MATHEMATICS HIGH SCHOOL

Determine the intercepts of the line. yy y y -intercept: (\Big( ( left parenthesis ,, , comma )\Big) ) right parenthesis xx x x -intercept: (\Big( ( left parenthesis ,, , comma )\Big) ) right parenthesis

Answers

Answer 1
Answer:

Final answer:

To find the y and x intercepts of a line, set x and y to zero individually and solve the equation for y and x respectively. For example, in the equation y = 2x - 3, the y-intercept is (0, -3) and the x-intercept is (3/2, 0).

Explanation:

In Mathematics, when finding the intercepts of a line, we need to set y and x to zero individually and solve for x and y respectively. This will give us our x and y-intercepts. Let's say you have a line represented by the equation y = 2x - 3.

To find the y-intercept, you set x = 0 and solve for y. In that equation, if we substitute x with 0, we get y = 2*0 -3 which simplifies to y = -3. Thus, the y-intercept is (0, -3).

Similarly, to get the x-intercept, we set y = 0 and solve for x. In the equation, if we substitute y with 0, we get 0 = 2x -3. If we solve this, we find that x = 3/2. So, the x-intercept is (3/2, 0).

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What is the y-intercept of the equation: 3x + 6y = 42 *

Yis directly proportional to the square of xy=96 when x = 4

Find a formula for y in terms of x

Answers

Answer:

y=6x^2

Step-by-step explanation:

y being directly proportional to the square of x means that the ratio between the two will always be equal to some constant (let's call it k). In equation form, we'd say:

(y)/(x^2)=k

We're told that y = 96 when x = 4, so we can plug those values in to find k:

(96)/(4^2)=(96)/(16)=6=k

Our more general equation is now

(y)/(x^2)=6

If we want to put y in terms of x, we need to get the y by itself on one side of the equation, which we can do here by multiplying both sides by x², giving us

y=6x^2

Final answer:

The question is about finding the equation given that y is directly proportional to the square of x. Based on the values in the question, the constant of proportionality 'k' is calculated as 6. Hence, the formula for y in terms of x is y = 6 * x^2.

Explanation:

When we say, y is directly proportional to the square of x, it simply means there is a constant constant of proportionality 'k', such that y = k * x2. Given in the problem, when x = 4, y = 96, we can substitute these values into the equation to solve for 'k'. This results in 96 = k * (42) which simplifies to 96 = 16k, and solving this gives us k = 6. Therefore, the formula for y in terms of x is y = 6 * x2.

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Search results for "A shipment of 18 cars, some weighing 3,000 pounds, and the others weighing 5,000 pounds each. Together the shipment has a total weight of 30 tons. (60,000 lbs). Find the number of each kind of car."

Answers

The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it's two different kinds of cars. Let's call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:

 x+y=18 (because the problem tells you there were 18 cars in total)
3000x+5000y=60000 (because that is the total weight in the problem)

Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.

x=18-y

Then you have to plug that into the other equation to get:

3000(18-y)+5000y=60000

Simplify and solve for y:

54000-3000y+5000y=60000
54000+2000y=60000
2000y=6000
y=3

Now that you know what y equals, you can put it into the equation we solved for x:

x=18-3
x=15

So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000.

Answer:

The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it's two different kinds of cars. Let's call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:

 x+y=18 (because the problem tells you there were 18 cars in total)

3000x+5000y=60000 (because that is the total weight in the problem)

Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.

x=18-y

Then you have to plug that into the other equation to get:

3000(18-y)+5000y=60000

Simplify and solve for y:

54000-3000y+5000y=60000

54000+2000y=60000

2000y=6000

y=3

Now that you know what y equals, you can put it into the equation we solved for x:

x=18-3

x=15

So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000.

Step-by-step explanation:

Simplify the expression fraction with numerator of the square root of negative one and denominator of the quantity three plus eight times i minus the quantity two plus five times i.fraction with numerator x-3 plus i and denominator 10
fraction with numerator negative 3 plus i and denominator 10
fraction with numerator 3 minus i and denominator 10
fraction with numerator negative 3 minus i and denominator 10

Answers

The simplified expression is: \mathbf{(i+13)/(170)}

The fraction is given as:

\mathbf{(√(-1))/(3 +8i -2 + 5i)}

Collect like terms

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (√(-1))/(3 -2+8i + 5i)}

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (√(-1))/(1+13i)}

In complex numbers, we have:

\mathbf{i =√(-1)}

So, we have:

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (i)/(1+13i)}

Rationalize

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (i)/(1+13i) * (1-13i)/(1-13i)}

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (i(1-13i))/(1^2-(13i)^2)}

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (i-13(-1))/(1-169(-1))}

\mathbf{(√(-1))/(3 +8i -2 + 5i) = (i+13)/(170)}

Hence, the simplified expression is: \mathbf{(i+13)/(170)}

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The right answer for the question that is being asked and shown above is that: "fraction with numerator negative 3 minus i and denominator 10." This is the simplified expression fraction with numerator of the square root of negative one and denominator of the quantity three plus eight times i minus the quantity two plus five times i.

Is this function linear or nonlinear?​

Answers

Answer:

yes

Step-by-step explanation:

Find z if X=27, μ=20, and α=3.4. Round to the nearest hundredth if necessary.A. 2.06


B. –2.06


C. 1.18


D. 0.35

Answers

Answer:

A. Z=2.06

Step-by-step explanation:

We want to find the Z-score of X=27 if the population mean is \mu=20,and the population standard deviation is \sigma=3.4.

We use the formula:

Z=(X-\mu)/(\sigma)

We substitute the values to obtain:

Z=(27-20)/(3.4)

Z=(7)/(3.4)

Z=2.06

The correct answer is A.

there are four toppings available for a pizza. how many flavor combinations are there for a pizza with two different toppings?

Answers

There are 6 different combinations available if you were to have 2 diff toppings each time
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