1 A recipe for sugar cookies requires 2 cups of
flour for every 2/3 cups of sugar.
At this rate, how many cups of sugar should be used if 5 cups of flour is included?

Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

----------------------------------------------------

Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]

2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35

2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

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Answer:

153.86 ft^2

Step-by-step explanation:

π=3.14

r=7ft

πr^2=3.14*7*7

=153.86 ft^2

Area of circle = π r²

Here , We have

Area of circle = 3.14 × (7)²

Area of circle = 3.14 × 49 ft²

Area of circle = 153.86 ft²

Answer:

solution -2/5+1/2 =-2*2+1*5/5*2 =-4+5/10 =1/10

Answer:

range is the y part and domain is the x so the range is the y coordinates

-6,-3,-2,-2,1,4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Some form of symetric i think....

The best describes the shape of this distribution is Unimodal symmetric.

A unimodal distribution is a distribution that has one clear peak. The values increase first, rising to a single highest point where they then start to decrease. A unimodal distribution can either be symmetrical or non-symmetrical. A symmetrical distribution is one where the mean, mode, and median are all equal.

Given is a histogram, we have to find the shape of this distribution,

Since, we can see that the graph only has a hump with equal distribution either side of the hump, which can say that the graph is a Unimodal symmetric

Therefore, the given distribution is Unimodal symmetric as the distribution has 1 hump.

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Answer:

8 tickets

Step-by-step explanation:

To find how many tickets he bought, we can divide.

66 / 8.25 = 8

Best of Luck!

Answer:

8

Step-by-step explanation:

66 divided by 8.25, bringing it to 8.

9514 1404 393

Answer:

  (b)  x> 3 or x<-3

Step-by-step explanation:

The ∨ symbol is understood to mean "or".

  p ∨ q ≡ (x < -3) or (x > 3) . . . . . . matches the 2nd choice

Answer:

Not too sure about this one, but I hope this helps.

Step-by-step explanation:

basically I just used the formula y=mx+b

m is the slope

and b is the y intercept

Answer:

6.875

Step-by-step explanation:

7- (1/2)^3​ = 7-1/8 = 6.875

Answer:

10

Step-by-step explanation:

It 10 bucks each ticket

Answer:

1000

Step-by-step explanation:

10³

= 1000

Answer:

10 * 10 * 10

Step-by-step explanation:

Cubing a number just means you are multiplying that number 3 times to itself. Since we have 10^3, we multiply 10 to itself three times.

Best of Luck!

Answer: 11/3

Step-by-step explanation:

-12/3 + n = - 1/3

n = -1/3 + 12/3

n = 11/3

Answer:

R = V/I

Step-by-step explanation:

I = V/R

Multiply both sides by r

IR = V

Divide both sides by I

R = V/I

Ex:

2 = 6/3

3 = 6/2

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

There are many ways this could be done, but the simplest way is to divide 18 into 72. That gives 4. So each plot is 4 * 20 = 80 m^2

If you are willing to use fractions, the answer could be 20*72 / 18 = 8 * 10  which is more feasible and still gives 80, but the land may not permit it. However math will.

It's hard to give an exact answer when it is this open ended.

Multiply the amount owed by 20% by changing the percent to a decimal.

20% = 0.20

200 x 0.20 = 40

The late fee is $40

Answer:

to find midpoint add both"X" coordinates and divide by 2

also add "Y" coordinates and divide by 2

then for line of segment use distance formula which is D=√[(x2-x1)²+(y2-y1)²]

Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

To determine the midpoint of two coordinates (x₁,y₁) and (x₂,y₂ )

Midpoint = [ (x₁ + x₂)/2 + (y₁ + y₂)/2 ]

The distance between two points (x₁,y₁) and (x₂,y₂ )

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

Hence "Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]".

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Step-by-step explanation:

solution :

cost of 18 drinks (is)=52

Answer:

140 boys

Step-by-step explanation:

x = boys, y = girls

x/y = 4/7, x+y=385

x = 140, y = 245

9514 1404 393

Answer:

  √8

Step-by-step explanation:

8 is between 2² = 4 and 3² = 9. 12 is not.

√8 falls between 2 and 3.

__

Your calculator can help with this.

  √8 ≈ 2.828 . . . . . between 2 and 3

  √12 ≈ 3.464 . . . . not between 2 and 3 (between 3 and 4)

65

Step-by-step explanation:

In goooooooogle you get your answer please Mark me as a brainlist

Answer:

R(-1,-9) But I know if the answer is correct or not

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

I guess it's 1.8 - 0.5

Step-by-step explanation:

Refer to the notes on long division

Answer:

infinite solutions, true for all x

Step-by-step explanation:

-6 - 8x = -2(4x + 3)

Distribute

-6-8x =-8x-6

Add 8x to each side

-6-8x+8x = -8x-6+8x

-6 =-6

Since this is always true, the equation is true for all x

-6-8x = -2(4x+3)

-6-8x = -8x-6

-8x+8x = -6+6

0=0

infinite solution

THANK YOU

Answer:

-11 - z

(-11) - (-11)

= 0

I hope I have helped.

Answer:

The equation is

[tex]{ \underline{ \sf{y = - 2 {e}^{ - 2x} + 7 }}}[/tex]

Step-by-step explanation:

[tex]{ \sf{ {e}^{2x} \frac{dy}{dx} = 1}} \\ \\ { \sf{dy = {e}^{ - 2x} dx}}[/tex]

integrate:

[tex]{ \sf{ \int dy = \int { - e}^{2x} dx}} \\ { \sf{y = - 2 {e}^{ - 2x} + c}}[/tex]

c is a constant.

when y is 5, x is 0:

[tex]{ \sf{y = { - 2e}^{ - 2x} + c}} \\ { \sf{5 = - 2 {e}^{( - 2 \times 0)} + c }} \\ { \sf{5 = - 2 {e}^{0} + c }} \\ { \sf{5 = ( - 2 \times 1) + c}} \\ { \sf{5 = - 2 + c}} \\ { \sf{c = 7}}[/tex]

therefore, equation:

[tex]y = - 2 {e}^{ - 2x} + 7[/tex]

Answer:

Step-by-step explanation:

All real number