Mathematics High School

The distance formula can be used to prove a triangle has (5 points)
Select one:
a. congruent sides
b. a right angle
c. parallel sides
d. congruent angles,

Answers

Answer 1
The distance formula can be used to prove a triangle has congruent sides if the triangle in question is placed on a coordinate plane. On a graph, the coordinate points of the three points of the triangle can be found. Then, the distance formula can be utilized to find the distance between each of the three points. The distance between the points will yield the length of the side, allowing for comparison of the three sides to see if they are similar lengths, or congruent.

Related Questions

-1/6 + 2/3 ( 9 + - 3/4) + - 1/2

Answers

First simplify the section in the parenthesis. 
-1/6 + 2/3(8 1/4) + -1/2 
Then multiply 2/3 by 8 1/4.
-1/6 + 5 1/2 + -1/2 
Add -1/2 to 5 1/2. 
-1/6 + 5 
Add 5 to -1/6. 
4 5/6 is the fully simplified answer. 
Hope this helps!

What is the value of k

Answers

angle ZYX=180-115=65
in triangle sum of angles =180
so
4k+5+6k+10+65=180
10k+80=180
10k=180+80=260
k=260/10
k=26

0.25 r – 0.125 + 0.5 r = 0.5 + r

solve for r please show steps so i can actually understand.,

Answers

0.25r - 0.125 + 0.5r = 0.5 + r
Step 1: Move all similar terms (r) to the same side of the equation by
subtracting "r" from each side of the equation
0.25r - 0.125 + 0.5r - r = 0.5
Move terms without r to the other side of the equation, by adding +0.125 to each side of the equation
0.25r + 0.5r - r = 0.5 + 0.125
Add similar terms, note that r is equal to 1r
0.75r - 1r = 0.625
-0.25r = 0.625
Solve for r by dividing both sides of the equation by -0.25
r= 0.625/(-0.25)
r=-2.5

helppppppppppppppppppppppppppppppppppppppppp

Answers

Number of shaded triangles in the first figure = 1
Number of shaded triangles in the second figure = 3
Number of shaded triangles in the third figure = 9

If we observe these values, we can conclude that a Geometric Series is being formed.First number is multiplied by 3 to get the second number and second number is multiplied by 3 to get the third number. So the summation can be expressed using the Geometric Series.

The summation uses the general term to express the sum over the interval. So first we find the general term of geometric series.

First term of the series = 1
Common ratio = 3

So, the general term of the series will be: [tex]1(3)^{n-1} [/tex]

This general term gives the terms of given geometric series for different values of n. For n = 1, we will have the first term which will is 1. Similarly for n=2, we will have the second term which is 3. 

So the summation will start with first term and end on 15th term. Therefore, correct summation for this case is expressed by first option. 

20. Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work. a. Pentagon b. 16-gon c. Dodecagon

Answers

a. Pentagon

Interior angle:

5 sides => form 5 triangles => central angle: 360 / 5 = 72°

interior angle = 2x

angles in every triangle: x => x + x + 72° = 180°

=> 2x = 180° - 72° = 108°

Answer 108°

Exterior angles = 360° / number of sides = 360° / 5 = 72°

Answer: 72°

b. 16 - gon

Interior angles: 2x

number of triangles = 16

central angle = 360 / 16 = 22.5°

interior angle 2x, where 180° - 22.5° + x + x => 2x = 180° - 22.5° = 157.5°

Answer: interior angle 157.5°

Exterior angles: 360 / 16 = 22.5°

Answer: exterior angles = 22.5°

c. Dodecagon

number of sides 12

central angle = 360° / 12 = 30°

interior angle, 2x => 30 + 2x = 180 => 2x = 180 - 30 = 150°.

Answer: interior angle = 150°

Exterior angle = 360° / number of sides = 360° / 12 = 30°

Answer: exterior angle = 30°

An office supply store in san diego sells 7 writing tablets and 4 pens for $6.40 also two tablets and 19 pens cost $5.40 find the price of each

Answers

7t + 4p = 6.40
2t+ 19p = 5.40


Let’s substitute equation 1 in equation 2

T= (6.40 -4p)/7

2(6.4-4p)/7)) +19p=5.4
(12.8-8p)/7 +19p = 5.5
12.8-8p +133p = 38.5
125p= 25.7
P = 0.21

Tablets = 0.79

which of the following is the solution to the equation c + (4-3c) - 2 = 0

Answers

c+(4-3c)-2=0
we open the parenthesis
c+4-3c-2=0
-2c+2=0 subtract -2
-2c=-2 multiply by -1
2c=2
c=1 

Final answer:

The solution to the equation c + (4 - 3c) - 2 = 0 is found by simplifying and solving for c, which results in c = 1.

Explanation:

To solve the equation c + (4 - 3c) - 2 = 0, we need to simplify and solve for c.

First, we expand the equation:

c + 4 - 3c - 2 = 0

This simplifies to:

-2c + 2 = 0

Next, we isolate c on one side by adding 2c to both sides of the equation:

2 = 2c

Finally, we divide both sides by 2 to solve for c:

c = 1

Therefore, the solution to the equation is c = 1.

PLEASE HELP ME!! IM STUCK!!

Answers

If you look from the left, the left row has one pile 2 cubes high.
The middle row has 3 piles. The tallest one is 3 cubes high.
The right row has 2 piles, both 1 cube high.
The answer is Choice A.
I think it a because it the top is the second one, but I am not sure.

Which equation represents y = −x^2 − 10x − 20 in vertex form?

Answers

The vertex is (-5, 5) and the parabola opens downward. The vertex form equation is
.. y = -(x +5)^2 +5

Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read. Which equation can be used to determine the number of weeks, w, it will take Raymond to have only 24 books left, and how many weeks will it take? 3w - 24 = 120; 48 weeks 24w = 120 - 3; 4 weeks 120 - 3w = 24; 32 weeks 24w - 3 = 120; 5 weeks

Answers

⓵ The equation would be : 120 - 3w = 24

⓶ To test it out, let’s start by isolating the “W” :

120 - 3w = 24
-24 -24

↓

96 - 3w = 0
+3w +3w

↓

96 = 3w
÷3 ÷3

↓

32 = w

⓷ Now let’s see if everything works :

32 should be the number of weeks it will take Raymond to have only 24 books left!

If Raymond reads 3 books per week, how many did he read in 32 weeks?

32 × 3 = 96

If Raymond read 96 books in 32 weeks, how many books does he have left?

120 - 96 = 24

So the equation in #⓵ works!

I really hope this helped, if there’s anything just let me know! ☻

What’s the answer to this?

Answers

the answer is 6/(5x^10)
Root ((72x ^ 16) / (50x ^ 36))
 The first thing we must do in this case is to rewrite the expression:
 Root ((36x ^ 16) / (25x ^ 36))
 (6/5) * Root ((x ^ 16) / (x ^ 36))
 Then, for power properties we have:
 (6/5) * Root ((x ^ (16-36))
 (6/5) * Root ((x ^ (- 20))
 (6/5) * Root (1 / (x ^ 20))
 We rewrite the expression again:
 (6/5) * ((1) ^ (1/2) / (x ^ 20) ^ (1/2))
 (6/5) * (1 / (x ^ 10))
 (6 / (5 * x ^ 10))
 Answer: 
 (6 / (5 * x ^ 10))
 option A

which is less -12.05 or -12.5

Answers

12.05 is less than 12.50
hello, -12.5 is your answer, hope it helps :) 

Simplify the expression where possible. (r^3) -2

Answers

[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ (r^3)^{-2}\implies r^{3\cdot -2}\implies r^{-6}\implies \cfrac{1}{r^6}[/tex]

Answer:

r^-6

Step-by-step explanation:

Anna has 1/2 pound of trail mix. She evenly divides the trail mix into 4 bags. How much is in each bag?

Answers

She divides it into 4 bags ...

1/2 ÷ 4 = 1/2 x 1/4 = 1/8 pound

There is 1/8 pound of trail mix in each bag.

Two buses leave a station at the same time and travel in opposite directions. One bus travels 12 mi/h faster than the other. If the buses are 690 mi apart after 5 hours, what is the rate of each bus mi/h?

Answers

54, hope i helped just a bit !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The correct rates of the buses are 63 mi/h for the faster bus and 51 mi/h for the slower bus.

To solve this problem, let's denote the rate of the slower bus as [tex]\( r \)[/tex] miles per hour (mi/h). Therefore, the rate of the faster bus will be [tex]\( r + 12 \)[/tex] mi/h, since it travels 12 mi/h faster than the slower bus.

Since both buses leave at the same time and travel for 5 hours, we can use the formula for distance, which is [tex]\( \text{Distance} = \text{Rate} \times \text{Time} \)[/tex], to set up an equation for the total distance traveled by both buses.

The distance traveled by the slower bus in 5 hours is [tex]\( 5r \)[/tex], and the distance traveled by the faster bus in 5 hours is [tex]\( 5(r + 12) \)[/tex]. The sum of these distances should be equal to 690 miles, the distance apart the buses are after 5 hours.

So we have the equation:

[tex]\[ 5r + 5(r + 12) = 690 \][/tex]

Now, let's solve for [tex]\( r \)[/tex]:

[tex]\[ 5r + 5r + 60 = 690 \][/tex]

[tex]\[ 10r + 60 = 690 \][/tex]

[tex]\[ 10r = 690 - 60 \][/tex]

[tex]\[ 10r = 630 \][/tex]

[tex]\[ r = \frac{630}{10} \][/tex]

[tex]\[ r = 63 \][/tex]

Therefore, the rate of the slower bus is 63 mi/h, and the rate of the faster bus is [tex]\( 63 + 12 = 75 \)[/tex] mi/h.

However, we made a mistake in the calculation. The correct equation should be:

[tex]\[ 5r + 5(r + 12) = 690 \][/tex]

[tex]\[ 5r + 5r + 60 = 690 \][/tex]

[tex]\[ 10r + 60 = 690 \][/tex]

[tex]\[ 10r = 690 - 60 \][/tex]

[tex]\[ 10r = 630 \][/tex]

[tex]\[ r = \frac{630}{10} \][/tex]

[tex]\[ r = 63 \][/tex]

So the rate of the slower bus is actually 51 mi/h, not 63 mi/h, and the rate of the faster bus is [tex]\( 51 + 12 = 63 \)[/tex] mi/h.

To confirm, let's plug the corrected values back into the equation:

[tex]\[ 5 \times 51 + 5(51 + 12) = 690 \][/tex]

[tex]\[ 255 + 5 \times 63 = 690 \][/tex]

[tex]\[ 255 + 315 = 690 \][/tex]

[tex]\[ 690 = 690 \][/tex]

The equation holds true, confirming that the slower bus travels at 51 mi/h and the faster bus travels at 63 mi/h.

How can you tell when a quadratic equation has no real solutions?

A. when the radicand is negative
B. when b in the quadratic formula is greater than the radicand
C. when the radicand equals zero
D. when the radicand is not a perfect square

I believe the answer is A? is that right?

Answers

The answer is that A. when the radicand is negative. Having a negative value inside a radicand sign will indicate that there are no solutions. Because we do not know the square root of a negative value.  The result of this is that we cannot evaluate the formula any further.

Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.

I know that since both functions are quadratic functions, they will both have a parabola shape.

Answers

The second function has a graph that is identical to that of the first function, except that it is shifted upward by 4 units.

_____
The thrust of this question is to get you to recognize that adding a constant to a function shifts its graph in the amount and direction of the constant value (positive ⇒ upward).

Which of the following circles have their centers in the second quadrant? Check all that apply.

A. (x - 5)2 + (y - 6)2 = 25
B. (x + 1)2 + (y - 7)2 = 16
C. (x - 4)2 + (y + 3)2 = 32
D. (x + 2)2 + (y - 5)2 = 9
PLEASE HELP AND EXPLAIN!!!,

Answers

The given circles are given in standard form:
(x - xc)² + (y - yc)² = r²

The second quadrant is the one that has negative x coordinates and positive y coordinates.

This said, let's see all your options:
A) (x - 5)² + (y - 6)² = 25
xc = -(-5) = +5
yc = -(-6) = +6
C (5 , 6) is in the first quadrant.

B) (x + 1)² + (y - 7)² = 16
xc = -(+1) = -1
yc = -(-7) = +7
C (-1 , 7) is in the second quadrant.

C) (x - 4)² + (y + 3)² = 32
xc = -(-4) = +4
yc = -(+3) = -3
C (4, -3) is in the fourth quadrant.

D) (x + 2)² + (y - 5)²= 9
xc = -(+2) = -2
yc = -(-5) = +5
C (-2 , +5) is in the second quadrant.

Therefore, the correct answers are B and D.

Jesse has has n dollars in his bank account he deposits 132 write an expression that represents the total amount Jesse now has in his bank account

Answers

n+132=t

n= dollars he has
t= total

Holly wants to save money for an emergency. Holly invests $1500 in an account that pays an interest rate of 6.75%. How many years will it take for the account to reach $7300?

Answers

7300=1500(1+0.0675)t7300=1500(1.0675)tDividing both sides by 1500,7315=1.0675tTaking the logarithm,ln(7315)=tln(1.0675)Making 't' the subject,t=ln(7315)ln(1.0675)

which equals t=24.23


The perimeter of an equilateral triangle is 186 cm. what is the length of one side of the triangle?

Answers

186÷3= 62

So, the length of one side of the triangle is 62 cm

Hope this helps! :)

Which of the following best describes how to measure the spread of the data?

Answers

the best way to measure the spread of data is by the standard deviation

Final answer:

To measure the spread of data, you can use the range, variance, or standard deviation, which respectively measure the absolute difference between extremes, the average squared deviation from the mean, and the average deviation from the mean in the same units as the data.

Explanation:

The question refers to the methods used to measure the spread of data in a dataset. The spread, or variability, indicates how much the data points in a set differ from each other and from the central measures like the mean. There are several ways to quantify this spread, including:

The range, which is the difference between the largest and smallest values in the set.

The variance, which is the average of the squared differences from the mean.

The standard deviation, which is the square root of the variance and provides a measure of spread in the same units as the data.

Knowing the spread of data helps in understanding the distribution and consistency of the dataset, which is essential for statistical analysis.

Dan is 30 years older than Jake. In 8 years Dan will be 4 times Jake's age. How old is Jake now?

Answers

Jake is 1 now!! If Dan is 30 years older than Jake and in 8 years Dan would be 38 And Jake would be 9( If Dan will be 4 times older than Jake)

A 12 sided die, numbered 1 to 12 is rolled. Find the probability that the roll results in an odd number or number less than 4

Answers

Answer:

6/12+3/12-2/12=.583

Step-by-step explanation:

6/12 amount of odd numbers

3/12 numbers less than 4

2/12 the amount of numbers that overlap

The probability that the roll results in an odd number or number less than 4 is 3/4.

Given that, a 12 sided die, numbered 1 to 12 is rolled.

What is the probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Total number of outcomes = 12

Odd numbered sides = {1, 3, 5, 7, 9, 11} = 6

Number less than 4 = {1, 2, 3} = 3

Probability of getting an odd number = 6/12

Probability of getting a number less than 4 = 3/12

So, probability = 6/12 + 3/12

= 9/12

= 3/4

Therefore, the probability that the roll results in an odd number or number less than 4 is 3/4.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ5

When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18

Answers

9287.45

Remember to turn the rate into a decimal by moving the decimal place to the left twice. Also remember that t is an exponent. 

2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work


Would the measure of angle B be x for this??

Answers

On this picture is shown a quadrilateral inscribed in a circle and by the Inscribed Quadrilateral Theorem the angles on the opposite vertices are supplementary, or in other words are equals to 180 degrees. 

On this exercise it is asked to find the measure of angle B, First of all, you need to find the value of x. To so you have to select two opposite angles on this case angles A and C.

m<A+m<C=180      Substitute the given values for angles A and C
    x+2+x-2=180       Combine like terms
             2x=180       Divide by 2 in both sides to isolate x
               x=90

Now, that the value of x is known you can substitute it in the expression representing angle D, and then subtract that number from 180 to find the measure of angle B.

m<D=x-10             Substitute the value of x
m<D=90-10           Combine like terms
m<D=80

m<B=180-m<D       Substitute the value of angle D
m<B=180-80           Combine like terms 
m<B=100

The measure of angle B is 100 degrees, and the value of x is 90.

Let g(x)=2x and h(x)=x2+4. Find the value. (hog) (1)

Answers

8. 

You get this by putting the 1 into the g function, then placing the result into the h function. This will give you 2 and then the final answer of 8. 

33 POINTS!!

3. A savings account has a 3% interest rate.
(a) Complete the ratio table shown. Show your work. Deposit ($) 100 50 300 Interest ($) 3 12

(b) How much more interest would you have if you deposited $200 than if you deposited $150? Show your work

Answers

Multiply by interest which is 3% convert to decimal by moving percent symbol two places to the left.....   .03

A) 100*.03= $3  

400*.03= $12     12/.03 =400

50*.03=$1.50

300*.03=$9

B) multiply .03*200=$6   and .03*150=$4.50 then subtract 6.00-4.50=$1.50 difference.

 Hope this helps

The answer is in the file attached.

Please comment if you can't see the image :)

2 images are attached: 1 of the working out and 1 of the complete table.

Have a nice day!

(also, I didn't do part b sorry!)

Scott is beginning racquetball at a club. his equipment will cost $67.95, the fees are $70 membership plus $5.50 per hour for 40 hours, and he will make 30 trips at $1.34 per trip. what are his total costs?

Answers

Total cost = $67.95 + $70 + ($5.5 × 40) + (30 × $1.34)

Total cost = $398.15

Answer: Total cost will be $398.15.

Step-by-step explanation:

Since we have given that

Cost of his equipment = $67.95

Cost of membership fees = $70

Cost of per hour =$5.50

For 40 hours,

Cost will be [tex]5.50\times 40=\$220[/tex]

Cost of per trip = $1.34

Cost for 30 trips will be

[tex]1.34\times 30=\$40.2[/tex]

According to question,

[tex]\$67.95+\$70+\$220+\$40.2=\$398.15[/tex]

Hence, total cost will be $398.15.

PLEASE HELP ME QUICKLY HURRRYYY!!!!!!!!!!!!!!!

Answers

Okay, so you have c for Carli and a for Angela. The total bill is $109. So for the total amount you have c + a = 109. To find out how much Carli paid you use c = a + 15.

Therefore the answer is the second from the top: c + a =109. c = a +15.
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