Answer:
D. The slingshot reaches a greater height at 150 feet, which is the vertex of the parabola.
Step-by-step explanation:
First let's examine the given equations
[tex]\displaystyle \rm\\(x -70)^2 + (y-77)^2 = 5184 ............. (1)\\y = -4x^2 + 40x + 50 ............... (2)[/tex]
Equation (1) is of the form of a standard equation for a circle
[tex]\displaystyle \rm (x-a)^2 + y-b)^2 = r^2\\\\[/tex]
where (a, b) is the center of the circle and r is the radius
Equation (2) is the standard equation of a parabola
y = ax² + bx + c where a, b and c are constant
So we know that the Ferris wheel motion is circular while the slingshot motion is parabolic
Let's compute the highest point at which the Ferris wheel reaches.
Given,
[tex]\displaystyle (x-70)^2 + (y-77)^2 = 5184[/tex]
We can see that r² = 5182 by comparing it to the circle equation[tex]\displaystyle x_v=-\dfrac{40}{2\left(-4\right)}[/tex]
Therefore r = √5184 = 72. The diameter = 144 which is the highest point vertically from the center of the circle
The highest point on the circle = 144 + 5= 149 m since there is a 5' gap between the Ferris wheel and the ground at the lowest point so that has to be taken into account
For the parabola the vertex is the highest point and its x-coordinate given by [tex]\displaystyle \dfrac{-b}{2a}[/tex] in the standard equation for a parabola
Comparing the given equation with the standard equation we see that a = -4, b = 40 and c= 50
Therefore [tex]x_v[/tex] the x-coordinate of the vertex:
[tex]\displaystyle x_v=-\dfrac{40}{2\left(-4\right)} = 5[/tex]
The y coordinate of the vertex can be found by plugging in this value into the parabolic equation
[tex]\displaystyle y_v=-4\cdot \:5^2+40\cdot \:5+50 = 150[/tex]
This being the vertical coordinate of vertex of the parabola, the highest point that the slingshot reaches is 150'
So correct answer is D
Find the missing interest rate.
I = $63
P = $420
r = %
t = 3 years
Answer: r=5%
Step-by-step explanation:
I=Prt
I/P=Prt/P
I/P=rt
I/(P*t)=rt/t
r=I/Pt
r=63/(420*3)
r=21*3/(420*3)
r=21/420
r=1/20
r=0.05
r=0.05 * 100%
r=5%
Please help math 50 points please dont lie
Answer:
8,250
Step-by-step explanation:
10 to the power of 2 is 100, move the decimal 2 spaces to the right.
Answer:
Hi, i think the answer would be the third option, 8,250.
Step-by-step explanation:
You do the exponents first in this equation according to the acronym PEMDAS. 10 to the second power is 100, so now you have
82.5 × 100
This would be equal to moving the decimal point two spaces to the right, giving us 8,250 as the answer
Does (2,2) make the inequality 5x+4y>20 true?
Answer:
No
Step-by-step explanation:
substitute the coordinates of the point into the left side of the inequality and check the value obtained against the right side.
5(2) + 4(2) = 10 + 8 = 18 < 20
then (2, 2 ) does not make the inequality true
need this real fast please
Answer:
slope = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 0) ← 2 points on the line
m = [tex]\frac{0-2}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex] = - [tex]\frac{2}{3}[/tex]
Answer:
-2/3
Step-by-step explanation:
The equation for slope is y2-y1 over x2-x1.
Or you can easily do rise over run.
Lets use the point (0,3.) So, we want to calculate slope, but the only other direct point is (0,2) so lets also use that.
If we start at the point (0,2) and go down 2 units, we just have to go over 3 units to get to (0,3) so thats convienient.
The rise is the -2 units, since you go down 2 units to get to the second point. You also have to run 3 units over to get to the second point.
The run is 3, and the rise is -2.
Rise over run
-2 (rise) over 3 (run)
-2/3
-2/3 is the slope.
Hope this helps!
A triangle has side lengths 4y, 5y and 9y. The longest side of the triangle is 5y. What value of y proves that this triangle is a right triangle?
Answer:
9y i can be rong
Step-by-step explanation:
Solve 6 + 1/4a = 3 for a.
Answer:
a= -12
Step-by-step explanation:
simply 8/-4 dived by -3/9
Answer:
-6
Step-by-step explanation:
m/4 - 3 = 5 HELPPPPPPPPP PLZZZXZZZZZZZZZZZZZZZZZZ
Find the length of the hypotenuse of a right triangle with legs of 8 and 6.
43. (09.01)
Let A = {15, 25, 35, 45, 55, 65} and B = {25, 45, 65}. What is ANB? (1 point)
O {15, 25, 35, 45, 55, 65}
O {15, 35, 55}
{25, 45, 65}
{15, 25, 35, 45}
Answer:
That is;
{25,45,65}
Step-by-step explanation:
Here, we want to find the set of A n B
That is the set that contains values that are present in both sets A and B
Mathematically, that will be;
{25,45,65}
for g(x)=1/2x-11, find x when g(x)=-5
Answer:
x = 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = 1/2x - 11
g(x) = -5
Step 2: Solve for x
Substitute: -5 = 1/2x - 11Isolate x term: 6 = 1/2xIsolate x: 12 = xRewrite: x = 12-4+5x-7=10+3x-2x. Solve for x
Answer:
-4 + 5x - 7 = 10 + 3x - 2x
5x - 3x + 2x = 10 + 4 + 7
4x = 21
x = 21/4
x = 5 1/4 or 5.25
Answer: 5=x
Step-by-step explanation:
-4+5x-7=10+3x-2x
Combine like terms:
-10+5x=10+x
Subtract 10 on both sides:
-10-10+5x=10-10+x
-20+5x=x
Subtract 5x on both sides:
-20+5x-5x=x-5x
-20=-4x
Divide -4 on both sides:
-20/-4=-4x/-4
5=x
which is an equation for the line passing through the points (-3,3) and (6,9)
Answer:
y=2/3x +5
hope this helps
Answer:
[tex] \red{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Explanation
[tex] slope \:of \:the\: required\:\: line \implies\\\frac{9-6}{6-(-3)}=\frac{6}{9} [/tex]
[tex] equation \:of \:the\: required\:\: line\implies\:\\y - 3 = \frac{6}{9} (x + 3)[/tex]
[tex] \implies \: 9y - 27 = 6x + 18[/tex]
[tex] \implies \: 6x - 9y + 45=0[/tex]
[tex] \implies\:2x-3y+15=0[/tex]
Hence the equation of the line is
[tex] \green{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Help pleasee due soon!! WIll give Brainliest
Answer:
9.7
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf x \approx 9.7}}[/tex]
Step-by-step explanation:
This is a right triangle, which we know because of the square in the corner of the triangle. We can use the right triangle trigonometric ratios.
[tex]sin( \theta) =opposite/hypotenuse[/tex] and [tex]cos (\theta) = adjacent /hypotenuse[/tex] and [tex]tan (\theta)=opposite/adjacent[/tex]
First, identify each side of the triangle as adjacent, opposite, or hypotenuse, relative to the 68 degree angle.
The x is next to, or adjacent, to the angle. The 24 is opposite. We are not given the hypotenuse.
[tex]adjacent= x \\opposite= 24 \\hypotenuse= unknown[/tex]
Since we have the adjacent and opposite, we must use tangent.
[tex]tan (\theta)=\frac{opposite}{adjacent}[/tex]
Substitute the values in. The theta (θ) is the angle.
[tex]tan (68)=\frac{24} {x}[/tex]
Solve for x. One way is by cross multiplying.
[tex]\frac{tan(68)}{1}=\frac{24}{x}[/tex]
Multiply the 1st numerator by the 2nd denominator. Then, multiply the 1st denominator by the 2nd numerator.
[tex]tan (68)*x=1*24[/tex]
[tex]tan(68)*x=24[/tex]
Evaluate tan(68) using a calculator.
[tex]2.47508685*x=24[/tex]
Divide both sides of the equation by 2.47508685. This will isolate the variable x. ( We divide because multiplication is occurring between 2.47508685 and x, and division is the inverse of multiplication).
[tex]\frac{2.47508685*x}{2.47508685}=\frac{24}{2.47508685}[/tex]
[tex]x=\frac{24}{2.47508685}[/tex]
[tex]x=9.69662943[/tex]
Round to the nearest tenth. The 9 in the hundredth place tells us to round up. The 6 becomes a 7.
[tex]x \approx 9.7[/tex]
In this right triangle, x is equal to about 9.7
Which fraction is BETWEEN 211 and 311?
Responses
Answer:
3/12 or 1/4
Step-by-step explanation:
To do this you can just increase the denominator by 1, at least for this question
3/11 is around 0.27, while 3/12 is 0.25. 2/11 is 0.19, which is smaller than 0.25, so
3/12 is a justificable answer.
express (x+7)^2 as a trinomial in standard form
Answer:
x^2 +14x+49
Step-by-step explanation:
The standard form of the polynomial (x+7)² is x² +14x+49.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The polynomial will be represented as,
E = (x+7)²
E = x² +14x+49.
To know more about polynomials follow
brainly.com/question/2833285
#SPJ2
Help me with number 11 please
umm I don't remember I would say if I remembered
I need the answer to this ASAP!!!! 30 points!!!
Answer:
6(1/4) or (25/4) pounds
Step-by-step explanation:
1 1(1/4) 1(1/2) 1(3/4) 2
<-----|---------|---------|------------|-----------|---->
X X X X X
X X X
X
X
X
1(1/4) or (5/4)
(5/4) x 5 = 6(1/4) or 25/4 pounds
I hope this helps!
Write an expression that represents the height of a tree that begins at 2 feet and increases by 4 feet per year. Let y represent the number of years. PLEASE HELP ME
Answer:
2+4y
Step-by-step explanation:
9) f(x) = 3-4x – 12
x2 + 3x + 2
y-int:
HA:
Hole:
VA:
x-int:
Answer:
x=3,2i,-2i
Step-by-step explanation:
In 5-7 complete sentences, write a real world situation that can be modeled by the equation. 3x = 5x + 10
Guys I need help : How do we find square of any number Ex.121.... for grade 5 and 6 ez method plis
Answer:
[tex]hey \: its \: easy[/tex]
(1) Square of 5 = 5 × 5 = 25
(2) Square of 10 = 10 × 10 = 100
(3) Square of 16 = 16 × 16 = 256
(4) Square of 25 = 25 × 25 = 625
(5) Square of 110 = 110 × 110 = 12100
like this you can also find it
hope it helps
pls mark as brainliest
Answer:
Step-by-step explanation:
You have to figure out what has to multiply by itself to get to that number.
So for example, 121. The square root is more than 10 because 10 times 10 equals 100. It's less than 15 because 15 times 15 is a little over 200. If you have your multiplication tables memorized, you'd know that 11 multiplied by itself is 121. Therefore, the square root to 121 is 11. Hope this helps! (:
1. 6(4x+1)=78
2. 2(x+10)=60
Solve for x
Answer:
1. x= -3
2. x= 20
Step-by-step explanation:
sorry if this is wrong,
The graph shows the number of bacteria presented in an experiment
What is the rate of change for the number of bacteria from t=2 to t= 4
Answer:
fdsvStep-by-step explanation:
Henry wanted to collect 65 pounds of cans in 7 days. How much should he collect each day to reach his goal? Which two whole numbers does your answer lie between?
find the missing value to complete the square.
x^2 +8x+ ___
Answer:
the answer is x^2+8x+ c
Step-by-step explanation:
If x 2 + b x + c is a perfect square, then there is always the same relation ship between b and c "Find half of b and square it" , so c = ( b /2 ) ^2
x^ 2 + 8 x + ( 8/ 2 )^2 =
x^ 2 + 8 x + 4^ 2 =
x^ 2 + 8 x + 16 =
( x + 4 ) ^2
I hope that helps you
. A electric jug was sold allowing 20% discount
with Profit of Rs.120. If the jug was sold
allowing 30% discount, there would have
been loss of Rs. 270. Find the MP of the jug.
solu
9514 1404 393
Answer:
marked price = Rs. 3900
Step-by-step explanation:
The difference between the discounts is 30% -20% = 10% of the marked price. The difference in Rs is 120 -(-270) = 390. If Rs. 390 is 10% of the marked price, then the marked price is (Rs. 390)/(0.10) = Rs. 3900.
The marked price is Rs. 3900.
_____
Check
A 20% discount from 3900 is a price of 3120. If the profit is 120, the cost price is 3000. A 30% discount from 3900 is 2730. This is 270 below the 3000 cost price, so our answer is consistent with problem requirements.
answer correctly pls and i will give BL
Answer:
I would say 4 more miles than you each week
Step-by-step explanation:
Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beach balls $4 each. She bought 10 items in total and it cost $34. How many beachballs did she got?
Answer:
6
Step-by-step explanation:
Find the unknown length. Round to the nearest tenth if necessary.
Answer:
55 i believe
28 + 27 = 55
Answer:
a = 7.4
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem:
c^2 = a^2 + b^2
28^2 = a^2 + 27^2
784 = a^2 + 729
55 = a^2
a = 7.4