MATHEMATICS MIDDLE SCHOOL

Chloe made a small pan of ziti and a smallpan of lasagna. She cut the ziti into 8 equal parts and
the lasagna into 9 equal parts. Her family ate 2_
3 of the
lasagna. If her family ate more lasagna than ziti, what
fraction of the ziti could have been eaten?

Answers

Answer 1
Answer: How many ziti was eaten?

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The line L is a tangent to the curve with equation y= 4x^2 +1 . The line L cuts the y axis at (0,8) and has a positive gradient. Find the equation of L in the form y = mx + c.y= 4x^(2) +1

Answers

Final answer:

To find the equation of a line tangent to the given curve, we need to find the derivative of the curve at the point of tangency and substitute the x-coordinate of the point of tangency to find the slope. The equation of the tangent line with 0 slope and y-intercept of 8 is y = 8.

Explanation:

To find the equation of a line tangent to a curve, we need to find the derivative of the curve at the point of tangency.

The given curve is y = 4x² + 1 (equation 1).

First, find the derivative of equation 1, which gives us dy/dx = 8x (equation 2).

Next, substitute the x-coordinate of the point of tangency into equation 2 to find the slope of the tangent line.

Since the line cuts the y-axis at (0,8), the x-coordinate of the point of tangency is 0.

Substituting x=0 into equation 2, we get the slope of the tangent line as m = 8(0) = 0.

The equation of a line in the form y = mx + c, where m is the slope and c is the y-intercept.

Since the slope of the tangent line is 0, the equation of the tangent line is y = 0x + c. And since the line cuts the y-axis at (0,8), the y-intercept is 8.

Therefore, the equation of the tangent line is y = 8.

Learn more about Equation of a tangent line here:

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A generic point on the graph of the curve has coordinates

(x, 4x^2+1)

The derivative gives us the slope of the tangent line at a given point:

f(x) = 4x^2+1 \implies f'(x) = 8x

Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through (k, 4k^2+1) and have slope 8k

So, we can write its equation using the point-slope formula: a line with slope m passing through (x_0, y_0) has equation

y-y_0 = m(x-x_0)

In this case, (x_0, y_0)=(k, 4k^2+1) and m=8k, so the equation becomes

y-4k^2-1 = 8k(x-k)

We can rewrite the equation as follows:

y-4k^2-1 = 8k(x-k) \iff y = 8kx - 8k^2+4k^2+1 \iff y = 8kx-4k^2+1

We know that this function must give 0 when evaluated at x=0:

f(x) = 8kx-4k^2+1 \implies f(0) = -4k^2+1 = 8 \iff -4k^2 = 7 \iff k^2 = -(7)/(4)

This equation has no real solution, so the problem looks impossible.

Pls help ASAP!!!On a certain hot​ summer's day, 622 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.50 for adults. The receipts for admission totaled $ 1375.00.  How many children and how many adults swam at the public pool that​ day? 22 POINTS

Answers

240 children and 382 adult swam at the public pool that day

Solution:

Let "c" be the number of childrens

Let "a" be the number of adults

Cost of 1 child ticket = $ 1.75

Cost of 1 adult ticket = $ 2.50

622 people used the public swimming pool

Therefore,

number of childrens + number of adults = 622

c + a = 622 ------ eqn 1

The receipts for admission totaled $ 1375.00

Therefore, we can frame a equation as:

number of childrens x Cost of 1 child ticket + number of adults x Cost of 1 adult ticket = 1375.00

c * 1.75 + a * 2.50 = 1375

1.75c + 2.50a = 1375 ----- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

c = 622 - a -------- eqn 3

Substitute eqn 3 in eqn 2

1.75(622 - a) + 2.50a = 1375

1088.5 - 1.75a + 2.50a = 1375

0.75a = 1375 - 1088.5

0.75a = 286.5

a = 382

Substitute a = 382 in eqn 3

c = 622 - 382

c = 240

Thus 240 children and 382 adult swam at the public pool that day

Find the area of the following rectangle

Answers

the are is 24 squared

i hope this helps

Tipos de ecuaciones ​

Answers

Answer:

Ecuaciones algebraicas. De primer grado o lineales. De segundo grado o cuadráticas...

Ecuaciones trascendentes, cuando involucran funciones no polinómicas, como las funciones trigonométricas, exponenciales, logarítmicas, etc.

Ecuaciones diferenciales. Ordinarias...

Ecuaciones integrales.

Ecuaciones funcionales.

Hope this helps! :)

Graph the equation on the coordinate plane y=1/3x

Answers

If you want to graph something on a coordinate plane online, I suggest you use Desmos. It is a free online graphing calculator.


Glad I could help!

What is 8/64 in lowest terms

Answers

if you reduce 8/64 it becomes 1/8
Since 8 goes into 64 eight times, the answer would be 1/8
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