Susan was supposed to use 5/4 of a cup of butter

in her recipe, but she only used 3/4 of a cup of butter.


a. What fraction of the butter that she should

have used did Susan actually use? Make a

math drawing to help you solve this problem

and explain your solution.


b. Describe the different unit amounts that occur

in part (a). Discuss how one amount can be de-

scribed with two different fractions depending

on what the unit amount is taken to be.

Answer:

c. x² + 2x -5 = 0

Step-by-step explanation:

 Given expression;

         [tex]\frac{5}{x}[/tex]   = [tex]\frac{x + 2}{3}[/tex]  

Unknown:

 The quadratic equation equivalent to this expression:

Solution:

  The common denominator here is 3x;

    So, multiply both sides by 3x

          [tex]\frac{5}{x}[/tex] x 3x  =  [tex]\frac{x + 2}{3} x[/tex] 3x

          5 x 3 = (x + 2)x

           15 = x² + 2x

     So;

          x² + 2x - 15

The quadratic expression is x² + 2x - 15

Answer:

cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = [tex]\sqrt{x^{2}+y^{2} }[/tex]

∵ x = 1 and y = -8

∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = [tex]\frac{x}{r}[/tex]

∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]

∵ sinФ = [tex]\frac{y}{r}[/tex]

∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]

∵ tanФ = [tex]\frac{y}{x}[/tex]

∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8

∵ secФ = [tex]\frac{r}{x}[/tex]

∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]

∵ cscФ = [tex]\frac{r}{y}[/tex]

∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]

∵ cotФ = [tex]\frac{x}{y}[/tex]

∴ cotФ = [tex]-\frac{1}{8}[/tex]    

Answer:

the answer is d because 0.978 cool number like yaaaa.

Step-by-step explanation:

Answer: Is there an image??

AE, BE, CE, and DE is the rays with endpoint E.

An item with both magnitude and direction is referred to be a vector.

A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.

Geometrical objects with magnitude and direction are called vectors.

A line with an arrow in its direction can also be used to represent a vector, and the length of the line relates to the vector's amplitude.

Given the figure,

The endpoint of all rays is E.

The rays associated with point E are;

AE, BE, CE, and DE

Hence "AE, BE, CE, and DE is the rays with endpoint E".

For more information about vector,

brainly.com/question/13322477

#SPJ2

Answer:

Y= -6x + 1

Step-by-step explanation:

Y=mx + b

M is your slope

B is your y intercept

9514 1404 393

Answer:

  C, M

Step-by-step explanation:

The second quadrant is the upper left quadrant. There, x-values will be negative and y-values will be positive.

__

Point G is on the boundary with the 3rd quadrant, so is probably not considered to be in either of those quadrants.

Answer: C M

Step-by-step explanation:

Answer:

dndnfhhfbdhdndndnmdmdndndnen

Answer:

the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now

Step-by-step explanation:

Answer:

Are there answers

Step-by-step explanation:

Answer:

answer

Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. ...

Answer:

= 1 × 10^-7

(scientific notation)

= 1e-7

(scientific e notation)

= 100 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.0000001

(real number)

Step-by-step explanation:

10^7 = 10000000

Answer:

S = 1 bag of popcorn

Y = 1 water

Step-by-step explanation:

S x 3 + Y x 4 = R

40 - R = (The Answer)

Answer:

A)  F(x) = 50 + ( x - 10 )*9  

B) Graph

C) lim ( x ⇒ 10) F(x) = 50

Step-by-step explanation:

A) F(x) = 50 + ( x - 10 )*9       since the first 10 hours are included in initial fee

B) In Annex

C) lim (x ⇒ 10) F(x) = 50 + ( 10 -10)*9

lim ( x ⇒ 10) F(x) = 50 + 0

lim ( x ⇒ 10) F(x) = 50

Answer:

14 depth per minute

Step-by-step explanation:

84/6 = 14

Answer:

Step-by-step explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

[tex]dV/dt = 4piR^2*dR/dt[/tex]

so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]

So the radius is decreasing at the rate of dR/dt= 0.142in/min

Answer:

4/3

Step-by-step explanation:

Multiply 2 by 2, and get 4, then we multiply 3 by 2 and get 6.

Since our denominators match, we can add the numerators. 4 + 4 = 8. That gives us the sum, which is 8/6. Then you divide by 2.  So 8/6 / 2 gives you 4/3.

Answer:

4/3 or 1 1/3

Step-by-step explanation:

1. 4/6 + 2/3

2. 4/6 + 4/6          You have to find the LCM (least common multiple) of the two  denominators. In this case it would be 6. You have to multiply 3 by 2 to get 6. What you do to the bottom you also do to the top so you have to also multiply the numerator (2) by 2.

3. 4/3 or 1 1/3       Afterward, you just have to add straight across without changing the denominator and then if you need to simplify you simplify. Without simplifying, you would get 8/6, but, most teachers will mark it as wrong if you don't simplify. You can then change the improper fraction into a mixed number depending on what your teacher wants.

Answer:

6.88 is what I think you're looking for

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

A deck of card:

Number of hearts = 13

Diamond = 13

Spade = 13

Club = 13

Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)

Hence, a club, diamond, spade and heart has one of each of the above numbers.

a. List the sample points in the event a jack is selected.

Jack : ( heart, club, diamond, spade)

B.) club is selected :

Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)

C)

Jack : ( heart, club, diamond, spade)

Queen : (heart, club, diamond, spade)

King : (heart, club, diamond, spade)

D) probability = required outcome / Total possible outcomes

P(jack selected) = 4 /52 = 1/13

P(club selected). = 13/52 = 1/4

P(face card selected) = 12 / 52 = 3/13

Answer:

[tex]\frac{1}{10} h\leq 10[/tex]

Step-by-step explanation:

Basically, we are just translating the phrase into an algebraic expression.

Answer:

a.) x>-1

b.) x/1 - 9 < -10

Step-by-step explanation:

a.)

5(x - 2) > -15

(divide both sides)

x-2>-3

(move the constant to the right)

x>-3+2

(calculate)

x>-1

(answer)

b.)

x/1 - 9 < -10

(divide)

x-9<-10

(move the constant to the right)

x<-10+9

(calculate)

x/1 - 9 < -10

(answer)

Answer:

18k^2+2m^2+20km

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.

The solution is:

a) V (max) = 36.6 in³

b) x = 1.3 in

The volume of a cube is:

V(c) = w×L×h  ( in³)

In this case, cutting the length  "x" from each side, means:

wide of the box    ( w - 2×x )   equal to  ( 7 - 2×x )

Length of the box ( L - 2×x )   equal to  ( 9 - 2×x )

The height  is  x

Then the volume of the box,  as a function of x is:

V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x

V(x) = ( 63 - 14×x - 18×x + 4×x²)×x

V(x) = 4×x³ - 32×x² + 63×x

Tacking derivatives,  on both sides of the equation

V´(x) = 12×x² - 64 ×x + 63

If   V´(x) = 0      then      12×x² - 64 ×x + 63 = 0

This expression is a second-degree equation, solving for x

x₁,₂ = [ 64 ± √ (64)² - 4×12*63

x₁ =  ( 64 + 32.74 )/ 24

x₁ = 4.03     this value  will bring us an unfeasible solution,  since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)

x₂ = ( 64 - 32.74)/24

x₂ = 1.30 in

The  maximum volume of the box is:

V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3

V(max) = 4.4 × 6.4 × 1.3

V(max) = 36.60 in³

To chek for maximum value of V when x = 1.3

we find the second derivative of V  V´´,  and substitute the value of x = 1.3,    if the relation is smaller than 0,  we have a maximum value of V

V´´(x) = 24×x - 64 for x = 1.3

V´´(x) = 24× 1.3 - 64            ⇒   V´´(x) < 0

Then the value  x = 1.3 will bring maximum value for V

Related Link: https://brainly.com/question/13581879

Answer:

poop i forgot my ramen noodles are in the microwave

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2

Answer:

id say its C but I'm not sure

Answer:

Step-by-step explanation:

Substitute a = -3 and b = -8 to the expression 10a²b⁰:

10(-3)²(-8)⁰ = 10(9)(1) = 90

a⁰ = 1 for any real number

Answer:

90

Step-by-step explanation:

10a^2b^0

Let a=–3, b=–8

10 (-3)^2 ( -8)^0

10 * 9 *1

90

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°