A cake recipe called for using 6 ¼ cups of sugar before baking and another 5 ¾ cups after baking. What is the total amount of sugar needed in the recipe?

Answer:

Step-by-step explanation:

Given that:

The height of the dock (h) = 6

Let represent d to be the distance between the boat and the dock

Let the length of the rope between the boat and the drum be denoted by (l)

Then, the rate of change for the length of the rope be:

dl/dt = -5 ft/s

Using Pythagoras rule to determine the relationship between these values, we have:

[tex]l^2 = h^2 +d^2[/tex]

[tex]l^2 = 6^2 + d^2[/tex]

[tex]l^2 = 36 + d^2[/tex]

We relate to:  [tex]2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}[/tex]

From the question;

l = 34,

So to find [tex]\dfrac{dd}{dt}[/tex], we get;

[tex]d = \sqrt{l^2 - 36}[/tex]

[tex]d = \sqrt{34^2 - 36}[/tex]

[tex]d = \sqrt{1156- 36}[/tex]

[tex]d = \sqrt{1120}[/tex]

d = 33.46

So, we have:

[tex]\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}[/tex]

[tex]\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5[/tex]

[tex]\dfrac{dd}{dt}= 1.016 \times - 5[/tex]

[tex]\dfrac{dd}{dt}=-5.08 \ ft/sec[/tex]

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

Explanation:

x and y are the two numbers

The product of those values is 1856, so xy = 1856

The sum is 90, so x+y = 90. Solve for y to get y = 90-x

Plug this into the first equation

xy = 1856

x(90-x) = 1856

90x-x^2 = 1856

0 = x^2-90x+1856

x^2-90x+1856 = 0

Now use the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-90)\pm\sqrt{(-90)^2-4(1)(1856)}}{2(1)}\\\\x = \frac{90\pm\sqrt{676}}{2}\\\\x = \frac{90\pm26}{2}\\\\x = \frac{90+26}{2} \ \text{ or } \ x = \frac{90-26}{2}\\\\x = \frac{116}{2} \ \text{ or } \ x = \frac{64}{2}\\\\x = 58 \ \text{ or } \ x = 32\\\\[/tex]

If x = 58, then,

y = 90-x

y = 90-58

y = 32

So one pair of values is (x,y) = (58,32)

We see that x*y = 58*32 = 1856

If x = 32, then,

y = 90-x

y = 90-32

y = 58

Showing (x,y) = (32,58) is the other solution. But this is just a mirror copy of the first solution. Effectively we're saying the same thing.

The two numbers 58 and 32 multiply to 1856, and they add to 90.

The difference in the two values is 58-32 = 26 which is the final answer.

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

In summary,

58*32 = 1856

58+32 = 90

58 - 32 = 26

Answer:26

Step-by-step explanation:

x+y=90

xy=1856

x*(90-x)=1856

-x^2 +90x -1856=0

or x^2 -90x +1856=0

Using quadratic equation

(x-58)*(x-32)=0

x=58, y=32

58-32=26

Answer:

A.

Step-by-step explanation:

Simplify the radical by breaking up the radicand up into a product of known factors, assuming positive real numbers.

Answer:

A)  4[tex]\sqrt15\\[/tex]

Step-by-step explanation:

Start by factoring 240 to its prime factors

√240 = √10 · 24 =√2·5·2·2·2·3

look for pairs of numbers.  There are 2 pairs of 2s, so take those out of the radical

=  2·2√5·3

=  4√15

Answer:

84 and more

Step-by-step explanation:

84+81+75

=240

240/3

=80

Answer:

a=(2,8) b=(8,8)

c=(8,2) d=(2,2)

Step-by-step explanation:

Answer:

this quadrilateral would be a square because all of the sides are equal.

Answer:

Y=-2x+5 (3 or C)

Step-by-step explanation:

Replace the value of x

Y= -2x(-1)+5

Solve

Y= 2+5

Y= 7

Answer:

It’s 40 I’m pretty sure because of the square. That’s how I was taught.

Answer:

In scientific notation, that would be;

7.0 * 10^-7 m

Step-by-step explanation:

Here, we want to write the given diameter in scientific notation

Mathematically, that can be done by moving the decimal point to the back of 7

The number of times we move will be counted as negative powers of 10 host

Thus, we have;

7.0 * 10^-7

Answer:

A-9:1 is correct i can confirm since i took the test

Step-by-step explanation:

Answer: D

Step-by-step explanation:

3x-4 = -22

3x = -18

x= -6

Answer:

X = -6

Step-by-step explanation:

3x - 4 = -22

3x = -22 + 4

3x = -18

x = -18/3

x= -6

Answer:

1+1=4

Step-by-step explanation:

Answer:

60degree ...........

Answer:

The measure of ∠O is 97.2° to the nearest tenth

Step-by-step explanation:

To solve this question, we will use the cosine rule

In Δ OPQ

Side o is opposite to ∠O

Side p is opposite to ∠P

Side q is opposite to ∠Q

By using the cosine rule

∵ o² = p² + q² - 2(p)(q)cos∠O

∵ o = 6.6 inches

∵ p = 2.1 inches

∵ q = 6 inches

→ Substitute them in the rule above

∴ (6.6)² = (2.1)² + (6)² - 2(2.1)(6)cos∠O

∴ 43.56 = 4.41 + 36 - 25.2cos∠O

→ Add the like terms in the right side

∴ 43.56 = 40.41 - 25.2cos∠O

→ Subtract 40.41 from both sides

∵ 3.15 = -25.2cos∠O

→ Divide both sides by -25.2 to find cos∠O

∴ -0.125 = cos∠O

→ Use your calculator to find ∠O

∵ m∠O = [tex]cos^{-1}(-0.125)[/tex]

∴ m∠O = 97.18075578

→ Round it to the nearest tenth ⇒ 2d.p.

∴ m∠O = 97.2°

Answer:

y=1

To check your answer:

20(1)-7=13

20-7=13

13=13

Answer:

The answer is 6 6/12

Step-by-step explanation:

Answer:

11 (positive)

Step-by-step explanation:

Answer:

e=11

Step-by-step explanation:

3(2e+5)+8(1-e)=1

6e+15+8-8e=1

-2e+23=1

-2e=-22

e=11

The B is 2. B is the Y Intercept.

Answer:

10.7

Step-by-step explanation:

i am not certain but since y is the 4 you will have 2(4) + 2.7 so you get 8+2.7 since you do 2x4 then you add 8 and 2.7 to get 10.7

Answer:

The cost would be $0.10. You would figure this out because 10 cents is a 10th of a dollar

Step-by-step explanation:

Answer:

2/4

Step-by-step explanation:

2/4 × 2= 4/8 hsuddhskshvshiseu

1/2 or 2/4

4÷8=1/2

4÷2/8÷2=2/4

Answer:

b

Step-by-step explanation:

Each box represents 1/3. 5/3 of white is 2 boxes more so red needs 2 boxes more than white. 5 red and 3 white is the only one that follows the criteria.

Answer:

802456

Step-by-step explanation:

Answer: y=3

Step-by-step explanation:

the initial statement is

y

∝

1

x

to convert to an equation multiply by k the constant

of variation

⇒

y

=

k

×

1

x

=

k

x

to find k use the given condition

y

=

15

when

x

=

5

y=kx⇒k=y x=15×5=75

equation is

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣22y=75x22∣∣

when x=25 then

y=75 25=3

Step-by-step explanation:

I hope understand this

Answer:

The probability that exactly 4 are in favor the new building project is 0.1672.

Step-by-step explanation:

Let X denote the number of people who are in favor of a new building project.

The proportion of people who are in favor of a new building project is, p = 0.60.

A random sample of n = 9 people are chosen.

Every person has independent opinion about the new building project.

Thus, the random variable X follows a binomial distribution with parameters n = 9 and p = 0.60.

Compute the probability that exactly 4 are in favor the new building project as follows:

[tex]P(X=4)={9\choose 4}(0.60)^{4}(1-0.60)^{9-4}\\\\=126\times 0.1296\times 0.01024\\\\=0.167215104\\\\\approx 0.1672[/tex]

Thus, the probability that exactly 4 are in favor the new building project is 0.1672.

Answer:

it's the last one i mean 4&1/4

Answer:

last image== four and one fourth

Answer:

3/5

Step-by-step explanation:

Both can be divided by 5. So, 15 divided by 5 is 3, and 25 divided by 5 is 5! Hoped this helped :)

Answer:

(x-2) and second slot is (x+7)

Second Answer= (x-2) and second slot is (x-8)

Answer:

(x-2),x-7) next set is (x-2),(x-8) then the next question is (x-2) your very welcome.

Step-by-step explanation:

Answer:

23.8

Step-by-step explanation:

68.4 - 44.6 = 23.8

Answer:

QR is 23.8

because 68.4 - 44.6 =23.8