number of cupcakes lynn made = x
number of cupcakes santo baked = 2x - 4
hope this helps and please mark me brainliesr. PLEASE!!!!
A quadratic equation x²+2(3x+p)=0 where p is a constant, has roots a and 2a, where a≠0
(a) find the value of a and of p
(b) hence, from a quadratic equation whose roots are a+1 and a-5
HELP ME PLISS
Answer:
a = -2 and p = 4.
Step-by-step explanation:
x²+2(3x+p)=0
x^2 + 6x + 2p = 0
For the general equation ax^2 + bx + c = 0, the sum of roots = -b/a and their product = c / a.
So here we have:
Sum of the roots:
a + 2a = -6/1 = -6
Product of the roots = 2a^2 = 2p/1 = 2p..
So 3a = -6 and
a = -2.
and
2(-2)^2 = 2p
8 = 2p
p = (-2)^2 = 4.
Answer:
see explanation
Step-by-step explanation:
Since x = a and x = 2a are roots, then substitute these values into the equation.
x = a
a² + 2(3a + p) = 0, that is
a² + 6a + 2p = 0 → (1)
x = 2a
(2a)² + 2(3(2a) + p) = 0
4a² + 12a + 2p = 0 → (2)
Solving simultaneously
Subtract (1) from (2) term by term to eliminate p
3a² + 6a = 0 ← in standard form
3a(a + 2) = 0 ← in factored form
Equate each factor to zero and solve for a
3a = 0 ⇒ a = 0
a + 2 = 0 ⇒ a = - 2
Since a ≠ 0 then a = - 2
Substitute a = - 2 into either of the 2 equations and solve for p
substituting into (1)
(- 2)² + 6(- 2) + 2p = 0
4 - 12 + 2p = 0
- 8 + 2p = 0 ( add 8 to both sides )
2p = 8 ( divide both sides by 2 )
p = 4
Thus a = - 2 and p = 4
--------------------------------------------
a + 1 = - 2 + 1 = - 1
a - 5 = - 2 - 5 = - 7
If x = - 1 and x = - 7 are roots then the corresponding factors are
(x + 1) and (x + 7) and the quadratic equation is the product of the factors, that is
(x + 1)(x + 7) = 0 ← expand left side using FOIL
x² + 8x + 7 = 0
If the radius is 11 mm, what is the height? Round the answer to the nearest tenth of a millimeter. 3.8 mm 3.8 mm3 14.7 mm 14.7 mm3
Answer: the answer is C. 14.7 mm
Step-by-step explanation:
Just took the quiz :)
Answer:
It's 14.7
Step-by-step explanation:
I just did the assignment(:
A hair stylist offers haircuts and hair coloring to his customers. A haircut costs $18 and hair coloring costs $42. Yesterday, the hair stylist had 12 customers and earned a total of $288. How many of the hair stylists customers received hair coloring yesterday
Answer:
haircut =9 and hair color= 3
Step-by-step explanation:
Step one:
GIven data
let the haircut be x
and hair color be y in numbers.
so
18x+42y=288------------1
x+y=12---------------------2
from 1
x=12-y, put this in 2, we have
18(12-y)+42y=288
216-18y+42y=288
collect like terms
24y=288-216
24y=72
divide both sides by 24
y=72/24
y=3
put y= 3 in 2
x+3= 12
x= 12-3
x=9
A ship travels 60 miles in the direction S 45° E, then travels 150 miles in the direction S 20° W. What is the distance, x, from the starting location?
Answer:
183.6 miles
Step-by-step explanation:
Kindly check the picture attached for the solution diagram
Using the cosine formula (Diagram has two sides and an included angle)
x² = y² + z² - 2zy * cosX
x² = 150² + 60² - 2(150*60) * cos115
x² = 22500 + 3600 - 18000 * −0.422618
x² = 22500 + 3600 + 7607.1287
x² = 33707.128 miles
x = √33707.128
x = 183.59501
x = 183.6 miles
Answer:
D
Step-by-step explanation:
183.60
Mr. Gregson packs ornaments into boxes. Each box holds eight ornaments. Which representation displays the relationship between x, the number of boxes packed, and y, the number of ornaments packed?
Answer:
y = 8x
Step-by-step explanation:
Given that :
Ornanment are packed in boxes
Number of ornament per box = 8
x = number of boxes packed
y = Number of ornaments
Number of Ornanments packed = (Number ornaments per box * number of boxes packed
y = 8 * x
y = 8x
Please help me !!! It’s due at 11:59pm
Answer:
it has to be 77.7
Step-by-step explanation:
Find question Mark then solve x
9/x = x/9
The answer is =9
Dave worked 3 1/2 hours at his grandpas farm. He was paid $12 for every 1/4 hour he worked. How much money did Dave make?
Answer: 56
Step-by-step explanation:
V = BH - 5
How do I solve for b in this equation
Answer:
[tex]B=\frac{V+5}{H}[/tex]
Step-by-step explanation:
Add 5 to both sides:
V+5=BH
Divide both sides by H:
[tex]B=\frac{V+5}{H}[/tex]
Which of the following are composite numbers check all that are true
Answer:
33, 49, and 21.
Step-by-step explanation:
its 33, 49, and 21
hope this helps
if 3 is related to 4 then 8 is related to
Answer:
9 most likely
Step-by-step explanation:
This is because 3 is one away from 4, so 8 is one away from 9.
Answer:
The answer is 9.
Step-by-step explanation:
3 Relates To 4.
8 Relates To 9.
WILL GIVE BRAINLIEST!!!!!!!!!!
A sandcastle can be modeled with four 6-inch-tall square prisms, one on top of the other, as shown in the figure below.
The base of the bottom prism has a side length of 30 inches, and the base of each of the other three prisms has a side length 7 inches less than the side length of the base of the prism below it. What is the volume of the sand castle?
Answer:
A 2808
Step-by-step explanation:
From top to bottom
The top one is 9
Second layer is 16
Third is 23
Bottom is 30
I did 9 x 6, 16 x 6, 23 x 6, 30 x 6 = 54, 96, 138, 180
Added all of them up and got 468 then I times it by 6 and got 2808
Heyo! ;D
The volume of the sandcastle above is 10,596 cubic inches.
Hope this helped! If so, please lmk! Tysm and good luck!
SOMEONE PLEASE HELP ME IM STRESSED OUT ILL GIVE OUT BRAINLIEST PLEASE DON’T ANSWER IF YOU DON’T KNOW THANK YOU
Answer:
2$
Step-by-step explanation:
16$ times 5 = 80
80 divided by 40 =2
Answer:
$2
Step-by-step explanation:
HELP ME!!!!!!!! Which choice represents the fraction below as a single exponential expression? This is unit is The Division Law of Exponents.
1 1/2 + 3 2/3 + 1 7/9
Answer:
125/18
Step-by-step explanation:
1 1/2+ 3 2/3+ 1 7/9 =125/18
Answer: 125/18
Step-by-step explanation:
10) Stan has $55. He wants to buy a belt that costs $14 and some T–shirts that cost $9 each. How many T–shirts can he buy?
a) Let n represent the number of T–shirts and translate into an inequality. b) How many T–shirts can he buy?
Answer:
4 T- shirts
Step-by-step explanation:
55- 14 = 41
41$ left and each T- shirt is 9$
count by 9s until you reach 41
9, 18, 27, 36 , 45
36 is the highest
A football team won 75% of 60 games in a season. How many games did they win?
Answer:45 games
Step-by-step explanation: 1+1 is 2 so yeah
Answer:
I think its 45 games
Step-by-step explanation:
75% times 60 = 45
*My school in middle school was rushed about math when we learned percent. Like the teachers were talking so fast, sorry if I'm wrong. <--- reason if I'm wrong.
Herman is decorating his bedroom ceiling with lights. If the rectangular ceiling is 15 meters by 8 meters, how long will the string of lights need to be to reach from one corner of the ceiling to the opposite corner?
Answer:
x = 17 m
Step-by-step explanation:
The dimensions of the rectangular ceiling are 15 m by 8 m
We need to find the length of the string of lights need to be to reach from one corner of the ceiling to the opposite corner. Let it is x.
We need to find the diagonal of the rectangular ceiling. It can be calculated using Pythagoras theorem.
[tex]x^2=15^2+8^2\\\\x^2=225+64\\\\x^2=289\\\\x=\sqrt{289}\\\\x=17\ m[/tex]
So, the length of the string of lights is 17 m.
2. Simplify the following fraction:
*
23
4
x^5 + ax^3 + bx^2 - 3 = (x^2 - 1)Q(x) - x - 2
find the value of a and b?
9514 1404 393
Answer:
a = -2b = 1Step-by-step explanation:
Subtracting the remainder from the original polynomial gives a polynomial that has (x^2 -1) as a factor. Dividing, we find the quotient and remainder to be ...
(x^5 +ax^3 +bx^2 +x -1)/(x^2 -1) = (x^3 +(1+a)x +b) remainder (2+a)x +(b -1)
Since we want the remainder to be zero, we require ...
2+a = 0 ⇒ a = -2
b -1 = 0 ⇒ b = 1
_____
The attachment shows the division as given in the problem statement (with the given remainder expression).
PLEASE HELP I WILL GIVE BRAINLIEST!
The coordinates of three corners of a square are (1, 7), (5, 3), and (9, 7). What are the coordinates of the fourth corner of the square?
A.
(5, 7)
B.
(5, 11)
C.
(9, 1)
D.
(13, 3)
Answer:
i think d is the correct one
Answer:
It's be 5,11
Step-by-step explanation:
[Function Composition] could someone help me with this answers or show work either is fine
Answer:
(f ￮ g)(8) = - 6
Step-by-step explanation:
Evaluate g(8), then substitute the value obtained into f(n)
g(8) = 8 - 2 = 6 , then
f(6) = - 6
Answer:
-62
Step-by-step explanation:
Two functions are given to us , which are ,
[tex]\bf\implies f(n)= -n \\\\\bf\implies g(n)= n - 2 [/tex]
We need to find , ( f • g )(8) . So ,
⇒ ( f • g) = - n ( n - 2 )
⇒ ( f • g) = -n² + 2
⇒ (f • g) = 2 - n²
==================================
Substituting n = 8 :-
⇒ ( f • g)(n) = 2 - n²
⇒ ( f • g)(8) = 2 - 8²
⇒ (f • g)(8) = 2 - 64
⇒ ( f • g)(8) = -62 .
Hence the required answer is (-62) .Two bags contain marbles. Bag A contains 112 marbles, and Bag B contains 140 marbles. What percent fewer marbles does Bag A have than Bag B?
Answer:
20%
Step-by-step explanation:
sorry if i am wrong
In a jar of blue and red marbles the ratio of blue marbles to red marbles is 5 to 3 there are 320 marbles in the jar how many red marbles are in the jar
Answer:
120 red marbles
Step-by-step explanation:
5 to 3 gives a total of 8
let x = # red marbles
3 = x
8 320
8x = 960
x = 120
Complete the following problems. It is over everything we've done the last few days. Take your time.
Make sure you insert your equation when having to write equations.
Question 3
5 pts
In 2015, 2200 students attended Polaris High School. The enrollment has been
declining 2% annually. If this trend continues, estimate how many students will be
enrolled in 2030.(Remember it is people that you have.)
Answer:
Welcome to Gboard clipboard, any text you copy will be saved here.
A group of friends wants to go to the amusement park. They have $94.25 to spend on parking and admission. Parking is $14.75, and tickets cost $13.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer: 6
Step-by-step explanation:
From the question, we are informed that a group of friends wants to go to the amusement park and that they have $94.25 to spend on parking and admission.
We are further told that Parking is $14.75, and tickets cost $13.25 per person, including tax. The equation that can be used to solve the number of people who can go to the amusement park would be:
= 14.75 + 13.25p
Since they've $94.25 to spend, the number of people that can go to the amusement park will be:
14.75 + 13.25p = 94.25
13.25p = 94.25 - 14.75
13.25p = 79.50
p = 79.50 / 13.25
p = 6
6 people can go to the amusement park
In March, you have $220 in your savings account. By the end of April, your savings have increased by 30%. How much money do you have in your savings account at the end of April?
Answer:
$286
Step-by-step explanation:
220:100=2.2
2.2 x 30 = 66
220+66=286
Anybody wanna help volunteer?
0.002347 written to three significant figures is
Answer:0.00234
Step-by-step explanation:
2 lb of grass seed will cover 50 square feet of a yard how many square feet will 5 lb of grass seed cover
Answer:
125 square feet of a yard.
Step-by-step explanation:
So 1 lb of grass seed will fill 25 square feet of yard. Multiply 25 by 5 and get 125.