All categories

2 years ago

If AB=x+4, BC=2x-10, and AC =2x+1, then find the value for x, AB, BC and AC

Mathematics

1 answer:

pshichka [43]2 years ago

8 0

If A, B and C are collinear, then:

$AB+BC=AC\\\\AB=x+4,\ BC=2x-10,\ AC=2x+1$

substitute:

$(x+4)+(2x-10)=2x+1\\\\(x+2x)+(4-10)=2x+1\\\\3x-6=2x+1\ \ \ |+6\\\\3x=2x+7\ \ \ \ |-2x\\\\x=7\\\\AB=x+4\to AB=7+4=11\\\\BC=2x-10\to BC=2(7)-10=14-10=4\\\\AC=AB+BC\to AC=11+4=15$

You might be interested in

How do you explain how to get h(t)=7(t-25)

Nutka1998 [239]

Hey There! :)

To Solve for t.
$h(t)=7(t-25)$
Distribute the brackets.
$h(t)=7*t-7*25$
$h(t)=7t-175$
Subtract 7t from both sides.
$(h(t))-7t=(7t-175)-7t$
$(h(t)-7t=-175$
$h*t-7t=-175$
Factor out variable, t.
$t(h-7)=-175$
Divide both sides by h-7.
$(t(h-7))/h-7=(-175)/h-7$
$t=-175/h-7$

Hope this helps!
-Benjamin

8 0

3 years ago

Please help me with this.

zheka24 [161]

The sin A is equal to 12/13 and the tan (A) is equal to 12/5.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: $hypotenuse^2=(leg_1)^2+(leg_2)^2$ . And the main trigonometric ratios are:

$sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\$

The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:

adjacent leg=5

hypotenuse=13

Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.

$hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12$

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

$sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}$

Finally, you can find the tan (A) since:

$tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}$

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

7 0

1 year ago

there are 12 boys and 10 girls in the gym class. If 6 more boys joined , how many more girls are needed to stay at the same rati

Travka [436]

Hope this helps good luck ☺

4 0

3 years ago

you flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble

Elodia [21]

If youre looking for probability i think it would be 2:1 <span />

5 0

3 years ago

A dataset shows that, on average, smokers do not live as long as nonsmokers and heavy smokers do not live as long as light smoke

leva [86]

<span>Given that A dataset shows that, on average, smokers do not live as long as nonsmokers and heavy smokers do not live as long as light smokers.

If you compute the least squares line for y = age at time of death and x = number of packets per day typically smoked, you will notice that as the number of packets per day a person smokes increases, the age at time of death of the person decreases.

Thus, the graph wil have a negative slope.

Therefore, the slope of your regression line will be less than 0.</span>

8 0

3 years ago