show that (x+1)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx+ d where a,b,c and d are all positive integers.
Answer:
x³ + 9x² + 23x + 15
Step-by-step explanation:
Given
(x + 1)(x + 3)(x + 5) ← expand the first pair of factors using FOIL
= (x² + 4x + 3)(x + 5)
Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is
x²(x + 5) + 4x(x + 5) + 3(x + 5) ← distribute the 3 parenthesis
= x³ + 5x² + 4x² + 20x + 3x + 15 ← collect like terms
= x³ + 9x² + 23x + 15 ← in the form ax³ + bx² + cx + d
the area of triangle LMN is 26 square units. the triangle is reflected across LM and then translated 3 units to the right and 4 units up. what is the area of the resulting triangle?
Answer:
26 square units
Step-by-step explanation:
Reflection and translation are rigid motions that do not affect the size or shape of the triangle. It has the same area as the original: 26 units².
simplify the expression -4(x - 5)
Answer:
-4x+20
Step-by-step explanation:
[tex]-4(x - 5)\\\\=-4x-4(-5)\\\\=-4x+20[/tex]
X/5=15 Question 7 options: 20 3 75 10
Answer:
x = 75
Step-by-step explanation:
X/5=15
Multiply each side by 5
x/5 * 5 = 15*5
x = 75
Answer:
Step-by-step explanation:
15*5=75
therefore answer is x=75
When 19,346 is divided by a number,the quotient is 841 and the remainder is 3.What is the number?
Answer
Hi mate,
Divided=divisor*quotient+remainder
19346=x*841+3
19346-3=841x
19343/841=x
x=23
Hope this helps u
Mark me as brainliest
Step-by-step explanation:
PLEASE HELP ASAP!!!!!
Answer:
D
Step-by-step explanation:
A file that is 242 megabytes is being downloaded. If the download is 17.1% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
4.1 megabytes
Step-by-step explanation:
well we use the rule of three
242 megabytes ------- 100%
x megabytes -------- 17.1%
(x megabytes)(100%)=(242 megabytes)(17.1%)
[tex]x=\frac{242*17.1}{100} \\\\x=\frac{4138.2}{100} \\\\x=4.1382\\\\x=4.1[/tex]
so there have been downloaded 4.1 megabytes
2. It takes 39,090 gallons of water to manufacture a new car. Sammy thinks that rounds up to about 40,000
gallons. Susie thinks it is about 39,000 gallons. Who rounded to the nearest thousand, Sammy or Susie?
Use pictures, numbers, or words to explain.
Answer:
Susie rounded to the nearest thousandth.
Step-by-step explanation:
since the 100th place is 0 it would round down to 39,000 when you are rounding to the nearest thousand.
what is the inverse of f={(1,3),(4,2),(5,1)}
Answer:
f={(3,1),(2,4),(1,5)}
This is my algebra I have a A+ but I wanna keep it up
Answer:
45 minutes
Step-by-step explanation:
We want to know how long it takes to an airplane to fly a distance of 375 miles, if the speed of the airplane is 500 miles per hour.
For this, we should divide the distance/speed to get the time that the plane needs.
T = 375mi/(500mi/h) = 0.75 hours
The plane needs 0.75 hours or 0.75*60 = 45 minutes to fly that distance.
determine which of the following pairs of triangles are similar.
Triangles given in Options (b) and (c) are similar.
Theorems of similar triangles: If two angles of a pair of triangles are equal in measure, then the triangles will be similar by A-A property. If corresponding sides of two triangles are proportional, both the triangles will be similar.
From the picture attached,
a). In triangle ABC,
∠A + ∠B + ∠C = 180° [By triangle sum theorem]
60° + ∠B + 40° = 180°
∠B = 80°
Similarly, in ΔDEF,
∠D + ∠E + ∠F = 180°
60° + 85° + ∠F = 180°
∠F = 35°
Since, measure of angles of both the triangles are different in measures, triangles will not be similar.
b). In ΔABC,
∠A + ∠B + ∠C = 180°
45° + 50° + ∠B = 180°
∠B = 85°
In ΔDEF,
∠D + ∠E + ∠F = 180°
50° + 85° + ∠F = 180°
∠F = 45°
Hence, ∠C ≅ ∠D, ∠A≅ ∠F and ∠B ≅ ∠E
Since, measure of corresponding angles are equal, both the
triangles (ΔABC ~ ΔFED) will be similar.
c). Here, corresponding sides of both the triangles are proportional,
[tex]\frac{AB}{DE}= \frac{CA}{FD}= \frac{BC}{EF}[/tex]
[tex]\frac{14}{7}= \frac{12}{6}= \frac{16}{8}[/tex]
[tex]\frac{2}{1}= \frac{2}{1}= \frac{2}{1}[/tex]
Both the triangles ΔABC and ΔDEF will be similar.
Therefore, Option B and Option C are the correct options.
Learn more about the similarity of two triangles here,
https://brainly.com/question/2499350?referrer=searchResults
A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed on the yellow side 29 times. what is the relative frequency of the chip landing with the yellow side facing up?
38%
42%
56%
58%
Answer:
58 %
Step-by-step explanation:
What is the slope of a line passing through points (-7,5) and (5,-3)?
Answer:
- 2/3
Step-by-step explanation:
Work out 5
5-² x 3√8
Give your answer as a decimal.
Answer:
I got -11.97056 as the answer
Combine like terms in the following equation:
18 – 5W + 7w - 4 = 28
Answer:
7
Step-by-step explanation:
Step 1:
18 - 5w + 7w - 4 = 28
Step 2:
14 + 2w = 28
Step 3:
2w = 14
Answer:
w = 7
Hope This Helps :)
Find the value of x that makes m
m
n
(2x + 20)
(32°
Answer: x= 20
Step-by-step explanation:
If m and n are parallel then the 3x and 2x+20 has to have the same measures which means they have to equal each other . So set them equal each other and solve for x.
2x + 20 = 3x
-2x -2x
20 = 1x
x= 20
52 regular playing cards are randomly dealt to four players with each players receiving 13 cards. What is the probability that each player will have exactly one ace
Answer:
The probability is 1/28,561
Step-by-step explanation:
Here, we want to find the probability that each of the players will receive exactly one ace.
In a deck of cards, we have 4 suites of 13 cards each, with each of the suites consisting of 1 ace.
So, the probability of getting an ace for each of the four players will be 4/52 = 1/13
Now, the probability of each of the players getting exactly one ace will be; first got one ace , second got one , third got one and fourth got one.
mathematically, this probability will be 1/13 * 1/13 * 1/13 * 1/13 = (1/13)^4 = 1/28,561
4(n+9)-3(2+n)
Help now plz
Answer:
n + 30
Step-by-step explanation:
[tex]4(n+9)-3(2+n)\\\\\mathrm{Expand}\:4\left(n+9\right):\quad 4n+36\\=4n+36-3\left(2+n\right)\\\\\mathrm{Expand}\:-3\left(2+n\right):\quad -6-3n\\=4n+36-6-3n\\\\\mathrm{Simplify}\:4n+36-6-3n:\\\quad n+30[/tex]
Answer:
4n + 36 - 6 -3n
n + 30
Step-by-step explanation:
what number is 10 times less than 20?
Answer:
180
Mathematically, 10 times less than 20 would be: Take 20, subtract (10 x 20). Answer: -180.
INTERPRETING EXPRESSIONS:
ln the expression 9x - 9, the variable is ___
The United States Tennis Association is researching the effect of what color the professional tennis players wear and
the number of foot faults called on them in one match. They collect data from every televised event of the year, noting
the color of the player's clothes and how many foot faults were called on the player. Which is this an example of?
-experiment
-simple random sample
-observational study
-convenience sample
Answer:
the answer is observation study
Step-by-step explanation:
Iola has $75. She buys a pair of shoes on sale for one-half off and a pair of socks for $6. She has $32 left. Which equation can be used to find x, the regular price of the shoes?
Answer:
To solve for the problem above, let x be the regular price of the shoe.
1/2x is the one-half price of the shoe then we add 6 for the pair of socks,
1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.
Step-by-step explanation:
BINGO
7 26 35 51 73
14 23 44 5563
6 19 FREE 48 64
12 22 32 54 70
11 16 33 47 69
What output corresponds with 12?
Answer:
23
Step-by-step explanation:
3m - 12 =18
Step by step
Answer:
3m=18+12
3m=30
divide both sides by 3
m=10
Answer:
m = 10
Step-by-step explanation:
3m - 12 =18
Add 12 to each side
3m - 12+12 =18+12
3m = 30
Divide by 3
3m/3 = 30/3
m = 10
Twice the sum of a number and 3 is equal to three times the difference of the number and 7. Find the number
Answer:
The number is 27
Step-by-step explanation:
Let us change the word statement to an algebraic equation
→ Assume that the number is x
→ Twice the sum of a number and 3, means add x by 3, then multiply the sum by 2
→ The algebraic expression is 2(x + 3)
→ Three times the difference of the number and 7, means subtract x and 7, then multiply the difference by 3
→ The algebraic expression is 3(x - 7)
→ Equate the two expressions
∴ 2(x + 3) = 3(x - 7)
→ Simplify each side
∵ 2(x + 3) = 2(x) + 2(3) = 2x + 6
∵ 3(x - 7) = 3(x) - 3(7) = 3x - 21
∴ 2x + 6 = 3x - 21
Let us solve the equation to find x
→ Subtract 6 from both sides
∴ 2x + 6 - 6 = 3x -21 - 6
∴ 2x = 3x - 21
→ Subtract 3x from both sides
∴ 2x - 3x = 3x - 3x - 27
∴ -x = -27
→ Divide both sides by -1
∴ x = 27
The number is 27
what is (4x^2y^3)^2=
16x⁴y⁶
Step-by-step explanation:(4x²y³)² =
= 4²x²ˣ²y³ˣ²
= 16x⁴y⁶
QR has endpoints at Q(2,6) and R(0,2). Find the midpoint M of QR
Answer:
Step-by-step explanation:
Well, the midpoint formula is M=((x↓1 +x↓2)/2,(y↓1 +y↓2)/2 ). (not exponents, they tell you which x or y value).
If you plug in your 2 points, it becomes m=((2+0)/2,(6+2)/2).
When you add, it is m=(2/2, 8/2)
When simplified, it is m=(1,4)
Compare the process of solving
|x - 1 + 1 < 15 to that of solving
1x – 1| + 1 > 15.
Answer:
x-1+1<15; this gonna be x<15 and 1x-1+1>15 this is gonna be the same
Step-by-step explanation:
HELP ME ASAP WILL GIVE 5 STARS AND A THANKS
Answer:
The mayor will lose by a large percentage.
Answer:
D??
Step-by-step explanation:
It may be D or A I’m not sure!!
HELP ME PLEASE i need this right now
Answer:
jimragarant 1
Step-by-step explanation:
pls can u help me with the questions i have posted i will give u anything u want
pls help its urgent
Answer:
108.8 yd²
Step-by-step explanation:
The area (A) of the triangle can be calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a, b are 2 sides and C the angle between them
Here a = 23, b = 9.5 and C = 85° , thus
A = 0.5 × 23 × 9.5 × sin85° ≈ 108.8 yd² ( to the nearest tenth )