Here all the given equations are in the form of
[tex]ax^2+bx+c=0[/tex]
The value of [tex]x[/tex] can be determined by the perfect square method as follows:
[tex]ax^2+bx+c=0[/tex]
[tex]\Rightarrow x^2+\frac{b}{a}+\frac{c}{a}=0[/tex]
[tex]\Rightarrow x^2+2\times\frac{b}{2a}+\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2+\frac{c}{a}=0[/tex]
[tex]\Rightarrow \left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}[/tex]
[tex]\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\;\cdots(i)[/tex]
Now, for [tex]x^2+3x-4=0[/tex]
[tex]a=1, b=3, c=-4[/tex]
So, from equation (i)
[tex]x=\frac{-3\pm\sqrt{3^2-4\times1\times(-4)}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{3\pm\sqrt{9+16}}{2}[/tex]
[tex]\Rightarrow x=\frac{3\pm5}{2}[/tex]
[tex]\Rightarrow x=\frac{3+5}{2},\frac{3-5}{2}[/tex]
[tex]\Rightarrow x= 4, -1[/tex]
Similarly, for [tex]9x^2+12x+4=0[/tex]
[tex]a=9, b=12, c=4[/tex]
So, from equation (i)
[tex]x=\frac{-12\pm\sqrt{12^2-4\times9\times4}}{2\times9}[/tex]
[tex]\Rightarrow x=\frac{-12\pm0}{18}[/tex]
[tex]\Rightarrow x=\frac{-2}{3}[/tex]
For [tex]x^2-2x-3=0[/tex]
[tex]a=1, b=-2, c=-3[/tex]
[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-3)}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{2\pm\sqrt{16}}{2}[/tex]
[tex]\Rightarrow x=\frac{2\pm4}{2}[/tex]
[tex]\Rightarrow x=\frac{6}{2},\frac{-2}{2}[/tex]
[tex]\Rightarrow x=3.00, -1.00[/tex]
For [tex]x^2-6x+9=0[/tex]
[tex]a=1, b=-6, c=9[/tex]
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times9}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{6\pm0}{2}[/tex]
[tex]\Rightarrow x=3.00[/tex]
For [tex]2x^2-4x-3=0[/tex]
[tex]a=2, b=-4, c=-3[/tex]
[tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-3)}}{2\times2}[/tex]
[tex]\Rightarrow x=\frac{4\pm\sqrt{40}}{4}[/tex]
[tex]\Rightarrow x=\frac{4\pm2\sqrt{10}}{4}[/tex]
[tex]\Rightarrow x=\frac{4+2\sqrt{10}}{4},\frac{4-2\sqrt{10}}{4}[/tex]
[tex]\Rightarrow x=2.58, -0.58[/tex]
The Hudson family went out to dinner. The meal cost $49.50.
If they also left a 15% tip, approximately how much did the entire dinner cost?
O $7.43
$49.50
O $56.93
O $61.24
Answer:
The tip is $7.43
The total answer $56.93
Step-by-step explanation:
Hope this helps!
Answer:
c 56.93
Step-by-step explanation:
49.5 × 1.15= 56.93
The Frosty Ice-Cream Shop sells sundaes for $4 and banana splits for $6. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $182. How many sundaes did they sell?
Answer:
23
Step-by-step explanation:
Answer:
They sold 48 sundaes.
Step-by-step explanation:
What is the slope of the line that passes through points (-6,-7) and (-24,-7) . Write your answer in the simplest form
Answer:
The slope of the line passing through both points is 0
Step-by-step explanation:
Mathematically, we can calculate the slope as follows;
m = (y2-y1)/(x2-x1)
where (x1,y1) = (-6,-7)
(x2,y2) = (-24,-7)
Thus m = (-7 -(-7))/(-24 + 6) = 0/18 = 0
The slope of both is 0
The University of Central Florida’s cheerleading team has eighteen males and twenty-one females. If h represents the height of a team member, the inequality 260 ≤ 4h + 28 < 324, represents the range of heights of the cheerleaders, in inches. Select all possible heights for the University of Central Florida’s cheerleaders.
Group of answer choices
6 feet, 2 inches
5 feet, 11 inches
5 feet, 3 inches
4 feet, 9 inches
5 feet, 8 inches
5 feet, 4 inches
4 feet, 10 inches
Answer:
5ft 11 inches , 5 feet 3 inches , 5 ft. and 8 in
Step-by-step explanation:
I think this is right . Plus if it isn't at least some are right so you can correct your answer. And anyway you should know this if they taught you this sin class
The possible heights for the University of Central Florida’s cheerleaders is:
5 feet, 11 inches
5 feet, 3 inches
4 feet, 9 inches
5 feet, 8 inches
Let h represents the height of a team member.
Since the height of a team member is given by the inequality 260 ≤ 4h + 28 < 324, hence:
260 ≤ 4h + 28 or 4h + 28 < 324
4h + 28 ≥ 260 or 4h + 28 < 324
4h ≥ 232 or 4h < 296
h ≥ 58 inches or h < 74 inches
Therefore the height of the team member is at least 58 inches (4 feet 10 inches) and less than 74 inches (6 feet 2 inches)
The possible heights for the University of Central Florida’s cheerleaders is:
5 feet, 11 inches
5 feet, 3 inches
4 feet, 9 inches
5 feet, 8 inches
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A rental company rents a luxury car at a daily rate of 39.11 $ plus $.50 per mile. Is allotted100 $ for car rental each day. Write an equation to represent the cost C of renting a c ar and driving x miles. How many miles can travel on the 100$?
Answer:
- The equation that represent the cost C of renting a car and driving x miles is C = $39.11 + $0.50x
- $100 can travel 121.78 miles
Step-by-step explanation:
From the question, a rental company rents a luxury car at a daily rate of 39.11 $ plus $.50 per mile, that is
$0.50 is added to the initial $39.11 for every mile.
The equation that represent the cost C of renting a car and driving x miles is
C = $39.11 + $0.50x
Now, to determine how many miles 100$ can travel,
we will put C = $100, and determine x in the above equation
$100 = $39.11 + $0.50x
$100 - $39.11 = $0.50x
$60.89 = $0.50x
x = $60.89/$0.50
x = 121.78
Hence, $100 can travel 121.78 miles
Help ! What’s the answer?
Answer:
48 feet
Step-by-step explanation:
6 feet wide
3 times as long as it's wide (width) = 6×3 = 18
18 + 6 + 18 + 6
= 24 + 24
= 48 feet
Describe the graph of the inequality x > -1.
Answer:
See below
Step-by-step explanation:
Given
Inequality x > -1This inequality covers the interval greater than - 1
( - 1, + oo)Its graph covers the space to the right from the point -1
The vertical line - 1 is a dotted line as - 1 is nor included
A store sells a 33-pound bag of oranges for \$ 3.60$3.60 and a 55-pound bag of oranges for \$ 5.25$5.25. What is the difference between the price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges?
Answer:
0.01364
Step-by-step explanation:
It is given that,
A store sells a 33-pound bag of oranges for $3.60 and a 55-pound bag of oranges for $5.25.
Price per pound of 33 pound bag is 3.60/33 = 0.10909 price per pound
Price per pound of 55 pound bag of oranges is 5.25/55 = 0.09545 price per pound
Difference between price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges is :
D = 0.10909 - 0.09545
D = 0.01364
Therefore, this is the required solution.
Three times the sum of twice n and 6 is the same as the product of four and n less 2. Find n
Answer:
n=12
Step-by-step explanation:
Gabby says that 8 is a common multiple of 16 and 24. Mark says that 8 is a common factor of 16 and 24. Who is correct?
Answer:
gabby is correct
Step-by-step explanation:
simplify 18 over 3/4
Answer:
What is 18/4 Simplified? - 9/2 is the simplified fraction for 18/4.
Step-by-step explanation:
Answer:
- 9/2
Step-by-step explanation:
HELPPPPPP PLZZ!!!!!!!
Answer:
B and E i think
Step-by-step explanation:
Find f(-1) if f(x)=3x^3 + 5x^2
Answer:
2
Step-by-step explanation:
f(x) = 3x^3 + 5x^2
f(-1)
so just substitute in the value -1 for x, and solve
f(-1) = 3(-1)^3 + 5(-1)^2
= 3 * -1 + 5 *1
= -3 + 5
= 2
The distance, D, travelled by a particle is directly proportional to the square of the time, t, taken. When t = 40, D = 30. find a formula for D in terms of t. Calculate the value of D when t = 64
Answer:
The formula for D in terms of t is D=0.01875t²
The value of D is 76.8
Step-by-step explanation:
See above for an image
Hope I helped!
After calculating by definition of proportionality, the value of D is 76.8
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The distance, D, travelled by a particle is directly proportional to the square of the time, t.
So, We can defined as;
⇒ D = k × t²
Where, 'k' is constant of proportion.
Here, When t = 40, D = 30,
⇒ D = k × t²
⇒ 30 = k × 40²
⇒ 30 = k × 1600
⇒ k = 30 / 1600
⇒ k = 3/160
So, When t = 64, the value of D is,
⇒ D = 3/160 × 64²
⇒ D = 76.8
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QUESTION 7, Saturday, October 10th, 2020
I have some geometry questions today. Please include your thoughts or reasoning with your answer. Please ignore the answer I selected for it was not an purpose. Thanks!
Answer:
DE≅JK
Step-by-step explanation:
already have aa need the side after or before the 2 angles
Answer:
DF≅JLStep-by-step explanation:
We have one side and one angle, need one more side such that the angle is between those sides. It will make SAS congruency
So required sides are
DF≅JLhelppp due in 21 mins
Answer:
Step-by-step explanation:
19. 12960
20. 6000
Solve: x/5 =10 can you help me solve that
Answer:
d
Step-by-step explanation:
10*5=50
could u vote me brainliest plz? thx :)
Answer:
50
Step-by-step explanation:
x/5 time 5 = 10 times 5
x = 50
If <3=50, then find the rest of the angles
-136 = 8(m - 1)
[tex] - 136 = 8(m - 1)[/tex]
There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white
Answer:
Finish the question
Step-by-step explanation:
Mr. Jones teaches 154 students in 7 classes. How many
students does he have per class? (per single class – unit
rate)
Please help mee
What is the slope of the line that passes through the points (-4,-2) and (-4,-22)
Answer:
It's a line parallel to the y-axis
Step-by-step explanation:
Note that the similar x value in both coordinates.
Then it's a line drawn parallel to the y-axis
Therefore, the slope is infinite as it makes a right angle with the x-axis.
A teacher has gallon of water. He pours the water into 5 glasses for children. Each child receives the same amount of water. There is no water left over. How much water, in gallons, does each child receive?
Answer:
ok ok i dont get it
the teacher has 1 gallon of water
the kids get the same amount from that one gallon
now how many GALLONS do EACH child recieve?
thats messed up
find the mistakes
What is the rate of change of this table?
Answer:
- 6
Step-by-step explanation:
The rate of change of the values is the slope m
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 32) and (x₂, y₂ ) = (0, 20) ← 2 ordered pairs from the table
m = [tex]\frac{20-32}{0+2}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6 ← rate of change
Make a table of ordered pairs for the equation y=-1/3x+1
Answer:
(0, 1)
(3, 0)
(6, -1)
(9, -2)
Antoine made $33,284 last year. He received a 4.5% annual raise.What will his new salary before the coming year
Answer:
$34781
Step-by-step explanation:
Find each sum or difference
-1/2 + 1/3
Answer:
The answer is -1/6
Step-by-step explanation:
Answer:
Sum: -1/6
Difference: -5/6
Step-by-step explanation:
Solve the equation for a
5n + 34 = -2(1 - 7n)
a equals
Answer:
n = 4
Step-by-step explanation:
Where's a or did you mean n?
Answer:
n=4
Step-by-step explanation:
5n+34=-2(1-7n)
1. So first expand.
5n+34=−2+14n
2 Regroup terms.
5n+34=14n−2
3 Subtract 5n from both sides.
34=14n−2−5n
4 Simplify 14n-2-5n to 9n-2.
34=9n−2
5 Add 22 to both sides.
34+2=9n
6 Simplify 34+2 to 36.
36=9n
7 Divide both sides by 9.
36/9=9
8 Simplify 36/9 to 4
4=n
9 Switch sides.
n=4
Enter your responses in the blank.
T= 2x + 3y - 2
____=3y
- 2x = 3y - 2
____ = y
HELP PLEASE HAVING BAD DAY
Jasmine drives every morning to her office that is 12 miles from her home.
If Jasmine's average driving speed is s mph, how many hours does it take her to drive from her home to the office?
Answer:
I need to know how fast the driver is going
Step-by-step explanation:
Answer:
12/s
Step-by-step explanation:
