All categories

11 days ago

What is true about △ABC? Select three options

Mathematics

2 answers:

Svet_ta [4.3K]11 days ago

5 0

Answer:

A) AB is perpendicular to AC

B) The triangle is classified as a right triangle.

C) The triangle qualifies as an isosceles triangle

Step-by-step explanation:

we understand that

the method for determining the distance between two points is as follows:

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Calculate the distance AB

we find

$A(-1,3), B(-5,-1)$

insert values into the formula

$d=\sqrt{(-1-3)^{2}+(-5+1)^{2}}$

$d=\sqrt{(-4)^{2}+(-4)^{2}}$

$d_A_B=\sqrt{32}\ units$

step 2

Calculate the distance BC

we determine

$B(-5,-1),C(3,-1)$

insert values into the formula

$d=\sqrt{(-1+1)^{2}+(3+5)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$d_B_C=8\ units$

step 3

Calculate the distance AC

we figure out

$A(-1,3),C(3,-1)$

apply the formula

$d=\sqrt{(-1-3)^{2}+(3+1)^{2}}$

$d=\sqrt{(-4)^{2}+(4)^{2}}$

$d_A_C=\sqrt{32}\ units$

step 4

Examine the lengths of the triangle's sides

$d_A_B=\sqrt{32}\ units$

$d_B_C=8\ units$

$d_A_C=\sqrt{32}\ units$

therefore

The triangle ABC is identified as an isosceles triangle, having two equal-length sides. It also meets the criteria for being a right triangle due to the Pythagorean theorem.

$BC^2=AB^2+AC^2$

$8^2=(\sqrt{32})^2+(\sqrt{32})^2$

$64=32+32$

$64=64$ ----> confirms the right triangle classification.

AB is perpendicular to AC since the legs in a right triangle are at right angles to each other.

Zina [3.9K]11 days ago

3 0

Response:

A B C

Detailed explanation:

Ed2020

You might be interested in

Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF Prove: m∠ABC = m∠GHI We are given that angle ABC and are congruent, and that angle GHI and an

AnnZ [3877]

1. Angle DEF

2. Definition of congruent angles

3. Measure of angle GHI

6 0

16 days ago

A company buys pens at the rate of $7.50 per box for the first 10 boxes, $5.50 per box for the next 10 boxes, and $4.50 per box

tester [3916]

Let's start by calculating the cost of the first 10 boxes, which totals $75, and the next 10 boxes cost $55.

Together, these 20 boxes amount to $130 spent. With $18 remaining, you can purchase 4 more boxes since 18 divided by 4.5 equals 4.

Therefore, the maximum number of boxes you can buy with $148 is 24.

4 0

16 days ago

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 1

AnnZ [3877]

Question:

Which statement is accurate concerning the function’s discontinuities $f(x) = \frac{x-5}{3x^2-17x-28}$

A) There are gaps at x = 7 and.

B) Asymptotes exist at x = 7 and.

C) Asymptotes exist at x = –7 and.

D) Gaps are present at (–7, 0) and.

Answer:

B) Asymptotes exist at x = 7 and $(x = \frac{-4}{3})$

Step-by-step explanation:

Given:

$f(x) = \frac{x-5}{3x^2-17x-28}$

Goal:

Identify the correct statement

$f(x) = \frac{x-5}{3x^2-17x-28}$

We need to factor the denominator first.

$f(x) = \frac{x-5}{(3x+4)(x-7)}$

To express x in terms of (3x+4) and (x-7):

3x + 4 =

3x = -4

Divide both sides by 3:

$x = \frac{-4}{3}$

x - 7

x = 7

Next, evaluate the limit when $(x = \frac{-4}{3})$ and at (x = 7)

lim f(x) as $(x = \frac{-4}{3})$ = ±∞

lim f(x) as (x=7) = ±∞

Since both scenarios result in the denominator approaching zero, they represent asymptotes.

Thus, asymptotes are found at $(x = \frac{-4}{3})$ and x=7

Option B is determined to be correct

6 0

3 days ago

12x+7<−11 AND5x−8≥4012

Svet_ta [4321]

Answer:

No solution

Step-by-step explanation:

Given: $12x+7$ and $5x-8\geq 40$

Handle each inequality separately.

$12x+7$ Utilizing the subtraction property of inequalities

$12x$

$x$

and

$5x-8\geq 40$ Utilizing the addition property of inequalities

$5x\geq 40+8$

$5x\geq 48$

$x\geq \dfrac{48}{5}$

Thus, the solution to the combined inequality is the overlap of both solutions.

Refer to the attached image for the number line representation.

No solution

8 0

11 days ago

Read 2 more answers

You’re working in a pharmacy, and are making a table to help with dosage amounts for a certain drug. The recommended dosage is 4

lawyer [4008]

Answer: Children who weigh 10 pounds require 12 teaspoons, those at 15 pounds need 18 teaspoons, and for 30 pounds, it is necessary to have 36 teaspoons.

Step-by-step explanation:

We have a recommended dose of 40 mg per 2.2 pounds of weight, given in three doses throughout the day every 8 hours.

Thus, for a single pound, the daily required dosage is calculated as $\dfrac{40}{2.2}=18.18\ ml$ .

Each individual dose corresponds to $\dfrac{18.18}{3}=6.06\ ml$ of the drug.

This means for one pound, the dosage needed per dose is 6.06 ml.

Thus, for 10 pounds, the calculation is 10 x 6.06 ml = 60.6 ml

To convert ml to teaspoons, knowing that 1 teaspoon equals 5 ml, we find: (60.6 ml ÷ 5) = 12.12 ≈ 12 teaspoons.

For a weight of 15 pounds, the drug requirement is 15 x 6.06 ml = 90.9 ml.

This translates to (90.9 ml ÷ 5) = 18.18 ≈ 18 teaspoons.

For the weight of 30 pounds, it is calculated as 30 x 6.06 ml = 181.8 ml.

Converting this gives us (181.8 ml ÷ 5) = 36.36 ≈ 36 teaspoons.

Therefore, children weighing 10 pounds need 12 teaspoons, those at 15 pounds require 18 teaspoons, and those at 30 pounds need 36 teaspoons.

7 0

10 days ago