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3 years ago

Line c passes through points (2, 1) and (6, 6). Line d is parallel to Line c. What is the slope to line d?

Mathematics

1 answer:

Lilit [14]3 years ago

8 0

Answer:

$\frac{5}{4}$

Step-by-step explanation:

We need to find the formula of line c

$\left \{ {{a*2+b=1} \atop {6*a+b=6} \right.$

Subtract these two

-4*a=-5

a= $\frac{5}{4}$

And lies c and d will be paraller if $a_{c}= a_{d}$

so $a_{d}$ = $\frac{5}{4}$

And that's the slope to line d

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Write the sentence as an inequality. Then solve the inequality.

Alex777 [14]

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3 years ago

A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?

nirvana33 [79]

Answer:

$Area = 26478cm^2$

Step-by-step explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

$Area = \frac{\pi r^2}{2}$

Where

$r = 60cm$

So:

$A_1 = \frac{3.14 * 60^2}{2}$

$A_1 = \frac{11304}{2}$

$A_1 = 5652cm^2$

Next, the area of the complete trapezium

$Area= \frac{1}{2}(a + b) * h$

Where

$a = 300$

$b = 2 * r = 2 * 60 = 120$

$h = 153$

So:

$A_2 = \frac{1}{2} * (300 + 120) * 153$

$A_2 = \frac{1}{2} * 420 * 153$

$A_2 = 32130cm^2$

The area of the desk is:

$Area = A_2 - A_1$

$Area = 32130cm^2 - 5652cm^2$

$Area = 26478cm^2$

8 0

3 years ago

consider the four corners of the front wall of a rectangular class room (upper right, upper left, lower left, upper left) which

professor190 [17]

(You copied 'upper left' twice, and you left out 'lower right'.
But we know what you mean.)

If those are the corners of the wall, then they're ALL in the plane of
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3 0

3 years ago

A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the

ANEK [815]

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been $y\neq 0$ . Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

3 0

3 years ago

PLEASE HELP ASAP!!!!

olchik [2.2K]

Hello from MrBillDoesmath!

Answer: "Distributive Property", the second bullet point from the top of the list

Regards, MrB

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3 years ago