Maths question!!! The angles in triangle ABC are given in degrees, prove that AB=AC

Answers

Answer 1

do 12x+20=40x-8 and solve for x

Answer 2

First, find out the value of x to confirm if they are really true.

We know that all the interior angles of a triangle equal to 180 degrees.

4x+5x-8+3x+20=180
12x=180-12
12x=168
x=168/12
x=14

Put in these values of to find if AB=AC.

(4×14)(3×14+20)=(4×14)(5×14-8)

Solve for LHS first,

(4×14)(3×14+20) = 56×62

=3472

Solve for RHS next,

(4×14)(5×14-8) = 56×62

=3472

Since LHS=RHS, AB is also equal to AC.

Hope I helped :)

Related Questions

What is the product of −412 and 212 ? Enter your answer as a mixed number, in simplified form, in the box.

Answers

Given that the statement requires the answer as a mixed number, it is evident that the factors involve fractions and not actually - 412 and 212.

It seems that the two factors are - 4 + 1/2 and 2 + 1/2.

Let's use latex for better underestanding:

[tex](-4 \frac{1}{2} ).(2 \frac{1}{2} ) = (-4 - \frac{1}{2} ).(2+ \frac{1}{2} )=(- \frac{9}{2} ).( \frac{5}{2})=- \frac{45}{4} = -( \frac{44 + 1}{4} ) = - 11 \frac{1}{4} [/tex]

Answer: - 11 1/4

A symmetrical binomial distribution with large sample size can be approximated by a __________

Answers

typical distribution?

Look at the figure. If doing a two-column proof, what will be the very last statement?

Question 1 options:

X = 15

MN¯¯¯¯¯¯¯ = RS¯¯¯¯¯

Division Property of Equality

3x+3 = 5x-27

Save

Answers

When doing a two-column proof, the very last statement is usually the statement to be proved.

In the given question, we are required to prove that x = 15

Therefore, the very last statement of the two-column proof for the given figure is x = 15.

solve the inequality
6n-3 > -18

a. n > -2.5
b. n > -3.5
c. n < -2.5
d. n > 2

Answers

-6n < -12
n > 2 {divided each side by -6 and changed the inequality sign}

B.) n > 2

A train travels from city a to city b and then to city
c. the distance from a to b is 200 miles and the distance from b to c is 70 miles. the average speed from a to b was 50 miles per hour, and the average speed from b to c was 35 mph. what was the average speed from a to c (that is for the entire trip) in miles per hour?

Answers

it would be 85 miles per hour your welcome for the answer

How can the pythagorean theorem be used to classify acute, right, and obtuse triangles?

Answers

you're familiar with the Pythagorean Theorem. ... triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Rectangle ABCD is transformed to AB’C’D’ by a dilation .What is the scale factor used for the dilation ?

Answers

the scale factor should be 3

Answer: The required scale factor that is used for the dilation is 3.

Step-by-step explanation: Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.

We are to find the scale factor that is used for the dilation.

We know that

the scale factor of dilation is defined as

[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]

From the graph, we see that

in rectangle ABCD, the length the side AB is 2 units

and

the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.

Therefore, the scale factor of dilation is given by

[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]

Thus, the required scale factor that is used for the dilation is 3.

A pair of shoes costs $25 to make. This means that you need to charge a price of at least ___ just to cover your cost.

Answers

I believe the answer is $50.

Answer: $25

Step-by-step explanation: you are not trying to make a profit. You are just trying to cover your cost and they cost $25 to make.

Write the base of −(−6)^5.

Answers

Giving directions, describing an object etc, if you're in school it depends on the subject but note taking.

Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?

line AB
line CD
line FG
line HJ

Answers

Line HJ is parallel to a line that has a slope of 3 and a y-int at (0,0). If you wrote this in slope intercept form, it is y=3x+0. The only line that has such a slope is the red one.

Answer:

line HJ

Step-by-step explanation:

we know that

The equation of the line that has a slope of [tex]3[/tex] and a y-intercept at [tex](0, 0)[/tex] is equal to

[tex]y=3x[/tex] -----> is a proportional relationship

Remember that

If two lines are parallel , then their slopes are the same

Find the slope of the line HJ

[tex]H(-1,-4), J(1,2)[/tex]

The formula to calculate the slope between two points is equal to

[tex]m=\frac{2+4}{1+1}[/tex]

[tex]m=\frac{6}{2}[/tex]

[tex]m=3[/tex]

therefore

The line HJ is parallel to the line [tex]y=3x[/tex]

The diameter of a small gear is 16 cm this is 2.5 more than 1/4 of the diameter of a larger gear ehat is the diameter of the larger gear

Answers

let's say the diameter of the larger gear is "x".

the small one has a diameter of 16cm, we know that, this is 2.5 more than (1/4)x.

[tex]\bf 16=\cfrac{1}{4}x+2.5\implies 16-2.5=\cfrac{x}{4}\implies 13.5=\cfrac{x}{4}\implies 4(13.5)=x \\\\\\ 54=x[/tex]

In Mrs. Johnson's class there are 28 student desks each desk measures 26.17 inches long if you were to line up all the desks end to end how long would all the desk be?

Answers

if you were to line them all up:

number of desks* how long it measures = total measurement

28*26.17
=732.76 inches

How to Graph y=4/5x-7

Answers

Final answer:

To graph the equation y = 4/5x - 7, plot the y-intercept at -7 and use the slope to find a second point before drawing a line through the two points.

Explanation:

To graph the equation y = 4/5x - 7, follow these steps:

Start by plotting the y-intercept at -7 on the y-axis.Use the slope 4/5 to find a second point by moving up 4 units and to the right 5 units. Plot this point.Draw a straight line through these two points to represent the graph of y = 4/5x - 7.

3y - 5z = -23
4x +2y +3z = 7
-2x - y - z = -3

In your answer, can you please show work so that I can understand it myself

Answers

Starting off, we can multiply the third equation by 2 and add it to the third to get rid of both the x and y variables. Next, we get z=1. Plugging that into 3y-5z=-23, we get 3y-5=-23. Adding 5 to both sides, we get 3y=-18. After that, we can divide both sides by 3 to get y=-6. Plugging that into -2x-y-z=-3, we get -2x+6-1=-3=-2x+5. Subtracting 5x from both sides, we get -2x=-8. After that, we can divide both sides by -2 to get x=4.

F(x) = |x − 1| find the derivative from the left at x = 1. if it does not exist, enter none.

Answers

Given: f(x) = |x - 1|

A graph of the function is shown below.
The function is either
f(x) = x-1, for x>1
or
f(x) = 1-x, for x<1

Therefore
f'(x) = 1, for x>1
and
f'(x) = -1, for x<1

Answer: -1

Suppose you need to buy fabric to make costumes for a school play. The budget is $16 for each costume.

You need 12 costumes made from brown fabric. Each brown costume needs 3.25 yards of fabric. You need 8 costumes made from red fabric. Each red costume needs 3.5 yards of fabric.

You have gotten prices from two stores.
Store A: Brown fabric is $4.25 per yard. Red fabric is $4.75 per yard. On any purchase over $40, you will receive a $10 coupon for your next purchase. This store is 5 miles from school.
Store B: Both fabrics are $4.50 per yard. This store is walking distance from school.

What is the maximum budget for the fabric?

Answers

The maximum budget for the fabric is $320.
Hope this helped!

Multiply the total number of costumes and the budget for each costume.
20 x 16 = 320
The maximum budget for the fabric is $320

If the area of a square is 49 square inches, how long must each side be?

Answers

Area of a square=(side)²
or,49 = (side)²
or,side = √49 or 7

So, each side is 7 inch long

Hello There!

As you may know, all sides of a square are equal.
Area = side².
In this case:
49 = side²
side = √49
side = 7.
Each side is 7 square inches.

Hope This Helps You!
Good Luck :)

- Hannah ❤

Solve the equation
9|9-8x|=2x+3 show work.

Answers

as you already know, an absolute value expression is a piece-wise in effect.

[tex]\bf 9|9-8x|=2x+3\implies |9-8x|=\cfrac{2x+3}{9}\\\\\\ \begin{cases} +(9-8x)=\cfrac{2x+3}{9}\\\\ -(9-8x)=\cfrac{2x+3}{9} \end{cases}\\\\ -------------------------------\\\\ 9-8x=\cfrac{2x+3}{9}\implies 81-72x=2x+3\implies 78=74x \\\\\\ \cfrac{78}{74}=x\implies \cfrac{39}{37}=x\\\\ -------------------------------\\\\ -(9-8x)=\cfrac{2x+3}{9}\implies -9+8x=\cfrac{2x+3}{9} \\\\\\ -81+72x=2x+3\implies 70x=84\implies x=\cfrac{84}{70}\implies x=\cfrac{6}{5}[/tex]

Final answer:

To solve the equation 9|9-8x|=2x+3, follow these steps: remove the absolute value by considering both positive and negative cases, combine like terms, solve for x, and simplify the solutions.

Explanation:

To solve the equation 9|9-8x|=2x+3, we need to isolate the variable x. Let's start by removing the absolute value by considering both positive and negative cases.

Case 1: Positive

9-8x = 2x+3

Combine like terms: -8x - 2x = 3 - 9

-10x = -6

Divide both sides by -10: x = -6/-10

Simplify: x = 0.6

Case 2: Negative

-(9-8x) = 2x+3

Distribute the negative sign: -9+8x = 2x+3

Combine like terms: 8x - 2x = 3 + 9

6x = 12

Divide both sides by 6: x = 12/6

Simplify: x = 2

Therefore, the solutions to the equation are x = 0.6 and x = 2.

Learn more about Solving Equations here:

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How many numbers are divisible by 100 between 1 and 6296?

Answers

62 numbers are divisible by 100 into a whole number

The probability that an event will occur is 100%. Which of these best describes the likelihood of the event occurring?

Likely
Certain
Unlikely
Impossible

Answers

Certain because the probably that an event will occur is 100%

Answer: Certain

Step-by-step explanation:

A probability is from 0 - 1, if not 0 or 1 it is a fraction, percentage, or decimal. 100% also equal to 1 is the highest amount you can get, therefore the answer is certain.

Please help me thank you.

Answers

It's going to be the symmetric property of equality. The property states that if [tex]a = b[/tex] then the equation [tex]b = a[/tex] is equivalent to the other equation.

Consider kite FGHJ. What are the values of a and b?

Answers

Answer:

Hmmm... interesting on my final I answered B: a=14, b=8 and got it wrong but, when I did it again I got C: a=17, b=6

Step-by-step explanation

Answer:

The value of a=17 cm and b=6 cm

C is correct option.

Step-by-step explanation:

Given: FGHJ is a kite.

Kite has property their adjacent sides are equal. Top two side of the kite is equal and bottom two side of the kite is equal.

FG=GH because ∠F=∠H.

30=2a-4

2a=34

a=17 cm

Similarly, ∠F=∠H

FJ=HJ

3b+6=24

3b=18

b=6 cm

Hence, The value of a=17 cm and b=6 cm

If you subtract twelve from twice a number, the result is eight. what is the number?

Answers

2x - 12 = 8
2x = 8 + 12
2x = 20
x = 20/2
x = 10 <== ur number

Let's represent the number with Y
Twice the number will be 2Y
12 is subtracted from it. That will be;
2Y-12
And it is equal to 8
2Y-12=8
-12 will go over the equality sign to become +12
2Y=8+12
2Y=20
Divide both sides by 2
Y=20/2
Y=10
The number is 10
Have a nice day

Which of the following points is a solution of the inequality y < -|x|?

a. (1,-2)

b. (1,-1)

c. (1,0)

Answers

a. (1,-2)
You can substitute each point into the inequality which gives you the answer of a

None of the given points is the solution to the inequality y < -|x|.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given inequality,

y < -|x|

As per the given below, the dotted line is not included in the region thus, point (1,-1) is not included.

Hence "None of the given points is the solution to the inequality y < -|x|".

For more about inequality,

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the proportion of the perimeter of two similar polygons is blank the proportion of any pair of corresponding side lengths

A. greater than
B. equal to
C. less than
D. variable to

Answers

The ratio of perimeters is the same as the ratio of corresponding side lengths in similar polygons.

Explain two ways to find the volume of a plastic cube.

Answers

Note that the length of EACH SIDE of a cube is the same.

1) Volume = s³ ; or; V = s³ .

in which; V = volume (in "cubic units");
s = the side length of any one of the sides of the cube.
_______________________________________________________
2) Volume = length * width * height ; or, ( "V = L * w * h) .
_______________________________________________________

V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.

What is three dimensional geometry?

Three-dimensional space is a geometric setting in which three values are required to determine the position of an element.

A cube is a three-dimensional figure with 6 faces, 8 vertices and 12 edges.

In a cube all the sides are equal like a square.

So the volume of cube can be measured by

V=a^3

where a is the measure of a side.

And the volume of cube can also be found by

volume=Length × Width × Height

Hence V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.

To learn more on three dimensional Geometry click:

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factor by grouping: 12x^3-20x+3x-5

Answers

1,728x-23x-5
1,705x-5

There are no rational roots
F(x) = 4x^2+1
Group 1: 3x-5
Group 2: 12x3-20x2

This is going to take a long time to explain so the answer is just (12x2 - 12x - 5) • (x + 1)

If Juan paid $21.30 for 7.1 pounds of salmon, what was the price of 1 pound of salmon?

Answers

First divide 21.30 by 7.1 and you'll get the unit price of 1 of 3.

So for 1 pound of salmon its $3.

find the sum of the first 30 terms of the equation below: an=4n+1

Answers

Let n = 30

We are actually looking for a_30.

a_30 = 4(30) + 1

a_30 = 120 + 1

a_30 = 121

Answer:

1,890 is the sum of the first 30 terms of the equation .

Step-by-step explanation:

[tex]a_n=4n+1[/tex]

if , n = 1

[tex]a_1=4\times 1+1=5[/tex]

If, n = 2

[tex]a_2=4\times 2+1=9[/tex]

If, n = 3

[tex]a_3=4\times 3+1=13[/tex]

The arithmetic sequence comes out to be:

5, 9, 13........

a = 5

d = [tex]a_2=a_1=9-5=4[/tex]

The sum of first 30 terms is given by:

[tex]S_n=\frac{n}{2}\times (2a+(n-1)d)[/tex]

[tex]S_{30}=\frac{30}{2}\times (2\times 5+(30-1)\times 4)[/tex]

[tex]S_{30}=1,890[/tex]

1,890 is the sum of the first 30 terms of the equation .

Factor this polynomial expression. 2x2 + 12x + 18

Answers

2(x-2)(x-4) this should be the correct answer. Hope this helps :)

Answer: 2(x+3)(x+3)

i just took the test

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