Each day, a restaurant serves x meals that consist of 1/4 of a chicken each. It also makes soup
using 1/2 of a chicken each day. The chef expresses the number of chickens she uses each day
1/4x+1/2. How many chickens does she use in three days?

Answer:

9)    a = ¾, vertex: (-4, 2),  Equation: y = ¾|x + 4| + 2

10)  a = ¼, vertex: (0, -3),  Equation: y = ¼|x - 0| - 3

11)   a = -4,  vertex: (3,  1),   Equation: y = -4|x - 3| + 1

12)  a = 1,    vertex: (-2, -2),  Equation: y = |x + 2| - 2

Step-by-step explanation:

I could only work on questions 9, 10, 11, 12 in accordance with Brainly's rules. Nevertheless, the techniques demonstrated in this post applies to all of the given problems in your worksheet.

The given set of graphs are examples of absolute value functions. The general form of absolute value functions is: y = a|x – h| + k, where:

|a|  = determines the vertical stretch or compression factor (wideness or narrowness of the graph).

(h, k) = vertex of the function

x = h represents the axis of symmetry.

Solve for a:

In order to solve for the value of a, choose another point on the graph, (0, 5) and substitute into the general form (equation):

y = a|x – h| + k

5 = a| 0 - (-4)| + 2

5 = a| 0 + 4 | + 2

5 = a|4| + 2

5 = 4a + 2

Subtract 2 from both sides:

5 - 2 = 4a + 2 - 2

3 = 4a

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{3}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¾

Therefore, given the value of a = ¾, and the vertex, (-4, 2), then the equation of the absolute value function is:

Equation:  y = ¾|x + 4| + 2

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -2) and substitute into the general form (equation):

y = a|x – h| + k

-2 = a|4 - 0| -3

-2 = a|4| - 3

-2 = 4a - 3

Add 3 to both sides:

-2 + 3 = 4a - 3 + 3

1 = 4a  

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{1}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¼

Therefore, given the value of a = ¼, and the vertex, (0, -3), then the equation of the absolute value function is:

Equation:  y = ¼|x - 0| - 3

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -3) and substitute into the general form (equation):

y = a|x – h| + k

-3 = a|4 - 3| + 1

-3 = a|1| + 1

-3 = a + 1

Subtract 1 from both sides to isolate a:

-3 - 1 = a + 1 - 1

a = -4

Therefore, given the value of a = -4, and the vertex, (3, 1), then the equation of the absolute value function is:

Equation:  y = -4|x - 3| + 1

Solve for a:

In order to solve for the value of a, choose another point on the graph, (-4, 0) and substitute into the general form (equation):

y = a|x – h| + k

0 = a|-4 - (-2)| - 2

0 = a|-4 + 2| - 2

0 = a|-2| - 2

0 = 2a - 2

Add 2 to both sides:

0 + 2  = 2a - 2 + 2

2 = 2a

Divide both sides by 2 to solve for a:

[tex]\LARGE\mathsf{\frac{2}{2}\:=\:\frac{2a}{2}}[/tex]

a = 1

Therefore, given the value of a = -1, and the vertex, (-2, -2), then the equation of the absolute value function is:

Equation:  y = |x + 2| - 2

Answer:True

Step-by-step explanation:

There is a constant rate of change. For x, it'd be +1. For y, it'd be +3.

Vote brainliest please!

Answer:

true

Step-by-step explanation:

This is because the slope is y= 3x, you can prove that by plugging in the x values, and if they equal the y then that slope is right.

Answer:

It takes 3/4 of an hour to go 1 mile

Step-by-step explanation:

You can do this by setting up a proportion and by using decimals for some fractions

2/3 = 0.66667 Miles

1/2 = 0.5  hours

0.66667/0.5 = 1/x                         Cross multiply

0.66667 * x = 0.5 * 1                     Simplify

0.66667 * x = 0.5                         Divide both sides by 0.66667

x = 0.5 / 0.66667

x =  0.74999625                           Notice when rounded this is 0.75

x = 0.75                                         Now notice that 0.75 as a fraction is 3/4

x = 3/4

Jeremy can row 2/3 of a mile in 1/2 hour then it will take him 3/4 hour to row 1 mile.

If Jeremy can row 2/3 of a mile in 1/2 hour, then the time it takes him to row 1 mile can be found by setting up a proportion:

(2/3 mile) / (1/2 hour) = 1 mile / (x hours)

Cross-multiply:

(2/3) × x = 1 × (1/2)

Now solve for x:

x = (1/2) / (2/3)

x = 3/4

So, it will take Jeremy 3/4 of an hour (or 45 minutes) to row 1 mile.

Learn more about mile here:

https://brainly.com/question/29806974

#SPJ3

Answer:

t = 2 half-lives = 2*60 days = 120 days

hope this helps

Step-by-step explanation:

Answer:

[tex]\huge\boxed{z=6;\ x=12.5}[/tex]

Step-by-step explanation:

If two figures are similar, then corresponding sides are in proportion.

Therefore:

[tex]\dfrac{z}{15}=\dfrac{4}{10}\qquad|\text{cross multiply}\\\\10z=(15)(4)\\\\10z=60\qquad|\text{divide both sides by 10}\\\\\boxed{z=6}[/tex]

[tex]\dfrac{x}{5}=\dfrac{10}{4}\qquad|\text{cross multiply}\\\\4x=(5)(10)\\\\4x=50\qquad|\text{divide both sides by 4}\\\\x=\dfrac{50}{4}\\\\\boxed{x=12.5}[/tex]

Answer:

parallel

Step-by-step explanation:

maybe I guess it parallel, cause it not perpendicular

Answer:

Step-by-step explanation:

3x - 8y = 19

    -8y = -3x + 19

        y = (3/8)x - 19/8

32x + 12y = 19

         12y = -32x + 19

             y = (-32/12)x + 19/12

             y = (-8/3)x + 19/12

as the slopes of the lines are negative reciprocals of each other, the lines are PERPENDICULAR

Answer:

70°

Step-by-step explanation:

isoceles so base angles are 55

55+55 is 110 so 180-110 is 70

Answer:

if the triangle is isosceles

Step-by-step explanation:

traingle angles= 180°

isosceles traingle= base angles are equal

180°-55°-55°= 70°

Answer:

linear association, correct

Answer:

There are two answers: it is Nonlinear association and Linear association

Step-by-step explanation:

Nonlinear association- When comparing two data sets if the data from one set increase, the data from the second set decrease (it basically means a scatter plot that is decreasing).

Linear association- arranged in extending along a straight or nearly straight line.

I also took the test it it was correct.

Answer:

30 and 35

Step-by-step explanation:

Put this question into equation form:

Let x be the smaller number, if the larger number is 5 more and the total is 65:

x + 5 + x = 65

2x + 5 = 65

Subtract 5 from both sides

2x + 5 - 5 = 65 - 5

2x = 60

Divide both sides by 2:

2x ÷ 2 = 60 ÷ 2

x = 30

As the larger number is 5 bigger:

30 + 5 = 35

So the two numbers are 30 and 35.

Hope this helps!

Answer:

Small number 30

Large Number 35

Step-by-step explanation:

The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:

x + y = 65

The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

Now solve equation B for x to get the revised equation B:

x - y = 5

x = 5 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 65

5 + y + y = 65

5 + 2y = 65

2y = 60

y = 30

Now we know y is 30. Which means that we can substitute y for 30 in equation A and solve for x:

x + y = 65

x + 30 = 65

X = 35

Therefore the large and small number us 35 and 30 respectively.

By isosceles triangle theorem,

Angle ZXY = Angle ZYX

The sum of the angles in a triangle is 180 degrees.

106 + 2 same angles (-106) = 180 (-106)  (Subtract 106 by both sides)

2 same angles (/ 2) = 74 (/ 2)   (Divide 2 by both sides)

V = 37

Answer:

The value of v is 37°.

Step-by-step explanation:

Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:

Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,

∠ZXY + ∠ZYX + ∠XZY = 180°

v + v + 106° = 180°

2v + 106° = 180°

2v = 180° - 106°

2v = 74°

v = 74 ÷ 2

v = 37°

If you plug 7 as x into:

(2x+45)

then you get

(2(7)+45)

(14+45)

(59)

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The area of the rectangle is ...

  A = lw = (21)(12)

The area of the shaded triangle is ...

  A = 1/2bh = 1/2(14)(12) = (7)(12)

Then the fraction of the rectangle that is shaded is ...

  (shaded area)/(rectangle area) = (7)(12)/((21)(12)) = 7/21 = 1/3

1/3 of the rectangle is shaded.

Answer:

None of the answer options are correct

Step-by-step explanation:

cs + rh = w

cs = w - rh

s = (w - rh)/c

The second one could be corrected by exchanging c with 1/c

The last one would be correct with judiciously applied parentheses.

The first and third have too many errors to even bother trying to correct.

answer could also be written

s = w/c - rh/c  

but it is not considered reduced form.

9514 1404 393

Answer:

  (d)  s = (w − rh)/c

Step-by-step explanation:

Undo what is done to the variable. It is multiplied by c and rh is added to that product.

  cs +rh = w . . . . . given

  cs = w -rh . . . . . undo the addition of rh: add -rh to both sides

  s = (w -rh)/c . . . . undo the multiplication by c: divide both sides by c

_____

Additional comment

Each entire side of the equation is divided by c. That means the entire expression (w-rh) is divided by c. It is incorrect to write that division as w-rh/c. The division bar (/) in plain text only refers to the immediately preceding and the immediately following tokens as its operands. When the expression is typeset, the division bar serves as a grouping symbol, showing you the entire numerator.

  [tex]s=\dfrac{w-rh}{c}[/tex]

Answer:

hello mam I don't know what to say to someone who makes the way to the way to the way to the way to the way to the way to work now where is my turn to the dark side I will be

Answer:

x intercept: (3/2, 0), y intercept: (0, -3)

Step-by-step explanation:

Answer: 4.65

Step-by-step explanation: 42.80 - 38.15 = 4.65

Step-by-step explanation:

14 ÷ 4 is the same as the corresponding fraction (because a fraction is nothing else than a mini-division) :

14/4 = 7/2

and 7 divided by 2 is 3 with a remainder of 1. that means 1 time 1/2 remains as fraction.

so, the mixed number is

3 1/2

Answer:

Hello!

Judging by the link you provided I have come up with the correct solution:

x= 61°

y= 29°

Step-by-step explanation:

I will link my work below:

The first step to finding the two solutions it to first identify one of them.

I chose to identify x first.

To identify the value of x in this problem you have to notice that the x value corresponds with the value "29°" to form a perfect right angle, being 90°.

Thus you can simply find the value of x by doing this formula:

x+29°=90°

You then subtract 29° from both sides to simplify, and you come up with the solution

x=61°

Now we need to find the value of y.

To find the value of y I noticed that again, like x, y corresponds with another variable (being x) to form a perfect right angle (90°).

The way I realized this is a perfect right angle is because, as you can see in the picture you provided, the y+x angle are alternate exterior angles with another angle that is 90°.

Thus you can assume that:

x+y=90°

x= 61°

61°+y=90°

You then subtract 61° from both sides to get:

y=29°

Answer:

Length = 6in

Width = 4in

The formula for solving the perimeter of a rectangle is:

P = 2(L+W)

The formula for finding the area of a rectangle is:

A = L x W

If we substitute our values, we will get:

P = 2(6 + 4)

P = 2(10)

P = 20in

A = 6 x 4

A = 24in²

Answer:

534,070.75 miles

Step-by-step explanation:

The circumference formula is [tex]d\pi[/tex] or [tex]2r\pi[/tex].

But since we're given the diameter, 170,000, all we have to do is multiply it by [tex]\pi[/tex].

[tex]170000*\pi = 534070.75 (Rounded)[/tex]

Answer:

y = x + 6

Step-by-step explanation:

Answer:

92.

Step-by-step explanation:

By proportion the mass of zinc = (345/ 15) * 4

= 92.

Answer:

sorry i can answer that the asy

Answer:

Q1 - 10080

(sorry couldn't do q2 haha)

step by step;

Step-by-step explanation:

Yes

If you connect the points plotted, they will form a line and will pass through the origin.

This is indication of the proportional relationship.

The equation of circumference is:

Since 2π is a constant value, the equation above represents a proportional relationship.

Answer:

-20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

one period is 5, so -5×4 = -20

Answer:

140%

Step-by-step explanation:

28-10 = 14 person enrolled

14/10 = 140%

If she read 52 pages in one hour, then she'll continue at a rate of 52 pages per hour.

Answer:

52 pages

Step-by-step explanation:

Since she reads 52 pages in 1 hour we multiply 52 by the amount of hours she reads.

52 pages times 1 hour equals 52 pages.

52 x 1 = 52