A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (
Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST
Find the common ratio for the geometric sequence for which [tex]a_1[/tex]=3 and [tex]a_5[/tex]=48. A. -3 B. -2 C. 3 D. 2
Answer:
An= A1 * r^n-1
A5= 3 * r^5-1
48= 3*r^4
48÷3=r^4
16=r^4
r=
[tex] \sqrt[4]{16} [/tex]
r=2
The answer is D. 2
Espero que te sirva
hsじぇいrんふぉそ具jんじょおlっっっkjか、
can someone please help me I need the answer urgently please
Answer:
Step-by-step explanation:
AB ≅ BC. So, ΔABC is an isosceles triangle
Opposite angles of equal sides are equal.
∠BAC = ∠BCA = x°
In ΔABC,
∠ABC + ∠BAC + ∠BCA = 180 {Angle sum property of triangle}
56 + x + x = 180
56 + 2x = 180
2x = 180 - 56
2x = 124
x = 124/2
x = 62°
∠BAC = ∠BCA = 62°
∠DCF = ∠BCA {Vertically opposite angles}
∠DCF = 62°
CDEF is a parallelogram.
In parallelogram, opposite angles are congruent.
∠DEF = ∠DCF
∠DEF = 62°
In a parallelogram, sum of adjacent angles = 180
∠DEF + ∠CDE = 180
62 + ∠CDE = 180
∠CDE = 180 - 62
∠CDE = 118°
∠CFE = ∠CDE {In parallelogram, opposite angles are congruent}
∠CFE = 118°
* * +:) help .........
1. -11 2.-3
Make sure to simplify the equation..
example: 3(2x - 7) = 6x - 21
because 3 x 2 = 6 and 3 x 7 = 21
PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!
Answer:
[tex]\huge\boxed{Option \ D}[/tex]
Step-by-step explanation:
4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)
Answer:
D
Step-by-step explanation:
The sum of angles that are formed on a straight line is 180.
4x + 5x = 180
Graph the solution to the following linear inequality in the coordinate plane 5x-y>-3
Answer:
Here's one way to do it
Step-by-step explanation:
1. Solve the inequality for y
5x - y > -3
-y > -5x - 3
y < 5x + 3
2. Plot a few points for the "y =" line
I chose
[tex]\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}[/tex]
You should get a graph like Fig 1.
3. Draw a straight line through the points
Make it a dashed line because the inequality is "<", to show that points on the line do not satisfy the inequality.
See Fig. 2.
4. Test a point to see if it satisfies the inequality
I like to use the origin,(0,0), for easy calculating.
y < 5x + 3
0 < 0 + 3
0 < 3. TRUE.
The condition is TRUE.
Shade the side of the line that contains the point (the bottom side).
And you're done (See Fig. 3).
Factor x^4+xy^3+x^3+y^3 completely showing work.
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x^4+xy^3+x^3+y^3\\\\=x^3*x+x*y^3+x^3+y^3\\\\=x(x^3+y^3)+x^3+y^3\\\\\boxed{=(x+1)(x^3+y^3)}\\[/tex]
Thank you
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
Work out the value of h and k
H and k are integer constants
Answer:
4hx - 8x - 3h - 4
k = ------------------------
5
8x + 5k + 4
h = ------------------------
4x - 3
Step-by-step explanation:
4 (hx - 1) - 3 (x + h) = 5 (x + k)
4hx - 4 - 3 (x + h) = 5 (x + k)
4hx - 4 - 3x - 3h = 5 (x + k)
4hx - 4 - 3x - 3h = 5x + 5k add 3h both sides
4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h simplify
4hx - 4 - 3x = 5x + 5k + 3h add 4 both sides
4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4 simplify
4hx - 3x = 5x + 5k + 3h + 4 subtract 5x from both sides
4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x simplify
4hx - 8x = 5k + 3h + 4
4hx - 8x - 3h - 4 = 5k
4hx - 8x - 3h - 4
k = ------------------------
5
solving for h;
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
8x + 5k + 4
h = ------------------------
4x - 3
The value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Given:
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
open parenthesis
4hx - 4 - 3x - 3h = 5x + 5k
4hx - 4 - 3x - 3h - 5x - 5k = 0
4hx - 8x - 3h - 5k - 4 = 0
For k
4hx - 8x - 3h - 4 = 5k
[tex]k = (4hx - 8x - 3h - 4) / 5[/tex]
For h
4hx - 8x - 3h - 5k - 4 = 0
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
[tex]h = (8x + 5k + 4) / (4x - 3)[/tex]
Therefore, the value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Read more:
https://brainly.com/question/21406377
What are the possibilities of “AI technology” in various fields of mathematics education.?
Please help fast
Answer:
it could be used to calculate higher deviations of calculus, to measure heights also for optimization algorithms for decision
making under uncertainty
If paul puts 300 dollars in a saving account that earns 3% interest how much interest will he earn after 2 years?
Answer:
[tex] \boxed{18 \: dollars}[/tex]Step-by-step explanation:
Principal ( P ) = $ 300
Rate ( R ) = 3%
Time ( T ) = 2 years
Now, let's find the simple Interest:
I = [tex] \mathsf {\frac{PTR}{100} }[/tex]
[tex] \mathsf{ = \frac{300 \times 2 \times 3}{100} }[/tex]
[tex] \mathsf{ = \frac{1800}{100} }[/tex]
[tex] \mathsf{ = 18}[/tex]
Extra information:
Simple Interest
In our daily life when we borrow a sum of money either from a moneylender or from any financial company, we have to pay the money back by adding with extra sum of money. This borrowed money is called principal. The extra money to be paid for the borrowing money is called interest , which is paid after certain duration in certain rate. At last, the borrowed money should be paid back along with interest which is called amount.
Interest is based on three factors : Principal ( P ) , Rate of interest ( R ) and Time ( T ). While computing the interest, the rate must be in percent and time in years.
[tex] \mathsf{ \: simple \: interest \: = \frac{PTR}{100} }[/tex]
On simplifying
[tex] \mathsf{p = \frac{I \times 100}{T \times R} }[/tex]
[tex] \mathsf{t = \frac{I \times 100}{P \times R} }[/tex]
[tex] \mathsf{r = \frac{I \times 100}{P \times T}} [/tex]
And from the definition,
Amount ( A ) = Principal ( P ) + Interest ( I )
Principal ( P ) = Amount ( A ) - Interest ( I )
Interest ( I ) = Amount ( A ) - Principal ( P )
Hope I helped!
Best regards!
Answer:$18
Step-by-step explanation:3% of $300 is $9.$9 is the interest of 1 year so the interest of 2 years is 2 multiplied by 9 which is $18.
A line passes (-8,-2) and has a slope of 5/4. Write an equation in Ax + By=C
Answer:
5x-4y = -32
Step-by-step explanation:
First write the equation in point slope form
y-y1 = m(x-x1)
y - -2 = 5/4 ( x- -8)
y+2 = 5/4 (x+8)
Multiply each side by 4 to clear the fraction
4( y+2 )= 4*5/4 (x+8)
4y +8 = 5(x+8)
4y+8 = 5x+40
Subtract 4y from each side
8 = 5x-4y +40
Subtract 40 from each side
-32 = 5x-4y
5x-4y = -32
Answer:
The answer is
5x - 4y = -32Step-by-step explanation:
To write an equation of a line given a point and slope use the formula
y - y1 = m( x - x1)
where
m is the slope
( x1 , y1) is the point
From the question
slope = 5/4
point (-8 , -2)
So the equation of the line is
[tex]y + 2 = \frac{5}{4} (x + 8)[/tex]Multiply through by 4
4y + 8 = 5( x + 8)
4y + 8 = 5x + 40
5x - 4y = 8 - 40
We have the final answer as
5x - 4y = -32Hope this helps you
On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q
Answer:
approximately 9.2195
Step-by-step explanation:
We can use Pythagorean theorem
one leg is 7 and the other leg is 6
square them
49 and 36
add
85
square root
approximately 9.2195
Which graph represents a function?
Answer:
The first one is the only function
Step-by-step explanation:
You cannot have points on the same y gridline
If it is a function is has to pass the pencil test
Answer:
[tex]\boxed{Graph A.}[/tex]
Step-by-step explanation:
Hey there!
Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.
Hope this helps :)
f(x) = x2. What is g(x)?
Answer:
g(x)=3x(superscript)2
Answer:
g(x) = 3x².
Step-by-step explanation:
In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).
Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.
So, g(x) = 3x².
Hope this helps!
What is a16 of the sequence 2,11,20
Answer:
137
Step-by-step explanation:
This is an arithmetic sequence with first term (a₁) being 2 and common difference (d) being 11 - 2 = 9.
Explicit formula: aₙ = a₁ + (n - 1) * d so our formula is:
aₙ = 2 + (n - 1) * 9
= 2 + 9n - 9
= 9n - 7
a₁₆ = 9(16) - 7 = 137
4 The surface area of a cube with side s is A = 682
Use the formula to find the surface area of a cube with s=4.
Answer:
96
Step-by-step explanation:
SA = 6*s^2
Since s = 4, we need to square it.
4^2 (4 Squared) = 16
Now we need to multiply 16 by 6 since there are 6 sides on a square.
16*6 = 96
So our Answer is 96.
--Variables
SA= Surface Area
s = Side Length or 4
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
Convert the mixed number to an improper fraction 1 13/15
━━━━━━━☆☆━━━━━━━
▹ Answer
28/15
▹ Step-by-Step Explanation
[tex]1\frac{13}{15} \\\\1 * 15 = 15\\15 + 13 = 28\\\\\\= \frac{28}{15}[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
ABC is an equilateral triangle, solve y
Answer:
y is 60⁰
because all sides are equal
Answer:
60 degrees
Step-by-step explanation:
In an equilateral triangle, the angles are equiangluar and the sides are equal.
180 degrees in a triangle/3 sides =
= 60 degrees per side
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.
Answer:
The coordinates of the point Q is (4, 1)
Step-by-step explanation:
The given parameters are;
The directed line segment extends from R(-2, 4), to S(18, -6)
The ratio in which the point Q partitions the directed line segment = 3:7
Therefore, the proportions of the R to Q = 3/(3 + 7) = 3/10 the length of RS
Which gives;
(-2 + (18-(-2))×3/10, 4 +(-6 -4)×3/10) which is (4, 1)
The coordinates of the point Q = (4, 1)
We check the length from R to S is given by the relation for length as follows
[tex]l =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
R(-2, 4) = (x₁, y₁)
S(18, -6) = (x₂, y₂)
Length of segment RS = 22.36
length from R to Q = 6.7086
We check RQ/RS = 6.7082/22.36 = 0.3
Also QS/RS = (22.36 - 6.7082)/22.36 = 0.6999≈ 0.7
The coordinates of the point Q = (4, 1).
I need help ASAP!
Possible answers are 9, 37, -37, 19, 24, 8, and -24
Answer:
37
Step-by-step explanation:
Hello!
First we add 15 to both sides
[tex]\frac{-5x-10}{5} = -2x + 35[/tex]
Multiply both sides by 5
-5x - 10 = -10x + 175
Add 10 to both sides
-5x = -10x + 185
Add 10x to both sides
5x = 185
Divide both sides by 5
x = 37
The answer is 37
Hope this helps!
[tex]\dfrac{-5x-10}{5}-15=-2x+20\quad|\cdot5\\\\-5x-10-75=-10x+100\\\\-5x+10x=100+10+75\\\\5x=185\quad|:5\\\\\boxed{x=37}[/tex]
Complete the Magic Square.
Answer:
+5
Step-by-step explanation:
So you can see the 5 pattern, so you add 9+5= 14 which goes in the middle square and 14+5=18 in the left square
Now between 18 and 11 it is 7 so you subtract 7 which equals 4 then - 5= -1 then -5= -6
Answer:
4 5 9
11 6 1
3 7 8
Step-by-step explanation:
In a magic square, all rows, columns, and diagonals have the same sum.
Let's call the cells a - i this way:
a b c
d e f
g h i
Now lets's fill in what we have:
a b 9
11 6 1
g h i
2nd row: 11 + 6 + 1 = 18
3rd column: 9 + 1 + i = 18; i = 8
a b 9
11 6 1
g h 8
Main diagonal: a + 6 + 8 = 18; a = 4
4 b 9
11 6 1
g h 8
1st row: 4 + b + 9 = 18; b = 5
4 5 9
11 6 1
g h 8
1st column: 4 + 11 + g = 18; g = 3
4 5 9
11 6 1
3 h 8
2nd column: 5 + 6 + h = 18; h = 7
4 5 9
11 6 1
3 7 8
Cory earns $9.50 per hour for the first 40 hours he works in a week. For any hours over 40 hours per week, his hourly rate is multiplied by 1.5. How much does he earn is he works for 43.5 hours in one week?
Answer:
429.88
Step-by-step explanation:
The first 40 hours is at 9.50
40 *9.50 =380
The remaining hours is at 9.50 * 1.5 or 14.25
43.5 -40 = 3.5
3.5 * 14.25
49.875 = 49.88 ( rounding to the nearest cent)
Add together
380+49.88 =429.88
Anna's back Garden consists of a rectangular lawn measuring 9m by 7m, surrounded by a gravel path of width X metres. Find, and simplify, an expression for the total area of the garden.
A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.
The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower
:
Let x = the width of flower bed
:
Then the overall dimensions (flower bed & lawn) will be:
(2x + 8) by (2x + 4)
:
Overall area
(2x+8)*(2x+4) = 165
FOIL
4x^2 + 8x + 16x + 32 = 165
A quadratic equation
4x^2 + 24x + 32 - 165 = 0
4x^2 + 24x - 132 = 0
Simplify, divide by 4, results:
x^2 + 6x - 33 = 0
Use the quadratic formula to solve this
Jess receives a $15000 salary for working as an engineer. If Jess has to spend $6000 of her salary on expenses each year, then what percent of Jess's money does she have to spend? Round your answer to the nearest whole number if necessary.
Answer:
Jess will have to spend 40% of her salary
Step-by-step explanation:
Jess salary = $15,000
Jess expenses = $6,000
what percent of Jess's money does she have to spend
Percentage of Jess expenses = Jess expenses / Total salary × 100
= 6,000 / 15,000 × 100
= 0.4 × 100
= 40%
Jess will have to spend 40% of her salary
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made 16of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank? Hint: You do not divide the volume of the main show tank by 6.
Answer:
see below
Step-by-step explanation:
If the original dimensions of the tank are x, y, and z, the mock dimensions will be 1/6x, 1/6y and 1/6z. The volume of the original tank is x * y * z = xyz whereas the volume of the mock-up tank is 1/6x * 1/6y * 1/6z = 1/216 * xyz. Therefore, we know that the volume of the mock-up tank is 1/216 th of the original tank.
1. Find 3 consecutive integers whose sum is 33.
Answer: 10, 11, 12
Step-by-step explanation: Think of the integers like this:
1st integer: x
2nd integer: x+1
3rd integer: x+2
That is necessary because they are consecutive integers. Since the sum is 33, we need to create an equation.
x+x+1+x+2=33.
Simplify:
3x+3=33.
Opposite operations:
3x=-3+33.
To get the 3 close to the 33, we needed to make it negative, which is the opposite operation of the positive 3.
So,
3x=30.
Divide by 3:
x=10.
The first integer, x, equals 10.
To go with the guide that we already created,
1st integer: x=10
2nd integer: x+1=11
3rd integer:x+2=12.
Therefore, the three consecutive integers are 10, 11, and 12.
To check that, add them up. They all equal 33 and they are consecutive, which means this is the right answer!
Answer:
10, 11, 12
Step-by-step explanation:
For problems involving consecutive integers, I like to consider their average value. For three consecutive integers, their average will be the middle one. It will be ...
average = sum / (number of numbers) = 33/3 = 11
The middle number is 11, so the numbers are ...
10, 11, 12
_____
If you want to write an equation, you can let x represent the middle number. Then the other two are x-1 and x+1, and their sum is ...
(x-1) +(x) +(x+1) = 33 = 3x
x = 11 ⇒ x-1 = 10, x+1 = 12
this one from maths pls help
Answer:
The total amount left by Manavi and Kuber is: (1) 399
Step-by-step explanation:
Manavi
saving account + amount spent at the mall: 1/'2 + 1/4 = 3/4
left over: 1 - 3/4 = 4-3/4 = 1/4
1260 ( 1/4) = 315
The total leftover for Manavi is Rs.315.
Now do the same steps with Kuber.
Kuber
saving account + amount spent at the mall: 1/3+ 3/5 = 14/15
left over: 1- 14/15 = 15-14/15 = 1/15
1260 (1/15) = 84
The total leftover for Kuber is Rs.84.
Lastly, just add both left over amount together.
315+84 = 399
The total amount left by Manavi and Kuber is: (1) 399
What’s the function of the Unit Circle and why is it called the unit Circle?
Answer:
It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.
Step-by-step explanation:
EXTRA POINTS. WILL GIVE A BRAINLIEST AND A THANK YOU. ANSWER ASAP... I want a clear, grammatically correct answer please, Part A and Part B separate; This is an essay, please write it as such. All steps! Easy to understand! Josh and his friends bought vanilla wafers for $4 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $45 to buy a total of 27 packets of wafers of the two varieties. Part A: Write a system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival. Define the variables used in the equations. (5 points) Part B: How many packets of chocolate wafers and vanilla wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
Answer:
Part A:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
Number of vanilla wafers packets bought = 6 and
Number of chocolate wafers packets bought = 21
Step-by-step explanation:
Given:
Cost of each packet of vanilla wafer = $4
Cost of each packet of chocolate wafer = $1
Total number of packets bought = 27
Total money spent = $45
Part A:
To write a system of equations for the given situation.
Here, we do not know the number of packets bought for each type of wafer.
We just know that total number of packets bought and the total money spent in buying those packets.
Let us suppose,
Number of packets of vanilla wafers bought = [tex]x[/tex] and
Number of packets of chocolate wafers bought = [tex]y[/tex]
Total number of packets = Number of packets of vanilla wafers bought Plus Number of packets of chocolate wafers bought:
i.e. [tex]x+y=27 ...... (1)[/tex]
Money spent on vanilla wafers packets = [tex]4 \times x[/tex]
Money spent on chocolate wafers packets = [tex]1 \times y[/tex]
Total money spent = [tex]4x+y = 45 ...... (2)[/tex]
So, the system of equations is:
[tex]x+y=27 \\4x+y = 45[/tex]
Part B:
To find number of packets bought for each flavor = ?
Here, we have two equations and two variables [tex]x[/tex] and [tex]y[/tex].
As, the coefficients of [tex]y[/tex] in both the equations are same.
Let us subtract equation (1) from (2):
[tex]4x+y-x-y=45-27\\\Rightarrow 3x = 18\\\Rightarrow \bold{x =6}[/tex]
By equation (1), putting the value of [tex]x[/tex] and solving for [tex]y[/tex]:
[tex]6+y=27\\\Rightarrow \bold{y =21}[/tex]
So, number of vanilla wafers packets bought = 6 and
number of chocolate wafers packets bought = 21
