Answers
Step-by-step explanation:
We can prove this by using similar triangles. We know that angle ABE and ACD are SIMILAR(we know that by the sign in between them).Therefore, we also know that CDA and BEA are similar, and EAB and DAC are similar. Since all the angles are similar, we also know that the side lengths are equal in proportion. AB/AE is equal to AC/AD. When assigned values, that would create a proportion that is equal since the smaller triangle is similar to the bigger one. If you want to create a proof, break each statement into its own section.
Related Questions
AC = 23. AB = 2x + 2, and BC = 3x + 6. Find BC
Answers
Answer:
21Step-by-step explanation:
Given AC = 23, AB = 2x + 2 and BC = 3x+6 then using vector notation;
BA+AC = BC
Since BA = -AB
The equation becomes -AB+AC = BC
Substituting the given equations;
-(2x+2)+23 = 3x+6
open the parenthesis
-2x-2+23 = 3x+6
-2x+21 = 3x+6
collect the like terms
-2x-3x = 6 - 21
-5x = -15
Divide both sides by -5
-5x/-5 = -15/-5
x = 3
TO get BC, we will substitute x = 3 into the expression BC = 3x+6
BC = 3(5)+6
BC = 15+6
BC = 21
Hence the length of BC is 21 units
Simplifying Radicals:
[tex] \sqrt{30} [/tex]
Answers
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 270 milliliters of a dressing that is 9% vinegar. How much of each brand should she use
Answers
Answer:
Amount of 8% vinegar = 216 mL
Amount of 13% vinegar = 54 mL
Step-by-step explanation:
First, of all, let x be the amount of 8% vinegar used
Since, the scientist needs 270 mL of vinegar, then;
Let 270 - x be the amount of 13% vinegar used
Now, we are told that she needs 270 mL of a 9% vinegar.
This means that;
8%x + 13%(270 - x) = 9%(270)
Simplifying this gives;
0.08x + 0.13(270 - x) = 0.09 × 270
Expanding the bracket gives;
0.08x + 35.1 - 0.13x = 24.3
0.13x - 0.08x = 35.1 - 24.3
0.05x = 10.8
x = 10.8/0.05
x = 216 mL
Thus, she will need to use 216 mL of the 8% vinegar.
Since 270 - x is the amount of 13% vinegar used , then;
the amount of 13% vinegar = 270 - 216 = 54 mL
Which numbers in Set A = {−7, −4, 2, 14, 21, 34, 42} are elements of both Set B and Set C, shown below? Set B = {even numbers} Set C = {multiples of 7} and Enter answers from smallest to largest THERE ARE TWO QUESTIONS
Answers
Answer:
14, 42
Step-by-step explanation:
Set A = {−7, −4, 2, 14, 21, 34, 42}
Set B = {even numbers}
Set C = {multiples of 7}
There is only one question asked
Which numbers in Set A are elements of both Set B and Set C,
We need it to be even and a multiple of 7
14 is even and a multiple of 7 and 42 is even and a multiple of 7
Answer:
[tex]\Huge \boxed{\mathrm{\{ 14, 42\} }}[/tex]
Step-by-step explanation:
[tex]\mathrm{Set \ A = \{-7, -4, 2, 14, 21, 34, 42\} }\\\\\\\mathrm{Set \ B = \{even \ numbers\} } \\\\\\\mathrm{Set \ C = \{multiples \ of \ 7\}}[/tex]
Whatever number is in Set A, it must also be in Set B and Set C.
The elements in Set A must be an even number and a multiple of 7.
Multiples of 7 from Set A are -7, 14, 21, 42.
The even numbers from these multiples of 7 are 14 and 42.
Subtract the polynomials. (x2+3x−7)−(3x2−5x+3)
Answers
Answer:
-2x^2+8x-10
Step-by-step explanation:
(x^2+3x−7)−(3x^2−5x+3)
Distribute the minus sign
(x^2+3x−7)−3x^2+5x-3
Combine like terms
-2x^2+8x-10
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ - 2 {x}^{2} + 8x - 10}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( {x}^{2} + 3x - 7) - (3 {x}^{2} - 5x + 3)}[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression. Also, remove the parentheses
⇒[tex] \sf{ {x}^{2} + 3x - 7 - 3 {x}^{2} + 5x - 3}[/tex]
Collect like terms
⇒[tex] \sf{ {x}^{2} - 3 {x}^{2} + 3x + 5x - 7 - 3}[/tex]
⇒[tex] \sf{ - 2 {x}^{2} + 8x - 10}[/tex]
Hope I helped!
Best regards!!
Simplify: (6x-4) (9x-2)
Answers
Step-by-step explanation:
6x(9x-2)-4(9x-2)
54x²-12x-36x+8
54x²-48x+8
If x-2=2^(2/3) + 2^(1/3), show that x3 - 6x3 + 6x-2=0
Answers
so x - 2 = 2^(2/3) + 2^(1/3)
=(x-2)^3 = [2^(2/3)+2^(1/3)]^3
use (a-b)^3= a^3 - b^3 - 3ab(a-b)
and (a+b)^3= a^3 + b^3 + 3ab(a+b) formulae.
or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2
The number that has the exponent over it is called the what?
Answers
Answer: An expression that represents repeated multiplication of the same factor is called a power .
I hope this is the answer you were looking for if it's not I'm really sorry:(
a town Pharmacy in hospital is doing it as a part of format of the town has a scale 18840.35 miles what is the distance between the pharmacy in the hospital on the map in inches pharmacy in hospital is doing it as a part it’s a map of the town has a scale where 1inch = 0.25 miles what is the distance between the pharmacy in the hospital on the map in inches
Answers
Answer:34344e4365655.6
Step-by-step explanation:
Given g(x) = -x + 3, find g(1).
Answers
If you were to describe a reflection of a triangle with information would you need to include in the description?
Answers
Answer:
the points and where it is located
Step-by-step explanation:
What’s the answer for number 9
Answers
Justin wants to cover the top of a circular swimming pool to keep insects out of the pool. If the diameter of the pool is 20 feet, what will be the area of the top of the cover (the portion of the cover that covers the surface of the pool)?
Answers
Answer: The area is approximately 314 ft^2
Step-by-step explanation:
Well if the diameter is 20 feet then the radius will be 10 because the radius is half the diameter, and to find the area of a circle, you use the formula
A= [tex]\pi r^{2}[/tex] where A is the area and pi times the radius squared.
We will represent pi by 3.14
A= 3.14* 10^2
A= 3.14 * 100
A = 314
A small newspaper company is downsizing and has lost employers at a steady rate. twelve months ago they had 65 employees, and now they have 29.
Answers
Answer:
each month 3 employees were laid off.
Step-by-step explanation:
the company started with 65 employees 12 months ago, and now there are 29. 65 - 29 = 36. In 12 months, 36 employees were laid off. 36 employees divided by 12 months = 3 employees per month.
solve x^3 = 1/8 please i’m dumb and don’t know
Answers
Answer:
1/2
Step-by-step explanation:
Cube root of .125 which is 1/8 is 1/2
Find a geometric representation for the following sequences of
numbers.
3, 4, 5, 6, 7, …
Answers
The sequence represents triangle,quadrilateral,pentagon,hexagon,heptagon.
What is a sequence ?A sequence is a set of numbers which represents some common relation or representation among these numbers.
The geometric representation of the sequence 3,4,5,6,7... can be.
Given it represents geometry so it can be angles,sides.It can also represent interior angles.
If this sequence represents sides then it is triangle, quadrilateral, pentagon, hexagon...
If it represents interior angles then this sequence is also of triangle, quadrilateral, pentagon, hexagon,heptagon.
learn more about sequence here :
https://brainly.com/question/21961097
#SPJ2
Guys, I am taking the SHSAT and I am not confident I don't think I am smart enough to pass. I study like crazy but nothing sticks in my mind and if I don't pass my parents will be disappointed. What do I do?
Answers
Answer:
hope this helps
Step-by-step explanation:
my parents are the same way so if you listen to classical music then things will stick in you head and you can draw things to remind you what they mean like if you had a definitions then draw what they mean
y=-|x-2|
Please help me
Answers
Answer:
y = -|x-2| (*)
2 cases:
case 1: for x≥2 <=> |x-2| = x-2
(*) <=> y = - (x-2)
<=> y = -x+2
<=> x+y = 2
case 2: for x>2 <=> |x-2| = 2-x
(*) <=> y = -(2-x)
<=> y = x-2
<=> x-y = 2
since there are 2 variables but just one equation, we cannot find the exact values of x and y. Instead, we can find some kind of connection between them.
Simplify –56 ⋅ 25 ⋅ 4. State a property that you can use.
Answers
Answer: [tex]-56\cdot 25\cdot 4 = -5600[/tex] .
Step-by-step explanation:
Associative property of multiplication : We can group numbers to multiply in any order like
[tex]p\times (q \times r) = (p\times q )\times r = p\times q\times r[/tex], where p , q and r can be any expression.
The given expression : [tex]-56\cdot 25\cdot 4[/tex]
By using associative property of multiplication, we have
[tex]-56\cdot(25\cdot 4)\\\\= -56\cdot 100\\\\=-5600[/tex]
Hence, [tex]-56\cdot 25\cdot 4 = -5600[/tex] .
A man weighing 340 pounds is admitted into a hospital for a special diet to lose no more than 6 pounds per week. What is the shortest time in weeks it could take the man to reduce his weight to 243 pounds?
Answers
Answer:
Step-by-step explanation:
340-243 =97
97/6 = 16
16 weeks to lose 6 pounds per week.
Answer:
Let's think.
If we want the man to be in the best case scenario in which he loses the most pounds that his limit lets him, we should always make the man lose the highest he could go: 6 pounds.
This is just a simple multi step problem if you break it down.
If his goal is to get to 243 pounds, we firstly subtract 243 from 340 to see how much he needs to lose.
340 - 243 = 97
The man wants to lose 97 pounds.
Let's divide this number by 6 with remainder.
I'll let you think for a bit.
97 / 6 = 16 remainder 1.
This means that in 16 weeks, he needs to lose 6 pounds while on the 17th week, he needs to lose 1 pound.
I'm sorry if i misunderstood.
Good luck Mate :)
Don't forget to try everyday !
The perimeter of the square kitchen floor measures 48 feet. What is the area of the kitchen floor?
32 feet
96 square feet
144 square feet
144 cubic feet
Answers
I hope this helps you...
After your first semester of college is over, you discover that the math department has changed textbooks (again) so the bookstore won't buy back your nearly-new book. You and your friend Amber decide to get creative. You go to the roof of a twelve-story building and look over the edge to the reflecting pool 160 feet below. You drop your book over the edge at the same instant that Amber chucks her book straight down at 48 ft/s. By how many seconds does her book beat yours into the water?
Answers
Answer:
about 2 or 3
Step-by-step explanation:
heres what u do go onlie and put the books up for sale.
Answer:
The book of amber will reach the pool 6.78 seconds before the other
Step-by-step explanation:
common sense
two strips of fabric measures 14 3/4 inches and 20 7/8 inches in length. to form one length, the strips are sown together using 1/2 inch from each strip to make the seam. what is the final length of the fabric after two strips are sewn together
Answers
Answer:
34 5/8 inches
Step-by-step explanation:
Let the two strips be fabric A and fabric B
Fabric A= 14 3/4 inches
Fabric B = 20 7/8 inches
To form one length, the strips are sown together using 1/2 inch
Length after sewing=
Fabric A - 1/2 inch
= 14 3/4 inches - 1/2 inch
= 59/4 - 1/2
= 59-2 /4
= 57/4 inches
Length after sewing=
Fabric B - 1/2 inch
= 20 7/8 inches - 1/2 inch
= 167/8 - 1/2
= 167-4 /8
= 163/8 inches
Final length of the fabric after two strips are sewn together
= 57/4 inches + 163/8 inches
= 114+163 /8
= 277/8
= 34 5/8 inches
Final length of the fabric after two strips are sewn together= 34 5/8 inches
Charlie and Clare are playing a number-guessing game. Charlie picked two numbers between 1 and 5. To win the game, Clare must guess both his numbers in three tries. Her guesses, simulated using a random-number generator, are shown in the table. If Charlie’s numbers are 1 and 3, what is the experimental probability that Clare won?
Answers
The experimental probability is 3/10 that Clare won if Charlie's numbers were 1 and 3
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Charlie picked two numbers between 1 and 5
So the numbers should be 2, 3, and 4
There is the number of favorable outcomes is 3
To win the game, Clare must guess both his numbers in three tries
The experimental probability that Clare won if Charlie's numbers were 1 and 3 = P(E)
There are 10 trials given
There are total number of possible outcomes is 10
So the required experimental probability P(E) = favorable outcomes/total outcomes
⇒ P(E) = 3/10
Hence, the experimental probability is 3/10 that Clare won if Charlie's numbers were 1 and 3.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ5
Answer: 3/10
Step-by-step explanation:
Hey please sorry its three questions thank you.
Answers
8(-5x + 3) use x = 6 how do i do this?
Answers
8(-5(6)+3)
then you would just solve
parentheses first so
8(-35+3)
8(-32)
=-256
A new electronic store opened recently. There are several sales associate positions that pay an hourly rate of $7.50 plus a 4.5% commission based on the sales associates total weeking sales. Sales assqqociates are guaranteed 30 hrs of work per week,but no more that 40 hrs. At the electronics store, sales associates average $7,000 in sales each week. USE THE AVERAGE WEEKLY SALES FIGURE OF $7,000 AND HOURLY RATE OF $7.50. WRITE AN EQUATION, CREATE A TABLE, AND CREATE A GRAPH FOR A SALES ASSOCIATE'S WEEKLY EARNINGS, f(x), where x represents the total number of hours the sales associate would work.
Answers
Answer: f(x) = 7.50x + 315
Step-by-step explanation:
Let x represent the number of hours
Given: rate = 7.50, commission = 4.5%(7,000) = 315
Equation: f(x) = 7.50x + 315
Table:
[tex]\boxed{\begin{array}{c||r|c||c}\underline{\text{Hours}}&\underline{\text{Wage}}&\underline{\text{Commission}}&\underline{\text{Weekly Earnings}}\\30&7.5(30)=225.00&315&540.00\\31&7.5(31)=232.50&315&547.50\\32&7.5(32)=240.00&315&555.00\\33&7.5(33)=247.50&315&562.50\\34&7.5(34)=255.00&315&570.00\\35&7.5(35)=262.50&315&577.50\\36&7.5(36)=270.00&315&585.00\\37&7.5(37)=277.50&315&592.50\\38&7.5(38)=285.00&315&600.00\\39&7.5(39)=292.50&315&607.50\\40&7.5(40)=300.00&315&615.00\end{array}}[/tex]
Graph: (see below)
Find the distance between the points: (-3, -4) and (5, 5). If necessary, round your answer to the nearest tenth. A.14.4 b.19 c.12 d.11.8
Answers
Answer:
The answer is option CStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-3, -4) and (5, 5)
The distance between them is
[tex]d = \sqrt{( { - 3 - 5})^{2} + ({ - 4 - 5})^{2} } \\ = \sqrt{ ({ - 8})^{2} + ( { - 9})^{2} } \\ = \sqrt{64 + 81} \\ = \sqrt{145} \\ = 12.04159 [/tex]We have the final answer as
12 units to the nearest tenthHope this helps you
What is -14 +(-3)
Ps. This is 7th-grade math
Answers
Answer:
-17
Step-by-step explanation:
-14 + (-3)
-14 - 3
-17
ration Numbers
Real Numbers
Integers
Whole
Numbers
Inational
Numbers
The subsets of the real numbers can be represented in a Venn diagram as shown
To which subsets of real numbers does 12 belong?
A
Integers and Whole Numbers only
8
Rational Numbers, Integers, and Whole Nmbers
Rational Numbers and Integers only
D
Irrational Numbers integers, and Whole dumbers
Answers
Answer:
12 belongs in the rational numbers, integers, and whole numbers
Step-by-step explanation:
12 is a whole number so it belongs in every category that has whole numbers.