Answer:
- 4
Step-by-step explanation:
(2x + 4)² + 1 = 5 ← expand left side using FOIL and simplify
4x² + 16x + 16 + 1 = 5
4x² + 16x + 17 = 5 ( subtract 5 from both sides )
4x² + 16x + 12 = 0 ( divide terms by common factor 4 )
x² + 4x + 3 = 0 ← in standard form
(x + 3)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 1 = 0 ⇒ x = - 1
Summation of solutions = - 3 + (- 1) = - 3 - 1 = - 4
Last year, the Galaxy Fair Amusement Park installed a family roller coaster they named The Twist. This coaster was designed to accommodate riders from age 4 to adult and features a tall climb hill and several banking turns. Overall, the park has been disappointed in the reception of The Twist, and very few families are riding the coaster this season. After some research, they discovered that park guests think the climb hill is too tall and fast for younger riders. Galaxy Fair Amusement Park has asked a roller coaster design firm to help them redesign The Twist during the coming off season. The quadratic function that represents the current climb hill is () = −0.102 + 3.6 − 2.4 and the quadratic function that represents the proposed redesign of the climb hill is () = −0.032 + 1.62 − 6.87. In these functions, the value of x represents the time, in seconds, since the roller coaster train cars have left the station, and the output variable is the height of the roller coaster track, in feet, above the ground. 1. Rewrite both () and () from standard form into vertex form. Explain your process. HINT: Each function has a common factor. Start by dividing it out. 2. State the vertex of each function. What does each vertex represent in context of The Twist? 3. Compare the a-value of () to the a-value of the parent quadratic function. What effect does this value have on a parabola? 4. Sketch both of the functions () and () on a single xy-plane. Describe the steps you took to create your sketch. 5. Use the vertex forms of () and () and the sketch you created in question 4 to describe the track changes that occur when the function that represents the climb hill is altered from () to (). Do you think these changes will help younger riders better enjoy The Twist? Explain.
Answer:
can you add a picture or summerize this
Step-by-step explanation:
How many 0.25 are there in 10.5?
Answer:
42
Step-by-step explanation:
to find how many 0.25 there are in 10.5 we have to divide 10.5 by 0.25
10.5÷0.25
=42
Hope this helped you- have a good day bro cya)
A farmer sold did he sell? of his sheep. His original flock was 300 sheep. How many sheep did he sell?
all of his sheep
Hope that helps :)
The perimeter of a rectangular garden is 332 m.
If the length of the garden is 93 m, what is its width?
Answer:
73
Step-by-step explanation:
332÷2= 166
166 - 93 = 73
help me again please 7⅕ ÷ ⅗ =
Answer:
7 3/5 is the correct answer
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Need Kona talaga para bukas please
Answer:8
Step-by-step explanation:
PLEASE HURRY HELP!
Find the product (3a4 + 4)2
Answer:
(3a4 + 4)2
= (12a+4)2
= 24a+8
Greatest common factor of 30 and 75
Step-by-step explanation:
The prime numbers 5 and 3 are both factors that are common to 30 and 75. The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.
Answer:
the Greatest common factor of 30 and 75 is 15
Step-by-step explanation:
The product of these factors is 3×5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15.
The school need to make $750 in order to cover all of their expenses.They estimate 200 students will come to the dance.If they made $150 from a fundraising bake sale what they need to charge per ticket to cover their cost?--
9514 1404 393
Answer:
$3
Step-by-step explanation:
The cost that hasn't been covered by bake sale proceeds is ...
$750 -150 = $600
If that cost is divided among 200 students, the amount each student needs to pay is ...
$600/(200 students) = $3/student
They need to charge $3 per ticket.
Which is the largest of the following numbers? 0.1, 0.02, 0.003, 0.0004, 0.00005
answer is the option 0.1
Answer:
0.1
Step-by-step explanation:
By looking at numbers after the decimal point, the largest number comes the soonest. Looking at our options here, 0.1 would be the largest since it is the closest to 1, whereas 0.00005 is the smallest because it is very far from 1.
9 is the cube root of (a) 343 (b) 729 (c) 629 (d) 81
Answer:
(b) 729
Step-by-step explanation:
9 × 9 × 9 = 9^3 = 729
Thus, 9 is the cube root of 729
find the values of x and y
Answer:
x = 68°, y=14
Step-by-step explanation:
∵ m║n
∴ m∠x = 180 - m∠112
m∠x = 68°
∵ ∠x and ∠(5y - 2) are vertically oppose
∴ m∠(5y - 2) = m∠x
m∠(5y - 2) = 68
Make equation
5y - 2 = 68
5y = 68 + 2
5y = 70
y = 70/5
y = 14
Hope this helps
Step-by-step explanation:
• The supplement of the angle with the measure of 112° is :
[tex]\bf x + 112 = 180 \\ \bf x = 180 - 112 \\ \bf \boxed{ \color{#FF0000}x = 68 }[/tex]
This angle of 68° and the angle sign x° are in angular positions.
Internal alternators
The lines m and n are parallel, these angles have the same measure.
The marking of the angle x and the marking of the angle (5y-2)° are opposite to the vertex.
They have the same measure:
[tex]\bf 5y - 2 = 68 \\ \bf 5y = 68 + 2 \\ \bf 5y = 70 \\ \bf y = 70 \div 5 \\ \bf \boxed{ \color{#FF0000}y = 14 }[/tex]
PLEASE HELP ITS MATH THANK YOUUUU
solve pls brainliest
(a) 305 (?)
(b) Fields, monroe
(c) Treevale
The perimeter of a rectangle is equal to 54 units. The length of the rectangle is 2k units, and the width of the rectangle is k units
Which expression represents the perimeter, and what is the width of the rectangle?
The expression to represents the perimeter is,
54 = 2 (2k + k)
And, The width of the rectangle is, 9 units.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of a rectangle is equal to 54 units.
And, The length of the rectangle is 2k units, and the width of the rectangle is k units.
Now, We know that;
Perimeter of rectangle = 2 (Length + Width)
Substitute the given values, we get;
Perimeter of rectangle = 2 (Length + Width)
54 = 2 (2k + k)
54 = 2 × 3k
54 = 6k
54/6 = k
k = 9
Hence, The width of the rectangle is, 9 units.
Learn more about the rectangle visit:
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Circle each input value. Underline each output value. 1. {(1, 1), (2, 3), (3,5)} 2. {(6,2), (5, 3), (4,8)}
Answer:
The first numbers in the sets are input and the second numbers are outputs.
1. {(1, 1), (2, 3), (3,5)}
Input = 1, 2, 3Output = 1, 3, 52. {(6,2), (5, 3), (4,8)}
Input = 6, 5, 4Output = 2, 3, 8How much work is done lifting a 100 Newton book onto a shelf that is 2 meters high on Earth?
We want to find the work done by lifting a book a given distance.
The answer is 200 N*m
We know that the book weighs 100 Newtons and that we lift it a distance of 2 meters.
Remember that the work needed to lift an object of mass M to a height H is:
W = M*g*H
where g is the gravitational acceleration.
Knowing that:
weight = M*g
We can replace the things we know to get the work:
W = 100N*2m = 200 N*m
If you want to learn more, you can read:
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7. In a quiz bee, Marlon scored 132 points during the first round. This score was thrice as much as his score during the second round. What score did he get in two rounds?
Answer:
II + III = 176
II = 44
III = 132
Step-by-step explanation:
Third round: 132
Second round: 3x=132
x=44 (second round)
2rounds: 132+44=176
MATH Topic - Coordinate system and Linear graphs Q.1) Complete the following tables and plot the points on the graph paper to represent the equations given below 1 2 3 X y=x+1 y=-3x (x, y) (x, y)
Step-by-step explanation:
Given Question
Complete the following tables and plot the points on the graph paper yo represents the equations given below :-
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
and
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\:y = x + 1[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = 1 + 1[/tex]
[tex]\rm \longmapsto\:y = 2[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = 2 + 1[/tex]
[tex]\rm \longmapsto\:y = 3[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = 3 + 1[/tex]
[tex]\rm \longmapsto\:y = 4[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf 2 & \sf 3 & \sf 4\\ \\ \sf (x,y)& \sf (1,2) & \sf (2,3) & \sf (3,4)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , 2), (2 , 3) & (3 , 4)
---------------------------------------------
Given equation is
[tex]\rm \longmapsto\:y = - 3x[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = - 3 \times 1[/tex]
[tex]\rm \longmapsto\:y = - 3[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = - 3 \times 2[/tex]
[tex]\rm \longmapsto\:y = - 6[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = - 3 \times 3[/tex]
[tex]\rm \longmapsto\:y = - 9[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf - 3 & \sf - 6 & \sf - 9\\ \\ \sf (x,y)& \sf (1, - 3) & \sf (2, - 6) & \sf (3, - 9)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , - 3), (2 , - 6) & (3 , - 9)
Who ever answers first will be marked brainliest
Answer:
The answer is x≥9.
Step-by-step explanation:
Answer:
x≥9
Step-by-step explanation:
this is the answer all you have to do is solve it
******Please help me help please help me ******
9514 1404 393
Answer:
y = 8
Step-by-step explanation:
If the variation is direct, any multiplier of the x-value will also multiply the y-value.
old value × -1 = new value
x: 4 × -1 = -4
y: -8 × -1 = 8
The new value of y is 8.
Do the fractions 6/7 and 16/25convert to repeating or terminating decumals numbers
Answer:
terminating decimals
Step-by-step explanation:
they don't seem to repeat numbers
Answer:
repeating
Step-by-step explanation:
6÷7= 1.111111111111
In the diagram, lines BC and DE are parallel.
What is the measure of Zx?
-1/3(4+z)=-5/6 I need answer ASAP
Answer:
-2/3
Step-by-step explanation:
:)
Answer:
z = - 1.5Step-by-step explanation:
Given equation:
-1/3(4 + z) = -5/6Multiply both sides by - 3 and simplify;
(-3)(-1/3(4 + z)) = (-3) (-5/6) 4 + z = 5/24 + z = 2.5z = 2.5 - 4z = - 1.5Please help out with this question
Step-by-step explanation:
5⁴+5³-6(5)²-5(5)-15
= 560
is a/b +b/c rational number
Answer:
Yes.
Step-by-step explanation:
Yes.
Assuming a, b and c are integers (not = 0)
a/b + b/c
= (ac + b^2) / bc which is a rational number.
If I want to buy a pair of shoes that cost 86.71 and 17% sales tax is added approximately how much are the shoes?
Answer:
$101.45
Step-by-step explanation:
change 17% to .17 then multiply it by 86.71=14.74 then add that to 86.71 and you get your answer $101.45
Find the slope and y intercept of the line 3x+2y=-6
Answer:
Step-by-step explanation:
Slope - -3/2
y-intercept- (0,-3)
If AB= 4 units and DC=4 units , what is the length of BC
Answer:
4 units i think
Step-by-step explanation:
i dont know how beacuse 4 is answer
wHaT iS tHe AnWsEr?????????????
2,000 +300000000000000000000000000000000000
Answer:
3.0 E35
Step-by-step explanation:
Thanks.