Answer:
The roots are real.
Step-by-step explanation:
Given quadratic equation to us is 4x² -4x -19 = 0.
With respect to Standard form ax² +bx +c = 0 , Discriminant of the quadratic equation is given by b² - 4ac . Here's a table for Nature of Roots .
[tex]\boxed{\begin{array}{|r|r|r|} \underline{\red{\bf S.no.}} & \underline{\red{\bf Condition }} & \underline{\red{\bf Nature \ of \ Roots }} \\\\ \sf 1 & \sf Discriminant > 0 & \sf Real \:Roots \\\\ \sf 2 &\sf Discriminant = 0 &\sf Equal \:Roots \\\\ \sf 3 & \sf Discriminant < 0 &\sf Complex \: Roots \end{array} }[/tex]
Hence here , wrt Standard form ,
• a = 4 , • b = -4 & •c = -19 .
[tex]\implies Discriminant = b^2-4ac \\\\\implies Discriminant = (-4)^2-4(4)(-19) \\\\\implies Discriminant = 16+304 \\\\\boxed{\red{\bf \implies Discriminant = 320 }}[/tex]
Hence since Discriminant is Greater than 0 , hence the nature of roots of the quadratic equation is real.
A fast food restaurant sells milkshake in a container composed of a cylinder with a radius of 2 inches and a height of 3 inches surmounted by a hemispherical top of a radius 2 inches.
a.) Compute the volume of milkshake that it contains
b.) Compute the surface area of the container
Answer:
Below in bold.
Step-by-step explanation:
(a) Volume = volume of the cylinder + volume of hemisphere
= pi r^2 h + 1/2 * 4/3 pi r^3
= pi 2^2 3 + 2/3 pi 2^3
= 12pi + 16pi/3
= 52pi/3
= 52pi/3 in^3
= 54.45 in^3 to nearest hundredth.
(b) Surface area = area of base + area of curved part + area of the hemisphere
= pi 2^2 + 3 * 2pi 2 + 2 pi 2^2
= 4pi + 8 pi + 12pi
= 24pi in^2
= 75.40 to nearest hundredth.
evaluate the following given f(x)=3x-7 find x when f(x)=17
Answer:
When f(x) equals 17, x is equal to 8.
Step-by-step explanation:
[tex]f(x) = 3x - 7\\17 = 3x - 7\\3x = 17 + 7\\3x = 24\\x = 24/3\\x = 8[/tex]
Could I get some help it’s important
Answer: yo plug it into desmos its ez
Step-by-step explanation:
Answer:
plot a point at (0,-7) and plot a point at (1, -4). Draw a line through those points.
Step-by-step explanation:
The equation tells you that your y intercept will be negative 7. The 3x means that your slope will be equal to up 3, and over 1 (or 3/1, which is equal to 3.)
Find the area. Round to the nearest hundredth if necessary
kill meStep-by-step explanation:
Answer:
8,667.14
Step-by-step explanation:
1. Multiply 29.1 by 20.4 = 593.64
2. Multiply 593.64 by 14.6 = 8,667.14
A flower bed has the shape of a rectangle 7 yards long and 4 yards wide. What is it’s area in square feet
Answer: 252 square feet
Step-by-step explanation:
lets remember that 1 yard= 3 feet
7 yards= 7*3=21 feet
4 yards= 4*3=12 feet
we know that area of a rectangle= LxW
21 x 12= 252 square feet
Wayne painted 1/8 of the walls in his bedroom on Monday. He painted 1/2 of the walls of his bedroom on Tuesday and 1/4 of the walls on Wednesday. What fraction of the bedroom still remains to be painted?
Answer:
1/8
Step-by-step explanation:
1/8 + 1/2 + 1/4 = 1/8 + 4/8 + 2/8 = 7/8
so 1/8 remains
Solve for x. Enter the solutions from least to greatest.
(x + 7)^2 - 49 = 0
Answer:
x = -14, 0
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Completing the SquareMultiple Roots/SolutionsStep-by-step explanation:
Step 1: Define
(x + 7)² - 49 = 0
Step 2: Solve for x
Add 49 to both sides: (x + 7)² = 49Square root both sides: x + 7 = ±7Subtract 7 on both sides: x = -7 ± 7Evaluate: x = -14, 0Step 3: Check
Plug in x values into original equation to verify they are a solution.
x = -14
Substitute in x: (-14 + 7)² - 49 = 0Add: (-7)² - 49 = 0Exponents: 49 - 49 = 0Subtract: 0 = 0Here we see that 0 does indeed equal 0.
∴ x = -14 is a solution of the equation
x = 0
Substitute in x: (0 + 7)² - 49 = 0Add: 7² - 49 = 0Exponents: 49 - 49 = 0Subtract: 0 = 0Here we see that 0 does indeed equal 0.
∴ x = 0 is also a solution of the equation.
Answer:
Lesser x=-14 Greater x=0
Step-by-step explanation:
x+7)
2
−49
(x+7)
2
(x+7)
2
=0
=49
=
49
Hint #22 / 3
\begin{aligned} x+7&=\pm7 \\\\ x&=\pm7-7 \\ \phantom{(x + 7)^2 - 49}& \\ x=-14&\text{ or }x=0 \end{aligned}
x+7
x
(x+7)
2
−49
x=−14
=±7
=±7−7
or x=0
Carol bought 24 stamps for $6, and Charles paid $13 for 52 stamps. If the amount paid for the stamps is proportional to the number of stamps bought, then what is the constant of proportionality?
HELP !!
Answer:
Yes
Step-by-step explanation:
$24 divided by 6 equals 4
$52 divided by 13 equals 4
For what value of k will the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent?
Answer:
After solve the equations we get value of k=3
Step-by-step explanation:
We need to find value of k for which the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent.
If the lines are concurrent, they pass through same point.
Let:
[tex]x+2y=0--eq(1)\\ 3x-4y-10=0--eq(2)\\ 5x+ky-7=0--eq(3)[/tex]
First solving equation 1 and 2 to find values of x and y
From eq(1) we find value of x and put it in eq(2)
[tex]From \ eq(1) x+2y=0\\x=-2y\\Put x=-2y \ in \ eq(2)\\3x-4y-10=0\\3(-2y)-4y-10=0 \\-6y-4y=10\\-10y=10\\y=\frac{10}{-10}\\y=-1[/tex]
After solving we get value of y=-1
Now putting in eq(1) to get value of x
[tex]x+2y=0\\x+2(-1)=0\\x-2=0\\x=2[/tex]
So, Value of x= 2
Now put value of x=2 and y=-1 into eq(3) to find value of k
[tex]5x+ky-7=0\\5(2)+k(-1)-7=0\\10-k-7=0\\-k+3=0\\-k=-3\\k=3[/tex]
So, After solve the equations we get value of k=3
HELP HELP HELP PLEASSSEEEE!!!!!!! THIS IS MAKING MY MIND GO NUTS!
Answer:
2.5 hours
Step-by-step explanation:
They are 22.5 miles apart. Chase is going 6 mph and Jada is going 3 mph.
6 × 2 = 12
6 × 0.5 = 3
12 + 3 = 15 miles
3 × 2 = 6
3 × 0.5 = 1.5
6 + 1.5 = 7.5 miles
15 + 7.5 = 22.5 miles
It would take them 2.5 hours to reach each other.
Hope that helps.
6/5 s = −2
solve for (s)
simplify the fraction 2/6
2/6
Reducing is another word simplify
Divide by 2 for the numerator and denominator
2/2= 1
2/6= 3
Answer : 1/3
$210 watch; 20% discount
Answer:
$168
Step-by-step explanation:
Answer:
20% = 0.20
0.20 x 210 = $42
$42 discount
210 - 42 = 168
Your total amount you would pay would be $168. The discount is $48.
(7 - 3t) + 3(-2t + 5)
Answer:
22-9t
Step-by-step explanation:
(7 - 3t) + 3(-2t + 5)
=
7+−3t+(3)(−2t)+(3)(5)=
7+−3t+−6t+15
=
Now you need to combine like terms.
7+−3t+−6t+15
=
(−3t+−6t)+(7+15)=
-9t+22=
22-9t
There you go.
Answer:
22 - 9t
Step-by-step explanation:
(7 - 3t) + 3(-2t + 5)
7 - 3t + -6t + 15
7 - 9t + 15
22 - 9t
5
2
A line passes through the point (-10, 8) and has a slope of
Answer:
you need more than one point to find the slope of a line?
Step-by-step explanation:
100 points. Function fis a quadratic function passing through the points (-4,0), (0, -12) Function gis modeled by the graph.
Answer:
Open points on 1 and 3 with ray connecting.
Step-by-step explanation:
Because it's right.
From the graph of the function |(f)| and |(g)|, the interval at which both functions are negative are 1 and 3.
What is a quadratic function?A quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the graph of a quadratic function is parabolic because it is u-shaped. From the graph of the function |(f)| and |(g)|, we can deduce that the interval at which both functions are negative are 1 and 3 as shown in the image attached below.
Read more on functions here: https://brainly.com/question/4246058
#SPJ2
the picture is below
Answer:
b, c, e
Step-by-step explanation:
50 points.........
A dolphin jumps from the water with an initial velocity of 44 feet per second at an elevation angle of 60°. Which parametric equations model the dolphin’s path through the air?
x(t) = sin(60°)t + 44 and y(t) = –16t2 + cos(60°)t + 44
x(t) = cos(60°)t + 44 and y(t) = –16t2 + sin(60°)t + 44
x(t) = 44sin(60°)t and y(t) = –16t2 + 44cos(60°)t
x(t) = 44cos(60°)t and y(t) = –16t2 + 44sin(60°)t
Answer:
B
Step-by-step explanation:
For your question: A dolphin jumps from the water with an initial velocity of 44 feet per second at an elevation angle of 60°. Which parametric equations model the dolphin’s path through the air?
After doing the math in my notebook, I got the answer D.
Please let me know if you have any other questions down below.
2. At 2:30 am the temperature in New York is 3F. The temperature drops 3/4 of a degree in 30
minutes.
What is the temperature in New York at 3:00 am?
Answer:
2.25 F
Step-by-step explanation:
I subtracted 3/4 from 3.
Hope this helped.
-Pepsi
quiz 4-1 : classifying and solving for sides/angles in triangles gina wilson (all things algebra) URGENT
Answer:
14.
[tex]x = 11[/tex] [tex]m<B = 108[/tex] [tex]m<C= 36[/tex] [tex]m<D = 36[/tex]
15.
[tex]x = 4[/tex] [tex]WX = 25[/tex] [tex]XY = 17[/tex] [tex]WY = 25[/tex]
Step-by-step explanation:
Solving (14):
[tex]BC = BD[/tex]
[tex]m<B = 13x - 35[/tex]
[tex]m<C = 5x - 19[/tex]
[tex]m<D = 2x + 14[/tex]
First, we solve for x.
Since sides [tex]BC = BD[/tex], then
[tex]m<C = m<D[/tex]
This is so because the theorem of ASA (Angle-Side-Angle)
So, we have:
[tex]5x - 19 = 2x + 14[/tex]
Collect Like Terms
[tex]5x - 2x = 19 + 14[/tex]
[tex]3x = 33[/tex]
Divide both sides by 3
[tex]x = 11[/tex]
Solving for m<B, m<C and m<D.
We simply substitute 11 for x in their respective expressions.
[tex]m<B = 13x - 35[/tex]
[tex]m<B = 13*11 - 35[/tex]
[tex]m<B = 143 - 35[/tex]
[tex]m<B = 108[/tex]
[tex]m<C = 5x - 19[/tex]
[tex]m<C= 5*11 - 19[/tex]
[tex]m<C= 55 - 19[/tex]
[tex]m<C= 36[/tex]
[tex]m<D = 2x + 14[/tex]
[tex]m<D = 2*11 + 14[/tex]
[tex]m<D = 22 + 14[/tex]
[tex]m<D = 36[/tex]
Solving (15):
[tex]<X = <Y[/tex]
[tex]WX = 9x - 11[/tex]
[tex]XY = 4x + 1[/tex]
[tex]WY = 7x - 3[/tex]
First, we solve for x.
Since [tex]<X = <Y[/tex], then
[tex]WX = WY[/tex]
This is so because the theorem of SAS (Side-Angle-Side)
So, we have:
[tex]9x - 11 = 7x - 3[/tex]
Collect Like Terms
[tex]9x - 7x = 11-3[/tex]
[tex]2x = 8[/tex]
Divide both sides by 2
[tex]x = 4[/tex]
Solving for WX, WY and XY
We simply substitute 4 for x in their respective expressions.
[tex]WX = 9x - 11[/tex]
[tex]WX = 9 * 4 - 11[/tex]
[tex]WX = 36 - 11[/tex]
[tex]WX = 25[/tex]
[tex]XY = 4x + 1[/tex]
[tex]XY = 4 * 4 + 1[/tex]
[tex]XY = 16 + 1[/tex]
[tex]XY = 17[/tex]
[tex]WY = 7x - 3[/tex]
[tex]WY = 7 * 4 - 3[/tex]
[tex]WY = 28 - 3[/tex]
[tex]WY = 25[/tex]
please help with question. The answer choices are:
14
8
5
22
Answer:
14
Step-by-step explanation:
If AC = 24, you just have to subtract AB = 10 from AC to find BC.
24 - 10 = 14
Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a 15\%15%15, percent tip.What is her total bill including tip?
Answer:
$51.75
Step-by-step explanation:
The meal cost $45. $45 is 100% of the cost. She wants to leave a 15% tip, so add 15% to 100%.
15% + 100% = 115%
She will pay 115% of $45.
115% of $45 = 1.15 * $45 = $51.75
8. If a runner’s power is 400 W as she runs, how much chemical energy does she convert into other forms in 10.0 minutes? E = P X t
Answer:
2400kJ
Step-by-step explanation:
Step one:
given data
power P= 400W
time = 10minutes
to seconds= 60*10 = 600 seconds
Required
the energy
Step two:
we know that Energy= power * time
E=P*t
E=400*600
E=240000
E=2400kJ
She converts 2400kJ into other forms
A sports equipment store rents road bikes for $23 an hour.
Over the summer, these bikes were rented for a total of
1,080 hours. How much money did the store make renting bikes?
Answer:
$24,840
Step-by-step explanation:
Please mark brainliest.
3 6/12 +4 1/2 tell me what it is
Answer:
8
Step-by-step explanation:
3 + 4 = 7
6/12 + 1/2 = 1
7+1 = 8
PLEASE HELP FAST Two identical buildings are 38.7 m apart. From her balcony, Kudo notices that the angle of the elevation to the top of the adjacent is 52 The angle of the depression to the base of the building is 21 find the height of the building to the nearest hundredth of a metre check the picture
Answer: 41.3m
Step-by-step explanation: Hope this helps
HURRY ANSWER THIS IM BEING TIMED
Answer:
D
Step-by-step explanation:
10(4 - 7)/-(4 - 1)
40-70/-4+1
-30/-3
=10
Every integer is a __________ number.
A. natural
B. rational
C. negative
D. whole
Answer:
B. rational
Explanation:
Every integer is a rational number since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number.
Find all solutions in the interval [0, 2π) for 2 sin^2 x = sin x
Option A: x = pi divided by three., two pi divided by three.
Option B: x = pi divided by two, three pi divided by two., pi divided by three., two pi divided by three.
Option C: x = 0, π, pi divided by six, five pi divided by six
Option D: x = pi divided by six, five pi divided by six
(Will mark brainliest)
Answer:
D
Step-by-step explanation:
2 sin²x=sin x
2 sin² x-sin x=0
sin x(2 sin x-1)=0
sin x=0
x=0,π
2 sin x-1=0
2 sin x=1
sin x=1/2= sin π/6,sin (π-π/6)
x=π/6,5π/6
Acellus help slope intercept
Greetings.
The answer is y = 2x + 7.
Explanation:
If you are an expert in graph then you are able to find the slope without calculating. (Rise over Run by looking at the graph.)
We can also find the slope by calculating m-value.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] ---> Rise Over Run
But how are we gonna calculate if we don't have any two given ordered pairs?
The answer is, we can just pick two ordered pairs that are part of the graph, or rather say that the graph passes through.
The graph passes through (-3,1) and (-2,3).
Then we can calculate the slope by using rise/run.
[tex]m=\frac{3-1}{-2-(-3)}\\m=\frac{2}{-2+3}\\m=\frac{2}{1}\\m=2[/tex]
Thus, the slope is m = 2.
However, we are not done yet. We just only found out the slope. We need to find the y-intercept too.
From Linear Function - [tex]y=mx+b[/tex]
Where m = slope and b = y-intercept.
Since b = y-intercept, we don't need to calculate/substitute x = 0. We simply find which number the graph has y-intercept at.
Which is (0,7), the y-intercept.
Then we substitute b = 7 as y-intercept.
Thus the answer is [tex]y=2x+7[/tex]