Answer:
10
Step-by-step explanation:
Set it up algebraically first. Let x be that unknown number
5x - 9 = 4x + 1
5x = 4x + 10
x = 10
So the number is 10
A Ferris wheel at an amusement park is modeled by (x – 70)2 + (y – 77)2 = 5,184, where the measurements are in feet. A slingshot attraction is modeled by y = –4x2 + 40x + 50. Which attraction reaches a greater height, and what does it represent in terms of the context?
A. The slingshot reaches a greater height at 50 feet, which is the vertex of the parabola.
B. The Ferris wheel reaches a greater height at 184 feet, which is the highest point on the circle.
C. The Ferris wheel reaches a greater height at 149 feet, which is the highest point on the circle.
D. The slingshot reaches a greater height at 150 feet, which is the vertex of the parabola.
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
1.Find the compound interest on Rs25000 for 3 years at 10% per annum ,Compounded annually.
Plzz answer this question in step by step explanation.
Answer:
The compound interest is Rs8275
Step-by-step explanation:
The rule of the compound interest is A = P[tex](1+\frac{r}{n})^{nr}[/tex], where
A is the new amountP is the initial amountr is the interest rate in decimaln is the number of periodst is the timeThe interest I = A - P
∵ The amount of investment is Rs25000 for 3 years
∴ P = 25000
∴ t = 3
∵ The rate of interest is 10% per annum, compounded annually
∴ r = 10% = 10 ÷ 100 = 0.1
∴ n = 1 ⇒ compounded annually
→ Substitute these value in the 1st rule above to find the new amount
∵ A = 25000[tex](1+\frac{0.1}{1})^{1(3)}[/tex]
∴ A = 25000[tex](1.1)^{3}[/tex]
∴ A = Rs33275
→ Use the 2nd rule above to find the interest
∵ I = 33275 - 25000
∴ I = 8275
∴ The compound interest is Rs8275
Two sides of a triangle have lengths 6 and 16. What must be true about the length of the third side?
Answer:
it is 6
Step-by-step explanation:
The European Working Time Directive (EWTD) directs that staff should work no more than an average of 48 hours a week, over a 13-week period. You work from 9:00 - 18:45 with a 30 minutes lunch break for three days a week and from 10:30 - 21:00 two days a week with a 45 minutes break. You also work from 10:00 – 14:00 every second Sunday. Are your hours EWTD compliant?
Answer:
it is not EWTD compliant
Step-by-step explanation:
Given that :
Directive = maximum average working hours per week = 48 hours
Engagement :
9:00 - 18:45 = (9 hrs 45 mins) - 30 mins = 9hrs 15 mins
9 hrs 15 mins for 3 days = 27 hours 45 mins
10:30 - 21:00 = (10 hrs 30 mins) - 45 mins = 9 hrs 45 minutes
Sundays (10:00 - 14:00) = 4 hours
Total work hours per week :
2(9hrs 15 mins) + 3(9hrs 45 mins) + 4 hours =;
18 hrs 30 mins + 29 hrs 15 minutes + 4 hours
(18 + 29 + 4) + 45 minutes
51 hours 45 minutes.
51 hours 45 minutes > 48 hours ; a Hence, it is not EWTD compliant
PLEASE HELP FAST I WILL GIVE EXTRA POINTS! Make sure you read the question!
Answer:
c
Step-by-step explanation:
Please due soon, please explain too.
Answer:
x>-15/4
Step-by-step explanation:
1/3(6/8+1/2x)>-3/8
3/4 + 1/2 x>- 9/8
6+4x>-9
4x>-9-6
4x>-15
x>-15/4
Two factory plants are making tb panels. yesterday, plant a produced 18,000 panels. two percent of the panels from plant a and 6% of the panels from plant b were defective. how many panels did plant b produce, if the overall percentage of defective panels from the two plants was 3%?
Plant B produces 6000 panels.
Given that, Plant A produces 18,000 panels out of 2% are defective and 6% of the panels produced by Plant B are defective.
Defective percentage : It is the number of defects divided by the sample size, multiplied by 100. So, if one tool is defective out of a sample size of 1,000, your percent defective is 0.1 percent.
No. of Defective Panels from Plant A + No. of Defective Panels from Plant B = Total No. of Defective panels
Let No. of Panels produced from Plant A = A and No. of Panels produce from Plant B = B
2% of 18000 + 6% of B = 3% of (18000 + B)
360 + 0.06*B = 0.03( 18000 + B)
360 + 0.06* B = 540 + 0.03*B
0.06*B - 0.03B = 540-360
0.03*B = 180
3B = 18000
B = 6000
CHECK:
2% of 18000 + 6% of 6000 = 360+360 = 720 defectives
18000 + 6000 = 24000
720 out of 24000 = 720/24000 = 72/2400 = 3%
Hence, Plant A produces 18000 panels and 2% of them , or 360, are defective.
Plant B produces 6000 panels and 6% of them, or 360, are defective.
Learn more about defective percentage here brainly.com/question/17646647
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What is the first step to isolate the variable term on one side of the equation?
Answer:
The basic technique to isolate a variable is to “do something to both sides” of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number. By repeating this process, we can get the variable isolated on one side of the equation.
Step-by-step explanation:
Question1Circle A has a diameter of 9 cm. Circle B has a radius of 5 cm. Circle has the larger circumference by centimeters. Use LaTeX: \pi=3.14,Question2 A circle's circumference is approximately 44 cm. Complete each statement using one of these values: 7, 11, 14, 22, 88,138, 154, 196, 380, 616.
a. The circle's diameter is approximately cm.
b. The circle's radius is approximately cm.
c. The circle's area is approximately cm2.
Answer:
1.) CIRCLE B
2.) 14 cm ; 7cm ; 154cm²
Step-by-step explanation:
Given that:
CIRCLE A:
Diameter (d) = 9cm
CIRCLE B:
Radius (r) = 5cm
Circumference of circle A:
Radius (r) = diameter / 2
C = 2 * pi * r = 2 * 3.14 * (9/2) = 28.26 cm
Circumference of Circle B:
C = 2 * pi * r = 2 * 3.14 * 5 = 31.4 cm
CIRCLE B has the larger Circumference.
2.) circle with Circumference (C) = 44cm
Diameter of circle ;
C = 2 * pi * (d/2)
44 = 2 * 3.14 * (d/2)
44 = 6.28d / 2
88 = 6.28d
d = 14.01 = 14.0 cm ( 1 decimal place)
B.) Circle's Radius
Radius = diameter / 2
Radius = 14.0 / 2 = 7 cm
C.) Area (A) of the circle :
A = pi * r^2
A = 3.14 * 7^2
A = 3.14 * 49
A = 153.86
A = 154 cm²
The space-x rocket had traveled 8,918 meters in 7 seconds after its launch. How fast was the rocket traveling in meters per second?
lebron is comparing flights departing from minneapolis. which 222 ways could lebron find the flight with the fastest average speed? choose 2 answers: choose 2 answers:
This problem is incomplete, but applying the relation between velocity, distance and time, LeBron could find the flight with the fastest average speed dividing distance by time.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
Hence, to find the fastest flight, he needs the highest speed, which is found dividing distance by time.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
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Answer:
Step-by-step explanation:
Find the value of x + 3.
X + 3
18 cm
2x - 4
Answer:
B. 14
Step-by-step explanation:
Those little lines on the sides of the triangles shows you which side is congruent to which, so x + 3 is congruent to the other triangle side which one small line, and 18cm and 2x - 4 is congruent.
2x - 4 = 18
add 4 to both sides
2x = 22
divide by 2
x = 11
Replace the x with 11
x + 3
11 + 3
14
What strategy would be the best to solve this problem?
A theater charges $8 for an adult ticket, and $6 for a children's ticket. On a certain day, a total of 255 tickets were sold for a total cost of $1,850. How many more children's tickets were sold than adult tickets?
A. guess, check and revise
B. use a formula
C. work backwards
D. look for a pattern
Answer:
B
Step-by-step explanation:
By making an equation where x = number of adult tickets and y = number of children tickets, we can get 2 equations:
8x + 6y = 1850
x + y = 255
then we solve the equation to get each of the amounts
What is the number 2.0847 to 2 decimal places?
Answer:
2.08
Step-by-step explanation:
Please help!!!! ASAP
Answer:
A
Step-by-step explanation:
I just put the first one in desmos to see if it was the same
In the diagram below, AB || CD, AD || BC, m ABC = 106°, mZVEE = 36° and mCCB= 42°. Find m DEC.
Answer:
wheres the diagram
Step-by-step explanation:
the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square
The ratio of the area of the smaller square to the area of the larger square, that have a perimeter ratio of 2:7 is 4:49
What is the ratio of the area given the ratio of the perimeters of the squares?The ratio of the perimeter of the squares = 2 : 7
Required: The ratio of the area of the smaller square to the larger square.
Solution: The perimeter of a square of side x is 4•x
The comparative length of the side of each square are therefore;
2/4 and 7/4
The comparative area are therefore;
(2/4)² and (7/4)²The ratio of the areas of the square is therefore;
(2/4)² : (7/4)² = 1/4 : 49/16
Multiplying both sides of the ratio by 16 gives;
16×1/4 : 16×49/16
4:49
The ratio of the area of the smaller square to the area of the larger square is 4 : 49Learn more finding the area of common shapes here:
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57.42
A car is traveling in a race. The car went from the initial velocity of 35 m/s to the final velocity of 65 m/s in 5 seconds.
What is the acceleration?
-13 m/s2
0-6 m/s2
6 m/s2
13 m/s2
Hi there!
[tex]\large\boxed{a = 6 m/s^{2}}[/tex]
Use the kinematic equation to solve for acceleration:
[tex]a = \frac{v_{f}-v_{i}}{t}[/tex]
Where:
vf = final velocity
vi = initial velocity
t = time
Plug in the given values:
[tex]a = \frac{65-35}{5}\\\\a = 30 / 5 \\\\=6 m/s^{2}[/tex]
Find the slope of the line satisfying the given conditions
a) through (-3,4) and (2,-8)
b) through (5,-3) and (1,-7)
Answer:
a) The slope of the line is [tex]-\frac{12}{5}[/tex]
b) The slope of the line is 1
Step-by-step explanation:
The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]
a)
∵ The line passes through points (-3, 4) and (2, -8)
∴ x1 = -3 and y1 = 4
∴ x2 = 2 and y2 = -8
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{-8-4}{2--3}[/tex] = [tex]\frac{-12}{2+3}[/tex] = [tex]\frac{-12}{5}[/tex]
∴ m = [tex]-\frac{12}{5}[/tex]
∴ The slope of the line is [tex]-\frac{12}{5}[/tex]
b)
∵ The line passes through points (5, -3) and (1, -7)
∴ x1 = 5 and y1 = -3
∴ x2 = 1 and y2 = -7
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{-7--3}{1-5}[/tex] = [tex]\frac{-7+3}{-4}[/tex] = [tex]\frac{-4}{-4}[/tex]
∴ m = 1
∴ The slope of the line is 1
A 150-pound person uses 5.1 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 230 calories?
Answer: 45.1 minutes
Step-by-step explanation:
From the question, we are informed that a 150-pound person uses 5.1 calories per minute when walking at a speed of 4 mph. The number of.
minutes that the person must walk at this speed to use at least 230 calories will be:
Let the number of minutes to walk be represented by x
(5.1 × x) = 230
5.1x = 230
x = 230 / 5.1
= 45.1 minutes
help me 20 POINTS
math math math by the way do questions 10 and 13 on page 176
Answer:
Step-by-step explanation:
12.
13. Yes it is propoitinal because they are even
I need help with the car questions. Pls it’s due in 10 minutes
Answer:
1250 7500 3
Step-by-step explanation: im just smart
HARD QUADRATICS!!!! A quadratic of the form $-2x^2 + bx + c$ has roots of $x = 3 + \sqrt{5}$ and $x = 3 - \sqrt{5}.$ The graph of $y = -2x^2 + bx + c$ is a parabola. Find the vertex of this parabola.
Answer:
hold up this will take a min to work out
Step-by-step explanation:
brainlyyy!!!!!! pls help
Answer:
2 juices
because 32 is 16 multiplied by 2, so to get the answer, you have to multply everything by two, and sense it does't ask for the amount of ounces, you simply say, to juices
hope i helped......
Answer:
12 OUNCES
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
What transformation is represented by the rule?
Answer:
rotation 180 about the origin
Step-by-step explanation:
Answer:
Rotation of 180° about the origin.
Plot the x- and y-intercepts to graph the equation.
Y =
= 1x – 1
Answer:
plot points (0, -1) and (3, 0)
Step-by-step explanation:
compare the given equation to
y=mx +b where b is the y-intercept
y= 1/3 x -1 so thhe y-intercept is at point (0, -1)
to find the x-intercept make y=0
x/3 -1 =0
x/3 =1
x= 3 so x-intercept is at point (3, 0)
Find the gradient of the line segment between the points (0,-3) and (1,-8).
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{ - 5}}}}[/tex]
☪[tex] \tt{Question} : [/tex]
Find the gradient / slope of the line segment between the points points ( 0 , - 3 ) and ( 1 , -8 ).☥ [tex] \tt{Step - by - step \: explanation : }[/tex]
☄[tex] \tt{Solution : }[/tex]
[tex] \sf{Step \: 1} : [/tex] Assign one of the ordered pairs to be ( x₁ , y₁ ) and another to be ( x₂ , y₂ )
[tex] \sf{(0 \: - 3) \longrightarrow}[/tex] ( x₁ , y₁ )[tex] \sf{(1 \: - 8 \: ) \longrightarrow}[/tex] ( x₂ , y₂ )[tex] \sf{Step \: 2} : [/tex] Substitute values into the slope formula and then simplify :
[tex] \boxed{ \sf{slope = \frac{y2 - y1}{x2 - x1}}} [/tex]
↦ [tex] \sf{ \frac{ - 8 - ( - 3)}{1 - 0}} [/tex]
↦ [tex] \sf{ \frac{ - 8 + 3}{1} }[/tex]
↦ [tex] \boxed{ \sf{ - 5}}[/tex]
Hence , Our answer is [tex] \boxed{ \sf{ - 5}}[/tex].
Hope I helped!
Have a wonderful day / night ツ
~TheAnimeGirl ♪
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Hurry please
What are the slope and y-intercept of the linear function
graphed to the left?
O slope: -2; y-intercept: 2
O slope: -1/2 y-intercept: 1
O slope: 1/2y-intercept: 2
O slope:2, y-intercept: 1
Answer:
B. slope: -1/2 , y-intercept: 1
rise over run. go down one, means a negative 1. too the right twice, means positive 2. y-intercept is obvious, it's just the point in which the line intercepts the y-axis.
Find the median of the following set of data 12,20,1,20,8
Answer:
ok, i hate questions like these because i don't want to answer them
Step-by-step explanation:
please help me out!! it’s either option 1, option 2, option 3, or option 4
Answer:
It's option 2
Step-by-step explanation:
parallel to the x-axis basically means that it mirrors the x-axis since parallel lines have the same slope. since the question wants the graph with the line that is also below the x-axis, the correct graph would be option 2
Answer:
Option 2 is parallel to the x axis because only option 1 and 2 are a line across and option 1 is 3.2 units above.