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3 years ago

What is the y-intercept of the line below? :y=-1/4x +1

Mathematics

1 answer:

andre [41]3 years ago

3 0

Answer:

Step-by-step explanation:

The y-intercept can be found by plugging in 0 for x, then solving for y.

Plugging in 0 for x, we get:

$y=-1/4x+1\\y=-1/4(0)+1\\y=0+1\\y=1$

The y-intercept is

$(0,1)$

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Find the sum of two consecutive numbers of the smallest one is n − 2.

Zina [86]

Answer:

2n - 3

Step-by-step explanation:

(n-2) + (n-1) = 2n - 3

6 0

3 years ago

Alejandro has gone to school StartFraction 5 Over 7 EndFraction of the last 35 days. Which expression can be used to determine t

Katarina [22]

Answer:

35 times StartFraction 5 Over 7 EndFraction

Step-by-step explanation:

Alejandro has gone to school (5/7) of the last 35 days.

We need to find the expression that can be used to determine the number of days Alejandro has gone to school.

$x=\dfrac{5}{7}\times 35\\\\=5\times 5\\\\=25$

So, the correct option is (b) "35 times StartFraction 5 Over 7 EndFraction".

6 0

3 years ago

A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from G

goblinko [34]

Answer: 5.61333333 h

If the length between Garden city to dodge city is 84.2km the answer would be 5.61333333 hours [non-terminating decimal]

Step-by-step explanation:

So ummm, i dunno if the answer is right but yeahh

1h = 15 miles

Distance between GC AND DC = 84.2

84.2 * 15 = 5.6133333

3 0

1 year ago

Taylor needs to repair her car but cannot spend more than $260 for the repairs. The part needed for the repair will cost $80 and

Oksanka [162]

Answer: 6 hours

Step-by-step explanation:

Taylor cannot spend over $260.

Subtract the cost of the part needed for the repair:

= 260 - 80

= $180

$180 is left for fixing the car after buying the part.

As the labor costs $30 and now she cannot exceed $180 for labor, the total number of hours the mechanic can work is:

= 180 / 30

= 6 hours

6 0

3 years ago

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago