Answer:
The quadratic equation representing the area of the rectangular television screen is [tex]x^2 +24x-3456=0[/tex].
Height of the rectangular television screen [tex]=48[/tex] inches, and the width of the rectangular television screen [tex]= 72[/tex] inches.
Step-by-step explanation:
Given: The area of a rectangular television screen is [tex]3456\: in^{2}[/tex]. The width of the screen is [tex]24[/tex] inches longer than the height.
To find: The quadratic equation that represents the area of the screen, and what are the dimensions of the screen?
Solution:
Let the height of rectangular television screen be [tex]x[/tex] inches, then width of the rectangular screen be [tex](x+24)[/tex] inches.
Now, we know that area of a rectangle [tex]= \text{length}\times\text{width}[/tex].
As per question,
[tex]x(x+24)=3456[/tex]
[tex]\implies x^{2} +24x=3456[/tex]
[tex]\implies x^2+24x-3456=0[/tex]
So, the quadratic equation representing the area of the rectangular television screen is [tex]x^2 +24x-3456=0[/tex].
Now, to find the dimensions, we need to solve [tex]x^2 +24x-3456=0[/tex].
[tex]x^2 +24x-3456=0[/tex]
[tex]\implies x^2 -48x+72x-3456=0[/tex]
[tex]\implies x(x-48)+72(x-48)=0[/tex]
[tex]\implies (x-48)(x+72)=0[/tex]
[tex]\implies x-48=0[/tex] or [tex]x+72=0[/tex]
[tex]\implies x=48[/tex] or [tex]-72[/tex]
Since, [tex]x[/tex] is the height of the rectangular television screen, and height cannot be negative. So, height of the television is [tex]48[/tex] inches, and width of the television screen is [tex]48+24=72[/tex] inches.
Hence, the quadratic equation representing the area of the rectangular television screen is [tex]x^2 +24x-3456=0[/tex].
Height of the rectangular television screen [tex]=48[/tex] inches, and the width of the rectangular television screen [tex]= 72[/tex] inches.
Which ordered paur is a part of the equation? 3x-y=13
Answer:
(6,5), (3,-4) either one of those...
30 POINTS PLEASE HELP ME OUT
HELP ME PLEASE!!!!!!!!!!!
PLEASE HELP ME!! Graph the line, y+4=1/5(x-1)
Answer:
Look at picture attached
Step-by-step explanation:
I have created the graph on DESMOS. I recommend you use that website as it helps a lot with visualizing graphs :)
Edit: The second attachment shows the point you can plot.
Find the unknown side length. Write your answer in simplest radical form.
Answer: 1. x= 20 units, 2. x= [tex]5\sqrt{3}[/tex] units 3. x= [tex]4\sqrt{2}[/tex] units.
Step-by-step explanation:
In a right triangle,
[tex]Hypotenuse^2= Perpendicular^2+Base^2[/tex] (Pythagoras theorem)
1. Hypotenuse = x , Base = 16, Perpendicular = 12
[tex]\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20[/tex]
2. Hypotenuse = 14 , Base = 11, Perpendicular = x
[tex]\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}[/tex]
3. Hypotenuse = 9 , Base = x, Perpendicular =7
[tex]\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}[/tex]
A triangle has angles that measure 40° and 80°. What is the measure of the third angle of the triangle?
Enter the correct answer in the box. (Be sure to attach the degree symbol to your answer.)
Answer:
60°
Step-by-step explanation:
The sum of all three triangle angles add up to 180°. To solve for the last angle, add the sides you know together and subtract the sum from 180. This will leave you with the third angle's measurement,
40 + 80 = 120
180 - 120 = 60
The third angle of the triangle is 60°
What is a triangle?A polygon with three angles, side, and vertices is called a triangle.
Given that, a triangle has angles that measure 40° and 80°.
We know that the sum of the interior angles of a triangle is 180°
Let the third angle be x,
40° + 80° + x = 180°
x = 180°-120°
x = 60°
Hence, the third angle of the triangle is 60°
For more references on triangles, click;
https://brainly.com/question/2773823
#SPJ2
Please help and Imma be postin these all night I literally suck at algebra two so just check my profile if your good at math :)
Answer:
The range of the equation is y ≥ 9 ⇒ C
Step-by-step explanation:
The quadratic equation y = ax² + bx + c, represents by a parabola of vertex (h, k), where h = [tex]\frac{-b}{2a}[/tex] and k is the value of y at x = h
The range of the quadratic if it has a minimum vertex is y ≥ k, and y ≤ k if it has a maximum vertexThe parabola has a minimum vertex if the value of a is positive and a maximum vertex if the value of a is negative∵ The equation is y = x² + 9
→ Compare it with the form above to find a and b
∴ a = 1 and b = 0
∵ a is a positive number
∴ The parabola has a minimum vertex
→ By using the 1st rule above
∴ The range is y ≥ k
→ Use the rule of h above to find it
∵ h = [tex]\frac{-(0)}{2(1)}[/tex] = [tex]\frac{0}{2}[/tex]
∴ h = 0
→ To find k substitute x by the value of h and y by k
∵ k = (0)² + 9
∴ k = 0 + 9
∴ k = 9
∴ The range of the equation is y ≥ 9
Your kite is stuck in a tree that is 40 feet tall. The angle your string makes with the ground is 72°. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?
Answer:
42 feet of string
Step-by-step explanation:
First, draw a diagram of the string, the height and the angle.
the length of the string is equal to the hypotenuse of the triangle
let length of the string=x
sin(θ)=opp/hyp
sin(72°)=40ft/x
x=40ft/sin(72°)
x=42.05848897ft≈42ft
A system of equations is shown below.
y = 2x - 3
y = 5x + 6
What is the value of x + y?
A. -12
B. -9
C. 9
D. 12
Please help me!!!!
Answer:
-12
Step-by-step explanation:
Step1: Add 3 to both sides of the equation
2x -3 = 5x +6
+3 +3 = 9
Step2: subtract 5x from both sides of the equation
2x = 5x +9
-5 -5
Step3: divide both sides of the equation by the same term
-3x(/ -3) = 9(/-3)
X=-3Step4: multiply -3 with 2
-3x2= -6
Step4: subtract -6 with 3
-6 - 3= -9
Y=-9Step5: add the -9 to -3
-9 + -3 = -12
ANSWER: -12
PLEASE HELP! I NEED THIS DONE BY TOMORROW!
1. In January, a mobile phone shop sold 100 phones. In February, they sold 92 phones. Represent this difference as a percentage change.
2. A piece is cut from a 130cm length of wood so that the remaining length is 104cm. What percentage of the wood has been cut off?
3. There are now 30 boys in a class that originally had 24 boys in it. What was the percentage increase in the number of boys in the class?
4. Last year, there were 300 students in Year 7. This year there are 315 students. Show that this is a 5% increase.
5. A piece of art was bought for £600. Six months later, it was sold for £675. What percentage of profit did the seller make?
6. In a sale, trainers originally costing £70 are reduced to £49. Calculate the percentage change.
7. Josh invests £3500. When his investment matures, he receives £4200. Work out the percentage
increase in his investment.
8. A car company bought a car for £8000. Two years later they sold the car for £7200. Calculate their
percentage loss.
Answer
down below
Step-by-step explanation:
i did it on your last post
please give me a brainliest!!
A computer has a sales price of $150, and is advertised for 25% off of the original price.
What is the original price?
Answer:
Original price:$150
Markdown percentage:25%
Sale price:$112.50
Discount savings:$37.50
Step-by-step explanation:
PLEASEEE HELPPPP ASAPPP PLEASE
Please help I cannot figure out this math problem
Giving brainliest!!!! Asap
Answer:
B
Step-by-step explanation:
y=8x
y=8(2)
y=16
y=8(4)
y=32
Answer:
B
Step-by-step explanation:
cross multiply
24 • 4 =?
? ÷ 3 = 32
What’s the slope of the line on the graph?
What is X+Y?? and ( x+ y)- 7+8
Step-by-step explanation:
What is X+Y?
First note that if x + y = xy then neither x nor y can be equal to 1.
That being said, as a previous user already noted y = x/(x-1) and hence x - y = x - x(x-1) = x(x-2)/(x-1). Assume x - y = D. Then your question becomes what can D be so that the equation x(x-2)/(x-1) = D has a solution different than 1.
Rewrite this equation as x(x-2) = D(x-1) and note that x(x-2) = (x-1)^2 - 1. Replace x - 1 with z. So your question is what can D be so that the equation z^2 - 1 = Dz has a nonzero solution? Given that 0 cannot be a solution anyway of the previous equation. The question is really, for which D does the quadratic equation z^2 - Dz - 1 = 0 have solutions? By elementary 9th grade math, this equation has a solution when its discriminant D^2 + 4 is nonnegative. But D^2 + 4 is strictly positive regardless of the value of D. Hence D can be anything.
How to solve your question
Your question is
(+)−7+8
Simplify
1. Eliminate redundant parentheses
(+)−7+8
+−7+82
Add the numbers
+−7+8
++1
Solution
++1
z varies directly with q. when z=2,q=1 .
find a formula connecting z and q
z=???
Answer:
[tex]z = \frac{q}{2} [/tex]
Step-by-step explanation:
[tex]z \infty q[/tex]
[tex]z = kq[/tex]
[tex]z = 2 \: and \: q = 1[/tex]
[tex]2 = k1[/tex]
[tex]k = \frac{2}{1} [/tex]
[tex]z = \frac{1}{2} q[/tex]
[tex]z = \frac{q}{2} [/tex]
9514 1404 393
Answer:
z = 2q
Step-by-step explanation:
The formula for direct variation is ...
z = kq . . . . . k is the constant of proportionality
We can find k using the given values of z and q:
k = z/q = 2/1 = 2
Then the equation connecting z and q is ...
z = 2q
Rewrite 4% as a decimal.
Answer:
0.04
Step-by-step explanation:
Answer:
0.04
Step-by-step explanation:
simple math the 4 is in the ones place
pls help!!!!!!!!!!11
Answer: A
Step-by-step explanation: Every hour the temperature goes down 2 degrees and the h wouldn't go on the 32! Good luck! :D
Answer:
C. t = –4h + 21
Step-by-step explanation:
We know that when h = 0, t = 21°F. Replacing h = 0 in equation A and D we get:
A.
t = 21h + 4
t = 21(0) + 4
t = 4
D.
t = –21h + 4
t = –21(0) + 4
t = 4
So, none of them are correct.
The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in equation B and C we get:
B.
t = 4h + 21
t = 4(1) + 21
t = 25
C.
t = –4h + 21
t = –4(1) + 21
t = 17
In consequence, C is the correct option.
Explain how to find the constant rate of change from the verbal description below.
Joe can drive his motorcycle 124 miles in 2 hours. If he goes at a constant speed what is the constant rate of change? (solve it but also explain how you would solve it)
Answer:
62miles/1hr
Step-by-step explanation:
In order to get the rate of change I divided 124 miles by 2 hours to get 62 miles.
Find the slope of the line whose equation is 7x - 2y = 4.
-2
7/2
4/7
hiii please help! i’ll give brainliest if you give a correct answer tysm!
Answer: to wirte and solve for a missing side length of a rectangle, do your perimeter equation backwards, hope this helps
Step-by-step explanation:
Help. I have a D in this class.
Complete the square to re-write the quadratic function in vertex form:
Answer:
y = (x - 4)² - 26
Step-by-step explanation:
To complete the square, all we need to do is take term -8x, and add enough to make the equation come out to the square of half that. Half of -8 is -4, so we need to add 26 to the equation to end up at 16:
[tex]y = x^2 - 8x - 10\\y + 26 = x^2 - 8x + 16\\y + 26 = (x - 4)^2\\y = (x - 4)^2 - 26[/tex]
Giving us the final result
Maria is bringing her sick dog, Pedro in for a series of appointments at the veterinary clinic. Her total cost over the course of treatment will be $150 for tests and medicine plus $30 per appointment "a". A) Write an equation to show the total cost, "t" she will owe. *
Answer:
t = 150 + 30a
Step-by-step explanation:
Treatment of Pedro costs = Expenditure for tests and medicines + fees given for appointments.
If number of appointments = a
Cost per appointment = $30
Cost of 'a' appointments = $30a
Therefore, equation representing the total cost 't' of the treatment will be,
t = 150 + 30a
Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle? Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle?
Answer:
a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle? Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle?
Step-by-step explanation:
Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle? Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in a 6-ounce bottle?
Imari's family lights 372 diyas (oil lamps) during the Diwali festival. They are arranged in 12 rows. Suppose each lamp measures 2.5 inches by 2.5 inches. What are the dimensions of the rectangular display of diyas?
Answer: 77.5 inches by 30 inches
need help asap please
Answer:
c=7.17
Step-by-step explanation:
23=6c-20
43=6c
7.17=c
Answer:
7.16
I think this is correct
10z + 3 =9z solve for z
z=-3
Step-by-step explanation:
Answer:
z = -3
Step-by-step explanation:
10z + 3 = 9z
10z + 9z - 3
10z - 9z = -3
z = -3
I need help please ( i dont know what to do )
Answer:
a) 10cm
b) 11.6 cm( approximately)
Step-by-step explanation:
Use pythagorean theorem
Simplify the expression to a polynomial in standard form:
(3x – 10)(x2+ 2x - 1 )
Answer:
[tex]3x ^{3} - {4}^{2} - 23x + 10[/tex]
