Evaluate piecewise functions

Answer:

y = -1/2x + 2

Step-by-step explanation:

If two lines are perpendicular then the product of their slopes are -1

m1*m2 = -1

where m1 amd m2 is slope of two lines.

_______________________________________

Given line

y = 2x-3\

it is in form of y = mx+c (slope intercept form)

where m is slope and c is y intercept

Thus, slope of line  y = 2x-3 is 2

Now we know that product of two lines are -1

let m be slope of other line

then m*2 = -1

m = -1/2

thus, slope of required line is -1/2

let the line be y = mx+c but m = -1/2

thus

y = -1/2 x + c

given that point(-6,5) lies on it

we use -6 in plca of x and 5 in place of y

5 = -1/2 *-6 + c

=>5 = 3 +c

=> c = 5-3 = 2

Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2

Answer:

i hope this helps and its clear !

Answer:

false

Step-by-step explanation:

Answer:

m = 8 and c = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 8x ← is in slope- intercept form, that is y = 8x + 0

with m = 8 and c = 0

1 pound = 1.62 dollars.

Multiply total pounds by 1.62 for total dollars.

650 x 1.62 = $1,053

Answer:

6

Step-by-step explanation:

Since the two triangles are similar, their ratios of sides must be constant. Therefore:

[tex]\dfrac{9}{3}=\dfrac{x}{2} \\\\x=2\cdot 3=6[/tex]

Hope this helps!

Answer:

A = 3[tex]r^{2}[/tex]

Step-by-step explanation:

r = [tex]\sqrt{\frac{A}{3} }[/tex]

r = [tex](\frac{A}{3})^{1/2}[/tex]

square both sides:

[tex]r^{2}[/tex] = [tex]\frac{A}{3}[/tex]

multiply 3 to both sides:

3[tex]r^{2}[/tex]  = A

Answer:

[tex] a= 3r {}^{2} [/tex]

[tex] \sqrt{ \frac{a}{3} } = r \\ \frac{1}{3a} = r {}^{2} \\ \frac{1}{3a} \frac{1}{3} = r {}^{2} \frac{1}{3} \\ a = 3r {}^{2} [/tex]

Answer:

From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees

Step-by-step explanation:

Given that the triangles are eight in number we have;

1)  (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down

2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns

3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top

4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°

5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew

6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.

Step-by-step explanation:

5f

5 + n times of a number

Answer:

The correct option are;

1) Could not

2) Is

Step-by-step explanation:

The parameters given are;

The survival rate of drivers using seat-belt = 67%

The survival rate of drivers not using seat-belt = 41.5%

The chance of getting the survival rate results without a correlation with the use of seat-belt < 0.0001

Given that the chance of obtaining the given survival rates without the seat-belt having an effect on survival rate is less than 0.01 percent we have;

The probability shows that the sample results could not have occurred by chance. It appears that there is sufficient evidence to conclude that seat-belts do have an effect on survival rate.

Answer:

63 cm

Step-by-step explanation:

piece 1: x

piece 2: x - 18

First you would subtract 2x - 18 = 108

Second you would add 108 + 18 = 2x

Third you would divide 126 divided by 2x = 63

So that would mean x = 63

Answer:

63cm

Step-by-step explanation:

2 pieces of rope, and one is shorter by 18cm.

piece 1: x

piece 2: x-18

Add the equations together, combine both pieces

2x-18

2x-18 = 108

108+18 = 2x

126 = 2x

x = 63

Answer:

Step-by-step explanation:

The slope is 3 and the y-intercept is 2 or (0, 2)

Answer:

The y-intercept of the equation is -2.

Step-by-step explanation:

This equation is in slope-intercept form (y = mx + b). b represents the y-intercept, and m represents the slope.

Answer:

529 plan

Step-by-step explanation:

The 529 plan investment account is a type of account used to save for future education purposes and are sponsored by educational institutions and the state. They are of two types, The prepaid tuition plan and the education saving plan. The prepaid tuition plan is used to pay for future tuition fee at present rates while the education saving plan are used to pay for qualified education expenses

Answer:

529 plan

Step-by-step explanation:

A 529 college savings plan works much like a Roth 401(k) or Roth IRAby investing your after-tax contributions in mutual funds, ETFs and other similar investments. Your investment grows on a tax-deferred basis and can be withdrawn tax-free if the money is used to pay for qualified higher education expenses.

Answer:

17

Step-by-step explanation:

Plot in the points for each variable to find the y-intercept.

1=-4(4)+c

1=-16+c

1+16=c

17=c

9=-4(2)+c

9=-8+c

9+8=c

17=c

Answer:

Step-by-step explanation:

Given:

2 Points

(4,1) and

(2,9)

Slope

m = (y2 - y1)/(x2 - x1)

y2 = 9

y1 = 1

x2 = 2

x1 = 4

m = (9 - 1) / (2 - 4)

m = 8 / - 2

m = - 4

y intercept

y = mx + b

y = -4x + b

Use (9, 1) to find the y intercept

1 = - 4*9 + b

1 = - 36 + b

b = 37

Answer

The equation is y = - 4x + 37

Answer:

3fx

Step-by-step explanation:

f(x)+f(x)+f(x)

remove parenthesis: (a)=a

add similar elements: fx+fx+fx

=3fx

Answer: for edge

3f(x)

3x2

12

Answer: [tex]y \leq \frac{1}{2} x+3[/tex]

Step-by-step explanation:

If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.

First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.

You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.

3 - 1 = 2

0 - (-4) = 4

2/4 = 1/2

The new equation is:

[tex]y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3[/tex]

Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, [tex]\leq[/tex]

Answer:

B

Step-by-step explanation:

Answer:

1.0712

Step-by-step explanation:

if you increase by 4%, it means you will have a new total of 104%. In decimals it is 1.04 (divide your percentage by 100) after that you do the same with the 3% increase. you'll have a new total of 103%. In decimals 1.03. If you want to know what single multiplier you can use, you need to multiply the both decimals. So you get 1.04 x 1.03 = 1.0712

hope this will help you, have a nice day!

Answer:

2/6 or 1/3

Step-by-step explanation:

There are two numbers who are equal or less than 2 its 1 and 2

And the total is 6 so its 2/6 which is 1/3

Sorry if this is late

Answer:

0.33

Step-by-step explanation:

Answer:

A car can travel 45 miles every hour, because I multiply 3/4 (0.75) by 60. Because of this, 60 minutes is an hour.

Step-by-step explanation:

Answer:

45 people prefered coffee, 81 people prefered tea. A total of 126 people were surveyed.

Step-by-step explanation:

Let t be the people who prefer tea, and let c be the people who prefer coffee.

The ratio between tea and coffee is 9:5, thus we have t/c=9/5. Cross products  give us 5t=9c.

Also, we have 36 more people prefer tea than coffee, so we have c+36=t

Thus we have: 5(c+36)=9c

5c+180=9c

180=4c

c=45

c+36=t

45+36=81

Answer:

[tex](f*g)(x) = x^4-7x^3[/tex]

Step-by-step explanation:

[tex]f(x) = x-7\\g(x) = x^3[/tex]

Multiplying both would make

[tex](f*g)(x) = x^4-7x^3[/tex]

Answer:

unanswerable,don't censore the question

Step-by-step explanation:

sorry pal

Answer:

n is the seventh term=5832

Step-by-step explanation:

a1=8

r=3

a(n)=a1*r^(n-1)=

an=8*3(n-1)

8+24+72+216+648+1944+5832=8744

The answer of this is C: 43

Answer:

C)43ft

Step-by-step explanation:

Area= pi*r(squared)

Pi*3.7(squared)=43.00

So answer=43pi(squared)

Answer:

4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

[tex]a_{n}[/tex] = 11 +(n - 1)4 , then

d = 4

The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 4

Answer:

The answer is 4

Step-by-step explanation:

Answer:

A=1.5 units²

Step-by-step explanation:

a²+b²=c²

2.5²+1.5²=c²

a²+2.25=6.25

a²=4.00

a=2

A=1/2 x b x h

A=1/2 x 1.5 x 2

A=1.5 units²

Answer:

1.5

Step-by-step explanation:

Use the pythagorean theorem.  a^2+b^2=c^2.  a and b are the legs, or the shorter sides of the triangle.  If you don't know which ones are shorter, just know that c is opposite of the right angle which is 2.5 in this case.  So c is 2.5 and a is 1.5.  Now you plug the values into the equation

1.5^2+b^2=2.5^2

2.25+b^2= 6.25 .Simplify the equation

b^2= 4 .Subtract 2.25 from both sides.

b= 2.  Square root both sides.  

Based on the picture, a is the base and b is the height.  The area of a triangle is 1/2(bh) .You already know the base and height you you plug it in again

1/2(1.5*2)= 1/2(3)= 1.5  

Answer:

so 2a+3b=±13

Step-by-step explanation:

4a²+9b²=97

ab=6

2a+3b=?

by using formula

(a+b)²=a²+b²+2ab

(2a+3b)²=(2a)²+(3b)²+2(2a)(3b)

(2a+3b)²=4a²+9b²+12ab

putting values

(2a+3b)²=97+12(6)

(2a+3b)²=97+72

(2a+3b)²=169

taking square root on both sides

√(2a+3b)²=√169

2a+3b=±13

i hope it will help you

Answer:

2a+3b = 13

Step-by-step explanation:

Using this formula

[tex](x+y)^2 = x^2+y^2+2xy[/tex]

Where,

x = 2a and y = 3b

Putting in the above formula

=> [tex](2a+3b)^2=4a^2+9b^2+12ab[/tex]

Putting  4a²+9b² = 97 and ab = 6

=> (2a+3b)² = 97+12(6)

=> (2a+3b)² = 97+72

=> (2a+3b)² = 169

Taking sqrt on both sides

=> 2a+3b = 13