Which equation represents this line in point-slope form?

A.
`(y + 4) = (4)/(3) (x + 3)`

B.
`(y −4) = -(4)/(3) (x +3)`

C.
`y= -(3)/(4)x`

D.
`4y− 3x = 0`

Answer:

-13

Step-by-step explanation:

-4-3(3)

-4-9 = -13

The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.

let

x + y = 54

4x + 3y = 200

From equation (1)

x = 54 - y

4x + 3y = 200

4(54 - y) + 3y = 200

216 - 4y + 3y = 200

216 - y = 200

- y = 200 - 216

-y = -16

y = 16

x + y = 54

x + 16 = 54

x = 54 - 16

x = 38

Learn more about simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

Answer:

m∠GBC = 56°

Step-by-step explanation:

Well because m∠GBH is equal to m∠HBC all you have to do is 28 add to 28. We know that m∠GBH is equal to m∠HBC because of the two dashes marked in the angles and because m∠GBC = m∠GBH + m∠HBC  this can be rewritten as m∠GBC = 28 + 28 adn from there we can find out that m∠GBC = 56°.

I hope this was helpful. If not tell me in the comment section below.

The average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have:

In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The slope:

\(\rm m =\dfrac{16717-12078}{2017-2009}\)

m = 4639/8

m = 579.875

Thus, the average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

Learn more about the slope here:

brainly.com/question/3605446

#SPJ1

Answer:

To find the percentage of the bid that is lumber, we need to divide the cost of the lumber by the total bid and multiply by 100:

Percentage of bid that is lumber = (cost of lumber / total bid) x 100%

Substituting the given values, we get:

Percentage of bid that is lumber = (2980 / 9930) x 100%

Percentage of bid that is lumber = 0.3 x 100%

Percentage of bid that is lumber = 30%

Therefore, 30% of the bid is for lumber.

Answer:

-6

Step-by-step explanation:

-10-(-4)=-1+4=-6

Hope this helps plz mark brainliest ;D

Answer:

3p=1/2

Step-by-step explanation:

3 p's balance with 1/2 making them equal

Answer:

$20.93

Step-by-step explanation:

2.99 x 7= 20.93

Answer:

\(\displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

Step-by-step explanation:

We are given a function:

\(\displaystyle \large{y = t^2 \sin (2t)}\)

To differentiate a function, we are going to use the product rules since there are two functions which are t^2 and sin(2t) multiplying together.

From the product rules, \(\displaystyle \large{y = f(x)g(x) \to y\prime = f\prime (x) g(x)+f(x) g\prime (x)}\)

Therefore, \(\displaystyle \large{y = t^2 \sin (2t) \to y\prime = (t^2)\prime \sin (2t) + t^2 (\sin (2t))\prime}\)

Before we start differentiating, I’d like you to look at [sin(2t)]’. A function like this, you cannot just directly derive and answer. You need to use chain rules.

We know that, \(\displaystyle \large{y = \sin (x) \to y\prime = \cos (x)}\) but what if the “x” is another function? Like sin(3x), sin(x^2) as examples. The insides are another function, can be expressed as fog(x) or gof(x) is composite function.

Basically, chain rule is a rule or formula for composite function and it’s the most common and useful as well as being always used in differentiation.

Chain Rules

\(\displaystyle \large{\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}}\)

where u is another function in a bracket. From the formula above, it can be also written as:

\(\displaystyle \large{[f(g(x))]\prime = f(g(x))\prime \cdot g(x)\prime\)

To simply say, you differentiate the whole function first then multiply with the chain or inner derived function.

So from the function, we obtain:

\(\displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot (2t)\prime}\\ \displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot 2}\\ \displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

The factored form would be:

\(\displaystyle \large{y\prime = 2t ( \sin (2t) + t \cos (2t))}\)

From above, for polynomial function, to differentiate, you can do by using the power rules.

Power Rules

\(\displaystyle \large{y = ax^n \to y\prime = nax^{n-1}}\)

Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

The relationship between the distance that birds fly in relation to the time they do so, is positive.

There are about 3 outliers but for the most part, the relationship is positive.

The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.

There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.

Find out more on relationship at https://brainly.com/question/1599922

#SPJ1

31.51

r=−5

d=19

h<53

Step-by-step explanation:

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

To know more about continuous here

https://brainly.com/question/30089268

#SPJ1

a) The probability that the computer will be fixed by either A or B is 58%.

b) The probability that it was fixed by B is 57.14%

Given data:

a)

To find the probability that the computer will be fixed by either A or B, we can use the principle of addition for probabilities.

The probability that A can fix the computer is 30% or 0.30, and the probability that B can fix the computer if A cannot is 40% or 0.40.

Therefore, the probability that either A or B can fix the computer is the sum of these probabilities:

P(A or B) = P(A) + P(B if A cannot) = 0.30 + (0.70 * 0.40) = 0.30 + 0.28 = 0.58

Therefore, there is a 58% probability that the computer will be fixed by either A or B.

b)

Let's denote event A as A fixing the computer and event B as B fixing the computer.

P(A) = 0.30 (probability A can fix the computer)

P(B|A') = 0.40 (probability B can fix the computer given that A cannot)

To find P(B|A), the probability that B fixes the computer given that it was fixed, use Bayes' theorem:

P(B|A) = (P(A|B) * P(B)) / P(A)

Since the computer is fixed, P(A) + P(A') = 1, so P(A) = 1 - P(A') = 1 - 0.30 = 0.70

P(B|A) = (P(A|B) * P(B)) / P(A)

P(B|A) = (1 * 0.40) / 0.70

P(B|A) = 0.40 / 0.70

P(B|A) ≈ 0.5714

Hence, if the computer is fixed, there is a 57.14% probability that it was fixed by B.

To learn more about Bayes's theorem, refer:

https://brainly.com/question/29598596

#SPJ4

Answer:

The correlation is 0.373 . There is a moderate positive linear association between Dollars and Satisfaction.

Step-by-step explanation:

Given the data:

Dollars Satisfaction

70.99 32

76.01 34

67.24 27

69.33 17

67.59 23

74.06 29

76.04 25

72.63 31

68.01 26

67.98 31

Using technology, the Pearson correlation Coefficient calculator ; we can obtain the Pearson correlation Coefficient is 0.3729

Interpretating this value, a correlation Coefficient value of 0.3729 is positive, this means a positive linear relationship exists between the values. Also 0.3729 is closer to 0 than 1 ; this mean that the strength of their relationship is moderate to weak .

Hence, a correlation Coefficient value of 0.3729 means that a weak positive relationship exists between dollar and satisfaction

Answer:

12

Step-by-step explanation:

Hey there!

\(Answer:\boxed{\text{False}}\)

\(Explanation:\)

\(6^3+5^2=18+5^2\text{ True or False}\)

The answer is False because \(6^3+5^2\) is equal to 61 and \(18+5^2\) is equal to 41 so it is false.

\(\boxed{\text{False}}\text{ is the answer.}\)

Hope this helps!

\(\text{-TestedHyperr}\)

Given:

The vertices of ΔABC are A(-4,4), B(-2,5), and C(-5,2).

The triangle ABC is reflected across the line y-axis to produce the image ΔA'B'C'.

To find:

The coordinates of ΔA'B'C'.

Solution:

If a figure is reflected across the y-axis, then

\((x,y)\to (-x,y)\)

Using this rule, we get

\(A(-4,4)\to A'(4,4)\)

\(B(-2,5)\to B'(2,5)\)

\(C(-5,2)\to C'(5,2)\)

Therefore, the vertices of the ΔA'B'C' are A'(4,4), B'(2,5) and C'(5,2).

Answer: 4/5

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

quick maths :>

Answer:

Step-by-step explanation:

Given that:

sin2xcos x + cos2xsin x = -1

Recall that;

SInAcosB + cosASinB = SIn (A+B)

SIn (2x +x) = -1

Sin (3x) = -1

\(x = \bigg [\dfrac{Sin ^{-1} (-1)}{3} \bigg ]\)

\(x = \dfrac{\pi}{2} + \dfrac{2 \pi \ k}{3}\)

\(x = \dfrac{\pi}{2}, \dfrac{7 \pi}{6}, \dfrac{11 \pi}{6}\)

Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines.  From inspection of the graph, the point of intersection is at (1, 5).

Proof

The solution to a system of equations is the point at which the two lines meet.  

⇒ g(x) = f(x)

⇒ 3x + 2 = |x - 4| + 2

⇒ 3x = |x - 4|

⇒ 3x = x - 4   and   3x = -(x - 4)

⇒ 3x = x - 4

⇒ 2x = -4

⇒ x = -2

Inputting x = -2 into the 2 equations:

⇒ g(-2) = 3 · -2 + 2 = -4

⇒ f(-2) = |-2 - 4| + 2 = 8

Therefore, as the y-values are different, x = -2 is NOT a solution

⇒ 3x = -(x - 4)

⇒ 3x = 4 - x

⇒ 4x = 4

⇒ x = 1

Inputting x = 1 into the 2 equations:

⇒ g(1) = 3 · 1 + 2 = 5

⇒ f(1) = |1 - 4| + 2 = 5

Therefore, as the y-values are the same, x = 1  IS a solution

and the solution is (1, 5)

Step-by-step explanation:

I hope this answer is helpful ):

Answer: the opposite of 15

Step-by-step explanation:

Every number 'a' on number line is exactly opposite of '-a'.

So, 15 is the opposite of '-15'

Also absolute value for any number gives its positive value, soabsolute value of 15 = 15

Moving 0 to 15 gives the  distance between zero and 15.

So all statements are true except "the opposite of 15".

Hence, the required statement is "the opposite of 15".

Answer:

do 50/6 which is 8.333 repeating that is the amount of gallons per hour so then divide 150 by 8.333 repeating for your answer so 150/8.33 which is 18.00072 so 18.00072 hours is the answer. I hope this helps!

Step-by-step explanation:

A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).

In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;

f(x) = −x² + 2x - 15

f(x) = −2x + 2

0 = −2x + 2

2x = 2

x = 2/2

x = 1

For the maximum value of function 2, we have:

f(1) = −(1)² + 2(1) - 15

f(1) = -14

For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.

Read more on maximum and function here: https://brainly.com/question/1800006

#SPJ1

number one and  four

The counterexample to the conditional statement "If an animal is brown, then it is a dog" is represented by:

4. Squirrel

A conditional statement is represented as follows:

x -> y.

And it is read as:

If x, then y.

A counterexample to it is something for which:

In this problem, the statement is:

"If an animal is brown, then it is a dog"

Hence:

A counterexample is given by a brown animal that is not a dog, which is the case for a Squirrel, hence option 4 is correct.

More can be learned about a conditional statement at https://brainly.com/question/11073037

#SPJ1

The simplified form of the given expression as a fraction is 7x/x-7

Fractions  are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.

Given the expression below;

(1/7+1/x)/(1/49+1/x²)

Find the LCM to have:

(x+7/7x)/(x²-49)/49x²

Divide to have:

x+7/7x * 49x²/(x²-49)

(x+7) * 7x/(x+7)(x-7)

Cancel out the like terms to have:

1 * 7x/x-7

= 7x/x-7

Hence the simplified form of the given expression as a fraction is 7x/x-7

Learn more on fractions simplification here: https://brainly.com/question/78672

#SPJ1