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3 years ago

What is the distance between the points (-7, -8) and (10, -8)

Mathematics

1 answer:

grigory [225]3 years ago

3 0

Answer:

Step-by-step explanation:

so you count down until 0 then go up till 10

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Which pair of terms can be used to represent any two consecutive odd numbers? x and x + 1 x and x + 2 x and 2 x + 1 2 x and 2 x

polet [3.4K]

Answer:

x + x + 2

Step-by-step explanation:

cuz if its consecutive odd then its every 2 numbers so if x = 3 then you add two to x

4 0

3 years ago

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At what points on the given curve x = 4t3, y = 3 + 8t − 10t2 does the tangent line have slope 1?

Bess [88]

Answer:

(4/3, 4 5/9) and (-32, -53)

Step-by-step explanation:

When a curve is given as a set of parametric equations, as this one is, then the slope of the tangent line to the curve is

dy/dt

dy/dx = ------------

dx/dt

which here is

dy/dt 8 - 20t

dy/dx = ----------- = --------------

dx/dt 12t^2

If the slope at a certain point on this curve is 1, then we conclude that:

8 - 20t = 12t^2, or

12t^2 + 20t - 8 = 0, or

3t^2 + 5t - 2 = 0

We have to solve this equation for the parameter, t:

Here a = 3, b = 5 and c = -2, and so the discriminant is

b^2 - 4ac = 25 - 4(3)(-2), or 49, and the square root of that is 7.

Thus, the roots are:

-5 ± 7

t = --------- = 1/3 and t = -2

2(3)

Evaluate x and y twice, once each for each t value.

Case 1: t = 1/3

x = 4(1/3) and y = 3 + 8(1/3) - 10(1/3)^2, or

x = 4/3 and y = 3 + 8/3 - 10/9: (4/3, 4 5/9)

Case 2: t = -2

x = 4(-2)^3 and y = 3 + 8(-2) - 10(-2)^2, or y = 3 - 16 - 40, or y = -53.

This gives us the point (-32, -53)

6 0

3 years ago

Craig likes to collect vinyl records. Last year he had 10 records in his collection. Now he has 12 records. What is the percent

navik [9.2K]

Answer:

Craig's collection increased by 20%.

Step-by-step explanation:

Original amount: 10

New amount: 12

To find the percent increase, we first need to find how much Craig's record collection increased by. To do this, subtract the old amount from the new amount:

12 - 10 = 2

The amount his collection increased by is 2. To find the per cent increase, divide 2 by the original amount of records:

$\frac{2}{10}=\frac{1}{5}= 0.20$

Convert the decimal into a percentage:

0.20 * 100 = 20%

The percent increase of Craig's record collection is 20%.

8 0

3 years ago

The value of x in the equation log(x-1)9=2 is

mel-nik [20]

$\log_{(x-1)} 9=2$

the domain:
$x-1 >0 \ \land \ x-1 \not=1 \\
x>1 \ \land \ x \not= 2 \\
x \in (1; 2) \cup (2;+\infty)$

the equation:
$\log_{(x-1)}9=2 \\
(x-1)^2=9 \\
\sqrt{(x-1)^2}=\sqrt{9} \\
|x-1|=3 \\
x-1=3 \ \lor \ x-1=-3 \\
x=4 \ \lor \ x=-2$

4 is in the domain
-2 is not in the domain

The answer:
$x=4$

***
Also, the answer in 13 is {8}. -3 is not in the domain. Replace x with -3 and you'll see:
$x=\sqrt{5x+24} \\
-3=\sqrt{5 \times (-3)+24} \\
-3=\sqrt{-15+24} \\
-3=\sqrt{9} \\
-3=3$
It's not true so -3 isn't a solution to this equation.

4 0

3 years ago

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Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual

irina [24]

Using how tall it is over how wide
=>tall/wide
The model 15in/1.5in
The actual x/55ft

Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in

So
15in/1.5in = x/660in
Now solve for x my multiplying both side by 660in
660in *15in/1.5in=x
x= 6600in tall

5 0

3 years ago

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