 = 18x + 54

Subtract 54 from both sides

360 - 54 = 18x

306 = 18x

Divide both sides by 18

x = 306 / 18

= 17

x = 17 cm

a = parallel side 1 = x

x = 17 cm

b = parallel side 2 = x + 6

x + 6

= 17 + 6

= 23 cm

Answer:

48 items

Step-by-step explanation:

6 packs of cupcakes with 4 in them, is 24 items. and 3 packs of candy with 8 pieces in them is also 24. 24+24=48. so (6×4)+(8×3)=48

Answer:

48

Step-by-step explanation:

Answer:

The measure of angle A is 53 degrees

The measure of angle B is 37 degrees

Step-by-step explanation:

Here in this question, we are interested in calculating the measure of the two angle.

When how angles are complementary, it means the sum of both equals 90 degrees

mathematically ;

(7x + 4) + (4x + 9) = 90

7x + 4x + 4 + 9 = 90

11x + 13 = 90

11x = 90-13

11x = 77

x = 77/11 = 7

The measure of angle A = 7x + 4 = 7(7) + 4 = 49 + 4 = 53 degrees

The measure of B = 4x + 9 = 4(7) + 9 = 28 + 9 = 37 degrees

Answer:

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Step-by-step explanation:

i googled it

Answer:

M= 7/3 hope that helps ya out

Answer:

24 buses

Step-by-step explanation:

In order to find the answer, we need to divide the number of students by the capacity of each bus. There are 800 students and each bus carries 34.

800/34=23.5

Since we can't have half of a bus, we round up to 24.

24 buses

Answer:

2w-2=16

Step-by-step explanation:

w=9

2w-2

2(9)-2

18-2

16

Answer:

16

Step-by-step explanation:

When we have an expression and we are given the value of the variable, we can substitute inside the expression and find it’s value.

[tex]2w-2[/tex], we know [tex]w=9[/tex] so:

[tex](2\cdot 9) - 2[/tex]

[tex]2\cdot9=18[/tex]

[tex]18-2\\\\16[/tex]

Hope this helped!

Answer:

5y-35

Step-by-step explanation:

since we don't know what y is you have to multiply y and 7 by 5 and you'd get 5y and 35 and then just add the subtraction and bam there's your answer

Answer:

R'(4, -1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, dilation and reflection.

If a point A(x, y) is  rotated 90° counterclockwise about the origin, the new point is A'(-y, x)

From the image attached, below are the location of the points:

P(-3, -1), Q(-1, -1), R(-1, -4) and S(-3, -4)

If point R(-4, -1) is rotated 90° counterclockwise about the origin, its new location would be at R'(4, -1)

Answer:

x = 3 , y = 1

Step-by-step explanation:

Solve the following system:

{y = x - 2 | (equation 1)

y = 7 - 2 x | (equation 2)

Express the system in standard form:

{-x + y = -2 | (equation 1)

2 x + y = 7 | (equation 2)

Swap equation 1 with equation 2:

{2 x + y = 7 | (equation 1)

-x + y = -2 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{2 x + y = 7 | (equation 1)

0 x+(3 y)/2 = 3/2 | (equation 2)

Multiply equation 2 by 2/3:

{2 x + y = 7 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{2 x+0 y = 6 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 3 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = 3 , y = 1

[tex]\huge\boxed{\boxed{\bold{(3, 1)}}}[/tex]

[tex]\hrulefill[/tex]

I'm assuming you need to find the solution to this system of equations (where the lines intersect).

We can use the substitution method to solve this system. Take the value of [tex]y[/tex] from the second equation and substitute it into the first:

[tex]-2x+7=x-2[/tex]

Add [tex]2x[/tex] to both sides of the new equation:

[tex]7=3x-2[/tex]

Now add [tex]2[/tex] to both sides of the equation:

[tex]9=3x[/tex]

Divide both sides by [tex]3[/tex]:

[tex]\boxed{3}=x[/tex]

Now let's solve for [tex]y[/tex] by substituting the known value of [tex]x[/tex] into the first equation:

[tex]y=3-2[/tex]

Simplify using subtraction:

[tex]y=\boxed{1}[/tex]

This means our solution is:

[tex]\large\boxed{(3, 1)}[/tex]

Answer:

(5,7)

Step-by-step explanation:

Answer:

2.5(x-1)+4.5(-x-2)

2.5x-2.5-4.5x-9

-2x-11.5

Step-by-step explanation:

Answer:

2x-11.5

Step-by-step explanation:

[tex]2.5(x-1)+4.5(-x-2)\\2.5x-2.5+4.5x-9\\2.5+2x-9\\2x-11.5[/tex]

hope this helps

Answer:

8

Step-by-step explanation:

Answer:

there is a button on the side of your keyboard that turns off all caps

ACTUAL ANSWER: 1 dollar a pound

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Subsitude -2 to where x is and you get -1o then subtract by -3 and the total is -13

Step-by-step explanation:Step 1: Simplify both sides of the equation.

4−(2y−1)=2(5y+9)+y

4+−1(2y−1)=2(5y+9)+y(Distribute the Negative Sign)

4+−1(2y)+(−1)(−1)=2(5y+9)+y

4+−2y+1=2(5y+9)+y

4+−2y+1=(2)(5y)+(2)(9)+y(Distribute)

4+−2y+1=10y+18+y

(−2y)+(4+1)=(10y+y)+(18)(Combine Like Terms)

−2y+5=11y+18

−2y+5=11y+18

Step 2: Subtract 11y from both sides.

−2y+5−11y=11y+18−11y

−13y+5=18

Step 3: Subtract 5 from both sides.

−13y+5−5=18−5

−13y=13

Step 4: Divide both sides by -13.

−13y

−13

=

13

−13

y=−1

 Answer: y =-1

Here, this is a linear equation in one variable because only one variable is there, y. We need to find the solution i.e the value of y.

Given, equation:

[tex]4 - (2y - 1) = 2(5y + 9) + y[/tex]

We need to find y, So let's isolate y in any one side of the equation. Before that, let's open the parentheses.

[tex]4 - 2y + 1 = 10y + 18 + y[/tex]

[tex]5 - 2y = 11y + 18[/tex]

Now, let's add 2y to both sides, So that -2y on the left hand side gets cancel.

[tex]5 - 2y + 2y = 11y + 18 + 2y[/tex]

[tex]5 = 13y + 18[/tex]

Flipping the equation for easy calculation,

[tex]13y + 18 = 5[/tex]

Solving further,

[tex]13y = - 13[/tex]

[tex]y = \frac{ - 13}{13} [/tex]

[tex] \boxed{y = - 1}[/tex]

Hence, we are done !!

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Answer: B

Step-by-step explanation:

-6.53, -6 1/4, 6.57, 6 3/4.

Answer:

I think the answer would be the fourth answer or the second answer.

sorry if its not the correct answer.

Step-by-step explanation:

D; 10.5x + 45 < 12.5x + 35

We are told that;

C_a = 10.5x + 45

Similarly, we are told that;

C_b = 12.5x + 35

Since we want to make C_a < c_b

Then, we will have;

10.5x + 45 < 12.5x + 35

Read more at; brainly.com/question/4853862

The distance between the given points is 13 units.

We have two coordinate points  A(8, -4) and B(3, 8).​

We have to determine the distance between these two points.

The distance between two points -

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

According to the question, we have -

Coordinates of 1st point -  A(8, -4)

Coordinates of 2nd point -  B(3, 8)

Using the distance formula given -

d = [tex]\sqrt{(3-8)^{2} + (8-(-4)^{2} }[/tex]

d = [tex]\sqrt{(-5)\times (-5) + (12)\times (12)}[/tex]

d = [tex]\sqrt{25 + 144}[/tex]

d = [tex]\sqrt{169}[/tex]

d = 13 units

Therefore, the distance between the given points is 13 units.

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Answer:

The y-intercept of the line would be (C) 8

Step-by-step explanation:

The slope of the line with the equation y = -3x - 5 is -3. When figuring out a slope perpendicular to another line you would use the negative reciprocal of the slope which would lead to the slope of the line to be 1/3.

We know it passes through the point (-3,7), substituting x and y, we would then get our new equation, [tex](7) = \frac{1}{3}( -3) + b[/tex].

Solve the equation by multiplying -3 with 1/3 and the product would be -1. Add negative one on both sides and you would get 8 = b.

12^2 - s^2 is area of the large square minus area of the smaller square. It's the only correct option.

An expression is defined as a set of numbers, variables, and mathematical operations. The expression represents the area of the frame in square inches is 12² - s².

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The area of the two squares can be written as,

Area of the larger square = 12²

Area of the smaller square = s²

Now, The area of the frame

= Area of the larger square - Area of the smaller square

= 12² - s²

Hence, the expression represents the area of the frame in square inches is 12² - s².

Learn more about Expression:

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Answer:

7 hours

Step-by-step explanation:

Her rate (speed) is

v = d/t = (792 miles) / (11 hrs) = 72 mph

To drive a distance D = 504 miles, it will take her a time T given by

T = D/v = (504 miles) / (72 mph) = 7 hours

Step-by-step explanation:

[tex] - 9 + 6p = 5p[/tex]

[tex]6p - 5p = 9[/tex]

[tex]p = 9[/tex]

is the answer.

The things to Note:-

☃️ Hope it HELPS ☃️

the remainder is - 1

when (x ³ - 7x + 5) is divided by (x + 3) the remindeer is f( -3 )

x + 3 = 0 => x = - 3

f(-3) = (-3)³ - 7(-3) + 5

= - 27 + 21 + 5

= - 1

===========================================

Explanation:

For now, ignore the variables. Let's just focus on the coefficients 12 and 16.

The GCF of 12 and 16 is 4 because this is the largest factor they have in common.

12 = 4*3

16 = 4*4

You could create a factor tree to get the prime factorization of each number

12 = 2*2*3

16 = 2*2*2*2

Each factor tree has two copies of '2' leading to the GCF 2*2 = 4.

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Now let's go back to the variables. The term 12n and 16w^3 do not have any variables in common. So the final answer won't have any variables in it. If both terms had say a 'w' in them, then w would somehow be involved in the GCF. But that's not the case here. So we just stick to 4 as our answer.

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Side note: If you had 12n+16w^3 and you wanted to factor, then you would factor out the GCF 4 to get 12n+16w^3 = 4(3n+4w^3). Use the distribution rule to confirm this.