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3 years ago

The statement "two points determine a line" is an example of a __________.

Mathematics

1 answer:

VLD [36.1K]3 years ago

7 0

Postulate, because we just assume that it is a true fact.

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A rectangle is _____ a rhombus. A. Sometimes B. Always C. Never

Nastasia [14]

The answer is A. sometimes a rhombus

7 0

3 years ago

Read 2 more answers

Find two complex numbers that have a sum of 10i, a difference of -4 and a product of -29

HACTEHA [7]

Let these two numbers be $z$ and $w$ . Their sum is $10i$ , their difference is -4, and their product is -29:

$z+w=10i$

$z-w=-4$

$zw=-29$

Add the first two equations together to eliminate $w$ :

$(z+w)+(z-w)=10i-4\implies 2z=-4+10i\implies z=-2+5i$

Then

$w=10i-z\implies w=10i-(-2+5i)=2+5i$

Just to confirm this is correct, check their product:

$(-2+5i)(2+5i)=-4+25i^2=-4-25=-29$

5 0

3 years ago

Which expression can be used to determine the total weight of b baseballs that weight 5.25 ounces each and s softballs that weig

storchak [24]

5.25b + 6.5s
if we had for example 5 baseballs it would be 5 times 5.25 so we have b therefore it is b times 5.25

4 0

3 years ago

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Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%

grandymaker [24]

Answer:

$A=42000(1.04)^n$

Step-by-step explanation:

This is a compound interest formula expressed as:

$A=P(1+i)^n$

Where:

$n$ is time in years
$i$ is the rate of interest
$A$ is the accumulated amount after n years
$P$ is the initial amount.

#We substitute the given values to determine amount after n years as follows:

$A=P(1+i)^n\\\\=42000(1+0.04)^n\\\\=42000(1.04)^n$

Hence, the amount earned after n years is given by the expression $A=42000(1.04)^n$

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3 years ago

When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance

bekas [8.4K]

a) $v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

The average speed is equal to the ratio between the total distance ( $d_{tot}$ and the total time taken ( $t_{tot}$ ):

$v=\frac{d_{tot}}{t_{tot}}$

the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:

$d_1 = (3 h)(60 mph)=180 mi$

So the total distance is

$d_{tot}=d_1 +d_2 = 180 mi+20 mi=200 mi$

The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:

$t_{tot}=3 h +t_2$

So, the equation can be rewritten as:

$v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

b) 0.50 h (half a hour)

Since we know the value of the average speed, $v=57.14 mph$ , we can substitute it into the previous equation to find the value of $t_2$ , the time the trucker drove in the city:

$v=\frac{200 mi}{3h +t_2}\\3h+t_2 = \frac{200 mi}{v}\\t_2 = \frac{200 mi}{v}-3h=\frac{200 mi}{57.14 mph}-3 h=0.50 h$

3 0

3 years ago