If ΔABC is an equilateral triangle with, AB = 2x + 17, BC = 6x - 19, AC = 4x-1, find x and the measure of each side

Answer:

[tex]x=9, AB=BC=AC=35[/tex]

Step-by-step explanation:

Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that [tex]AB=BC=AC[/tex]. We are given the lengths of all 3 sides in terms of [tex]x[/tex], but we only need to set two of them equal to each other to solve for [tex]x[/tex]. Let's use [tex]AB[/tex] and [tex]BC[/tex] to solve for [tex]x[/tex]. We know that [tex]AB=BC[/tex], [tex]AB=2x+17[/tex], and [tex]BC=6x-19[/tex]. Therefore, we can write the following equation to solve for

[tex]AB=BC\\2x+17=6x-19[/tex] (Substitute given values into equation)

Solving for [tex]x[/tex], we get:

[tex]2x+17=6x-19\\2x+17-17=6x-19-17[/tex] (Subtract [tex]17[/tex] from both sides of the equation to isolate constants)

[tex]2x=6x-36[/tex] (Simplify)

[tex]2x-6x=6x-36-6x[/tex] (Subtract [tex]6x[/tex] from both sides of the equation to isolate [tex]x[/tex])

[tex]-4x=-36[/tex] (Simplify)

[tex]\frac{-4x}{-4}=\frac{-36}{-4}[/tex] (Divide both sides of the equation by [tex]-4[/tex] to get rid of [tex]x[/tex]'s coefficient)

[tex]x=9[/tex] (Simplify)

Therefore, [tex]AB=2x+17=2*9+17=18+17=35[/tex], and [tex]AB=BC=AC=35[/tex]. Hope this helps!  

Answer for BRAINLIEST

There are 60 cookies and 10 cupcakes leftover at a
bake sale. What is the ratio of cupcakes to
cookies? Your answer it must be in simplest form.

Calculate and express your answer in decimal form (0.25)•60

1.) A florist sells bouquets for $12.25 each. Amiyah
has $61.25 to spend. How many bouquets can she
afford?

Use x to represent the number of bouquets that
Amiyah can afford.

Equation: Choose one.
a) x + 12.25 = 61.25
b) x - 12.25 = 61.25
c) 12.25x= 61.25
d) 61.25x = 12.25
Solve. Show work

Giving 20 points please helpppp

plz help third time putting this

2 is what percent of 20?

0.6x = 1.2x + 6 A) −1 B) −10 C) 1 D) 10

Can someone help me with this :( .

Last year at a certain high school, there were 75 boys on the honor roll and 120 girls on the honor roll. This year, the number of boys on the honor roll increased by 24%, and the number of girls on the honor roll increased by 10%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

True or False?
4/5 x 3 = 12/15

quick i leave school soon

The cafeteria can serve 32 lunches in 5 minutes. How long will it take them to serve 57 lunches?

What is the slope of a line that passes through the points (–3, 2) and (–6, 5)?
A. 1
B. -3
C. -1
D. 1/3

The image of the point (2, 1) under a translation is (-3, -2). Find
the coordinates of the image of the point (-2, -9) under the same
translation.

..........................

please help asap! i’ll give brainliest

Write the fraction 9/54 in simplest form.​

options are a)80° b)100° c)40° d)90°
please help​

A scatterplot has a positive, linear correlation. Which statement is true about the relationship between the x- and y-
values?
o As the x-values increase, the y-values tend to increase.
As the x-values increase, the y-values tend to decrease.
As the x-values decrease, the y-values tend to increase.
O As the x-values decrease, the y-values tend to vary randomly.

help me pleaseeee ( measurement )

Sylvia wants to rent a kayak. Company A charges $20 plus $6 per hour. Company B charges $8 plus $12 per
hour.
At how many hours will the price to rent a kayak from Company A and Company B be the same?
Be precise in your answer (label your answer).

what is the value of the expression 0.5 (3x + 2/y) when x = 2 and y = 4

During a sale each item in the store is 80% off it's regular price if the regular price of a t-shirt is $18 how much is the discount ?

what is the Riemann hypothesis

HELP ME PLEASE PLEASE HURRY MATH FOR A P EX

PLEASE PLEASE I NEED HELP

People of different ages were asked the question "Do you listen to audiobooks?" The frequency table displays the
percentage of "yes" responses for different age groups
13-17
8%
18-25
15%
26-35
23%
36-45
45%
46 and over
48%
Would it be appropriate to display the data with a pie chart?
O Yes, because the data are grouped into categories
O Yes, because the data can be displayed by a relative frequency compared with the whole
O No, because the data display the percentage of time spent by each age group, not a relative frequency compared
with the whole
O No, because the data categories are too broad
Save and Exit
Next
Submit
art this and rem

4 - 2y + (-8y) +6.7 =

How many 1/8s are there in jacob's 6 aquriums

how would I solve this?

can anyone give me the answer?