Answer:
x=1 must satisfy both equations.
Step-by-step explanation:
1)Y=X+4
2)Y=3X+2
IT Means x+4=3x+2
3x-x=4-2;
2x=2 ; x=1 must satisfy both equations
PLEASE HELP! I NEED HELP Use synthetic division!
A rock is thrown upward from the top of a high cliff overlooking the ocean at a speed of 96 feet per second . The rock's height above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . How long will it take seconds for the rock to hit the ocean? Do not include units in your answer.
Answer:
7
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
The height of the rock after t seconds is given by the following equation:
[tex]H(t) = -16t^2 + 96t + 112[/tex]
How long will it take in seconds for the rock to hit the ocean?
This is t for which:
[tex]H(t) = 0[/tex]
So
[tex]-16t^2 + 96t + 112 = 0[/tex]
Simplifying by -16
[tex]t^2 - 6t - 7 = 0[/tex]
So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]
[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]
Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.
A container has 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the container and draw another marble. What is the probability of pulling out a yellow marble, followed by a blue marble?
Write the equation of the line in slope intercept form that passes through the point (-6, 1) and has a slope of 1/6.
Answer:
y = 1/6x + 2
Step-by-step explanation:
point: (-6, 1)
slope 1/6
Our standard equation can be in the slope-intercept form: y = mx + b
m is the slope, which we know if 1/6. Plug this into our equation.
y = 1/6x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (-6, 1). Plug in the x and y values into the x and y of the standard equation.
1 = 1/6(-6) + b
To find b, multiply the slope and the input of x(-6)
1 = -1 + b
Now, add 1 from both sides to isolate b.
2 = b
Plug this into your standard equation.
y = 1/6x + 2
This is your equation.
Hope this helps!
help please!!!! don't understand
Answer:
1.5
Step-by-step explanation:
23-17=6
6/4= 1.5
Solve for n. 24 = 3(n-5)
Answer:
Step-by-step explanation:
Given
24 = 3(n - 5)
24/3 = n - 5
n- 5 = 8
n = 8+5
n = 13
hope it helps :)
Answer:
n = 13
Step-by-step explanation:
8=n-5
-n=-5-8
-n=-13
n=13
What is the value of 8+(7+1)^2÷4(1/2)^4
Will Mark Brainliest
^=exponents
Answer:
264
Step-by-step explanation:
8+(7+1)^2 / 4(1/2)^4
8+ 8^2 / 4(1/2)^4
8+64/4(1/16)
8+64 / 1/4
8 + (64*4)
8+256
264
what is the amount returned on a deposit of $1,000 held for 2 years at 10% interest compound annually?
Answer:
since its 10%percent annualy(compound interest),at the end of 1year it would be 1000+(1/10 *1000)that is 1100,then for the second year it would be 1100+(1/10 * 1100)that is 1210.please mark me as brainliest
If the perimeter of the rectangle is 52 inches, find the value of x -
height is (x+2) inches
length is 3x-1 inches
Answer:
25/4
Step-by-step explanation:
perimeter is total length of all side
height =2(x+2) (×2 bcause has 2 side)
length =2(3x-1) (×2 bcause has 2 side)
2x+4+6x-2=52
8x-2=52
8x=50 (8x is 8 times x, so move to the other side become divide)
x=50/8
simplify
x= 25/4
This week, Leigh spent a total of
$24.47 on groceries. Her total for
last week was $30.16. Solve the
equation $30.16 − $24.47 = y
to find out how much more
money Leigh spent last week
than this week.
find the measure lol
what is the simplified expression of 6h +(-7.1d)-15+4d-3.4h
Answer:
6h+ (-7.1d) -15+4d-3.4h
Step-by-step explanation:
Definition the value of a number regardless of its sign Definition
SEND HELP YO Find and simplify the area (You need to completely multiply it out and include units in your answer):
2m* - 3 cm
.
2m" – 3 cm
Answer:
[tex]Area = 2m^8 - 6m^4 + 4.5[/tex]
Step-by-step explanation:
Given
[tex]Base = 2m^4 - 3[/tex]
[tex]Height = 2m^4 - 3[/tex]
Required
The area
This is calculated as:
[tex]Area = 0.5 * Base * Height[/tex]
[tex]Area = 0.5 * (2m^4 - 3) * (2m^4 - 3)[/tex]
Open brackst
[tex]Area = 0.5 * (4m^8 - 6m^4 - 6m^4 + 9)[/tex]
[tex]Area = 0.5 * (4m^8 - 12m^4 + 9)[/tex]
Open bracket
[tex]Area = 2m^8 - 6m^4 + 4.5[/tex]
What is the percentage of data between 90 and 140?
Answer:
50%
Step-by-step explanation:
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°. Find the length of h, to the nearest inch.
Answer:
143
Step-by-step explanation:
delta math
The length of h, to the nearest inch. is 57.4 inch.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
Here, given that,
In ΔGHI, i = 64 inches, g = 91 inches and ∠H=134°
Now. we know that,
a sinA =b sinB =c sinC
We get,
length of h = 57.4 inch.
hence, The length of h, to the nearest inch. is 57.4 inch.
To learn more on triangle click:
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5(n+1)-15=0, what is the answer to this equation? i need step by step explanation
Answer:
5n+5-15=0
5n-10=0
5n=10
therefore n = 10/5 = 2
therefore n=2
Sandy brought 64 dozen cookies to the bake sale. Alejandro brought
dozen fewer cookies than Sandy brought. Pierre brought 2 dozen
fewer cookies than Alejandro brought. How many dozen cookies
did Pierre bring?
Which of the following shapes have an area of 48 square feet? Select all that apply.
A scalene triangle with a base of 8 feet and a height of 6 feet.
A right triangle with a base of 9 feet and a height of 10 2/3 feet.
A rectangle with a base of 19.2 feet and a height of 2.5 feet.
A parallelogram with a base of 16 feet and a height of 3 feet.
HELP PLSSSSS I BEG YOUUUUUUUUUUUUUUUUU
Answer:
just shade in the same thing
just shade in the same thing
A drone is flying at kilometers per hour at a constant altitude of km above a straight road. The drone pilot uses radar to determine that an oncoming motorcycle is at a distance of exactly kilometers from the drone, and that this distance is decreasing at kph. Find the speed of the motorcycle. Note: Round to the nearest hundredth. Hint: At the end, remember to consider that the drone is moving towards the motorcycle at kph. Speed cannot be negative. Note: Round to the nearest tenth.
Answer:
Hello your question is poorly written attached below is the complete question
answer : 166.41 kph
Step-by-step explanation:
Given data :
Drone speed = 180 kph
Altitude of drone = 1 km
distance of motorcycle from drone = 2 km
distance of motorcycle decreases at 200 kph
calculate the speed in kph of the motorcycle
attached below is a detailed solution of the problem
Keith is riding his bicycle. He rides at a speed of 13 kilometers per hour for 32.5 kilometers. For how many hours does he ride?
Answer:
422.50
Step-by-step explanation:
just multiply 13 × 32.5=422.50
What is the perimeter of the shape?
40 feet
43 feet
51 feet
67 feet
Answer:
40 feet?
Step-by-step explanation:
11 ft + 3 ft + 4 ft + 6 ft + 3 ft + 3 ft + 4 ft + 6 ft = 40
HELP HELP HELP!!! NUMBER 3 PLEASE!!!
Answer:
see the attachment, answers there
Question 6
If a truck can drive 24,4 miles in 1 gallon, how many miles would I be able to drive with a filled 30 gallon tank?
Answer: 732 mi
Step-by-step explanation:
Assuming you meant 24.4
Mr. Smith’s factory produces 58 brake pads per hour with the current machines. He has decided to invest in new machines that produce 86 brake pads per hour. By what approximate percent will the new machines increase the production of brake pads at the factory?
Answer:
48%
Step-by-step explanation:
Kylee bought a backpack at Tilly's for $32. The same backpack is on sale today for $24. What is the percent
of change? Round your answer to the nearest tenth.
Answer:
25
Step-by-step explanation:
Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (−5)(50−2) to represent her profit based on the price per scarf,
Use the drop-down menus to complete the statements about Sofie's profit.
Answer:
The first part is 5
The maximum it can be is 200
Step-by-step explanation:
Because I said So
Sofie will not make a profit if she sells her scarves for $5 or less.
The maximum profit Sofie can make is $200.
What is a parabola?A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
According to the given problem,
y = (x - 5)(50 - 2x)
⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)
⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)
⇒ y - (x - 5)(-2x + 50) = 0
⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0
⇒ y - ( -2x² + 50x + 10x - 250) = 0
⇒ y - ( - 2x² + 60x - 250 ) = 0
⇒ y + 2x² - 60x + 250 = 0
⇒ 2x² -60x + y + 250 = 0
⇒ ( 2x² - 60x ) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{60}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{2^{2} *3*5}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - 30x ) + y + 250 = 0
⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0
⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0
⇒ 2( x - 15 )² + y = -2(-225) - 250
⇒ 2( x - 15 )² + y = 450 - 250
⇒ 2( x - 15 )² + y = 200
⇒ y = -2( x - 15 )² + 200
This equation is in the form of y = a(x - h)² + k where the vertex of the parabola is (h , k).
Therefore the vertex of the parabola is at (15 , 200)
Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.
Learn more about parabola here:
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Figure A is a scale image of Figure B. Figure A: 7.2 , 4. Figure B: 3 , x. What is the value of x
Answer: 5.4
Step-by-step explanation:
Answer:
5.2
Step-by-step explanation:
What is -3/4x + 1/2y - 9/4x - 11/2y in simplest form?
Answer: -3x-5y
Step-by-step explanation: