Answer:
After a dilation, the pre-image and image have the same shape but not the same size. In a dilation, the sides of the pre-image and the corresponding sides of the image are proportional.
Step-by-step explanation:
I need help on rational numbers and coordinates planes. I don't quite understand it.
Answer:
A Rational Number can be made by dividing two integers
The cordinate plane can be used to plot points and graph lines
1. 9(2+3x)=45
2. 8(4+x)=64
Solve for x
Answer:
1) x=1
2)x=4
Step-by-step explanation:
Solved the equation and checked using calculator
Which of the following are square roots of —8 + 8i/3? Check all that apply.
Answer:
Options (2) and (3)
Step-by-step explanation:
Let, [tex]\sqrt{-8+8i\sqrt{3}}=(a+bi)[/tex]
[tex](\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2[/tex]
-8 + 8i√3 = a² + b²i² + 2abi
-8 + 8i√3 = a² - b² + 2abi
By comparing both the sides of the equation,
a² - b² = -8 -------(1)
2ab = 8√3
ab = 4√3 ----------(2)
a = [tex]\frac{4\sqrt{3}}{b}[/tex]
By substituting the value of a in equation (1),
[tex](\frac{4\sqrt{3}}{b})^2-b^2=-8[/tex]
[tex]\frac{48}{b^2}-b^2=-8[/tex]
48 - b⁴ = -8b²
b⁴ - 8b² - 48 = 0
b⁴ - 12b² + 4b² - 48 = 0
b²(b² - 12) + 4(b² - 12) = 0
(b² + 4)(b² - 12) = 0
b² + 4 = 0 ⇒ b = ±√-4
b = ± 2i
b² - 12 = 0 ⇒ b = ±2√3
Since, a = [tex]\frac{4\sqrt{3}}{b}[/tex]
For b = ±2i,
a = [tex]\frac{4\sqrt{3}}{\pm2i}[/tex]
= [tex]\pm\frac{2i\sqrt{3}}{(-1)}[/tex]
= [tex]\mp 2i\sqrt{3}[/tex]
But a is real therefore, a ≠ ±2i√3.
For b = ±2√3
a = [tex]\frac{4\sqrt{3}}{\pm 2\sqrt{3}}[/tex]
a = ±2
Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)
Options (2) and (3) are the correct options.
Answer: b and c
Step-by-step explanation:
whats 28 11/14 in simplest form
Answer is:
29/2 = 14.5
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
x + y = -4
Answer:
y = -x - 4
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
x + y = -4
Step 2: Rewrite
Find slope-intercept form
Subtract x on both sides: y = -x - 4The table below shows the height and the hand span of five students. What pattern of association best describes the relationship between the height and the hand span?
1) no association
2) non linear association
3) positive linear association
4) negative linear association
Answer:
2
Step-by-step explanation:
2
what is the answer to this?!
2/3x−1/5x=x−1
Answer: x = 15/8
Explanation: I used a calculator on a website.
Answer:
15/8
Step-by-step explanation:
Hope this helps: )
What could you do to solve the problem below?
There are 5 members in a jazz band. If the band gets paid $220 for a show
and they split the money evenly, how much will each member receive?
A. Add 5 to 220
B. Subtract 5 from 220
229
C. Multiply 5 by 220
D. Divide 220 by 5
Answer:
Step-by-step explanation:
$220
5 members
220/5
=44
Steve has 10 biscuits in a tin. There are 5 digestive, 3 chocolate and 2 ginger biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.
Answer:
Probability of choosing two different types of biscuits is [tex]\frac{31}{90}[/tex].
Step-by-step explanation:
We have 10 biscuits in a tin.
There are 5 digestive, 3 chocolate, 2 ginger.
Steve takes two biscuits at random.
There are three combinations of biscuits.
P(d, c) + P(c,g)+P(d,g)
Let's find probability of each.
P(d,c)= P(d)* p(c)
= [tex]\frac{5}{10}*\frac{3}{9}[/tex]
Let's simplify it, we get [tex]\frac{1}{6}[/tex]
Like so, for P(c,g)
P(c,g)= P(c) * P(g)
=[tex]\frac{3}{10}*\frac{2}{9}[/tex]
Let's multiply and simplify, we get [tex]\frac{1}{15}[/tex].
Now, for p(d,g)
P(d, g)= P(d)* p(g)
=[tex]\frac{5}{10} *\frac{2}{9}[/tex]
Let's simplify and multiply, we get [tex]\frac{1}{9}[/tex].
Now, add them together
[tex]\frac{1}{6} +\frac{1}{15} +\frac{1}{9}[/tex]
Now, find LCD to make the denominators as same and then add them together.
LCD is 90
So, find equivalent fraction of each which has denominator as 90.
[tex]\frac{15}{90}+\frac{6}{90} +\frac{10}{90}[/tex] = [tex]\frac{31}{90}[/tex]
need help will mark brainliest for best answer
Answer: True
Step-by-step explanation:
The function is even and negative. A negative function opens down. With this information, the statement is true: the function opens down.
Answer:
True
Step-by-step explanation:
Given a parabola in vertex form
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then the graph opens up
• If a < 0 then the graph opens down
Given
f(x) = - (x + 3)² + 2 ← in vertex form
with a = - 1 < 0 then graph opens down is True
Which situation is best represented by the equation below?
5W + 7 = 127
HELP ME PLEASE
can someon please help me
Answer:
8.0018.018.19111316Step-by-step explanation:
simplify the expression -3/5(-8 + 5/9x -3)
Please help me on this
ABDE is an isosceles trapezoid. Select all
pairs of congruent triangles.
A. Triangle ABE and triangle DBE
B. Triangle ABD and triangle DAE
C. Triangle ABE and triangle BAD
D. Triangle AED and triangle BDE
E. Triangle EAB and triangle EDB
Answer:
Step-by-step explanation:
triangles that are the same are congruent
A) no
B) no
C) yes
D) yes
E) no
Seperate 82 in two parts so that one of the parts is 3 times bigger than the other part
Answer:
one part = 20.5
the other part = 61.5
Step-by-step explanation:
let one part = x
let another part = y
(1) create two equations
i) 82 is separated into 2 parts, x and y. it means x plus y equals to 82
x+y = 82
ii) one part is bigger than the other. if x is the bigger part, it is 3 times bigger than y
x = 3y
(2) use substitution method to find the value of x and y
x+y = 82 -------- (1)
x = 3y ---------- (2)
substitute (2) into (1)
x+y = 82
3y+y = 82
4y = 82
y = 82/4
y = 20.5
substitute y = 20.5 into (2)
x = 3y
x = 3(20.5)
x = 61.5
How do you get from one number 100 to 90
65% of what number is 27
Answer:
41.54
Step-by-step explanation:
PLEASE HELP I WILL GIVE YOU 5 STARS AND A THANKS AND BRAINLIEST (If you tell me how to make you brainliest, lol) What is 81.818182% rounded to the nearest hundredthh???????/
Answer:
81.82%
Step-by-step explanation:
cuz meth
Answer:
81.82
Step-by Step
In order to round to the nearest thousand, you simply have to move the decimal point to the RIGHT. Hope it helps!
~Happy holidays
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 5.3 gallons in the 12-gallon tank on the coldest day of the year. Lou filled the tank with gas that cost $3.80 per gallon. How much did Lou spend on gas? He spent $__ on gas.
Answer:
$26.98
Step-by-step explanation:
1. You have the following information given in the problem above:
- Lou filled the tank with gas that cost $3.80 per gallon.
- Lou's car had 5.9 gallons in the 13-gallon tank.
2. Therefore, if he filled the tank, you can calculate the total amount of money Lou spent, by subtracting 13 gallons and 5.9 gallons and multiplying the result by $3.80.
Answer:
26.98
Step-by-step explanation: 5.3 * 3.8 = 26.98
The population of new york city in 2013 was about 8,406,000 people which number best appoximates the population as a single digit times a power of ten
Answer:
8 * 10^6
Step-by-step explanation:
The question is asking us to represent the value 8,406,000 in standard. The standard form of an expression is expressed as;
A * 10^n
A is any integer between 1 and 10
n is any integer.
Given the value 8,406,000
8,406,000.
We are going to move the decimal point at the end to first digit value. This point will be shifted 6 times to have;
8,406,000 = 8.6 * 10^6 (Note that n is positive since the value given is greater than 1)
Since we are to express as a single digit times a power of ten, the required answer will be 8 * 10^6
Suppose over several years of offering AP Statistics, a high school finds that final exam scores are normally distributed with a mean of 78 and a standard deviation of 6.a. What are the mean, standard deviation, and shape of the distribution of x-bar for n = 50?b. What’s the probability a sample of scores will have a mean greater than 80?c. Sketch the distribution curve for part B, showing the area that represents the probability you found.
Answer:
ux = 78
s= 0.8485
P ( z>0.33) = 0.3707
Step-by-step explanation:
According to central limit theorem the mean of the population is equal to the mean of the sample and the standard deviation is found by dividing the standard deviation of the population with the square root of the sample size
Thus
ux = u= 78
σ= 6
s= σ/√n= 6/√50= 6/7.07106= 0.8485
We find the z score
Z= X- u / σ
z= 80-78/6
z= 2/6= 1/3=0.333
P ( z>0.33) = 1 - P(z=0.33)
= 1- 0.6293
= 0.3707
We see in the figure that the blue area represents the area greater than z= 0.333 or area greater than 1/3.
The probability of z= 0.33 from the table is 0.6293
We find the probability of area greater than 0.33 by subtracting from 1 .
For 3/4 (three fourths) of a pound of peanuts, Jimmy paid $2.25. What is
the unit rate (dollars per pound)?
1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.
A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.
B) Who makes more from stuffing the same number of envelopes? Explain how you know using the information above.
C) Anna has savings of $100 at the beginning of the summer and she saves all of her earnings from her job. Graph her savings as an equationof the number of envelopes she’s stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the initial value and slope in each case?
D)You survey 6 other employees and findthe following data on envelopesstuffed (x) and dollars earned(y). Plot a trend lineon the graph. Find the equation of the trend line.
Answer:
The answer is below
Step-by-step explanation:
A) i)
For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]
The table is:
x: 200 400 600 800 1000
y: 10 20 30 40 50
ii)
For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]
The table is:
x: 200 400 600 800 1000
y: 8 16 24 32 40
The graph is plotted using geogebra online graphing
b) From the table above we can see that Anna makes more stuffing than Jason.
c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]
We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.
The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)
For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100
D) The line pass through (10, 10) and (100, 40), hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]
Write the possible subset of C= {2,4,6}
Step-by-step explanation:
For this set there are 8 subsets and 7 proper subsets
the subsets are:
{}
{2}
{4}
{6}
{2,4}
{2,6}
{4,6}
{2,4,6}
4. What is the solution to the equation
-3.5(x + 12) = -2x + 18?
A. X = -40
C. X=4
B. X=-4
D. X= 40
Answer:
A. x = -40
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
-3.5(x + 12) = -2x + 18
Step 2: Solve for x
Distribute -3.5: -3.5x - 42 = -2x + 18Add 3.5x on both sides: -42 = 1.5x + 18Subtract 18 on both sides: -60 = 1.5xDivide 1.5 on both sides: -40 = xRewrite: x = -40Solve each system using substitution or elimination. Show all required work. Y=-5x^2+2x-3 Y=-3x-3
Step-by-step explanation:
y = -5x² + 2x - 3 and y = -3x - 3.
=> -5x² + 2x - 3 = -3x - 3
=> 5x² - 5x = 0
=> 5x(x - 1) = 0
=> x = 0 or x = 1.
When x = 0, y = -3(0) - 3 = -3.
When x = 1, y = -3(1) - 3 = -6.
The solutions are (0,-3) and (1,-6).
a teacher has 90 pencils to give to her students. the pencil came in boxes of 6. how many boxes of pencils does she have
Answer:
she has 15 boxes of pencils
Step-by-step explanation:
if we have 90 total pencils that need to be split into groups of 6, the way to find how many groups there are is by dividing 90/6, which gives you 15 groups or, in this case, 15 boxes. and you can check your work by multiply the 15 boxes by the 6 pencils in each box, which gives you 90 pencils total, so you're all good!
factorize the following expressions
Answer:
6) b(3a^4-5c³)
7) 3x³yz(2x+5y)
8) 4a²b²c³(2bc-3a)
9) 4xy(2y+7z-1)
10) 2mn(5n²+2m-3n)
Step-by-step explanation:
6) Factor out the b and you get b(3a^4-5c³)
7) Factor out the 3x³yz and you get 3x³yz(2x+5y)
8) Factor out the 4a²b³c³ and you get 4a²b²c³(2bc-3a)
9) Factor out the 4xy and you get 4xy(2y+7z-1)
10) Factor out the 2mn and you get 2mn(5n²+2m-3n)
42 students are going on a field trip and need to ride in a bus. Each bus can hold 4 students. How many buses will the students fill completely?
Answer:
11 buses
Step-by-step explanation:
Divide 42 by 4 to get 10 and a remainder of 2. The 2 students not on the bus need another bus so you need 10+1=11 buses
Jessie estimates the weight of her cat to be 10 pounds. The actual weight of the cat is 1375 pounds. Find the percent of error.
Answer:
The percent error is 99%
Step-by-step explanation
Estimated weight of cat = 10 pounds
Actual weight of cat = 1375 pounds
We need to find the percent of error.
The formula used is: [tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100[/tex]
Putting values and finding percent of error.
[tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100\\Percent\:Error=\frac{|10-1375|}{1375}\times 100 \\Percent\:Error=\frac{|-1365|}{1375}\times 100 \\Percent\:Error=\frac{1365}{1375}\times 100\\Percent\:Error=0.99\times 100 \\Percet\:Error=99\%[/tex]
So, the percent error is 99%