MATHEMATICS MIDDLE SCHOOL

Joseph walks at a constant speed. He walked to a store that is 0.5 miles away in 6 minutes. How many miles, m, can he walk in t minutes?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

if he can walk 0.5 miles in 6 minutes at a constant rate then you can say that he can walk 1 mile in 12 minutes.

therefore he can walk 1/12 mile ever one minute

so m=1/12t

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How do you write this in a algebraic equation: 6 more than 7 times a number is 41

tour takes his dog to be groomed. The fee to groom the dog is $75 plus 6.75 % tax. Is $80 enough to pay for the service? explain

Answers

Tour takes his dog to get groomed on a budget of $80

Now the fee to groom the dog is $75 plus 6.75% tax.
The question asks if the budget is enough to cover the fee.

lets find the total cost:

$75 + ($75 x 0.0675)
= 75 + 5.06
= 80.06

$80 is not enough to pay for the dog to get groomed

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:

brainly.com/question/39323392

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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.

80% of what number is 94

Answers

It's 80% of 117.5

Hope this helps :)

6r + r = 7 what is the answer

Answers

6r+r=7 6-7=1 6+1=7 R=1 please answer my recent question

What is 1/6 x 4/5 simplified to

Answers

Answer:2/15

Step-by-step explanation:

First we multiply 1/6* 4/5 by multiply the nominator and the denominator to get one fraction.

So 1*4/5*6= 4/30

Next, we simplify this fraction by dividing by 2 to both 4 and 30

So, after dividing we get: 2/15.

So the answer is 2/15.

I hope this helps!

Andre wants to put a protector on the visible part of a book cover to keep it from tearing. The book measures 9 in. × 7 in. × 2 in.What is the total area the book protector will cover?

A. 144 sq. in.

B. 154 sq. in.

C. 162 sq. in.

D. 190 sq. in.

Answers

Total area of the book=2(9 in x 7 in)+2(9 in x 2 in) + 2(7 in x2 in)=
=2(63 in²)+2(18 in²)+2(14 in²)=126 in² + 36 in²+28 in²=190 in².

answer: D.190 in²

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